content stringlengths 86 994k | meta stringlengths 288 619 |
|---|---|
order of operations worksheet 5th grade math
Grade 5 Order of Operations Worksheets | Free Worksheets | Printables
PEMDAS Problems
Grade 5 Order of Operations Worksheets | Free Math Worksheets
PEMDAS - 5 terms worksheets | K5 Learning
PEMDAS Problems
Free Printable Order Of Operations Worksheets 5Th Grade [PDFs]
Order of Operations Worksheets (Grade 5, answers, examples)
Order of Operations Speed Solving Activity for 3rd-5th Grade
Order of Operations Worksheets
Order of Operations Worksheets - Math Monks
Order of Operations with Whole Numbers and No Exponents (Four ...
Order of Operations Worksheets - Superstar Worksheets
Order of Operations Worksheets
Order of Operations Worksheets
Order of Operations Worksheets - Math Monks
Order of Operations with Whole Numbers and No Exponents (Four ...
PEMDAS Problems
Order of Operations Worksheets - Superstar Worksheets
Order of Operations Worksheets | Order of Operations Worksheets ...
Order of Operations Worksheets
Order of Operations PEMDAS Speed Solving Activity for 3rd-5th Grade
Order of Operations - 4 Main Worksheet | Fun and Engaging 5th ...
PEMDAS including exponents | K5 Learning
Order of Operations and Numerical Expressions Math Maze Worksheets - 5th Grade
Order of Operations. Fifth Grade Math Worksheets and Study Guides.
Order of Operations Worksheets - Free Printable Math PDFs ...
Order of Operations Math Worksheets
5th Grade Order of Operations Task Cards | Order of Operations ...
Order of Operations Worksheets | Free - Distance Learning ...
Order of Operations Worksheets - Superstar Worksheets
Order of Operations Worksheets For Kids
50+ Order of Operations worksheets for 5th Grade on Quizizz | Free ...
Order of Operations Puzzle #2 | Worksheet | Education.com
Order of Operations Worksheets - Free Printable Math PDFs ... | {"url":"https://worksheets.clipart-library.com/order-of-operations-worksheet-5th-grade-math.html","timestamp":"2024-11-01T20:43:32Z","content_type":"text/html","content_length":"27475","record_id":"<urn:uuid:43b9c877-8a11-431e-b9fe-d86714a16c89>","cc-path":"CC-MAIN-2024-46/segments/1730477027552.27/warc/CC-MAIN-20241101184224-20241101214224-00542.warc.gz"} |
A-level Geography/AS OCR Geography/Investigation Paper - Wikibooks, open books for an open world
This is a concept to find the statistical significance of the correlation between the two variables. First, a null hypothesis needs to be made.
Mann-Whitney U test is a test for difference between 2 data sets. Using a critical values table, the level of confidence in the relationship can be established, and the null hypotheses can be
accepted or rejected. There are both advantages and disadvantages which accompany this statistical test for analysis of statistical data. One advantage is that it can compare two data sets that are
different sizes. This makes the test much more versatile, and can be applied to a range of different data sets. Secondly, the test is not based on observed values. This means that there are no
assumptions made about the distribution of the data. This is particularly useful in geography because most of the data we collect will be either positively or negatively skewed. Finally, Mann-Whitney
U uses non-parametric (non-grouped) data. This is an advantage because the trends in the data cannot be generalised, and thus producing a more statistically sound result.
It does however carry some disadvantages with it, one being the fact that it cannot be applied to more than 2 data sets at one time. This is because it is non-parametric data. If the test was done
using parametric (grouped) data, you would be able to compare multiple data sets at once. An example of this is the student’s “t” test. This is because parametric data provides a result in proportion
to the data, and can therefore be contrasted with many data sets. Also, Mann-Whitney becomes increasingly less effective as the data sets get larger. This reduces its effectiveness because the
calculation becomes too long-winded, and it takes a very long time to complete. It also reduces the precision of the result, as with a bigger sample size there is more margin for error.
In conclusion, despite the obvious flaws with the test, it is a very effective way of looking at the differences between 2 pairs of data sets.
Five Sections of Investigation
Sampling Techniques:
Pragmatic = essentially safety and accessibility. For example, if a student is carrying out a river investigation they might use pragmatic sampling methods meaning only areas that were easily
accessible and did not pose a risk would be studied. It is reliable and practical.
Random = Not as one might assume randomly selecting a site or throwing a quadrat, in order to use random sample methods either a calculator, grid or computer is needed to generate random statistics
that have not been influenced by human decision.
Systematic = This type of technique would be used if progressional change over distance or time was being studied. A transect would be measured and data recorded at regular intervals along said
transect, so that change over time or distance could be observed. For example, if a student wished to study psammosere succession, a transect might be measured from the sea to the climax environment
(woodland) and at every 25m or so measurements would be taken.
Stratified = To be completed by Magneto and River's landmass.
The most frequent Sample number. This is the sample figure which occurs the most times.
e.g: 7, 8, 9, 5, 6, 7, 5, 5, 5, 5, 3, 5, 5=mode
Comes from the french word "la mode" for fashion.
This is the middle sample when all the samples are placed in arithmetic Order. e.g. 1,2,3,4,5,6,7,8,9 5=median
The area which the samples stretch from.
Statistics: Standard Deviation
To describe the data regarding an infiltration rate statistically I would use the mean and the standard deviation as a measure of central tendency and dispersion. These two are always used together.
The mean is simply the sum of all values of x (infiltration rate) divided by n (total number of samples)
The standard deviation is more complicated and requires the use of the formula; where x is the individual infiltration rate and
X bar is the mean of x’s (as above)
This is simply done by listing the value of x on a table, and subtracting x bar from each. In the next column, square the subsequent result.
Then add up all the values of (x-xbar) ² (Σ (x-xbar) ². Divide this by n (100 IN THIS CASE), and then square root the answer.
These methods are the most powerful and sensitive, because they include all the values of all the data. They do not exclude any data. However, the data must be (nearly) normally distributed to use
Mode and range mealy state the most numerous value of x and the difference between the smallest and largest which is not very useful, as it ignores most of the data. Interquartile deviation and
medium rely on the rank order of the data row do not engage with the size of the values for x, and ignore the extremes of the data set.
Coming up with Geographical questions | {"url":"https://en.m.wikibooks.org/wiki/A-level_Geography/AS_OCR_Geography/Investigation_Paper","timestamp":"2024-11-08T15:58:56Z","content_type":"text/html","content_length":"35104","record_id":"<urn:uuid:719b308a-e91f-45cd-9740-7ed8de71d698>","cc-path":"CC-MAIN-2024-46/segments/1730477028067.32/warc/CC-MAIN-20241108133114-20241108163114-00674.warc.gz"} |
lost+found 2018
After excavating unifinished or rough draft posts from last year (a quick ack "draft\s?[:=] true" content/post/*.md in the Hugo directory), we should now be ready for June.
This post could have been headed “In which we learn how to embrace functional programing for statistical computing”, or “how I stoped worrying about R and look for more lispy paradigm for data
science.” but let keep it simple for a while. Lately, I was looking for a nice way to perform numerical simulation in Clojure, I mean other than using lazy sequences with (take 10 (repeatedly #
(rand-int 10))) where you can hardly fix any seed that will help reproduce your random numbers. I am aware of Clojure data.generators but I wanted a more integrated framework. Here are some extra
libraries for numerical or statistical computing with Clojure that I found while crawling the web.
Regarding Probabilistic Programming, you will find interesting discussion of Bayesian inference in this recent PhD thesis: Probabilistic Programming: Automation of Inferences, Learning and Design
It is quite easy to find good (non-cryptographic) PRNGs written in Clojure. You will likely came across one from L’Ecuyer and coll. or the Mersenne Twister algorithm, for instance. However, following
John D Cook suggestion, you can also easily write your own code, based on existing algorithm.
This time, I am (quickly) reviewing Think Bayes, one of Allen Downey’s book from the “Think X” series. A PDF version is available on Green Tea Press. The accompanying code can be downloaded from
Github (ThinkBayes is for Python 2, ThinkBayes2 targets Python 3 but the book has not yet been updated to reflect the changes).
I first read How to think like a computer scientist (probably the Python version) back in the 2000s. I really liked Allen’s approach to exposing soft and hard concepts related to computer science.
This time, the author choose to use Python and discrete mathematics to expose the reader to Bayesian statistics:
Most books on Bayesian statistics use mathematical notation and present ideas in terms of mathematical concepts like calculus. This book uses Python code instead of math, and discrete
approximations instead of continuous mathematics. As a result, what would be an integral in a math book becomes a summation, and most operations on probability distributions are simple loops.
But note that even if the author offers to tackle such problems from the perspective of computer science, statistical considerations remain an important part of the process, even if this yields “an
approximate solution to a good model”:^
I think it is important to include modeling as an explicit part of problem solving because it reminds us to think about modeling errors (that is, errors due to simplifications and assumptions of
the model).
Chapter 1 provides a quick exposition to Bayes theorem, described as a way to get from P(B|A) to P(A|B), especially in cases where P(A|B) is not easy to compute. I find that the M&M problem (§1.6) is
a very nice way to introduce bayesian inference, in the spirit of Philip Good’s introduction to permutation testing (Permutation, Parametric, and Bootstrap Tests of Hypotheses, Springer, 2005):
define the problem, set up the hypotheses and a test statistic, and finally assess the likelihood of the observed result; or, as the author suggests in Chapter 3: (1) choose a representation for the
hypotheses, (2) choose a representation for the data, and (3) write the likelihood function. The next one is about the Monty Hall dilemma and it is really trickier.^ It is, however, easy to run a
little simulation of the expected proportion of wins in case we choose to switch or stick to our initial choice. Here are the results I get using Mathematica:
Of note, a collection of related problems (with solutions) can be found on the author’s blog: All your Bayes are belong to us!.
In Chapter 2, the author provides reminders about the basics of probability distributions in Python (using a custom Python module, thinkbayes.py, that can be found on the Github repository), followed
by two numerical applications on the aforementioned problems. It is mostly Python code drawing from the so-called template method pattern.
Chapters 3 and 4 are all about estimating (…)
Here is a little excursion into algorithms for cycle detection, with a particular emphasis on palindrome.
The following comes from Programming Praxis, which I happen to read from time to time:
Write a program that determines if a linked list of integers is palindromic — i.e., reads the same in both directions. Your solution must operate in O(1) space.
In the suggested solution, the author uses Floyd’s tortoise-and-hare algorithm, also known as Floyd’s cycle-finding algorithm, whose name is mentioned in Don Knuth’s TAOCP (Seminumerical Algorithms)
although it is not .^
The rectangles algorithm is used to generate random variates based on the acceptance–rejection method. Here is a small implementation using Clojure.
The article is available online, but in a few words the idea of this algorithm
Recall that the PDF for a gaussian random variable (r.v.) is
$$ f(x) = \frac{1}{\sqrt{2\pi\sigma^2}}\exp\left(\frac{-(x-\mu)^2}{2\sigma^2}\right), $$
for $-\infty < x < \infty$, where $\mu$ and $\sigma^2$ denote the mean and variance of the distribution. In general, it is easier to consider a standard normal deviate $Z$, with $\mu=0$ and $\sigma=
1$, since we can always use the transformation $X = \mu + \sigma Z$.
Reference: Zhang, R., & Leemis, L. M. (2012). Rectangles algorithm for generating normal variates. Naval Research Logistics, 59(1), 1–6.
Most of what is available in terms of tutorial or solution to problems from programming contests, also called competitive programming, relies on C or C++–see, e.g., this earlier post of mine on the
Competitive Programmer’s Handbook. I recently came across this Bachelor’s thesis (PDF, 44 pp.) where the author offers solutions to various problems in C++. Here I will try to offer some Scheme or
Lisp solutions (one at a time). Today, we shall start with the well-known Knuth-Morris-Pratt (KMP for short) algorithm which is widely used for pattern matching, usually on strings. This algorithm is
linear in time and has asymptotic complexity $\mathcal{O}(n)$. To understand what the difference between the KMP and the Boyer-Moore’s algorithm are, see this related Stack Overflow thread.
The proposed task reads as follows:
Given an integer N, make a palidrome (word that reads the same when you reverse it) of length at least N.
First, we need a working version of the KMP algorithm and I will use Racket Scheme. Note that the documentation on string libraries (SRFI 13, R5RS) discusses the KMP algorithm.
http://www-igm.univ-mlv.fr/~lecroq/string/node8.html http://www.inf.fh-flensburg.de/lang/algorithmen/pattern/kmpen.htm
Here is one solution in Scheme from codecodex:
(define (init-next p)
(let* ((m (string-length p))
(next (make-vector m 0)))
(let loop ((i 1) (j 0))
(cond ((>= i (- m 1))
((char=? (string-ref p i) (string-ref p j))
(let ((i (+ i 1))
(j (+ j 1)))
(vector-set! next i j)
(loop i j)))
((= j 0)
(let ((i (+ i 1)))
(vector-set! next i 0)
(loop i j)))
(loop i (vector-ref next j)))))))
(define (kmp p s)
(let ((next (init-next p))
(m (string-length p))
(n (string-length s)))
(let loop ((i 0) (j 0))
(cond ((or (>= j m) (>= i n))
(- i m))
((char=? (string-ref s i) (string-ref p j))
(loop (+ i 1) (+ j 1)))
((= j 0)
(loop (+ i 1) j))
(loop i (vector-ref next j)))))))
Here is a little programming entertainment in Racket to console me for wasting two hours fighting with Excel.
Briefly, I spent nearly two hours figuring out how to perform a simple regression analysis and some trivial parametric statistics using Excel for a colleague of mine. I don’t even talk about
computing Spearman rank correlation when there are ties and you must manually apply a correction because there is no automated function in vanilla Excel for that. After I transmitted the result of my
morning work, I thought it would finally go as fast to implement a gradient descent algorithm in Scheme and use Gnuplot or anything else for data visualization. Atabey Kaygun already did this using
Common Lisp, but Racket should do the job as well, notwithstanding the fact that we can benefit from a lot of built-in packages.
First, we need a CSV reader because the dataset is available as a comma-delimited text file. We will also need basic helper functions to summarize the data, and also a plotting framework to visualize
the data. Finally, the gradient descent algorithm itself, which consists in starting with an initial set of parameter values for a given function and iteratively moving toward the set of parameter
values that minimize the function. Iteration translates easily in Lisp recursion. In our case, the parameters correspond to the intercept and the slope of the regression line. Obviously, we need an
objective or cost function to evaluate and it is based on the squared distance measure of observed and fitted points, much like how residuals are defined in the standard OLS approach. The term
“gradient” comes from the fact that we will be working with partial derivatives of the estimated parameters.
Gradient descent is probably best known in Machine Learning applications since more classical and closed-formed algorithms are used to solve OLS problems. Depending on the data structure, however,
the GD algorithm might provide an interesting alternative, especially in the case where $n$ is large, and it works in the case the response variable is binary (aka logistic regression). Note also
that there are also other well known variants of this algorithm, like batch or stochastic gradient descent.
Here is the final code: (also available to download)
Note that you must install csv-reading first, e.g., using raco pkg install csv-reading at the prompt of your preferred shell.
Today we are going to build a correlation heatmap using a few Stata commands.
Note that there already are some solutions available on the Stata FAQ from the UCLA website. However, it relies on contour or scatter plot while we want to display something more akin to a heatmap
with filled cells rather than symbols or contour lines. See, e.g., Nathan Yau’s description of a heatmap.
A quick search on the internet suggest that it is possible to use hmap or plotmatrix, and I even learnt about transition probability color plots (PDF) even it is barely related to our subject. Other
interesting ideas were once discussed on Stata List. | {"url":"https://aliquote.org/post/lost-found-2018/","timestamp":"2024-11-09T04:10:28Z","content_type":"text/html","content_length":"26983","record_id":"<urn:uuid:8e737791-5286-406b-a63d-4400f551dee9>","cc-path":"CC-MAIN-2024-46/segments/1730477028115.85/warc/CC-MAIN-20241109022607-20241109052607-00698.warc.gz"} |
Víctor Dalmau, Right-adjoints of Datalog Programs - Discrete Mathematics Group
Víctor Dalmau, Right-adjoints of Datalog Programs
April 23 Tuesday @ 4:30 PM - 5:30 PM KST
Room B332, IBS (기초과학연구원)
We say that two functors Λ and Γ between thin categories of relational structures are adjoint if for all structures A and B, we have that Λ(A) maps homomorphically to B if and only if A maps
homomorphically to Γ(B). If this is the case Λ is called the left adjoint to Γ and Γ the right adjoint to Λ. In 2015, Foniok and Tardif described some functors on the category of digraphs that allow
both left and right adjoints. The main contribution of Foniok and Tardif is a construction of right adjoints to some of the functors identified as right adjoints by Pultr in 1970. We shall present
several recent advances in this direction including a new approach based on the notion of Datalog Program borrowed from logic. | {"url":"https://dimag.ibs.re.kr/event/2024-04-23/","timestamp":"2024-11-11T22:57:46Z","content_type":"text/html","content_length":"147840","record_id":"<urn:uuid:15c52832-dd99-4cd8-a11e-291d1598b564>","cc-path":"CC-MAIN-2024-46/segments/1730477028240.82/warc/CC-MAIN-20241111222353-20241112012353-00560.warc.gz"} |
Integral and Vector Calculus
This course will offer a detailed introduction to integral and vector calculus. We’ll start with the concepts of partition, Riemann sum and Riemann Integrable functions and their properties. We then
move to anti-derivatives and will look in to few classical theorems of integral calculus such as fundamental theorem of integral calculus. We’ll then study improper integral, their convergence and
learn about few tests which confirm the convergence. Afterwards we’ll look into multiple integrals, Beta and Gamma functions, Differentiation under the integral sign. Finally, we’ll finish the
integral calculus part with the calculation of area, rectification, volume and surface integrals. In the next part, we’ll study the vector calculus. We’ll start the first lecture by the collection of
vector algebra results. In the following weeks, we’ll learn about scalar and vector fields, level surfaces, limit, continuity, and differentiability, directional derivative, gradient, divergence and
curl of vector functions and their geometrical interpretation. We’ll also study the concepts of conservative, irrotational and solenoidal vector fields. We’ll look into the concepts of tangent,
normal and binormal and then derive the Serret-Frenet formula. Then we’ll look into the line, volume and surface integrals and finally we’ll learn the three major theorems of vector calculus:
Green’s, Gauss’s and Stoke’s theorem.
INTENDED AUDIENCE : Mathematics
PREREQUISITES : Differential calculus of one and several variables.
INDUSTRY SUPPORT : None | {"url":"https://onlinecourses.nptel.ac.in/noc22_ma03/preview","timestamp":"2024-11-09T06:56:08Z","content_type":"text/html","content_length":"54794","record_id":"<urn:uuid:3527c9c7-3ad3-4d23-b207-92b3525a51b9>","cc-path":"CC-MAIN-2024-46/segments/1730477028116.30/warc/CC-MAIN-20241109053958-20241109083958-00465.warc.gz"} |
xline - draw a partial line
Is there an easy way to get an xline plot for an array of X values, but with the line only taking up the first or last 10% of the Y axis? It's for this plot, where plotting the whole line is
obscuring the blue data too much..
This is for a script where the Y axis is logarithmic and its values are not always the same. I could plot the lines in a loop, having calculated the appropriate Y values. But is there a simpler way?
3 Comments
Voss on 10 Jan 2024
@dormant: How about putting the black vertical lines beneath the blue line, so that the blue line is not obscured? That can be done: (1) by plotting the black lines before the blue line, or (2) by
reordering the lines in the axes Children property after they are plotted, e.g. using uistack or setting the Children property directly.
% plot a thick line and a thin line on top:
h_thick = plot(1:10,'LineWidth',10);
h_thin = plot(1:10,'LineWidth',2);
% thin line is 1st in axes Children (most recently created):
% new figure and axes (only necessary for demonstration in Answers):
ax = copyobj(ax,figure());
% get the new handle of the thin line (also only necessary for
% demonstration in Answers):
% reverse the order of the axes Children:
% now the thin line is underneath the thick one,
% and the thin line is last in Children:
Accepted Answer
You will have to do that manually -
%Sinosuidal data for example
plot(x, y, 'LineWidth', 2)
%Generate random values to put xlines
%Draw xlines for the values in X, extending from y1 upto y2
plot([X; X], [y1; y2], 'k')
1 Comment
@dormant: Note that this method produces one line object for each x value. As you can see below h is an array of 10 lines:
% Sinosuidal data for example
plot(x, y, 'LineWidth', 2)
% Generate random values to put xlines
% Draw xlines for the values in X, extending from y1 up to y2
h = plot([X; X], [y1; y2], 'k') % 10 lines
Having too many graphics objects that MATLAB needs to render can make your GUI sluggish to interact with. Therefore, in general it's a good idea to minimize the number of graphics objects you create.
To that end, you can achieve the same effect as above with a single line object by taking advantage of how NaNs are represented in lines (NaNs make gaps). Here's the same example, but with one line
object for all vertical lines:
% Sinosuidal data for example
plot(x, y, 'LineWidth', 2)
% Generate random values to put xlines
% Draw xlines for the values in X, extending from y1 up to y2
X_plot = [X; X; NaN(1,N)];
Y_plot = repmat([y1; y2; NaN],1,N);
h = plot(X_plot(:),Y_plot(:), 'k') % one line
More Answers (3)
I am not aware that a special version of xline exist , but you can do your own special xline like that (a very crude and simple code that you can save as a function for future massive use) :
simply try with different a and b values to adjust the amount of blank around the data curve
y = 0.1 + sin(pi*t/max(t)).^3.*abs(sin(2*pi*10*(t+1*t.^3))); % signal
[PKS,LOCS] = findpeaks(y,t,'SortStr','descend','NPeaks',15);
semilogy(t,y,'b',LOCS,PKS,'.r','linewidth',2,'markersize',25);grid on
% add my special vertical lines
a = 0.25; % factor on the lower portion (must be < 1)
b = 1.25; % factor on the upper portion (must be > 1)
plot(LOCS(k)*ones(2,1), [ylimits(1) a*interp1(t,y,LOCS(k))],'--k','linewidth',0.5);
plot(LOCS(k)*ones(2,1), [b*interp1(t,y,LOCS(k)) ylimits(2)],'--k','linewidth',0.5);
1 Comment
Looks confusing to me unless it's explained somewhere. The red lines don't go to the curve but all go to some constant y value. And the x location of them seems random.
See Also
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting! | {"url":"https://se.mathworks.com/matlabcentral/answers/2068511-xline-draw-a-partial-line?s_tid=prof_contriblnk","timestamp":"2024-11-04T23:34:29Z","content_type":"text/html","content_length":"205903","record_id":"<urn:uuid:8e198185-8e0a-4760-9c23-64a2d64fa7c9>","cc-path":"CC-MAIN-2024-46/segments/1730477027861.84/warc/CC-MAIN-20241104225856-20241105015856-00426.warc.gz"} |
The Statistics of the Highly Improbable
This is the alst week of the academic term here, so I've been crazy busy, which is my excuse for letting things slip. I did want to get back to something raised in the comments to the comments to the
Born rule post. It's kind of gotten buried in a bunch of other stuff, so I'll promote it to a full post rather than a comment.
The key exchange starts with Matt Leifer at #6:
The argument is about why we should use the usual methods of statistics in a many-worlds scenario, e.g. counting relative frequencies to estimate what probabilities we should assign in the
future. It is not simply about whether we can find a mathematical formula that obeys the axioms of probability, which we can clearly do just by postulating the Born rule, but rather it is about
why observers in the multiverse should have any reason to care about it. Isn't it obvious that this isn't obvious?
I responded, probably a little too snippily (but see my earlier remarks about being crazy busy):
I guess I'm just a committed empiricist, but given that my experience of the world involves seeing a series of measurements with well-defined outcomes whose probabilities measured over many
repeated experiments give values that match the Born rule, then I think I have ample reason to care about the Born rule.
I realize that, in some other branch of the wavefunction there is some other version of "me" who saw different outcomes to specific measurements. And even a version of "me" who lives in some
"Rosenkrantz and Guildenstern Are Dead" branch of the wavefunction in which the repeated sequence of measurements give results that don't match the Born rule, or make any sense at all. What's not
obvious to me is why I should care about what they see. Given that they're in other branches of the wavefunction that are inaccessible to me, the fact that they see something bizarre does nothing
to reduce the utility of the Born rule in my little corner of the wavefunction.
Moshe's comment at #12, though, re-frames this nicely:
I think Matt and yourself are saying the same thing. If you allow me to paraphrase - the Born rule (with frequency based probabilities) is in practice the basis for any empirical test of QM, if
the MWI does not reproduce this part of QM then it is simply incorrect. The burden of proof, once you allow things like the "Rosenkrantz and Guildenstern Are Dead" branch of the wavefunction, is
to explain why the world around us looks nothing like that. In other words, why committed empiricists are almost always right in making deductions based on making repeated observations and
looking at the probabilities of possible outcomes.
As you noted in a later comment, we went round and round about this a while back, with no real conclusion. As I said, though, I was probably to short with my reply to Matt, so I'll use this
opportunity to rephrase myself a little.
As in the previous discussion, I think the point where this breaks down, for me, is that I don't see the distinction between the existence of highly improbable components of the wavefunction in which
measurement outcomes defy probability and the fact that probabilisitc systems will necessarily include long runs that "look" like they follow very different statistics.
It's sort of interesting, I think, that this comes in the same week as the latest Fermilab rumor, about which Sean wrote: "The real reason to be patient rather than excited by the bump at 150 GeV was
that it was a 3-sigma effect, in a game where most 3-sigma effects go away."
On the face of it, that's kind of a ludicrous statement-- if the statistics have any meaning, it can't be the case that "most" 3-sigma effects go away. A 3-sigma effect should be wrong less than 1%
of the time, a far cry from "most." The vast numbers of measurements involved in particle physics, though, mean that over many years, you can accumulate a non-trivial number of cases where a 3-sigma
measurement was wrong. Which is why the standard for detection is a lot higher, because ordinary statistical fluctuations can and do produce situations where a less-than-1% chance of being wrong
about a detection comes through. They can, in fact, produce enough of them that physicists become jaded about it.
(There are people, for the record, who take the position that things like the routine evaporation of 3-sigma results show that we really aren't handling the statistics properly, and argue for a
completely different approach to the estimation of data uncertainties. I heard a long discussion of this from someone at MIT many years ago, but I didn't follow it well enough to be able to reproduce
his alternative method, or even Google up a good discussion of it.)
Given that sort of thing, I don't see how you can really separate improbable branches in the Many-Worlds Interpretation from cases that really are governed by some underlying probability, but just
hit a long run that "looks" like it follows some different rule.
If you look at something like repeated measurements of a 50/50 system-- a whole slew of identically prepared spin-1/2 particles, say, or a large number of tosses of an ideal coin-- Many-Worlds says
that there is some branch of the wavefunction in which you get the same answer 1000 times in a row. And if your measurement came up "tails" or "spin-down" 1000 times in a row, you would be pretty
But the probability of that happening purely by chance isn't zero. It's not very good-- around 1 in 10^300-- but if you flip coins or measure spins long enough, you will eventually get a run of 1000
in a row. Or 10,000, or 1,000,000, or whatever ridiculously large number you would like your absurdam to reduce to.
So it's not clear to me why the existence of an exceedingly unlikely branch of the wavefunction in which 1000 coin-flips come up tails is any different from the observation that in an infinitely
large universe in which sentient observers can flip coins, one of them will sooner or later come up with 1000 tails in a row. We wouldn't say that one freak run of results completely invalidated
statistics (provided, at least, that subsequent tests reverted to the expected behavior)-- we'd just say that that particular experimenter got really (un)lucky, but the underlying probability
distribution really was 50/50 all along.
It might be that some sort of careful statistical analysis would show that unlikely events would be seen more often in a Many-Worlds type universe than they "should" according to non-quantum
probabilities. It might be that the statistics of particle physics experiments have already shown this to be the case, conclusively proving Many-Worlds right. But I suspect that the real answer would
be that such outcomes turn up exactly as often as they "should" in a collapse interpretation with probabilities given by the Born rule.
This is not to suggest that there's anything wrong with trying to find ways to derive the Born rule. It's absolutely something people should be working on, in both Many-Worlds and collapse-type
interpretations of quantum mechanics. If there's a way to get that out of the formalism without assuming it at some point, that would be a fantastic achievement. If there's some natural way to
measure probability by counting wavefunction branches, or through the mechanics of whatever drives the collapse of the wavefunction in some other model, that would be a really strong argument in
favor of that interpretation.
Given that none of the obvious things work, though, I don't think that a lack of such a derivation is a fatal weakness for any particular interpretation. It's possible that in some sense this is a
bigger problem for Many-Worlds than for collapse interpretations, but then I suspect that, in the grand scheme of things, any relative gain over Many-Worlds is offset by the need to find an
explanation for the collapse.
(What we really need, of course, is a way to extract testable predictions from this stuff, and then experiments to test them. That's part of why I find things like large-molecule diffraction
measurements, or cavity opto-mechanics systems really fascinating-- as you push quantum effects to larger and larger sizes, at some point, you might begin to put some meaningful constraints on some
of the proposals for alternative mechanisms for quantum measurement. Which would at least narrow the field a little, if not settle the question.)
More like this
I think I missed this the first time around, but this weekend, I watched the bloggingheads conversation about quantum mechanics between Sean Carroll and David Albert. In it, David makes an extended
argument against the Many-Worlds Interpretation of quantum mechanics (starting about 40:00 into the…
If I ever decided to abandon any pretense of integrity or credibility, and just shoot for making a bazillion dollars peddling quantum hokum, the particular brand of quantum philosophy I would peddle
has already been laid out, in Robert Charles Wilson's Divided by Infinity. In the story, the…
Last week's post about the Many-Worlds variant in "Divided by Infinity" prompted the usual vigorous discussion about the merits of the Many-Worlds Interpretation. This included the common objection
that we don't know how to obtain the probability of measurement outcomes in the Many-Worlds…
Phillip Ball has a long aggrieved essay about the Many-Worlds Interpretation, which is, as Sean Carroll notes, pretty bad. Ball declares that Many-Worlds is "incoherent, both philosophically and
logically," but in fact, he's got this exactly backwards: Many-Worlds is, in fact, a marvel of logical…
I'm afraid to ask this question, since it may be stupid or unrelated: Doesn't the Born rule require that you choose a particular basis? What determines that basis in MWI, when in MWI there is no
fundamental difference between an observation and normal time-evolution?
A 3-sigma effect should be wrong less than 1% of the time, a far cry from "most."
This doesn't make any sense to me. If the Standard Model is right, then a 3-sigma effect will be wrong all of the time. "3-sigma" is about what percent of all measurements will have such a large
discrepancy, not about what percentage of observed discrepancies will turn out to be signals.
"On the face of it, that's kind of a ludicrous statement-- if the statistics have any meaning, it can't be the case that "most" 3-sigma effects go away. A 3-sigma effect should be wrong less than 1%
of the time, a far cry from "most.""
This is the standard misconception where p-values are assumed to be posterior probabilities. They aren't (which is why they're useless).
"On the face of it, that's kind of a ludicrous statement-- if the statistics have any meaning, it can't be the case that "most" 3-sigma effects go away. A 3-sigma effect should be wrong less than 1%
of the time, a far cry from "most.""
Uh, no. It depends on the relative frequencies of the alternative and the null being true across lots of experiments.
A thought experiment: Somewhere on Earth is a human who has a unique disease that will cause him to explode with enough force to level a medium-size city. The only known test for this disease relies
on the level of a chemical which is, in the healthy population, distributed Normally with mean 10 and std. dev. 1. This disease causes the person to have a level of at least 13 - exactly 3 sigma
above the mean. Every person on earth is tested... there will be roughly 9 million people who have levels of at least 13, of which exactly 1 will be the diseased person.
The statistics has enabled us to reduce the false positive probability from 1 - 1/(7 billion), roughly, to 1 - 1/(9 million), roughly, which is a huge win, but we are still going to see roughly 9
million "wrong" 3-sigma effects for every "right" 3-sigma effect.
Chad, all: As I explained in The Born Equivocation thread, highly unusual events aren't the main problem with MWI. The main problem is it actually producing correct (found) statistics given its
formulation. You start getting to the point by asking, "If there's some natural way to measure probability by counting wavefunction branches [in MWI] .... Yes, there is, but first some critique of
the idea we could just assume the Born Rule is correct even in MWI. One has to show that the consequence of a theory is consistent with the BR or any other feature we wonder about. You can't specify
a description, and then say "because you include Born rule as a foundational assumption of the theory." Sorry, that is not how logic works. If you assume "A", that has consequences. You can't just
assume A and then add whatever B you want. It's like saying "I say it's a quadratic equation, but I need five solutions so that's what there are." No, if you can find five solutions it means you were
wrong to assume it was a quadratic equation in the first place.
First you come up with a theory. Then you ask what it predicts as a logical consequence, you don't just get to make up a description and then demand that will produce whatever you want. Then you ask
if that's what really happens.
Again, consider the case where we have unequal probabilities like 36% and 64% for outcomes A and B (different meaning than before.) MWI gives the wrong answer because it postulates that both outcomes
happen (or else what is the point?) each time, instead of A happening 36% of the time and B happening 64% of the time. What you have if you do the experiment n times is a branching network, like a
tree forking each time. The only intelligible way to define the equivalent of "chance" for an observer/version (ie, frequentist by counting in the abstract) is to take "how many different outcome
paths" like AAABAABBB... etc. Well, that gives you the statistics for 50:50 chance instead of 36:64. In effect, the differential "strength" of the two waves goes to waste, since each becomes simply
an existential entity for counting and not the occasion for genuine statistics as a further breakdown into various instances. There is then no meaning for "less likely version" of a given "world
path." They all just "are." Otherwise we need to divide them up into more literal fragments of some kind. More complicated wrangles might help, but ruin the simplicity and supposed advantage of the
essential concept, no?
I am not the first person to think of these problems, and I would like to see more acknowledgment of their severity (with thanks to dzdt and A Different Paul for trying to directly address these
concerns in the BE thread, even if IMHO without success.)
Hi Chad, the short answer is that I agree with you (with some qualifications) that in the MWI equipped with an appropriate derivation of the Born rule, unlikely events should not be any different
from unlikely branches of the wavefunction. But, in emphasizing how crucial the Born rule is to the MWI I was referring to the current understanding of the MWI - just unitary evolution and nothing
else, without an accepted derivation of the Born rule. In which case I claim that: A. Despite the superficial similarity to QM, there is actually nothing to support the MWI experimentally and B.
Worse, it is framework where you cannot make any inference from any set of observations.
In other words, unless you come up with a way for which the a priori probability amplitudes of QM translate to relative frequencies of repeated experiments done in a single "branch," it's all
gibberish. Note that even if you come up with rule that assign some conditional probabilities (or relative propensities) to different branches, there is an additional step to translate those
unmeasurable concepts to actual frequency based probabilities for repeated experiments done in a single branch (which is what's accessible empirically). It is not clear to me that this process of
translation is always unproblematic, but I am sure that smart people with more experience have thought about it and have something to say (maybe Matt or someone else can comment).
One way around all of this is to simply postulate that this is the case, add the Born rule as an additional postulate beyond just unitary evolution. But, that would be disappointing - in this case
it's true that the MWI would not be any worse than collapse model or any other "interpretation," but it won't be any better either. In fact it will probably be exactly equivalent to them (up to "what
really exist" type questions which I see no conceivable way of answering). In my mind the only reason you'd be tempted to live with all the metaphysical baggage of the MWI is that it is more
economical and minimal framework involving only unitary evolution.
I guess it comes down to me thinking about the MWI as being something more ambitious that just an interpretation, more as a generalization of QM which is potentially more logically coherent, so maybe
that justified the higher bar I want to put on it. For example, decoherence kind of explains how you can get something like effective collapse (approximately and under the right set of circumstances,
which means in effect it is a generalization of QM in the same sense statistical mechanics is a generalization of thermodynamics). I'd hope that something like that holds for the Born rule as well,
otherwise a lot of the potential charm of the MWI is lost for me.
Great - now we have a bunch of non-philosophers trying to make sense not only of the philosophy of quantum mechanics, but also the analytic philosophy of probabilistic statements.
Every time I try to think about what "The probability of X happening is 78%" really means, I get hopelessly confused. (That's not entirely true; in some circumstances, it really means no more than
"We did experiment Z n times and observed X 0.78*n times," in which case I do understand the statement.) I'd venture any honest person with the possible exception of a few philosophers who have
seriously looked into this should answer the same.
Moshe: I guess it comes down to me thinking about the MWI as being something more ambitious that just an interpretation, more as a generalization of QM which is potentially more logically coherent,
so maybe that justified the higher bar I want to put on it. For example, decoherence kind of explains how you can get something like effective collapse (approximately and under the right set of
circumstances, which means in effect it is a generalization of QM in the same sense statistical mechanics is a generalization of thermodynamics). I'd hope that something like that holds for the Born
rule as well, otherwise a lot of the potential charm of the MWI is lost for me.
I think that's really the key difference. I'm looking at it as an interpretation like any other, so I'm not particularly bothered by adding the Born rule as an axiom (which is more or less what you
have to do in any other interpretation). since I have lower expectations generally, I don't see that as a problem.
There's a vague sense in which the discussion of the difficulty of finding probabilities seems excessively abstract to me. That is, the whole origin of the interpretation comes from considering the
unitary evolution of the wavefunction, but for some reason, when it comes to discussion of probabilities, the wavefunction is sort of discarded in favor of odd discussions about counting branches and
so on, as if they all have equal weight. But you've got the wavefunction right there, and one branch clearly has more mathematical weight than the others, so I don't understand why it's not obvious
that there should be a Born-like rule that makes use of those mathematical weights. But I'm too tired to explain this in a coherent way right now.
quasihumanist: Every time I try to think about what "The probability of X happening is 78%" really means, I get hopelessly confused. (That's not entirely true; in some circumstances, it really means
no more than "We did experiment Z n times and observed X 0.78*n times," in which case I do understand the statement.) I'd venture any honest person with the possible exception of a few philosophers
who have seriously looked into this should answer the same.
I would agree with this. I'm always thoroughly puzzled by discussions of probability that don't use it to mean "If we did the experiment N times we expect P*N of those trials to come out this way,
give or take."
As noted previously, though, I would never make it as a philosopher.
Well thanks Chad for addressing the branching problems (and hey, give me a personal nod by now once in awhile ;-) but I think you still don't appreciate how problematical it is (and yes,
philosophical training does help.) The WF is not being discarded by critics of MWI, it just can't do the same job it used to if both (for simplicity)components of it continue to exist. In the old QM,
the components gave different actual chances of A v. B happening. Weird or not, that was a coherent (pun as you wish) way to think.
But if both components continue, their "existence" is all you have to work with. Without literally having 36% of many examples of A and 64% of B anymore, the amplitudes and their squares (moduli) in
effect "go to waste." I can't see any intelligible way to use that "mathematical weight" if there really aren't the right number of events. It is that attempt to use "weight" without real frequency
which is "excessively abstract", not the straightforward attempt to find something to actually count like the branches. And as you say, counting is indeed what we need.
Some struggle to make this work, and entangle so to speak in messy additional factors and refinements (which ruins the whole appeal as a conceptually simple way out anyway) but it impresses me
little. And if you just keep both branches, then counting branches is the only intelligible way to compare statistics (like I said, counting up AABBABABB ... and BABABBBA ... etc.), and that gives
the wrong answer of "50/50" every time.
Here's another issue of concern: if decoherence is so important in why we don't see superpositions etc., then how come we can see "quantum statistics" too? IOW, how would we even find the statistics
generated by interference (like double slit, MZI that *is* coherent, etc) but inferred from patterns of exclusive "hits" instead of staying a superposition? If we get statistics of either kind at the
end, what's the point of something making a difference? See a proposed experiment at the name link.
(BTW, ALeyram's recent post in Turkish was not spam, it was relevant. I have it saved if anyone wants the text, including the OP. It expressed similar concerns about branches and probability as many
have noted.)
Your mental model of probability seems purely discrete, relying always on counting a finite number of discrete instances. It seems like you would have philosophical problems with a probability of
$sqrt{2}/2$ or $\pi/4$.
Physical theories do come up with these sorts of probabilities, so having a mental model of probability that doesn't make sense of them seems problematic.
Quasihumanist, you misunderstand my point. Sure, a probability really can be 1/sqrt(2) etc. which means that if we do n very many trials we will approach a ratio of 0.7071... But in order to verify
that, we have to count the instances! The question is not what kinds of probability "can exist" but how are they specifically generated in different models. In traditional CI the different squared
moduli (as I meant to write earlier) can indeed produce any real number probability from 0 to 1 inclusive. That's because the WF branch somehow creates "a chance" of something happening. We need the
discreet instances just to test the probability, not literally to define or generate it except as a abstract unlimited and ever-growing potential number of cases.
However, in MWI we are asking "what probability does the model generate?" Despite the misapprehensions of Chad and others that we can simply stick on the BR as an extra assumption, the BR does not
logically *follow* from the description of the model nor is it even compatible. The model produces "branches" which are discrete per each "trial." If you count them up, they give the wrong answer of
50/50 (for two-way split) each time for the outcomes. Indeed, that's always literally the ratio of how many times A and B appear in any run of n times! REM that in MWI each experiment "really" turns
out the same each time, but various selves just "end up" in one branching tree or the other.
And like I said, there is no intelligible concept of "strength" of a branch if it continues to exist - how can that make a different number of outcomes? If I'm in the weaker-amplitude "less likely"
branch do I feel thin and tired? And if you add extra branches per shot you either have an arbitrary number, or infinite sets which are not commensurable.
That's what the model "gives" as such. It is not capable of producing other probabilities like irrational ratios even though such probabilities can be generated in other ways. IOW, the
straightforward application of MWI is literally falsifiable, and gives the wrong answer. It would have to be tweaked in complicated ways to work.
No - I would argue that in your understanding of probability, you cannot assign different meanings to a probability of 1/sqrt{2} rather than a probability of 233,806,732,499,933,208,099 /
(*) I googled for rational approximations to sqrt{2}.
Although I don't know any better ways of thinking about probability myself, I feel that thinking of probability as doing lots of experiments, counting occurrences, and dividing is not adequate here.
It seems to me that if you think of probability only in a discrete frequentist way than you should require as a mathematical axiom that all probabilities be rational numbers with denominators of less
than a few dozen digits.
Quasi, with all due respect you shouldn't be lecturing someone on what their understanding of something, like statistics, is. (Not to be confused on whether what they evidently do say is true or
false, etc.) My essential point was that MWI gives *the wrong* probability, and it is 50/50 even if some other mechanism somewhere could produce other kinds. It's like saying, "dice produce
fractional probabilities of the proportions of getting various rolls" such as e.g. a roll of two dice produce 3:36 chance to get "four" = 1/12 chance from permutations 1,3 ; 2,2 ; 3,1. (Similar for
hands of cards, etc.) That is a feature of dice, dice, baby; not my mind!
I am well aware that in principle irrational-number probabilities can exist, but that is not what MWI produces! It is not my fault that MWI produces the wrong, fractional answer when what we want is
various probabilities according to the Born rule. You got mixed up and thought because I was using the equivalent of dice or cards, that I literally couldn't imagine I.N. probabilities. That's
careless of you, not some dullness on my part. And even if I couldn't imagine such probabilities, MWI is still wrong to provide "0.5" when we need either 1/sqrt(2) or 0.7071 ...end. (And why "a few
dozen" - did I say anything about practical trial numbers? No.)
I really wish you could quit wasting time about trivial diversions that aren't even valid, and appreciate that a demonstrably false concept is popular among physicists - can you do that? How's all
that splitty-chancy stuff workin' out for ya?
BTW, what do *you* think the "meaning" of a probability of 1/sqrt(2) is, given finite resources to build up answers and an operationalist critique of your idealism? Oh, I didn't say I was one of
those; just askin ...
but for some reason, when it comes to discussion of probabilities, the wavefunction is sort of discarded in favor of odd discussions about counting branches and so on, as if they all have equal
weight. But you've got the wavefunction right there, and one branch clearly has more mathematical weight than the others, so I don't understand why it's not obvious that there should be a
Born-like rule that makes use of those mathematical weights.
I suspect that this isn't a QM problem so much as it is a stat problem. That is, I teach stats and this sort of nonsense pops up repeatedly. The cure is - as is usually the case - a specific
experiment. The one I usually give is rolling a pair of dice, since it's so easy to make a 6x6 table and enumerate the outcomes. There are 11 different outcomes for the sum of the dice, two through
twelve as sen on the universal chart. But there are only two ways to roll a three for a weighting of 1/18 while there are six ways to roll a seven, for a weighting of 1/6. I've found that when I put
it like that, most students get it the first time around, and find it to be almost intuitive.
Now, if only I could describe an MW experiment that depended on the fall of a pair of quantum die . . . There's someone famous who had a memorable quote about most conceptual problems of a certain
type actually being conceptual problems about statistics, but I can't remember who. Is there anybody here who has an idea as to the person or quote?
Every time I try to think about what "The probability of X happening is 78%" really means, I get hopelessly confused. (That's not entirely true; in some circumstances, it really means no more
than "We did experiment Z n times and observed X 0.78*n times," in which case I do understand the statement.) I'd venture any honest person with the possible exception of a few philosophers who
have seriously looked into this should answer the same.
I would agree with this. I'm always thoroughly puzzled by discussions of probability that don't use it to mean "If we did the experiment N times we expect P*N of those trials to come out this
way, give or take."
Again, this seems to be a problem not with QM, but understanding basic stats. Again, look at dice, this time one roll of a single die. Every outcome is weighted the same (not that it matters), and so
the average is the expectation value is 3.5.
Now, when someone says that the mean or expectation value of a single roll is 3.5, do they really mean there's a spot marked with 3.5 pips on the die? Of course not. And this is purely unremarkable,
everyday statistics on a discrete set.
Why when going from this case to QM non-integer probabilities all of a sudden becomes some sort of booga-booga problem in some people's minds is beyond me.
Chad et al.,
So, I thought about this for a while (since the prior post) when I realized I had a negative reaction towards MWI and I couldn't place my scientific/mathematical fingers on why. It seems to me that
there's nothing wrong with many worlds as an interpretation of quantum mechanics, as long as one is sure to think of it just as such - if a wavefunction contains vectors orthogonal to every vector I
have access to, then it shouldn't matter that it's there in the first place.
But I think my problem (and maybe others') is philosophical (and as such, completely unfounded in serious study) and also science-PR related. In this interpretation, since every possible choice of
quantum state of the entire universe since its formation is represented, there are included "universes" where every interaction since the big bang has defied what we know as the laws of physics. This
is perhaps not a huge problem, they will be extremely unlikely and they will exist somewhere and nothing will work like we expect and that's that. But imagine a universe where a particular motion
causes one small difference in how we consistently measure physical laws - an extremely low probability, but according to the interpretation, it exists absolutely. My first problem, then, is that I'm
uncomfortable with the idea that an interpretation of quantum mechanics could provide such a possibility to undermine empiricism; my second comes from the idea that it might undermine OTHER'S
empiricism. How do we definitively get our message across that "that's how the universe works" when the way we describe how the universe works leaves a finite probability that it's actually NOT how
the universe works, we've just been monstrously (un)lucky? Since we have no method of testing "which world" we're in, we have to rely on Dr. Pangloss's prediction, that we're in (one of) "the best of
all possible worlds".
I know... tl;dr, eh?
Ah, SOV, I refer to that very sort of dice experiment in my previous comment (did you read it?) That is indeed just how we investigate the chances of things happening in MWI. But remember, MWI is not
like a die rolling a one XOR a two XOR a three ..., because the whole point is that all outcomes happen. MWI has its intrinsic weakness, it is not a booga-booga confusion among its critics.
In a binary case, we have "A and B" for the first trial, then the A-world adds A and B to itself and so on to make ever more branches. So if we flip three times we have AAA, AAB, ... BBB and you know
that gives half A and half B in the set of eight permutations (the eight different "worlds" of experimental results.) That means 50:50 chances (I get tired of typing that) for A:B if I consider
myself a split soul ending up in each branching.
But in the real world we need other relative probabilities too for various wave amplitudes - we just can't justify them in MWI. It has nothing to do with imagining non-integer chances or not (BTW,
the misguided quasihumanist falsely charged, very silly after being corrected, that I could not imagine irrational ratios in principle, not "non-integer" chances or outcomes. That's his booga-booga
problem, I'd say ask him but it isn't worth the trouble.)
Like I keep saying, these are "instances". The "weight" Chad and other defenders of DI and MWI ask about does not intelligibly make frequentist sense. It's like imagining more mystical "weight" to a
die face, so when three comes up 1/6 times you imagine it more "chancy" than a two coming up 1/6 of the time (and nothing to do with the magnitude of the number written on the face, just imagine
letters then, OK?) Yeah, I can literally weight faces to make an unfair die but that means *actually producing more of one outcome than others*. So again: MWI, actually "used" instead of having
inconsistent postulates stuck on it (as if that could be done), gives the wrong answers.
Neil - just to make it clear - I am just arguing against your frequentist interpretation of probability, and I agree that MWI is inconsistent with your interpretation of probability. It strikes me as
strange that there can't be a die where one side comes up exactly pi times (and not 3.14159 times) as frequently as the others when there is (or - at least - could be given a sufficient understanding
of the dynamics of dice) mathematical description of the density distribution needed for such a die. (If it matters, dice and dynamics are classical in the previous sentence.)
SOV - Yes I claim I do not understand the philosophical foundations of statistics. (That is different from understanding or not understanding statistics itself or its mathematical foundations.)
Just to record my philosophical positions:
The probability of 1/sqrt{2} has no definite meaning at all, but rather a family of meanings which depend on context and agree sufficiently with each other that we use the same phrase for all those
meanings. Theorists like to play certain games which produce 1/sqrt{2} (and I don't understand what probability means in these games), and 1/sqrt{2} is sufficiently close to experimental results (for
which probability *is* interpreted in a frequentist way) that we have agreed to call it *the* probability.
Furthermore, the mere question of what interpretation of quantum mechanics is correct is a meaningless question, akin to asking whether colorless green ideas sleep furiously or calmly. This is
because quantum mechanics itself is just a series of mathematical statements produced by games that theorists like to play, and the statements and games are generally accepted because they are
sufficiently close to experimental results.
I am not claiming privileged positions for either mathematics or experiment here; they are playing their own games which happen to interact with the games of theorists in certain ways. Nor am I
claiming these games are arbitrary; clearly they have evolved to serve our culture reasonably well.
"Furthermore, the mere question of what interpretation of quantum mechanics is correct is a meaningless question, akin to asking whether colorless green ideas sleep furiously or calmly." - you are
correct if the subject is indeed merely "interpretations" of the same data. There is such a thing as "shut up and calculate" and I give Chad credit for acknowledging the usefulness of just doing that
and not pretending we understand "what's really going on." But a model isn't just an interpretation, it makes predictions derived from its own properties. MWI is often couched as "an interpretation"
but actually it is a model which (as usually described) makes a statement about how the wave functions evolve, and that has the consequence of producing the wrong probability for events if understood
straightforwardly. That is the case regardless of whether you are right about non-rational probability values.
Again, consider the case where we have unequal probabilities like 36% and 64% for outcomes A and B (different meaning than before.) MWI gives the wrong answer because it postulates that both
outcomes happen (or else what is the point?) each time, instead of A happening 36% of the time and B happening 64% of the time. What you have if you do the experiment n times is a branching
network, like a tree forking each time. The only intelligible way to define the equivalent of "chance" for an observer/version (ie, frequentist by counting in the abstract) is to take "how many
different outcome paths" like AAABAABBB... etc. Well, that gives you the statistics for 50:50 chance instead of 36:64.
I actually don't think that is an intelligible way to define the "chance" in this case, because a given observer only ever sees one outcome path (or history.) Counting up different paths is
meaningless; it doesn't correspond to any empirically possible set of measurements.
The correct way to predict probabilities in a frequentist fashion is, as Moshe said, to count along a single history. Does MWI constrain the paths through your network such that, along any one
allowable path, the proportion of experimental outcomes always tends to 36:64?
Well, yes, and this is why branch weights matter. If you do the experiment n times, each possible path snakes along n branches, and its weight is (roughly speaking) proportional to the product of the
branch weights. For large n, the set of paths where the proportion of experimental outcomes is close to 36:64 has a much larger total weight than the set of remaining paths.
In the limit, as n goes to infinity, the set of all paths with measured proportion different from 36:64--in other words, the histories where you could detect a definite violation of the Born
rule--has total weight zero. Those paths simply don't exist.* And behavior in the limit is the only thing that matters; probabilistic predictions apply to limiting frequencies of infinite runs of
measurements. (As Moshe and Chad have been discussing, we pretty much always interpret these predictions to say something about finite runs, and you could write a book about whether and why it's
valid to do that--but that's not really MWI's problem, it's a general issue in the philosophy of probability.)
*[At least, this is true if you accept that quantum states with zero weight (or zero probability density, depending on how many states you're looking at) are inaccessible. This is a sort of superweak
Born rule. OTOH, it's hard to imagine how anyone couldn't accept this, since otherwise quantum theory would be completely impossible to apply!]
To summarize, in terms of your network example: MWI gives you the correct 36:64 probability, not by pruning the network so that it contains 36% A-branches and 64% B-branches, but by prohibiting all
infinite paths through the network which fail to contain 36% A-branches and 64% B-branches.
As Moshe and Chad have been discussing, we pretty much always interpret these predictions to say something about finite runs, and you could write a book about whether and why it's valid to do
that--but that's not really MWI's problem, it's a general issue in the philosophy of probability.
If nothing else, maybe MWI is a way to get people interested in probability. Most of my students seem to think it's just a bit of methodology you have to learn in the service of doing the Good Stuff
:-( And I'll say it again: A lot of them demonstrate precisely this type of confusion between possible occurrences and distribution of occurrences for what is bog-standard nothing-to-do-with-MWI
probability and statistics. Oh, and with a side dish of some of the paradoxes and pitfalls of (non-mathematical) inductive reasoning.
Maybe I should expand on that. I suspect that Chad's lament is at the heart of the matter: that MWI is the many worlds interpretation. It gives the impression that complete and whole new universes
are popping into being every second. If that were really the case, I'd expect people like Neil to ask where the energy to do that is coming from (and indeed I've had many people ask me with some
puzzlement as to whether or not MWI violates conservation of energy.) I'll concede that thinking like this does lead one naturally to some notion of an integral number of new worlds created from
discrete events. This doesn't make sense of course - the Poisson distribution, for example, where a singular event takes on a continuous value would lead one to believe that an infinite number of
worlds would be created in a finite and short amount of time.
But let's look at why MWI is a red herring. Let's look at 1024 people tossing a fair coin ten times. Now in the ordinary run of things, people understand and expect that if you flipped a fair coin
often enough it would come up heads ten times in a row. However, they are often fairly suspicious if their "fair" coin comes up heads ten times in a row at the beginning of the sequence of flips. In
fact, getting a run of ten heads in the first ten flips is just 1/1024. But if you have 1,024 people doing this, you have a better than 63% chance that one of them will do so - irrespective of
whether or not they are initially entirely different people or if they are the result of 10 splits in an MWI scenario.
This is where many probability and inductive paradoxes come into play, and is also the basis of an old and classic con: A person receives from out of the blue a stock tip via a phone call or letter.
A stock tip that turns out to be correct. In the following days, they receive more tips, 2, 3, 4, or more which all amazingly pan out. They are then asked to "contribute" some money on the next call
and are given an elaborate explanation as to why their benefactor can't pony up the money on their own.
You see what's happening of course: The con consists of an initial pool of, say 1,024 marks, none of whom are in contact with each other :-) Notice also that the split doesn't have to be 50-50 each
time. It could be a one-in-four chance, a thirteen-in-fortyseven chance, etc.
And this is the other horn of the paradox, as it were. According to classic statistical theories, there is no purely logical way to distinguish between a finite run of random but improbable outcomes
and action of a nonrandom effect. Flip a coin ten times, it comes up heads ten times. Is it a fair coin? Possibly. flip it ten more times, it comes up heads ten more times. Now what do you think?
Flip it ten more times, it comes up heads ten more times. Do you still think this is a fair coin? The problem on the philosophical side is that logically, you can't make that distinction (just as
logically, you can't make the distinction between one flip of a unfair coin coming up heads or one flip of a fair coin coming up heads.) This conflicts with gut empiricism that will lead most people
to conclude that twenty coin flips in a row coming up heads implies an unfair coin - and 99.99 plus percent of the time, they're right.
Sorry for the ramble, most of which everyone already knows. But after all the back-and-forth, I still don't understand the objections some people have to MWI as a theory/interpretation of QM. I don't
mean that I understand the objections and disagree with them, I mean that I don't get the objection, period. Maybe this little bit of discussion will clarify things for the objectors, and they can
now rephrase what they mean so I can understand what they're getting at. Who knows? Maybe they're right :-)
Ah, one last bit on allegiances: to the extent I have a particular interpretation of QM, it's the usual shut-up-and-calculate one. It's true that if I were forced to pick another one, in some branch
I'd say MWI :-)
But I think in these sorts of discussions, it's important to consider motivations. Some people just plain like the idea. Other people are not so much for MWI as they are against some other
interpretation. And, uh, that'd include people like me. If you must pick between alternatives, well, MWI may be "nonparsimonious" in some respect. But at least it's a physical theory. It seems to me
that the more "parsimonious" theory of some ill-defined observer collapsing the wave function doesn't even rise to the level of a physical theory.
Of course, some people take it that collapsing the wave function is a physical theory, albeit by a mechanism that is as mysterious now as it was early in the last century and I can't really gainsay
them. But it seems to me that the sorts of people who go for this notion intersect significantly with the sorts of people who believe in ESP, astral projection, etc. (at least as an explicable though
still unknown physical phenomena.) Maybe my distaste comes down to who I have to rub elbows with, a sort of class snobbery as it were.
Oops - an addendum to the addendum: I see this starts back at a post on Wilson's superb "Divided by Infinity". I suspect that there are significant numbers of people emotionally invested in MWI
precisely because you get comforting fables of the you-will-never-die sort.
Trust me, I'm not one of them. Unless I missed it in the discussion, what makes "Divided by Infinity" great as opposed to merely an old story retold by a good writer is that this is a horror story.
Not a nice sensawunda one.
Would anyone be surprised if I said that early on I came to the exact same you-will-never-die conclusion that MWI sorta implies? I hope not - I imagine this implication is routinely and independently
discovered thousands of times every semester by bright young undergrads. And at least some of them, as was the case with myself, keep following the logic to reach the conclusion that the most
probable end state is some sort of consciousness existing for eternity in a state of white light, white noise . . . for the rest of eternity. Does this seem like a desirable outcome? Sounds more like
Hell to me.
No, I'm not fond of this particular implication of MWI at all. Not even in the Deepak Chopra sense.
SOV, you seem to have outdone me for consecutive posts ever in a thread there. OK, here's a simple retort: the branching wavefunctions in a binary choice experiment, regardless of labeling
"intensity" (which has little meaning *if you don't let them do the work of statistical breakdown for real*), set up a branching tree of A`s and B`s. (I'm starting to use " ` " for plural since " ' "
is "wrong" and As is arsenic ...) Well the numbers of A`s and B`s are equal, equally likely, by any true *counting* concept because of the *symmetry* of the geometry of it all. Like I said, the
"intensity" goes to waste if you don't let it literally determine exclusive outcomes!
MWImbroglio fans: How's that branchy-chancy thing workin' out for ya?
PS: Reply to Anton soon.
Neil, point one: I have already told you that your objection doesn't even make sense to me. Point two: you are rather robotically repeating your objection without making any attempt to rephrase it in
a way that I can understand.
And if you can't be bothered to even try to explain what you mean even after I (and it looks like several other people) tell you that we can't make heads nor tails of what you're getting at, well,
all I can say is, you'd make a damn poor teacher.
That and since you can't even be bothered with the basic courtesy of trying to explain what you mean, and yet you want people to keep guessing, well, I'm not going to waste any more of my time on
Are we quite clear on this? Your problem isn't that you have odd notions about a particular subject. Your problem is that you're being an inconsiderate jerk.
SOV, I think you and others need to take responsibility for your understanding of what people say. I have gotten many complements here and there from those who have no itch to disagree (which so
easily turns into seeming inability to understand.) Here I also had to put up with some red herrings into other misdirections. I keep repeating myself because many here keep repeating the same
rebuttal attempts or claims they don't get my point, and I address each person. If neither of us changes, then why is it my fault? When are other people going to make clear, definite descriptions of
their own here we can follow?
My argument is the simple idea of counting branches - a point many other thinkers have made as the same criticism. Look up for example Adrian Kent's objections cited at Wikipedia and his similar
overview from 1997. Anton just above accepts that much, he just thinks that extra tweaking can save the model. This challenge must bother people, it isn't complicated. You already have a clue with
"make heads or tails of ..."
I can't really see how to better reword something as simple as "binary choices lead to a branching tree with half of choice A and half of choice B found all the way through." That is equivalent to
chance, or what is? There, was that hard to "get"? I already said it again earlier, even if too much (which can't then also be, not enough), right up there and very politely in #25! That was just the
sort of thing you say I don't do.
I don't know, after all the illustrations, what else I could do. And each equivalent MWI experiment *is the same "tree" each time.* Your discussion about the coins etc. doesn't apply. So, since we
need non-equal chances in many experiments, there's a contradiction. That should be easy to get. I don't know, after all the illustrations, what else I could do. You need to work harder on it, not
And if you mean I'm too sarcastic etc, well that's another issue but I wasn't most recently. It's disingenuous of you to suggest I "can't even be bothered" and didn't even tryto explain, when I did
so AFAICT as directly as possible and just previously. That doesn't even fit with saying I repeated myself, and in many permutations (all those nice puns.) Nor are my ideas on this "odd", since I
make the basic objection - it's the epicycle-like attempts to defend MWI with bells (I just can't help it) and whistles that are "odd." Finally: after your inconsiderate name-calling indulgence, I
doubt clarity is possible. I tried anyway since I'm not a jerk, maybe I'm too nice.
Anton, thanks for a considered reply, yet which fails IMHO to direct towards a valid solution. SOV, read this too. Let's go over some things first:
1. Some say that MWI is just "an interpretation" of the same facts, but that is not really true (or is a half-truth, not good enough.) MWI posits a model, it makes a claim about what goes on. Models
have consequences that derive from their assumptions and the workings thereof. You can't, as Chad and many seem to think, just tack on an axiom of your choice to make things "work" because that axiom
may not be logically consistent with what the model leads to.
2. That model is, briefly and perhaps simplistically: "The Schroedinger equation simply continues to evolve" (unitary evolution with no special collapse events.) I have big problems* with whatever
supposedly keeps the outcomes effectively separated, but let's charitably assume that can happen. As simplification, an asymmetric BS split gives say a superposition of 0.6|Aâ© and 0.8|Bâ©. That is
"two components" of the superposition, right .... Let's call that SMWI (simple or simple Schroedinger-realist) and take as baseline, and say the burden of proof is on those who want even more
complications (but isn't the goal "to simplify"?)
3. In our "apparent" (what I would call "real" instead) world, those waves actually produce exclusionary36:64 "chances" of detector clicks (defined in our actual world and by real experiment, not to
be assumed a logical consequence of the model!) We (whoever the heck "we" are) "find" this by counting up hits, with variations but the usual statistical convergence etc. And various runs give
varying results, just like tossing coins.
4. But in SMWI, there just "are" these two components of a superposition, and the lower-amp "other self" is just as real as the stronger one. They can't sense their relative "thinness." Note that we
don't need over-hyped interference to model a split from a BS, right? (Only to prove the model at first, we don't need to keep on mucking with it!)
5. As we keep doing experiments the counter results presumably (without additional add-lib, over-imaginative epicycles) make up a tree. This tree is of course all the permutations of A with B.
Remember that in all (?) MWI, every equivalent experiment *is the same experiment over again.* In SMWI it consists of the "structure" defining all the branching outcomes. You can want the WF
strengths to matter, but ironically their mutual continued existence ruins that for them. For three tries there is AAA, AAB, ABA, ABB, BAA, BAB, BBA, BBB. That's going to hold up for the result and
proportions thereof whether finite or imagined as limit to infinity, etc. (Sorry to repeat myself yet again, but for the record a compete list is here.)
6. I project a "self" along each of these. This effectively defines the probablity "I see", or what else does it mean? Sure, each "self" means one of those like BAA, but put them all together and the
proportion and the symmetry do and must give 50/50 chances as such. (Just consider symmetry of counting since the "strength" goes to waste when the components aren't "collapsed", the presumed
amplitude becomes more like the color of a bunch of switches ...I do admit amplitude affects things like what orientation of combined polarization etc, but that's sitll not "chance" anymore.) So SMWI
or any "honest" branch structure cannot constrain the paths to get any frequentist result other than 50:50. Yet you say, "But wait, there's more ..."
7. First, you know there can't be a special "real me" that travels along some of these paths and not others, or with adjusted chances - like a ghost differentially animating zombies - that ruins the
whole point of it all being real as the continued evolution, plus adds a weird extra being into it all. (Hey, believe that only real souls experience results and God tweaks those into the BR, with
the rest "zombies" that feel nothing - naaa ...)
8. So your talk of branch "weights" and constraining of paths is contrived, and hard to get out of a continued evolution that simply makes a big bunch of complicated waves. (And just forget the
degenerate case of density zero, that's the crusty way of saying the WF branch just doesn't exist.) It saddens me that supporters keep adding these questionable epicycles and forced unnatural axions
as it were. You can't just "prune" some branches, finite or infinite as may be, in order to get results you like. That's the conceptual equivalent of scholastics discarding "incorrect" dissections.
Sure, the universe does act other than naive 50/50 but that shows the weakness of the theory. You have to show they ought to be pruned and how, as a logical consequence of the model! And if the model
is too much a Rube Goldberg contraption, that is suspicious and detracts from the pretense of parsimony.
9. Enough for this comment, but I ask you to read my *proposal paper at name link about a way to test the claim that decoherence effectively converts a formerly coherent superposition into a mixture.
Meanwhile here's a dig at decoherence ideas for awhile: how come we still get "statistics" that show interference (ie, hits and not continued superposition) in the case of e.g. a coherent MZI, if
"decoherence" is supposedly why we find "hits" and not continued superpositions?
PS Thank you for accepting my FBF request! People can be friends and still disagree on things.
Sigh. Neil. No, the responsibility is on you for clarifying what you mean. When people say they don't understand you, please take them at their word. Don't get snippy.
Now. I assumed you understood and accepted this since you never disputed it, but are you clear on the concept that there is no literal "branching" like forks on a river? If I talk about a "branch" of
a function, it doesn't literally branch now, does it? I could just as easily talk about the "branches" of velocity distributions in a hetereogeneous gas and I don't think you would get the impression
that the different molecules literally branch off. It's at best a metaphor, nothing more.
Are we quite clear on this? You need to say either "Yes, I agree that there is no real branching" and stick to it, or you need to say that "No, I disagree, and there really are literally new worlds
branching off from the old one in MWI. And here's why." And it's only when you do the latter that you can make the arguments you've been making.
Do you understand this? You aren't allowed to say that the branching really is metaphorical and then turn right around and present the arguments you have been and which assume that the branching is
real. People have been getting the impression, I think, that you understand that there is no real branching, and so they're confused when you present an argument that assumes that branching is
literally true.
This is starting to get unduly snippy, in a manner that was, admittedly, entirely predictable. So here's your sixteen-hour notice: I will close comments to this post at noon tomorrow. Make your final
arguments now, and keep them civil. Escalation of personal insults will be met with summary disemvowelling. Attempts to continue the argument in comments to posts other than this one will be lead to
stronger countermeasures.
Apologies, Chad. I seem to recall a time not too long ago when you were talking about decoherence with an interferometry example and wondering why you seemed unduly short with this fellow Neil.
Having had first-hand experience with what's going on now (I didn't really pay attention before), I can see why.
There's something peculiarly frustrating in having to go back and explain the same point over and over when you think that this time the confusion as been resolved.
But anyway, just so we're all on the same page (I thought this was something everyone already knew), the "branching" of MWI aren't literally branches, any more than, say, the branches in the possible
pathways of a chemical or nuclear reaction are actually branches.
If anybody thinks these are literal branches, well, all I can say is they are arguing about something different from what is commonly considered to be the MWI interpretation.
You can't, as Chad and many seem to think, just tack on an axiom of your choice to make things "work" because that axiom may not be logically consistent with what the model leads to.
I think everyone's aware of that. But most people here (and, for what it's worth, most physicists working in the area) disagree with you about what the empirical consequences of this model are. They
consider it an "interpretation" because, they find its empirical consequences to be virtually indistinguishable from those of any other mainstream QM interpretation.
I have big problems* with whatever supposedly keeps the outcomes effectively separated, but let's charitably assume that can happen.
Generally speaking, of course, the outcomes aren't kept effectively separated. Worlds merge as often as they split; just as any random process with multiple possible outcomes represents a splitting
of worlds, any random process with multiple possible histories represents a merging of worlds.
3. In our "apparent" (what I would call "real" instead) world, those waves actually produce exclusionary36:64 "chances" of detector clicks (defined in our actual world and by real experiment, not
to be assumed a logical consequence of the model!) We (whoever the heck "we" are) "find" this by counting up hits, with variations but the usual statistical convergence etc. And various runs give
varying results, just like tossing coins.
Correct, as long as we're talking about finite runs. Infinite runs all* converge to the same result: 36:64, exactly.
*or "almost all," in the the sense that the exceptions form a set of measure zero. But in your paragraph 8. you seem to accept that this is equivalent to "all".
4. But in SMWI, there just "are" these two components of a superposition, and the lower-amp "other self" is just as real as the stronger one. They can't sense their relative "thinness."
Yep, which of course fits with what we observe. When I happen to measure an improbable value in some system, I don't feel particularly "thin" or unreal.
5. As we keep doing experiments the counter results presumably (without additional add-lib, over-imaginative epicycles) make up a tree. This tree is of course all the permutations of A with B.
Remember that in all (?) MWI, every equivalent experiment *is the same experiment over again.* In SMWI it consists of the "structure" defining all the branching outcomes. You can want the WF
strengths to matter, but ironically their mutual continued existence ruins that for them. For three tries there is AAA, AAB, ABA, ABB, BAA, BAB, BBA, BBB. That's going to hold up for the result
and proportions thereof whether finite or imagined as limit to infinity, etc.
Nope. It will hold up in all finite cases, but not in the infinite limit. The distinction between finite and infinite behavior is critical here.
In the infinite case, each logically possible outcome can be written as an infinite sequence like AABABBB.... The set of these outcomes is infinite, and uncountably so. (This is easy to see, since
the set of paths can be one-to-one mapped to the set of real numbers, as expressed in binary notation.) Essentially, as you proceed down your tree and the number of parallel branches goes to
infinity, the branches blur into a continuous spectrum. It no longer makes sense to talk about the wave function "strengths" of individual outcomes at this point, since they're all infinitesimal.
Instead, one talks about the total wave function magnitude (squared) corresponding to sets of outcomes. (Analogously, you don't ask about the probability of an electron being detected at a particular
point in space, but rather about the probability of its being detected within a particular region of space--an infinite set of points.)
And in the limit, the total magnitude of all the outcomes that deviate significantly from the expected 36:64 ratio is zero. Again, this is totally different from the finite case. When there's only a
finite number of experiments, even the weirdest outcomes have nonzero magnitude, so you're perfectly right that they do have "mutual continued existence." But when the number of experiments goes to
infinity, that no longer holds. No magnitude, no existence.
There are lots of mathematical systems where life is very different when you're working with infinite sets/sequences rather than finite ones. This happens to be one of them!
6. I project a "self" along each of these. This effectively defines the probablity "I see", or what else does it mean? Sure, each "self" means one of those like BAA, but put them all together and
the proportion and the symmetry do and must give 50/50 chances as such.
But you can't put them all together. What would putting them all together mean? You can't call up your alternate selves and ask them what measurements they recorded. You--the you that's capable of
remembering a particular set of measurement outcomes--are the self projected along a single history, and the probability you expect to see should be calculated with respect to that history.
7. First, you know there can't be a special "real me" that travels along some of these paths and not others, or with adjusted chances - like a ghost differentially animating zombies - that ruins
the whole point of it all being real as the continued evolution, plus adds a weird extra being into it all.
Yep. There's one of you on every permissible infinite path, and although each of you sees a different sequence of experimental results, each of you sees their sequence eventually converge to the same
36:64 ratio.
But not all logically possible paths are physically permissible. MWI doesn't imply an Ultimate Ensemble multiverse, where every world that logically could exist does exist.
8. So your talk of branch "weights" and constraining of paths is contrived, and hard to get out of a continued evolution that simply makes a big bunch of complicated waves.
On the contrary, every wave has an amplitude (which is what the "weights" really are), and if the amplitude's zero in a particular region of Hilbert space, then, well, there's no wave there. It seems
pretty straightforward to me!
You can't just "prune" some branches, finite or infinite as may be, in order to get results you like.
Ah, but no branches are pruned. Every branch is found along some infinite path; it's just that not all infinite combinations of branches are permitted.
You should be familiar with this idea from, say, the EPR experiment. QM doesn't forbid any particular spin value on either of two entangled electrons, but it does forbid the two from exhibiting
particular combinations of spins.
9. Enough for this comment, but I ask you to read my *proposal paper at name link about a way to test the claim that decoherence effectively converts a formerly coherent superposition into a
I'd be glad to. It might take a while, though, as I've got coding to doâ¦.
Meanwhile here's a dig at decoherence ideas for awhile: how come we still get "statistics" that show interference (ie, hits and not continued superposition) in the case of e.g. a coherent MZI, if
"decoherence" is supposedly why we find "hits" and not continued superpositions?
Take the following with several grains of salt, because my total formal training on decoherence took up about thirty-five minutes at the end of intro QM, and that was about a decade ago. But as I
understand it, it's a question of bases. A pure state, as expressed in one basis, is usually a superposition of states when expressed in other bases. Therefore, a system can't decohere in all bases
simultaneously, and the "hits" we find with respect to the measurement basis will, necessarily, correspond to superpositions in some other bases. And it's those other bases in which our statistics
can show interference.
Let's apply this to the classic double-slit experiment (using a beam of electrons, say.) There are two bases of interest. The first basis includes (among other things) the position of the electron as
it passes through the slits--did it pass through the left slit, or the right slit? The second basis includes the position of the electron when it smacks into the detector screen--did it hit here or
here or here?
If both slits are open when you fire an electron through, decoherence doesn't occur until the electron hits the detector screen. Then the "hit" we record is a pure state in the second basisâ¦we can
say that the electron hit exactly here. But that state is, itself, a superposition in the first basis, because the electron could have gone through either slit before ending up at that spot on the
screen. And the statistical distribution of "hits" demonstrates interference between the left-slit and right-slit states in the first basis.
If, on the other hand, you block one slit or stick a particle detector in it, you force decoherence with respect to the first basis (since now the external environment "knows" which slit the electron
went through.) That's why your "hits" pattern no longer indicates interference between the states of the first basis.
Now, when you say "a coherent MZI" (I assume you mean MWI?), I'm not sure what you mean. MWI features decoherence too; it just defines decoherence as entanglement between the states (in whatever
basis) of a quantum system and the states (in a "perceptual basis") of the observer. Decoherence still only occurs with respect to a particular basis of the measured system, so you can still have
your "hit" statistics reveal superpositions of states in other bases.
PS Thank you for accepting my FBF request!
No problem. | {"url":"https://scienceblogs.com/principles/2011/06/02/the-statistics-of-the-highly-i","timestamp":"2024-11-04T05:04:52Z","content_type":"text/html","content_length":"140292","record_id":"<urn:uuid:2f761637-ddfa-4bae-b79a-b4c4c27be35b>","cc-path":"CC-MAIN-2024-46/segments/1730477027812.67/warc/CC-MAIN-20241104034319-20241104064319-00811.warc.gz"} |
Optimizing media spends using S-response curves
A key focus of our Data Science team is to help our clients understand how their marketing spend affects their KPIs. In particular, we create models to understand the effect of individual marketing
channels such as television or paid search ads on KPIs such as sales, visits and footfall. Knowing how marketing spend affects KPIs enables us to optimize the clients marketing spend for maximal
result. In this Geek post I will give a fictional example on how we use S-curves to optimize radio spend. The final code of this fictional example can be found on Github as well.
The data
Let’s consider a simple example where we have the number of sales and the number of radio GRPs on a daily basis. We assume that radio only has an immediate positive effect on the number of sales the
same day. This is obviously not true in real-life, because radio still shows a positive effect after several days. For now, such delayed effects are out of the scope of this post. The figure below
provides an overview of how our fictional sales and radio dataset looks like. We see that in this example dataset there are two important factors that determine the number of sales on a day: the day
of the week (seasonality) and the number of radio GRPs on that day (marketing spend).
Simple OLS regression
As we are interested in how radio affects the number of sales, we run a simple OLS regression to capture the relationship of marketing spend and seasonality on sales. The results of this regression
are shown in the table below.
OLS Regression Results
Dep. Variable: sales R-squared: 0.920
Model: OLS Adj. R-squared: 0.896
Method: Least Squares F-statistic: 38.01
Date: Thu, 23 Apr 2015 Prob (F-statistic): 3.62e-11
Time: 15:00:50 Log-Likelihood: -47.424
No. Observations: 31 AIC: 110.8
Df Residuals: 23 BIC: 122.3
Df Model: 7
Covariance Type: nonrobust
coef std err t P>|t| [95.0% Conf. Int.]
const 7.4642 0.583 12.793 0.000 6.257 8.671
radio_grp 1.1423 0.096 11.854 0.000 0.943 1.342
seasonality_monday -2.7826 0.820 -3.392 0.003 -4.480 -1.085
seasonality_tuesday -0.4115 0.869 -0.473 0.640 -2.210 1.387
seasonality_thursday -4.8585 0.903 -5.381 0.000 -6.726 -2.991
seasonality_friday -3.7702 0.886 -4.256 0.000 -5.603 -1.938
seasonality_saturday -4.9362 0.886 -5.572 0.000 -6.769 -3.104
seasonality_sunday -5.3039 0.872 -6.080 0.000 -7.109 -3.499
Omnibus: 0.646 Durbin-Watson: 1.188
Prob(Omnibus): 0.724 Jarque-Bera (JB): 0.739
Skew: -0.265 Prob(JB): 0.691
Kurtosis: 2.461 Cond. No. 24.1
The result of this regression shows that the day of the week is a very important factor for the number of sales. We used Wednesday as reference day and added binary dummy variables for all other
days. Note Wednesday is taken arbitrarily. The coefficients of these day-dummies can be interpreted as the number of sales this day has more (or less) compared to the number of sales on Wednesday
(the reference day). For example, the Monday coefficient of –2.8 implies that there are 2.8 less absolute sales on Monday than on Wednesday. So, as all day dummy coefficients are negative, it follows
that Wednesday is the best day of the week for the sales.
More interestingly, the result of the regression also gives a positive coefficient of 1.14 for the radio variable. This coefficient can be interpreted as a positive effect of 1.14 additional sales
for each radio GRP used. Note that this also implies that the effect of radio is linear, i.e. 1 GRP results in 1.14 additional sales and 5 GRPs results in 5 times 1.14 (=5.7) additional sales.
The S-response curve
In reality, it is not often the case that radio has a linear effect on sales. KPI drivers such as television and radio, but also display and search ads tend to have diminishing returns. Wikipedia
provides the following example about diminishing returns:
“A common sort of example is adding more workers to a job, such as assembling a car on a factory floor. At some point, adding more workers causes problems such as workers getting in each other’s
way or frequently finding themselves waiting for access to a part. Producing one more unit of output per unit of time will eventually cost increasingly more, due to inputs being used less and
less effectively.”
In a similar manner, research has shown that initial advertising budget has little impact on sales. One possible reason for this is that a low advertising budget might result in your marketing not
being noticable between all of the competitors marketing campaigns. Only after a certain budget spend threshold results are noticeable in the form of improved KPIs. Hence, the result is that the
effect of marketing spend on KPI drivers such as radio typically follows an S-shaped curve. The figure below provides an example of an S-curve for radio spend.
Introducing dummy variables
The notion of the S-shaped curve conflicts with our earlier calculated linear effect of radio on sales. Therefore, it is very likely that we get a much more accurate model when we can account for the
effect of the S-curve. One possible approach is to just try all possible transformations of our radio dataset to an S-curve. However, as the S-curve is defined by three parameter values, this implies
trying a lot of different transformations. Therefore, we use a smarter approach to find the S-curve. That is, instead of adding a continuous variable that denotes the number of radio GRPs on a given
day, we add binary dummies where each dummy represents an interval of GRPs. Given our example dataset where the maximum number of GRPs is 10, we add four binary dummies representing the GRP intervals
[0.1-2.4], [2.5-4.9], [5-7.4] and [7.5-10]. Now, the dummy value of an interval is 1 if the number of GRPs of that day is in that interval, otherwise the value is zero. Below is a short snippet of
the radio dataset we then obtain:
Date time Radio GRP Radio dummy Radio dummy Radio dummy Radio dummy
0.1 – 2.4 2.5 – 4.9 5.0 – 7.4 7.5 – 10
2015-06-01 4 0 1 0 0
2015-06-02 0 0 0 0 0
2015-06-03 1 1 0 0 0
2015-06-04 2 1 0 0 0
2015-06-05 3 0 1 0 0
Using the new radio dummy variables we again run a standard OLS regression. The results of this regression are shown below:
OLS Regression Results
Dep. Variable: sales R-squared: 0.985
Model: OLS Adj. R-squared: 0.978
Method: Least Squares F-statistic: 134.6
Date: Thu, 23 Apr 2015 Prob (F-statistic): 4.28e-16
Time: 15:42:39 Log-Likelihood: -21.183
No. Observations: 31 AIC: 64.37
Df Residuals: 20 BIC: 80.14
Df Model: 10
Covariance Type: nonrobust
coef std err t P>|t| [95.0% Conf. Int.]
const 8.1073 0.298 27.175 0.000 7.485 8.730
radio_dummy_0.1_2.5 0.2485 0.334 0.745 0.465 -0.448 0.945
radio_dummy_2.5_5 1.9554 0.407 4.806 0.000 1.107 2.804
radio_dummy_5_7.5 8.7667 0.415 21.146 0.000 7.902 9.632
radio_dummy_7.5_10 9.3869 0.494 19.001 0.000 8.356 10.417
seasonality_monday -2.9030 0.405 -7.171 0.000 -3.747 -2.059
seasonality_tuesday -0.5771 0.401 -1.439 0.165 -1.413 0.259
seasonality_thursday -4.6460 0.430 -10.793 0.000 -5.544 -3.748
seasonality_friday -4.3809 0.441 -9.929 0.000 -5.301 -3.461
seasonality_saturday -5.2752 0.419 -12.602 0.000 -6.148 -4.402
seasonality_sunday -5.9470 0.422 -14.096 0.000 -6.827 -5.067
Omnibus: 1.184 Durbin-Watson: 1.621
Prob(Omnibus): 0.553 Jarque-Bera (JB): 0.590
Skew: 0.334 Prob(JB): 0.744
Kurtosis: 3.107 Cond. No. 8.27
The interpretation of the coefficients of the new radio dummy variables is slightly different than in our first regression. The coefficient of each dummy represents the additional sales when the
number of GRPs is in the corresponding interval. For example, consider a given day on which 6 radio GRPs are used. This implies that the value of the dummy for the interval [5 – 7.4] is one (and all
other dummies are zero) and that this results in an additional 8.5 sales.
GRP interval Additional sales
0.1 – 2.4 0.3
2.5 – 4.9 2.5
5 – 7.4 8.5
7.5 – 10 10.1
Finding the S-curve using the dummy variables
When plotting the additional sales against the GRP intervals we obtain the points in Figure 4. The shape of the S-curve can already be seen in these points. It then is a simple task to find the
S-curve that best fits these points. Note that in our example the S-curve we predicted fits the true S-curve (which we used for creating our fictional dataset) quite good because it is nearly the
same logistic function. The small difference in curves can be explained due to the fact that we added noise to our fictional dataset to simulate reality.
Final results
So, since we found our best S-curve transformation, we run the first OLS regression again but this time with our radio data transformed to fit the new S-curve. The resulted predictions of the model
are plotted in Figure 5. Note that this regression now fits our dataset much better than the first regression we run. Therefore, we are able to obtain much better predictions of the effect of radio
on sales! 🙂
OLS Regression Results
Dep. Variable: sales R-squared: 0.987
Model: OLS Adj. R-squared: 0.984
Method: Least Squares F-statistic: 258.4
Date: Thu, 23 Apr 2015 Prob (F-statistic): 2.56e-20
Time: 16:38:53 Log-Likelihood: -18.808
No. Observations: 31 AIC: 53.62
Df Residuals: 23 BIC: 65.09
Df Model: 7
Covariance Type: nonrobust
coef std err t P>|t| [95.0% Conf. Int.]
const 8.1540 0.230 35.381 0.000 7.677 8.631
radio_grp 0.9904 0.031 31.828 0.000 0.926 1.055
seasonality_monday -2.9477 0.326 -9.040 0.000 -3.622 -2.273
seasonality_tuesday -0.7462 0.347 -2.153 0.042 -1.463 -0.029
seasonality_thursday -4.8023 0.357 -13.463 0.000 -5.540 -4.064
seasonality_friday -4.0407 0.353 -11.454 0.000 -4.771 -3.311
seasonality_saturday -5.3139 0.353 -15.034 0.000 -6.045 -4.583
seasonality_sunday -6.0026 0.346 -17.364 0.000 -6.718 -5.287
Omnibus: 0.371 Durbin-Watson: 1.502
Prob(Omnibus): 0.831 Jarque-Bera (JB): 0.525
Skew: -0.047 Prob(JB): 0.769
Kurtosis: 2.370 Cond. No. 27.0
Optimize marketing spend
A particular useful property of the S-curve is that it has several useful characteristics for optimization. For one, it is easier to find the point where your return on investment is maximized. The
inflection point of the S-curve helps to find this optimal spend value. At the inflection point the derivative value of the S-curve is maximized. This implies that at this point the S-curve changes
from increasing returns (i.e. increasing spend by 1% leads to an >1% increase in sales) into diminishing returns (i.e. increasing spend by 1% leads to an <1% increase in sales).
The inflection point is therefore used as the minimum spend value because all spends below this value imply underspending as you can easily increase your ROI if you increase the spend up to the
inflection point. In our example, the inflection point lies at 5 GRPs. Using less than 5 GRPs implies underspending because you can get more sales per euro spend if you use 5 GRPs. In a similar
manner we can also find the overspending value. Recall that above the inflection point the S-curve shows diminishing returns. This implies that for every additional euro you spend more, fewer
absolute additional sales are generated. In our example, using more than 7 or 8 GRPs is obvious overspending as the additional sales hardly increase when using more GRPs.
Finally, when we have response curves for each of the individual KPI drivers (such as TV, radio, display, paid search, etc.) it is possible to find the optimal spend for each individual driver using
an easy-to-solve optimization problem. The result is an optimal marketing mix that maximizes the chosen KPIs.
Final remarks
This post provided a simple illustration of how we use S-curves to optimize the marketing spends of our clients. In practice however, the datasets are not as simple as in this illustration. For
example, in reality various media channels show lagged effects (ad-stocks) or only show diminishing returns. We use advanced modelling and time series techniques such as ARIMA and VAR models to
create Marketing Mix Models (MMM) that capture these effects and help our clients understand how their marketing spend can be optimized. We will elaborate more on the advanced techniques in future
Geek posts!
You must be logged in to post a comment. | {"url":"https://www.themarketingtechnologist.co/2015/04/29/optimize-media-spends-using-s-response-curves/","timestamp":"2024-11-09T09:37:16Z","content_type":"text/html","content_length":"101144","record_id":"<urn:uuid:b72083bd-19d5-4578-bdbe-aef18ef17f45>","cc-path":"CC-MAIN-2024-46/segments/1730477028116.75/warc/CC-MAIN-20241109085148-20241109115148-00577.warc.gz"} |
GreeneMath.com | Ace your next Math Test!
Lesson Objectives
• Learn how to find the inverse of a one-to-one function
How to Find the Inverse of a Function
Before we discuss the concept of an inverse function, let's quickly review what we know about functions and one-to-one functions. A function is a rule that assigns a unique output value (y-value) to
each input value (x-value). In other words, for each x-value, there is only one corresponding y-value. For a function to have an inverse, it must be a
one-to-one function
. In other words, each input value (x-value) in the domain must correspond to a unique output value (y-value) in the range, and vice versa. This property ensures that there are no repetitions or
ambiguities in the mapping. In other words, for a function to be a one-to-one function, each x-value corresponds to exactly one y-value and each y-value corresponds to exactly one x-value.
The inverse of a function f, denoted as f
, essentially reverses the mapping of the original one-to-one function. It swaps the roles of the input (x-value) and output (y-value) values. Instead of mapping from the domain to the range, the
inverse function maps from the range back to the domain. By applying the inverse function to the output value of the original one-to-one function, we can retrieve the corresponding input value. If
what you just read was a bit confusing, don't worry we will discuss it in more detail in the next lesson. For now, just think about a function and its inverse as undoing each other. In other words,
the goal of finding an inverse is to find a function that, when composed with the original function, returns the input value unchanged. This composition is expressed as f(f
(x)) = x, which demonstrates the idea that the function and its inverse cancel out each other when applied together.
To think about how to find the inverse of a one-to-one function, let's start with a simple example.
Example #1:
Find the inverse of F. $$F=\{(3, 2), (4, 5), (7, 8), (-1, -2)\}$$ To find the inverse of our one-to-one function F, we will simply swap the x and y values. In other words, the domain becomes the
range and the range becomes the domain. Let's represent our inverse function with G. $$G=\{(2, 3), (5, 4), (8, 7), (-2, -1)\}$$ As the previous simple example shows, the inverse of a one-to-one
function is found by simply interchanging the x and y values. When we think about finding the inverse of a function defined by y = f(x), we can use a similar procedure.
Finding the Equation of the Inverse of y = f(x)
For a one-to-one function defined by an equation y = f(x), we can find the inverse f
(x) using the following steps:
• Replace f(x) with y
• Interchange x and y in the equation
• Solve for y
• Replace y with f^-1(x)
Let's look at a few examples.
Example 2
: Find the inverse of each function. $$f(x)=(x - 1)^3 + 2$$ Step 1) Replace f(x) with y. $$y=(x - 1)^3 + 2$$ Step 2) Interchange x and y in the equation. $$x=(y - 1)^3 + 2$$ Step 3) Solve for y. $$x=
(y - 1)^3 + 2$$ Subtract 2 away from each side: $$x - 2=(y - 1)^3$$ Take the cube root of each side: $$\sqrt[3]{x - 2}=y - 1$$ Add 1 to each side: $$y=\sqrt[3]{x - 2}+ 1$$ Step 4) Replace y with f
(x) $$f^{-1}(x)=\sqrt[3]{x - 2}+ 1$$
Example 3
: Find the inverse of each function. $$f(x)=\frac{2}{x - 3}+ 1$$ Step 1) Replace f(x) with y. $$y=\frac{2}{x - 3}+ 1$$ Step 2) Interchange x and y in the equation. $$x=\frac{2}{y - 3}+ 1$$ Step 3)
Solve for y. $$x=\frac{2}{y - 3}+ 1$$ Subtract 1 away from each side: $$x - 1=\frac{2}{y - 3}$$ Multiply both sides by (y - 3)/(x - 1):
$$\require{cancel}\frac{(y - 3)}{\cancel{(x - 1)}}\cdot \cancel{(x - 1)}=\frac{2}{\cancel{(y - 3)}}\cdot \frac{\cancel{(y - 3)}}{(x - 1)}$$
$$y - 3=\frac{2}{x - 1}$$ Add 3 to each side: $$y=\frac{2}{x - 1}+ 3$$ Get a common denominator (optional): $$y=\frac{2}{x - 1}+ \frac{3(x - 1)}{x - 1}$$ $$y=\frac{2}{x - 1}+ \frac{3x - 3}{x - 1}$$
$$y=\frac{2 + 3x - 3}{x - 1}$$ $$y=\frac{3x - 1}{x - 1}$$ Step 4) Replace y with f
(x) $$f^{-1}(x)=\frac{3x - 1}{x - 1}$$
Skills Check:
Example #1
Find the inverse of each. $$g(x)=x - 6$$
Please choose the best answer.
$$g^{-1}(x)=\frac{4x + 3}{3}$$
$$g^{-1}(x)=\frac{1}{2}x - \frac{5}{2}$$
Example #2
Find the inverse of each. $$g(x)=-x^5$$
Please choose the best answer.
$$g^{-1}(x)=\sqrt[5]{x}- 2$$
Example #3
Find the inverse of each. $$f(x)=-\frac{1}{x - 1}+ 3$$
Please choose the best answer.
$$f^{-1}(x)=\frac{3}{x}- 2$$
$$f^{-1}(x)=-\frac{1}{x - 3}+ 1$$
$$f^{-1}(x)=-\frac{3}{x + 2}- 2$$
Congrats, Your Score is 100%
Better Luck Next Time, Your Score is %
Try again?
Ready for more?
Watch the Step by Step Video Lesson | Take the Practice Test | {"url":"https://www.greenemath.com/College_Algebra/102/Inverse-of-a-FunctionLesson.html","timestamp":"2024-11-08T01:27:26Z","content_type":"application/xhtml+xml","content_length":"15070","record_id":"<urn:uuid:c436e883-6c69-413b-9db0-3e3eb586b969>","cc-path":"CC-MAIN-2024-46/segments/1730477028019.71/warc/CC-MAIN-20241108003811-20241108033811-00226.warc.gz"} |
Calculation of the two-dimensional supersonic flow of a two-phase fluid in the presence of condensation
The application of the Lax-Wendroff finite-difference scheme to the numerical solution of a system of hyperbolic differential equations for the evolution of the two phases in a steady-state gas flow
is made possible by replacing the equation for the kinetics of condensation of a vapor in the two-phase steady-state gas flow in a two-dimensional configuration by four equations describing the
particle-size distribution in the condensed phase. The theoretical results reveal how the two-dimensional effect due to nozzle geometry can affect the physical flow parameters along the two-phase
fluid streamlines, the characteristics of the nucleation growth zones of the condensed nuclei, and the shape of the line of onset of condensation.
International Journal of Heat and Mass Transfer
Pub Date:
October 1977
□ Condensing;
□ Supersonic Flow;
□ Two Dimensional Flow;
□ Two Phase Flow;
□ Finite Difference Theory;
□ Gas Flow;
□ Hyperbolic Differential Equations;
□ Mathematical Models;
□ Nozzle Geometry;
□ Nucleation;
□ Particle Size Distribution;
□ Fluid Mechanics and Heat Transfer | {"url":"https://ui.adsabs.harvard.edu/abs/1977IJHMT..20.1003M/abstract","timestamp":"2024-11-09T21:24:36Z","content_type":"text/html","content_length":"37568","record_id":"<urn:uuid:049a39ea-ff03-4be8-ae1d-41b33a8286cd>","cc-path":"CC-MAIN-2024-46/segments/1730477028142.18/warc/CC-MAIN-20241109182954-20241109212954-00320.warc.gz"} |
[S:Deleted text in red:S] / Inserted text in green
An Equivalence Relation is a binary relation [S:*:S] EQN:\equiv on a set A which has the following properties:
For all a, b and c EQN:\epsilon A
* Transitivity: if [S:a * b:S] EQN:a\equiv{b} and [S:b * c:S] EQN:b\equiv{c} then [S:a * c:S] EQN:a\equiv{c}
Reflexivity: a:S] * [S:a
:S] Symmetry: if [S:a * b:S] EQN:a\equiv{b} then [S:b:S] EQN:b\equiv{a}
* Reflexivity: EQN:a\equiv{a}
Once you have an equivalance relation on a set, you can take one element (say, x) and look at all
the elements that are equivalent to it. This is called the !/ equivalence class !/ of x.
* EQN:E(x)=\{y\in{A}:~y{\equiv}x~\}
It's clear that a finite set can be divided up into a finite number of non-empty, disjoint
sets, each of which is an equivalence class (of some element). Most people would agree that
a countably infinite set can also be divided up into equivalence classes.
It's less clear that dividing up an uncountably infinite set can always be accomplished.
This has a connection with the Axiom of Choice. | {"url":"https://www.livmathssoc.org.uk/cgi-bin/sews_diff.py?EquivalenceRelation","timestamp":"2024-11-08T02:57:54Z","content_type":"text/html","content_length":"2687","record_id":"<urn:uuid:a96a3ff9-5704-4889-aca5-1827bbb52c8b>","cc-path":"CC-MAIN-2024-46/segments/1730477028019.71/warc/CC-MAIN-20241108003811-20241108033811-00213.warc.gz"} |
Rolling Resistance - Advanced Steam Traction
Locomotive and Train Resistance
A locomotive’s tractive force is required to overcome the resistance to motion of both locomotive and train. When the tractive force is greater than the resistance, then the train will accelerate in
accordance with Newton’s law of motion: Force = Mass x Acceleration or Acceleration = Force ÷ Mass. If the tractive force is equal to the resistance, then the train will travel at constant speed.
If the tractive force is less than the resistance, then the train will slow down.
There are various forms of resistance that need to be considered.
Locomotive Resistance
• Starting resistance, associated with static friction which is usually higher than dynamic friction – i.e. it needs to be overcome before the locomotive will start moving;
• Internal (mechanical/frictional) resistance from the locomotive’s motion etc;
• Rolling resistance deriving from axle bearings and wheels on rail – it increases in proportion to the speed;
• Wind resistance increases in proportion to the square of the speed;
• Gravitational resistance when on an incline – equals the locomotive weight x the gradient;
• Rail curvature resistance applies only to curved track – being proportional to the curvature of the track (or inversely proportional to the radius of curvature).
Train Resistance
• Starting resistance, associated with static friction which is usually higher than dynamic friction – i.e. it needs to be overcome before the train will start moving. In the case of roller
bearing stock, this value is close to zero, but can be significant where journal bearings are fitted to wagons;
• Rolling resistance deriving from axle bearings and wheels on rail – it increases in proportion to the speed;
• Wind resistance increases in proportion to the square of the speed;
• Gravitational resistance when on an incline – equals the train weight x the gradient;
• Rail curvature resistance – being proportional to the curvature of the track (or inversely proportional to the radius of curvature), but applying only to the length of train on the curved track.
In addition, inertial resistance has also to be considered (e.g. when a train is being accelerated).
The term “specific resistance” means the resisting force per tonne of (train) weight. It is pertinent to note that the specific resistance of empty freight trains and of passenger trains is much
higher than that of loaded freight trains. This is largely because the wind resistance of an empty or lightly loaded train is the same as or higher (see below) than that of a full train. Since the
wind resistance becomes dominant at higher speeds, the total resistance per tonne of train weight becomes higher. In the case of open-topped wagons, the wind resistance of empty wagons is higher
than of full wagons because of the increased in air turbulence inside and around the empty wagon bodies. This is illustrated in the graphs at the bottom of this page.
It might also be mentioned that wind resistance is higher when the wind comes from an angle to the direction of the train than when the wind is directly head-on to the train. This is because the
wind has more impact on the ends of each wagon or carriage than when the wind is directly in front of the train where slipstreaming from one wagon or carriage to the next reduces drag.
Train resistance can be measured by the force in the coupling connecting the locomotive to its train (e.g. using a dynamometer car, or in latter days using an electronic load cell). Locomotive
rolling resistance is harder to measure.
There are no exact methods for estimating locomotive or train resistance and reliance has to be placed on empirical formulae based on measured values. Almost every country’s railway has its own
formulae for estimating rolling resistance, all (presumably) being based on recorded measurements.
Most resistance formulae are divided into three sections:
1. a fixed constant, representing a fixed part of the rolling resistance,
2. a term proportional to the train speed, representing a variable part of the rolling resistance, and
3. a term proportional to the square of the train speed representing wind resistance.
One of the more recent national train resistance formula to be developed was the Serbian one that was formulated in 2005 based on tests undertaken by M. Radosavljevic from the Department of
Mechanical Engineering, the Institute of Transportation in Belgrade. He wrote a paper on his findings entitled “Measurement of Train Traction Characteristics” published in the Proceedings of the
Institution of Mechanical Engineers Vol 220 Part F: J. Rail and Rapid Transit. A copy of the formulae and their graphical representation is copied below. (See below for further comparisons)
The above formulae are compared with additional train resistance formulae in the Excel graph below [click on the image for a full-sized PDF image.] The additional formulae covered are as follows
• China National Railways (full wagons)
• China National Railways (empty wagons)
• Canadian National Railway (full wagons)
• An (unnamed) Australian mineral railway (full wagons)
• An (unnamed) Australian mineral railway (empty wagons)
• Koffman’s formula for BR carriages as used by Wardale in
FDC 1.1
It will be readily seen that (as explained above) the specific resistance of empty wagons is much higher than that of full wagons and that for BR Carriages is also high by comparison with loaded
wagons (due to their relatively light loaded weight). On the other hand the majority of formulae give very similar estimates for the specific rolling resistance of full wagons, with the exception of
the (unnamed) Australian mineral railway figures which show much lower figures. This is probably because the wagons are much larger and more heavily loaded than those in the other countries listed.
Wardale’s Resistance Calculations
In FDC 1.1 (line 24) and FDC 1.2 (line 2) Wardale uses the following formulae for calculating locomotive and carriage rolling resistence (respectively):
• Locomotive rolling resistance: R ≈ (45 + 0.24v + 0.0036v2) N/Tonne
• Carriage rolling resistance: R = (1.1 + 0.021v + 0.000175v2) kg/tonne – from Koffman applying to BR coaches.
where R is the specific rolling resistance in N/Tonne of weight and v = speed in km/h.
• In
FDC 1.3
line 164, Wardale quotes Koffman to assume a
specific starting resistance
on level tangent track for roller bearing stock of 7.0 kg/tonne (= 6.99 N/kN).
• In
FDC 1.3
line 166, Wardale uses a figure of 100 N/tonne (=10.2 N/kN) for the
specific starting resistance
for a locomotive.
Chinese National Railways Resistance Calculations
For the record, various resistance formulae used by Chinese National Railways are summarized as follows, using the notation:
• R = resistance in Newtons
• W = weight in kN (not tonnes)
• V = speed in km/h
• Grade = slope in ^o/[oo] [e.g. 1 in 100 = 10^o/[oo]]
• Rad = curved track radius in metres.
• L[t] = length of train in metres.
• L[c] = length of curve in metres; L[c ]= L[t] where L[t] ≤ L[c]
Rolling Resistance of Locomotives – in Newtons:
• QJ with 6 axle tender; R= W x [(1.09 + 0.0038 V + 0.000586 V^2) + Grade + 600/Rad]
• QJ with 4 axle tender: R= W x [(0.70 + 0.0243 V + 0.000673 V2) + Grade + 600/Rad]
• JS: R= W x [(0.74 + 0.0168 V + 0.000700 V2) + Grade + 600/Rad]
• SY: R= W x [(0.74 + 0.0168 V + 0.000700 V2) + Grade + 600/Rad]
Rolling Resistance of Wagons – in Newtons:
• Roller Bearing Wagons: R= W x [(0.92 + 0.0048 V + 0.000125 V2) + Grade + 600/Rad x L[c]/L[t]]
• Journal Bearing Wagons: R= W x [(1.07 + 0.0011 V + 0.000236 V2) + Grade + 600/Rad x L[c]/L[t]]
• Empty Wagons: R= W x [(2.23 + 0.0053 V + 0.000675 V2) + Grade + 600/Rad x L[c]/L[t]]
Starting Resistance
• Locomotives: 8 N/kN (weight)
• Roller bearing wagons: 3.5 N/kN
• Journal bearing wagons: 5 N/kN
Canadian National Railway Resistance Formulae
Chapter 2.1 of AREMA (American Railway Engineering and Maintenence-of-Way Association) Manaul for Railway Engineering, dated 1999 and titled “Resistance to Movement” provides data and formulae used
by Canadian National Railways. The document can be downloaded from this website by clicking here. | {"url":"https://advanced-steam.org/ufaqs/rolling-resistance/","timestamp":"2024-11-11T10:47:05Z","content_type":"text/html","content_length":"119265","record_id":"<urn:uuid:80baebc4-f798-4c86-ab17-0fc39d16273c>","cc-path":"CC-MAIN-2024-46/segments/1730477028228.41/warc/CC-MAIN-20241111091854-20241111121854-00397.warc.gz"} |
If Bayes was sitting on Copacabana beach... - Significance magazine
This is the first post of a fairly regular series dedicated to the impending FIFA World Cup. Marta and I discussed this at the end of a barbecue at our place a few weeks back and since then we have
done some work to develop this model.
Our main idea is to extend the
model we developed
to predict football results, for international games. Basically, we have considered a dataset of nearly 4,000 games, including the last six world cups (from Italia 90 onwards) and the last four years
(including friendlies, qualifiers, continental finals and Confederation Cup). The rationale for including these games is that:
1. We wanted to have some direct evidence on World Cup games; we restricted it to the last six WCs which all have a very similar format (with a first round of games and then a knockout stage,
starting with a round of 16).
2. We also want to have evidence on most recent performances of the teams affiliated with FIFA.
I think it's worth noting that many people (eg Goldman Sachs or FiveThirtyEight) who have had a go at a similar exercise have decided to discard friendlies. But it seems to me that these may be
indicative of some general trend and so we decided to keep them in our dataset.
The main outcome of our model is the number of goals scored by each team in each of the games. In particular, we want to account for the fact that the two counts are correlated. We model
${y}_{i}\sim \text{Poisson}\left({\theta }_{i}\right)$
where ${y}_{i}$ is the number of goals scored in game $i$. Note that we replicate the same game twice, looking at it from each of the two teams' perspective, respectively. So, for example, the first
game in the dataset is Argentina vs Cameroon, the opening game of Italia 90 and the first two rows in our dataset describe the game from the perspective of Argentina and Cameroon, respectively, like
│Game│Team │Opponent │Goal│…│
│1 │Argentina │Cameroon │0 │…│
│1 │Cameroon │Argentina │1 │…│
The 'propensity' of the team in row $i$ to score when they play against the team in row $i+1$, which we indicate as ${\theta }_{i}$, is modelled as
$\text{log}\left({\theta }_{i}\right)=\mu +{\beta }_{\text{home}}{\text{Home}}_{i}+{\beta }_{\text{away}}{\text{Away}}_{i}+{\beta }_{\text{type}}{\text{Type}}_{i}+{\beta }_{\text{form}}{\text{Form}}_
{i}+{\gamma }_{{\text{team}}_{i}}+{\delta }_{{\text{oppt}}_{i}}.$
The linear predictor is made by:
1. The overall intercept $\mu$;
2. A set of unstructured effects β, accounting for the effect of i) playing at home, away or on neutral ground (Home and Away are dummies, so that when they are both 0, then the game is played on
neutral ground); ii) the type of the game, which could be 'finals' (World Cup or Continental tournament, or the Confederation Cup), or 'other' (including friendlies and qualifiers); iii) the
difference in recent forms between the two opponents − this is computed by accounting the mean number of points obtained in the last two games played by each team. These are rescaled in the interval
[0;1] so that the difference is a continuous variable defined in [-1;1] (a value of 1 indicates that a team is much more 'in form' − and thus potentially stronger − than their opponent for that
3. A set of structured effects ${\gamma }_{t}$ and ${\delta }_{t}$ these are team-specific random effects, modelled as exchangeable. Effectively, they can be interpreted as 'attack' (for the team)
and 'defence' (for the opponent) strength.
We fit a Bayesian model (using INLA to speed the computation up − it runs quite smoothly and quickly; about 30 seconds on a medium range computer).
Then, for each of the future games (ie those to be played starting this week) we can simulate from the posterior distributions of the linear predictors ${\theta }_{i}$. When opportunely rescaled,
these can be used to simulate the number of goals scored in the next games by the two teams playing.
In particular, given evidence that at the World Cups usually fewer goals are scored, we have inflated the chance of seeing a 0, so that the prediction is made as
${y}_{i}^{\text{new}}\sim \left(1-\pi \right)\text{Poisson}\left({\theta }_{i}^{\text{new}}\right)$
Where $\pi$ is given an informative distribution based on the assumption that the chance of excess 0s in the observed number of goals at the World Cup is centered around 0.035 with a standard
deviation of 0.02 − in actual facts, we've tried a few alternatives, but this assumption does not affect the estimation/prediction massively.
In addition, for the yet-to-be-played games, the value of the 'recent form' variable (which sort of determines the difference in strength between the two teams playing in a game − we indicate this as
${\omega }_{t}$ and ${\omega }_{s}$ for teams $t$ and $s$, respectively) is based on an evidence synthesis of the available odds for each of the team, rather than on the actual past 2 games. It is
easy to find data on lots of bookies offering odds for each of the 32 teams involved in the WC − we've based our evidence synthesis on the 20 values.
I think there is a good reason for doing this: the last two games observed in the dataset are friendly games played in preparation for the finals. In those games, teams tend to train really, but do
not give their 100%. On the other hand, the valuations of the bookmakers should be a more reliable indication of the actual relative strength of the teams involved at the moment.
Rather than predicting all the way to the final based on the model and data available right now, we decided to take it step by step. I think there is a very good argument to do so. In fact, it is
quite likely that recent form will be modified by the games that will be played in the course of the first round.
For example, Group D (including Uruguay, Costa Rica and my personal derby of England and Italy) is arguably the closest with 3 relatively strong teams (FiveThirtyEight seem to think so too). So, if
Italy beat England on Saturday this surely will swing the odds in their favour, thus probably modifying quite massively the behaviour of the other teams in the next games (eg if England lost on
Saturday, then they'll have to win their next game against Uruguay, while Italy may be happy to get a draw against Uruguay in their final game of the round, etc…).
So, in order to make more sense of the model, we'll only predict batches of games; before any game is played and based on the current model and data, we'll predict the first 16 games to be played −
that's when all the finalists will have played their first game. Then we will update the recent form variable based on the observed results and re-run the model to predict the next batch of 16 games.
And then we'll repeat this step again and predict the final batch of 16 games for the group stage.
This article first appeared on Gianluca Baio’s personal blog. | {"url":"https://significancemagazine.org/if-bayes-was-sitting-on-copacabana-beach/","timestamp":"2024-11-13T02:17:56Z","content_type":"text/html","content_length":"101749","record_id":"<urn:uuid:f4ad88b2-a17b-4a70-b484-811012eca900>","cc-path":"CC-MAIN-2024-46/segments/1730477028303.91/warc/CC-MAIN-20241113004258-20241113034258-00890.warc.gz"} |
Sterling Moore and Split-Play WPA
Sterling Moore posted a stellar +0.47 +WPA in Sunday's AFC championship game. That's very good -- only Patrick Willis (+0.52) and teammate Dane Fletcher (+0.49) beat that mark for defenders on
championship weekend. After all, Moore made arguably the defensive play of the weekend when he knocked what would have been the go-ahead touchdown pass out of Lee Evans's hands with mere seconds to
But most of Moore's +WPA actually comes from his contributions on the following play, the failed third down pass targeted for Dennis Pitta which set up the fateful fourth down on which Billy Cundiff
kicked the Ravens out of the playoffs. The Ravens were still in excellent shape on that third down, and the failure to convert or score a touchdown took their win probability down from 83% to 43%,
giving Moore a +0.40 WPA on the play. That leaves just +0.07 for his other successful play, the strip of Evans in the end zone.
That seems intuitively way too low, and that intuition is correct. Although technically the entire play from snap to throw to almost-catch to strip just cost the Ravens 7% of a win, if Evans holds on
to the ball and Moore doesn't strip it, Baltimore's ticket to the Super Bowl is all but punched. But with the way the data is fed into our system, it's impossible to give out separate credit for
different aspects of plays.
But let's say for a second it was possible. How would each aspect of that play have played out in the eyes of WPA?
Snap: Second and 1 from the NE 14, 27 seconds remain: 90% win probability.
Things looked great for the Ravens even before this play. With just 14 yards needed for a touchdown and the field goal if they couldn't punch it in just a mere chip shot, the Ravens were sitting
pretty. Basically, the only two things which could sink the Ravens were a turnover or the missed field goal.
Throw and catch: Ravens lead 26-23 pending extra point, 22 seconds left: 99% win probability.
It's not over until 0:00, but the Patriots would have needed a Music City Miracle-esque finish to take this one back had Evans held on to the pass for the touchdown. Moore was beat by Evans on the
play, but obviously not by much, because...
Strip: Third and 1 from the NE 14, 22 seconds remain: 83% win probability.
Although we can debate how Moore should be credited for this play -- was the throw good enough we don't blame him for less-than-perfect coverage and we merely credit him for the strip, or does the
strip just make up for allowing the ball to get to Evans in the first place? Regardless, the actual act of the strip brought the Patriots win probability up from 1% to 17%
So how would I give credit for this play?
Flacco, Evans: +0.09 WPA for the pass and "catch."
Evans: -0.16 WPA for the drop, for a total of -0.07.
Moore: +0.16 +WPA for the strip.
The question of credit is one of the biggest questions those who use and develop statistics for team sports need to answer. Unfortunately, trying to answer these questions in real time makes it
almost impossible to give fair answers, and given the subjectivity of certain things, it's almost impossible in retrospect as well.
Keep in mind with the version of WPA presented here, we are only able to give credit based on the entirety of the play. If you see a number that doesn't match up with intuition or common sense,
remember the inner workings of an entire play may hold the answer.
18 Responses to “Sterling Moore and Split-Play WPA”
Jared Doom says:
"Third and 1 from the NE 14, 22 seconds remain: 83% win probability."
That seems high. I'm assuming eventual TD leads to GWP ~ 1.0, eventual FG leads to GWP ~ 0.5, and failure to score leads to GWP ~ 0.
Assuming the probability of FG OR TD is 0.95, that implies the probability of an eventual TD is 0.71 [(0.71 * 1.0 + (0.95 - 0.71) * 0.5 + (1.0 - 0.95) * 0) = 0.83].
Given only 22 seconds left a 71% chance of scoring an eventual TD on 3rd & 1 from the opponent's 14 seems high. Am I wrong (assuming yes, but still surprised)?
Anonymous says:
Flacco screwed up that play. He clearly had enough room to run it and dive for the first down. Lots of room! Ugh.
Anonymous says:
I was also surprised with that, Jarod. I won't use your math (because I don't know it), but the probability of Baltimore kicking a FG at that point should have over 75%. Then it's
overtime on the road against a superior team (per EPA).
How that translates into the Ravens having a 83% WP, I don't know.
Anonymous says:
In the 2011 regular season, FGs of 1-29 yards were missed 11 times; total is 301 for 312, or 96% if I counted right. (I didn't count XPs, but there were 6 missed). So that's a good SWAG.
Where the 83% comes from is that in addition to scoring the immediate third down touchdown, they could get a first down instead and run a couple more plays before kicking the FG. I don't
believe the WP generator takes TOs into effect, and I can't remember if BAL had one left or not.
Jared Doom says:
Anon #3 - To be fair I did say *eventual* TD, so I was accounting for a TD on any following play, and still thought 83% was high, given the limited number of plays you can run with 22
seconds left.
I think the WP model implicitly (kind of) accounts for timeouts because I think it is based on historical data (albeit probably smoothed for situations with sparse data points).
Kulko says:
Wo doesnt Know how many timeouts a Team has. It just considers how many Teams historically habe scored a Td, or Made a FG in that Situation. Teams typically pass in this Situation and
that means 22 Sec correspond to about 4 plays. Even Ehen you waste a play in getting the 1st thats enough chances for scoring
Independent George says:
I might be misunderstanding the math, but I came up with about a 35% chance of a touchdown.
Assuming a TD is ~100% WP, and a FG is ~100% overtime, the WP is the probability of a TD + probability of a FG + OT win
0.83 = P(TD) + P(FG)*0.5
If P(FG) = 0.95, then
0.83 = P(TD) + 0.95*0.5
0.83 = P(TD) + 0.475
0.355 = P(TD)
Anonymous says:
Should say AFC, not NFC, in the firs sentence.
Dave Archibald says:
I'm not sure even with the further breakdown this intuitively makes sense. Moore's (first) play is significant because without it the Patriots lose - going from 90% probability of losing
to essentially 100% is a more important play than going from 50% to 60% at some other point in the game.
There's almost a compounding effect here: without Moore's 2nd-down play, the 3rd-down pass breakup and the FG miss (both more important in terms of WP) can't happen. Then again, without
those two events, his pass breakup is just a footnote. So maybe WP is "right" and it just feels inaccurate because I have the benefit of hindsight.
Jared Doom says:
Independent George - FG & TD are mutually exclusive outcomes so P(FG) + P(TD) must be less than 1.
In your example P(FG) + P(TD)= 1.305.
In my example I assumed 5% chance of no score, which means 95% chance of score, so I assumed P(FG) + P(TD) = 0.95. If you assume TD gives 100% WP, FG gives 50% WP, and no score gives 0%
WP, then you have
0.83 = 100%*P(TD)+50%*P(FG)+0%*P(no score).
I forget what this is called in linear algebra but it has a unique solution.
Independent George says:
Ah, crap, you're right.
James says:
There's something screwy with the Win Probability Calculator. It says that 3rd and 1 has a WP of 83%, while first and 10 from the same spot has a WP of 63%. I don't see how having a first
down lowers your WP at all, much less so drastically. Even 1st and goal from the 8 only has a WP of 70%.
Parameters: Score differential of -3, time left 0:22, 4th quarter, Field Position is opponent's 14, 3rd down and 1 to get WP of 83%.
Changed field position to 13, down to 1 and "To Go" to 10, get WP of 63%.
Dave Archibald says:
This comment has been removed by the author.
tunesmith says:
I have seen some oddities with WPA in other situations. For instance, in New England's game against Denver in the Divisional round, New England had the ball on first down. They threw an
incomplete pass, and their WPA went up, +0.08 . Brian, I have an open question about it on its "live" page if you want to check it out. Also, I thought I'd point out that the game logs
that drive the graphs often have missing plays, almost always when the time-remaining is the same as a previous play. (I only notice this because I've absolutely loved poring through the
data this season - thanks again for providing such a cool way of looking at everything!)
By the way, I've seen a few other examples of split-play that could more clearly be identified. One clear example would be when a play gets called back due to penalty. Denver@Buffalo,
week 16 - Eddie Royal returns a kickoff for a touchdown, nullified by penalty. The penalty was worth negative WPA, but not a lot. However, figuring in the positive WPA of the lost
touchdown, it was a huge play. Although I'm not sure if you allocate WPA to players for penalties.
Dave Archibald says:
The EP aren't adjusted for time. With :27 seconds left on the 14, the Ravens are given a +4.74 EPA, with a 83% chance of a FD and a 45% chance of a TD. If I change that to 3 seconds left,
the EP doesn't change, even though no coach in the league would (or should) go for a TD at that point.
For WP to be accurate in end-of-game situations, it needs to take into account the clock as a factor. The Ravens didn't have a 45% chance of scoring a TD from the 14 with that little time
left, because the number of plays they could run in 27 seconds with one time out (and needing to kick a FG if they didn't get the TD) was just as much a constraint as the downs were.
EDIT: deleted some comments with typos.
Dan S says:
I think it's been well established in the past that WP values are not at all precise, particularly in the end-game situations that we're most interested in. And I don't mean that in an
intuitive, "no way is that the actual prob" way. The calculator can clearly be shown to be directly contradictory of itself.
Rather than try to smooth out the sparse and incomplete play-by-play data, it's probably better to write an algorithm that can calculate probabilities at the point where it because
reasonable to predict the number of plays left in the game.
In any case, I love this site but cringe any time I see a final drive WPA analysis like this one.
Brian Burke says:
Dan S makes a good point. The WP calculator puts out smoothed empirical averages. In very tight final-minute situations, it is imprecise.
Often, when I'll do a specific analysis, I'll go back to the data and built a customized look at the situation to include timeouts and other factors. But not everyone has that luxury and
it takes a lot of time.
Other types of models may be superior at this point in such a game. It's one reason why I'm a fan of Keith's drive Markov model. For example, in many cases where the 2 models produce
contradictions we can learn where teams are making sub-optimum choices.
Anonymous says:
i think this is stupid because you cant drop a catch like that with couple seconds to go there is no reason to drop that ball. The defender did what he had to do which is break that play | {"url":"http://www.advancedfootballanalytics.com/2012/01/sterling-moore-and-split-play-wpa.html?showComment=1327608115922","timestamp":"2024-11-02T06:16:18Z","content_type":"application/xhtml+xml","content_length":"126020","record_id":"<urn:uuid:784e0ea1-6a74-485e-b3a6-8b4907f48c78>","cc-path":"CC-MAIN-2024-46/segments/1730477027677.11/warc/CC-MAIN-20241102040949-20241102070949-00427.warc.gz"} |
separation studio 4 crack - Full Version Softwares
Email : crackrequestnet@gmail.com
Spot Process Separation Studio 4™
The industry standard for image separations used by over 100K screen printers. Sep Studio 4 delivers even more ability to screen printers. Be a winner.
Video Proof
250 thoughts on “separation studio 4 crack”
1. info please
1. please check i sent an email
2. hola ocupo ese programa
1. information sent
3. can you send me info please. Thanks
1. information sent on your email please check
4. how much for the link and how long is the life time use?
1. info sent on your email
1. I need this please send me a link to download
1. information sent on your given email address
5. i need this software.
1. information sent on your email
6. PUEDES ENVIARME LA INFORMACION
1. information sent on your email
7. Hello, requesting the files if still available please and thank you
1. info sent
8. How much is this crack?
Do you have a crack for Separation Studio NXT?
1. check your email informatin sent
9. Do you have a MacOs version ?
1. info sent
2. hola tambien quiero el programa donde lo obtengo?
1. info sent
10. Hi can I please have it thx for your hard work
1. info sent
11. could i get the link please! ty
1. info sent
12. Can I get this info please? Thank you!
1. info sent
13. por favor enviarme del separation studio 4
1. info sent
1. May I have Sep Studio 4
1. info sent
14. can i have it thank you : anhtuannguyen711@gmail.com
1. info sent
15. May I have it, please?
1. info sent
16. Favor enviarme toda la información
1. info sent
17. Please could you send me the info for the crack
1. info sent
18. send link to this with crack please
1. info sent
19. Hi–can you please send link?
1. info sent
20. Great! please send it to me too.
1. info sent
21. please send me the link for this software and crack
1. info sent
1. Hi, please can you send me the link and crack for this seperation studio
1. info sent
22. Please send to me
1. info sent
23. I need this please sen me too.
1. info sent
24. I Need This
1. information sent
25. Im interested, please send me the info
1. information sent
26. porfavor me podrían colaborar con el crack de sep studio 4
1. information sent
27. info please
1. info sent
28. info please
1. check your email
29. Could you please send me the crack for Seperation Studio 4 or NXT?
1. info sent
30. Please share the crack for spot process separation studio 4.
1. info sent
31. Got this from you a few years ago, still works excellent. Have you done the new version yet, Separation Studio NXT?
32. info pls
1. information sent
33. me interesa el programa
enviame informacion
1. info sent
1. Awesome how can I purchase this thanks
1. info sent
1. Í need crack for Separation Studio 4 or serial number
2. info sent
2. Need separation studio 4 full
Version cracked
1. info sent
34. please sent me
1. info sent
35. Me podrias brindar info, me interesa …
1. info sent
36. Write me more infos, please!
1. please check your email.
37. estoy interesado
1. please check your email.
1. Link please
1. information sent
38. me interesa
1. please check your email.
2. Buen día, información sobre Sep Studio 4 por favor. Necesito el programa, ayúdeme! 🙏🏻
1. info sent
39. hi can you send me the info please?
1. please check your email.
40. May I have it please?
1. please check your email.
41. Hola. Me interesa el programa y su crack!! Por favor!! Gracias!!
1. please check your email.
42. May I really have it?
1. please check your email.
43. Me interesa mucho
1. please check your email.
44. hi pls sent for me
1. Nothing was sent to me
1. check your email.
2. please check your email.
45. Please send me the crack and download link
1. please check your email.
46. me interesa mucho
1. info sent check your email
47. información me pasa el crack por favor
1. check your email.
48. Info plis, i need this program
1. check your email.
49. Can i get this crack, thank you so much
1. check your email.
50. Hello please send me this crack.
1. check your email.
51. How can I get the crack?
1. check your email
52. Hi, I will like to get this software on windows please
1. check your email.
53. Hallo, Please I want this software for Windows.
1. check your email..
54. Hi even I want this software for Windows. Please
1. check your email.
55. i am interested in the software.
1. check your email.
56. Is this for Mac?
1. check your email.
57. info pls
1. check your email.
58. info
1. check your email.
59. send Info please
1. check your email.
60. Info please
1. check your email.
61. Can I get it
62. info pls
1. check your email.
63. hola, this is my info .
1. check your email.
64. info pls
1. check your email.
2. hello brad
please crack
thanks u verymuch
1. info sent please check
65. how much and link to purchase
1. check your email.
66. I would like to get this please
1. check your email.
67. info please
1. check your email.
68. Could you please give me the info about the crack?
1. check your email
69. info tmfexotico@gmail.com
1. check your email.
70. hola enlace y crack . skar.tera@outlook.es
1. check your email.
71. Interested
1. check your email.
72. Me interesa
1. check youremail.
73. I want it
1. check your email.
74. Hola, me podrias enviar info por favor? Gracias.
1. check your email.
75. hola! podrias enviarme mas info? ceovictoriano@gmail.com
1. check your email.
76. Is this crack version free? Can i get it?
1. check your email.
77. Me interesa mi correo viewzaha_@hotmail.com
1. check your email.
78. Is this crack version free? Can i get it?
1. check your email.
79. Me interesa mi correo yin_18@hotmail.com
1. check your email.
80. any info?
1. check your email.
81. estoy interesado
1. check your email.
82. Estoy interesado
1. check yourvemail.
83. informacion porfavor
1. check your email.
84. I’m interested pls
1. check your email.
85. Hola me interesa mucho
1. check your email.
86. Hola! me interesa, mi correo impresionesid2014@yahoo.com.mx
1. check your email.
87. Info please, Stampanogales@gmail.com
1. check your email.
88. me pls
1. check your email.
89. crack your email
1. check your email.
90. info please
1. check your email.
91. İ need this ..
1. check your email.
92. Could you please give me the info about the crack?
1. check your email.
93. Costo por favor.
1. check your email.
94. How much does it cost
1. check your email.
95. Precio por fabor
1. check your email.
96. info por favor $$$
1. check your email
97. emel crack please
1. check your email
98. give me
1. check your email
99. how much?
1. check your email
100. info sent
1. check your email
101. I’m seeing $5.97 as the original price, only a $3 savings?
1. check your email
102. info plse
1. check your email
103. info please
1. info sent
104. Hello,
Does this crack still work? I noticed their trials and purchases are currently unavailable. If so, how much
1. check your email
105. Вход в казино Вавада осуществляется при помощи кнопки
“Войти”, которая располагается в правом верхнем углу любой страницы сайта.
1. cheak your email
106. akunbarucandle2@gmail.com please sent me the email
1. check your email
1. check your email
108. info soy de argentina
1. check your email
109. how much
1. check your email
110. im interested in the software can you send the price
1. check your email
111. im interested in the software
1. check your email
1. info sent
113. how much and link to purchase
1. info sent
114. what the value?
1. check your email
115. 45USD?
1. info sent
This site uses Akismet to reduce spam. Learn how your comment data is processed. | {"url":"https://crackrequest.net/2019/07/11/separation-studio-4-crack/","timestamp":"2024-11-06T04:32:35Z","content_type":"text/html","content_length":"375915","record_id":"<urn:uuid:7d8f9e20-cea8-4ba6-9596-65ef9f1e84e3>","cc-path":"CC-MAIN-2024-46/segments/1730477027909.44/warc/CC-MAIN-20241106034659-20241106064659-00431.warc.gz"} |
Consumer Price Index (CPI) in context of yearly rate
31 Aug 2024
The Consumer Price Index (CPI): A Measure of Inflation
The Consumer Price Index (CPI) is a widely used statistical measure that tracks the average change in prices of a basket of goods and services consumed by households over time. This article provides
an overview of the CPI, its methodology, and its significance in measuring inflation at the yearly rate.
Inflation is a sustained increase in the general price level of goods and services in an economy over a period of time. The Consumer Price Index (CPI) is a key indicator used to measure inflation,
providing insights into the purchasing power of consumers. The CPI is calculated by tracking the prices of a representative basket of goods and services, which are then weighted according to their
importance in household expenditure.
The CPI is calculated using the following formula:
CPI = (Σ(Pi * Wi)) / Σ(Wi)
• Pi represents the price of each item in the basket
• Wi represents the weight assigned to each item based on its importance in household expenditure
• Σ denotes the sum of the products
The weights are typically derived from a survey of household expenditure patterns, ensuring that the CPI accurately reflects the average consumer’s spending habits.
Yearly Rate
To calculate the yearly rate of inflation, the following formula is used:
Yearly Rate = ((CPI(t) - CPI(t-1)) / CPI(t-1)) * 100
• CPI(t) represents the current period’s CPI
• CPI(t-1) represents the previous period’s CPI
This formula calculates the percentage change in the CPI from one year to the next, providing a measure of inflation at the yearly rate.
The Consumer Price Index (CPI) is a crucial indicator for measuring inflation and tracking changes in the general price level. By understanding the methodology behind the CPI and its calculation,
policymakers and researchers can gain valuable insights into the economic health of an economy. The yearly rate formula provides a straightforward way to calculate inflation at the yearly rate,
making it a useful tool for monitoring economic trends.
Related articles for ‘yearly rate’ :
• Reading: Consumer Price Index (CPI) in context of yearly rate
Calculators for ‘yearly rate’ | {"url":"https://blog.truegeometry.com/tutorials/education/bb68a6bca0dfc7b04091880817f273ac/JSON_TO_ARTCL_Consumer_Price_Index_CPI_in_context_of_yearly_rate.html","timestamp":"2024-11-04T07:27:00Z","content_type":"text/html","content_length":"15809","record_id":"<urn:uuid:13ae12f4-2ece-421f-9385-03c1851d0f99>","cc-path":"CC-MAIN-2024-46/segments/1730477027819.53/warc/CC-MAIN-20241104065437-20241104095437-00546.warc.gz"} |
Reading: Lesson 5 - Dividend Yield Plus Growth Rate & Discounted Cash Flow Approach
8.5.A - Dividend Yield Plus Growth Rate & Discounted Cash Flow Approach
1. Dividend-Yield-Plus-Growth-Rate
1. In Unit 7, we saw that if an investor expects dividends to grow at a constant rate and if the company makes all payouts in the form of dividends (the company does not repurchase stock), then the
price of a stock can be found as follows:
2. Here ^P0 is the intrinsic value of the stock for the investor, D1 is the dividend expected to be paid at the end of Year 1, g is the expected growth rate in dividends, and rs is the required rate
of return. For the marginal investor, the required return is equal to the expected return. If this investor is the marginal investor then ^P0 = P0, the market price of the stock, and we can solve
for rs to obtain the required rate of return on common equity:
3. Thus, investors expect to receive a dividend yield, D1/P0, plus a capital gain, g, for a total expected return of ^r. In equilibrium this expected return is also equal to the required s return,
rs. This method of estimating the cost of equity is called the discounted cash flow, or DCF, method. Henceforth, we will assume that markets are at equilibrium (which means that rs = ^rs), and
this permits us to use the terms rs and ^rs interchangeably.
2. Estimating Inputs for the DCF Approach
1. Three inputs are required to use the DCF approach: the current stock price, the current dividend, and the marginal investor’s expected dividend growth rate. The stock price and the dividend are
easy to obtain, but the expected growth rate is difficult to estimate.
2. If earnings and dividend growth rates have been relatively stable in the past, and if investors expect these trends to continue, then the past realized growth rate may be used as an estimate of
the expected future growth rate. Unfortunately, such situations occur only at a handful of very mature, slow-growing companies, which precludes the usefulness of historical growth rates as
predictors of future growth rates for most companies.
3. Most firms pay out some of their net income as dividends and reinvest, or retain, the rest. The more they retain, and the higher the earned rate of return on those retained earnings, the larger
their growth rate. This is the idea behind the retention growth model. The payout ratio is the percent of net income that the firm pays out in dividends, and the retention ratio is the complement
of the payout ratio: Retention ratio = (1 − Payout ratio). To illustrate, consider Aldabra Corporation, a mature company. Aldabra’s payout ratio has averaged 63% over the past 15 years, so its
retention rate has averaged 1.0 − 0.63 = 0.37 = 37%. Also, Aldabra’s return on equity (ROE) has averaged 14.5% over the past 15 years. We know that, other things held constant, the earnings
growth rate depends on the amount of income the firm retains and the rate of return it earns on those retained earnings, and the retention growth equation can be expressed as follows:
4. Using Aldabra’s 14.5% average ROE and its 37% retention rate, we can use the Equation above to find the estimated g:
5. Although easy to implement, this approach requires four major assumptions: (1) the payout rate, and thus the retention rate, remain constant; (2) the ROE on new investments remains constant and
equal to the ROE on existing assets; (3) the firm is not expected to repurchase or issue new common stock, or, if it does, this new stock will be sold at a price equal to its book value; and (4)
future projects are expected to have the same degree of risk as the firm’s existing assets. Unfortunately, these assumptions apply in very few situations, limiting the usefulness of the retention
growth model.
6. A third technique calls for using security analysts’ forecasts. As we discussed earlier, analysts publish earnings’ growth rate estimates for most of the larger publicly owned companies. For
example, Value Line provides such dividend forecasts on about 1,700 companies. Several sources compile analysts’ earnings forecasts on a regular basis, and these earnings growth rates can be used
as proxies for dividend growth rates.
3. An Illustration of the DCF Approach
1. To illustrate the DCF approach, suppose Aldabra’s stock sells for $32, its next expected dividend is $1.82, and its expected constant growth rate is 5.4%. Aldabra is not expected to repurchase
any stock. Aldabra’s stock is thought to be in equilibrium, so its expected and required rates of return are equal. Based on these assumptions, its estimated DCF cost of common equity is 11.1%:
2. As previously noted, it is difficult to apply the DCF approach because dividends do not grow at a constant rate for most companies. Surveys show that 16% of responding firms use the DCF approach,
down from 31% in 1982.
Last modified: Tuesday, August 14, 2018, 8:50 AM | {"url":"https://christianleaders.org/mod/page/view.php?id=48349","timestamp":"2024-11-07T04:08:12Z","content_type":"text/html","content_length":"54915","record_id":"<urn:uuid:3fb0d363-04f8-4c76-ab2f-7dc831c1d4c8>","cc-path":"CC-MAIN-2024-46/segments/1730477027951.86/warc/CC-MAIN-20241107021136-20241107051136-00771.warc.gz"} |
reckless (2013 123movies)
This shopping feature will continue to load items when the Enter key is pressed. Use the Amazon App to scan ISBNs and compare prices. There are 0 customer reviews and 9 customer ratings. Enter your
mobile number or email address below and we'll send you a link to download the free Kindle App. There's a problem loading this menu right now. Please try again. Thank you very much:), Reviewed in the
United States on August 4, 2019, Reviewed in the United States on August 14, 2018, Reviewed in the United States on November 20, 2019. There was a problem loading your book clubs. Please try again.
Don't purchase this and waste your money. The 13-digit and 10-digit formats both work. Lesson 2: Using Mental Math to This bar-code number lets you verify that you're getting exactly the right
version or edition of a book. Bring your club to Amazon Book Clubs, start a new book club and invite your friends to join, or find a club thats right for you for free. Access codes and supplements
are not guaranteed with used items. This item: Envision Math 2017 Student Edition Grade 5 Volume 1 by Scott Foresman Paperback $33.88. This item cannot be shipped to your selected delivery location.
This shopping feature will continue to load items when the Enter key is pressed. Master Study Skills: Interactive Workshop for Young Patrons, Apps for Students, Parents and Teachers Lumos Apps, Lumos
SchoolUp A Community App for Parents, Testimonials Online practice tests and summer learning cources, Contact Lumos Learning Proven Study Programs by Expert Teachers, Lesson 5: Comparing and Ordering
Decimals, Lesson 2: Rounding Whole Numbers and Decimals, Lesson 3: Estimating Sums and Differences, Lesson 4: Modeling Addition and Subtraction of Decimals, Lesson 5: Draw a Picture and Write an
Equation, Lesson 7: Multiplying 2-Digit by 2-Digit Numbers, Lesson 9: Draw a Picture and Write an Equation, Lesson 1: Dividing Multiples of 10 and 100, Lesson 7: Draw a Picture and Write an Equation,
Lesson 2: Estimating Quotients with 2-Digit Divisors, Lesson 7: Estimating and Dividing with Greater Numbers, Lesson 1: Multiplying Decimals by 10, 100, or 1,000, Lesson 2: Estimating the Product of
a Decimal and a Whole Number, Lesson 3: Number Sense: Decimal Multiplication, Lesson 4: Models for Multiplying Decimals, Lesson 5: Multiplying a Decimal by a Whole Number, Lesson 1: Dividing Decimals
by 10, 100, or 1,000, Lesson 5: Dividing a Whole Number by a Decimal, Lesson 6: Dividing a Decimal by a Decimal, Lesson 1: Using Variables to Write Expressions, Lesson 5: Addition and Subtraction
Expressions, Lesson 6: Multiplication and Division Expressions, Lesson 4: Estimating Sums and Differences of Fractions, Lesson 5: Common Multiples and Least Common Multiple, Lesson 7: Adding
Fractions with Unlike Denominators, Lesson 8: Subtracting Fractions with Unlike Denominators, Lesson 9: More Adding and Subtracting Fractions, Lesson 10: Draw a Picture and Write an Equation, Lesson
1: Improper Fractions and Mixed Numbers, Lesson 2: Estimating Sums and Differences of Mixed Numbers, Lesson 3: Modeling Addition and Subtraction of Mixed Numbers, Lesson 6: More Adding and
Subtracting Mixed Numbers, Lesson 2: Multiplying Fractions and Whole Numbers, Lesson 9: Dividing Whole Numbers by Unit Fractions, Lesson 10: Dividing Unit Fractions by Non-Zero Whole Numbers, Lesson
11: Draw a Picture and Write an Equation, Lesson 3: Use Objects and Solve a Simpler Problem, Lesson 1: Converting Customary Units of Length, Lesson 2: Converting Customary Units of Capacity, Lesson
3: Converting Customary Units of Weight, Lesson 4: Converting Metric Units of Length, Lesson 5: Converting Metric Units of Capacity, Lesson 6: Converting Metric Units of Mass, Lesson 2: Distances on
a Coordinate Plane. ENVISION MATHEMATICS 2020 COMMON CORE STUDENT EDITION GRADE 5 VOLUME 2, ENVISION MATHEMATICS 2020 ADDITIONAL PRACTICE WORKBOOK GRADE 5, MATH 2016 COMMON CORE STUDENT EDITION GRADE
2 VOLUME 1, Envision Math 2017 Student Edition Grade 5 Volume 1, Math 2016 Common Core Student Edition Grade 5 Volume 2, MATH 2012 COMMON CORE STUDENT EDITION (HARDCOVER) GRADE 5. There was an error
retrieving your Wish Lists. Created by Teachers (180 Days of Practice). This bundle include presentations for Pearson EnVision 5th Grade Volume 1 (Topics 1-8). Series, and Kindle books on your
smartphone, tablet, or computer no! Very useful not useful at all, 1996-2020, Amazon.com, Inc. or its affiliates shopping will. 'S a problem loading this menu right now App, enter your number! By
Scott Foresman Paperback $ 21.08 original audio series, and Kindle books recent Than the other of a book device required selected Delivery location no Kindle device required tablet! System considers
things like how recent a review is and if the reviewer bought the item on Amazon product been. Shipped to your door, 1996-2020, Amazon.com, Inc. or its affiliates Delivery location star. Edition
Grade 4 Volume 2 by Scott Foresman Paperback $ 34.00 in Stock Practice ) next or heading. To load items when the enter key is pressed interested in $ $. $ }. 'S a problem loading this menu right now
2020 COMMON CORE Student Edition Grade 5 Volume 1 Scott! Like how recent a review is and if the reviewer bought the on! To load items when the enter key is pressed right now your mobile number or
email below! Dvd-Rom Grade 5 Volume 1 by Scott Foresman Paperback $ 34.00 in Stock FBA items qualify for free Shipping Amazon! Of using of using exclusive access to Envision Math 2017 Student Edition
Grade Volume! Useful at all i bought this book because this is the same they! Your selected Delivery location useful at all you are interested in the overall star and! $ } mobile phone number
Foresman Paperback $ 34.00 in Stock you grow your business FBA items qualify for Shipping! Download the free App, enter your mobile number or email address below we I could it teaches skills that are
not guaranteed with used items interested in getting! Version or Edition of a book we don t use a simple. Send you a link to download the free App, enter your mobile phone number interested in to
Lets you verify that you 're getting exactly the right version or Edition of book. Each presentation acts as a supplement when teaching the Pearson Envision 5th Topics That you 're getting exactly
the right version or Edition of a book be shipped to your door, 1996-2020. You are interested in Grade 5 9780328849550 your heading shortcut key to navigate out of this carousel use!
Anthony Duclair Family, How To Preserve Acorns For Deer, What The World Needs Now Boss Baby, Dear Mama Wanda Coleman, Serial Mom Scotty, Lg Gsl961pzbv Not Making Ice, Antique Gold Scales For Sale,
Allegra Versace Instagram, Noel Harrison Net Worth, | {"url":"http://www.dismexfood.com/site/8e8b00-reckless-%282013-123movies%29","timestamp":"2024-11-11T13:52:11Z","content_type":"text/html","content_length":"63009","record_id":"<urn:uuid:88f2b1f5-b824-44de-bc02-70fd13476162>","cc-path":"CC-MAIN-2024-46/segments/1730477028230.68/warc/CC-MAIN-20241111123424-20241111153424-00060.warc.gz"} |
Prologue to this blog..
Self reference invariably leads to contradiction, and Bertrand Russell's eponymous paradox, which he communicated to Gotlieb Frege around the turn of the (20th) century, was no exception, rather, it
would become the canonical example that shook the axiomatic foundation of naive set theory and mathematics itself.
It really shouldn't have had such a profound impact, to be honest; It was no more surprising (nor resolvable) than children's diversions such as "This statement is false. Is my statement true or
false?". It caused a great deal of consternation amongst logicians because they're a breed that has little tolerance for the indefinitive, unlike Euler for instance, who famously solved the Basel
Problem on intuition, but didn't rigorously prove the result, at least by present day standards. The gulf between the two is vast. Russell's Paradox is easily conceived by anyone, whereas Euler's
solution was devilishly clever and had evaded the best mathematical minds of Europe for about a century.
To frame the problem for the gentle reader without any knowledge of set theory, imagine the infinite lists of things that could be constructed. Some of those lists themselves contain other lists, eg:
List A
-the list of long haired dogs
-one particular Etruscan knife
-list A
Notice that the last item is 'List A' itself. So, lists can contain any object, includng both other lists, themselves, or other lists that contain themselves. What Russell suggested was The List Of
All Lists That Do Not Contain Themselves, and asked, does this list contain itself?
Now, I got to contemplating preludes and fugues last night, and their inherently self referential nature, particularly when, as I often have, the composer of such odious objects constructs the
prelude out of motivic material borrowed from the fugue's episodic passages or countersubjects. In fact, early on, I endeavored to construct the prelude exclusively from the elements of the
corresponding fugue that were not the fugue's subject(s) proper, in order to lend some thematic continuity and significance to the pairing, instead of merely sticking two pieces together that sounded
nice, or complementary, side by side.
Yet this still falls short of an absolute motivic coupling of the prelude and fugue, without the introduction of the subject itself to the prelude. And while we're there, why not just present the
exposition, too? Well, you can imagine, this epiphany tore me from my chair, slammed my against the wall, slapped my face and embraced me in a passionate kiss, just as in one of those old, corny
war-era movies.
I saw at once the artistic economy and an opprtunity for respite from the arduous and miserable task of composing these verbose, bloated objects of immitative tedium we smugly refer to as 'fugues'.
My contempt for fugue welled up inside as I envisioned a musical lanscape liberated from the abject objects of contrapuntal trickery, a brave new world in which preludes are written to themselves.
And these benefits are not constrained to just the prelude and fugue. One can easily imagine the analogous dismissal of books, stories, and essays, as well, where prologues to themselves serve the
purpose succintly. The world is cluttered with books and fugues, and I've been guilty of contributing to that littering on my own part, but I'm trying to change my ways.
a draft of Prelude to Itself and Itself in G:
Self-reference is not necessarily a bad thing. Computer programming, for example, often deals with recursion and reification, both of which involve self-reference. Recursion is as old as math
itself, and leads to things like the Fibonacci sequence and functional fixed points (cf. orbits and chaotic bifurcation). Reification is the act of representing (some or all aspects of) a program
within itself, so that it can inspect itself and direct its computations accordingly. Java's class introspection is an example of an application of this concept.
Also, there are alternative set theories that actually allow self-referential sets. For example, the so-called New Foundations is a set theory that allows the Quine Atom: a set that contains
itself. Interestingly enough, NF is constructed in such a way that Russell's paradox is not constructible within the theory. So the theory does not suffer from such contradictions or paradoxes.
But enough about math. When it comes to art, there is no obligation to avoid contradiction. In fact, I daresay art thrives on contradiction, on the juxtaposition of unlike or contradictory
elements in order to produce a lasting impression on the audience. Like Escher's mind bending geometries, the impossible cube, the tumbling cube illusion, the staircase looped back upon itself
upon which you could ascend or descend indefinitely, a river flowing downstream that becomes its own source - such things are impossible in the real world, but art is not confined by such
practical considerations. Indeed it thrives on the impossible.
And so even though I have written 9 odd fugues (and have many more WIPs), I have never written a prelude that goes along with them. Never intended to emulate Bach in that sort of way, and never
felt the need to preface my fugues with preludes. Maybe one of these days I could try it out just to get a taste of what it's like, but I feel no obligation binding me to commit to such a form.
So just as you have a prelude to itself, I have fugues unto themselves. 😄 Maybe I should write a fugue whose subject is the fugue itself... now *that* would be something interestingly
self-referentia. 😋
No matter how you attempt to rally to the defense of necromancers, witches, and warlocks who might practice their dark arts of self referential immitative contrapuntal moral deceipt, and heap its
iniquities and corruption upon unsuspecting mankind, I have exposed the dark [motiffs]
But you gotta admit, a fugue on itself as the subject is an awesome self-referential idea that must be explored at some point. 😉🤪
It would be the musical equivalent of a Grothendieck universe, built up by basic operations (fugal devices) iterated transfinitely to a strongly inaccessible cardinal.
"Fugue on itself"
Yes, this was the objective of my Fractal Transform Algorithm, if you recall. Those were fun, and challenging, too.
This reply was deleted.
You need to be a member of composersforum to add comments! | {"url":"https://composersforum.ning.com/blog/prologue-to-this-blog","timestamp":"2024-11-07T06:02:07Z","content_type":"text/html","content_length":"73645","record_id":"<urn:uuid:38a2cc9a-9123-4d32-a86a-36c6e8c620de>","cc-path":"CC-MAIN-2024-46/segments/1730477027957.23/warc/CC-MAIN-20241107052447-20241107082447-00280.warc.gz"} |
odular form
Let \(f\) be a modular form on a finite index subgroup \(\Gamma\) of $\SL_2(\Z)$, and suppose $\Gamma$ contains the matrix $T:=\left(\begin{matrix}1&1\\0&1\end{matrix}\right)$. Then $f$ is periodic
with period 1, so it has a Fourier expansion of the form \[ f(z)=\sum_{n\ge 0}a_n q^n , \] where $q=e^{2 \pi i z}$. That is the Fourier expansion of $f$ around the cusp $\infty$, with Fourier
coefficients $a_n$. If one says "the Fourier expansion of $f$", is it understood to refer to the expansion at $\infty$.
For other cusps of $\Gamma$, suppose $w$ is the width of the cusp $\gamma\infty$, for some cusp representative $\gamma$. Then we can write $f$ as $f(z)=g_\gamma(e^{2\pi iz/w})$ for some holomorphic
function $g_\gamma$ on the punctured unit disk. We can expand $g$ as a Laurent series: \[ g_\gamma(q^{1/w})=\sum_{n\geq0}a_\gamma(n)q^{n/w}\quad\text{for}\quad0<|q|<1. \]
We then define the Fourier expansion of $f$ around the cusp $\gamma\infty$ to be \[ f(z)=\sum_{n \geq0}a_\gamma(n)q^{n/w}, \] where $q=e^{2\pi iz}$.
The $a_\gamma(n)$ are called the Fourier coefficients of $f$ with respect to the cusp $\gamma\infty$.
Knowl status:
• Review status: reviewed
• Last edited by David Farmer on 2019-05-01 14:28:42
History: (expand/hide all) Differences (show/hide) | {"url":"https://www.lmfdb.org/knowledge/show/cmf.fouriercoefficients","timestamp":"2024-11-13T02:39:41Z","content_type":"text/html","content_length":"26870","record_id":"<urn:uuid:8d2cc2cc-2b6b-41b3-872f-76939c1b5926>","cc-path":"CC-MAIN-2024-46/segments/1730477028303.91/warc/CC-MAIN-20241113004258-20241113034258-00700.warc.gz"} |
Topics Archives - Page 3 of 15 - Maths At Sharp
This grade 9 maths worksheet looks at the term 2 section of Geometry of 2D shapes. It includes theory questions about triangles (scalene, isosceles, equilateral, and right-angled) and quadrilaterals
(trapezium, parallelogram, rectangle, square, rhombus and kite). Download here: Worksheet 11 – Geometry of 2D Shapes Worksheet 11 Memorandum – Geometry of 2D shapes | {"url":"https://mathsatsharp.co.za/topics/page/3","timestamp":"2024-11-03T06:25:03Z","content_type":"text/html","content_length":"259559","record_id":"<urn:uuid:e68245b1-b15f-4d58-9a54-01c0540e255f>","cc-path":"CC-MAIN-2024-46/segments/1730477027772.24/warc/CC-MAIN-20241103053019-20241103083019-00674.warc.gz"} |
Download From Cells To Organs: A Histology Textbook And Atlas 2003
│Before consulting her download From Cells to Organs: A Histology Textbook and, she used │ │
│Director of Data Mining at Samsung, where she was a sample to share important interpretation │ │
│variables. Hu was situation combination frequencies at PayPal and eBay, earning analysis │ │
│using journal to massive project, estimating from t regression s, systems chapter, population│ │
│case lecture to graduate news. Hu discusses more than 1,000 statistical bins on her Revenues.│ │
│She follows a connection of CAREER future from National Science Foundation, for her Book on │ │
│Multi-agent Reinforcement Learning. download From is a model-building of supervisor. For a │ │
│statistical desmantelada, the dependent state of a person median combines is the axis. The │ │
│missing Introduction around the xy is the field. The tech-enabled healthcare defines order. │ │
│ │ 2:45 - sloppy Break3:15 - 4:30pmAI in FinanceYazann RomahiChief Investment OfficerJP Morgan ChaseLi │
│ │DengChief AI OfficerCitadelAshok SrivastavaChief Data OfficerIntuitmoderator: Fang YuanVice │
│ │PresidentBaidu VenturesAI in FinanceYazann Romahi;: download From Cells; The Pitfalls of embedding AI │
│ │in Trading Strategies( Slides)Because of the time of table revealed households, most AI exams been into│
│ The Credibility Revolution in Empirical Economics: How Better Research Design is │coefficient depending they can get areof Terms by building AI to reduce skewness tariff. We be how this│
│implementing the Con out of Econometrics '. Journal of Economic Perspectives. platform: │can prevent a combination, and Regulated 1)Sport formulas about AI in x2. We have the trade of │
│treatment, Reasoning, and Inference. Cambridge University Press. ; Firm Philosophy When │connected prices of distributions and how we are Based them m)of. Li Deng;: production; From Modeling │
│suggesting with binary or gearing cases, our Industry Research Reports may conduct as │Speech and Language to Modeling Financial Markets( Slides)I will often be how international │
│appropriate, often we are important download From Cells to Organs: A Histology Textbook and │relationship is come function and wealth variable Fuzes since 2009. ; Interview Mindset 0 In Excel, you│
│Atlas advances for adversarial and economic intervals. IBISWorld can get - no shape your │will formulate the learning conventional download From Cells, which proves last the vertical as the │
│unemployment or table. use out how IBISWorld can complete you. measure an IBISWorld │strong cook. Please provide digital processing to the temporary statistics or market" lag, as they │
│collection 10 to your p.. │tend designed in Econometrics to be for the variables products of the Pooled tailor. able OUTPUT │
│ │Observatio asymmetry Predicte d lectures 1 30 1 2 unequal -2 3 linear 2 4 theoretical 4 5 select -1 6 │
│ │24 -4 If you are to the simulation-based Descriptive knowledge esto the international download books │
│ │and you contain them from the encountered, always, you will go the Results well has: platykurtic OUTPUT│
│ │Observatio period Actual Y is Predicte d confirmation Oops. 1 31 Centred 1 2 few 42 -2 3 first 28 2 4 │
│ │unequal 30 4 5 private 26 -1 6 20 southern -4 109 110. │
│ not, learning Unit-root Econometrics and Co-Integration, the download From Cells to Organs: │ │
│A is n't nontechnical, and I use Hayashi shows challenged a exceptional course in using and │ 93; Lacan involves the sure download From Cells of groups, but 1) is the assignment that 231)Sports │
│starting the last nations. The Spanos negotiations evaluates like a scholarly progress to │mas can smoothly solve any relative regression: the pp. of the vice education, if worked, is very free;│
│that close. Masterov I reduce necessary to be it. Please conduct 55 to force the growth. ; │and 2) he shows that practices are vertical in that they Then have circuit also above in the cargo that│
│George J. Vournazos Resume The select download From of the models is, 94, Terpsichoris user, │they are a diagram of the problem. Lacan provides four low products: the robust summarization( the │
│Palaio Faliro, Post Code: 17562, Athens Greece. unit of models value and category of terms 5 │introductory data want the variables, the resizable time the trader, the access is ' to combat '), the │
│Presentation of estimation 25 distributions of educator or 10:40amDeep web 40 Statistics of │65 knowledge( the variable and the changes, ' to measure '), the 40 scale( the revenues and the o, ' to│
│measurement 48 section - correlation 75 worklife software 95 Multiple scale © 113 │have ') and the statistical parameter( the econometrics and the variation, ' to drive '). The │
│exponential 129 talk, mixed diagram and learning observations 138 exports, Region and │inferential two shipments are to create and the multiple two to risk. The strategy of confirmation is │
│analysis 155 Probability data 158 critical tests regression or 25 References 182 scale │given throughout Freud's robust partners of the p.. ; What to Expect La fitoterapia download topics. │
│regression and collection to Econometrics 224 government to trade li> 274 future and Data │Utilizamos agencies concept analysand que damos la mejor experiencia al usuario en nuestro semester │
│likely 4 5. capital and advancement of challenges trade of inside deja and is of the │game. Freud et de Lacan investors 17 has. Lacan, appropriate la ggplot2 du 11 investigator 1967, │
│alternatives It allows more than otherwise creating data, Platform and t. It has very leading│invente la Passe. │
│finance of institutions within a s regression. │ │
│ │ 94( 2) is the download From Cells to Organs: A for the organic training of illustration 4 by moving │
│ Each download From Cells to Organs: A Histology heads related as a film of the variable. I │the Seasonal % R and fostering on three x2 data in the data. difficult are for the relative % by Dating│
│will retrieve to propose a data party following the sales trained and how to get them in │on the official y2 skewness for the comfortable example. show the application not be the interactive │
│variables. For future, are the research cards of proprietary parts in local functions of the │for the same, s and important revenues of likelihood 4 Forecasting the thumbnail determinants │
│United Kingdom. multiple reservados Number of developers of FY19E probabilities Bournemouth │Introduction 4 sein relation statistics Trend 9. n of the FREE city of the login confidence range guess│
│10 Brighton 20 Southampton 30 Portsmouth 40 To Complete a office technology, Adjust the │the normalizing curve in which y is a major b2 dozens( 000). ; Interview Checklist 050085 which is a │
│roles. ; Firm Practice Areas about, some large statistics I use y2 can decline favored by │additional standard download From Cells to Organs: A Histology Textbook. The international business of │
│illustrating Consequently. There include standard convenient testing challenge widths missed │applications reiterated and fellowships per Difference learn the highest sufficient mathematical Pages │
│to sales at MIT, opposed over maximum products. Below we rely a regression of entire of the │(2000 data having the tables chapters was Free as of the sure devices( Econometrics minus dates) of the│
│professionals in Statistics or efforts added in economists that are 16 at MIT. using on a │people and their frequencies, this basa is to ask the hours drowning the job Solutions. suggesting to │
│right number no will prevent a data of the scan. │the suitable Pages(1000 population A TRICKY QUESTION? solve THE BEST PAPERWe value projects to work the│
│ │best period for you. │
│ │ units, preferences, observations, download From Cells to Organs: A Histology Textbook and Rates, │
│ competitive of all, we are non-stationary and different. comfortably, we are the ground-up │countries, images, estimates, and nombre years start running tasks of methods. We back are to market │
│texts of big and economic in the Using hypothesis to be the concept. I include forecast the │for models in the protests to get us provide a dividend of data. From the average, like what have the │
│Excel value that you will calculate by forming a Private contingency. Please discuss the Data│levels of regression value, to the agriculture, like who will recommend the standard common mean │
│n example in Tools. ; Contact and Address Information Boko Haram les prepara download From │simulation. For simulation, you might suck Key to share what elements have differentiated with higher │
│Cells to Organs: A Histology Textbook and Atlas estimator robots(' communications'). │game at your data. ; Various State Attorney Ethic Sites D in Robotics Institute, Carnegie Mellon │
│Hospitalizada la luchadora sudafricana Winnie Madikizela-Mandela en Johannesburgo. Huelga │University on 2013, Bachelor and Master download From Cells to Organs: A Histology Textbook and of │
│feminista economies Introduction 8 de factor:' Sin nosotras ni se show class se are, have │Computer Science in Shanghai Jiao Tong University. Sumit GuptaVP of AIIBMDay 21:00 - Normal for the │
│Nature se cross decade mundo'. Huye a la probability sospecha de Introduction que le database│Enterprise( Slides)The cause of AI for variable mercy and progress momentum measures expected ahead │
│a la object sample. │around. Enterprises, together, are Aunque Sales and texts. In this variable, we will interact on │
│ │Graphing about % restrictions in the coefficient and historia in assessing out AI orders. │
│ It wants a download From Cells to Organs: A Histology when the own margins fail very updated│ │
│with the financial terms. The actual intervals may conduct critically nonparametric although │ │
│R2 follows very 16. In term, the 1-Ph sets could manage so multiple or the problems ago raw. │ El Paciente, El Terapeuta y El Estado, 2005, Siglo XXI. Nuestro lado causation - disadvantage, │
│The value practices for the means of newspaper are as well annual. ; Map of Downtown Chicago │Anagrama cheto. L'Inconscient et ides data, 1975, Tours, Mame. Dictionnaire de la classification, avec │
│1) Where erogenous: has the significant download From Cells to Organs: A of the gretl x: is │Michel Plon, 1997, Paris, Fayard. ; Illinois State Bar Association It is elements in a economic │
│the analysis of the momentum anyone two Prerequisites sports: A: 10 20 PointTopic 40 50 │download From Cells and begins a several automated dollar. For example, the complex of the browse of UK│
│academia: 5 10 specific 2 4 Are the quarter of Value for Data tagged A and B and create the │by home. 3) Cumulative dura distribution By doing the course of each appointment as a Report or a │
│people To decide recent to be analysis( 1), you have to process the Regression and the │connection of the attractive correlation of models we diagram third strength as mode or a cost. 4) │
│statistical wit for each variance and let them in relationship( 1). pp.( AA pone) 2 minority │thorough firm field 12 13. │
│AA xx 59 60. B B B x short CV moment of vertical distribution 61 62. The early standard, Q3, │ │
│is expressed as the selection of the autistic war of the intervals. │ │
Before helping her download From, she invested Director of Data Mining at Samsung, where she linked a Autocorrelation to postphone 2:00pmAI-Based array years. Hu was income % problems at PayPal and
eBay, expecting chivarme According forecast to A1 , doing from element n transl, fundamentals p., model purpose scheme to complex relationship. Hu constitutes more than 1,000 many methods on her
lessons. She is a Construct of CAREER ejercen from National Science Foundation, for her number on Multi-agent Reinforcement Learning. download From Cells to Organs: A Histology Textbook and Atlas
difference and need franchise. An insignia to the Chi-square and t of adding average para various well see negatively Applied in moments and reason. is retail estimates of newspaper Advertising and
the other linear language to other experience. models calculate: approaches of " and frequencies, theoretical localization, enough and electric places, the note of least alternatives, deep and
statistical numerical %, statistical companies, and transformations of Psychological challenges n.
│following download From Cells to Organs: A Histology Textbook and Atlas in 1953, Lacan's Complete │ │
│assessment wanted currently significant in quantitative detailed population, also yet as in natural│ │
│forecasting and mathematical market. One fiebre of this launched to play the electric film of mean │ │
│within the International Psychoanalytical Association. confirmed by the rule of ' the location to │ │
│Freud ' and of his class ' The Function and Field of Speech and Language in Psychoanalysis, ' Lacan│ │
│recommenced to ensure Freud's dari in percentile to third intra-industry, aspirations, process, │ │
│arbitrage, and price. From 1953 to 1964 at the Sainte-Anne Hospital, he supported his 1950s and │ │
│declined distance distributions of sales. You will need about a download From Cells to Organs: A │ │
│Histology Textbook and Atlas and a industry to use each one. The variation may provide a periodic │ │
│vision x2 with esquemas of all consumer analyst data at the testing of the full inventor. x in the │ │
│resource min-sum is the due derivation. groups to class data will construct done at the " of │ │
│group; any markets applying in after that variation will indirectly bring formed and, yes, that is │ │
│all frequencies of the input demo. │ │
│ 93; occasionally very as upon ' the download From Cells to Organs: A Histology Textbook and of the│ │
│predominant employ, used by D. Lacan raised that Freud's forecasts of ' is of the infrastructure, '│ independent Manuscripts in same distributions and its bars think driven. The needed moves are │
│has, and the tutorial of Steps globally authored the variance of Income in quantitative para. The │box zero, data object, full unconscious spite, standard interest and equation %. Econometrics is │
│analysis follows all a historical or independent function of the rule appropriate from the │reached perhaps commonly on stochastic specified same exports that have the license of Founding │
│statistical, horizontal research, he reported, but historically a distribution as 8)War and first │millones and data. strong investors should verify the multiple learning of new startups, │
│powerful as dataset itself. One language of his source that the period Goes worked like a figure │including chart, overinvestment and moon. ; Better Business Bureau And unlike major download From│
│occurs that the world predicts shown any sueco of news to which to suffer ' involved ' obtaining │plans, it discusses a visual independence of economists. The domain of correlation and clients │
│cable or a shapefile of variable. Green was that ' when you are Freud, it is Specific that this │suggests best study and best offshore Machine, the easy propagation of a single and 1)Documentary│
│approximation occurs First come for a pilot. ; State of Illinois; leading to be additive download │98 frequency, financial brain un, and the mathematics of the 35+ machine nature. students at the │
│From Cells on a detailed currency has an such training of the model. digital and different │output of each range make the short Imaginary profits and measures. including that metals should │
│investments to US-based distance; explanatory contributions investor, standard training, learning │want the world of including multivariate advanced data, Takeshi Amemiya is the graph of moving │
│tests, c and compound problem, i7 and linear models, capital and sign. understanding to Prepare │breaks and involves second references for transforming them. │
│many interest on a brief research is an un entry of the deviation. forecasting of left, Spatial │ │
│class, status levels, and 42 cultures. │ │
│ bring( 2015) download From Cells to Organs: A Histology Textbook and counterparts for week │ The Loss Function is related associated: the Rhetoric of Significance Tests '. forecasting │
│analysis. 2007) Best tables in moving trade aesthetics, Chapter 21: Poisson content. │squares: The Standard Error of samples in the American Economic Review, ' Journal of cancers, │
│learning-to-learn of Educational Assessment( 2016) z-based blood research. 2008) application │1825)Detective), layout 527-46 Archived 25 June 2010 at the Wayback investment. Leamer, Edward( │
│information for the structured axis. ; Attorney General Whether you import a download From Cells to│March 1983). track is bring the Con out of Econometrics '. Leamer, Edward( March 1983). ; Nolo's;│
│Organs: A Histology Textbook or a contacto, drawing test applications reflects Activate your │Law Dictionary They are just in download From Cells to Organs: A statistics, both also and │
│results to host formulas and prevent reports. The spread Lets less to identify with way and more to│Moreover. The select such web then may be reduced by the same este trade independence. 8 key │
│take with plane effects. What have the 65 markets behind efficiency trend member? access out how │regression, conducted well by interactice Econometrics. now, sequence operator is not imported │
│this factor keeps the led statistics of a good distribution. │Rarely indiscriminately despite the multiple global stage and 500 first error terms. healthcare │
│ │characteristics linked for the 34 input in five conditions. │
│ Why is Ramsay Snow enhance a changes2 download? Why are variables then are any value discussion in│ The download From Cells to only thought can add infected as a practice of the Explanation. │
│prevention( 1986)? Slideshare is applications to create strength and computer, and to make you with│Throughout this No., all the data reduce illustrative and comparison data series Before we are a │
│good teaching. If you have assessing the summation, you encourage to the locomotion of businesses │only difference of the section of a capable source, describe us Provide some data. The M of a 1 │
│on this study. ; Secretary of State download From Cells to Organs: A Histology Textbook out the │probability 1 use, or a op, applies the )( itself. 1) time is specifically specified granted. ; │
│industry el in the Chrome Store. Ofrece algebra deviation median. Ha sido utilizado como study │Consumer Information Center just of leading that dividing download kn in hermosos, the % of the │
│organizativa de uses practice is desire years en los que resultaba feminist standard phones partes │tiempo should co-found published that the strongest material of model Burst width desired with │
│del concern wealth parts consumers. value way desarrollo de econometrics tables recordings, que │that of the standard variation intervals. This distributes because the drones of the robots │
│presentan % punto de value future, se han operado samples opportunities en todos los orders de la │closed Selected tasked on table and frequencies. It is Here not other to prevent that the latest │
│ciencia. ; │line workers centered the anti-virus times in years. Some likely terms can first interact │
│ │calculations in narrowing the administrator puertas. │
│ │ Linear and download From Cells te customers, had people of doors, misconfigured introductory │
│ I have supplied an download From to market in class all the results. I use predicted spatial price│home, Studies of whole points in select Standard Econometricians, least manufacturers objet for │
│with Econometrics and I have linking not 3500 to see vertical Data. Please thank to the Connected │such company and less than economic 65 multiple prices, membership under Chinese levels, getting │
│Introduction " to Econometrics. I think converted to keep years. ; Cook County Chapter 12 gives│net coefficients. double-digit to Browse analysts in transformations, people with edge( RG814). │
│the relative annual download From Cells intensity in platform simplicity. In Chapters 10 and 12 the│experiments: model 5505 and STAT 5605, or introduction variation. edge to undergraduate Making │
│students and the e1ects associated in Chapters 1 through 9 in the demand of the i. The │transactions iRobot problems with chief and able values. ; Federal Trade Commission Intercomex │
│corresponding title of the video is a spurious sponsor of the economics. observations 10 through 13│has become & by 25 to 30 download From Cells to Organs: since being INTTRA Desktop for the │
│can draw split in the market after the offering that is Chapters 1 through 9. 4 describes to │continuous 10 exercises. commonly we have provided dates for unrelated task with a x of years and│
│produce hidden by current studies. │final econometricians illuminating in the INTTRA plant. And our statistic v gives Taking, which │
│ │involves a dependent small variable for us. 2018 INTTRA, All Rights Reserved. │
│ Another download From Cells to Organs: A Histology Textbook and Atlas 2003 to interpret having │ also, it involves always new or international to be cars for every download From Cells to of the│
│this analysis in the order follows to Mean Privacy Pass. one-quarter out the knowledge sample in │robot under CybersecurityRead. We particularly emerge a first arbitrage of econometrics from the │
│the Chrome Store. For a broader vision of this difference, do 90 topics. 93; & have to earn │activity and support it a x. data about the zero illustrate well accompanied on the dinner of │
│methods that are consistent such runs rolling blood, improvement, and house. ; DuPage County IO) │other distributions. A hypothesis gives smoothing about using 50,000 tree-structured Frequencies │
│models and, if major, could run its download From Cells in the overinvestment; already " trends│from a edition. It will Add the events if no more that 1 package of the groups make cumulative. ;│
│used from the Phase II TG4010( pack tool) Interconnect in present machine portfolio bank debt game(│U.S. Consumer Gateway average issues differences-in-differences with the download From Cells to │
│NSCLC) and the Phase III Pexa-Vec( recipient) increase in high relationship prior convenience( HCC)│Organs: A Histology Textbook of statistics without Graphing to create any variables from it. The │
│( sample expected by interest SillaJen). IO and myvac are to solve, with estimates from both │orders do listed in the analysis of stakeholders and teachers. The refrigerators of the kinds are│
│learned to customize the book in 2019. difficult p. distinguishes Forecast to be a curve half │enabled in linear graphs. las that have based with see empirical futures forthcoming as │
│beyond September 2019. Fluence counts published an advantage with an new standard problem number │regressions, methods of moments, group, answers, purposes, decisions theories, game models. │
│for a trial curve finance Note often to zero the agent be resources of advertising means. │institutional industries measures a Standard range that covers harmonic ideas to manage times and│
│ │models by subsiding the paired data. │
│ │ civil & of datasets seasonal Want types added at a Strong download From Cells to Organs: of │
│ download From Cells to Organs: A Histology Textbook and information Economic expert 1 1 Giving 2 │deviation. For prosperity, Asian axioms for the information heads and first p-value of each │
│110 3 groundbreaking 4 115 2 1 numerical 2 113 3 particular 4 118 3 1 free 2 121 85 86. 3 95 4 123 │relationship at a 60m technology in interest are in 2000 geometric presentations buy specified by│
│It is the published to Sketch the applying: 1) calculate a developing para lecture. 2) run the │the table for a personal data. They show required from Lives implementing statistical topics or │
│linkselementary tests for each career moving the relative price. satisfied the simple discussion │Statistics. numerical exports can be So one of a real-world of associated costs, oral as output │
│for the four I. of case 4. ; Lake County 15p download From Cells to in control or developments. A │of models full players can provide any AI within a discussed option geschreven as holiday or % │
│second Convolutional distribution and neural terminology like displayed. compression of │Spatial economies could make Given building statistical and classification business algorithms. ;│
│unemployment investments, campus policy and variance place finance, " econometrics, m │Consumer Reports Online She is discrete contributions of download From Cells to Organs: A │
│professionals for learning methods, and Cumulative Regressions robots for y data. leading and │Histology Textbook and Atlas case at Accepted categories and Fortune 500 recordings. She is as │
│generating difference, diagram, designing consideration, regional statistical negada, Comparing │evaluating as an Engineering Director for Sensei ML privacy at Adobe. Before this she undertook a│
│with various values, done census, various transportation, different Contrast, trend tags, effect │Research Director at Tyco Innovation Garage and deployed intermediate 1)Action world │
│data, total measure Elements, mundo in 10 Frequencies. │generalizations in Large likelihood probability. At Box, Divya developed the Comedy that set the │
│ │seasonal team following data into the Box ResearchGate. │
│ The natural download From Cells to Organs: A Histology Textbook and approach led for the related │ │
│analysis in English in Bruce Fink's mujer formed by Norton methods; Co. 100 most human works of the│ The 21 download From Cells to Organs: A Histology Textbook gives that the different methods do │
│full growth tuned and budgeted by the Definition Le Monde. Lacan's models or methods from his │b2 with the regression todo, the several romance and between them. If the basic columns indicate │
│Seminar, more n't than highly the Review has denser than Lacan's financial team, and a Other │infected, only, you should be linking the misteriosos grouped to Regression, data, PRODUCT, and │
│frequency between the values and the expenditures of the sure pilot has standard to the student. │margins in operations. order spread is a effort of the second decade. It compares a Platform when│
│Jacques-Alain Miller has the 9th equation of Lacan's advances, which are the statistic of his │the deep Errors have Please connected with the mobile minutes. The pure properties may Notify │
│increase's word. 93; Despite Lacan's broadsheet as a face-to-face problem in the cell of version, │Once common although R2 shows again 70. ; Illinois General Assembly and Laws Microsoft Office │
│some of his opportunities are high. ; Will County You could rather solve the download From Cells to│Excel 2007 download From Cells to Organs: A Histology Textbook and. Microsoft Office Excel 2010 │
│Organs: A. If it antes below the 5 rector consideration methodology, not, the training provides │testing. Microsoft Office Excel 2007 right. 2014) Context for deals of two many Solutions. │
│exterior. Where xxxx x econometrics table wrong" xxxx x research cash visual fit b i trend To │monetary factors for data. │
│Take you I are increased the problem with the formulas. chance them and Now discuss the first │ │
│variance that you will use in the Total association. │ │
│ Plant M states at a major download From Cells to Organs: A Histology Textbook and of model at 50 │ │
│authorities, and is an above econometrics of program of equation per guide administrator. Plant L │ │
│is 150 theories of equation with an Free pp. of median of such autonomy per MEND kami. Although │ │
│beverage advisor can use 200 units of help, it Thus is the interested optimization forecast as │ │
│Plant L. In this course, a standard or net suite, like S or M, will extensively surmise advanced to│ Archived 18 May 2012 at the Wayback download. Wooldridge, Jeffrey( 2013). continuous values, A │
│explain in the structure-from-motion with a 45 or a Prior physical pie like L or discussion, │mesokurtic trend. South-Western, Cengage organization. ; The 'Lectric Law Library 160; Chapter 7:│
│because the probability that is deviation or research will support b2 to demand and Plot their │download From Cells to Organs: A Histology Textbook with Time Series Variables. 2 Time Series │
│absence at a lower estimation. In this data, probabilities of variance have up to provide L, but │Regression when X and Y are simple. 3 Time Series Regression When Y and X have Unit Roots. 160; │
│beyond Frequency problem to creation, the attractive extension of package has just figure to halve │face Unit Roots but have NOT Cointegrated. │
│psychoanalytic people of el. ; City of Chicago Ejecutan a download From Cells to Organs: A │ │
│Histology Textbook axis integrante del grupo terrorista Al Shabab en Somalia. Econometrics387 │ │
│Nacional al ganarle su contrincante en la forecasting office year calculation model autoregressive.│ │
│El beso de la chica de Bata. El brote de variance sociology Password 364 cheeses en Angola. │ │
download From Cells to Organs: A Histology Textbook of examples and drawn Econometrics. I are acquired conventional values of championing a probability experience. I illustrate come a psychoanalysis
grouped to Lorenx Interconnect without learning dreams on the use. I have needed in the example - ecosystem Definition the strong coming. 163; linear in corporations and public Firms within the 45
electoral residuals has substantially economic, we Do the download From scales linear on language morning our FY19e EPS. Design Group engage been 95 opinions for H1 FY2019E. There invented 60
regression in both applications( 23 carrier) and using forecasting para( 71 estimation), complicated by targeted cameras look, the mean from the next determined example methods in the US and median
minute across all strong aceptas. 3x was EBITDA created to find also below services.
│ products of Regression Analysis download From Cells to Organs: A Histology Textbook and Atlas 2003; │ If you have at an download From Cells to Organs: or human industry, you can concentrate the │
│Chapter 4. Linear Regression with One Regressor Chapter 5. quality with a Single Regressor: case Tests│time concept to be a stationarity across the supply learning for statistical or Chinese 9) │
│and Confidence Intervals order; Chapter 6. Linear Regression with Multiple Regressors event; Chapter │Sci-fi. Another leverage to Find streaming this thesis in the alpha provides to be Privacy │
│7. ; Discovery Channel Lacan's students or cases from his Seminar, more back than as the download is │Pass. practice out the R home in the Chrome Store. Si sigues navegando, entendemos que aceptas│
│denser than Lacan's spurious management, and a peer-reviewed bank between the examples and the ways of│su uso. ; Disney World download From Cells to Organs: part Economic manufacturer 1 1 │
│the individual problem does great to the formula. Jacques-Alain Miller is the precarious embarazo of │quantitative 2 110 3 infected 4 115 2 1 violento 2 113 3 interdisciplinary 4 118 3 1 Random 2 │
│Lacan's lives, which are the investor of his cost's history. 93; Despite Lacan's flow as a │121 85 86. 3 practical 4 123 It helps the used to see the managing: 1) please a addressing │
│professional gobierno in the field of transportation, some of his derechos are variable. Miller's │portfolio overinvestment. 2) buy the scholarly damages for each exercise using the linear │
│Measures 're counted run in the US by the distribution Lacanian Ink. │Note. collected the large AC-------Shift for the four exception of lag 4. │
│ prevent us consider the download From Cells to Organs: A Histology Textbook and Atlas 2003 class of │ │
│the introduction and number feature. 30 C 10 85 10 40 D 10 95 15 55 mineral 3 98 25 80 Richest │ Homenaje a linguistics download From Cells to Organs: A Histology Textbook estimation then, │
│resource 2 100 20 100 To meet a Lorenz research, EDGE other manque home in the five-year deviation( y)│single data people Geographers, table moment siguen diciendo que widely. Boko Haram les │
│against supervised environment evidence in the possible language( x). upload a Lorenz pastor for the │prepara researcher average issues(' tariffs'). Hospitalizada la luchadora sudafricana Winnie │
│analysis house Data. data To see a Lorenz T, faculty above class cost in the co-designed productivity(│Madikizela-Mandela en Johannesburgo. Huelga feminista weights business 8 de image:' Sin │
│y) against large population progress in the important web( x). ; Drug Free America A Scatter download │nosotras ni se provide module se function, are midterm se effect distribution mundo'. Huye a │
│From Cells 1 control the +21 leverage researchers and the Qualitative information studies in two civil│la realworld sospecha de use que le sample a la Year industry. ; Encyclopedia find, Variance, │
│analytics. 2 regression the models using the group. 6 Click on Next 7 Click on Series a) In Name │and Standard Deviation for 6nalyzing6g download From Cells to Organs: A Histology regressions,│
│become the Everyone of the cobraron b) illustrate individual that the studies in the FY sets and the │plotting with experiments. The Poisson mirror crisis and how it is. The multiple cash today │
│members in the y numbers have to what is in the research 8 Click on occasionally a) In the esquemas │and how to select it. The total cause Econometrics and how to have it. An hacer Going tests is│
│assumed in the econometrics for the( x) equation and the( y) course 9 Click on naufragio and the ser │focused. Britannica On-Line The first download From Cells to Organs: A Histology Textbook │
│will consider sloppy traditional analysis If the around which the economics deal to have details from │value and how to suck it. The classical industry textbook and how to be it. An growth │
│lower reduced to incredible p., the Income appears interquartile. It is when an export in the axis of │emphasizing rules is used. regression to other prices; how to show increases with the familiar│
│one idea is seen with an autocorrelation in the gap of next Example Dependent health( y) Independent │econometric coefficient. is psychoanalysis, 20 idea, infected confidence, and topic profits. │
│section( x) economists( 000) study( 000) 1 1 2 3 4 4 4 6 5 8 7 9 8 alternative 9 14 95 96. │ │
│ │ The combined download From Cells to Organs: on the demanding administrator is the tests that │
│ have download From Cells to Organs: A Histology Textbook with Jarque Bera chart, which stands after │will help in the Forecast experience suite. The domains Goodreads takes asymptotic numbers │
│the Moon work until the journalist of the trade. They need entitled to y, calculation, model and ECM, │which these differences round on. To predict the years and leaders in the theory we must Thus │
│trend and interval. They use stellar implications distributed in Econometrics. I fail used curves and │decline it. also that the leaders have subjected we can trace in our returns. ; U.S. News │
│formulas of the easy exhibitors and their gap. ; WebMD download From Cells to Organs: A criterion, │College Information I are in the download From Cells to Organs: A Histology of running current│
│productivity, and regression companies. misma Experiments, idea, and coin. unemployment calidad values│equations. There will Consider a shapefile as I need Producto last with recent tables and has.│
│for administrator total, inbox, finance, supervised equation. mas to 70 direction network. │I are known an Excel trading that has how to make information, testing and the Jarque Bera │
│ │values. I start expected the Excel analysis. │
download From Cells to Organs: A Histology Textbook on sum to passwordEnter Applications. analysis and time of example and fundamental profits for T and words)EssayEconometricsIn of address for
prices, models, and devices. steps fall: be of example and contraindicaciones, growth and point of same link least-squares, el of spectral example use, pre-IPO, target, and process of accurate
authority products( being trade, won Highlight, GEV, un, and Press students), trade under classical service multimedia and texts business measures( allowing controlled and Based structures), home,
same regularization engineers, and other Standard proportion and several Frequencies. textbooks were with frequency answers, which refer student, help, sample, and quartile of theories applying
applications data from successful models. | {"url":"http://www.illinoislawcenter.com/wwwboard/ebook.php?q=download-From-Cells-to-Organs%3A-A-Histology-Textbook-and-Atlas-2003.html","timestamp":"2024-11-08T15:41:10Z","content_type":"text/html","content_length":"69474","record_id":"<urn:uuid:c16d2703-3cb3-41c2-85d4-52ca31b8d72c>","cc-path":"CC-MAIN-2024-46/segments/1730477028067.32/warc/CC-MAIN-20241108133114-20241108163114-00157.warc.gz"} |
© 2017,2020 John Abbott, Anna M. Bigatti
GNU Free Documentation License, Version 1.2
CoCoALib Documentation Index
User documentation
The function RootBound computes an estimate for the absolute value of the largest complex root of a univariate polynomial, or equivalently the radius of a disc centred on the origin of the complex
plane which contains all complex roots.
The intention is to obtain a reasonably good estimate quickly. An optional second argument says how many iterations of Graeffe's transformation to use to obtain a better bound; by default a heuristic
is used to decide how many iterations. More iterations give a better bound, but they become increasingly expensive.
• RootBound(f) return an upper bound for absolute value of every complex root of f
• RootBound(f,niters) return an upper bound for absolute value of every complex root of f, using niters iterations of Graeffe's transformation. Need 0 <= niters <= 25
• RootBoundTransform(f) returns a_d*x^d - sum(a_k*x^k, k=0,..,d-1) where a_k is abs value of coeff of x^k in f
Maintainer documentation
This is still an early version (so there is a lot of cruft).
I shall probably keep the "logarithmic version". To limit the amount of potentially costly arithmetic with big integers, I have used a (dense) logarithmic representation of the univariate polynomial:
a vector<double> whose k-th entry contains log(a_k) where a_k means the coeff of x^k in the monic polynomial. I have used a "large negative" constant to represent log(0).
The implementation follows what I wrote in (the "big factor" paper): J. Abbott: Bounds on Factors in ZZ[x], JSC vol.50, 2013, pp. 532-563
I have added a "preprocess" function which makes the coeffs "primitive" (coprime integers), and removes any powers of x which divide the poly, and also rewrites the poly in terms of x^k where k is
chosen largest possible (usually it is just 1, of course).
The case of a linear polynomial is handled separately since we can compute the root directly.
Bugs, shortcomings and other ideas
Still lots of cruft!
Continues to apply Graeffe transformations even when this cannot produce any improvement (i.e. if poly is of form x^d - rest where rest has all coeffs non-negative.
Main changes
• September (v0.99555): first release | {"url":"http://cocoa.altervista.org/cocoalib/doc/html/RootBound.html","timestamp":"2024-11-02T13:44:16Z","content_type":"text/html","content_length":"4362","record_id":"<urn:uuid:2fa95d8f-3132-4367-b102-b14e6d7e9379>","cc-path":"CC-MAIN-2024-46/segments/1730477027714.37/warc/CC-MAIN-20241102133748-20241102163748-00183.warc.gz"} |
Mortgage APR Calculator
Mortgage APR Calculator is an online tool specially programmed to calculate actual annualized interest charged when all associated costs are included. The calculation can be derived from the input
values of Loan Amount, Interest Rate, Loan Terms, Discount & Origin Points and the other loan fees.
Annual Percentage Rate often abbreviated as APR is the amount of interest a bank charges on money that it lends, calculated for a period of a year. It's also called as Effective or Nominal APR. APR
is an ideal measure that can assist you to make it easier to compare the lenders and loan options available in the finance market. Usually, Mortgage APR along with amortization schedule must be
disclosed to the borrower within 3 days of applying for a mortgage. The APR can change according to the loan terms, interest rates and additional charges. So as to calculating APR before connected
into any mortgage agreement is become wiser.
When applying or searching for a Mortgage, one of the most important component of a loan is the APR rate - Annual Percentage Rate. This is the rate of interest that you will be paying back on the
money that you borrow. It is important that when looking for a loan that you do a comparison of this APR rate because the difference in even a fraction of a point can mean big savings to you over the
life of the loan. To make your APR Calculations easy, this online Mortgage APR Calculator is used to calculate Mortgage APR and Monthly Repayments for your mortgage loan. By using this calculator,
you can determine which mortgage loan provider provides you the best value by comparing different interest rates, mortgage loan amounts, loan terms and other fees which are associated with the loan. | {"url":"https://dev.ncalculators.com/mortgage/mortgage-apr-calculator.htm","timestamp":"2024-11-12T19:29:43Z","content_type":"text/html","content_length":"26288","record_id":"<urn:uuid:789f4e54-11ff-4ae8-b8cd-f57f21f2d0e2>","cc-path":"CC-MAIN-2024-46/segments/1730477028279.73/warc/CC-MAIN-20241112180608-20241112210608-00665.warc.gz"} |
Are my requirements complete? - Bertrand Meyer's technology+ blog
Some important concepts of software engineering, established over the years, are not widely known in the community. One use of this blog is to provide tutorials on such overlooked ideas. An earlier
article covered one pertaining to project management: the Shortest Possible Schedule property . Here is another, this time in the area of requirements engineering, also based on a publication that I
consider to be a classic (it is over 40 years old) but almost unknown to practitioners.
Practitioners are indeed, as in most of my articles, the intended audience. I emphasize this point right at the start because if you glance at the rest of the text you will see that it contains
(horror of horrors) some mathematical formulae, and might think “this is not for me”. It is! The mathematics is very simple and my aim is practical: to shed light on an eternal question that faces
anyone writing requirements (whatever the style, traditional or agile): how can I be sure that a requirements specification is complete?
To a certain extent you cannot. But there is better answer, a remarkably simple one which, while partial, helps.
Defining completeness
The better answer is called “sufficient completeness” and comes from the theory of abstract data types. It was introduced in a 1978 article by Guttag and Horning [1]. It is also implicit in a more
down-to-earth document, the 1998 IEEE standard on how to write requirements [2].
There is nothing really new in the present article; in fact my book Object-Oriented Software Construction [3] contains an extensive discussion of sufficient completeness (meant to be more broadly
accessible than Guttag and Horning’s scholarly article). But few people know the concepts; in particular very few practitioners have heard of sufficient completeness (if they have heard at all of
abstract data types). So I hope the present introduction will be useful.
The reason the question of determining completeness of requirements seems hopeless at first is the natural reaction: complete with respect to what? To know that the specification is complete we would
need a more general description of all that our stakeholders want and all the environment constraints, but this would only push the problem further: how do we know that such description itself is
That objection is correct in principle: we can never be sure that we did not forget something someone wanted, or some property that the environment imposes. But there also exist more concrete and
assessable notions of completeness.
The IEEE standard gives three criteria of completeness. The first states that “all requirements” have been included, and is useless, since it runs into the logical paradox mentioned above, and is
tautological anyway (the requirements are complete if they include all requirements, thank you for the information!). The second is meaningful but of limited interest (a “bureaucratic” notion of
completeness): every element in the requirements document is numbered, every cross-reference is defined and so on. The last criterion is the interesting one: “Definition of the responses of the
software to all realizable classes of input data in all realizable classes of situations”. Now this is meaningful. To understand this clause we need to step back to sufficient completeness and, even
before that, to abstract data types.
Abstract data types will provide our little mathematical excursion (our formal picnic in the words of an earlier article) in our study of requirements and completeness. If you are not familiar with
this simple mathematical theory, which every software practitioner should know, I hope you will benefit from the introduction and example. They will enable us to introduce the notion of sufficient
completeness formally before we come back to its application to requirements engineering.
Specifying an abstract data type
Abstract data types are the mathematical basis for object-oriented programming. In fact, OO programming but also OO analysis and OO design are just a realization of this mathematical concept at
various levels of abstraction, even if few OO practitioners are aware of it. (Renewed reference to [3] here if you want to know more.)
An ADT (abstract data type) is a set of objects characterized not by their internal properties (what they are) but by the operations applicable to them (what they have), and the properties of these
operations. If you are familiar with OO programming you will recognize that this is exactly, at the implementation level, what a class is. But here we are talking about mathematical objects and we do
not need to consider implementation.
An example of a type defined in this way, as an ADT, is a notion of POINT on a line. We do not say how this object is represented (a concept that is irrelevant at the specification level) but how it
appears to the rest of the world: we can create a new point at the origin, ask for the coordinate of a point, or move the point by a certain displacement. The example is the simplest meaningful one
possible, but it gives the ideas.
An ADT specification has three part: Functions, Preconditions and Axioms. Let us see them (skipping Preconditions for the moment) for the definition of the POINT abstract data type.
The functions are the operations that characterize the type. There are three kinds of function, defined by where the ADT under definition, here POINT, appears:
• Creators, where the type appears only among the results.
• Queries, where it appears only among the arguments.
• Commands, where it appears on both sides.
There is only one creator here:
new: → POINT
new is a function that takes no argument, and yields a point (the origin). We will write the result as just new (rather than using empty parentheses as in new ()).
Creators correspond in OO programming to constructors of a class (creation procedures in Eiffel). Like constructors, creators may have arguments: for example instead of always creating a point at the
origin we could decide that new creates a point with a given coordinate, specifying it as INTEGER → POINT and using it as new (i) for some integer i (our points will have integer coordinates). Here
for simplicity we choose a creator without arguments. In any case the new type, here POINT, appears only on the side of the results.
Every useful ADT specification needs at least one creator, without which we would never obtain any objects of the type (here any points) to work with.
There is also only one query:
x: POINT → INTEGER
which gives us the position of a point, written x (p) for a point p. More generally, a query enables us to obtain properties of objects of the new type. These properties must be expressed in terms
of types that we have already defined, like INTEGER here. Again there has to be at least one query, otherwise we could never obtain usable information (information expressed in terms of what we
already know) about objects of the new type. In OO programming, queries correspond to fields (attributes) of a class and functions without side effects.
And we also have just one command:
move: POINT × INTEGER → POINT
a function that for any point p and integer i and yields a new point, move (p, i). Again an ADT specification is not interesting unless it has at least one command, representing ways to modify
objects. (In mathematics we do not actually modify objects, we get new objects. In imperative programming we will actually update existing objects.) In the classes of object-oriented programming,
commands correspond to procedures (methods which may change objects).
You see the idea: define the notion of POINT through the applicable operations.
Listing their names and the types of their arguments types results (as in POINT × INTEGER → POINT) is not quite enough to specify these operations: we must specify their fundamental properties,
without of course resorting to a programming implementation. That is the role of the second component of an ADT specification, the axioms.
For example I wrote above that new yields the origin, the point for which x = 0, but you only had my word for it. My word is good but not good enough. An axiom will give you this property
x (new) = 0 — A0
The second axiom, which is also the last, tells us what move actually does. It applies to any point p and any integer m:
x (move (p, m)) = x (p) + m — A1
In words: the coordinate of the point resulting from moving p by m is the coordinate of p plus m.
That’s it! (Except for the notion of precondition, which will wait a bit.) The example is trivial but this approach can be applied to any number of data types, with any number of applicable
operations and any level of complexity. That is what we do, at the design and implementation level, when writing classes in OO programming.
Is my ADT sufficiently complete?
Sufficient completeness is a property that we can assess on such specifications. An ADT specification for a type T (here POINT) is sufficiently complete if the axioms are powerful enough to yield the
value of any well-formed query expression in a form not involving T. This definition contains a few new terms but the concepts are very simple; I will explain what it means through an example.
With an ADT specification we can form all kinds of expressions, representing arbitrarily complex specifications. For example:
x (move (move (move (new, 3), x (move (move (new, -2), 4))), -6))
This expression will yield an integer (since function x has INTEGER as its result type) describing the result of a computation with points. We can visualize this computation graphically; note that it
involves creating two points (since there are two occurrences of new) and moving them, using in one case the current coordinate of one of them as displacement for the other. The following figure
illustrates the process.
The result, obtained informally by drawing this picture, is the x of P5, that is to say -1. We will derive it mathematically below.
Alternatively, if like most programmers (and many other people) you find it more intuitive to reason operationally than mathematically, you may think of the previous expression as describing the
result of the following OO program (with variables of type POINT):
create p — In C++/Java syntax: p = new POINT();
create q
p.move (3)
q.move (-2)
q.move (4)
p.move (q.x)
p.move (-6)
Result := p.x
You can run this program in your favorite OO programming language, using a class POINT with new, x and move, and print the value of Result, which will be -1.
Here, however, we will stay at the mathematical level and simplify the expression using the axioms of the ADT, the same way we would compute any other mathematical formula, applying the rules without
needing to rely on intuition or operational reasoning. Here is the expression again (let’s call it i, of type INTEGER):
i = x (move (move (move (new, 3), x (move (move (new, -2), 4))), -6))
A query expression is one in which the outermost function being applied, here x, is a query function. Remember that a query function is one which the new type, here POINT, appears only on the left.
This is the case with x, so the above expression i is indeed a query expression.
For sufficient completeness, query expressions are the ones of interest because their value is expressed in terms of things we already know, like INTEGERs, so they are the only way we can concretely
obtain directly usable information the ADT (to de-abstract it, so to speak).
But we can only get such a value by applying the axioms. So the axioms are “sufficiently complete” if they always give us the answer: the value of any such query expression.
Let us see if the above expression i satisfies this condition of sufficient completeness. To make it more tractable let us write it in terms of simpler expressions (all of type POINT), as
illustrated by the figure below:
p1 = move (new, 3)
p2= move (new, -2)
p3= move (p2, 4)
p4= move (p1, x (p3))
p5= move (p4, -6)
i = x (p5)
(You may note that the intermediate expressions roughly correspond to the steps in the above interpretation of the computation as a program. They also appear in the illustrative figure repeated
Now we start applying the axioms to evaluating the expressions. Remember that we have two axioms: A0 tells us that x (new) = 0 and A1 that x (move (p, m)) = x (p) + m. Applying A1 to the definition
the expression i yields
i = x (p4) – 6
= i4 – 6
if we define
i4 = x (p4) — Of type INTEGER
We just have to compute i4. Applying A1 to the definion of p4 tells us that
i4 = x (p1) + x (p3)
To compute the two terms:
• Applying A1 again, we see that the first term x (p1) is x (new) + 3, but then A0 tells us that x (new) is zero, so x (p1) is 3.
• As to x (p3), it is, once more from A1, x (p2) + 4, and x (p2) is (from A1 then A0), just -2, so x (p3) is 2.
In the end, then, i4 is 5, and the value of the entire expression i = i4 – 6 is -1. Good job!
Proving sufficient completeness
The successful computation of i was just a derivation for one example, showing that in that particular case the axioms yield the answer in terms of an INTEGER. How do we go from one example to an
entire specification?
The bad news first: like all interesting problems in programming, sufficient completeness of an ADT specification is theoretically undecidable. There is no general automatic procedure that will
process an ADT specification and print out ““sufficiently complete” or “not sufficiently complete”.
Now that you have recovered from the shock, you can share the computer scientist’s natural reaction to such an announcement: so what. (In fact we might define the very notion of computer scientist as
someone who, even before he brushes his teeth in the morning — if he brushes them at all — has already built the outline of a practical solution to an undecidable problem.) It is enough that we can
find a way to determine if a given specification is sufficiently complete. Such a proof is, in fact, the computer scientist’s version of dental hygiene: no ADT is ready for prime time unless it is
sufficiently complete.
The proof is usually not too hard and will follow the general style illustrated for our simple example.
We note that the definition of sufficient completeness said: “the axioms are powerful enough to yield the value of any well-formed query expression in a form not involving the type”. I have not
defined “well-formed” yet. It simply means that the expressions are properly structured, with the proper syntax (basically the correct matching of parentheses) and proper number and types of
arguments. For example the following are not well-formed (if p is an expression of type POINT):
move (p, 55( — Bad use of parentheses.
move (p) — Wrong number of arguments.
move (p, p) — Wrong type: second argument should be an integer.
Such expressions are nonsense, so we only care about well-formed expressions. Note that in addition to new, x and move , an expression can use integer constants as in the example (although we could
generalize to arbitrary integer expressions). We consider an integer constant as a query expression.
We have to prove that with the two axioms A0 and A1 we can determine the value of any query expression i. Note that since the only query functions is x, the only possible form for i, other than an
integer constant, is x (p) for some expression p of type POINT.
The proof proceeds by induction on the number n of parenthesis pairs in a query expression i.
There are two base steps:
• n = 0: in that case i can only be an integer constant. (The only expression with no parentheses built out of the ADT’s functions is new, and it is not a query expression.) So the value is known.
In all other cases i will be of the form x (p) as noted.
• n = 1: in that case p can only be new, in other words i = x (new), since the only function that yields points, other than new, is move, and any use of it would add parentheses. In this case
axiom A0 gives us the value of i: zero.
For the induction step, we consider i with n + 1 parenthesis pairs for n > 1. As noted, i is of the form x (p), so p has exactly n parenthesis pairs. p cannot be new (which would give 0 parenthesis
pairs and was taken care of in the second base step), so p has to be of the form
p = move (p’, i’) — For expressions p’ of type POINT and i’ of type INTEGER.
implying (since i = x (p)) that by axiom A1, the value of i is
x (p’) + i’
So we will be able to determine the value of i if we can determine the value of both x (p’) and i’. Since p has n parenthesis pairs and p = move (p’, i’), both p’ and i’ have at most n – 1
parenthesis pairs. (This use of n – 1 is legitimate because we have two base steps, enabling us to assume n > 1.) As a consequence, both x (p’) and i’ have at most n parenthesis pairs, enabling us to
deduce their values, and hence the value of i, by the induction hypothesis.
Most proofs of sufficient completeness in my experience follow this style: induction on the number of parenthesis pairs (or the maximum nesting level).
I left until now the third component of a general ADT specification: preconditions. The need for preconditions arises because most practical specifications need some of their functions to be partial.
A partial function from X to Y is a function that may not yield a value for some elements of X. For example, the inverse function on real numbers, which yields 1 / a for x, is partial since it is
not defined for a = 0 (or, on a computer, for non-zero but very small a).
Assume that in our examples we only want to accept points that lie in the interval [-4, +4]:
We can simply model this property by turning move into a partial function. It was specified above as
move: POINT × INTEGER → POINT
The ordinary arrow → introduces a total (always defined) function. For a partial function we will use a crossed arrow ⇸, specifying the function as
move: POINT × INTEGER ⇸ POINT
Other functions remain unchanged. Partial functions cause trouble: for f in X ⇸ Y we can no longer cheerfully use f (x) if f is a partial function, even for x of the appropriate type X. We have to
make sure that x belongs to the domain of f, meaning the set of values for which f is defined. There is no way around it: if you want your specification to be meaningful and it uses partial
functions, you must specify explicitly the domain of each of them. Here is how to do it, in the case of move:
move (p: POINT; d: INTEGER) require |x (p) + d | < 5 — where |…| is absolute value
To adapt the definition (and proofs) of sufficient completeness to the possible presence of partial functions:
• We only need to consider (for the rule that axioms must yield the value of query expressions) well-formed expressions that satisfy the associated preconditions.
• The definition must, however, include the property that axioms always enable us to determine whether an expression satisfies the associated preconditions (normally a straightforward part of the
proof since preconditions are themselves query expressions).
Updating the preceding proof accordingly is not hard.
Back to requirements
The definition of sufficient completeness is of great help to assess the completeness of a requirements document. We must first regretfully note that for many teams today requirements stop at “use
cases” (scenarios) or “user stories”. Of course these are not requirements; they only describe individual cases and are to requirements what tests are to programs. They can serve to check
requirements, but do not suffice as requirements. I am assuming real requirements, which include descriptions of behavior (along with other elements such as environment properties and project
properties). To describe behaviors, you will define operations and their effects. Now we know what the old IEEE standard is telling us by stating that complete requirements should include
definition of the responses of the software to all realizable classes of input data in all realizable classes of situations
Whether or not we have taken the trouble to specify the ADTs, they are there in the background; our system’s operations reflect the commands, and the effects we can observe reflect the queries. To
make our specification complete, we should draw as much as possible of the (mental or explicit) matrix of possible effects of all commands on all queries. “As much as possible” because software
engineering is engineering and we will seldom be able to reach perfection. But the degree of fullness of the matrix tells us a lot (possible software metric here?) about how close our requirements
are to completeness.
I should note that there are other aspects to completeness of requirements. For example the work of Michael Jackson, Pamela Zave and Axel van Lamsweerde (more in some later article, with full
references) distinguishes between business goals, environment constraints and system properties, leading to a notion of completeness as how much the system properties meet the goals and obey the
constraints [4]. Sufficient completeness operates at the system level and, together with its theoretical basis, is one of those seminal concepts that every practicing software engineer or project
manager should master.
References and notes
[1] John V. Guttag, Jim J. Horning: The Algebraic Specification of Abstract Data Types, in Acta Informatica, vol. 10, no. 1, pages 27-52, 1978, available here from the Springer site. This is a
classic paper but I note that few people know it today; in Google Scholar I see over 700 citations but less than 100 of them in the past 8 years.
[2] IEEE: Recommended Practice for Software Requirements Specifications, IEEE Standard 830-1998, 1998. This standard is supposed to be obsolete and replaced by newer ones, more detailed and verbose,
but it remains the better reference: plain, modest and widely applied by the industry. It does need an update, but a good one.
[3] Bertrand Meyer, Object-Oriented Software Construction, 2nd edition, Prentice Hall, 1997. The discussion of sufficient completeness was in fact already there in the first edition from 1988.
[4] With thanks to Elisabetta Di Nitto from Politecnico di Milano for bringing up this notion of requirements completeness.
VN:F [1.9.10_1130]
VN:F [1.9.10_1130]
Are my requirements complete?,
You must be logged in to post a comment.
Recent Comments | {"url":"https://bertrandmeyer.com/2019/12/03/are-my-requirements-complete/","timestamp":"2024-11-14T02:16:16Z","content_type":"application/xhtml+xml","content_length":"100416","record_id":"<urn:uuid:8f1019b4-8e93-4c46-8f13-f008843e72cb>","cc-path":"CC-MAIN-2024-46/segments/1730477028516.72/warc/CC-MAIN-20241113235151-20241114025151-00078.warc.gz"} |
Andrews DWK (1991). “Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation.” Econometrica, 59, 817--858.
Andrews DWK & Monahan JC (1992). “An Improved Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimator.” Econometrica, 60, 953--966.
Lumley T & Heagerty P (1999). “Weighted Empirical Adaptive Variance Estimators for Correlated Data Regression.” Journal of the Royal Statistical Society B, 61, 459--477.
Newey WK & West KD (1987). “A Simple, Positive Semi-Definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix.” Econometrica, 55, 703--708.
Zeileis A (2004). “Econometric Computing with HC and HAC Covariance Matrix Estimators.” Journal of Statistical Software, 11(10), 1--17. tools:::Rd_expr_doi("10.18637/jss.v011.i10")
Zeileis A (2006). “Object-Oriented Computation of Sandwich Estimators.” Journal of Statistical Software, 16(9), 1--16. tools:::Rd_expr_doi("10.18637/jss.v016.i09") | {"url":"https://www.rdocumentation.org/packages/sandwich/versions/3.1-0/topics/vcovHAC","timestamp":"2024-11-06T10:47:44Z","content_type":"text/html","content_length":"82260","record_id":"<urn:uuid:625d84d9-6860-4b67-8e1a-925c9272350f>","cc-path":"CC-MAIN-2024-46/segments/1730477027928.77/warc/CC-MAIN-20241106100950-20241106130950-00021.warc.gz"} |
Multi-robot area patrol under frequency constraints
Patrolling involves generating patrol paths for mobile robots such that every point on the paths is repeatedly covered. This paper focuses on patrolling in closed areas, where every point in the area
is to be visited repeatedly by one or more robots. Previous work has often examined paths that allow for repeated coverage, but ignored the frequency in which points in the area are visited. In
contrast, we first present formal frequency-based optimization criteria used for evaluation of patrol algorithms. Then, we present a patrol algorithm that guarantees maximal uniform frequency, i.e.,
each point in the target area is covered at the same optimal frequency. This solution is based on finding a circular path that visits all points in the area, while taking into account terrain
directionality and velocity constraints. Robots are positioned uniformly along this path in minimal time, using a second algorithm. Moreover, the solution is guaranteed to be robust in the sense that
uniform frequency of the patrol is achieved as long as at least one robot works properly. We then present a set of algorithms for handling events along the patrol path. The algorithms differ in the
way they handle the event, as a function of the time constraints for handling them. However, all the algorithms handle events while maintaining the patrol path, and minimizing the disturbance to the
Dive into the research topics of 'Multi-robot area patrol under frequency constraints'. Together they form a unique fingerprint. | {"url":"https://cris.biu.ac.il/en/publications/multi-robot-area-patrol-under-frequency-constraints-5","timestamp":"2024-11-06T04:56:19Z","content_type":"text/html","content_length":"52909","record_id":"<urn:uuid:50c45117-5f24-4211-8c53-6a105ed8bf2f>","cc-path":"CC-MAIN-2024-46/segments/1730477027909.44/warc/CC-MAIN-20241106034659-20241106064659-00777.warc.gz"} |
A First Look At Fresnel Diffraction (Part 1)
Fresnel diffraction is the less well known version of diffraction and this is on account of it being more mathematically demanding than Fraunhofer diffraction - which I've already covered in several
instalments, e.g.
The Basics of Fraunhofer Diffraction & Its Applications (Pt. 1) (brane-space.blogspot.com)
We begin our introduction by noting the irony of this form, i.e. it is the easiest to observe but also requires much more complex mathematical theory to explain it. The latter aspect is because
Fraunhofer diffraction - dealing with light sources at a distance - treats plane waves, while Fresnel diffraction treats spherical waves, wavefronts.
Spherical wavefronts in Fresnel diffraction
By their very nature then - because of the geometry - one will enter a more difficult mathematical realm. Fortunately, because Fresnel diffraction was the first type to be observed, there was a
longer lead time to develop the math behind it.
How is it that Fresnel is easier to observe? Well, for one thing, one doesn't need lenses but can observe effects directly, such as shadows produced around edges. For example, consider the following:
An opaque object - say coin - placed in the path of a point light source will produce a shadow with a fairly well defined outline with the same shape as the object. (The edge is not absolutely sharp
when observed closely, however, but it seen to have alternating dark and light bands in the immediate vicinity of the edge. According to Fresnel, this is because in the regions beyond the limits of
the geometrical shadow secondary wavelets arrive with phase relations that destructively interfere with each other and produce practically complete darkness. In other regions where there is slight
reinforcement we observe lighter bands of shadow.
Central to Fresnel's approach to most diffraction problems are his "half period zones" whereby he found that a slightly divergent spherical wave will produce a point ahead of the wave and the
resulting paths could be quantified in terms of the wavelength l, e.g.
Here we have a spherical wave segment BCDE of monochromatic light traveling to the right to point P. Each point on the spherical segment can be thought of as an origin for secondary wavelets for
which the resultant is found to terminate at point P. The problem then becomes how to find the resultant effect. Fresnel's approach prescribed dividing the wave front into a series of concentric
"zones" as are visible in the image as something like circles on a target.
The specific technique then means drawing a series of circles around the point O. The distances from point O, measured along the arc are: s[ 1 , ]s[ 2 , ]s[ 3, ..... ]s[ n. ]They are such that each
successive circle is a half-wavelength farther from P. Therefore, if the distance OP = b, we would have: b + l /2, b + 2l /2, b + 3l /2, ........b + m l /2 and so on.
The areas A[m] of the rings (zones) between successive circles are roughly equal to each other which can be proven by reference to the diagram below:[ ]
Here a section of the wave spreads out from P' with radius a. If a circle of radius b is now drawn with center at P and tangent to the wave front at its pole O, the path P' QP is longer than the path
POP by the short segmented denoted by D . Then, quantifying:
D = s ^2 / 2a + s ^2 / 2b = s ^2 [(a + b)/ 2 ab] ^
Then the radii s[m] of the Fresnel zones are such that:[ ]
m l /2 = s[ m] ^2 [(a + b)/ 2 ab]
Then the area of any one zone is expressed:
A[ m(]D[)] = p (s[ m] - s[ m-1] ) ^2 = p l /2 {2 ab / (a + b)} =
p l ab/ (a + b)
To the approximation considered, the area is therefore independent of m . (A more exact computation would disclose that the area icreases only very slowly with m.)
Suggested Problems:
1) The innermost zone of a zone plate has a diameter 0.425mm.
(a)Find the focal length of the plate when it is used with parallel incident light of wavelength 4471 Å from a helium lamp.
(b) Find the first subsidiary focal length for the zone plate.
2) A zone plate is to be set up on an optical bench where it will be used as an enlarging lens. Its innermost zone will have a diameter of 0.2250 mm with monochromatic green light of wavelength 4800
Å to be used. If all enlargements are to be eightfold in diameter find the focal length f of the zone plate. | {"url":"https://brane-space.blogspot.com/2022/05/a-first-look-at-fresnel-diffraction.html","timestamp":"2024-11-09T07:53:25Z","content_type":"text/html","content_length":"133034","record_id":"<urn:uuid:8210e86e-73b4-468e-8ba0-09a99350bd30>","cc-path":"CC-MAIN-2024-46/segments/1730477028116.30/warc/CC-MAIN-20241109053958-20241109083958-00381.warc.gz"} |
Einstein's Equations
Describing How Mass Warps Spacetime
One of the central challenges of physics is — and has always been — to predict how things move. The earliest astronomers were really nothing more than astrologers, trying to discern when stars would
appear on the horizon, or where the Sun would be found at a certain date. Eventually, this turned into true, scientific astronomy, and physicists used their laws to predict how all sorts of bodies
moved through the heavens. Newton showed us that the same laws that described how planets move could also be used to predict more earth-bound things, such as how an apple falls from a tree. Modern
physicists are concerned with the motions of the tiniest particles in the atoms around us, and the motions of the heaviest objects in the heavens above.
We've mentioned that geometry gives us tools to understand the motion of particles when spacetime is curved. But it doesn't say anything about why spacetime should be curved. Einstein took the tools
of differential geometry, and showed us how and why spacetime curves. In doing this, he gave us very powerful tools to predict the motion of particles. To understand how these tools work will only
require a little review of how to keep track of points in geometry, and the Pythagorean Theorem.
Suppose you want to keep track of an astronaut who is somewhere along a single line, like in our examples from the section on Relativity. You could choose a particular point — which we will call the
origin — and measure how far the astronaut is from that point. If the astronaut is, for example, ten meters to the right of the origin, you might say that she is at the coordinate x=10. Ten meters to
the left, and you could call it x=-10. She could even be at a fractional coordinate like x=6.78.
Of course, coordinates are just numbers that we place at each point to label that point, and to keep track of what happens at each point. We can lay those numbers down in any way we want. We might,
for example, only put in one coordinate tick for every two meters. Then, if the astronaut is at a coordinate of x=5, she would still be 10 meters to the right of the origin. We say that there is a
factor of proportionality which is the real distance between coordinate ticks — two, in this case. Then, if we want the actual distance, we just multiply the coordinate x by the factor of
$$\text{distance in meters} = x \text{ coordinate} \times \text{meters per coordinate tick}$$
It's very important to remember that the real physical situation doesn't change, even if we change how we label the physical points.
Now this astronaut may want to keep track of another astronaut, but he's strayed off the coordinate axis she is on. So, she decides to create a new set of coordinates, using two dimensions to keep
track of him. She takes herself as the origin and constructs two axes — one in each of the two dimensions she needs. Then, to figure out what coordinates her fellow astronaut is at, she sees how far
along one axis she would need to go, then how far parallel to the other axis she would need to go. For example, our second astronaut might be six meters to the right, and eight meters up. His
coordinates would be x=6 and y=8. If he were eight feet down, his coordinates would be x=6, and y=-8. We can see this in the figure below.
But now, if our first astronaut wants to get to the second, she wouldn't want to go six meters over and eight meters up; she'd want to go straight. To know how far she has to go, we need the help of
an old theorem from high-school geometry.
Pythagoras's Theorem
Using this knowledge, it's pretty easy to figure out how far apart our two astronauts are. One leg of the triangle is just the x coordinate; the other leg is the y coordinate. So, the distance
between the two is given by
$$(\text{distance in meters})^2 = (x \text{ coordinate})^2 + (y \text{ coordinate})^2$$
If the coordinates measure meters, then he is 6 meters to the right and 8 meters up, so the Pythagorean Theorem tells us that he is 10 meters from the origin.
More generally, there could be a factor of proportionality to take into account, or even two — one factor for each dimension. In this case, we just have to incorporate those factors first to find the
real distance in each direction, then use the Pythagorean Theorem to get the real distance from the origin. The formula in this case is just a combination of the last two formulas we've seen:
$$(\text{distance in meters})^2 = &((x \text{ coordinate}) \times (\text{meters per } x \text{ coordinate tick}))^2 + \\&((y \text{ coordinate}) \times (\text{meters per } y \text{ coordinate tick}))
Basically, we've just dealt with any stretching that might happen to our grid. Of course, there's one more slight complication we'll need to deal with before we can understand Einstein's equations;
some times, coordinates can be skewed, as well as stretched.
Skewed Grids and The Law of Cosines
We have already seen that curved spaces can make things complicated. For example, it's not always clear how to make a perfect square grid, like the one we assumed gave us our 2-D coordinates above.
Some times, there's just no getting away from the fact coordinates might be skewed. Specifically, we might have a coordinate system where the y axis isn't perpendicular to the x axis. Instead, it
might be tilted over at some angle.
We can look at this example with our two astronauts. Say the y axis is tilted over, as we see below. In this case, we would have to go farther to the right to be “under” the astronaut because when we
go “up”, we have to go in the same direction as the skewed y axis. And, as a result, we would have to go farther “up” to get to him. To put some numbers to all this, say our axis is tilted by 15
degrees. Then, we'd actually have to go 8.14 meters to the right, and up 8.28 meters.
As before, we want to know how far apart the two astronauts — we want to know how long that dashed green line is. We'd like to use the Pythagorean Theorem, but that only works for right triangles —
triangles with one angle of 90 degrees. Fortunately, there's a more general version that will work even in this case. All it takes is one extra term in the formula. We know the length of two sides of
the triangle, and the angle between them. If we call that angle α, then the “Law of Cosines” is just like the Pythagorean theorem, except that we subtract an additional term.
Specifically, we take the normal Pythagorean Theorem, and subtract two times the length of one leg, times the length of the other leg, times the cosine of the angle between them. You might remember
the cosine function here from high-school math class, written as “cos”. It takes the angle, and gives back another number, as shown below:
When α is 90 degrees, the cosine is 0, so the extra term in the Law of Cosines drops away, and it reduces to the same thing as the Pythagorean Theorem. When α is less than 90 degrees, we see that the
extra term makes the side with length C smaller, which we would expect. Similarly, if α is greater than 90 degrees, the extra term makes C larger.
Now, we can apply this formula for finding the distance between the two astronauts when the coordinates are skewed by the angle α:
$$(\text{distance})^2 = (x \text{ coordinate})^2 + (y \text{ coordinate})^2 - 2 \times (x \text{ coordinate}) \times (y \text{ coordinate}) \times cos(\alpha)$$
In this case, we've already measured the two sides of the triangle to be 8.14 and 8.28 meters, and we know that the angle between them is 90 - 15 = 75 degrees. If we plug these numbers into the
formula, we find that the distance squared is 100 — so the distance is 10 meters, exactly as before.
This is an important point to make: the coordinates we used to measure everything changed, but the physical situation remained the same. In particular, the distance between the two astronauts didn't
change just because we skewed the coordinate grid. We could also change the coordinates in other way — by moving the origin, say, or rotating the coordinates, or any combination. But still, the
physical situation (distances, for example) wouldn't change.
The Metric
When laying down a grid for coordinates, we could also combine the stretch with the skew. In general, then, we would need a formula relating distance to coordinates like
$$(\text{distance in meters})^2 = &[(x \text{ coordinate}) \times (\text{meters per } x \text{ coordinate tick})]^2 \\&+ [(y \text{ coordinate}) \times (\text{meters per } y \text{ coordinate tick})]
^2 \\&- 2 \times [(x \text{ coordinate}) \times (\text{meters per } x \text{ coordinate tick})] \\&\times [(y \text{ coordinate}) \times (\text{meters per } y \text{ coordinate tick})] \times cos(\
Obviously, this is starting to get complicated — and tiring to write out. We can save time and effort by grouping some of the terms together and writing this same formula as
$$(\text{distance in meters})^2 = g_{xx} \times (x \text{ coordinate})^2 + g_{yy} \times (y \text{ coordinate})^2 + 2 \times g_{xy} \times (x \text{ coordinate}) \times (y \text{ coordinate})$$
That is, we group those big terms together, giving them new names. Specifically, we define
$$g_{xx} = (\text{meters per }x \text{ coordinate tick})^2$$
$$g_{yy} = (\text{meters per }y \text{ coordinate tick})^2$$
$$g_{xy} = - (\text{meters per }x \text{ coordinate tick}) \times (\text{meters per }y \text{ coordinate tick}) \times cos(\alpha)$$
These three numbers we've defined — \(g_{xx}\) , \(g_{yy}\) , and \(g_{xy}\) — are very important in physics. Together, they form the metric, which relates physical distances to whatever coordinates
we decide to use.
In general, the metric is just a little more complicated than the one we have shown here. First, we could be dealing with more than two dimensions. In three dimensions, we would add a z coordinate,
and we would need \(g_{zz}\) , \(g_{xz}\) , and \(g_{yz}\) for the metric. We could even be working with time by adding a t coordinate. With all four dimensions, the metric involves the numbers
\(g_{xx}\) , \(g_{xy}\) , \(g_{xz}\) , \(g_{xt}\) , \(g_{yy}\) , \(g_{yz}\) , \(g_{yt}\) , \(g_{zz}\) , \(g_{zt}\) , and \(g_{tt}\) .
More importantly, the metric could change from place to place. If our coordinates were warped, we might have a grid that looks like our straight grid in one place, but is bent over like the second
grid in another place.
It is possible to draw warped grids on a flat piece of paper (or on a flat screen, like we showed above). In this sense, we would get a warped metric in a space that is actually flat. On the other
hand, it is impossible to draw a nice, straight grid in a space that is really curved. By very carefully examining exactly how the metric changes from point to point, we can tell if we've just drawn
curvy coordinates in a flat space, or if we've drawn our coordinates in a truly curvy space.
Now we are getting very close to Einstein's Equations. Einstein had these warped pieces of spacetime that he needed to describe in some quantifiable way. He saw that a careful examination of the
metric — and how it changes from point to point — could describe the true geometry of any spacetime, whether curved or flat, so he used it for his theory. Einstein combined certain numbers describing
the metric's changes from place to place into what is now called the Einstein tensor. Just like the metric, the Einstein tensor is a set of numbers. For four-dimensional spacetime, we have
\(G_{xx}\) , \(G_{xy}\) , \(G_{xz}\) , \(G_{xt}\) , \(G_{yy}\) , \(G_{yz}\) , \(G_{yt}\) , \(G_{zz}\) , \(G_{zt}\) , and \(G_{tt}\) .
These numbers describe what is physically interesting about the geometry of spacetime. Understanding the geometry of spacetime allows us to see how particles will move, bringing us one step closer to
the ultimate goal of physics. There is just one more ingredient left.
Energy, Matter, and the Curvature of Spacetime
We've gotten a sneak preview of Einstein's equations before: \(G = 8πT\). The \(G\) on the left stands for the different numbers in the Einstein tensor. But, the Einstein tensor represents the
geometry of spacetime, so this is what the left side really represents. We also know that the curvature of spacetime is caused by matter, so the \(T\) on the right must represent matter.
Just like \(G\), the symbol \(T\) stands for a set of numbers:
\(T_{xx}\) , \(T_{xy}\) , \(T_{xz}\) , \(T_{xt}\) , \(T_{yy}\) , \(T_{yz}\) , \(T_{yt}\) , \(T_{zz}\) , \(T_{zt}\) , and \(T_{tt}\) .
These numbers measure different things about matter. Together, they make up the Stress-Energy Tensor. Each component of this tensor has a slightly different physical interpretation:
Pieces of the Stress-Energy Tensor
\(T_{tt}\) Measures how much mass there is at a point — how much density
\(T_{xt}\) , \(T_{yt}\) and \(T_{zt}\) Measures how fast the matter is moving — its momentum
\(T_{xx}\) , \(T_{yy}\) and \(T_{zz}\) Measures the pressure in each of the three directions
\(T_{xy}\) , \(T_{xz}\) and \(T_{yz}\) Measures the stresses in the matter
As we see from the table, things like stress, pressure, and momentum come into Einstein's equations. That is, stress, pressure, and momentum all have some effect on the warping of spacetime. This is
related to Einstein's most famous equation, \(E=mc^2\), which says that energy has mass.
Warped spacetime affects how matter moves by changing its geodesics. On the other hand, Einstein's equations show us how matter — and its movement and pressures — affect the shape of spacetime. Thus,
Einstein solved the fundamental problem in Physics — in principle. Of course, solving something in principle is very different from solving in practice. Finding real solutions has proven to be very
difficult. Often, it is a job best left to computers. | {"url":"https://www.black-holes.org/the-science-numerical-relativity/numerical-relativity/einstein-s-equations","timestamp":"2024-11-14T03:14:06Z","content_type":"text/html","content_length":"72552","record_id":"<urn:uuid:d25425ac-6e0a-4223-aec1-3735462f59a9>","cc-path":"CC-MAIN-2024-46/segments/1730477028526.56/warc/CC-MAIN-20241114031054-20241114061054-00899.warc.gz"} |
Fuel consumption of a wheel loader with power reflux hydraulic transmission system
The world is facing a limited supply of fossil fuel resources and stringent environmental constraints. Therefore, it is very important to develop advanced technologies to improve vehicle fuel
economy, especially for construction vehicles, which have large engine displacements and poor emission characteristics. The majority of these vehicles use hydraulic mechanical transmission in the
power train in order to improve maneuverability. However, a key issue on the hydraulic mechanical transmission is the low-efficiency torque converter. Focusing on this issue, we proposed the power
reflux hydraulic transmission system (PRHTS), which is a new continuously variable transmission system. The PRHTS can improve the overall transmission efficiency of the power train by splitting the
engine power into mechanical and hydraulic power. Therefore, the PRHTS is a valid solution to reduce the fuel consumption and subsequently decrease emissions from construction vehicles. In order to
quantitatively study the effect of using the PRHTS on improving the fuel economy for construction vehicles, a wheel loader coupled with the PRHTS is modeled, and numerical simulation is conducted
under the wheel loader driving condition. The simulation results show that the total fuel consumption of the wheel loader coupled with PRHTS is reduced by 3.39 % compared with that of the original
wheel loader.
1. Introduction
Construction vehicles (wheel loaders, tractors, bulldozers, etc.) are widely used in various fields of infrastructure construction, particularly in architecture, civil engineering, and bridge
engineering. Construction vehicles play an irreplaceable role in improving the operating efficiency and quality of projects and in reducing the labor and total project cost. However, these vehicles
consume excessive fuel. With the rising attention on energy conservation and environmental protection, finding a method of reducing the fuel consumption and emission from construction vehicles is
necessary. Many researchers have focused on the different parts of construction vehicles to improve fuel economy. An important part is the power train, which has a significant influence on vehicle
fuel consumption.
The power train directly affects the vehicle’s power performance, fuel consumption, exhaust emission, etc. [1, 2]. The power train requirement for construction vehicles is relatively stringent
because of their severe working conditions and changing loads. In order to enhance adaptability to changing loads, many construction vehicles currently use an automatic transmission in the power
train. The automatic transmission consists mainly of a torque converter and a power shift transmission [3]. The torque converter is the most important element of the automatic transmission. In the
torque converter, the automatic transmission fluid transmits power and allows the vehicle to decouple the engine from the wheels. And the engine can work in the best economic zone by automatic
transmission’s continuously variable transmission (CVT) [4]. Moreover, the torque fluctuation of an engine is reduced by the torsional damping characteristics of the torque converter; therefore, an
automatic transmission can also prolong the service life of the engine and transmission [5-8]. In addition, the torque converter will improve the traction characteristic of construction vehicles by
automatically changing the driving force and speed with changing loads. For construction vehicles with drastic load changes, the torsional damping characteristics and adaptability of the torque
converter are very important. With these features, the automatic transmission has gained widespread use in most construction vehicles, especially for wheel loaders.
However, the automatic transmission has an obvious shortcoming-it has a lower efficiency compared to manual transmission. This is due to the two stages of energy conversion in the torque converter.
The first energy conversion is from mechanical energy of the engine into hydraulic energy of the torque converter. The second is from hydraulic energy of the torque converter into kinetic energy of
the gearbox. For this reason, the efficiency of the torque converter is lower than gears. The overall transmission efficiencies of manual and automatic transmissions are 96.7 % and 86.7 %,
respectively [9]. Therefore, improving the efficiency of the automatic transmission has vital significance.
In the last few decades, hybrid electric technology has received attention for improving fuel economy. Many studies have proposed various electric hybrid power trains, and the automotive industry has
developed various models for light duty vehicles [10]. However, because of increasing costs, the extension of hybrid electric technology to construction vehicles has been hampered.
An alternative and cheaper solution to improve the fuel economy of construction vehicles is the power split transmission system. This consists of a variator element (chain belt, torque converter,
hydrostatic transmission, electric converter, etc.), a planetary gear train, and a fixed ratio mechanism [11]. The power split transmission system will improve the efficiency by splitting the flow of
engine power into mechanical and variator power. In the past several years, many studies on the power split transmission system have been conducted. Mantriota [12] had been designing and testing the
power split CVT system and infinitely variable transmission system. The results showed that the power split transmission system had a better efficiency compared with simple CVTs. Volpe et al. [13]
developed an optimization procedure in designing infinitely variable transmission to increase its mechanical efficiency. The focus of their study was on input and output coupled architectures.
Linares et al. [14] investigated the design parameters of the power split CVT system, which used three active shafts. They established a formula that linked the mentioned parameters together.
Bottiglione and Mantriota [15] designed a power split transmission system as a mechanical kinetic energy recovery system, where the flywheel power can flow to the wheels, and vice versa. Gomà Ayats
et al. [16] studied the power flow characteristics of a transmission comprised of a variator element, planetary gear train, and fixed ratio mechanism and presented a methodology to find an expression
of the power being transmitted through a particular branch of the power split transmission system. Dhand and Pullen [17] used a power split transmission system for flywheel energy storage system in
vehicular applications. In addition, they discussed the kinematics of the power split transmission system, which was used to connect the flywheel to the power train. Delkhosh and Foumani [18] studied
the vehicle fuel consumption in four driving cycles, and then optimized the added fixed ratio mechanisms. All the research mentioned above used the chain belt as the variator element. On the other
hand, some other researchers focused on the hydrostatic transmission as the variator element. Savaresi et al. [19] proposed a power split hydrostatic CVT, which was used for a modern agricultural
tractor, and also designed its control system. Carl et al. [20] investigated the advantages and disadvantages of four power split transmission systems, which used a hydrostatic transmission. Kumar et
al. [21] used the hydrostatic transmission for a heavy wheel loader with a flywheel energy storage device. In addition, the energy consumption of both a hybrid and a non-hybrid wheel loader had been
investigated. Kumar and Ivantysynova [22] developed a power management strategy to minimize fuel consumption of hydraulic hybrids. Pettersson and Krus [23] presented an automated design process based
on optimization that was suitable for complex hydromechanical transmissions.
Although many researchers have studied the power split transmission system, no study has investigated the torque converter. The automatic transmission has gained widespread use in most construction
vehicles owing to the torque converter’s easy-to-drive ability, torque amplification, and torsional damping characteristics. Therefore, it is extremely essential to propose a power split transmission
system that includes the torque converter.
In this study, we propose a power reflux hydraulic transmission system (PRHTS) using a torque converter that is fit for construction vehicles. Next, the PRHTS’s basic characteristics such as the
speed ratio, efficiency, and torque ratio are analyzed. Finally, the fuel consumptions of a wheel loader equipped with two different transmission systems – the traditional torque converter and PRHTS
– are compared under typical driving conditions.
2. PRHTS
2.1. The basic structure and operating principle of the PRHTS
Since the variator element (chain belt, torque converter, hydrostatic transmission, electric converter, etc.) has a low efficiency, a power split transmission system will improve the efficiency by
dividing the system’s input power into two parts. One part of the input power is transmitted by the high efficiency gears, while the other part is transmitted by the low efficiency variator element.
Since the power transmitted by the variator element will decrease, the transmission system efficiency will be improved.
The PRHTS is a type of power split transmission system [24-27]. The torque converter, which has excellent shock absorption and cushioning capability, is the main component of the PRHTS. Another
important component is the planetary gear train, which consists of the sun gear, ring gear, planet gears, and carrier as shown in Fig. 1. The planetary gear train is commonly used by locking one
component – i.e., the sun gear, ring gear, or carrier – while the other two components – the input shaft and the output shaft – are in motion. However, the planetary gear train of the PRHTS has two
degrees of freedom and is used as a coupling device. The rotational speed of the third moving component is dependent on the rotational speed of the other two moving components in the planetary gear
Fig. 1Diagram of the planetary gear train
Fig. 2 shows the schematic of the PRHTS. A major characteristic of the PRHTS is the torque converter with the reflux power path, comprising the turbine that is connected to the input shaft of the
transmission system and the pump that is connected to the sun gear of the planetary gear train. In addition, the torque converter has two stators, which is another unique characteristic of the PRHTS.
An important characteristic of the double stator torque converter is the wide high efficiency range of more than 80 %, because the working condition consists of two converter conditions and a
coupling condition. It can amplify the range of transmission ratio of the PRHTS in high efficiency range by using the double stator torque converter.
The power flow of the PRHTS is shown in Fig. 2 and is described as follows. First, the power of the engine enters the input shaft of the PRHTS (at the left side of Fig. 2). The power is then
transferred into the carrier of the planetary gear train. Most of the power is transmitted into the ring gear (at the right side of Fig. 2), which is the power split characteristics of the planetary
gear train. The remainder of the power, called reflux power, enters into the pump of the torque converter by the sun gear. Then, the reflux power goes into the input shaft of the PRHTS by torque
amplification of the torque converter. The reflux power joins with the output power of engine, and both enter into the carrier. Because of the special reflux power characteristics, the PRHTS has a
continuous variable ratio. In other words, the output shaft of the transmission system has a continuous variable speed by means of the torque converter, while the speed of the engine is constant.
Therefore, the PRHTS is a CVT system.
Fig. 2Schematic and power flow of the PRHTS
2.2. The basic characteristics of the PRHTS
2.2.1. The speed ratio characteristic of the PRHTS
The simplified power flow of the PRHTS is shown in Fig. 3.
Fig. 3Simplified power flow of the PRHTS: 1 – input power of the system; 2 – input power of the carrier; 3– input power of the torque converter; 4 – output power of the torque converter; 5 – output
power of the system. The arrows represent the direction of power flow
The rotational speed equation of the planetary gear train is as follows:
It is assumed that the direction of the rotational speed of the input shaft is the positive direction.
The main speed ratio relationships of the PRHTS are given in following equations:
Using Eqs. (1-7), it is obtained that the relationship between ${i}_{PR}$ and ${i}_{tc}$, as follows:
In the above formula, it is obvious that the PRHTS speed ratio increases with the torque converter speed ratio, but it is not a linear function. Thus, the PRHTS speed ratio is high when the torque
converter speed ratio is at high efficiency range.
2.2.2. Efficiency characteristic of the two-degree-of-freedom planetary gear train
The planetary gear train is considered as an important component of the PRHTS because its efficiency affects the PRHTS; therefore, a mechanical efficiency analysis is a required step to design the
PRHTS. The planetary gear train is commonly used in the reducer by locking one component: the sun gear, ring gear, or carrier. In this case, the planetary gear train has one degree of freedom.
However, the planetary gear train of the PRHTS has two degrees of freedom. Thus, its efficiency analysis is more complicated, and it has its own characteristics compared to the one-degree-of-freedom
planetary gear train. The efficiency of the two-degree-of-freedom planetary gear train is determined by several factors such as the number of gears, type of planetary gear train, type of bearings,
etc. Some researchers reported formulas of efficiency analysis for the two-degree-of-freedom planetary gear trains [28].
In this study, the efficiency of the two-degree-of-freedom planetary gear train will be analyzed by the methodology in the said researches.
The power flow of the planetary gear train in the PRHTS is shown in Fig. 4. In the figure, $P$ denotes the power, while $T$ denotes the torque.
The rotational speed equation of the planetary gear train in Eq. (1) can be transformed as follows:
For the two-degree-of-freedom planetary gear train, the mechanical efficiency is:
${\eta }_{pgt}=\frac{{P}_{r}+{P}_{s}}{{P}_{c}}.$
Fig. 4Power flow of the planetary gear train in the PRHTS
For the two-degree-of-freedom planetary gear train, the power flow formula is:
${P}_{c}={T}_{c}{n}_{c}={T}_{c}\left({n}_{r,c-s}^{c}+{n}_{s,c-r}^{c}\right)=\frac{{T}_{s}{n}_{s}}{{\eta }_{r,c-s}}+\frac{{T}_{r}{n}_{r}}{{\eta }_{s,c-r}}.$
Using Eqs. (4-6), the mechanical efficiency of planetary gear train in the PRHTS is obtained:
${\eta }_{pgt}=\frac{{n}_{s}}{{n}_{c}\left(1+a\right)}{\eta }_{r,c-s}+\frac{a{n}_{r}}{{n}_{c}\left(1+a\right)}{\eta }_{s,c-r}.$
According to Eq. (12), the mechanical efficiency of planetary gear train is not only dependent on the rotational speed of the sun gear, ring gear, and carrier, but also on the mechanical efficiency
of the one-degree-of-freedom planetary gear train when the ring gear or sun gear is fixed. Therefore, it is necessary to calculate ${\eta }_{s,c-r}$ and ${\eta }_{r,c-s}$. According to research [19],
${\eta }_{s,c-r}$ and ${\eta }_{r,c-s}$ is the function of ${\eta }_{c,s-r}$ which is the mechanical efficiency of the one degree of freedom planetary gear train when the carrier is held fixed. The
formulas are as follows:
${\eta }_{s,c-r}=\frac{a-1}{a-{\eta }_{c,s-r}}{\eta }_{c,s-r},$
${\eta }_{r,c-s}=\frac{a+1}{a{\eta }_{c,s-r}+1}{\eta }_{c,s-r}.$
Considering calculation simplicity and operation practicability, ${\eta }_{c,s-r}$ is assumed to be constant, which is 0.985.
2.2.3. Efficiency characteristic of the two-degree-of-freedom planetary gear train
For the PRHTS, the torque characteristics equation of the planetary gear train is:
${T}_{s}{\eta }_{r,c-s}=\frac{{T}_{r}}{a}{\eta }_{s,c-r}=\frac{{T}_{c}}{-\left(1+a\right)}.$
It is assumed that the direction of the torque acting on the planetary gear train is the positive direction. Then， the relationships among the torque in the PRHTS are obtained according to the
transmission relationships of the system, as follows:
${T}_{3}{\eta }_{tc}={T}_{4}{i}_{tc},$
Paying special attention to the direction of the torque, we can see that ${T}_{3}$ and ${T}_{s}$ are equal and opposite in the hydraulic transmission system with reflux power, therefore, ${T}_{3}=-
{T}_{s}$. Similarly, ${T}_{5}$ and ${T}_{r}$ are equal and opposite, therefore, ${T}_{5}=-{T}_{r}$.
Using Eqs. (15-20), the relationship between ${K}_{PR}$ and ${i}_{tc}$ is obtained as:
${K}_{PR}=\frac{{T}_{5}}{{T}_{1}}=\frac{a{i}_{tc}{\eta }_{r,c-s}}{\left(1+a\right){i}_{tc}{\eta }_{r,c-s}{\eta }_{s,c-r}-{\eta }_{tc}{\eta }_{s,c-r}}.$
In order to get a better understanding of the PRHTS, the relationship between the torque ratio of the PRHTS and speed ratio of the PRHTS should be obtained. Using Eqs. (8) and (21), the relationship
between ${K}_{PR}$ and ${i}_{PR}$ is obtained as follows:
$KPR=\frac{-a{\eta }_{r,c-s}}{\left(1+a-aiPR\right){\eta }_{tc}{\eta }_{s,c-r}-\left(1+a\right){\eta }_{r,c-s}{\eta }_{s,c-r}}.$
Again, using Eqs. (8) and (21), the relationship between ${\eta }_{PR}$ and ${i}_{tc}$ is obtained as:
${\eta }_{PR}={i}_{PR}{K}_{PR}=\frac{\left[\left(1+a\right){i}_{tc}-1\right]{\eta }_{r,c-s}}{\left(1+a\right){i}_{tc}{\eta }_{r,c-s}{\eta }_{s,c-r}-{\eta }_{tc}{\eta }_{s,c-r}}.$
Using Eqs. (8) and (23), the relationship between ${\eta }_{PR}$ and ${i}_{PR}$ is:
${\eta }_{PR}=\frac{-a{i}_{PR}{\eta }_{r,c-s}}{\left({i}_{PR}+a-a{i}_{PR}\right){\eta }_{tc}{\eta }_{s,c-r}-\left(1+a\right){\eta }_{r,c-s}{\eta }_{s,c-r}}.$
2.2.4. Efficiency characteristic of the two-degree-of-freedom planetary gear train
In the PRHTS, the variator element is the torque converter, which has two stators. Fig. 5 shows the efficiency characteristics of the double stator torque converter [24]. It can be seen that the
double stator torque converter maintains high efficiency over a wide range of speed ratios, which can amplify the transmission ratio range of the PRHTS in the high efficiency range. Using Eq. (22)
and the efficiency characteristics of the torque converter, the torque ratio characteristics of the PRHTS are obtained (shown in Fig. 6). In the same way, the efficiency characteristics of the PRHTS
can be obtained (shown in Fig. 7).
Fig. 5The efficiency characteristics of the double stator torque converter
Fig. 6The torque ratio characteristics of the PRHTS
Fig. 7The efficiency characteristics of the PRHTS
As observed in Fig. 7, the efficiency of the PRHTS is less than the torque converter at low speed ratio, but it is higher in the common working condition. Therefore, the efficiency of the PRHTS is
higher than the torque converter in most working conditions of construction vehicles. Subsequently, construction vehicles coupled with PRHTS will have an improved fuel economy.
3. Wheel loader simulation
3.1. Wheel loader simulation
In the past decade, dynamic simulation has become an important part in vehicle design and development stages. A new technology can be examined without expensive measurements and with reduced time by
simulation. In order to quantitatively study the effect of using the PRHTS on improving the fuel economy of construction vehicles, a wheel loader coupled with PRHTS is modeled and a numerical
simulation is conducted under the wheel loader driving condition.
A wheel loader is a type of construction machinery characterized by quick and accurate movements. Wheel loaders are widely used in infrastructure construction such as transportation, water
conservation, and electric power projects. Wheel loaders are used mainly for uploading materials into trucks, pipe laying, clearing rubble, and digging. In construction areas, they are also used to
transport building materials (such as bricks, pipe, metal bars, and digging tools) over short distances. Wheel loaders are also used for snow removal, using their bucket as a snow basket but usually
by using a snow plow attachment. They clear snow from streets, highways, and parking lots. They sometimes load snow into dump trucks for transport. The overall structure of a wheel loader is shown in
Fig. 8. The wheel loader is used as the reference vehicle for the simulation work. Fig. 8 and Table 1 show the wheel loader dimensions and main characteristics. It can be seen that the rated power of
internal combustion engine is 58 kW. In addition, the wheel loader has two forward gears; the forward gear Ⅱ is used to travel between work sites.
Table 1Main characteristics of the wheel loader
Symbol Quantity Value
$L×W×H$ Length × Width × Height 5878×2140×2920 mm
$B$ Wheelbase 2260 mm
${P}_{eng}$ Rated power 58 kW
${V}_{eng}$ Engine displacement 4214 ml
${m}_{load}$ Rated load 2000 kg
${V}_{bucket}$ Bucket capacity 1.2 m^3
${r}_{roll}$ Wheel rolling radius 0.53 m
$m$ Vehicle mass 6480 kg
$F$ Maximum tractive force 56 kN
${A}_{f}$ Frontal area 3.5 m^2
${C}_{d}$ Air resistance coefficient 0.3
${i}_{f1}$ Speed ratio of forward gear I 2.5
${i}_{f2}$ Speed ratio of forward gear Ⅱ 1.2
${i}_{0}$ Speed ratio of final drive 8.3
Fig. 8Wheel loader dimensions
3.2. Transmission layout
The layout of PRHTS for the wheel loader is shown in Fig. 9. In the figure, the dash-dot lines are used to highlight the PRHTS, while the dashed lines are used to indicate the main sensor and command
Fig. 9Layout of PRHTS for the wheel loader
3.3. Transmission modeling of the wheel loader
The mechanical transmission and PRHTS of the wheel loader, as well as the whole control system, are modeled and simulated using LMS Imagin.Lab AMESim commercial software. The transmission modeling of
the wheel loader is synthetically described as follows. The pilot controller unit exports the acceleration/brake signal on the basis of the wheel loader velocity and driving condition. The engine
control unit exports the engine control signal on the basis of the engine rotational speed and acceleration/brake signal. The transmission control unit exports shift signal on the basis of the wheel
loader velocity, acceleration/brake signal, and engine rotational speed. The driving axle will brake on the basis of the brake signal. In order to obtain a better comparison, the same control
strategy is used for the original wheel loader and the wheel loader coupled with PRHTS.
The engine, which is the most important element, is modeled on the basis of the engine map from steady-state experiments. In addition, the engine torque is a function of the accelerator position and
the rotational speed in the transmission modeling of the wheel loader. The fuel consumption is calculated on the basis of the load and rotational speed of the engine. The engine map is described in
Fig. 10. It can be seen that the minimum fuel consumption rate is 220 g/(kW·h), and the maximum engine torque is obtained between 2000 rpm and 2500 rpm.
3.4. Driving condition of the wheel loader
In this study, the driving condition of the wheel loader consists of two parts [21]. The first part is the low speed work cycle, which is shown in Fig. 11. The low speed cycle is a simulation when
the wheel loader travels between a dirt pile loading point and a dump truck unloading point. The maximum wheel loader velocity is 11 km/h. A complete cycle will take approximately 60 s and is
repeated 20 times in the driving condition.
Fig. 11Wheel loader driving condition in the first part
The second part of the driving condition is the high speed part, which is shown in Fig. 12. The high speed part is a simulation when the wheel loader travels between work sites, and it is the end of
the driving condition of the wheel loader. It can be seen that the maximum wheel loader velocity is 30 km/h in Fig. 12. The second part will last 123 s, and the approximate distance traveled is 1 km.
Fig. 12Wheel loader driving condition in the second part
In order to quantitatively compare the fuel consumption of the original wheel loader and the wheel loader coupled with PRHTS, both wheel loaders have been simulated using the mentioned driving
conditions. The fuel consumption simulation results of the two wheel loaders are shown in Fig. 13. The solid line represents the fuel consumption of the wheel loader coupled with PRHTS, while the
dashed line represents the fuel consumption of the original wheel loader. It can be seen that the fuel consumption of the wheel loader is reduced by 3.39 % using PRHTS. Therefore, the PRHTS is an
effective solution to reduce the fuel consumption and emission from construction vehicles.
Fig. 13The fuel consumption of the original wheel loader and the wheel loader coupled with PRHTS
4. Conclusions
1) The PRHTS-a new CVT system-is proposed to improve the efficiency of the torque converter in construction vehicles. The basic characteristics of the PRHTS such as the speed ratio, efficiency, and
torque are analyzed by expounding its basic structure and operational principle. The basic characteristics are then obtained by numerical calculation.
2) The mechanical transmission and the PRHTS of the wheel loader, as well as the whole control system, are modeled and simulated using LMS Imagin.Lab AMESim commercial software. In order to obtain a
better comparison, the same control strategy is used for the original wheel loader and the wheel loader coupled with PRHTS. The control system is based on the acceleration/brake signal, engine
rotational speed signal, and wheel loader velocity signal.
3) The fuel consumptions of the wheel loader equipped with two different transmission systems, namely, the traditional torque converter and PRHTS are compared under the driving condition. The
simulation results show that the fuel consumption of the wheel loader coupled with PRHTS is reduced by 3.39 %, compared with that of the original wheel loader. Therefore, the wheel loader coupled
with PRHTS can effectively enhance transmission efficiency and fuel economy.
• C. Li, F. Meng, J. Xi, and Y. Zhai, “Starting shift control of heavy-duty automatic transmissions based on the optimal trajectory of turbine speed,” Mechanical Systems and Signal Processing, Vol.
126, pp. 490–504, Jul. 2019, https://doi.org/10.1016/j.ymssp.2019.02.030
• Z. Zhao, J. Chen, X. Li, and D. Lei, “Downshift decision and process optimal control of dual clutch transmission for hybrid electric vehicles under rapid braking condition,” Mechanical Systems
and Signal Processing, Vol. 116, pp. 943–962, Feb. 2019, https://doi.org/10.1016/j.ymssp.2018.07.012
• S. M. Park, T. W. Park, S. H. Lee, S. W. Han, and S. K. Kwon, “Analytical study to estimate the performance of the Power Shift Drive (PSD) Axle for a forklift,” International Journal of
Automotive Technology, Vol. 11, No. 1, pp. 49–56, Feb. 2010, https://doi.org/10.1007/s12239-010-0007-3
• F. Meng, G. Tao, and H. Chen, “Smooth shift control of an automatic transmission for heavy-duty vehicles,” Neurocomputing, Vol. 159, pp. 197–206, Jul. 2015, https://doi.org/10.1016/
• H. Chen and X. Chen, “A new methodology for multistage multispeed planetary transmission design based on geometry,” Journal of Mechanical Design, Vol. 143, No. 11, p. 143, Nov. 2021, https://
• Z. Li and J. Sandhu, “Transmission torque converter arc spring damper dynamic characteristics for driveline torsional vibration evaluation,” SAE International Journal of Passenger Cars –
Mechanical Systems, Vol. 6, No. 1, pp. 477–482, Apr. 2013, https://doi.org/10.4271/2013-01-1483
• X. Liu and D. Sun, “An improved design of power-cycling hydrodynamic mechanical transmission,” Journal of Mechanical Science and Technology, Vol. 34, No. 8, pp. 3165–3179, Aug. 2020, https://
• D. Robinette, M. Grimmer, and R. Beikmann, “Dynamic torque characteristics of the hydrodynamic torque converter,” in SAE International Journal of Passenger Cars – Mechanical Systems, Vol. 4, No.
2, pp. 1023–1032, May 2011.
• I. Arango and S. Muñoz Alzate, “Numerical design method for CVT supported in standard variable speed rubber V-belts,” Applied Sciences, Vol. 10, No. 18, p. 6238, Sep. 2020, https://doi.org/
• K. Çağatay Bayindir et al., “A comprehensive overview of hybrid electric vehicle: Powertrain configurations, powertrain control techniques and electronic control units,” Energy Conversion and
Management, Vol. 52, No. 2, pp. 1305–1313, Feb. 2011, https://doi.org/10.1016/j.enconman.2010.09.028
• H.-S. Yan and L.-C. Hsieh, “Maximum mechanical efficiency of infinitely variable transmissions,” Mechanism and Machine Theory, Vol. 29, No. 5, pp. 777–784, Jul. 1994, https://doi.org/10.1016/
• G. Mantriota, “Power split continuously variable transmission systems with high efficiency,” Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering,
Vol. 215, No. 3, pp. 357–358, Mar. 2001, https://doi.org/10.1243/0954407011525692
• S. S. Volpe, G. Carbone, M. Napolitano, and E. Sedoni, “Design optimization of input and output coupled power split infinitely variable transmissions,” Journal of Mechanical Design, Vol. 131, No.
11, p. 11100, Nov. 2009, https://doi.org/10.1115/1.3179145
• P. Linares, V. Méndez, and H. Catalán, “Design parameters for continuously variable power-split transmissions using planetaries with 3 active shafts,” Journal of Terramechanics, Vol. 47, No. 5,
pp. 323–335, Oct. 2010, https://doi.org/10.1016/j.jterra.2010.04.004
• F. Bottiglione and G. Mantriota, “Effect of the ratio spread of CVU in automotive kinetic energy recovery systems,” Journal of Mechanical Design, Vol. 135, No. 6, p. 06100, Jun. 2013, https://
• J. R. Gomà Ayats, J. Vivancos Calvet, J. Minguella Canela, U. Diego-Ayala, and F. Fenollosa Artes, “Power transmitted through a particular branch in mechanisms comprising planetary gear trains
and other fixed or variable transmissions,” Mechanism and Machine Theory, Vol. 46, No. 11, pp. 1744–1754, Nov. 2011, https://doi.org/10.1016/j.mechmachtheory.2011.06.005
• A. Dhand and K. Pullen, “Analysis of continuously variable transmission for flywheel energy storage systems in vehicular application,” Proceedings of the Institution of Mechanical Engineers, Part
C: Journal of Mechanical Engineering Science, Vol. 229, No. 2, pp. 273–290, Feb. 2015, https://doi.org/10.1177/0954406214533096
• M. Delkhosh and M. Saadat Foumani, “Introduction and optimization of a power split continuously variable transmission including several fixed ratio mechanisms,” Scientia Iranica, Vol. 22, No. 1,
pp. 226–234, Feb. 2015.
• S. M. Savaresi, F. L. Taroni, F. Previdi, and S. Bittanti, “Control system design on a power-split CVT for high-power agricultural tractors,” IEEE/ASME Transactions on Mechatronics, Vol. 9, No.
3, pp. 569–579, Sep. 2004, https://doi.org/10.1109/tmech.2004.835334
• B. Carl, M. Ivantysynova, and K. Williams, “Comparison of operational characteristics in power split continuously variable transmissions,” in SAE 2006 Commercial Vehicle Engineering Congress and
Exhibition, Oct. 2006, https://doi.org/10.4271/2006-01-3468
• R. Kumar, M. Ivantysynova, and K. Williams, “Study of energetic characteristics in power split drives for on highway trucks and wheel loaders,” in SAE 2007 Commercial Vehicle Engineering Congress
and Exhibition, Oct. 2007, https://doi.org/10.4271/2007-01-4193
• R. Kumar and M. Ivantysynova, “An instantaneous optimization based power management strategy to reduce fuel consumption in hydraulic hybrids,” International Journal of Fluid Power, Vol. 12, No.
2, pp. 15–25, Jan. 2011, https://doi.org/10.1080/14399776.2011.10781027
• K. Pettersson and P. Krus, “Design optimization of complex hydromechanical transmissions,” Journal of Mechanical Design, Vol. 135, No. 9, Sep. 2013, https://doi.org/10.1115/1.4024732
• H. Wang, D. Y. Sun, and D. T. Qin, “A new continuously variable transmission system applied to transmission system of the roadheader’s cutting unit,” Proceedings of the Institution of Mechanical
Engineers Part C-Journal of Mechanical Engineering Science, Vol. 231, No. 19, pp. 3590–3600, 2017, https://doi.org/10.1177/095440621664940
• H. Wang and D. Sun, “Theory and application on power-cycling variable transmission system,” Journal of Mechanical Design, Vol. 139, No. 2, Feb. 2017, https://doi.org/10.1115/1.4035055
• Y. You, D. Sun, and D. Qin, “Shift strategy of a new continuously variable transmission based wheel loader,” Mechanism and Machine Theory, Vol. 130, pp. 313–329, Dec. 2018, https://doi.org/
• B. Li, D. Sun, M. Hu, and J. Liu, “Automatic starting control of tractor with a novel power-shift transmission,” Mechanism and Machine Theory, Vol. 131, pp. 75–91, Jan. 2019, https://doi.org/
• E. Pennestri` and F. Freudenstein, “The mechanical efficiency of epicyclic gear trains,” Journal of Mechanical Design, Vol. 115, No. 3, pp. 645–651, Sep. 1993, https://doi.org/10.1115/1.2919239
• G. Mantriota, “Theoretical and experimental efficiency analysis of multi-degrees-of-freedom epicyclic gear trains,” Multibody System Dynamics, Vol. 9, No. 4, pp. 389–408, 2003, https://doi.org/
• E. Pennestrı` and P. P. Valentini, “A review of formulas for the mechanical efficiency analysis of two degrees-of-freedom epicyclic gear trains,” Journal of Mechanical Design, Vol. 125, No. 3,
pp. 602–608, Sep. 2003, https://doi.org/10.1115/1.1587157
• E. Pennestrì, L. Mariti, P. P. Valentini, and V. H. Mucino, “Efficiency evaluation of gearboxes for parallel hybrid vehicles: Theory and applications,” Mechanism and Machine Theory, Vol. 49, pp.
157–176, Mar. 2012, https://doi.org/10.1016/j.mechmachtheory.2011.10.012
About this article
Vibration in transportation engineering
fuel economy
construction vehicles
hydraulic mechanical transmission
torque converter
continuously variable transmission
The authors would like to acknowledge the support and contribution from the Key Laboratory of Advanced Manufacturing Technology for Automobile Parts, Chongqing University of Technology, China. The
study was funded by the National Natural Science Foundation of China (Grant No. 52005067 and No. 52172355), Natural Science Foundation Project of Chongqing Science and Technology Commission
(cstc2021jcyj-msxmX0555), The Cultivation Plan for the Research and Innovation Team of Chongqing University of Technology (2023TDZ011), Youth Project of Science and Technology Research Program of
Chongqing Education Commission of China (No. KJQN202201159).
Data Availability
The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.
Conflict of interest
The authors declare that they have no conflict of interest.
Copyright © 2023 Huan Wang, et al.
This is an open access article distributed under the
Creative Commons Attribution License
, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. | {"url":"https://www.extrica.com/article/22980","timestamp":"2024-11-05T13:32:31Z","content_type":"text/html","content_length":"167187","record_id":"<urn:uuid:d646c307-83ce-4a75-ba49-ee23771c5151>","cc-path":"CC-MAIN-2024-46/segments/1730477027881.88/warc/CC-MAIN-20241105114407-20241105144407-00211.warc.gz"} |
What is low average rate of return
The Rate of Return (ROR) is the gain or loss of an investment over a period of time copmared to the initial cost of the investment expressed as a percentage. This guide teaches the most common
formulas for calculating different types of rates of returns including total return, annualized return, ROI, ROA, ROE, IRR.
rave = average rate of return In the other years, the return was higher or lower -- sometimes much higher (as in year 7) or much lower (as in year 2). Now look The rate of return an investor
receives from buying a common stock and A stock with a beta of 1.00—an average level of systematic risk—rises and falls at the The well-diversified CAPM investor would view the stock as a low-risk
security. This is the “average” periodically compounded rate of return that gives a net present value of 0.0; for a more complete explanation, see Notes below. decimal. What is a reasonable rate of
return to expect on your investment? try to guess how much money a Low Risk investment would earn on average over a ten or The ARR method calculates the average annual percentage return an each
machine and the annual estimated net profits are provided in the table below:.
7 Apr 2019 A small difference in your assumed rate of return can drastically change On the low-end, I'm saving too little and on the high-end, I'm saving too much. and 12 percent for average annual
returns over a lifetime of investing.
17 May 2019 timing and the price you paid for the shares will determine your return when the average annual growth rate of the fund's share price from March 31, at once is one way to lower the risk
that you'll invest at the wrong time. 9 Apr 2019 What is the aggregate real rate of return in the economy? Safe returns have been low on average in the full sample, falling in the 1%–3% 24 Oct 2016
Remember, the IRR is the annualized percentage return. The 16.2% represents the average annual return over the four years of this investment 30 Aug 2018 In all seriousness though, calculating a rate
of return; also known as “return on Compounded average return represents the cumulative effect of a series of returns which are not generally lower than the published return. 24 Jul 2013 The required
rate of return, the minimum return the investor will accept for an stock – then the cost of equity will be a weighted average of the different return rates. Joey performs the calculation below to
find his answer:. 13 May 2015 But given today's low interest rates and relatively lofty stock quite a bit, so some years you'll do better than the average, some years worse.
Calculating Payback Period and Average Rate of Return as 'N' years, then the accept-reject criterion under the Payback Period (PBP) method is stated below:.
Accounting Rate of Return - ARR: The accounting rate of return (ARR) is the amount of profit, or return, an individual can expect based on an investment made. Accounting rate of return divides the
The Rate of Return (ROR) is the gain or loss of an investment over a period of time copmared to the initial cost of the investment expressed as a percentage. This guide teaches the most common
formulas for calculating different types of rates of returns including total return, annualized return, ROI, ROA, ROE, IRR. So in a nutshell, my opinion is that you would be fortunate to average
around 7-8% rate of return over a long-term basis. There will be periods in which you get a 20% rate of return. These are the great times. But there will also be times in which you are getting a -15%
rate of return. The 5-year average for the S&P 500 from 1995-1999 was 28.56%. Vanguard Chief Global Economist Joe Davis shares what his team projects as a realistic return over the next decade for a
balanced portfolio—meaning one comprised of 60% equities and 40% fixed income investments—which at 4 to 4.5% is below historical averages. Average return is the simple mathematical average of a
series of returns generated over a period of time. An average return is calculated the same way a simple average is calculated for any set of Rate of Return: A rate of return is the gain or loss on
an investment over a specified time period, expressed as a percentage of the investment’s cost. Gains on investments are defined as income
What Is the Difference Between an IRR & an Accounting Rate of Return? Techniques to Identify Commercial Risk. Also Viewed.
The highest returns on a per-country basis are recorded for low- and middle- income countries. Overall, the average rate of return on another year of schooling is 1 Feb 2020 An investment return
assumption that is set too low will overstate Figure 2: Average nominal and real rate of return, and average assumed. Usually, IRR is expressed as an annualized rate of return—the average percentage
by which any on risk principal grows The formula for IRR appears below. 8 Oct 2019 Over the weekend, I was asked the difference between average annual return and compounding (or compound annual
growth rate). Really, the 22 Nov 2019 But the tax benefits of a Roth IRA can increase your effective returns. IRAs as a certificate of deposit, which typically has a lower rate of return. 26 Feb
2020 Now, this can have profound effects on your rate of return over time. Say everything is going well, you've been investing for 20 or 30 years, and Calculating Payback Period and Average Rate of
Return as 'N' years, then the accept-reject criterion under the Payback Period (PBP) method is stated below:.
So in a nutshell, my opinion is that you would be fortunate to average around 7-8% rate of return over a long-term basis. There will be periods in which you get a 20% rate of return. These are the
great times. But there will also be times in which you are getting a -15% rate of return. The 5-year average for the S&P 500 from 1995-1999 was 28.56%.
Compare that with a lower rate of return, such as the 3% annual average historical returns from bonds, which would take about 24 years to double your initial investment--more than twice as long. Keep
in mind that the Rule of 72 is not an exact calculation. It's most accurate for low rates of return but becomes less so the higher the rate. The 90-year inflation-adjusted 7% rate of return is an
average of some high peaks and deep troughs. Some stock market sell-offs have lasted for many years. U.S. Treasury yields are low Accounting Rate of Return - ARR: The accounting rate of return (ARR)
is the amount of profit, or return, an individual can expect based on an investment made. Accounting rate of return divides the The Rate of Return (ROR) is the gain or loss of an investment over a
period of time copmared to the initial cost of the investment expressed as a percentage. This guide teaches the most common formulas for calculating different types of rates of returns including
total return, annualized return, ROI, ROA, ROE, IRR. So in a nutshell, my opinion is that you would be fortunate to average around 7-8% rate of return over a long-term basis. There will be periods in
which you get a 20% rate of return. These are the great times. But there will also be times in which you are getting a -15% rate of return. The 5-year average for the S&P 500 from 1995-1999 was
28.56%. Vanguard Chief Global Economist Joe Davis shares what his team projects as a realistic return over the next decade for a balanced portfolio—meaning one comprised of 60% equities and 40% fixed
income investments—which at 4 to 4.5% is below historical averages.
So in a nutshell, my opinion is that you would be fortunate to average around 7-8% rate of return over a long-term basis. There will be periods in which you get a 20% rate of return. These are the
great times. But there will also be times in which you are getting a -15% rate of return. The 5-year average for the S&P 500 from 1995-1999 was 28.56%. Vanguard Chief Global Economist Joe Davis
shares what his team projects as a realistic return over the next decade for a balanced portfolio—meaning one comprised of 60% equities and 40% fixed income investments—which at 4 to 4.5% is below
historical averages. Average return is the simple mathematical average of a series of returns generated over a period of time. An average return is calculated the same way a simple average is
calculated for any set of Rate of Return: A rate of return is the gain or loss on an investment over a specified time period, expressed as a percentage of the investment’s cost. Gains on investments
are defined as income The same $10,000 invested at twice the rate of return, 20%, does not merely double the outcome; it turns it into $828.2 billion. It seems counter-intuitive that the difference
between a 10% return and a 20% return is 6,010x as much money, but it's the nature of geometric growth. Another example is illustrated in the chart below. Investors with a low appetite for risk are
better served by placing investments in less volatile allocations that could result in lower rates of return over time. It's an average rate of | {"url":"https://optionserofn.netlify.app/dziewanowski57789kys/what-is-low-average-rate-of-return-tebo.html","timestamp":"2024-11-14T03:46:07Z","content_type":"text/html","content_length":"35502","record_id":"<urn:uuid:c5eac668-0b21-4ba9-bc65-b21f0da35618>","cc-path":"CC-MAIN-2024-46/segments/1730477028526.56/warc/CC-MAIN-20241114031054-20241114061054-00206.warc.gz"} |
Two corrector-predictor interior point algorithms are proposed for solving mono\-tone linear complementarity problems. The algorithms produce a sequence of iterates in the $\caln_{\infty}^{-}$
neighborhood of the central path. The first algorithm uses line search schemes requiring the solution of higher order polynomial equations in one variable, while the line search procedures of the
second algorithm … Read more
Towards nonsymmetric conic optimization
In this paper we propose a new interior-point method, which is based on an extension of the ideas of self-scaled optimization to the general cones. We suggest using the primal correction process to
find a {\em scaling point}. This point is used to compute a strictly feasible primal-dual pair by simple projection. Then, we define … Read more
Packing and Partitioning Orbitopes
We introduce orbitopes as the convex hulls of 0/1-matrices that are lexicographically maximal sub ject to a group acting on the columns. Special cases are packing and partitioning orbitopes, which
arise from restrictions to matrices with at most or exactly one 1-entry in each row, respectively. The goal of investigating these polytopes is to gain … Read more
OSiL: An Instance Language for Optimization
Distributed computing technologies such as Web Services are growing rapidly in importance in today’s computing environment. In the area of mathematical optimization, it is becoming increasingly
common to separate modeling languages from optimization solvers. In fact, the modeling language software, solver software, and data used to generate a model instance might reside on different
machines … Read more
A unified approach for inversion problems in intensity-modulated radiation therapy
We propose and study a unified model for handling dose constraints (physical dose, equivalent uniform dose (EUD), etc.) and radiation source constraints in a single mathematical framework based on
the split feasibility problem. The model does not impose on the constraints an exogenous objective (merit) function. The optimization algorithm minimizes a weighted proximity function that … Read
Nonserial dynamic programming and local decomposition algorithms in discrete programming
One of perspective ways to exploit sparsity in the dependency graph of an optimization problem as J.N. Hooker stressed is nonserial dynamic programming (NSDP) which allows to compute solution in
stages, each of them uses results from previous stages. The class of discrete optimization problems with the block-tree-structure matrix of constraints is considered. Nonserial dynamic … Read more
On forests, stable sets and polyhedras associated with clique partitions
Let $G=(V,E)$ be a simple graph on $n$ nodes. We show how to construct a partial subgraph $D$ of the line graph of $G$ satisfying the identity: $\overline \chi(G)+\alpha(D)=n$, where $\overline \chi
(G)$ denotes the minimum number of cliques in a clique partition of $G$ and $\alpha(D)$ denotes the maximum size of a stable set of … Read more
A Particle Swarm Pattern Search Method for Bound Constrained Nonlinear Optimization
In this paper we develop, analyze, and test a new algorithm for the global minimization of a function subject to simple bounds without the use of derivatives. The underlying algorithm is a pattern
search method, more specifically a coordinate search method, which guarantees convergence to stationary points from arbitrary starting points. In the optional search … Read more
On the Quality of a Semidefinite Programming Bound for Sparse Principal Component Analysis
We examine the problem of approximating a positive, semidefinite matrix $\Sigma$ by a dyad $xx^T$, with a penalty on the cardinality of the vector $x$. This problem arises in sparse principal
component analysis, where a decomposition of $\Sigma$ involving sparse factors is sought. We express this hard, combinatorial problem as a maximum eigenvalue problem, in … Read more
The p-median polytope of restricted Y-graphs
We further study the effect of odd cycle inequalities in the description of the polytopes associated with the p-median and uncapacitated facility location problems. We show that the obvious integer
linear programming formulation together with the odd cycle inequalities completely describe these polytopes for the class of restricted Y-graphs. This extends our results for the … Read more | {"url":"https://optimization-online.org/2006/03/","timestamp":"2024-11-10T08:24:47Z","content_type":"text/html","content_length":"106518","record_id":"<urn:uuid:a925a998-f396-4611-8b6c-44a93ecae6f4>","cc-path":"CC-MAIN-2024-46/segments/1730477028179.55/warc/CC-MAIN-20241110072033-20241110102033-00751.warc.gz"} |
Tutorial: Clustering Techniques for Larges Data Sets
From the Past To the Future
Abstract: Because of the fast technological progress, the amount of information which is stored in databases is rapidly increasing. In addition, new applications require the storage and retrieval of
complex multimedia objects which are often represented by high-dimensional feature vectors. Finding the valuable information hidden in those databases is a difficult task. Cluster analysis is one of
the basic techniques which is often applied in analyzing large data sets. Originating from the area of statistics, most cluster analysis algorithms have originally been developed for relatively small
data sets. In the recent years, the clustering algorithms have been extended to efficiently work on large data sets, and some of them even allow the clustering of high-dimensional feature vectors.
Many such methods use some kind of an index structure for an efficient retrieval of the required data; other approaches are based on preprocessing for a more efficient clustering.
The main goal of the tutorial is to provide an overview of the state-of-the-art in cluster discovery methods for large databases, covering well-known clustering methods from related fields such as
statistics, pattern recognition, and machine learning, as well as database techniques which allow them to work efficiently on large databases. The target audience of the tutorial are researchers and
practitioners from statistics, databases, and machine learning, who are interested in the state-of-the art of cluster discovery methods and their applications to large databases. The tutorial
especially addresses people from academia who are interested in developing new cluster discovery algorithms, and people from industry who want to apply cluster discovery methods in analyzing large
Alexander Hinneburg: 25. Sept. 2000 | {"url":"https://users.informatik.uni-halle.de/~hinnebur/ClusterTutorial/","timestamp":"2024-11-01T22:30:34Z","content_type":"text/html","content_length":"3291","record_id":"<urn:uuid:dfa1634a-10db-4f3f-92a2-e5a797780d6d>","cc-path":"CC-MAIN-2024-46/segments/1730477027599.25/warc/CC-MAIN-20241101215119-20241102005119-00258.warc.gz"} |
Where can I hire MATLAB assignment experts for mathematical modeling? | Hire Someone To Do My Assignment
Where can I hire MATLAB assignment experts for mathematical modeling? I have many students who work on different models, developing a structured exam score for math by applying MATLAB on multiple
parts of data. Only MATLAB knows something, as in even the mathematical data when only one part i was reading this completed. Can MATLAB be a reliable substitute for MAT but still maintain a good
simulation quality? The Matlab module uses a lot of hard work to map the missing dimension in the matrix into the same dimension. Therefore, this is most accurate matlab, but the domain is hard. With
this, you need to transform the data matrices into the desired dimensions. Do MATLAB access your variables and plot results? Does MATLAB find performance parameters? If you are calculating and
plotting samples, then MATLAB doesn’t want you to look at the exact parameters from the data. When this happens, it also needs to present the results for your model and evaluate it against the
results for the other Models. If you make a model prediction to the last model, then MATLAB cannot show you how to get that model and compute the approximation. I need to see all this details if
possible, so that I can see what I’m missing. Related: Matlab Multi-Model Approach (Matmatic) There are many more ways to do this but I simply want to focus the learning on my own work and build an
application. These three might be a little bit different to what you require. No idea, but MATLAB shows the results for different Models. If you have additional matrices, so that I can see which
model to use, but other then defining the dimensions, I also need to change the text boxes for each row and column. Most importantly, I need to know the accuracy for each scale in the given model. I
recently implemented Excel’s R-i-p tests. This tutorial is for MATLAB and it has a lot of details to help. In the test, I am checking to see if the MATLAB and Excel window functions are working and
then adding the formula elements. I am not sure if the formula is working from MATLAB, but if so, it should be. This is my own work for this exercise so that I can understand the overall problem
better. I started by setting up Excel, was done pre-set up, made all kinds of basic data, and it was so quick to complete.
Do My Math Homework For Money
Now, the Matlab formulas is updated for each Model by changing the test table lookyouth, etc. It was with this thinking that I decided to use Matlab to do the calculations and the evaluation. The
Matlab code is here… // A method/function that runs pre-set-up function Calculation() return 3; // The methods for putting the values into the box function Cell() use ggplot2; function CheckBox()
return click for more function SearchBox(s_box) return 3; // Form the box with values function Box1(c_Box_1) use ggplot2; // Calculate that box check_box = 3; // Get the boxes and perform the
calculation box = Field(box); // Replace the values that were put in boxes with // values that not in boxes const Field.c_Box_1 = &Box(c_Box_1); if (check_box) return; if (Box1(4)) return; if (Box1
(3)) return; if (CheckBox(Box1(4))) returnWhere can I hire MATLAB assignment experts for mathematical modeling? By means of MATLAB Assignment Expert, I share my knowledge regarding Matlab (3rd
edition) assignment. As MathLAB Assignment Experts, Math has a comprehensive knowledge base which is very extensive and you can find the methods which are used by your company. You can find a wide
range of various assignments for Math assignment, there are also a great list. In general, Matlab has a major requirement for performing some kind of assignment on cells of cells. It was presented
earlier, it should be decided on the data type in your case cell. Therefore, we can often use MATLAB Assignment expert for performing an assignment in MATLAB. If you are working with MATLAB
application, make sure to give it such an example to get an idea about your requirements. This is the method, MATLAB assignment experts are her latest blog useful in solving real problems. Often,
they are experts when to work on the most real problems. This course usually includes some basics related to MATLAB Assignment Expert, and one of these is MATLAB Assignment Expert Basics, which used
to be the basis of Matlab assignment expert for more than a you could look here For MATLAB more helpful hints Assignment, we start with QL (Qmaqlla-CADIN), it includes several functions and procedure
functions. The * Qmaqlla-CD (MQQLCAD) has been launched. Qmaqlla-CD is a software for applying mathematical data stored in QLADIN database for model solution. In Qmaqlla-CD we should consider * QCAD
(CAVICAD) is a database for classification and regression analysis for AI, model, control, search, and learning algorithms. CVAD has been developed for different kinds of AI, model, and control *
QCADV (QCLADV) has been developed for applying mathematical data stored in QCLADV.
Paid Homework Help Online
In QCADV they are used with different types of data. These methods are described as follows: QCLADV: QMAQLAD, QCAD, QCADV: CVAD. The following * QCADV: QCAD, QCADV * -QCLADV, QCADV. This is the
method based on QMCLADV. The following * QMCLADV: QCAD, QCLADV * -QMCLADV * VAD (cvAD) is the core of QCAD. With QCAD the function of using QCLADV in MATLAB is called with that of using QMCLADV for
the student command by itself you will have Since in this course you can consider the process in Matlab, there are other tools for solving many real problems, MATLAB Assignment Expert gives you a few
examples read more MATLAB Assignment Expert and Matlab Assignment Expert Basics. -QMSIS, a software for building mathematical models on the database by handling parameters and other inputs in MATLAB.
-IMAP, (International Matlab Association® Network) software for building advanced projects- AIMA, (International Matlab Association®) -Q3/4 etc, it’s description above. It contains some basic
functions and procedures for the user, where you can find more information for your needs. Don’t forget for the next chapter, if you want to know more about MATLAB Assignment Expert, your
registration price is approximately $2. These parameters go very much to building a MATLAB Assignment Expert. It’s important to bear in mind, if you are using MATLAB Assignment Expert for the
management of the calculations processing, you have to look at some common options, such as Database Management System (DMS) or Database-Client-Server, or Database-Client Manager. The main reason for
using DatabaseWhere can I hire MATLAB assignment experts for mathematical modeling? I suggest hiring MATLAB experts for modeling. Even if WEE/DAE is designed correctly and/or with a good deal of time
/confidence to work, and you have a clear understanding of how you can make it start, it will take long because you have to get an assignment. I highly doubt you can even come up with an expert’s
ready-to-use assignment to handle code quality issues involving the right approach. MATLAB experts can quickly diagnose different cases around the problem, but MATLAB will have to keep working to
solve them and make them work better. Frequently asked questions 1 Answer To solve the problem of RAVA, let’s assume that I have a series or matrix of variables that are distributed over multiple
levels among values of your series or matrix, with each of these values being a vector of values from your series. The code based on this exercise will build on the examples we have already given.
Matlab experts can quickly solve the problem of solving your problem based on the method of solution provided above and the results provided in the previous exercise, or they can solve it with the
next step – to the next line of code in this exercise. If you want to talk more with MATLAB experts, contact me important site tjkabau@matslab.
Pay For Homework Assignments
info as soon as I start a research project in MATLAB™. We have now included a pre-processing work in our MATLAB exercises which addresses each of the categories you were asking about here. In fact,
the more topics we cover in the next subsection, the more basic step for the development of MATLAB, is creating the open-source tool for R’s RStudio™ or MATLAB MFC™. What is R’s RStudio™ environment?
In RStudio™, I am using R’s RStudio™ and MATLAB™ to create and run R programs. R, RMLM™ and Rmcat™ are written in the R file RML is the default file format for R/RML, but it is also the IDE for R/RML
and other projects, and we are using the IDE called Rmcat™ in the RStudio™. Why would you do this? Of course, the more RStudio, RMLM, or Rmcat you use, the more your code works. The best things you
can say about RStudio are that it is not a Java environment. Why not a Visual Studio user interface and graphical visualisation within RStudio itself, or a simple IDE built-in. It is a graphical way
of operating in command-line RStudio™, where you can create RML files, and run R a command using the command line like you can with the R command-line™. If you like RStudio™, and other | {"url":"https://assignmentinc.com/where-can-i-hire-matlab-assignment-experts-for-mathematical-modeling","timestamp":"2024-11-11T09:52:48Z","content_type":"text/html","content_length":"111725","record_id":"<urn:uuid:9063c675-d8ac-4fdd-be5b-8a37726998db>","cc-path":"CC-MAIN-2024-46/segments/1730477028228.41/warc/CC-MAIN-20241111091854-20241111121854-00563.warc.gz"} |
Declaration [src]
gsk_path_point_get_tangent (
const GskPathPoint* point,
GskPath* path,
GskPathDirection direction,
graphene_vec2_t* tangent
Description [src]
Gets the tangent of the path at the point.
Note that certain points on a path may not have a single tangent, such as sharp turns. At such points, there are two tangents — the direction of the path going into the point, and the direction
coming out of it. The direction argument lets you choose which one to get.
If the path is just a single point (e.g. a circle with radius zero), then tangent is set to 0, 0.
If you want to orient something in the direction of the path, gsk_path_point_get_rotation() may be more convenient to use.
Type: GskPath
The path that point is on.
The data is owned by the caller of the method.
Type: GskPathDirection
The direction for which to return the tangent.
Type: graphene_vec2_t
Return location for the tangent at the point.
The argument will be set by the function.
The returned data is owned by the instance. | {"url":"https://docs.gtk.org/gsk4/method.PathPoint.get_tangent.html","timestamp":"2024-11-10T04:32:35Z","content_type":"text/html","content_length":"8913","record_id":"<urn:uuid:072beddb-e14b-4b71-9c3c-edae3d85661d>","cc-path":"CC-MAIN-2024-46/segments/1730477028166.65/warc/CC-MAIN-20241110040813-20241110070813-00445.warc.gz"} |
Background Checks with Lastname
Search over 300 million background checks which include full name, current address, phone number, address history, marriage records, divorce records, criminal records, criminal background checks,
court records, police records, bankruptcy records, property records, arrest records, driving offenses records, felonies, misdemeanors, sex offender records, convictions, incarcerations, inmate
records, and other court documents.
Michael Kempton, Christopher Kempton, Jason Kempton, David Kempton, James Kempton, John Kempton, Robert Kempton, Brian Kempton, William Kempton, Matthew Kempton, Joseph Kempton, Daniel Kempton, Kevin
Kempton, Eric Kempton, Jeffrey Kempton, Richard Kempton, Scott Kempton, Mark Kempton, Steven Kempton, Thomas Kempton, Timothy Kempton, Anthony Kempton, Charles Kempton, Joshua Kempton, Ryan Kempton,
Jeremy Kempton, Paul Kempton, Andrew Kempton, Gregory Kempton, Chad Kempton, Kenneth Kempton, Jonathan Kempton, Stephen Kempton, Shawn Kempton, Aaron Kempton, Adam Kempton, Patrick Kempton, Justin
Kempton, Sean Kempton, Edward Kempton, Todd Kempton, Donald Kempton, Ronald Kempton, Benjamin Kempton, Keith Kempton, Bryan Kempton, Gary Kempton, Jose Kempton, Nathan Kempton, Douglas Kempton,
Brandon Kempton, Nicholas Kempton, George Kempton, Travis Kempton, Peter Kempton, Craig Kempton, Bradley Kempton, Larry Kempton, Dennis Kempton, Shane Kempton, Raymond Kempton, Troy Kempton, Jerry
Kempton, Samuel Kempton, Frank Kempton, Jesse Kempton, Jeffery Kempton, Juan Kempton, Terry Kempton, Corey Kempton, Phillip Kempton, Marcus Kempton, Derek Kempton, Rodney Kempton, Joel Kempton,
Carlos Kempton, Randy Kempton, Jacob Kempton, Jamie Kempton, Tony Kempton, Russell Kempton, Brent Kempton, Billy Kempton, Antonio Kempton, Derrick Kempton, Kyle Kempton, Erik Kempton, Johnny Kempton,
Marc Kempton, Carl Kempton, Philip Kempton, Roger Kempton, Bobby Kempton, Brett Kempton, Danny Kempton, Curtis Kempton, Jon Kempton, Vincent Kempton, Cory Kempton, Jimmy Kempton, Victor Kempton,
Lawrence Kempton, Dustin Kempton, Gerald Kempton, Walter Kempton, Alexander Kempton, Joe Kempton, Christian Kempton, Chris Kempton, Alan Kempton, Shannon Kempton, Wayne Kempton, Jared Kempton,
Gabriel Kempton, Martin Kempton, Jay Kempton, Willie Kempton, Luis Kempton, Micheal Kempton, Henry Kempton, Wesley Kempton, Randall Kempton, Brad Kempton, Darren Kempton, Roy Kempton, Albert Kempton,
Arthur Kempton, Ricky Kempton, Lance Kempton, Allen Kempton, Lee Kempton, Bruce Kempton, Andre Kempton, Mario Kempton, Frederick Kempton, Louis Kempton, Darrell Kempton, Damon Kempton, Shaun Kempton,
Nathaniel Kempton, Zachary Kempton, Casey Kempton, Adrian Kempton, Jesus Kempton, Jeremiah Kempton, Jack Kempton, Ronnie Kempton, Dale Kempton, Tyrone Kempton, Manuel Kempton, Ricardo Kempton, Harold
Kempton, Kelly Kempton, Barry Kempton, Reginald Kempton, Ian Kempton, Glenn Kempton, Ernest Kempton, Steve Kempton, Seth Kempton, Eugene Kempton, Clinton Kempton, Miguel Kempton, Tommy Kempton, Eddie
Kempton, Leonard Kempton, Maurice Kempton, Roberto Kempton, Dwayne Kempton, Jerome Kempton, Ralph Kempton, Marvin Kempton, Francisco Kempton, Jorge Kempton, Neil Kempton, Alex Kempton, Dean Kempton,
Kristopher Kempton, Calvin Kempton, Kurt Kempton, Theodore Kempton, Ruben Kempton, Jermaine Kempton, Tracy Kempton, Edwin Kempton, Stanley Kempton, Melvin Kempton, Howard Kempton, Mitchell Kempton,
Duane Kempton, Trevor Kempton, Jeff Kempton, Geoffrey Kempton, Hector Kempton, Terrence Kempton, Terrance Kempton, Oscar Kempton, Jaime Kempton, Clifford Kempton, Harry Kempton, Kirk Kempton, Tyler
Kempton, Jody Kempton, Greg Kempton, Earl Kempton, Angel Kempton, Daryl Kempton, Mathew Kempton, Heath Kempton, Clayton Kempton, Clarence Kempton, Karl Kempton, Raul Kempton, Alfred Kempton, Isaac
Kempton, Javier Kempton, Wade Kempton, Mike Kempton, Luke Kempton, Ramon Kempton, Joey Kempton, Warren Kempton, Ray Kempton, Francis Kempton, Norman Kempton, Toby Kempton, Leon Kempton, Glen Kempton,
Lonnie Kempton, Rafael Kempton, Cody Kempton, Pedro Kempton, Byron Kempton, Fred Kempton, Franklin Kempton, Omar Kempton, Fernando Kempton, Alejandro Kempton, Bernard Kempton, Clint Kempton, Darin
Kempton, Gilbert Kempton, Andy Kempton, Lucas Kempton, Alvin Kempton, Cedric Kempton, Eduardo Kempton, Roderick Kempton, Armando Kempton, Don Kempton, Leroy Kempton, Darryl Kempton, Dana Kempton,
Jessie Kempton, Cameron Kempton, Ross Kempton, Kelvin Kempton, Marco Kempton, Evan Kempton, Johnathan Kempton, Clifton Kempton, Fredrick Kempton, Vernon Kempton, Dominic Kempton, Lewis Kempton, Colin
Kempton, Donnie Kempton, Damian Kempton, Rene Kempton, Stacy Kempton, Herbert Kempton, Sergio Kempton, Alberto Kempton, Grant Kempton, Leslie Kempton, Jonathon Kempton, Erick Kempton, Marlon Kempton,
Julio Kempton, Ivan Kempton, Dwight Kempton, Micah Kempton, Darrin Kempton, Brendan Kempton, Spencer Kempton, Orlando Kempton, Nelson Kempton, Lloyd Kempton, Julian Kempton, Edgar Kempton, Marshall
Kempton, Kent Kempton, Jarrod Kempton, Lamont Kempton, Kerry Kempton, Trent Kempton, Garrett Kempton, Gordon Kempton, Alfredo Kempton, Damien Kempton, Charlie Kempton, Stuart Kempton, Demetrius
Kempton, Devin Kempton, Guy Kempton, Gene Kempton, Arturo Kempton, Rick Kempton, Bryant Kempton, Enrique Kempton, Cesar Kempton, Scotty Kempton, Jim Kempton, Neal Kempton, Jimmie Kempton, Johnnie
Kempton, Jackie Kempton, Allan Kempton, Antoine Kempton, Ben Kempton, Marty Kempton, Bradford Kempton, Chadwick Kempton, Floyd Kempton, Jayson Kempton, Noah Kempton, Gerardo Kempton, Dan Kempton,
Bret Kempton, Felix Kempton, Preston Kempton, Roland Kempton, Gregg Kempton, Angelo Kempton, Ted Kempton, Jordan Kempton, Blake Kempton, Freddie Kempton, Tyson Kempton, Israel Kempton, Lorenzo
Kempton, Leo Kempton, Perry Kempton, Tim Kempton, Ethan Kempton, Rickey Kempton, Bill Kempton, Salvador Kempton, Noel Kempton, Abraham Kempton, Lester Kempton, Ernesto Kempton, Dewayne Kempton, Rudy
Kempton, Nick Kempton, Tom Kempton, Carlton Kempton, Austin Kempton, Darnell Kempton, Andres Kempton, Kenny Kempton, Terence Kempton, Herman Kempton, Milton Kempton, Jamal Kempton, Frankie Kempton,
Robbie Kempton, Marcos Kempton, Brady Kempton, Robin Kempton, Matt Kempton, Courtney Kempton, Sam Kempton, Quincy Kempton, Terrell Kempton, Clyde Kempton, Clay Kempton, Quentin Kempton, Bryce
Kempton, Ron Kempton, Stacey Kempton, Max Kempton, Ashley Kempton, Cecil Kempton, Drew Kempton, Dion Kempton, Lamar Kempton, Chester Kempton, Alfonso Kempton, Brock Kempton, Rodolfo Kempton, Dylan
Kempton, Randolph Kempton, Josh Kempton, Gerard Kempton, Loren Kempton, Pablo Kempton, Caleb Kempton, Cornelius Kempton, Salvatore Kempton, Kendrick Kempton, Timmy Kempton, Harvey Kempton, Sammy
Kempton, Dexter Kempton, Nicolas Kempton, Malcolm Kempton, Sidney Kempton, Levi Kempton, Bryon Kempton, Julius Kempton, Donovan Kempton, Oliver Kempton, Wendell Kempton, Arnold Kempton, Kris Kempton,
Rocky Kempton, Dallas Kempton, Rolando Kempton, Everett Kempton, Garry Kempton, Rusty Kempton, Myron Kempton, Scottie Kempton, Gilberto Kempton, Eli Kempton, Cary Kempton, Sheldon Kempton, Simon
Kempton, Otis Kempton, Abel Kempton, Alonzo Kempton, Scot Kempton, Jamey Kempton, Kendall Kempton, Elijah Kempton, Rex Kempton, Randal Kempton, Jake Kempton, Guillermo Kempton, Roman Kempton, Morgan
Kempton, Benny Kempton, Felipe Kempton, Sherman Kempton, Derick Kempton, Ismael Kempton, Claude Kempton, Hugh Kempton, Mickey Kempton, Stephan Kempton, Darrick Kempton, Damion Kempton, Virgil
Kempton, Darius Kempton, Beau Kempton, Ira Kempton, Rogelio Kempton, Devon Kempton, Desmond Kempton, Owen Kempton, Teddy Kempton, Gustavo Kempton, Bart Kempton, Earnest Kempton, Kareem Kempton, Curt
Kempton, Lyle Kempton, Elias Kempton, Forrest Kempton, Erin Kempton, Thaddeus Kempton, Stewart Kempton, Dante Kempton, Dominick Kempton, Xavier Kempton, Wallace Kempton, Ramiro Kempton, Guadalupe
Kempton, Alton Kempton, Pete Kempton, Morris Kempton, Jess Kempton, Monte Kempton, Moses Kempton, Carey Kempton, Donny Kempton, Colby Kempton, Saul Kempton, Trenton Kempton, Marion Kempton, Rory
Kempton, Tracey Kempton, Darrel Kempton, Gavin Kempton, Reynaldo Kempton, Erich Kempton, Bennie Kempton, Fabian Kempton, Luther Kempton, Tomas Kempton, Blaine Kempton, Jerald Kempton, Dave Kempton,
Shad Kempton, Edmund Kempton, Reuben Kempton, Clark Kempton, Kory Kempton, Jarrett Kempton, Sonny Kempton, Donnell Kempton, Demond Kempton, Robby Kempton, Aron Kempton, Leonardo Kempton, Jamison
Kempton, Lionel Kempton, Kurtis Kempton, Deon Kempton, Elliott Kempton, Stefan Kempton, Emanuel Kempton, Nickolas Kempton, Efrain Kempton, Kristian Kempton, Archie Kempton, Joesph Kempton, Graham
Kempton, Lynn Kempton, Jerrod Kempton, Wilson Kempton, Esteban Kempton, Reggie Kempton, Mason Kempton, Sylvester Kempton, Leland Kempton, Hugo Kempton, Willard Kempton, Vance Kempton, Ken Kempton,
Miles Kempton, Taylor Kempton, Jeffry Kempton, Will Kempton, Jean Kempton, Rodrick Kempton, Willis Kempton, Antwan Kempton, Hans Kempton, Rudolph Kempton, Daren Kempton, Jefferson Kempton, Roosevelt
Kempton, Amos Kempton, Emmanuel Kempton, Elmer Kempton, Grady Kempton, Joaquin Kempton, Tommie Kempton, Jeromy Kempton, Dorian Kempton, Dane Kempton, Tobias Kempton, Anton Kempton, Santiago Kempton,
Sterling Kempton, Freddy Kempton, Shon Kempton, Rico Kempton, Jarvis Kempton, Brant Kempton, Monty Kempton, Collin Kempton, Nolan Kempton, Alexis Kempton, Quinton Kempton, Bob Kempton, Stevie
Kempton, Avery Kempton, Aric Kempton, Emilio Kempton, Shayne Kempton, Carlo Kempton, Conrad Kempton, Jed Kempton, Denny Kempton, Elliot Kempton, Laurence Kempton, Delbert Kempton, Jennifer Kempton,
Doug Kempton, Landon Kempton, Moises Kempton, Zachariah Kempton, Kristofer Kempton, Buddy Kempton, Ignacio Kempton, Elvis Kempton, Chuck Kempton, Torrey Kempton, Jonas Kempton, Humberto Kempton,
Aubrey Kempton, Elton Kempton, Chance Kempton, Marlin Kempton, Vicente Kempton, Solomon Kempton, Horace Kempton, Kim Kempton, Tory Kempton, Royce Kempton, Wilbert Kempton, Dirk Kempton, Thad Kempton,
Ervin Kempton, Louie Kempton, Jonah Kempton, Raphael Kempton, Wilfredo Kempton, Santos Kempton, Shelby Kempton, Noe Kempton, Hubert Kempton, Mack Kempton, Van Kempton, Branden Kempton, Ali Kempton,
Marcel Kempton, Jamel Kempton, Jamar Kempton, Jasen Kempton, Rodger Kempton, Pierre Kempton, Blair Kempton, Harley Kempton, Johnathon Kempton, Winston Kempton, Ellis Kempton, Marquis Kempton, Galen
Kempton, Dewey Kempton, Reid Kempton, Bert Kempton, Brain Kempton, Bradly Kempton, Dusty Kempton, Darian Kempton, Wyatt Kempton, Alphonso Kempton, Vaughn Kempton, Brenton Kempton, Waylon Kempton,
Benito Kempton, Kirby Kempton, Jeramy Kempton, Jarod Kempton, Isaiah Kempton, Lane Kempton, Rufus Kempton, Domingo Kempton, Jackson Kempton, Jerod Kempton, Edmond Kempton, Tad Kempton, Ernie Kempton,
Quinn Kempton, Percy Kempton, Andrea Kempton, Lowell Kempton, Cornell Kempton, Rhett Kempton, Shelton Kempton, Rickie Kempton, Korey Kempton, Cleveland Kempton, Deandre Kempton, Nathanael Kempton,
Arron Kempton, Theron Kempton, Boyd Kempton, Logan Kempton, Ariel Kempton, Brendon Kempton, Adan Kempton, Donte Kempton, Doyle Kempton, Reed Kempton, Rodrigo Kempton, Josue Kempton, Cole Kempton, Rob
Kempton, Zane Kempton, Jeremie Kempton, Kenyatta Kempton, Barrett Kempton, Rocco Kempton, Sebastian Kempton, Michel Kempton, Denis Kempton, Brooks Kempton, Danial Kempton, Garth Kempton, Heriberto
Kempton, Nakia Kempton, Giovanni Kempton, Mauricio Kempton, Agustin Kempton, Cedrick Kempton, Tyron Kempton, Brice Kempton, Darwin Kempton, Carter Kempton, Kip Kempton, Garland Kempton, Malik
Kempton, Elbert Kempton, Gerry Kempton, Deshawn Kempton, Ronny Kempton, Issac Kempton, Jeramie Kempton, Emmett Kempton, Adolfo Kempton, Daron Kempton, Rashad Kempton, Lincoln Kempton, Homer Kempton,
Jacques Kempton, Nicky Kempton, Dino Kempton, Markus Kempton, Ahmad Kempton, Kristoffer Kempton, Wilbur Kempton, Antione Kempton, Jan Kempton, Ezra Kempton, Antony Kempton, Gino Kempton, Mikel
Kempton, Ari Kempton, Tremayne Kempton, Judson Kempton, Garrick Kempton, Kasey Kempton, Kraig Kempton, Rigoberto Kempton, Diego Kempton, Edwardo Kempton, Jarred Kempton, Chet Kempton, Hunter Kempton,
Jude Kempton, Billie Kempton, Elvin Kempton, Alvaro Kempton, Lenny Kempton, Irvin Kempton, Jasper Kempton, Judd Kempton, Carson Kempton, Kenyon Kempton, Keven Kempton, Sammie Kempton, Keenan Kempton,
Darron Kempton, Russel Kempton, Leif Kempton, Tyree Kempton, Woodrow Kempton, Chase Kempton, Tod Kempton, Richie Kempton, Randell Kempton, Vito Kempton, Deron Kempton, Gregorio Kempton, Federico
Kempton, Weston Kempton, Davis Kempton, Torrance Kempton, Ulysses Kempton, Trey Kempton, Jeremey Kempton, Riley Kempton, Vince Kempton, Nigel Kempton, Chauncey Kempton, Davin Kempton, Leonel Kempton,
Tobin Kempton, Michelle Kempton, Bernardo Kempton, Dedrick Kempton, Titus Kempton, Osvaldo Kempton, Wilfred Kempton, Errol Kempton, Jade Kempton, Carmen Kempton, Cliff Kempton, Kenya Kempton, Jammie
Kempton, Kelley Kempton, Harrison Kempton, Lonny Kempton, Abdul Kempton, Coy Kempton, Denver Kempton, Robb Kempton, Telly Kempton, Carroll Kempton, August Kempton, Tristan Kempton, Fidel Kempton,
Octavio Kempton, Dameon Kempton, Josef Kempton, Eloy Kempton, Dax Kempton, Barton Kempton, Eddy Kempton, Cyrus Kempton, Broderick Kempton, Zachery Kempton, Hiram Kempton, Raymundo Kempton, Giuseppe
Kempton, Terrill Kempton, Burton Kempton, Hank Kempton, Sedrick Kempton, Jamil Kempton, Germaine Kempton, Myles Kempton, Maxwell Kempton, Harlan Kempton, Norris Kempton, Emil Kempton, Kennith
Kempton, Deric Kempton, Bobbie Kempton, Levar Kempton, Francesco Kempton, Hassan Kempton, Jerrold Kempton, Jayme Kempton, Josiah Kempton, Junior Kempton, Laron Kempton, Duncan Kempton, Kenton
Kempton, Sandy Kempton, Brennan Kempton, Jamaal Kempton, Brook Kempton, Coby Kempton, Augustine Kempton, Merle Kempton, Abram Kempton, Rod Kempton, Jefferey Kempton, Frederic Kempton, Eldon Kempton,
Nathanial Kempton, Silas Kempton, Gonzalo Kempton, Greggory Kempton, Brannon Kempton, Demarcus Kempton, Erwin Kempton, Shea Kempton, Lon Kempton, Alec Kempton, Antwon Kempton, Melissa Kempton, Phil
Kempton, Adrain Kempton, Hal Kempton, Mitchel Kempton, Antonia Kempton, Irving Kempton, Derik Kempton, Tavares Kempton, Edgardo Kempton, Gus Kempton, Paris Kempton, Kimberly Kempton, Jevon Kempton,
Carmelo Kempton, Britt Kempton, Efren Kempton, Moshe Kempton, Shanon Kempton, Dominique Kempton, Cordell Kempton, Kermit Kempton, Whitney Kempton, Lashawn Kempton, Jovan Kempton, Chadd Kempton,
Dedric Kempton, Chadrick Kempton, Lars Kempton, Kelsey Kempton, Marcellus Kempton, Dejuan Kempton, Tanner Kempton, Braden Kempton, Cortez Kempton, Ezekiel Kempton, Christoper Kempton, Donell Kempton,
Delvin Kempton, Timmothy Kempton, Linwood Kempton, Lisa Kempton, Alfonzo Kempton, Tate Kempton, Douglass Kempton, Quintin Kempton, Bennett Kempton, Pat Kempton, Cruz Kempton, Garret Kempton, Aldo
Kempton, Brandy Kempton, Jereme Kempton, Arnulfo Kempton, Taurus Kempton, Dereck Kempton, Ned Kempton, Trever Kempton, Kirt Kempton, Liam Kempton, Angela Kempton, Marques Kempton, Amy Kempton, Roscoe
Kempton, Aurelio Kempton, Genaro Kempton, Nestor Kempton, Dwain Kempton, German Kempton, Tarik Kempton, Cristopher Kempton, Forest Kempton, Barney Kempton, Chaim Kempton, Eliseo Kempton, Thurman
Kempton, Donta Kempton, Che Kempton, Mariano Kempton, Lanny Kempton, Donavan Kempton, Jameson Kempton, Andreas Kempton, Isidro Kempton, Anderson Kempton, Jedediah Kempton, Rahsaan Kempton, Baron
Kempton, Emery Kempton, Michale Kempton, Jered Kempton, Charley Kempton, Bronson Kempton, Odell Kempton, Armand Kempton, Shay Kempton, Grover Kempton, Carmine Kempton, Norberto Kempton, Deangelo
Kempton, Brandt Kempton, Chandler Kempton, Otto Kempton, Dannie Kempton, Torrence Kempton, Buck Kempton, Darby Kempton, Lindsey Kempton, Trinity Kempton, Cale Kempton, Franco Kempton, Damond Kempton,
Jerad Kempton, Reinaldo Kempton, Wiley Kempton, Ivory Kempton, Everette Kempton, Leopoldo Kempton, Andra Kempton, Dario Kempton, Dalton Kempton, Ward Kempton, Brien Kempton, Paulo Kempton, Lazaro
Kempton, Emory Kempton, Westley Kempton, Marcelino Kempton, Emerson Kempton, Mary Kempton, Kwame Kempton, Toney Kempton, Marcelo Kempton, Rasheed Kempton, Derrell Kempton, Jermey Kempton, Russ
Kempton, Vincenzo Kempton, Raheem Kempton, Asa Kempton, Lemuel Kempton, Murray Kempton, Pasquale Kempton, Burt Kempton, Hollis Kempton, Valentin Kempton, Bernie Kempton, Jamin Kempton, Lenard
Kempton, Roel Kempton, Weldon Kempton, Ahmed Kempton, Cortney Kempton, Tito Kempton, Claudio Kempton, Kristin Kempton, Lorne Kempton, Enrico Kempton, Marlo Kempton, Loyd Kempton, Amir Kempton,
Arnoldo Kempton, Harris Kempton, Cristobal Kempton, Mac Kempton, Corbin Kempton, Cullen Kempton, Shedrick Kempton, Maria Kempton, Jermain Kempton, Ramsey Kempton, Torey Kempton, Nicole Kempton, Corry
Kempton, Anson Kempton, Heather Kempton, Parker Kempton, Elizabeth Kempton, Tye Kempton, Lesley Kempton, Lamonte Kempton, Sanford Kempton, Karim Kempton, Stephanie Kempton, Toriano Kempton, Bruno
Kempton, Estevan Kempton, Jerel Kempton, Orville Kempton, Brion Kempton, Demetrios Kempton, Anibal Kempton, Reginal Kempton, Lavar Kempton, Rosendo Kempton, Romeo Kempton, Simeon Kempton, Elisha
Kempton, Stan Kempton, Vidal Kempton, Enoch Kempton, Prince Kempton, Eugenio Kempton, Leigh Kempton, Mervin Kempton, Bartholomew Kempton, Delmar Kempton, Khalid Kempton, Kristen Kempton, Johnpaul
Kempton, Carnell Kempton, Domenic Kempton, Adalberto Kempton, Jaron Kempton, Luciano Kempton, Kai Kempton, Stanford Kempton, Uriah Kempton, Demarco Kempton, Jabari Kempton, Zackary Kempton, Ritchie
Kempton, Ezequiel Kempton, Basil Kempton, Brenden Kempton, Garett Kempton, Major Kempton, Jerold Kempton, Wes Kempton, Yancy Kempton, Benjamen Kempton, Fredric Kempton, Jerrell Kempton, Benji
Kempton, Barron Kempton, Chip Kempton, Michele Kempton, Britton Kempton, Milo Kempton, Samir Kempton, Charlton Kempton, Royal Kempton, Rubin Kempton, Stoney Kempton, Kieth Kempton, Javon Kempton,
Derwin Kempton, Duke Kempton, Antone Kempton, Daryle Kempton, Demetric Kempton, Layne Kempton, Reyes Kempton, Walker Kempton, Fletcher Kempton, Freeman Kempton, Jarret Kempton, Delano Kempton, Oren
Kempton, Marcell Kempton, Trinidad Kempton, Luigi Kempton, Rustin Kempton, Shan Kempton, Sharif Kempton, Isiah Kempton, Levon Kempton, Brody Kempton, Coleman Kempton, Ollie Kempton, Thor Kempton,
Darell Kempton, Desi Kempton, Horacio Kempton, Kiley Kempton, Mauro Kempton, Vinson Kempton, Dimitrios Kempton, Kevan Kempton, Merlin Kempton, Monroe Kempton, Rebecca Kempton, Rashawn Kempton, Tyrell
Kempton, Zackery Kempton, Samson Kempton, Darcy Kempton, Donavon Kempton, Jessica Kempton, Napoleon Kempton, Muhammad Kempton, Trevis Kempton, Berry Kempton, Antwain Kempton, Eliezer Kempton, Kendell
Kempton, Lamarr Kempton, Micky Kempton, Demian Kempton, Seneca Kempton, Tucker Kempton, Cheyenne Kempton, Davon Kempton, Norbert Kempton, Regan Kempton, Adolph Kempton, Jerimiah Kempton, Benton
Kempton, Jeb Kempton, Rian Kempton, Corwin Kempton, Jameel Kempton, Tyrus Kempton, Alexandro Kempton, Benson Kempton, Darien Kempton, Augustus Kempton, Erie Kempton, Gil Kempton, Raymon Kempton,
Abelardo Kempton, Terance Kempton, Tremaine Kempton, Cristian Kempton, Jedidiah Kempton, Christina Kempton, Homero Kempton, Rueben Kempton, Rey Kempton, Jace Kempton, Caesar Kempton, Hakim Kempton,
Lydell Kempton, Marcello Kempton, Parrish Kempton, Isaias Kempton, Johnie Kempton, Tavis Kempton, Eliot Kempton, Fermin Kempton, Nikolas Kempton, Orion Kempton, Alden Kempton, Clement Kempton, Lucio
Kempton, Rondell Kempton, Ronnell Kempton, Demetris Kempton, Juston Kempton, Len Kempton, Cade Kempton, Detrick Kempton, Sherwin Kempton, Truman Kempton, Reymundo Kempton, Danielle Kempton, Domenico
Kempton, Octavius Kempton, Anwar Kempton, Christofer Kempton, Dwaine Kempton, Leander Kempton, Reese Kempton, Houston Kempton, Conor Kempton, Dillon Kempton, Mitch Kempton, Demario Kempton, Artis
Kempton, Boris Kempton, Samual Kempton, Dustan Kempton, Gorge Kempton, Jory Kempton, Stanton Kempton, Amit Kempton, Julie Kempton, Kelby Kempton, Kody Kempton, Christos Kempton, Fritz Kempton, Lyndon
Kempton, Constantine Kempton, Erasmo Kempton, Jodie Kempton, Brooke Kempton, Conan Kempton, Kane Kempton, Merrill Kempton, Bryson Kempton, Isreal Kempton, Woody Kempton, Tadd Kempton, Emiliano
Kempton, Cyril Kempton, Davey Kempton, Gabe Kempton, Pernell Kempton, Curtiss Kempton, Jacky Kempton, Nicholaus Kempton, Hasan Kempton, Davy Kempton, Oswaldo Kempton, Tammy Kempton, Felton Kempton,
Jarrad Kempton, Rosario Kempton, Yusef Kempton, Anthoney Kempton, Dimitri Kempton, Donn Kempton, Graig Kempton, Glendon Kempton, Alain Kempton, Alonso Kempton, Dwane Kempton, Laura Kempton, Millard
Kempton, Milan Kempton, Everardo Kempton, Taj Kempton, Kendal Kempton, Prentice Kempton, Hilario Kempton, Hayden Kempton, Lukas Kempton, Lorin Kempton, Stevan Kempton, Benedict Kempton, Ferdinand
Kempton, Renard Kempton, Geoff Kempton, Raleigh Kempton, Amanda Kempton, Jules Kempton, Marshal Kempton, Ephraim Kempton, Patricia Kempton, Sarah Kempton, Kalvin Kempton, Sky Kempton, Vladimir
Kempton, Kipp Kempton, Rashid Kempton, Burke Kempton, Derrek Kempton, Margarito Kempton, Rojelio Kempton, Von Kempton, Wayland Kempton, Mohammad Kempton, Sandro Kempton, Renato Kempton, Shiloh
Kempton, Torry Kempton, Kenji Kempton, Del Kempton, Elgin Kempton, Booker Kempton, Chistopher Kempton, Lavell Kempton, Mohammed Kempton, Refugio Kempton, Damen Kempton, Nicola Kempton, Daryn Kempton,
Elwood Kempton, Kenric Kempton, Andrae Kempton, Christine Kempton, Clemente Kempton, Corby Kempton, Edmundo Kempton, Channing Kempton, Maynard Kempton, Roderic Kempton, Wilton Kempton, Kedrick
Kempton, Kieran Kempton, Lucius Kempton, Cliffton Kempton, Geraldo Kempton, Adrien Kempton, Hershel Kempton, Reco Kempton, Dudley Kempton, Jame Kempton, Michal Kempton, Omari Kempton, Christophe
Kempton, Delton Kempton, Lindsay Kempton, Philippe Kempton, Faron Kempton, Brandan Kempton, Williams Kempton, Adonis Kempton, Jeanpaul Kempton, Mckinley Kempton, Bertram Kempton, Randel Kempton,
Audie Kempton, Fransisco Kempton, Gideon Kempton, Lafayette Kempton, Renaldo Kempton, Winfred Kempton, Lacy Kempton, Ravi Kempton, Denton Kempton, Bjorn Kempton, Demetrice Kempton, Duwayne Kempton,
Lavon Kempton, Porfirio Kempton, Eldridge Kempton, Hosea Kempton, Lupe Kempton, Corbett Kempton, Grayson Kempton, Sanjay Kempton, Emile Kempton, Emmitt Kempton, Olin Kempton, Ramone Kempton, Yusuf
Kempton, Leandro Kempton, Amado Kempton, Leighton Kempton, Malachi Kempton, Stephon Kempton, Wilford Kempton, Keon Kempton, Timmie Kempton, Errick Kempton, Jarad Kempton, Kaleb Kempton, Dayton
Kempton, Jelani Kempton, Rance Kempton, Corrie Kempton, Jerrad Kempton, Yancey Kempton, Jonpaul Kempton, Theo Kempton, Amador Kempton, Jamaine Kempton, Lorenza Kempton, Valentino Kempton, Dee
Kempton, Eleazar Kempton, Jarett Kempton, Justen Kempton, Lauren Kempton, Tyronne Kempton, Willy Kempton, Elroy Kempton, Esequiel Kempton, Ike Kempton, Renee Kempton, Karen Kempton, Herschel Kempton,
Konstantinos Kempton, Arlo Kempton, Buford Kempton, Rasheen Kempton, Reagan Kempton, Tobey Kempton, Haywood Kempton, Khristopher Kempton, Patricio Kempton, Zack Kempton, Jamon Kempton, Khary Kempton,
Augustin Kempton, Benjiman Kempton, Ishmael Kempton, Wally Kempton, Faustino Kempton, Hamilton Kempton, Jami Kempton, Vincente Kempton, Griffin Kempton, Jeramiah Kempton, Manny Kempton, Santino
Kempton, Vern Kempton, Richardo Kempton, Franklyn Kempton, Wilmer Kempton, Christpher Kempton, Derric Kempton, Drake Kempton, Lino Kempton, Nathen Kempton, Ryon Kempton, Vernell Kempton, Johann
Kempton, Khalil Kempton, Cris Kempton, Foster Kempton, Gale Kempton, Teodoro Kempton, Creighton Kempton, Farrell Kempton, Jai Kempton, Chirstopher Kempton, Lavelle Kempton, Mikal Kempton, Orin
Kempton, Ceasar Kempton, Pietro Kempton, Sedric Kempton, Sydney Kempton, Val Kempton, Dawayne Kempton, Odis Kempton, Wardell Kempton, Murphy Kempton, Nevin Kempton, Quenton Kempton, Santo Kempton,
Slade Kempton, Dawn Kempton, Marko Kempton, Ricco Kempton, Rogers Kempton, Abe Kempton, Jerimy Kempton, Jessy Kempton, Montrell Kempton, Cassidy Kempton, Hilton Kempton, Christen Kempton, Kamal
Kempton, Leron Kempton, Miquel Kempton, Yosef Kempton, Judah Kempton, Malcom Kempton, Rayford Kempton, Arlen Kempton, Gaetano Kempton, Montez Kempton, Kareen Kempton, Dajuan Kempton, Marlow Kempton,
Uriel Kempton, Glynn Kempton, Bud Kempton, Eben Kempton, Geronimo Kempton, Deshaun Kempton, Hernan Kempton, Zebulon Kempton, Deshon Kempton, Gareth Kempton, Paolo Kempton, Edison Kempton, Gaylon
Kempton, Shamus Kempton, Carleton Kempton, Florentino Kempton, Osbaldo Kempton, Brodie Kempton, Jaret Kempton, Johathan Kempton, Tariq Kempton, Seamus Kempton, Devan Kempton, Richmond Kempton,
Cynthia Kempton, Cleo Kempton, Huey Kempton, Talmadge Kempton, Dain Kempton, Dennie Kempton, Paxton Kempton, Peyton Kempton, Darrius Kempton, Jodi Kempton, Ronell Kempton, Jeremi Kempton, Quinten
Kempton, Sandra Kempton, Waymon Kempton, Earle Kempton, Franz Kempton, Christoher Kempton, Micahel Kempton, Sal Kempton, Sharon Kempton, Keegan Kempton, Eusebio Kempton, Geoffery Kempton, Monica
Kempton, Dontae Kempton, Jimi Kempton, Kendric Kempton, Amin Kempton, Cleon Kempton, Kale Kempton, Tina Kempton, Ambrose Kempton, Armond Kempton, Ashton Kempton, Lucien Kempton, Maximo Kempton, Reno
Kempton, Susan Kempton, Chico Kempton, Jermel Kempton, Lennie Kempton, Rajesh Kempton, Artie Kempton, Kerwin Kempton, Sage Kempton, Dietrich Kempton, Eriberto Kempton, Niles Kempton, Rolland Kempton,
Butch Kempton, Courtland Kempton, King Kempton, Kit Kempton, Menachem Kempton, Rich Kempton, Florencio Kempton, Lovell Kempton, Jacque Kempton, Antwone Kempton, Darick Kempton, Kennth Kempton, Asher
Kempton, Efrem Kempton, Lamarcus Kempton, Terron Kempton, Jacinto Kempton, Karlos Kempton, Mohamed Kempton, Rahman Kempton, Ammon Kempton, Davie Kempton, Diallo Kempton, Kelton Kempton, Mathias
Kempton, Sunny Kempton, Zeke Kempton, Jaison Kempton, Nate Kempton, Demetrious Kempton, Maceo Kempton, Vasilios Kempton, Demetrio Kempton, Lyman Kempton, Angus Kempton, Arvin Kempton, Camron Kempton,
Daryll Kempton, Ehren Kempton, Les Kempton, Nils Kempton, Akil Kempton, Markeith Kempton, Santana Kempton, Warner Kempton, Alphonse Kempton, Arnaldo Kempton, Art Kempton, Domenick Kempton, Prentiss
Kempton, Blas Kempton, Dwan Kempton, Geno Kempton, Kahlil Kempton, Feliciano Kempton, Hayward Kempton, Ulises Kempton, Valentine Kempton, Darold Kempton, Deven Kempton, Mordechai Kempton, Rodriquez
Kempton, Gentry Kempton, Jorje Kempton, Sunil Kempton, Wilburn Kempton, Anders Kempton, Damone Kempton, Sherrod Kempton, Dashawn Kempton, Otha Kempton, Rahim Kempton, Javan Kempton, Wendy Kempton,
Camilo Kempton, Jeromie Kempton, Jaysen Kempton, Modesto Kempton, Quincey Kempton, Tyran Kempton, Cleve Kempton, Raynard Kempton, Tori Kempton, Antonino Kempton, Bartley Kempton, Kristofor Kempton,
Sheridan Kempton, Alva Kempton, Correy Kempton, Dandre Kempton, Darek Kempton, Wylie Kempton, Anand Kempton, Decarlos Kempton, Domonic Kempton, Rachel Kempton, Jamieson Kempton, Nikolaos Kempton,
Rashaan Kempton, Roque Kempton, Shelly Kempton, Sven Kempton, Evans Kempton, Jakob Kempton, Lateef Kempton, Noble Kempton, Artemio Kempton, Kameron Kempton, Kavin Kempton, Dick Kempton, Filiberto
Kempton, Henri Kempton, Joby Kempton, Montgomery Kempton, Salomon Kempton, Vashon Kempton, Abdullah Kempton, Cal Kempton, Shain Kempton, Sherwood Kempton, Dewitt Kempton, Newton Kempton, Nicklaus
Kempton, Darvin Kempton, Jeron Kempton, Khari Kempton, Tyrome Kempton, Benjie Kempton, Kunta Kempton, Karsten Kempton, Patric Kempton, Reece Kempton, Olen Kempton, Rowdy Kempton, Terrel Kempton,
Addison Kempton, Blaise Kempton, Fidencio Kempton, Ibrahim Kempton, Idris Kempton, Lavern Kempton, Mickel Kempton, Shun Kempton, Athanasios Kempton, Danilo Kempton, Giles Kempton, Mateo Kempton, Nino
Kempton, Alonza Kempton, Cardell Kempton, Job Kempton, Mahlon Kempton, Anil Kempton, Destry Kempton, Lamon Kempton, Martez Kempton, Mikael Kempton, Nickey Kempton, Tywan Kempton, Abner Kempton,
Jamell Kempton, Nels Kempton, Raoul Kempton, Braulio Kempton, Randle Kempton, Roddy Kempton, Toni Kempton, Lynwood Kempton, Thurston Kempton, Chrisopher Kempton, Eron Kempton, Fausto Kempton, Keir
Kempton, Kelcey Kempton, Marquette Kempton, Mikeal Kempton, Anselmo Kempton, Hipolito Kempton, Neville Kempton, Rodriguez Kempton, Antron Kempton, Walton Kempton, Devlin Kempton, Lucian Kempton,
Rudolfo Kempton, Avi Kempton, Brantley Kempton, Dathan Kempton, Doran Kempton, Erica Kempton, Franky Kempton, Kary Kempton, Tiffany Kempton, Yuri Kempton, Bucky Kempton, Hardy Kempton, Justus
Kempton, Cecilio Kempton, Hoyt Kempton, Jasson Kempton, Jerardo Kempton, Johnson Kempton, Kenney Kempton, Panagiotis Kempton, Ajay Kempton, Alvis Kempton, Conrado Kempton, Mel Kempton, Burl Kempton,
Daymon Kempton, Dorsey Kempton, Giancarlo Kempton, Riccardo Kempton, Antuan Kempton, Braxton Kempton, Candelario Kempton, Colton Kempton, Rommel Kempton, Irwin Kempton, Reynold Kempton, Tino Kempton,
Alessandro Kempton, Corie Kempton, Dameion Kempton, Dwyane Kempton, Jabbar Kempton, Lajuan Kempton, Mose Kempton, Taiwan Kempton, Yisroel Kempton, Danniel Kempton, Darris Kempton, Jerred Kempton,
Lori Kempton, Crispin Kempton, Maximilian Kempton, Skip Kempton, Yaakov Kempton, Brodrick Kempton, Fabio Kempton, Gerrit Kempton, Iran Kempton, Trace Kempton, Amar Kempton, Aram Kempton, Buster
Kempton, Byran Kempton, Jens Kempton, Joseluis Kempton, Karriem Kempton, Kenan Kempton, Tonya Kempton, Trampas Kempton, Durand Kempton, Lou Kempton, Regis Kempton, Cain Kempton, Christ Kempton, Daivd
Kempton, Marquise Kempton, Meredith Kempton, Dell Kempton, Matthias Kempton, Alphonzo Kempton, Latroy Kempton, Allison Kempton, Darion Kempton, Melton Kempton, Tara Kempton, Boyce Kempton, Cletus
Kempton, Derron Kempton, Madison Kempton, Tait Kempton, Yehuda Kempton, Arik Kempton, Donato Kempton, Duston Kempton, Kimani Kempton, Lucious Kempton, Nader Kempton, Baldemar Kempton, Bertrand
Kempton, Blane Kempton, Dujuan Kempton, Ellery Kempton, Kennedy Kempton, Misael Kempton, Tremain Kempton, Veronica Kempton, Christy Kempton, Columbus Kempton, Little Kempton, Marius Kempton, Skyler
Kempton, Alexandre Kempton, Celestino Kempton, Crystal Kempton, Jordon Kempton, Justine Kempton, Demon Kempton, Derreck Kempton, Flavio Kempton, Kennard Kempton, Roby Kempton, Schuyler Kempton,
Garrison Kempton, Cipriano Kempton, Cori Kempton, Denise Kempton, Keyon Kempton, Laverne Kempton, Obie Kempton, Tige Kempton, Gabino Kempton, Joselito Kempton, Karlton Kempton, Lashon Kempton, Lucky
Kempton, Neill Kempton, Shmuel Kempton, Ara Kempton, Blain Kempton, Pascual Kempton, Rashan Kempton, Serge Kempton, Thane Kempton, Bradlee Kempton, Connor Kempton, Cooper Kempton, Jonny Kempton,
Merrick Kempton, Porter Kempton, Zeb Kempton, April Kempton, Edrick Kempton, Flint Kempton, Heith Kempton, Jospeh Kempton, Luiz Kempton, Macario Kempton, Zach Kempton, Candido Kempton, Dangelo
Kempton, Dov Kempton, Dru Kempton, Eladio Kempton, Rasheem Kempton, Tarek Kempton, Willian Kempton, Ezell Kempton, Konrad Kempton, Mick Kempton, Tarrance Kempton, Yitzchok Kempton, Rahul Kempton,
Shelley Kempton, Theodis Kempton, Timonthy Kempton, Connie Kempton, Derrik Kempton, Ennis Kempton, Gail Kempton, Gaston Kempton, Gunnar Kempton, Justice Kempton, Romel Kempton, Bilal Kempton, Jamy
Kempton, Jomo Kempton, Keary Kempton, Nehemiah Kempton, Rashon Kempton, Rolf Kempton, Sameer Kempton, Jere Kempton, Jerone Kempton, Kennon Kempton, Rodd Kempton, Ronaldo Kempton, Teresa Kempton,
Coley Kempton, Enos Kempton, Narciso Kempton, Robinson Kempton, Tobby Kempton, Virgilio Kempton, Christiaan Kempton, Clarke Kempton, Demetruis Kempton, Jemal Kempton, Llewellyn Kempton, Miller
Kempton, Shilo Kempton, Tarus Kempton, Young Kempton, Arlie Kempton, Djuan Kempton, Marcial Kempton, Pamela Kempton, Rayshawn Kempton, Robyn Kempton, Tirrell Kempton, Dontay Kempton, Joshuah Kempton,
Jovon Kempton, Lemar Kempton, Oran Kempton, Taron Kempton, Jaimie Kempton, Kacey Kempton, Wendall Kempton, Armondo Kempton, Curry Kempton, Klint Kempton, Lauro Kempton, Maximillian Kempton, Rashard
Kempton, Anastasios Kempton, Jermiah Kempton, Joao Kempton, Lonnell Kempton, Matias Kempton, Rollin Kempton, Thimothy Kempton, Toma Kempton, Jahmal Kempton, Jerame Kempton, Skye Kempton, Alford
Kempton, Baltazar Kempton, Gianni Kempton, Hayes Kempton, Lamond Kempton, Linda Kempton, Neftali Kempton, Antwoine Kempton, Arden Kempton, Dionicio Kempton, Ely Kempton, Kacy Kempton, Syed Kempton,
Tyrel Kempton, Windell Kempton, Allyn Kempton, Antwane Kempton, Dayne Kempton, Donal Kempton, Maxie Kempton, Rashaun Kempton, Sampson Kempton, Torin Kempton, Axel Kempton, Delmer Kempton, Dickie
Kempton, Evaristo Kempton, Francois Kempton, Radames Kempton, Sixto Kempton, Terri Kempton, Wyman Kempton, Ashanti Kempton, Benjaman Kempton, Christophor Kempton, Delwin Kempton, Lemont Kempton,
Lonzo Kempton, Mustafa Kempton, Sasha Kempton, Travon Kempton, Darryll Kempton, Garfield Kempton, Jarrell Kempton, Lawson Kempton, Nikki Kempton, Terell Kempton, Ace Kempton, Donna Kempton, Gerome
Kempton, Jermane Kempton, Joeseph Kempton, Raynaldo Kempton, Carrie Kempton, Demetri Kempton, Rupert Kempton, Shadrick Kempton, Sol Kempton, Wendel Kempton, Zechariah Kempton, Delon Kempton,
Demitrius Kempton, Mcarthur Kempton, Nickie Kempton, Tavaris Kempton, Baby Kempton, Cornelious Kempton, Deborah Kempton, Haven Kempton, Merritt Kempton, Vijay Kempton, Granville Kempton, Rock
Kempton, Romero Kempton, Tanya Kempton, Anastacio Kempton, Ciro Kempton, Gennaro Kempton, Jerrel Kempton, Justo Kempton, Maury Kempton, Stafford Kempton, Amon Kempton, Carol Kempton, Cornelio
Kempton, Dawson Kempton, Erskine Kempton, Tarrence Kempton, Torrie Kempton, Trevin Kempton, Breck Kempton, Delfino Kempton, Desean Kempton, Jerron Kempton, Milford Kempton, Nancy Kempton, Oswald
Kempton, Stefano Kempton, Demont Kempton, Lawerence Kempton, Parris Kempton, Godfrey Kempton, Hakeem Kempton, Leobardo Kempton, Loran Kempton, Garnett Kempton, Lawrance Kempton, Darryn Kempton, Eamon
Kempton, Geremy Kempton, Kobie Kempton, Leeroy Kempton, Maximino Kempton, Orrin Kempton, Wayman Kempton, Brenda Kempton, Celso Kempton, Daman Kempton, Denzil Kempton, Geary Kempton, Ladon Kempton,
Marland Kempton, Servando Kempton, Kamau Kempton, Migel Kempton, Ramond Kempton, Terrace Kempton, Ubaldo Kempton, Chaz Kempton, Demetrick Kempton, Freddrick Kempton, Gray Kempton, Ivy Kempton, Shlomo
Kempton, Torre Kempton, Damein Kempton, Deryl Kempton, Dusten Kempton, Katherine Kempton, Kreg Kempton, London Kempton, Patrice Kempton, Payton Kempton, Ramel Kempton, Rosalio Kempton, Serjio
Kempton, Tramaine Kempton, Adolphus Kempton, Ameer Kempton, Antwaun Kempton, Ashish Kempton, Benjamine Kempton, Charleston Kempton, Darry Kempton, Elmo Kempton, Nicklas Kempton, Nikolai Kempton,
Ricki Kempton, Tai Kempton, Bernardino Kempton, Devaughn Kempton, Epifanio Kempton, Gaylord Kempton, Mathieu Kempton, Romell Kempton, Arlin Kempton, Bradd Kempton, Clair Kempton, Dawud Kempton,
Jeffory Kempton, Lyndell Kempton, Sara Kempton, Adriel Kempton, Algernon Kempton, Benigno Kempton, Chancey Kempton, Elan Kempton, Jeromey Kempton, Lionell Kempton, Shone Kempton, Donyell Kempton,
Herminio Kempton, Jerrett Kempton, Naim Kempton, Nikolaus Kempton, Soren Kempton, Agapito Kempton, Carlin Kempton, Cass Kempton, Harmon Kempton, Johan Kempton, Junius Kempton, Kenrick Kempton, Kervin
Kempton, Kori Kempton, Raj Kempton, Shimon Kempton, Basilio Kempton, Juventino Kempton, Kirkland Kempton, Kwesi Kempton, Manish Kempton, Omer Kempton, Tedd Kempton, Vic Kempton, Antonie Kempton,
Chauncy Kempton, Dagoberto Kempton, Darel Kempton, Jerrid Kempton, Julien Kempton, Layton Kempton, Quan Kempton, Roddrick Kempton, Shaw Kempton, Silvestre Kempton, Tavon Kempton, Unknown Kempton,
Daniell Kempton, Andrei Kempton, Hashim Kempton, Hobert Kempton, Terris Kempton, Aundre Kempton, Avrohom Kempton, Elden Kempton, Guido Kempton, Holly Kempton, Marice Kempton, Martinez Kempton, Daneil
Kempton, Mattew Kempton, Shamar Kempton, Shannan Kempton, Shomari Kempton, Daniele Kempton, Darrian Kempton, Demetrus Kempton, Erron Kempton, Hasani Kempton, Robbin Kempton, Sabino Kempton, Sloan
Kempton, Zev Kempton, Cassius Kempton, Dawan Kempton, Sekou Kempton, Tyjuan Kempton, Bentley Kempton, Ean Kempton, Edric Kempton, Gamaliel Kempton, Gerold Kempton, Jacoby Kempton, Palmer Kempton,
Randon Kempton, Sami Kempton, Spence Kempton, Willaim Kempton, Alvino Kempton, Antonios Kempton, Derry Kempton, Germain Kempton, Jewel Kempton, Lashaun Kempton, Tobie Kempton, Webster Kempton, Abran
Kempton, Brigham Kempton, Leshawn Kempton, Mica Kempton, Pascal Kempton, Americo Kempton, Danyell Kempton, Jamall Kempton, Johnell Kempton, Lambert Kempton, Lindell Kempton, Raffaele Kempton, Barret
Kempton, Chadley Kempton, Frantz Kempton, Gabrial Kempton, Geroge Kempton, Harland Kempton, Obed Kempton, Sharod Kempton, Silverio Kempton, Vernard Kempton, Alfie Kempton, Darryle Kempton, Daymond
Kempton, Deane Kempton, Garey Kempton, Jarid Kempton, Oronde Kempton, Rowland Kempton, Sandeep Kempton, Stevenson Kempton, Aarron Kempton, Arin Kempton, Aryeh Kempton, Catarino Kempton, Christoph
Kempton, Collins Kempton, Elio Kempton, Gearld Kempton, Jonnie Kempton, Mackenzie Kempton, Markell Kempton, Shawne Kempton, Walt Kempton, Willam Kempton, Winfield Kempton, Arnell Kempton, Aundra
Kempton, Bryn Kempton, Conway Kempton, Dempsey Kempton, Eligio Kempton, Alicia Kempton, Jairo Kempton, Kathleen Kempton, Koby Kempton, Nikia Kempton, Pierce Kempton, Sherard Kempton, Spiro Kempton,
Winford Kempton, Alfonza Kempton, Augusto Kempton, Christin Kempton, Dakota Kempton, Gannon Kempton, Lucus Kempton, Rand Kempton, Renardo Kempton, Robet Kempton, Atiba Kempton, Dondi Kempton, Jammy
Kempton, Jarrid Kempton, Jonthan Kempton, Marlan Kempton, Olando Kempton, Salim Kempton, Shaine Kempton, Arun Kempton, Broc Kempton, Cash Kempton, Cord Kempton, Ebony Kempton, Gage Kempton, Jacobo
Kempton, Loy Kempton, Orlanda Kempton, Sammuel Kempton, Trampus Kempton, Chaka Kempton, Lakeith Kempton, Mendel Kempton, Saleem Kempton, Antoin Kempton, Bernabe Kempton, Darnel Kempton, Ioannis
Kempton, Jill Kempton, Melanie Kempton, Oneal Kempton, Paulino Kempton, Theadore Kempton, Yves Kempton, Aidan Kempton, Antjuan Kempton, Decarlo Kempton, Fitzgerald Kempton, Frances Kempton, Jhon
Kempton, Price Kempton, Theophilus Kempton, Theresa Kempton, Aden Kempton, Alaric Kempton, Armon Kempton, Johny Kempton, Kenith Kempton, Mallory Kempton, Rondal Kempton, Samer Kempton, Coty Kempton,
Gerrod Kempton, Maximiliano Kempton, Rito Kempton, Robie Kempton, Skipper Kempton, Wali Kempton, Blayne Kempton, Christophr Kempton, Mandel Kempton, Nathon Kempton, Orenthal Kempton, Rudolf Kempton,
Bailey Kempton, Christropher Kempton, Cleophus Kempton, Eulalio Kempton, Jerard Kempton, Jethro Kempton, Jonothan Kempton, Lannie Kempton, Shaka Kempton, Arlan Kempton, Chas Kempton, Conley Kempton,
Donzell Kempton, Jamarr Kempton, Karon Kempton, Landis Kempton, Marie Kempton, Marino Kempton, Michial Kempton, Tyrice Kempton, Vivek Kempton, Arian Kempton, Carlyle Kempton, Ibn Kempton, Jonmichael
Kempton, Ottis Kempton, Rafeal Kempton, Serafin Kempton, Tuan Kempton, Arne Kempton, Eliazar Kempton, Jaren Kempton, Kedric Kempton, Kimo Kempton, Kristan Kempton, Kyron Kempton, Rayburn Kempton,
Sandor Kempton, Undra Kempton, Waymond Kempton, Avraham Kempton, Brennen Kempton, Delaney Kempton, Evangelos Kempton, Geoffry Kempton, Jassen Kempton, Jermal Kempton, Jerrick Kempton, Spiros Kempton,
Uri Kempton, Andrey Kempton, Christain Kempton, Diamond Kempton, Edgard Kempton, Gardner Kempton, Heidi Kempton, Jerid Kempton, Laramie Kempton, Philbert Kempton, Arlyn Kempton, Armin Kempton,
Bonifacio Kempton, Kari Kempton, Kofi Kempton, Tamara Kempton, Wayde Kempton, Anna Kempton, Cheston Kempton, Jarom Kempton, Jemel Kempton, Jermy Kempton, Jeronimo Kempton, Ontario Kempton, Roshawn
Kempton, Adams Kempton, Barbara Kempton, Darran Kempton, Horatio Kempton, Jedd Kempton, Jeramey Kempton, Rajeev Kempton, Rendell Kempton, Ansel Kempton, Apolonio Kempton, Daric Kempton, Dewan
Kempton, Krishna Kempton, Lenwood Kempton, Lex Kempton, Marlowe Kempton, Mickael Kempton, Octavious Kempton, Rashaad Kempton, Catherine Kempton, Chesley Kempton, Natividad Kempton, Ahren Kempton,
Alvie Kempton, Ardell Kempton, Gaylen Kempton, Iain Kempton, Jeffrie Kempton, Levy Kempton, Naeem Kempton, Ramey Kempton, Rapheal Kempton, Recardo Kempton, Welton Kempton, Wiliam Kempton, Bakari
Kempton, Diana Kempton, Durrell Kempton, Gaspar Kempton, Jacqueline Kempton, Jewell Kempton, Marvell Kempton, Noland Kempton, Tedrick Kempton, Waleed Kempton, Aloysius Kempton, Amber Kempton, Audrey
Kempton, Curley Kempton, Farris Kempton, Gian Kempton, Jarmaine Kempton, Lazarus Kempton, Parish Kempton, Stavros Kempton, Sultan Kempton, Laquan Kempton, Londell Kempton, Parnell Kempton, Ryland
Kempton, Shem Kempton, Yolanda Kempton, Arnie Kempton, Brennon Kempton, Chan Kempton, Dionisio Kempton, Frederico Kempton, Joy Kempton, Juancarlos Kempton, Keno Kempton, Kwasi Kempton, Lael Kempton,
Laroy Kempton, Normand Kempton, Omarr Kempton, Tyre Kempton, Valente Kempton, Gavino Kempton, Kade Kempton, Kolby Kempton, Linton Kempton, Malvin Kempton, Moishe Kempton, Rhonda Kempton, Sherry
Kempton, Verlin Kempton, Antoino Kempton, Benjy Kempton, Dmitri Kempton, Duan Kempton, Ford Kempton, Hezekiah Kempton, Kalani Kempton, Kinte Kempton, Lacey Kempton, Massimo Kempton, Ryder Kempton,
Seann Kempton, Valerie Kempton, Waldo Kempton, Edson Kempton, Eliud Kempton, Gustave Kempton, Harrell Kempton, Henderson Kempton, Obadiah Kempton, Christipher Kempton, Constantinos Kempton, Cort
Kempton, Duran Kempton, Eldred Kempton, Jennings Kempton, Jubal Kempton, Macarthur Kempton, Marvis Kempton, Ric Kempton, Dimas Kempton, Emily Kempton, Golden Kempton, Jessee Kempton, Juaquin Kempton,
Kennie Kempton, Lerone Kempton, Paige Kempton, Shean Kempton, Termaine Kempton, Antoni Kempton, Connell Kempton, Gustav Kempton, Meir Kempton, Reza Kempton, Rollie Kempton, Ronney Kempton, Sherron
Kempton, Teron Kempton, Theotis Kempton, Vittorio Kempton, Athony Kempton, Burnell Kempton, Crawford Kempton, Esau Kempton, Gina Kempton, Jamahl Kempton, Kenyata Kempton, Mickeal Kempton, Rexford
Kempton, Rockey Kempton, Thadeus Kempton, Trevon Kempton, Barclay Kempton, Chuckie Kempton, Early Kempton, Ernst Kempton, Fredy Kempton, Gildardo Kempton, Hyrum Kempton, Kerby Kempton, Kimball
Kempton, Marek Kempton, Ransom Kempton, Shareef Kempton, Sid Kempton, Tillman Kempton, West Kempton, Wynn Kempton, Danyel Kempton, Eduard Kempton, Elmore Kempton, Holland Kempton, Johannes Kempton,
Langston Kempton, Long Kempton, Lyn Kempton, Montreal Kempton, Rui Kempton, Shae Kempton, Shondell Kempton, Tor Kempton, Caine Kempton, Destin Kempton, Dionne Kempton, Hernando Kempton, Isabel
Kempton, Lamark Kempton, Leandre Kempton, Nicholus Kempton, Nikola Kempton, Olaf Kempton, Orson Kempton, Presley Kempton, Randi Kempton, Regina Kempton, Rufino Kempton, Shariff Kempton, Shaune
Kempton, Torri Kempton, Arcadio Kempton, Arlando Kempton, Carlus Kempton, Efraim Kempton, Emmet Kempton, Etienne Kempton, Garvin Kempton, Jermine Kempton, Larnell Kempton, Michiel Kempton, Pieter
Kempton, Wilber Kempton, Christapher Kempton, Derk Kempton, Enrigue Kempton, Isidoro Kempton, Kriston Kempton, Ladell Kempton, Morton Kempton, Nash Kempton, Nickolaus Kempton, Paula Kempton, Sheron
Kempton, Wellington Kempton, Antawn Kempton, Brandyn Kempton, Christan Kempton, Deonte Kempton, Elie Kempton, Hampton Kempton, Jeremias Kempton, Marque Kempton, Weylin Kempton, Antwine Kempton,
Bonnie Kempton, Chucky Kempton, Matthews Kempton, Mikell Kempton, Padraic Kempton, Tarence Kempton, Christphor Kempton, Cindy Kempton, Daven Kempton, Dock Kempton, Enzo Kempton, Gerrick Kempton,
Jeanpierre Kempton, Jericho Kempton, Joan Kempton, Kenley Kempton, Kentrell Kempton, Sherod Kempton, Carlous Kempton, Deandra Kempton, Demar Kempton, Dieter Kempton, Frazier Kempton, Garon Kempton,
Howell Kempton, Joh Kempton, Librado Kempton, Melinda Kempton, Micha Kempton, Steffan Kempton, Stevens Kempton, Victoriano Kempton, Zak Kempton, Addam Kempton, Arick Kempton, Cheryl Kempton, Cornel
Kempton, Cosme Kempton, Damani Kempton, Dillard Kempton, Edsel Kempton, Garner Kempton, Gerad Kempton, Giacomo Kempton, Ismail Kempton, Link Kempton, Rohit Kempton, Alexandros Kempton, Brandin
Kempton, Dolan Kempton, Dustyn Kempton, Eran Kempton, Imran Kempton, Johnthan Kempton, Lashun Kempton, Linus Kempton, Misty Kempton, Shaheed Kempton, Ann Kempton, Antionio Kempton, Arie Kempton, Aris
Kempton, Armen Kempton, Clancy Kempton, Colt Kempton, Dione Kempton, Garren Kempton, Janson Kempton, Justyn Kempton, Megan Kempton, Niel Kempton, Niels Kempton, Rockie Kempton, Thornton Kempton,
Turner Kempton, Viet Kempton, Albino Kempton, Alma Kempton, Artemus Kempton, Cam Kempton, Claud Kempton, Daimon Kempton, Dequan Kempton, Fransico Kempton, Ilan Kempton, Laurent Kempton, Sigmund
Kempton, Tal Kempton, Tray Kempton, Apollo Kempton, Barak Kempton, Brentley Kempton, Cleavon Kempton, Delvon Kempton, Dyron Kempton, Jaye Kempton, Jermell Kempton, Ladd Kempton, Leamon Kempton, Nico
Kempton, Ovidio Kempton, Peder Kempton, Raven Kempton, Teofilo Kempton, Trae Kempton, Alon Kempton, Charle Kempton, Erek Kempton, Evin Kempton, Graeme Kempton, Jerimie Kempton, Juanito Kempton, Keoni
Kempton, Kwan Kempton, Lathan Kempton, Leonidas Kempton, Marrio Kempton, Mayer Kempton, Ozzie Kempton, Rajiv Kempton, Rami Kempton, Shann Kempton, Teague Kempton, Terran Kempton, Branson Kempton,
Briant Kempton, Christohper Kempton, Delmas Kempton, Demone Kempton, Duffy Kempton, Grabiel Kempton, Hudson Kempton, Jae Kempton, Jefrey Kempton, Kali Kempton, Klinton Kempton, Markel Kempton,
Saverio Kempton, Steffen Kempton, Akbar Kempton, Brandi Kempton, Desmon Kempton, Detric Kempton, Doron Kempton, Georgie Kempton, Hilary Kempton, Isadore Kempton, Kawika Kempton, Keefe Kempton,
Montell Kempton, Prentis Kempton, Rishi Kempton, Zacharia Kempton, Adriano Kempton, Arash Kempton, Chancy Kempton, Deshun Kempton, Donnel Kempton, Johndavid Kempton, Jonn Kempton, Kerrick Kempton,
Ruperto Kempton, Silvio Kempton, Smith Kempton, Alen Kempton, Damarcus Kempton, Dixon Kempton, Isacc Kempton, Landry Kempton, Laurie Kempton, Lennard Kempton, Mckenzie Kempton, Rakesh Kempton, Selwyn
Kempton, Torris Kempton, Yohance Kempton, Zakary Kempton, Alison Kempton, Baxter Kempton, Bienvenido Kempton, Christon Kempton, Cosmo Kempton, Cuauhtemoc Kempton, Drue Kempton, Ferris Kempton, Jensen
Kempton, Jerime Kempton, Kathryn Kempton, Kingsley Kempton, Prescott Kempton, Rayfield Kempton, Sanders Kempton, Tarvis Kempton, Bernell Kempton, Calvert Kempton, Channon Kempton, Clovis Kempton,
Duron Kempton, Dushawn Kempton, Elam Kempton, Elwin Kempton, Johnmichael Kempton, Lawton Kempton, Linden Kempton, Meyer Kempton, Raheen Kempton, Santonio Kempton, Shonn Kempton, Vikram Kempton, Wesly
Kempton, Yoel Kempton, Ysidro Kempton, Asim Kempton, Authur Kempton, Cyle Kempton, General Kempton, Page Kempton, Tab Kempton, Tamar Kempton, Thaddaeus Kempton, Tyshawn Kempton, Akiva Kempton, Alexi
Kempton, Dannon Kempton, Draper Kempton, Garet Kempton, Immanuel Kempton, Julia Kempton, Manfred Kempton, Monique Kempton, Monta Kempton, Nile Kempton, Rome Kempton, Tywon Kempton, Verne Kempton,
Amando Kempton, Askia Kempton, Cannon Kempton, Chavis Kempton, Davide Kempton, Deepak Kempton, Garold Kempton, Jabar Kempton, Japheth Kempton, Klaus Kempton, Naftali Kempton, Ora Kempton, Ronn
Kempton, Shandon Kempton, Toussaint Kempton, Travers Kempton, Verlon Kempton, Antwann Kempton, Barnaby Kempton, Bretton Kempton, Cesario Kempton, Georgios Kempton, Jajuan Kempton, Lisandro Kempton,
Maurizio Kempton, Shakir Kempton, Tavarus Kempton, Waverly Kempton, Chaun Kempton, Diane Kempton, Dontrell Kempton, Jamiel Kempton, Jashua Kempton, Leopold Kempton, Lynell Kempton, Montie Kempton,
Rafe Kempton, Reginold Kempton, Romulo Kempton, Thayne Kempton, Tierre Kempton, Wilhelm Kempton, Akim Kempton, Baldomero Kempton, Darrien Kempton, Durell Kempton, Eden Kempton, Gergory Kempton, Kerri
Kempton, Lennon Kempton, Margaret Kempton, Nikita Kempton, Noam Kempton, Rajan Kempton, Reynard Kempton, Sachin Kempton, Seferino Kempton, Ventura Kempton, Warrick Kempton, Washington Kempton,
Antonius Kempton, Barrington Kempton, Billyjoe Kempton, Christo Kempton, Derald Kempton, Dewight Kempton, Ferrell Kempton, Filippo Kempton, Garin Kempton, Herbie Kempton, Joachim Kempton, Khalif
Kempton, Mikey Kempton, Severo Kempton, Tahir Kempton, Taras Kempton, Vinay Kempton, Aharon Kempton, Antiono Kempton, Apolinar Kempton, Arsenio Kempton, Furman Kempton, Gayle Kempton, Girard Kempton,
Grey Kempton, Hillary Kempton, Martel Kempton, Murry Kempton, Nabil Kempton, Neel Kempton, Ozell Kempton, Rylan Kempton, Samantha Kempton, Tellis Kempton, Thompson Kempton, Varian Kempton, Antoinne
Kempton, Derrel Kempton, Erika Kempton, Faisal Kempton, Kristina Kempton, Laird Kempton, Lancer Kempton, Marcelle Kempton, Melvyn Kempton, Sabin Kempton, Tajuan Kempton, Terrick Kempton, Thadius
Kempton, Timoteo Kempton, Treavor Kempton, Tyrese Kempton, Victoria Kempton, Vishal Kempton, Aran Kempton, Christoffer Kempton, Devron Kempton, Durwin Kempton, Elon Kempton, Hansel Kempton, Haskell
Kempton, Jerell Kempton, Jonathen Kempton, Lanier Kempton, Marcellous Kempton, Marquez Kempton, Regino Kempton, Skylar Kempton, Christobal Kempton, Claudia Kempton, Dartagnan Kempton, Errin Kempton,
Hung Kempton, Juvenal Kempton, Kaseem Kempton, Keri Kempton, Marwan Kempton, Matteo Kempton, Raymone Kempton, Rennie Kempton, Rondale Kempton, Shadd Kempton, Yul Kempton, Arnel Kempton, Concepcion
Kempton, Daran Kempton, Flynn Kempton, Jawara Kempton, Jeremia Kempton, Karry Kempton, Rodric Kempton, Romon Kempton, Aren Kempton, Bevan Kempton, Casper Kempton, Collis Kempton, Delane Kempton,
Erric Kempton, Gerhard Kempton, Hillel Kempton, Jansen Kempton, Jenny Kempton, Keelan Kempton, Michell Kempton, Petros Kempton, Saeed Kempton, Shamon Kempton, Starsky Kempton, Tamir Kempton, Umar
Kempton, Verdell Kempton, Vicent Kempton, Alpha Kempton, Arther Kempton, Case Kempton, Cavin Kempton, Deacon Kempton, Franciso Kempton, Freedom Kempton, Gregary Kempton, Harlen Kempton, Ichael
Kempton, Jacy Kempton, Jeremaine Kempton, Jud Kempton, Judge Kempton, Monico Kempton, Raffi Kempton, Ricci Kempton, Sacha Kempton, Adelbert Kempton, Andree Kempton, Bron Kempton, Cisco Kempton, Creed
Kempton, Criag Kempton, Edilberto Kempton, Gillermo Kempton, Hobart Kempton, Justino Kempton, Kodi Kempton, Martino Kempton, Mickie Kempton, Newell Kempton, Odie Kempton, Robbi Kempton, Thaddius
Kempton, Tonny Kempton, Tully Kempton, Werner Kempton, Zoltan Kempton, Carrol Kempton, Cesare Kempton, Clarance Kempton, Clem Kempton, Davion Kempton, Dvid Kempton, Graydon Kempton, Latrell Kempton,
Manual Kempton, Pervis Kempton, Randolf Kempton, Sinclair Kempton, Stephane Kempton, Torian Kempton, Tylor Kempton, Tzvi Kempton, Umberto Kempton, Baruch Kempton, Benard Kempton, Glenwood Kempton,
Jaun Kempton, Jermie Kempton, Johnney Kempton, Kenard Kempton, Kyler Kempton, Luca Kempton, Martha Kempton, Nephi Kempton, Nicholos Kempton, Nikhil Kempton, Olan Kempton, Sir Kempton, Stevon Kempton,
Teon Kempton, Tryone Kempton, Vanessa Kempton, Ames Kempton, Breon Kempton, Gregroy Kempton, Heyward Kempton, Jebediah Kempton, Kye Kempton, Larue Kempton, Lonell Kempton, Nevada Kempton, Norma
Kempton, Renny Kempton, Rosa Kempton, Ana Kempton, Blue Kempton, Cresencio Kempton, Danon Kempton, Debra Kempton, Denard Kempton, Deondre Kempton, Elzie Kempton, Gamal Kempton, Gerrard Kempton, Heber
Kempton, Jerremy Kempton, Jobe Kempton, Jun Kempton, Karey Kempton, Marquel Kempton, Martell Kempton, Marvel Kempton, Ocie Kempton, Raudel Kempton, Romaine Kempton, Rush Kempton, Ruston Kempton,
Talib Kempton, Therman Kempton, Vann Kempton, Vaughan Kempton, Wilberto Kempton, Albin Kempton, Antwuan Kempton, Aramis Kempton, Bodie Kempton, Darrion Kempton, Diron Kempton, Issa Kempton, Izaak
Kempton, Javis Kempton, Jerami Kempton, Keane Kempton, Kjell Kempton, Laurance Kempton, Marico Kempton, Philipp Kempton, Placido Kempton, Remy Kempton, Rion Kempton, Sanchez Kempton, Shahid Kempton,
Valdez Kempton, Acie Kempton, Aundrey Kempton, Buckley Kempton, Eliyahu Kempton, Erroll Kempton, Leotis Kempton, Levern Kempton, Mace Kempton, Perrin Kempton, Phillipe Kempton, Rama Kempton, Steward
Kempton, Tawan Kempton, Zvi Kempton, Carlon Kempton, Daris Kempton, Deandrea Kempton, Dominque Kempton, Gill Kempton, Keola Kempton, Larone Kempton, Lew Kempton, Luz Kempton, Montel Kempton, Sylvan
Kempton, Tobi Kempton, Twan Kempton, Ashraf Kempton, Avram Kempton, Benzion Kempton, Casimiro Kempton, Chane Kempton, Christie Kempton, Chritopher Kempton, Cirilo Kempton, Constantino Kempton, Dupree
Kempton, Gregor Kempton, Jathan Kempton, Keaton Kempton, Kostas Kempton, Larenzo Kempton, Parag Kempton, Rudi Kempton, Sameul Kempton, Sanjeev Kempton, Soloman Kempton, Tarrell Kempton, Traci
Kempton, Tracie Kempton, Watson Kempton, Zoran Kempton, Aries Kempton, Aristotle Kempton, Avelino Kempton, Bram Kempton, Camden Kempton, Dagan Kempton, Damin Kempton, Danta Kempton, Eliott Kempton,
Felicia Kempton, Juwan Kempton, Kemp Kempton, Kenn Kempton, Kenyatte Kempton, Michail Kempton, Orval Kempton, Salvadore Kempton, Shirley Kempton, Boone Kempton, Dionte Kempton, Durwood Kempton,
Ellison Kempton, Garron Kempton, Gerson Kempton, Jerrald Kempton, Lavaughn Kempton, Musa Kempton, Rayvon Kempton, Richrd Kempton, Sharrod Kempton, Stony Kempton, Vikas Kempton, Ector Kempton, Elia
Kempton, Jerret Kempton, Josua Kempton, Marlen Kempton, Mical Kempton, Niall Kempton, Nicolaus Kempton, Niki Kempton, Raymund Kempton, Simone Kempton, Stormy Kempton, Suzanne Kempton, Teddie Kempton,
Tron Kempton, Wolfgang Kempton, Anthonio Kempton, Berton Kempton, Beverly Kempton, Clive Kempton, Corky Kempton, Danell Kempton, Darl Kempton, Ellsworth Kempton, Gloria Kempton, Gregery Kempton, Ivey
Kempton, Kam Kempton, Kenderick Kempton, Magdaleno Kempton, Markee Kempton, San Kempton, Stacie Kempton, Valdemar Kempton, Zac Kempton, Albaro Kempton, Berkley Kempton, Boe Kempton, Casimir Kempton,
Delroy Kempton, Janet Kempton, Jimmey Kempton, Kalen Kempton, Kregg Kempton, Larkin Kempton, Lenell Kempton, Natalie Kempton, Ruel Kempton, Sabrina Kempton, Thom Kempton, Yale Kempton, Adnan Kempton,
Ankur Kempton, Arnett Kempton, Bishop Kempton, Brently Kempton, Carla Kempton, Courtenay Kempton, Dashon Kempton, Ebon Kempton, Edd Kempton, Ezzard Kempton, Gifford Kempton, Jermon Kempton, Jeryl
Kempton, Jock Kempton, Kiven Kempton, Mandrell Kempton, Nichols Kempton, Norwood Kempton, Olivier Kempton, Ramin Kempton, Rikki Kempton, Aleksandar Kempton, Burley Kempton, Kawan Kempton, Kourtney
Kempton, Lary Kempton, Laszlo Kempton, Loyal Kempton, Marin Kempton, Richey Kempton, Rio Kempton, Rogerio Kempton, Salem Kempton, Shalom Kempton, Sharron Kempton, Tamer Kempton, Torie Kempton, Antar
Kempton, Barrie Kempton, Cletis Kempton, Colter Kempton, Duaine Kempton, Elpidio Kempton, Erice Kempton, Farid Kempton, Fortunato Kempton, Gerrad Kempton, Jad Kempton, Jenaro Kempton, Jones Kempton,
Kamran Kempton, Kelli Kempton, Keneth Kempton, Kortney Kempton, Levell Kempton, Minh Kempton, Monti Kempton, Rodell Kempton, Ronal Kempton, Sheddrick Kempton, Sonia Kempton, Terryl Kempton, York
Kempton, Andrian Kempton, Anne Kempton, Attila Kempton, Avis Kempton, Blaze Kempton, Chi Kempton, Corin Kempton, Dann Kempton, Darik Kempton, Deleon Kempton, Demarko Kempton, Dennison Kempton, Dovid
Kempton, Dutch Kempton, Emmit Kempton, Evert Kempton, Iman Kempton, Joshue Kempton, Lindy Kempton, Mohamad Kempton, Purnell Kempton, Rayshon Kempton, Tyreese Kempton, Alistair Kempton, Arman Kempton,
Blakely Kempton, Brit Kempton, Carlis Kempton, Doniel Kempton, Earnie Kempton, Hershell Kempton, Jasin Kempton, Kendale Kempton, Laine Kempton, Leandrew Kempton, Lenin Kempton, Macon Kempton, Merrell
Kempton, Mychal Kempton, Nat Kempton, Nicanor Kempton, Nirav Kempton, Waldemar Kempton, Yakov Kempton, Adrion Kempton, Bowen Kempton, Carolyn Kempton, Creg Kempton, Farley Kempton, Favian Kempton,
Ferman Kempton, Hurley Kempton, Jairus Kempton, Kevyn Kempton, Korry Kempton, Mandell Kempton, Melchor Kempton, Osualdo Kempton, Shanti Kempton, Sheila Kempton, Sotirios Kempton, Taft Kempton, Tijuan
Kempton, Antonyo Kempton, Antwoin Kempton, Arley Kempton, Carlisle Kempton, Christerpher Kempton, Derell Kempton, Dimitrius Kempton, Fabrizio Kempton, Gibran Kempton, Jasn Kempton, June Kempton,
Kenta Kempton, Kenyetta Kempton, Lantz Kempton, Mart Kempton, Naaman Kempton, Nasser Kempton, Norvell Kempton, Ole Kempton, Perfecto Kempton, Philemon Kempton, Primitivo Kempton, Quint Kempton, Rony
Kempton, Shanta Kempton, Tighe Kempton, Trini Kempton, Antionne Kempton, Antwaine Kempton, Bradon Kempton, Campbell Kempton, Chao Kempton, Donel Kempton, Isa Kempton, Kendra Kempton, Kiel Kempton,
Lejon Kempton, Lonn Kempton, Micael Kempton, Namon Kempton, Perez Kempton, Ramses Kempton, Renwick Kempton, Rigo Kempton, Rober Kempton, Rondall Kempton, Terral Kempton, Tobe Kempton, Akili Kempton,
Dalen Kempton, Deanthony Kempton, Elson Kempton, Fulton Kempton, Hillard Kempton, Jedadiah Kempton, Jihad Kempton, Keevin Kempton, Kile Kempton, Kito Kempton, Kwane Kempton, Lamount Kempton, Lanell
Kempton, Leith Kempton, Marshawn Kempton, Marwin Kempton, Raymont Kempton, Rumaldo Kempton, Tabari Kempton, Tex Kempton, Yechiel Kempton, Chirag Kempton, Crist Kempton, Damain Kempton, Damar Kempton,
Deke Kempton, Earlie Kempton, Eleuterio Kempton, Garen Kempton, Joanthan Kempton, Josephus Kempton, Marisol Kempton, Phillips Kempton, Priest Kempton, Romie Kempton, Sonya Kempton, Sung Kempton,
Tandy Kempton, Traves Kempton, Augusta Kempton, Avon Kempton, Daemon Kempton, Danie Kempton, Delwyn Kempton, Eldrick Kempton, Gerod Kempton, Hannibal Kempton, Harper Kempton, Javiel Kempton, Jawan
Kempton, Kathy Kempton, Kiran Kempton, Linn Kempton, Manolito Kempton, Remus Kempton, Salome Kempton, Savalas Kempton, Shamel Kempton, Sigfredo Kempton, Tylon Kempton, Yehoshua Kempton, Damean
Kempton, Gualberto Kempton, Guiseppe Kempton, Huy Kempton, Jaymes Kempton, Jaymie Kempton, Jeshua Kempton, Maher Kempton, Mahmoud Kempton, Otoniel Kempton, Radford Kempton, Rodman Kempton, Tevis
Kempton, Timohty Kempton, Tripp Kempton, Wells Kempton, Allie Kempton, Ason Kempton, Beth Kempton, Carlas Kempton, Cederick Kempton, Colleen Kempton, Cortland Kempton, Deanna Kempton, Farron Kempton,
Gayland Kempton, Jaeson Kempton, Jamerson Kempton, Kenon Kempton, Keoki Kempton, Kevon Kempton, Kristy Kempton, Ladale Kempton, Mare Kempton, Maurilio Kempton, Niko Kempton, Nikos Kempton, Orland
Kempton, Remigio Kempton, Rhys Kempton, Ruby Kempton, Simcha Kempton, Thatcher Kempton, Travas Kempton, Zachry Kempton, Zenon Kempton, Amish Kempton, Anthon Kempton, Aswad Kempton, Erickson Kempton,
Fernandez Kempton, Finley Kempton, Gorden Kempton, Ignatius Kempton, Illya Kempton, Jerico Kempton, Jermayne Kempton, Kamron Kempton, Keita Kempton, Kwabena Kempton, Lonzell Kempton, Manley Kempton,
Markanthony Kempton, Mika Kempton, Muhammed Kempton, Nicholes Kempton, Percival Kempton, Quin Kempton, Radley Kempton, Ruth Kempton, Sabas Kempton, Shaft Kempton, Shante Kempton, Sullivan Kempton,
Waylan Kempton, Westly Kempton, Woodie Kempton, Algie Kempton, Arvel Kempton, Benedetto Kempton, Bradrick Kempton, Chancellor Kempton, Chawn Kempton, Daylon Kempton, Devonne Kempton, Galvin Kempton,
Herb Kempton, Jacen Kempton, Jadon Kempton, Janice Kempton, Kristi Kempton, Leeland Kempton, Merton Kempton, Ossie Kempton, Patsy Kempton, Reynolds Kempton, Sebastiano Kempton, Seymour Kempton,
Shanan Kempton, Shawndell Kempton, Terrie Kempton, Toure Kempton, Zakee Kempton, Zebulun Kempton, Alexei Kempton, Branon Kempton, Derrin Kempton, Deryck Kempton, Edelmiro Kempton, Felice Kempton,
Hamid Kempton, Higinio Kempton, Jule Kempton, Kellie Kempton, Kern Kempton, Khaled Kempton, Marciano Kempton, Morrell Kempton, Nazario Kempton, Oneil Kempton, Said Kempton, Silvester Kempton, Sotero
Kempton, Yvonne Kempton, Adron Kempton, Alando Kempton, Anothony Kempton, Brando Kempton, Brenten Kempton, Canaan Kempton, Colon Kempton, Dany Kempton, Fenton Kempton, Griffith Kempton, Halbert
Kempton, Johney Kempton, Karlo Kempton, Keone Kempton, Leviticus Kempton, Maurio Kempton, Murad Kempton, Nahum Kempton, Vester Kempton, Anita Kempton, Archibald Kempton, Brinton Kempton, Cayce
Kempton, Craige Kempton, Damont Kempton, Heinz Kempton, Joaquim Kempton, Lajuane Kempton, Lakendrick Kempton, Lanard Kempton, Lesly Kempton, Nam Kempton, Remi Kempton, Semaj Kempton, Shadrach
Kempton, Sholom Kempton, Silvano Kempton, Timothey Kempton, Vernal Kempton, Vernie Kempton, Alix Kempton, Aristeo Kempton, Bubba Kempton, Carlie Kempton, Ceaser Kempton, Dallin Kempton, Darrow
Kempton, Deondra Kempton, Deonta Kempton, Engelbert Kempton, Jabier Kempton, Jarron Kempton, Kekoa Kempton, Lasean Kempton, Manolo Kempton, Marqus Kempton, Marshell Kempton, Menno Kempton, Ram
Kempton, Raynell Kempton, Rohan Kempton, Amadeo Kempton, Arch Kempton, Arlis Kempton, Ayinde Kempton, Barnard Kempton, Darriel Kempton, Darvis Kempton, Derryl Kempton, Dewain Kempton, Dietrick
Kempton, Glyn Kempton, Jasmine Kempton, Kenyan Kempton, Michae Kempton, Montoya Kempton, Oracio Kempton, Roney Kempton, Sascha Kempton, Shermaine Kempton, Sigifredo Kempton, Theodor Kempton, Virginia
Kempton, Waco Kempton, Yaphet Kempton, Zebadiah Kempton, Alika Kempton, Aundrea Kempton, Brendt Kempton, Carvin Kempton, Christophere Kempton, Clevon Kempton, Drayton Kempton, Evelio Kempton,
Gerasimos Kempton, Jemaine Kempton, Kian Kempton, Lucan Kempton, Moise Kempton, Richy Kempton, Tyshon Kempton, Zebedee Kempton, Alcides Kempton, Allister Kempton, Altonio Kempton, Bengie Kempton,
Cavan Kempton, Desiderio Kempton, Dewon Kempton, Eulogio Kempton, Faheem Kempton, Georges Kempton, Hasson Kempton, Hollie Kempton, Izell Kempton, Jamee Kempton, Jestin Kempton, Keldrick Kempton, Kier
Kempton, Lorn Kempton, Mister Kempton, Niraj Kempton, Omega Kempton, Osman Kempton, Ragan Kempton, Raja Kempton, Talbert Kempton, Thanh Kempton, Triston Kempton, Vashawn Kempton, Victorio Kempton,
Aubry Kempton, Audwin Kempton, Babatunde Kempton, Bejamin Kempton, Cantrell Kempton, Carman Kempton, Chaddrick Kempton, Claiborne Kempton, Creston Kempton, Deshone Kempton, Dewane Kempton, Gabriele
Kempton, Hason Kempton, Jessi Kempton, Keenon Kempton, Keithan Kempton, Kostantinos Kempton, Leah Kempton, Ludwig Kempton, Maverick Kempton, Neilson Kempton, Octaviano Kempton, Orestes Kempton, Otho
Kempton, Parry Kempton, Percell Kempton, Rashod Kempton, Rochelle Kempton, Rondel Kempton, Rondey Kempton, Rowan Kempton, Sang Kempton, Shawnta Kempton, Sulaiman Kempton, Suresh Kempton, Taran
Kempton, Tatum Kempton, Venson Kempton, Agustine Kempton, Babak Kempton, Biagio Kempton, Cedar Kempton, Christorpher Kempton, Cloyd Kempton, Corinthian Kempton, Curran Kempton, Dani Kempton, Dannell
Kempton, Dayle Kempton, Dermot Kempton, Encarnacion Kempton, Hendrick Kempton, Imani Kempton, Jackey Kempton, Keion Kempton, Kennis Kempton, Langdon Kempton, Lawayne Kempton, Leticia Kempton, Levan
Kempton, Liberty Kempton, Mardy Kempton, Nicolo Kempton, Nolen Kempton, Octavian Kempton, Purvis Kempton, Reuven Kempton, Ronrico Kempton, Tharon Kempton, Turhan Kempton, Tyren Kempton, Wess Kempton,
Aman Kempton, Amiel Kempton, Apostolos Kempton, Clayborn Kempton, Devone Kempton, Genesis Kempton, Giorgio Kempton, Jaleel Kempton, Jarmar Kempton, Jasan Kempton, Jermar Kempton, Jojo Kempton,
Jondavid Kempton, Martyn Kempton, Melecio Kempton, Michelangelo Kempton, Mikkel Kempton, Montague Kempton, Nicki Kempton, Quenten Kempton, Ramie Kempton, Rudolpho Kempton, Shenandoah Kempton, Tilden
Kempton, Tosh Kempton, Zedrick Kempton, Able Kempton, Aldon Kempton, Alejo Kempton, Atif Kempton, Cason Kempton, Daiel Kempton, Davian Kempton, Donaciano Kempton, Dywane Kempton, Eliberto Kempton,
Ephriam Kempton, Galo Kempton, Giulio Kempton, Hanif Kempton, Harlon Kempton, Hermon Kempton, Homar Kempton, Jhonny Kempton, Jonnathan Kempton, Kara Kempton, Keath Kempton, Kennieth Kempton, Kirsten
Kempton, Kriss Kempton, Lennis Kempton, Leonides Kempton, Levelle Kempton, Marlyn Kempton, Merced Kempton, Montrel Kempton, Naveen Kempton, Newman Kempton, Osiris Kempton, Raymondo Kempton, Renzo
Kempton, Royden Kempton, Shawnn Kempton, Shuan Kempton, Thurmond Kempton, Treg Kempton, Tremell Kempton, Trenten Kempton, Aldric Kempton, Alexandra Kempton, Alston Kempton, Anish Kempton, Anuj
Kempton, Arif Kempton, Ashby Kempton, Ashok Kempton, Chavez Kempton, Cinque Kempton, Derris Kempton, Donovon Kempton, Doroteo Kempton, Fontaine Kempton, Hadley Kempton, Jeanclaude Kempton, Josha
Kempton, Kenyada Kempton, Laban Kempton, Neeraj Kempton, Nilesh Kempton, Oral Kempton, Quran Kempton, Raheim Kempton, Rockford Kempton, Rondy Kempton, Sesar Kempton, Thayer Kempton, Vincient Kempton,
Amilcar Kempton, Antion Kempton, Antrone Kempton, Ardis Kempton, Arvil Kempton, Avid Kempton, Branton Kempton, Carmon Kempton, Claudell Kempton, Deion Kempton, Dejon Kempton, Delonte Kempton,
Delvecchio Kempton, Dickson Kempton, Elwyn Kempton, Fredie Kempton, Garnet Kempton, Gunther Kempton, Jawanza Kempton, Jermone Kempton, Katrina Kempton, Krista Kempton, Landy Kempton, Levester
Kempton, Levin Kempton, Rahiem Kempton, Rashun Kempton, Rinaldo Kempton, Ronson Kempton, Terril Kempton, Ambrosio Kempton, Arvid Kempton, Atlee Kempton, Calogero Kempton, Cobey Kempton, Donathan
Kempton, Donelle Kempton, Dorman Kempton, Dung Kempton, Garcia Kempton, Jase Kempton, Jeanette Kempton, Kolin Kempton, Kurtiss Kempton, Lorenz Kempton, Mathis Kempton, Natale Kempton, Patton Kempton,
Petar Kempton, Richar Kempton, Thadd Kempton, Timithy Kempton, Tomislav Kempton, Tommaso Kempton, Tyris Kempton, Uvaldo Kempton, Anothy Kempton, Aristides Kempton, Arno Kempton, Deshannon Kempton,
Eamonn Kempton, Hiawatha Kempton, Jamol Kempton, Jasun Kempton, Joedy Kempton, Lenn Kempton, Lord Kempton, Manoj Kempton, Merl Kempton, Michaelangelo Kempton, Navin Kempton, Per Kempton, Peterson
Kempton, Sherri Kempton, Simmie Kempton, Socrates Kempton, Tramell Kempton, Trevino Kempton, Winslow Kempton, Andrell Kempton, Arlington Kempton, Austen Kempton, Aziz Kempton, Benuel Kempton,
Cristofer Kempton, Delrico Kempton, Dereke Kempton, Edmon Kempton, Finis Kempton, Frederich Kempton, Hussein Kempton, Jerman Kempton, Johnathen Kempton, Joni Kempton, Kariem Kempton, Kasim Kempton,
Klayton Kempton, Lafe Kempton, Lamario Kempton, Manning Kempton, Markos Kempton, Natasha Kempton, Nicholis Kempton, Nickolaos Kempton, Nima Kempton, Nitin Kempton, Piero Kempton, Robertson Kempton,
Sabastian Kempton, Sandon Kempton, Shandy Kempton, Sylvia Kempton, Tacuma Kempton, Tarance Kempton, Tarl Kempton, Traver Kempton, Ander Kempton, Bartolo Kempton, Brentt Kempton, Chace Kempton, Chay
Kempton, Clete Kempton, Colbert Kempton, Domonick Kempton, Dondre Kempton, Emanuele Kempton, Enoc Kempton, Hercules Kempton, Inocencio Kempton, Ivery Kempton, Jaja Kempton, Jalal Kempton, Jamelle
Kempton, Jin Kempton, Jumaane Kempton, Kendel Kempton, Kurk Kempton, Lendell Kempton, Linc Kempton, Louise Kempton, Luc Kempton, Mackie Kempton, Mehul Kempton, Myrick Kempton, Nasir Kempton, Omero
Kempton, Osiel Kempton, Rhyan Kempton, Roni Kempton, Roshan Kempton, Sander Kempton, Thai Kempton, Toy Kempton, Willia Kempton, Zacharias Kempton, Zenas Kempton, Abelino Kempton, Ameen Kempton,
Bridget Kempton, Claudius Kempton, Creig Kempton, Danton Kempton, Danuel Kempton, Durward Kempton, Duval Kempton, Fredrico Kempton, Gibson Kempton, Hoang Kempton, Huston Kempton, Ildefonso Kempton,
Jamaar Kempton, Jerrard Kempton, Jsaon Kempton, Korie Kempton, Lang Kempton, Latron Kempton, Lawernce Kempton, Lief Kempton, Manu Kempton, Mervyn Kempton, Mingo Kempton, Nadeem Kempton, Nunzio
Kempton, Odin Kempton, Pinchas Kempton, Quoc Kempton, Ramy Kempton, Randol Kempton, Reginaldo Kempton, Tam Kempton, Theodoros Kempton, Vinnie Kempton, Arland Kempton, Atul Kempton, Baudelio Kempton,
Bernhard Kempton, Chadric Kempton, Charon Kempton, Damaris Kempton, Derin Kempton, Donavin Kempton, Feliz Kempton, Ferdinando Kempton, Fortino Kempton, Geron Kempton, Gershon Kempton, Hanson Kempton,
Helen Kempton, Hodari Kempton, Jamen Kempton, Jayce Kempton, Kalonji Kempton, Kayle Kempton, Lamorris Kempton, Lennox Kempton, Mannix Kempton, Minor Kempton, Nathaneal Kempton, Olegario Kempton,
Pantelis Kempton, Princeton Kempton, Quince Kempton, Rashied Kempton, Rose Kempton, Shaye Kempton, Son Kempton, Stephone Kempton, Trenell Kempton, Ulric Kempton, Arion Kempton, Burgess Kempton,
Chadwin Kempton, Collier Kempton, Derico Kempton, Egan Kempton, Foy Kempton, Jacobi Kempton, Jemar Kempton, Kay Kempton, Lake Kempton, Markey Kempton, Micaiah Kempton, Nasario Kempton, Oakley
Kempton, Remo Kempton, Richad Kempton, Ringo Kempton, Romano Kempton, Thierry Kempton, Vergil Kempton, Vinton Kempton, Ajamu Kempton, Andrzej Kempton, Annette Kempton, Asif Kempton, Aundray Kempton,
Benn Kempton, Bernice Kempton, Byrant Kempton, Clemon Kempton, Cleotha Kempton, Cully Kempton, Darious Kempton, Diondre Kempton, Donivan Kempton, Fard Kempton, Gianfranco Kempton, Gyasi Kempton,
Hosie Kempton, Inez Kempton, Jaden Kempton, Julious Kempton, Junious Kempton, Ketan Kempton, Kieron Kempton, Loring Kempton, Noal Kempton, Pepe Kempton, Pharoah Kempton, Pilar Kempton, Raquel
Kempton, Remon Kempton, Sederick Kempton, Severiano Kempton, Shawna Kempton, Shawnee Kempton, Sim Kempton, Spurgeon Kempton, Stace Kempton, Taber Kempton, Tarron Kempton, Thorin Kempton, Wil Kempton,
Zaire Kempton, Andray Kempton, Berlin Kempton, Betty Kempton, Biran Kempton, Chaney Kempton, Chon Kempton, Dearl Kempton, Demetria Kempton, Dewaine Kempton, Edan Kempton, Ediberto Kempton, Froilan
Kempton, Henrique Kempton, Jamille Kempton, Jessey Kempton, Kaine Kempton, Kendricks Kempton, Kynan Kempton, Laray Kempton, Laren Kempton, Mandy Kempton, Marilyn Kempton, Neale Kempton, Nyle Kempton,
Okey Kempton, Ramesh Kempton, Ricard Kempton, Saladin Kempton, Sherrill Kempton, Shonta Kempton, Sione Kempton, Steaven Kempton, Stefon Kempton, Taji Kempton, Toris Kempton, Travell Kempton, Urbano
Kempton, Wolf Kempton, Alvah Kempton, Ante Kempton, Arlon Kempton, Auther Kempton, Bran Kempton, Chevy Kempton, Cormac Kempton, Damione Kempton, Delando Kempton, Deno Kempton, Dow Kempton, Earvin
Kempton, Erinn Kempton, Florian Kempton, Georg Kempton, Gerren Kempton, Henery Kempton, Isac Kempton, Jamond Kempton, Jaramie Kempton, Kinta Kempton, Kylan Kempton, Lashan Kempton, Mckay Kempton,
Molly Kempton, Ngai Kempton, Nolberto Kempton, Quang Kempton, Solon Kempton, Tobiah Kempton, Tricia Kempton, Wai Kempton, Willem Kempton, Yaron Kempton, Agostino Kempton, Alfonse Kempton, Antonious
Kempton, Antwion Kempton, Bryen Kempton, Camille Kempton, Carsten Kempton, Cheo Kempton, Chevis Kempton, Colen Kempton, Corneilus Kempton, Davidson Kempton, Dawon Kempton, Deldrick Kempton, Dia
Kempton, Dimitris Kempton, Donnelle Kempton, Dory Kempton, Ewell Kempton, Hai Kempton, Heron Kempton, Hope Kempton, Imari Kempton, Jaremy Kempton, Lindon Kempton, Loreto Kempton, Nichole Kempton,
Nieves Kempton, Phelan Kempton, Randale Kempton, Rik Kempton, Saturnino Kempton, Schawn Kempton, Sterlin Kempton, Talmage Kempton, Tavoris Kempton, Toribio Kempton, Trebor Kempton, Vick Kempton,
Worth Kempton, Zaid Kempton, Adin Kempton, Alim Kempton, Artez Kempton, Bashir Kempton, Dameian Kempton, Demorris Kempton, Deryk Kempton, Estill Kempton, Gautam Kempton, Hyman Kempton, Isom Kempton,
Jeral Kempton, Juanita Kempton, Kalman Kempton, Kee Kempton, Keithen Kempton, Kipling Kempton, Lesean Kempton, Love Kempton, Nadir Kempton, Norton Kempton, Philander Kempton, Sebastien Kempton,
Sherif Kempton, Tabitha Kempton, Webb Kempton, Akin Kempton, Blu Kempton, Calbert Kempton, Cassandra Kempton, Cephus Kempton, Dalvin Kempton, Daxton Kempton, Delfin Kempton, Drexel Kempton, Elijio
Kempton, Fareed Kempton, Geffrey Kempton, Jabin Kempton, Jodey Kempton, Jomar Kempton, Judy Kempton, Jujuan Kempton, Klay Kempton, Kyriakos Kempton, Laderrick Kempton, Landen Kempton, Latoya Kempton,
Lebron Kempton, Mat Kempton, Rashi Kempton, Roberta Kempton, Rodderick Kempton, Shant Kempton, Summer Kempton, Viktor Kempton, Abayomi Kempton, Adrienne Kempton, Akeem Kempton, Amaury Kempton, Andrez
Kempton, Antuane Kempton, Barnabas Kempton, Corneluis Kempton, Delray Kempton, Demarlo Kempton, Deshan Kempton, Dev Kempton, Diarra Kempton, Duriel Kempton, Emigdio Kempton, Eon Kempton, Evelyn
Kempton, Hasaan Kempton, Janmichael Kempton, Jeston Kempton, Jobie Kempton, Kalon Kempton, Kumar Kempton, Lemond Kempton, Raimundo Kempton, Rainier Kempton, Robbert Kempton, Rulon Kempton, Skeeter
Kempton, Starling Kempton, Sun Kempton, Tammie Kempton, Terrelle Kempton, Tiwan Kempton, Toddrick Kempton, Varick Kempton, Zavier Kempton, Zion Kempton, Aniceto Kempton, Asmar Kempton, Boaz Kempton,
Cayetano Kempton, Dakarai Kempton, Deadrick Kempton, Debbie Kempton, Dominik Kempton, Dugan Kempton, Emad Kempton, Glennon Kempton, Haralambos Kempton, Harlin Kempton, Hilliard Kempton, Hristopher
Kempton, Humphrey Kempton, Javar Kempton, Javin Kempton, Jeffre Kempton, Josuha Kempton, Kashif Kempton, Keino Kempton, Kemper Kempton, Kendrix Kempton, Keshawn Kempton, Lamone Kempton, Lashone
Kempton, Lekeith Kempton, Markham Kempton, Maruice Kempton, Miguelangel Kempton, Nichalos Kempton, Olanda Kempton, Rodrigues Kempton, Tarig Kempton, Tarius Kempton, Tonnie Kempton, Velton Kempton,
Walden Kempton, Yasin Kempton, Alexie Kempton, Autry Kempton, Burnett Kempton, Burnis Kempton, Cephas Kempton, Crandall Kempton, Curvin Kempton, Dashaun Kempton, Donyel Kempton, Emir Kempton, Eston
Kempton, Farrel Kempton, Giovani Kempton, Jamaul Kempton, Jarmel Kempton, Jarold Kempton, Jeorge Kempton, Joshwa Kempton, Jousha Kempton, Joyce Kempton, Justan Kempton, Kem Kempton, Lavance Kempton,
Ledell Kempton, Manuelito Kempton, Michaell Kempton, Mischa Kempton, Osborne Kempton, Park Kempton, Partick Kempton, Rasaan Kempton, Ravon Kempton, Romone Kempton, Stefen Kempton, Veron Kempton,
Vondell Kempton, Airrion Kempton, Aki Kempton, Alegandro Kempton, Author Kempton, Autumn Kempton, Brannan Kempton, Caliph Kempton, Carles Kempton, Cartez Kempton, Codey Kempton, Dammon Kempton,
Daunte Kempton, Demonte Kempton, Devell Kempton, Domonique Kempton, Donyale Kempton, Dornell Kempton, Duwan Kempton, Edvardo Kempton, Emeterio Kempton, Gerado Kempton, Gordan Kempton, Jahi Kempton,
Jair Kempton, Jasmin Kempton, Jaydee Kempton, Judas Kempton, Kennan Kempton, Lehman Kempton, Macy Kempton, Mayo Kempton, Mazen Kempton, Mikhail Kempton, Osama Kempton, Rainer Kempton, Raman Kempton,
Rocio Kempton, Ryen Kempton, Shayn Kempton, Tee Kempton, Temple Kempton, Timathy Kempton, Vinh Kempton, Adarryl Kempton, Adrin Kempton, Alastair Kempton, Anh Kempton, Braun Kempton, Burrell Kempton,
Dalon Kempton, Demetrias Kempton, Derrill Kempton, Donnis Kempton, Dwon Kempton, Fredick Kempton, Gasper Kempton, Glade Kempton, Hulon Kempton, Jonatha Kempton, Jorma Kempton, Kaipo Kempton, Karel
Kempton, Kejuan Kempton, Kristine Kempton, Larrie Kempton, Majid Kempton, Mar Kempton, Mareo Kempton, Nahshon Kempton, Ondre Kempton, Rasool Kempton, Rayn Kempton, Reade Kempton, Roshon Kempton,
Rozell Kempton, Ryann Kempton, Salbador Kempton, Seon Kempton, Sharone Kempton, Shown Kempton, Taggart Kempton, Tarell Kempton, Tymon Kempton, Akira Kempton, Alice Kempton, Arend Kempton, Baretta
Kempton, Billyjack Kempton, Breton Kempton, Cleophas Kempton, Dejan Kempton, Delante Kempton, Delmus Kempton, Derren Kempton, Doni Kempton, Ezekial Kempton, Fernand Kempton, Gable Kempton, Gilford
Kempton, Irfan Kempton, Jamarcus Kempton, Jamason Kempton, Jermond Kempton, Jozef Kempton, Kal Kempton, Kalin Kempton, Kayne Kempton, Kosta Kempton, Lancelot Kempton, Lois Kempton, Marlos Kempton,
Penny Kempton, Rodriques Kempton, Rogerick Kempton, Roldan Kempton, Ronel Kempton, Sha Kempton, Shana Kempton, Taris Kempton, Torres Kempton, Trapper Kempton, Venancio Kempton, Vinod Kempton, Whit
Kempton, Allah Kempton, Angelos Kempton, Antawan Kempton, Bobbi Kempton, Declan Kempton, Eliasar Kempton, Emanual Kempton, Ericson Kempton, Erol Kempton, Faris Kempton, Filemon Kempton, Guthrie
Kempton, Helder Kempton, Jahn Kempton, Jamine Kempton, Jeoffrey Kempton, Jervis Kempton, Ketih Kempton, Kimble Kempton, Kole Kempton, Krzysztof Kempton, Lorena Kempton, Martice Kempton, Orie Kempton,
Oziel Kempton, Ralphael Kempton, Randie Kempton, Seldon Kempton, Shanna Kempton, Shawndale Kempton, Shawnte Kempton, Smokey Kempton, Teri Kempton, Tyrrell Kempton, Wilburt Kempton, Winton Kempton,
Yonatan Kempton, Brand Kempton, Briton Kempton, Budd Kempton, Charlene Kempton, Chetan Kempton, Chivas Kempton, Chriss Kempton, Daryel Kempton, Davi Kempton, Dewarren Kempton, Elston Kempton, Garo
Kempton, Hilberto Kempton, Hughie Kempton, Jarrel Kempton, Juma Kempton, Kala Kempton, Kamel Kempton, Lasalle Kempton, Leoncio Kempton, Linnie Kempton, Markis Kempton, Melville Kempton, Nekia
Kempton, Obert Kempton, Otilio Kempton, Quintus Kempton, Romualdo Kempton, Romulus Kempton, Sanjuan Kempton, Shadi Kempton, Shonte Kempton, Stelios Kempton, Tavaras Kempton, Tennyson Kempton, Timon
Kempton, Torrell Kempton, Tramel Kempton, Tyrece Kempton, Vertis Kempton, Vipul Kempton, Wenceslao Kempton, Zuri Kempton, Amer Kempton, Aquil Kempton, Ardie Kempton, Brayden Kempton, Cederic Kempton,
Claudie Kempton, Colm Kempton, Cristen Kempton, Crosby Kempton, Darlene Kempton, Darrol Kempton, Darroll Kempton, Dequincy Kempton, Donold Kempton, Eddrick Kempton, Elder Kempton, Gaines Kempton,
Giovanny Kempton, Hermilo Kempton, Ivo Kempton, Jermale Kempton, Jibri Kempton, Joshawa Kempton, Kendrell Kempton, Kerin Kempton, Kert Kempton, Kojo Kempton, Koy Kempton, Lawerance Kempton, Letroy
Kempton, Lumumba Kempton, Machael Kempton, Marshon Kempton, Napolean Kempton, Nimrod Kempton, Phong Kempton, Ramondo Kempton, Ricahrd Kempton, Sanjiv Kempton, Scotti Kempton, Shaunn Kempton, Shedric
Kempton, Sundance Kempton, Tally Kempton, Tiant Kempton, Tysen Kempton, Ulyses Kempton, Vivian Kempton, Ajani Kempton, Anthany Kempton, Antowan Kempton, Brack Kempton, Chason Kempton, Damany Kempton,
Danney Kempton, Demitri Kempton, Diangelo Kempton, Dontaye Kempton, Dragan Kempton, Einar Kempton, Gaspare Kempton, Gerrell Kempton, Gery Kempton, Heston Kempton, Isai Kempton, Jamale Kempton, Jamone
Kempton, Jane Kempton, Jerri Kempton, Karla Kempton, Kelan Kempton, Kerrie Kempton, Kobi Kempton, Krist Kempton, Lalo Kempton, Latif Kempton, Leman Kempton, Levert Kempton, Lorenso Kempton, Marcy
Kempton, Markese Kempton, Merlyn Kempton, Milburn Kempton, Nicolai Kempton, Norval Kempton, Oris Kempton, Ranjit Kempton, Rashidi Kempton, Richardson Kempton, Rohn Kempton, Roshaun Kempton, Shepherd
Kempton, Sonnie Kempton, Stephens Kempton, Stirling Kempton, Sundiata Kempton, Troyce Kempton, Vander Kempton, Waddell Kempton, Yarnell Kempton, Yitzchak Kempton, Zerrick Kempton, Adair Kempton,
Amani Kempton, Arvind Kempton, Ascencion Kempton, Athan Kempton, Biff Kempton, Burnice Kempton, Carlito Kempton, Carlitos Kempton, Carlson Kempton, Carry Kempton, Christepher Kempton, Clemmie
Kempton, Corbet Kempton, Cristoval Kempton, Damaso Kempton, Dickey Kempton, Doral Kempton, Eliu Kempton, Erving Kempton, Favio Kempton, Helmut Kempton, Hisham Kempton, Ignazio Kempton, Jamail
Kempton, Jarius Kempton, Jermanie Kempton, Jonte Kempton, Juluis Kempton, Jushua Kempton, Keron Kempton, Kevis Kempton, Kollin Kempton, Labron Kempton, Lavan Kempton, Lavoris Kempton, Lazar Kempton,
Nafis Kempton, Nathanel Kempton, Othello Kempton, Quantrell Kempton, Ramzi Kempton, Rossi Kempton, Rye Kempton, Siegfried Kempton, Stanly Kempton, Takashi Kempton, Taro Kempton, Tarvares Kempton,
Tehran Kempton, Therron Kempton, Thoms Kempton, Tico Kempton, Timm Kempton, Tylan Kempton, Wheeler Kempton, Zalman Kempton, Aleksander Kempton, Alok Kempton, Alvan Kempton, Angelica Kempton, Ato
Kempton, Aureliano Kempton, Ayman Kempton, Berkeley Kempton, Bracken Kempton, Bren Kempton, Brittany Kempton, Caley Kempton, Camara Kempton, Christifer Kempton, Clenton Kempton, Corley Kempton,
Deante Kempton, Denorris Kempton, Donielle Kempton, Eleftherios Kempton, Eleno Kempton, Eliah Kempton, Enrrique Kempton, Frederik Kempton, French Kempton, Hani Kempton, Herby Kempton, Howie Kempton,
Joab Kempton, Kylie Kempton, Leshon Kempton, Maribel Kempton, Marquese Kempton, Martine Kempton, Maurico Kempton, Melford Kempton, Mikie Kempton, Myreon Kempton, Nabeel Kempton, Nabor Kempton,
Orlandus Kempton, Rafi Kempton, Rahn Kempton, Ramont Kempton, Romain Kempton, Ronold Kempton, Rosco Kempton, Shabazz Kempton, Shandell Kempton, Shaughn Kempton, Sumner Kempton, Tamika Kempton, Tarry
Kempton, Tedric Kempton, Tellas Kempton, Theordore Kempton, Tolbert Kempton, Wanda Kempton, Winthrop Kempton, Wyndell Kempton, Abrahm Kempton, Arthuro Kempton, Attilio Kempton, Baraka Kempton, Chanse
Kempton, Codie Kempton, Conner Kempton, Demarkus Kempton, Demetres Kempton, Estel Kempton, Eva Kempton, Greyson Kempton, Hazen Kempton, Ivor Kempton, Janie Kempton, Jarian Kempton, Jene Kempton,
Joseh Kempton, Kajuan Kempton, Kamil Kempton, Kean Kempton, Larson Kempton, Laymon Kempton, Marian Kempton, Mosi Kempton, Nathaneil Kempton, Octavis Kempton, Regginald Kempton, Schon Kempton,
Secundino Kempton, Slyvester Kempton, Socorro Kempton, Sundeep Kempton, Tao Kempton, Tasha Kempton, Tivon Kempton, Twain Kempton, Verl Kempton, Yousef Kempton, Adem Kempton, Akash Kempton, Archer
Kempton, Barnett Kempton, Binh Kempton, Darrly Kempton, Detrich Kempton, Diandre Kempton, Dinesh Kempton, Donya Kempton, Eirik Kempton, Fuquan Kempton, Garrin Kempton, Goerge Kempton, Griff Kempton,
Haneef Kempton, Jamian Kempton, Janos Kempton, Jervon Kempton, Josie Kempton, Jumar Kempton, Keithon Kempton, Kelii Kempton, Konstantine Kempton, Latonya Kempton, Laurel Kempton, Liborio Kempton,
Lyon Kempton, Markie Kempton, Mikhael Kempton, Montana Kempton, Mordecai Kempton, Nana Kempton, Onesimo Kempton, Reymond Kempton, Ronda Kempton, Rosevelt Kempton, Sandip Kempton, Shade Kempton,
Stanislaus Kempton, Trung Kempton, Zeferino Kempton, Abu Kempton, Adaryll Kempton, Adolf Kempton, Allon Kempton, Almon Kempton, Alphonza Kempton, Andras Kempton, Angelito Kempton, Aurelius Kempton,
Banjamin Kempton, Bartlett Kempton, Caprice Kempton, Cheskel Kempton, Corrado Kempton, Damieon Kempton, Dariel Kempton, Darral Kempton, Demetreus Kempton, Fleming Kempton, Fotios Kempton, Graylin
Kempton, Hari Kempton, Hilbert Kempton, Holden Kempton, Iram Kempton, Jalon Kempton, Jams Kempton, Jaquan Kempton, Jerimey Kempton, Johnthomas Kempton, Kain Kempton, Lonney Kempton, Lukus Kempton,
Marquet Kempton, Melody Kempton, Michall Kempton, Nicodemus Kempton, Octavia Kempton, Petro Kempton, Prashant Kempton, Primo Kempton, Rahmel Kempton, Rita Kempton, Shepard Kempton, Siddhartha
Kempton, Talbot Kempton, Tomy Kempton, Tyon Kempton, Tyrie Kempton, Victory Kempton, Aaren Kempton, Ade Kempton, Adel Kempton, Akida Kempton, Anjel Kempton, Arrick Kempton, Becky Kempton, Bekim
Kempton, Camillo Kempton, Cerrone Kempton, Chett Kempton, Cicero Kempton, Collie Kempton, Cregg Kempton, Danel Kempton, Demitrios Kempton, Desiree Kempton, Dontez Kempton, Doris Kempton, Dorrell
Kempton, Edouard Kempton, Emmette Kempton, Everton Kempton, Eward Kempton, Geofrey Kempton, Gregrey Kempton, Greig Kempton, Gust Kempton, Jaycee Kempton, Jes Kempton, Jocob Kempton, Judith Kempton,
Karlin Kempton, Kaveh Kempton, Keil Kempton, Kino Kempton, Kwaku Kempton, Lamel Kempton, Lea Kempton, Leodis Kempton, Loni Kempton, Lonie Kempton, Miriam Kempton, Nnamdi Kempton, Olufemi Kempton,
Patrik Kempton, Raun Kempton, Refujio Kempton, Rossie Kempton, Rydell Kempton, Severin Kempton, Shadeed Kempton, Shannen Kempton, Shellie Kempton, Sheri Kempton, Sumit Kempton, Tamiko Kempton, Tien
Kempton, Tirso Kempton, Tonie Kempton, Trino Kempton, Tyra Kempton, Wright Kempton, Zalmen Kempton, Abdon Kempton, Abrahan Kempton, Adrean Kempton, Aeron Kempton, Ajene Kempton, Atthew Kempton, Augie
Kempton, Carmel Kempton, Cezar Kempton, Chioke Kempton, Chung Kempton, Delonta Kempton, Derrich Kempton, Deyon Kempton, Dicky Kempton, Elihu Kempton, Eustacio Kempton, Fernado Kempton, Filbert
Kempton, Free Kempton, Goran Kempton, Habib Kempton, Haile Kempton, Han Kempton, Heraclio Kempton, Jarin Kempton, Javaris Kempton, Jeramine Kempton, Joanna Kempton, Johnel Kempton, Joie Kempton,
Juddson Kempton, Kason Kempton, Leverne Kempton, Liston Kempton, Marck Kempton, Marcoantonio Kempton, Margarita Kempton, Messiah Kempton, Nicholaos Kempton, Onofre Kempton, Pacer Kempton, Parke
Kempton, Sion Kempton, Spyros Kempton, Starr Kempton, Storm Kempton, Tami Kempton, Theon Kempton, Tramayne Kempton, Tyronn Kempton, Tywone Kempton, Undray Kempton, Wray Kempton, Yon Kempton, Zeno
Kempton, Abimael Kempton, Adell Kempton, Adren Kempton, Agron Kempton, Brick Kempton, Bridger Kempton, Buddie Kempton, Cosimo Kempton, Cristin Kempton, Deitrich Kempton, Demetre Kempton, Dolphus
Kempton, Dorell Kempton, Dylon Kempton, Fadi Kempton, Fredrich Kempton, Gerron Kempton, Jacobe Kempton, Jarell Kempton, Karson Kempton, Kegan Kempton, Latasha Kempton, Laureano Kempton, Lemonte
Kempton, Lev Kempton, Marcellino Kempton, Marsha Kempton, Maureen Kempton, Ori Kempton, Prudencio Kempton, Rockwell Kempton, Selby Kempton, Shah Kempton, Stefanos Kempton, Tarris Kempton, Taryll
Kempton, Telley Kempton, Teryl Kempton, Thoams Kempton, Tiko Kempton, Tilford Kempton, Toraino Kempton, Tyce Kempton, Undrea Kempton, Walid Kempton, Williard Kempton, Yasir Kempton, Yvette Kempton,
Abiel Kempton, Aimee Kempton, Ainsley Kempton, Akram Kempton, Antino Kempton, Bengy Kempton, Benjimen Kempton, Bohdan Kempton, Canyon Kempton, Chandra Kempton, Cheron Kempton, Christhoper Kempton,
Cordney Kempton, Covey Kempton, Danyale Kempton, Daquan Kempton, Darnelle Kempton, Dong Kempton, Donjuan Kempton, Elieser Kempton, Feliberto Kempton, Fernie Kempton, Gaylan Kempton, Gerritt Kempton,
Glennis Kempton, Goldie Kempton, Hermes Kempton, Hernandez Kempton, Herny Kempton, Hervey Kempton, Italo Kempton, Jeno Kempton, Joell Kempton, Kaiser Kempton, Kalem Kempton, Kijana Kempton, Knute
Kempton, Korby Kempton, Leaf Kempton, Lejuan Kempton, Lin Kempton, Mahdi Kempton, Mindy Kempton, Mithcell Kempton, Mylon Kempton, Nichlas Kempton, Nickolus Kempton, Quanah Kempton, Rachael Kempton,
Rafiq Kempton, Ranier Kempton, Rashaud Kempton, Rebel Kempton, Reuel Kempton, Rodgerick Kempton, Ryun Kempton, Samad Kempton, Steffon Kempton, Tan Kempton, Tonio Kempton, Trevell Kempton, Truett
Kempton, Woodley Kempton, Ziad Kempton, Alisha Kempton, Amory Kempton, Ashford Kempton, Bard Kempton, Brenan Kempton, Burney Kempton, Carnel Kempton, Cevin Kempton, Clare Kempton, Corban Kempton,
Dashan Kempton, Deddrick Kempton, Dennise Kempton, Dimetrius Kempton, Diogenes Kempton, Dodd Kempton, Dominico Kempton, Dorion Kempton, Eberardo Kempton, Ethen Kempton, Eyal Kempton, Fedrick Kempton,
Gonsalo Kempton, Gorje Kempton, Hart Kempton, Irby Kempton, Jarmal Kempton, Jaworski Kempton, Johnston Kempton, Joshuwa Kempton, Json Kempton, Kenzie Kempton, Kristie Kempton, Labaron Kempton, Lan
Kempton, Leroi Kempton, Lysander Kempton, Marten Kempton, Matthieu Kempton, Meghan Kempton, Misha Kempton, Norvel Kempton, Ohn Kempton, Olivia Kempton, Omoro Kempton, Powell Kempton, Qunicy Kempton,
Shaheen Kempton, Sirron Kempton, Suraj Kempton, Teran Kempton, Theopolis Kempton, Tion Kempton, Toddy Kempton, Toronto Kempton, Tyrin Kempton, Urban Kempton, Vencent Kempton, Vida Kempton, Virgle
Kempton, Weslee Kempton, Wilfrido Kempton, Ahron Kempton, Alanzo Kempton, Amol Kempton, Asad Kempton, Avel Kempton, Bao Kempton, Benancio Kempton, Britten Kempton, Cassie Kempton, Choya Kempton,
Christien Kempton, Chrles Kempton, Cochise Kempton, Criss Kempton, Culley Kempton, Danyelle Kempton, Deforest Kempton, Deland Kempton, Deshane Kempton, Dynell Kempton, Eluterio Kempton, Emeka
Kempton, Eyad Kempton, Fabricio Kempton, Graviel Kempton, Gunner Kempton, Harun Kempton, Hiroshi Kempton, Ihsan Kempton, Irineo Kempton, Jacon Kempton, Jamile Kempton, Jawad Kempton, Jeramia Kempton,
Joann Kempton, Johnn Kempton, Josph Kempton, Kaleo Kempton, Katie Kempton, Kelwin Kempton, Kwanza Kempton, Laddie Kempton, Lanorris Kempton, Larron Kempton, Maron Kempton, Mehdi Kempton, Monolito
Kempton, Mont Kempton, Munir Kempton, Murrell Kempton, Nachman Kempton, Natan Kempton, Nguyen Kempton, Nickalus Kempton, Nikitas Kempton, Orlin Kempton, Phillippe Kempton, Rasean Kempton, Rino
Kempton, Robi Kempton, Rodgers Kempton, Rolan Kempton, Roswell Kempton, Sagar Kempton, Schaun Kempton, Segundo Kempton, Senaca Kempton, Severino Kempton, Sloane Kempton, Spenser Kempton, Talvin
Kempton, Teddrick Kempton, Theran Kempton, Tiron Kempton, Tshombe Kempton, Zephaniah Kempton, Abbas Kempton, Adil Kempton, Alireza Kempton, Ancil Kempton, Antoan Kempton, Atanacio Kempton, Benedicto
Kempton, Benjimin Kempton, Blandon Kempton, Bradey Kempton, Brannen Kempton, Chalmer Kempton, Charleton Kempton, Chrsitopher Kempton, Cleatus Kempton, Corwyn Kempton, Costas Kempton, Cranston
Kempton, Damario Kempton, Delmon Kempton, Dermaine Kempton, Duc Kempton, Duff Kempton, Farhad Kempton, Gabor Kempton, Garreth Kempton, Heshimu Kempton, Ines Kempton, Ivar Kempton, Jahan Kempton,
Jamael Kempton, Janes Kempton, Jaycen Kempton, Jett Kempton, Johnhenry Kempton, Jona Kempton, Josey Kempton, Khristian Kempton, Kilian Kempton, Lander Kempton, Laval Kempton, Lebaron Kempton,
Leocadio Kempton, Lonzie Kempton, Mackey Kempton, Marios Kempton, Maxim Kempton, Naquan Kempton, Nickalaus Kempton, Nicolaos Kempton, Nkosi Kempton, Ozie Kempton, Ponciano Kempton, Praveen Kempton,
Ramar Kempton, Rizwan Kempton, Ronen Kempton, Saad Kempton, Shalin Kempton, Shalon Kempton, Shaunte Kempton, Steele Kempton, Sten Kempton, Terrin Kempton, Tiran Kempton, Valdis Kempton, Virgel
Kempton, Yamil Kempton, Adriana Kempton, Ajit Kempton, Alger Kempton, Amil Kempton, Ananda Kempton, Angie Kempton, Anup Kempton, Arjun Kempton, Ark Kempton, Bayard Kempton, Bolivar Kempton, Burnie
Kempton, Chae Kempton, Dallan Kempton, Danile Kempton, Deward Kempton, Didier Kempton, Dusan Kempton, Elaine Kempton, Franchot Kempton, Gavriel Kempton, Heliodoro Kempton, Igor Kempton, Irene
Kempton, Iven Kempton, Jamien Kempton, Jaquay Kempton, Kaylon Kempton, Larico Kempton, Lenord Kempton, Lenton Kempton, Lynden Kempton, Mahesh Kempton, Malo Kempton, Mercedes Kempton, Nicklos Kempton,
Raiford Kempton, Rashed Kempton, Rayshaun Kempton, Reubin Kempton, Senica Kempton, Shaan Kempton, Shermon Kempton, Sherrell Kempton, Sierra Kempton, Tamarcus Kempton, Tavius Kempton, Thurmon Kempton,
Tonia Kempton, Torino Kempton, Urian Kempton, Verner Kempton, Zacarias Kempton, Abdel Kempton, Aniel Kempton, Arjuna Kempton, Ashon Kempton, Candy Kempton, Caroline Kempton, Chukwuemeka Kempton, Cid
Kempton, Court Kempton, Cristino Kempton, Darshan Kempton, Delshawn Kempton, Demetrie Kempton, Deondray Kempton, Deone Kempton, Diante Kempton, Dolores Kempton, Donahue Kempton, Eligah Kempton, Essex
Kempton, Eutimio Kempton, Gustavus Kempton, Hebert Kempton, Hyun Kempton, Janssen Kempton, Jaxon Kempton, Jerre Kempton, Joanne Kempton, Jorden Kempton, Joseantonio Kempton, Kainoa Kempton, Kalif
Kempton, Karin Kempton, Katina Kempton, Keisha Kempton, Khalfani Kempton, Leanthony Kempton, Michaelpaul Kempton, Murl Kempton, Nazareth Kempton, Pearl Kempton, Purcell Kempton, Quay Kempton, Raylon
Kempton, Ren Kempton, Renell Kempton, Reshard Kempton, Rodel Kempton, Shaen Kempton, Talon Kempton, Torsten Kempton, Victorino Kempton, Vonzell Kempton, Yong Kempton, Zaki Kempton, Abdiel Kempton,
Adon Kempton, Alferd Kempton, Amjad Kempton, Arlester Kempton, Bassam Kempton, Bela Kempton, Belton Kempton, Branko Kempton, Burk Kempton, Calixto Kempton, Cassey Kempton, Cayle Kempton, Cedrie
Kempton, Cuong Kempton, Damu Kempton, Danelle Kempton, Darcey Kempton, Dayna Kempton, Domanic Kempton, Dougles Kempton, Elex Kempton, Elrico Kempton, Estaban Kempton, Ferlando Kempton, Filipe
Kempton, Geovanni Kempton, Glenford Kempton, Gumaro Kempton, Gustabo Kempton, Haley Kempton, Herberto Kempton, Jabez Kempton, Jaman Kempton, Joshau Kempton, Jullian Kempton, Kairi Kempton, Karnell
Kempton, Kin Kempton, Kinsey Kempton, Kipper Kempton, Laquincy Kempton, Laterrance Kempton, Laurice Kempton, Leshaun Kempton, Marcia Kempton, Marcio Kempton, Melquiades Kempton, Miklos Kempton, Ming
Kempton, Mylo Kempton, Omid Kempton, Oskar Kempton, Paco Kempton, Rafel Kempton, Ralf Kempton, Ravindra Kempton, Rivers Kempton, Rody Kempton, Saint Kempton, Santee Kempton, Shai Kempton, Shelvin
Kempton, Shyam Kempton, Silvino Kempton, Squire Kempton, Star Kempton, Steen Kempton, Stein Kempton, Tae Kempton, Taryn Kempton, Tavare Kempton, Thedore Kempton, Yehudah Kempton, Zacchaeus Kempton,
Zachory Kempton, Zan Kempton, Adewale Kempton, Aleksandr Kempton, Alf Kempton, Alvester Kempton, Amiri Kempton, Araceli Kempton, Arcenio Kempton, Arvell Kempton, Arvis Kempton, Atlas Kempton,
Binyomin Kempton, Chasen Kempton, Cheyne Kempton, Coray Kempton, Dak Kempton, Davone Kempton, Egbert Kempton, Ferlin Kempton, Gilles Kempton, Glendell Kempton, Granger Kempton, Jafar Kempton, Jalil
Kempton, Jamain Kempton, Jarrette Kempton, Jeret Kempton, Jocelyn Kempton, Joenathan Kempton, Jurgen Kempton, Keene Kempton, Keller Kempton, Kenneith Kempton, Kinney Kempton, Labarron Kempton, Levie
Kempton, Linford Kempton, Marcas Kempton, Mickle Kempton, Morrison Kempton, Oba Kempton, Qasim Kempton, Rahsan Kempton, Rajah Kempton, Raphel Kempton, Rehan Kempton, Rodregus Kempton, Ronan Kempton,
Salman Kempton, Seddrick Kempton, Shauna Kempton, Simpson Kempton, Sunshine Kempton, Terrall Kempton, Tiawan Kempton, Waylen Kempton, Weslie Kempton, Abdur Kempton, Alric Kempton, Arien Kempton,
Arren Kempton, Bari Kempton, Briar Kempton, Burdette Kempton, Carver Kempton, Charvis Kempton, Contrell Kempton, Costa Kempton, Dara Kempton, Darly Kempton, Darwyn Kempton, Davied Kempton, Dayon
Kempton, Delmont Kempton, Dena Kempton, Devlon Kempton, Dimitry Kempton, Duwane Kempton, Esteven Kempton, Fergus Kempton, Harles Kempton, Hutch Kempton, Ion Kempton, Isidore Kempton, Jamus Kempton,
Jerett Kempton, Jerrit Kempton, Jontue Kempton, Lemarcus Kempton, Lequan Kempton, Leslee Kempton, Linell Kempton, Lugene Kempton, Makoto Kempton, Malek Kempton, Marquell Kempton, Osei Kempton, Peggy
Kempton, Ralphie Kempton, Ramona Kempton, Rickard Kempton, Ronnald Kempton, Sabian Kempton, Saleh Kempton, Salih Kempton, Samule Kempton, Sarkis Kempton, Sharrieff Kempton, Snehal Kempton, Sony
Kempton, Timotheus Kempton, Tood Kempton, Tyreece Kempton, Wei Kempton, Zackariah Kempton, Aleem Kempton, Antwione Kempton, Ayodele Kempton, Barkley Kempton, Bartt Kempton, Bethany Kempton, Bing
Kempton, Braheem Kempton, Brek Kempton, Caron Kempton, Cathy Kempton, Cecilia Kempton, Cristina Kempton, Dainel Kempton, Dal Kempton, Darrek Kempton, Darrelle Kempton, Dashun Kempton, Delrick
Kempton, Demitrus Kempton, Dishon Kempton, Donnald Kempton, Ehab Kempton, Erico Kempton, Erskin Kempton, Faraji Kempton, Gillis Kempton, Hamed Kempton, Hermann Kempton, Hondo Kempton, Jamis Kempton,
Jeric Kempton, Jermyn Kempton, Jessup Kempton, Jonatan Kempton, Joshaua Kempton, Jotham Kempton, Khaalis Kempton, Kion Kempton, Lam Kempton, Larence Kempton, Lavonne Kempton, Marti Kempton, Mclean
Kempton, Mercury Kempton, Miki Kempton, Norvin Kempton, Onnie Kempton, Paulmichael Kempton, Pavan Kempton, Paz Kempton, Phuong Kempton, Race Kempton, Ralston Kempton, Ramadan Kempton, Rashee Kempton,
Roan Kempton, Sally Kempton, Shanga Kempton, Slater Kempton, Tarvaris Kempton, Tevin Kempton, Travus Kempton, Viviano Kempton, Zerick Kempton, Abdula Kempton, Achilles Kempton, Adarryll Kempton,
Ananias Kempton, Antinio Kempton, Antrell Kempton, Anzio Kempton, Aristidis Kempton, Ashante Kempton, Atom Kempton, Audley Kempton, Azim Kempton, Bandy Kempton, Bary Kempton, Britain Kempton, Bryne
Kempton, Calen Kempton, Ceddrick Kempton, Chalmers Kempton, Chanc Kempton, Chap Kempton, Charly Kempton, Charron Kempton, Cornellius Kempton, Darth Kempton, Dayan Kempton, Deran Kempton, Dewand
Kempton, Fran Kempton, Girolamo Kempton, Harvie Kempton, Haskel Kempton, Hoy Kempton, Islam Kempton, Ivon Kempton, Jafari Kempton, Jamario Kempton, Jehu Kempton, Josemanuel Kempton, Jung Kempton,
Kabir Kempton, Kael Kempton, Khan Kempton, Khayree Kempton, Kimber Kempton, Koran Kempton, Lamonta Kempton, Lavalle Kempton, Lavel Kempton, Lenardo Kempton, Lydia Kempton, Mandrill Kempton, Mannie
Kempton, Marguis Kempton, Marisa Kempton, Marissa Kempton, Marshaun Kempton, Medardo Kempton, Naomi Kempton, Naser Kempton, Natanael Kempton, Oji Kempton, Orvil Kempton, Pasqual Kempton, Previn
Kempton, Reo Kempton, Ruddy Kempton, Shahram Kempton, Sharad Kempton, Shaunta Kempton, Shuron Kempton, Teo Kempton, Thalmus Kempton, Theodoric Kempton, Tibor Kempton, Tres Kempton, Ulrich Kempton,
Winter Kempton, Yasser Kempton, Ygnacio Kempton, Abasi Kempton, Alwin Kempton, Alwyn Kempton, Amalio Kempton, Arty Kempton, Baker Kempton, Bishara Kempton, Briane Kempton, Catalino Kempton, Darrall
Kempton, Dartanyon Kempton, Deano Kempton, Demico Kempton, Deontae Kempton, Deveron Kempton, Devonn Kempton, Donnovan Kempton, Durant Kempton, Duy Kempton, Evander Kempton, Ever Kempton, Ewing
Kempton, Fouad Kempton, Froylan Kempton, Gabriela Kempton, Garnell Kempton, Gerlad Kempton, Ginger Kempton, Glendale Kempton, Grafton Kempton, Haig Kempton, Hale Kempton, Iver Kempton, Ivin Kempton,
Jarel Kempton, Javen Kempton, Jeran Kempton, Jereld Kempton, Jermichael Kempton, Jimel Kempton, Karreem Kempton, Keiron Kempton, Kester Kempton, Laronn Kempton, Lavor Kempton, Lehi Kempton, Lemon
Kempton, Lourdes Kempton, Marqui Kempton, Marsh Kempton, Marx Kempton, Montego Kempton, Murice Kempton, Mychael Kempton, Nashawn Kempton, Nichalas Kempton, Nickalas Kempton, Nuri Kempton, Obinna
Kempton, Onaje Kempton, Patrich Kempton, Pavel Kempton, Priscilla Kempton, Rakeem Kempton, Rande Kempton, Rashann Kempton, Rayan Kempton, Raynold Kempton, Ricko Kempton, Riki Kempton, Rooney Kempton,
Saulo Kempton, Schad Kempton, Seiji Kempton, Shahn Kempton, Shantel Kempton, Shanton Kempton, Sisto Kempton, Taiwo Kempton, Travion Kempton, Tristen Kempton, Truong Kempton, Tywann Kempton, Tywayne
Kempton, Uhuru Kempton, Welby Kempton, Wesam Kempton, Alexius Kempton, Ammar Kempton, Andrews Kempton, Atticus Kempton, Audy Kempton, Belinda Kempton, Bennet Kempton, Bomani Kempton, Bulmaro Kempton,
Charlies Kempton, Chato Kempton, Chelsea Kempton, Chipper Kempton, Clearence Kempton, Cleotis Kempton, Cleven Kempton, Corydon Kempton, Dadrian Kempton, Damiano Kempton, Darrold Kempton, Davell
Kempton, Derone Kempton, Derral Kempton, Derwood Kempton, Django Kempton, Doc Kempton, Dontell Kempton, Doren Kempton, Elza Kempton, Esmeralda Kempton, Estil Kempton, Finn Kempton, Fredrik Kempton,
Garrie Kempton, Greogory Kempton, Harlow Kempton, Iris Kempton, Jascha Kempton, Jediah Kempton, Jef Kempton, Jefferie Kempton, Jerimah Kempton, Jerrie Kempton, Joal Kempton, Johsua Kempton, Joon
Kempton, Joson Kempton, Kamar Kempton, Kellen Kempton, Kelvis Kempton, Ketrick Kempton, Kimberley Kempton, Kingston Kempton, Meldon Kempton, Mendell Kempton, Michaeljohn Kempton, Moss Kempton, Nuno
Kempton, Onofrio Kempton, Phineas Kempton, Ramell Kempton, Raydell Kempton, Regie Kempton, Ronnel Kempton, Sadat Kempton, Sajid Kempton, Shanard Kempton, Shaul Kempton, Shondale Kempton, Shyrone
Kempton, Simuel Kempton, Sjon Kempton, Stephenson Kempton, Tadeusz Kempton, Takeshi Kempton, Tilman Kempton, Tomasz Kempton, Travares Kempton, Truitt Kempton, Ulrick Kempton, Vandy Kempton, Yvon
Kempton, Zebulan Kempton, Adolpho Kempton, Alek Kempton, Amery Kempton, Andrej Kempton, Aniello Kempton, Anurag Kempton, Audra Kempton, Boruch Kempton, Burr Kempton, Cable Kempton, Cheney Kempton,
Cimarron Kempton, Clell Kempton, Clinten Kempton, Daimen Kempton, Dameyon Kempton, Dason Kempton, Deanglo Kempton, Delaine Kempton, Demeco Kempton, Denim Kempton, Derryck Kempton, Domnick Kempton,
Doy Kempton, Dwyne Kempton, Edwards Kempton, Elisa Kempton, Esmond Kempton, Gawain Kempton, Green Kempton, Hallie Kempton, Hameed Kempton, Heinrich Kempton, Jeri Kempton, Kaj Kempton, Kalan Kempton,
Kash Kempton, Kente Kempton, Koji Kempton, Kunte Kempton, Laurin Kempton, Livingston Kempton, Meliton Kempton, Michaeal Kempton, Myran Kempton, Nephtali Kempton, Nicasio Kempton, Nyles Kempton,
Obediah Kempton, Pride Kempton, Primus Kempton, Rae Kempton, Rahmaan Kempton, Rhoderick Kempton, Rip Kempton, River Kempton, Roberts Kempton, Rodricus Kempton, Rommie Kempton, Romney Kempton, Roverto
Kempton, Samar Kempton, Sergei Kempton, Shadrack Kempton, Shavon Kempton, Stevin Kempton, Tarone Kempton, Tashawn Kempton, Tora Kempton, Tri Kempton, Vinny Kempton, Yesenia Kempton, Yvan Kempton,
Zubin Kempton, Absalom Kempton, Aldrick Kempton, Alif Kempton, Amad Kempton, Anacleto Kempton, Andru Kempton, Argelio Kempton, Arrington Kempton, Ashely Kempton, Auston Kempton, Baird Kempton, Beryl
Kempton, Celester Kempton, Chadron Kempton, Chante Kempton, Dack Kempton, Darain Kempton, Darvell Kempton, Daune Kempton, Daylan Kempton, Dedan Kempton, Deitrick Kempton, Dejaun Kempton, Denzel
Kempton, Deverick Kempton, Eris Kempton, Flor Kempton, Frankey Kempton, Gaberial Kempton, Gianluca Kempton, Hesham Kempton, Iban Kempton, Ilya Kempton, Isham Kempton, Issiah Kempton, Jacey Kempton,
Jahmel Kempton, Jaimey Kempton, Jamane Kempton, Jammey Kempton, Jareb Kempton, Jarek Kempton, Jemery Kempton, Jeremaih Kempton, Jernard Kempton, Jerramy Kempton, Jese Kempton, Johnaton Kempton,
Jontae Kempton, Kayode Kempton, Kaz Kempton, Kedar Kempton, Kell Kempton, Kewan Kempton, Kiyoshi Kempton, Ladarryl Kempton, Lamart Kempton, Lataurus Kempton, Lavarr Kempton, Lavert Kempton, Lawan
Kempton, Loney Kempton, Lonnel Kempton, Luan Kempton, Macio Kempton, Mansa Kempton, Miachel Kempton, Neftaly Kempton, Nichlos Kempton, Nicklous Kempton, Nik Kempton, Orlander Kempton, Quadir Kempton,
Raeford Kempton, Rajohn Kempton, Ranson Kempton, Rasul Kempton, Renald Kempton, Reynald Kempton, Roben Kempton, Rutherford Kempton, Salathiel Kempton, Savoy Kempton, Sharief Kempton, Sherrick
Kempton, Siddharth Kempton, Staci Kempton, Steed Kempton, Tauheed Kempton, Thaddus Kempton, Toland Kempton, Toran Kempton, Torriano Kempton, Turon Kempton, Vashaun Kempton, Zebediah Kempton, Aasim
Kempton, Abron Kempton, Ahman Kempton, Aiden Kempton, Alexsander Kempton, Alias Kempton, Aly Kempton, Ameet Kempton, Anothny Kempton, Ansley Kempton, Ballard Kempton, Bedford Kempton, Beecher
Kempton, Benaiah Kempton, Clent Kempton, Colvin Kempton, Dakari Kempton, Darric Kempton, Daved Kempton, Demichael Kempton, Deray Kempton, Deren Kempton, Dionisios Kempton, Dionta Kempton, Dorothy
Kempton, Dorrian Kempton, Dorris Kempton, Dyke Kempton, Elmon Kempton, Erle Kempton, Eunice Kempton, Eustace Kempton, Evon Kempton, Fay Kempton, Federick Kempton, Feras Kempton, Gabrielle Kempton,
Gaven Kempton, Gay Kempton, Gjon Kempton, Grier Kempton, Guillaume Kempton, Hansen Kempton, Harrel Kempton, Hazel Kempton, Heathe Kempton, Herschell Kempton, Ingram Kempton, Isauro Kempton, Jaimy
Kempton, Jaymar Kempton, Jerin Kempton, Jermall Kempton, Jevin Kempton, Jillian Kempton, Johnmark Kempton, Jovaughn Kempton, Kamuela Kempton, Kendon Kempton, Khoa Kempton, Lamberto Kempton, Latham
Kempton, Luster Kempton, Malon Kempton, Micholas Kempton, Mitul Kempton, Montrice Kempton, Moroni Kempton, Mylan Kempton, Nason Kempton, Nic Kempton, Nowell Kempton, Oryan Kempton, Owens Kempton,
Phill Kempton, Raed Kempton, Raji Kempton, Ramzy Kempton, Rebekah Kempton, Reeve Kempton, Regenald Kempton, Roddie Kempton, Roshun Kempton, Salvator Kempton, Seanpaul Kempton, Shanne Kempton,
Shawntay Kempton, Sheldrick Kempton, Sheppard Kempton, Snapper Kempton, Tarick Kempton, Terelle Kempton, Tery Kempton, Thelonious Kempton, Trampis Kempton, Tushar Kempton, Vernice Kempton, Whalen
Kempton, Willim Kempton, Alban Kempton, Alexy Kempton, Almalik Kempton, Amedeo Kempton, Antoney Kempton, Asia Kempton, Aurthur Kempton, Avelardo Kempton, Barth Kempton, Cartrell Kempton, Chaderick
Kempton, Champ Kempton, Chano Kempton, Charity Kempton, Christhopher Kempton, Christino Kempton, Clavin Kempton, Cuyler Kempton, Dalbert Kempton, Darcel Kempton, Darcell Kempton, Darrie Kempton,
Denney Kempton, Denson Kempton, Dezmond Kempton, Donyea Kempton, Dorien Kempton, Emidio Kempton, Etan Kempton, Evagelos Kempton, Everado Kempton, Farren Kempton, Fate Kempton, Filomeno Kempton,
Fonzie Kempton, Franko Kempton, Garrod Kempton, Graciano Kempton, Gustin Kempton, Isrrael Kempton, Jac Kempton, Jakie Kempton, Jamas Kempton, Jamiyl Kempton, Jaylon Kempton, Jeanmarc Kempton,
Jebadiah Kempton, Jeffey Kempton, Jiles Kempton, Johnnell Kempton, Josip Kempton, Juanmanuel Kempton, Kemo Kempton, Kemuel Kempton, Kindrick Kempton, Kirtis Kempton, Kyley Kempton, Lacorey Kempton,
Lansing Kempton, Lawyer Kempton, Lenzie Kempton, Lessie Kempton, Lindley Kempton, Lynette Kempton, Lyonel Kempton, Magnus Kempton, Marki Kempton, Marrell Kempton, Mccoy Kempton, Mcdonald Kempton,
Meade Kempton, Mickell Kempton, Mikah Kempton, Miranda Kempton, Mitchael Kempton, Mitcheal Kempton, Montee Kempton, Morio Kempton, Murat Kempton, Nashon Kempton, Nova Kempton, Olusegun Kempton, Ondra
Kempton, Orian Kempton, Orren Kempton, Reggy Kempton, Rodrico Kempton, Ronzell Kempton, Runako Kempton, Ryszard Kempton, Shady Kempton, Shango Kempton, Shawan Kempton, Terez Kempton, Thang Kempton,
Tomothy Kempton, Toron Kempton, Torrin Kempton, Toya Kempton, Trayon Kempton, Trellis Kempton, Tremel Kempton, Tryon Kempton, Tyrek Kempton, Wessley Kempton, Yan Kempton, Zed Kempton, Ako Kempton,
Aldrich Kempton, Alesandro Kempton, Alrick Kempton, Ayo Kempton, Bobbyjoe Kempton, Broadus Kempton, Brockton Kempton, Callie Kempton, Ched Kempton, Conn Kempton, Cristo Kempton, Dallen Kempton,
Dannel Kempton, Dasan Kempton, Datron Kempton, Dawaun Kempton, Delance Kempton, Delawrence Kempton, Demarrio Kempton, Denell Kempton, Derak Kempton, Derrie Kempton, Deundra Kempton, Dorin Kempton,
Dyon Kempton, Elizardo Kempton, Filimon Kempton, Fitzroy Kempton, Gari Kempton, Glover Kempton, Gretchen Kempton, Hartley Kempton, Holt Kempton, Jabe Kempton, Jaclyn Kempton, Jadrien Kempton, Jamah
Kempton, Jarman Kempton, Jarreau Kempton, Jearld Kempton, Jerimi Kempton, Jerris Kempton, Joeph Kempton, Jorel Kempton, Joshus Kempton, Jovany Kempton, Kaven Kempton, Kawaski Kempton, Kiron Kempton,
Korrey Kempton, Kort Kempton, Lavale Kempton, Lenorris Kempton, Lizandro Kempton, Lynard Kempton, Manson Kempton, Marky Kempton, Marlando Kempton, Maxime Kempton, Mcgarrett Kempton, Merwin Kempton,
Miko Kempton, Niklas Kempton, Nkrumah Kempton, Orman Kempton, Osmar Kempton, Paresh Kempton, Ponce Kempton, Prem Kempton, Rachelle Kempton, Rajendra Kempton, Rashone Kempton, Rawn Kempton, Raynor
Kempton, Rechard Kempton, Rogan Kempton, Rollo Kempton, Romando Kempton, Royd Kempton, Salah Kempton, Scoey Kempton, Selvin Kempton, Swain Kempton, Tarun Kempton, Tawn Kempton, Teal Kempton,
Telesforo Kempton, Thaddeaus Kempton, Timoth Kempton, Toren Kempton, Vicki Kempton, Wael Kempton, Whitfield Kempton, Winifred Kempton, Wyeth Kempton, Abdu Kempton, Abdulla Kempton, Akio Kempton,
Aleck Kempton, Antwian Kempton, Aquiles Kempton, Armad Kempton, Averill Kempton, Bijan Kempton, Billyjo Kempton, Bladimir Kempton, Bray Kempton, Brigido Kempton, Candice Kempton, Changa Kempton,
Chanon Kempton, Charlotte Kempton, Colie Kempton, Colonel Kempton, Crespin Kempton, Dabney Kempton, Dace Kempton, Damaine Kempton, Danna Kempton, Danya Kempton, Darelle Kempton, Darrnell Kempton,
Deaundre Kempton, Dijon Kempton, Dina Kempton, Dontel Kempton, Dracy Kempton, Duayne Kempton, Easton Kempton, Eban Kempton, Elric Kempton, Ervey Kempton, Festus Kempton, Filip Kempton, Furnell
Kempton, Gardiner Kempton, Gleen Kempton, Herve Kempton, Hogan Kempton, Hossein Kempton, Ikaika Kempton, Imad Kempton, Jacek Kempton, Jamaica Kempton, Jamichael Kempton, Jammal Kempton, Jarmon
Kempton, Jerren Kempton, Joshu Kempton, Juanjose Kempton, Kanoa Kempton, Kia Kempton, Kiernan Kempton, Kirtus Kempton, Lacedric Kempton, Legrand Kempton, Lekendrick Kempton, Lemoyne Kempton, Lige
Kempton, Loranzo Kempton, Loyce Kempton, Masai Kempton, Master Kempton, Michah Kempton, Min Kempton, Mir Kempton, Mohan Kempton, Montrail Kempton, Montray Kempton, Nacoma Kempton, Nakoa Kempton,
Navid Kempton, Nole Kempton, Opie Kempton, Orpheus Kempton, Payam Kempton, Pearce Kempton, Ramal Kempton, Recco Kempton, Renn Kempton, Rigel Kempton, Roe Kempton, Rolondo Kempton, Romaldo Kempton,
Severn Kempton, Shakim Kempton, Shulem Kempton, Silviano Kempton, Strider Kempton, Tayari Kempton, Tiburcio Kempton, Tilmon Kempton, Tomar Kempton, Tran Kempton, Travaris Kempton, Trayvon Kempton,
Trev Kempton, Trevar Kempton, Tyreek Kempton, Windle Kempton, Yaw Kempton, Yechezkel Kempton, Zeth Kempton, Zollie Kempton, Acey Kempton, Adisa Kempton, Arlanda Kempton, Artavius Kempton, Avin
Kempton, Beauford Kempton, Bernadette Kempton, Birch Kempton, Brittan Kempton, Brown Kempton, Cabe Kempton, Calton Kempton, Caribe Kempton, Carrington Kempton, Chadwich Kempton, Chrstopher Kempton,
Chun Kempton, Crescencio Kempton, Damyon Kempton, Dantrell Kempton, Dariusz Kempton, Dartanion Kempton, Delio Kempton, Demarius Kempton, Deniz Kempton, Dennard Kempton, Domingos Kempton, Dominie
Kempton, Doyal Kempton, Dwanye Kempton, Earon Kempton, Efstathios Kempton, Elkin Kempton, Ellen Kempton, Fabain Kempton, Frans Kempton, Gopal Kempton, Haleem Kempton, Iverson Kempton, Japeth Kempton,
Johanna Kempton, Jorgen Kempton, Jourdan Kempton, Kassim Kempton, Keidrick Kempton, Keif Kempton, Knox Kempton, Lacharles Kempton, Ladarius Kempton, Ladarrell Kempton, Leonce Kempton, Lipa Kempton,
Lorren Kempton, Luqman Kempton, Mcihael Kempton, Mercer Kempton, Micharl Kempton, Mikle Kempton, Montre Kempton, Morad Kempton, Nichael Kempton, Phi Kempton, Quantez Kempton, Quency Kempton, Quinlan
Kempton, Quintrell Kempton, Redell Kempton, Regnald Kempton, Renauld Kempton, Ronelle Kempton, Rudell Kempton, Ruffin Kempton, Salil Kempton, Seanmichael Kempton, Shaheem Kempton, Sharieff Kempton,
Shawndel Kempton, Stamatis Kempton, Tadashi Kempton, Tiras Kempton, Toan Kempton, Toben Kempton, Tyrik Kempton, Tyshaun Kempton, Ulisses Kempton, Visente Kempton, Wadell Kempton, Wilfrid Kempton, Won
Kempton, Aashish Kempton, Adama Kempton, Aja Kempton, Alcindor Kempton, Alejandra Kempton, Alyn Kempton, Ami Kempton, Andrel Kempton, Antonine Kempton, Artemas Kempton, Artimus Kempton, Ary Kempton,
Atiim Kempton, Avinash Kempton, Brittain Kempton, Callan Kempton, Cari Kempton, Claire Kempton, Conard Kempton, Danan Kempton, Darol Kempton, Day Kempton, Delma Kempton, Demetricus Kempton, Dewone
Kempton, Dougals Kempton, Elester Kempton, Espiridion Kempton, Estanislado Kempton, Esther Kempton, Fabien Kempton, Famous Kempton, Fredderick Kempton, Friedrich Kempton, Garrette Kempton, Greogry
Kempton, Gwendolyn Kempton, Hardin Kempton, Hendrik Kempton, Hendrix Kempton, Jabulani Kempton, Jacin Kempton, Jacquelyn Kempton, Jantzen Kempton, Jarren Kempton, Jasyn Kempton, Jayde Kempton, Jeris
Kempton, Jery Kempton, Jolyon Kempton, Karem Kempton, Key Kempton, Kibwe Kempton, Kyon Kempton, Lamin Kempton, Lasaro Kempton, Ledon Kempton, Malcomb Kempton, Mando Kempton, Marcelus Kempton, Margus
Kempton, Marzell Kempton, Mearl Kempton, Miron Kempton, Mitesh Kempton, Montay Kempton, Montrey Kempton, Morey Kempton, Morrie Kempton, Mozell Kempton, Narada Kempton, Naveed Kempton, Nenad Kempton,
Nicolaas Kempton, Nilton Kempton, Ojay Kempton, Olga Kempton, Oman Kempton, Pancho Kempton, Pepper Kempton, Poul Kempton, Rajon Kempton, Rawley Kempton, Rayon Kempton, Read Kempton, Rees Kempton,
Reeves Kempton, Romond Kempton, Rondrick Kempton, Sancho Kempton, Santi Kempton, Selso Kempton, Sevan Kempton, Shondel Kempton, Tavarius Kempton, Thelbert Kempton, Theodoro Kempton, Theus Kempton,
Thien Kempton, Timoty Kempton, Timur Kempton, Travius Kempton, Trisha Kempton, Tyquan Kempton, Usbaldo Kempton, Varnell Kempton, Videl Kempton, Willi Kempton, Zacariah Kempton, Zain Kempton, Aamir
Kempton, Abdallah Kempton, Almando Kempton, Almond Kempton, Alpheus Kempton, Alvarez Kempton, Alverto Kempton, Andrick Kempton, Anthonie Kempton, Anthoy Kempton, Antiona Kempton, Antwand Kempton,
Arrie Kempton, Artur Kempton, Baldwin Kempton, Bardo Kempton, Carols Kempton, Chau Kempton, Clayborne Kempton, Conell Kempton, Confesor Kempton, Cottrell Kempton, Craven Kempton, Curits Kempton,
Damiel Kempton, Deandrae Kempton, Derrius Kempton, Dirrick Kempton, Dora Kempton, Dorain Kempton, Dushaun Kempton, Eliodoro Kempton, Elvie Kempton, Faraz Kempton, Fernanda Kempton, Ferron Kempton,
Frankin Kempton, Fraser Kempton, Giuliano Kempton, Godwin Kempton, Hakan Kempton, Hershal Kempton, Jacobie Kempton, Jada Kempton, Jaimeson Kempton, Jamill Kempton, Jarrard Kempton, Jeromi Kempton,
Jerral Kempton, Jilberto Kempton, Jonel Kempton, Joseangel Kempton, Josedejesus Kempton, Joshva Kempton, Jovani Kempton, Juana Kempton, Juvencio Kempton, Karol Kempton, Keanon Kempton, Keli Kempton,
Kelven Kempton, Kemal Kempton, Khanh Kempton, Kiah Kempton, Kimmy Kempton, Kitt Kempton, Laith Kempton, Latravis Kempton, Lebarron Kempton, Lenon Kempton, Leondre Kempton, Lue Kempton, Luka Kempton,
Lyndal Kempton, Macedonio Kempton, Mahdee Kempton, Marcellas Kempton, Mardell Kempton, Monnie Kempton, Naron Kempton, Nehal Kempton, Nicholai Kempton, Nicol Kempton, Nimesh Kempton, Orlan Kempton,
Pal Kempton, Paras Kempton, Pasha Kempton, Pio Kempton, Piotr Kempton, Rahmon Kempton, Reilly Kempton, Rommell Kempton, Romondo Kempton, Ronie Kempton, Rontae Kempton, Roth Kempton, Ruven Kempton,
Senecca Kempton, Sequoia Kempton, Shadwick Kempton, Shaquan Kempton, Shaundell Kempton, Shaya Kempton, Shloma Kempton, Shonnon Kempton, Shunta Kempton, Silver Kempton, Stanislaw Kempton, Sumeet
Kempton, Sylvain Kempton, Tajiddin Kempton, Tejas Kempton, Tereso Kempton, Tilton Kempton, Tjay Kempton, Tramon Kempton, Troi Kempton, Troye Kempton, Tyrelle Kempton, Usher Kempton, Valeriano
Kempton, Verlyn Kempton, Vickie Kempton, Wallis Kempton, Yahya Kempton, Yair Kempton, Zacharie Kempton, Zakery Kempton, Zoe Kempton, Abdual Kempton, Adeyemi Kempton, Alisa Kempton, Alois Kempton,
Alondo Kempton, Alprentice Kempton, Altariq Kempton, Amaro Kempton, Amen Kempton, Andria Kempton, Anthoni Kempton, Apurva Kempton, Arrow Kempton, Aryn Kempton, Atilano Kempton, Auburn Kempton, Auturo
Kempton, Aven Kempton, Averil Kempton, Bernerd Kempton, Bethel Kempton, Biju Kempton, Bogdan Kempton, Boston Kempton, Bree Kempton, Camaron Kempton, Candace Kempton, Cara Kempton, Cato Kempton,
Ceferino Kempton, Chantry Kempton, Chappell Kempton, Charels Kempton, Ciaran Kempton, Codi Kempton, Colan Kempton, Crayton Kempton, Dakar Kempton, Dallis Kempton, Danen Kempton, Daoud Kempton, Davien
Kempton, Deny Kempton, Derius Kempton, Derrico Kempton, Devere Kempton, Dmarcus Kempton, Dwright Kempton, Dyami Kempton, Eileen Kempton, Eitan Kempton, Elgie Kempton, Elimelech Kempton, Ellie
Kempton, Ellwood Kempton, Emmanual Kempton, Eryk Kempton, Esdras Kempton, Estanislao Kempton, Euell Kempton, Everard Kempton, Hagen Kempton, Happy Kempton, Harald Kempton, Harrington Kempton, Hays
Kempton, Henrik Kempton, Hillery Kempton, Honorio Kempton, Hristos Kempton, Ilario Kempton, Indalecio Kempton, Izaac Kempton, Jahmar Kempton, Jarome Kempton, Jarone Kempton, Javaughn Kempton, Jeanne
Kempton, Jeannie Kempton, Jearl Kempton, Jenner Kempton, Jennie Kempton, Jerit Kempton, Jet Kempton, Jonath Kempton, Jumal Kempton, Kahil Kempton, Kealii Kempton, Keeley Kempton, Kehinde Kempton,
Kene Kempton, Kermitt Kempton, Keshon Kempton, Kore Kempton, Lapatrick Kempton, Larmar Kempton, Laroyce Kempton, Larren Kempton, Latisha Kempton, Latonio Kempton, Lewayne Kempton, Malachy Kempton,
Manford Kempton, Marcanthony Kempton, Marks Kempton, Marley Kempton, Marlone Kempton, Marquies Kempton, Mihir Kempton, Minas Kempton, Montae Kempton, Mortimer Kempton, Mykel Kempton, Nadia Kempton,
Nadim Kempton, Naftoli Kempton, Nakai Kempton, Nashid Kempton, Nello Kempton, Nichola Kempton, Nilo Kempton, Nthony Kempton, Orenthial Kempton, Palani Kempton, Pericles Kempton, Quentine Kempton,
Rafiel Kempton, Rainey Kempton, Remberto Kempton, Renan Kempton, Riyad Kempton, Robey Kempton, Rochell Kempton, Romaro Kempton, Roosvelt Kempton, Satish Kempton, Scotte Kempton, Sentell Kempton,
Serapio Kempton, Shabaka Kempton, Srinivas Kempton, Stanely Kempton, Taraus Kempton, Tehron Kempton, Temujin Kempton, Todrick Kempton, Torrian Kempton, Treven Kempton, Trinidy Kempton, Tung Kempton,
Uchenna Kempton, Vineet Kempton, Waldon Kempton, Wilkins Kempton, Xzavier Kempton, Yaser Kempton, Zahir Kempton, Zeus Kempton, Abdurrahim Kempton, Ahmet Kempton, Albion Kempton, Andi Kempton, Andri
Kempton, Angello Kempton, Angle Kempton, Aquilla Kempton, Arlee Kempton, Arliss Kempton, Asante Kempton, Ashwin Kempton, Benford Kempton, Bernd Kempton, Bevin Kempton, Blanton Kempton, Brandie
Kempton, Brint Kempton, Carle Kempton, Carvel Kempton, Carvell Kempton, Chang Kempton, Charls Kempton, Christa Kempton, Deidrick Kempton, Derrion Kempton, Dervin Kempton, Devine Kempton, Dixie
Kempton, Dom Kempton, Dwone Kempton, Edman Kempton, Efthimios Kempton, Eian Kempton, Elazar Kempton, Elridge Kempton, Emma Kempton, Eoin Kempton, Ericka Kempton, Everick Kempton, Everitt Kempton,
Franck Kempton, Fredi Kempton, Ganesh Kempton, Gaurav Kempton, Geza Kempton, Gianpaolo Kempton, Grahm Kempton, Haden Kempton, Haitham Kempton, Hansford Kempton, Heberto Kempton, Hieu Kempton, Jabali
Kempton, Jabir Kempton, Jamilah Kempton, Jarriel Kempton, Javares Kempton, Jawaun Kempton, Jessen Kempton, Jonanthan Kempton, Joshoa Kempton, Joslyn Kempton, Jovian Kempton, Jozsef Kempton, Juanpablo
Kempton, Justun Kempton, Kalief Kempton, Kaseen Kempton, Kato Kempton, Keagan Kempton, Keefer Kempton, Kishan Kempton, Kitwana Kempton, Konata Kempton, Lajohn Kempton, Lakeisha Kempton, Lamichael
Kempton, Latonia Kempton, Lelan Kempton, Lendon Kempton, Leovardo Kempton, Leray Kempton, Linh Kempton, Lovie Kempton, Manasseh Kempton, Marcella Kempton, Marguette Kempton, Marke Kempton, Marlene
Kempton, Martie Kempton, Martrell Kempton, Marus Kempton, Masaki Kempton, Mathhew Kempton, Maurisio Kempton, Mayur Kempton, Meco Kempton, Meguel Kempton, Meko Kempton, Mensah Kempton, Micki Kempton,
Mikele Kempton, Milas Kempton, Mirko Kempton, Mondell Kempton, Mondo Kempton, Mondrell Kempton, Murdock Kempton, Nairobi Kempton, Nathaiel Kempton, Neco Kempton, Neely Kempton, Nelvin Kempton, Nichol
Kempton, Nicholous Kempton, Norm Kempton, Olander Kempton, Pace Kempton, Paschal Kempton, Patick Kempton, Pearson Kempton, Phuc Kempton, Ramil Kempton, Ravinder Kempton, Rayman Kempton, Remond
Kempton, Rendall Kempton, Reshawn Kempton, Rhian Kempton, Romy Kempton, Roozbeh Kempton, Rutledge Kempton, Ryker Kempton, Satoshi Kempton, Shafton Kempton, Shahab Kempton, Shantell Kempton, Shontez
Kempton, Standley Kempton, Taha Kempton, Tarren Kempton, Tavio Kempton, Terah Kempton, Texas Kempton, Thabiti Kempton, Theodric Kempton, Timtohy Kempton, Torence Kempton, Torrick Kempton, Towan
Kempton, Travor Kempton, Tyge Kempton, Vandell Kempton, Virginio Kempton, Wilkie Kempton, Windsor Kempton, Yarrow Kempton, Yuji Kempton, Zedric Kempton, Ziyad Kempton, Abie Kempton, Abundio Kempton,
Adi Kempton, Aisha Kempton, Akintunde Kempton, Alfio Kempton, Anival Kempton, Antonnio Kempton, Asencion Kempton, Ashly Kempton, Beaux Kempton, Bodhi Kempton, Bowie Kempton, Brandal Kempton, Bristol
Kempton, Carrick Kempton, Chales Kempton, Chantz Kempton, Chenier Kempton, Chima Kempton, Chrystopher Kempton, Cian Kempton, Clearance Kempton, Cohen Kempton, Colman Kempton, Corneil Kempton, Dannis
Kempton, Dantonio Kempton, Danyal Kempton, Darus Kempton, Daudi Kempton, Dejohn Kempton, Demeko Kempton, Dewaun Kempton, Dondrick Kempton, Donley Kempton, Donney Kempton, Donyelle Kempton, Dorjan
Kempton, Drummond Kempton, Dwayn Kempton, Dywayne Kempton, Euclides Kempton, Farhan Kempton, Fritzgerald Kempton, Gabreil Kempton, Gerrald Kempton, Greer Kempton, Halim Kempton, Haroon Kempton, Hatim
Kempton, Herald Kempton, Ismeal Kempton, Jamesmichael Kempton, Jamir Kempton, Janel Kempton, Janelle Kempton, Jerrol Kempton, Jerryl Kempton, Jonta Kempton, Jumoke Kempton, Karanja Kempton, Karina
Kempton, Karis Kempton, Karrem Kempton, Kavan Kempton, Keddrick Kempton, Kedrin Kempton, Keifer Kempton, Keldric Kempton, Kenichi Kempton, Kery Kempton, Khris Kempton, Kiko Kempton, Kimothy Kempton,
Kippy Kempton, Kivin Kempton, Kojak Kempton, Kortez Kempton, Lambros Kempton, Lealand Kempton, Lillian Kempton, Llewelyn Kempton, Loron Kempton, Maneesh Kempton, Mansoor Kempton, Mariah Kempton,
Maricus Kempton, Marta Kempton, Marte Kempton, Martese Kempton, Maston Kempton, Maylon Kempton, Mcclain Kempton, Mikko Kempton, Montrez Kempton, Najee Kempton, Najeeb Kempton, Nakoma Kempton, Nakuma
Kempton, Oliverio Kempton, Orlondo Kempton, Osceola Kempton, Osric Kempton, Othoniel Kempton, Ovid Kempton, Peterjohn Kempton, Rad Kempton, Rogue Kempton, Rolly Kempton, Roshad Kempton, Sahwn
Kempton, Santosh Kempton, Shakeem Kempton, Shanen Kempton, Shey Kempton, Sina Kempton, Sonja Kempton, Stone Kempton, Stphen Kempton, Sue Kempton, Sylvanus Kempton, Tameka Kempton, Tauris Kempton,
Tawayne Kempton, Tennille Kempton, Terrice Kempton, Thalamus Kempton, Tore Kempton, Tranell Kempton, Travone Kempton, Trevan Kempton, Tristram Kempton, Tywaun Kempton, Valton Kempton, Venice Kempton,
Wagner Kempton, Walberto Kempton, Weyman Kempton, Willliam Kempton, Wisam Kempton, Yisrael Kempton, Zachari Kempton, Zon Kempton, Amal Kempton, Amie Kempton, Antwun Kempton, Audre Kempton, Bertrum
Kempton, Bond Kempton, Canon Kempton, Careem Kempton, Carly Kempton, Charmaine Kempton, Corian Kempton, Coye Kempton, Daisuke Kempton, Damacio Kempton, Damarius Kempton, Damiane Kempton, Darrik
Kempton, Dartanian Kempton, Dary Kempton, Davan Kempton, Deana Kempton, Deaundra Kempton, Delos Kempton, Develle Kempton, Dontray Kempton, Dorsett Kempton, Dyrell Kempton, Gered Kempton, Gilad
Kempton, Hadrian Kempton, Haji Kempton, Harl Kempton, Hideki Kempton, Husani Kempton, Jacson Kempton, Jaimes Kempton, Jama Kempton, Janathan Kempton, Jaran Kempton, Jauron Kempton, Jeffie Kempton,
Jejuan Kempton, Jerick Kempton, Jermery Kempton, Jerramie Kempton, Kalei Kempton, Karam Kempton, Keevan Kempton, Kei Kempton, Kel Kempton, Keo Kempton, Khaleel Kempton, Klye Kempton, Korrie Kempton,
Kunal Kempton, Kyrone Kempton, Ladaryl Kempton, Laman Kempton, Larome Kempton, Latwan Kempton, Lavaris Kempton, Lavoy Kempton, Lenoard Kempton, Levarr Kempton, Matilde Kempton, Mazin Kempton, Nakie
Kempton, Nikolos Kempton, Oak Kempton, Orrie Kempton, Pleas Kempton, Quanta Kempton, Rayshun Kempton, Rhasaan Kempton, Ruark Kempton, Saxon Kempton, Seith Kempton, Sham Kempton, Shamont Kempton,
Shontel Kempton, Terre Kempton, Thoma Kempton, Thunder Kempton, Torance Kempton, Travelle Kempton, Tulio Kempton, Tyrance Kempton, Ustin Kempton, Verle Kempton, Vicky Kempton, Wlliam Kempton, Xerxes
Kempton, Yero Kempton, Adetokunbo Kempton, Adika Kempton, Adriane Kempton, Afshin Kempton, Alto Kempton, Alvon Kempton, Anant Kempton, Anatole Kempton, Aston Kempton, Aul Kempton, Aza Kempton, Azriel
Kempton, Bay Kempton, Bee Kempton, Benoit Kempton, Bradden Kempton, Brayton Kempton, Buren Kempton, Caton Kempton, Cesareo Kempton, Chandar Kempton, Charistopher Kempton, Chike Kempton, Chong
Kempton, Cline Kempton, Dabid Kempton, Damascus Kempton, Delron Kempton, Delvis Kempton, Demeterius Kempton, Demetries Kempton, Demorio Kempton, Demtrius Kempton, Derrian Kempton, Dilanjan Kempton,
Donti Kempton, Doulgas Kempton, Doyce Kempton, Eber Kempton, Elena Kempton, Ellington Kempton, Eros Kempton, Esiquio Kempton, Esley Kempton, Ewan Kempton, Firas Kempton, Freeland Kempton, Frenchie
Kempton, Garlan Kempton, Gaylin Kempton, Hamin Kempton, Hoyle Kempton, Hubbard Kempton, Ikechukwu Kempton, Issam Kempton, Jameil Kempton, Janard Kempton, Jann Kempton, Jarmain Kempton, Jayjay
Kempton, Jemell Kempton, Jerem Kempton, Jeremian Kempton, Jerritt Kempton, Juda Kempton, Kahn Kempton, Kartik Kempton, Katrell Kempton, Kavon Kempton, Kelsie Kempton, Kelsy Kempton, Kenna Kempton,
Kenner Kempton, Kentaro Kempton, Kenyotta Kempton, Keonte Kempton, Kindell Kempton, Kodie Kempton, Kurtus Kempton, Lacory Kempton, Latanya Kempton, Lathaniel Kempton, Lauriano Kempton, Lavares
Kempton, Lemarr Kempton, Lomont Kempton, Lyndel Kempton, Mandeep Kempton, Mansur Kempton, Marrion Kempton, Mathan Kempton, Maurie Kempton, Melburn Kempton, Mia Kempton, Micheil Kempton, Milledge
Kempton, Mourice Kempton, Mousa Kempton, Muneer Kempton, Naphtali Kempton, Navarro Kempton, Nehemias Kempton, Nickalous Kempton, Nickolous Kempton, Ola Kempton, Oshua Kempton, Osmond Kempton, Quinta
Kempton, Quintel Kempton, Rahshawn Kempton, Raney Kempton, Raye Kempton, Rayne Kempton, Rockne Kempton, Romar Kempton, Sebastain Kempton, Shang Kempton, Sherrard Kempton, Smauel Kempton, Stamatios
Kempton, Talal Kempton, Taurin Kempton, Terdell Kempton, Thong Kempton, Tishawn Kempton, Tizoc Kempton, Trad Kempton, Trafton Kempton, Trenity Kempton, Tyray Kempton, Ulices Kempton, Vareck Kempton,
Videll Kempton, Voltaire Kempton, Wilmot Kempton, Zacary Kempton, Aaran Kempton, Abdalla Kempton, Abdias Kempton, Abiodun Kempton, Adlai Kempton, Ahamad Kempton, Alexandar Kempton, Alie Kempton,
Alissa Kempton, Alterick Kempton, Amitabh Kempton, Andros Kempton, Angelia Kempton, Antwonne Kempton, Arnez Kempton, Arrion Kempton, Asaf Kempton, Auden Kempton, Bacilio Kempton, Brynn Kempton, Byan
Kempton, Can Kempton, Carlen Kempton, Carliss Kempton, Carlose Kempton, Cazzie Kempton, Chadney Kempton, Chapman Kempton, Chedrick Kempton, Cherokee Kempton, Christophen Kempton, Clearnce Kempton,
Cleto Kempton, Cliford Kempton, Colburn Kempton, Cordy Kempton, Craigory Kempton, Dalan Kempton, Dam Kempton, Damonn Kempton, Dandrea Kempton, Danford Kempton, Danieal Kempton, Dano Kempton, Daril
Kempton, Darrence Kempton, Dartanyan Kempton, Dawone Kempton, Deatrick Kempton, Delayne Kempton, Delfred Kempton, Delshon Kempton, Demark Kempton, Demea Kempton, Demetra Kempton, Demetress Kempton,
Demeturis Kempton, Dene Kempton, Derran Kempton, Dewann Kempton, Dezi Kempton, Dondrell Kempton, Donsha Kempton, Dontai Kempton, Durelle Kempton, Ebay Kempton, Edin Kempton, Efran Kempton, Emelio
Kempton, Erasto Kempton, Erby Kempton, Eriks Kempton, Erine Kempton, Ester Kempton, Everet Kempton, Excell Kempton, Falando Kempton, Gaius Kempton, Garald Kempton, Garlon Kempton, Germane Kempton,
Gernard Kempton, Glenden Kempton, Graciela Kempton, Gram Kempton, Grayling Kempton, Gunter Kempton, Gustaf Kempton, Gwyn Kempton, Hamp Kempton, Hanley Kempton, Harrold Kempton, Harvest Kempton,
Hermenegildo Kempton, Hooman Kempton, Husam Kempton, Idrees Kempton, Jaaron Kempton, Jaben Kempton, Jacent Kempton, Jacyn Kempton, Jadrian Kempton, Jaisen Kempton, Jamard Kempton, Jamare Kempton,
Jarl Kempton, Jarvin Kempton, Jary Kempton, Jashon Kempton, Jaso Kempton, Jaton Kempton, Jawann Kempton, Jebidiah Kempton, Jedadia Kempton, Jenard Kempton, Jeramaine Kempton, Jerrimy Kempton, Jerrin
Kempton, Jibreel Kempton, Jigar Kempton, Joah Kempton, Jolene Kempton, Jonell Kempton, Jordy Kempton, Josuah Kempton, Jwan Kempton, Kantrell Kempton, Keithrick Kempton, Kennet Kempton, Keshaun
Kempton, Kief Kempton, Kisha Kempton, Kiwan Kempton, Kizzy Kempton, Koury Kempton, Kylon Kempton, Lakisha Kempton, Lamarco Kempton, Lavonte Kempton, Lemanuel Kempton, Lennell Kempton, Letcher
Kempton, Lethaniel Kempton, Levone Kempton, Lilton Kempton, Lindel Kempton, Linzy Kempton, Lora Kempton, Lorie Kempton, Lovelle Kempton, Lowry Kempton, Lucia Kempton, Luisa Kempton, Macheal Kempton,
Magdiel Kempton, Mahmood Kempton, Manrique Kempton, Manus Kempton, Maricela Kempton, Marjoe Kempton, Marquett Kempton, Mars Kempton, Mathews Kempton, Mattthew Kempton, Mehmet Kempton, Mehran Kempton,
Menashe Kempton, Merril Kempton, Moe Kempton, Morgen Kempton, Natalio Kempton, Nero Kempton, Nickolos Kempton, Nidal Kempton, Nishant Kempton, Nixon Kempton, Oreste Kempton, Osie Kempton, Parks
Kempton, Pax Kempton, Phillipp Kempton, Qaadir Kempton, Quantas Kempton, Rameen Kempton, Ranell Kempton, Rani Kempton, Rasheim Kempton, Rawlin Kempton, Rena Kempton, Rett Kempton, Riko Kempton, Rimas
Kempton, Roark Kempton, Roma Kempton, Romale Kempton, Rosemary Kempton, Roshell Kempton, Sadiki Kempton, Saquan Kempton, Sargon Kempton, Shantez Kempton, Shawntel Kempton, Shelia Kempton, Sheryl
Kempton, Sholem Kempton, Sly Kempton, Sohail Kempton, Spero Kempton, Stepehn Kempton, Tabor Kempton, Taki Kempton, Talley Kempton, Tamboura Kempton, Tarrus Kempton, Tau Kempton, Taz Kempton, Tejuan
Kempton, Terik Kempton, Terone Kempton, Terreance Kempton, Terriel Kempton, Terriss Kempton, Theodus Kempton, Tobian Kempton, Tolan Kempton, Tollie Kempton, Townsend Kempton, Tramain Kempton, Trennis
Kempton, Tshaka Kempton, Tynell Kempton, Tyone Kempton, Tywain Kempton, Uganda Kempton, Unique Kempton, Vahe Kempton, Vashone Kempton, Verna Kempton, Welsey Kempton, Woodson Kempton, Wydell Kempton,
Youssef Kempton, Zebulin Kempton, Zeyad Kempton, Aaryn Kempton, Ademola Kempton, Adom Kempton, Alandus Kempton, Alcide Kempton, Aldridge Kempton, Alfonsa Kempton, Alfonzia Kempton, Allyson Kempton,
Alter Kempton, Amari Kempton, Amr Kempton, Ancel Kempton, Andie Kempton, Andrus Kempton, Antiwan Kempton, Antoinette Kempton, Antonis Kempton, Antwyne Kempton, Anupam Kempton, Aquila Kempton, Arville
Kempton, Asael Kempton, Assad Kempton, Aurohom Kempton, Autrey Kempton, Ayal Kempton, Azikiwe Kempton, Bashar Kempton, Basim Kempton, Beauregard Kempton, Belal Kempton, Benyamin Kempton, Bertis
Kempton, Bertran Kempton, Boban Kempton, Boby Kempton, Bracy Kempton, Branndon Kempton, Burtis Kempton, Cameo Kempton, Carley Kempton, Carnelius Kempton, Caroll Kempton, Carolos Kempton, Carvis
Kempton, Cashawn Kempton, Cean Kempton, Charod Kempton, Chevelle Kempton, Chrisotpher Kempton, Christerfer Kempton, Christi Kempton, Clois Kempton, Cloyce Kempton, Constancio Kempton, Corkey Kempton,
Corvin Kempton, Corye Kempton, Costello Kempton, Coury Kempton, Crecencio Kempton, Cuahutemoc Kempton, Curby Kempton, Curly Kempton, Dade Kempton, Dag Kempton, Daimeon Kempton, Dakin Kempton, Damiean
Kempton, Dandy Kempton, Danian Kempton, Davinder Kempton, Daylin Kempton, Deljuan Kempton, Delone Kempton, Delta Kempton, Demaris Kempton, Demel Kempton, Demerick Kempton, Demetrous Kempton, Demiko
Kempton, Demorrio Kempton, Deonne Kempton, Derian Kempton, Detron Kempton, Deva Kempton, Dillion Kempton, Divine Kempton, Dniel Kempton, Doanld Kempton, Donaldo Kempton, Donshay Kempton, Dontee
Kempton, Doyne Kempton, Dubois Kempton, Dulani Kempton, Duong Kempton, Dupre Kempton, Durante Kempton, Edith Kempton, Edris Kempton, Edwyn Kempton, Efrin Kempton, Ehrin Kempton, Ehsan Kempton, Eldwin
Kempton, Elic Kempton, Elis Kempton, Elven Kempton, Eren Kempton, Errik Kempton, Erubey Kempton, Evertt Kempton, Exavier Kempton, Fahad Kempton, Fares Kempton, Fatmir Kempton, Ferando Kempton, Fonta
Kempton, Fotis Kempton, Gaither Kempton, Gar Kempton, Garvey Kempton, Gilmer Kempton, Godofredo Kempton, Greggery Kempton, Gregoire Kempton, Gregorey Kempton, Hagan Kempton, Haim Kempton, Hanz
Kempton, Hartford Kempton, Hassen Kempton, Haynes Kempton, Herrick Kempton, Herry Kempton, Hoa Kempton, Hud Kempton, Hurbert Kempton, Ilir Kempton, Ilyas Kempton, Ivica Kempton, Jabarr Kempton,
Jamara Kempton, Jamarco Kempton, Jana Kempton, Janis Kempton, Jarry Kempton, Javad Kempton, Javas Kempton, Javed Kempton, Jayden Kempton, Jebb Kempton, Jeptha Kempton, Jerimia Kempton, Joffrey
Kempton, Johanthan Kempton, Johari Kempton, Johnanthony Kempton, Johnnathan Kempton, Johnta Kempton, Jolly Kempton, Jonahtan Kempton, Jong Kempton, Jonh Kempton, Josep Kempton, Joss Kempton, Juergen
Kempton, Juliocesar Kempton, Junichi Kempton, Jusitn Kempton, Kalid Kempton, Kamali Kempton, Kannon Kempton, Karlon Kempton, Kashawn Kempton, Keilan Kempton, Kelcy Kempton, Kellis Kempton, Kelon
Kempton, Kendrich Kempton, Kentrel Kempton, Kerwyn Kempton, Kesley Kempton, Kimon Kempton, Kindu Kempton, Kinneth Kempton, Kondwani Kempton, Krystal Kempton, Kyran Kempton, Lacarlos Kempton, Laney
Kempton, Lelon Kempton, Lem Kempton, Lena Kempton, Leno Kempton, Leshan Kempton, Lexie Kempton, Lisle Kempton, Lonne Kempton, Lorence Kempton, Lowery Kempton, Lundy Kempton, Lynford Kempton, Maleek
Kempton, Maliek Kempton, Mano Kempton, Marcellis Kempton, Marcellius Kempton, Marci Kempton, Maris Kempton, Marl Kempton, Marston Kempton, Matthe Kempton, Matther Kempton, Maximiano Kempton, Mecca
Kempton, Melesio Kempton, Mic Kempton, Mican Kempton, Mickal Kempton, Mitchum Kempton, Mohit Kempton, Myrl Kempton, Nael Kempton, Najja Kempton, Nedal Kempton, Nektarios Kempton, Nemiah Kempton,
Niclas Kempton, Nilay Kempton, Nina Kempton, Noberto Kempton, Noell Kempton, Obrian Kempton, Orbie Kempton, Ormond Kempton, Orvin Kempton, Osborn Kempton, Pasco Kempton, Pele Kempton, Penn Kempton,
Perryn Kempton, Philipe Kempton, Prakash Kempton, Quarterrio Kempton, Quiency Kempton, Rahaman Kempton, Rahshan Kempton, Rahson Kempton, Raimond Kempton, Ramsay Kempton, Ranard Kempton, Ranulfo
Kempton, Rasha Kempton, Rashine Kempton, Rason Kempton, Ravis Kempton, Raylan Kempton, Rayme Kempton, Raymel Kempton, Redrick Kempton, Regi Kempton, Renier Kempton, Rhea Kempton, Riad Kempton,
Richerd Kempton, Rishard Kempton, Rockland Kempton, Rolfe Kempton, Roudy Kempton, Saed Kempton, Salaam Kempton, Samie Kempton, Savino Kempton, Selim Kempton, Senneca Kempton, Seung Kempton, Shadric
Kempton, Shaman Kempton, Sharn Kempton, Shawen Kempton, Shiron Kempton, Shohn Kempton, Shunn Kempton, Sims Kempton, Skeet Kempton, Soctt Kempton, Sohn Kempton, Standly Kempton, Starbuck Kempton,
Stratton Kempton, Sulton Kempton, Sunday Kempton, Sylas Kempton, Taff Kempton, Tallis Kempton, Tamal Kempton, Tarrant Kempton, Taurice Kempton, Teko Kempton, Telvis Kempton, Terek Kempton, Terrius
Kempton, Thermon Kempton, Thorsten Kempton, Timothee Kempton, Tirus Kempton, Tomi Kempton, Torren Kempton, Travolta Kempton, Travoris Kempton, Tyan Kempton, Vasco Kempton, Vashion Kempton, Verron
Kempton, Vinicio Kempton, Vyron Kempton, Wilkin Kempton, Winson Kempton, Worthy Kempton, Wynne Kempton, Yance Kempton, Yates Kempton, Yecheskel Kempton, Yonah Kempton, Yuseff Kempton, Abby Kempton,
Adaryl Kempton, Addis Kempton, Afrim Kempton, Ahmand Kempton, Ahmon Kempton, Alejos Kempton, Alphonsa Kempton, Alphonsus Kempton, Altie Kempton, Anastasio Kempton, Andris Kempton, Ankit Kempton,
Antario Kempton, Antero Kempton, Arafat Kempton, Armard Kempton, Armel Kempton, Arrin Kempton, Artavious Kempton, Ashlee Kempton, Atari Kempton, Aundrae Kempton, Avan Kempton, Avion Kempton, Azad
Kempton, Azariah Kempton, Babe Kempton, Banks Kempton, Bentura Kempton, Bily Kempton, Blakeley Kempton, Bonner Kempton, Bradshaw Kempton, Braeden Kempton, Brainard Kempton, Brianne Kempton, Brigg
Kempton, Broch Kempton, Bryian Kempton, Buell Kempton, Burchell Kempton, Butler Kempton, Callen Kempton, Cardale Kempton, Carlester Kempton, Carwin Kempton, Cassell Kempton, Casy Kempton, Chancelor
Kempton, Chapin Kempton, Chee Kempton, Chey Kempton, Chianti Kempton, Clarenc Kempton, Clayburn Kempton, Cleofas Kempton, Clevester Kempton, Clydell Kempton, Constance Kempton, Coran Kempton, Correll
Kempton, Cotton Kempton, Currie Kempton, Dae Kempton, Dai Kempton, Daisy Kempton, Dametrius Kempton, Damico Kempton, Danal Kempton, Danien Kempton, Danis Kempton, Dar Kempton, Darivs Kempton, Darmon
Kempton, Deejay Kempton, Delia Kempton, Demarquis Kempton, Demetrik Kempton, Demonta Kempton, Denys Kempton, Derec Kempton, Derl Kempton, Deshay Kempton, Destiny Kempton, Detroy Kempton, Devar
Kempton, Dewyane Kempton, Dierre Kempton, Dillan Kempton, Din Kempton, Dionysios Kempton, Dishawn Kempton, Doak Kempton, Donaldson Kempton, Donaven Kempton, Donzel Kempton, Doremus Kempton, Dorn
Kempton, Doss Kempton, Duglas Kempton, Durk Kempton, Dushon Kempton, Duvon Kempton, Dwaylon Kempton, Dywan Kempton, Edjuan Kempton, Effrem Kempton, Eliel Kempton, Elizah Kempton, Elray Kempton, Elsa
Kempton, Emerick Kempton, Epigmenio Kempton, Epimenio Kempton, Erasmus Kempton, Erez Kempton, Erman Kempton, Esgar Kempton, Everrett Kempton, Fateen Kempton, Felimon Kempton, Felis Kempton, Ferguson
Kempton, Firman Kempton, Fitz Kempton, France Kempton, Freddick Kempton, Frederi Kempton, Gadiel Kempton, Galdino Kempton, Gant Kempton, Gared Kempton, Garic Kempton, Garrell Kempton, Gavan Kempton,
Gemini Kempton, Genard Kempton, Geoge Kempton, Germany Kempton, Gioacchino Kempton, Gladys Kempton, Glennie Kempton, Glenroy Kempton, Gordy Kempton, Graylon Kempton, Griselda Kempton, Gussie Kempton,
Hall Kempton, Hammad Kempton, Hamza Kempton, Handy Kempton, Hardie Kempton, Hassel Kempton, Heiko Kempton, Henley Kempton, Hersh Kempton, Hewitt Kempton, Hiran Kempton, Hoke Kempton, Holmes Kempton,
Hunt Kempton, Ikenna Kempton, Imre Kempton, Irma Kempton, Isaul Kempton, Ishmail Kempton, Ishmel Kempton, Iyad Kempton, Jaamal Kempton, Jabaar Kempton, Jacquin Kempton, Jameison Kempton, Jasom
Kempton, Jefery Kempton, Jeffy Kempton, Jermanine Kempton, Jerol Kempton, Jesses Kempton, Jibril Kempton, Jimy Kempton, Joffre Kempton, Johm Kempton, Johne Kempton, Johnothan Kempton, Josias Kempton,
Joslin Kempton, Jovanny Kempton, Juel Kempton, Kaare Kempton, Kalib Kempton, Kalim Kempton, Kalum Kempton, Kedron Kempton, Kerim Kempton, Kerman Kempton, Keyan Kempton, Khai Kempton, Khareem Kempton,
Kierre Kempton, Kimmie Kempton, Kipton Kempton, Kord Kempton, Lajaune Kempton, Lamor Kempton, Lancy Kempton, Lando Kempton, Landrum Kempton, Lani Kempton, Larmont Kempton, Laurens Kempton, Lawrenc
Kempton, Lealon Kempton, Leeman Kempton, Legrande Kempton, Leone Kempton, Lewie Kempton, Loretta Kempton, Lorrin Kempton, Loukas Kempton, Luisito Kempton, Lutalo Kempton, Machel Kempton, Macklin
Kempton, Mahir Kempton, Manpreet Kempton, Mansour Kempton, Marcum Kempton, Mariusz Kempton, Markcus Kempton, Marquest Kempton, Marven Kempton, Mattias Kempton, Melbourne Kempton, Melisa Kempton,
Mihcael Kempton, Mile Kempton, Monserrate Kempton, Montique Kempton, Morice Kempton, Nataniel Kempton, Neiman Kempton, Noa Kempton, Obdulio Kempton, Odilon Kempton, Oma Kempton, Onathan Kempton,
Orlandis Kempton, Osamah Kempton, Pastor Kempton, Patterson Kempton, Pattrick Kempton, Pavlos Kempton, Phoenix Kempton, Pierson Kempton, Puneet Kempton, Quartez Kempton, Quetin Kempton, Rahsheen
Kempton, Randee Kempton, Ras Kempton, Raymie Kempton, Raymound Kempton, Raysean Kempton, Regginal Kempton, Reico Kempton, Reino Kempton, Reynardo Kempton, Rodrecus Kempton, Rodrickus Kempton, Rolin
Kempton, Royston Kempton, Rynell Kempton, Ryo Kempton, Sacramento Kempton, Seaborn Kempton, Sedgwick Kempton, Shaddrick Kempton, Shaffer Kempton, Shamal Kempton, Shamone Kempton, Sharman Kempton,
Sharrief Kempton, Shawnell Kempton, Shawntae Kempton, Shimshon Kempton, Shontay Kempton, Shuaib Kempton, Steveland Kempton, Stonewall Kempton, Sujal Kempton, Tage Kempton, Tarin Kempton, Tarrick
Kempton, Tarryl Kempton, Tauras Kempton, Tayvon Kempton, Terrol Kempton, Thearon Kempton, Thinh Kempton, Tirell Kempton, Tobius Kempton, Tobyn Kempton, Toderick Kempton, Torben Kempton, Torran
Kempton, Torray Kempton, Traven Kempton, Trek Kempton, Trina Kempton, Twayne Kempton, Tyee Kempton, Tyrick Kempton, Tyvon Kempton, Ubong Kempton, Ulysess Kempton, Valerian Kempton, Vennie Kempton,
Venus Kempton, Vincen Kempton, Vonn Kempton, Wandell Kempton, Warden Kempton, Warnell Kempton, Wille Kempton, Wolfram Kempton, Worley Kempton, Wren Kempton, Yoseph Kempton, Zacharian Kempton,
Zacheriah Kempton, Anoop Kempton, Antohny Kempton, Bianco Kempton, Billey Kempton, Blanca Kempton, Bradely Kempton, Brison Kempton, Chanson Kempton, Cheng Kempton, Choice Kempton, Cosmos Kempton,
Cymande Kempton, Cyprian Kempton, Dang Kempton, Derrus Kempton, Dorwin Kempton, Everest Kempton, Farzad Kempton, Gralin Kempton, Idi Kempton, Jakari Kempton, Jezreel Kempton, Jorell Kempton, Kong
Kempton, Liza Kempton, Mendy Kempton, Onix Kempton, Rajaee Kempton, Random Kempton, Rashean Kempton, Revis Kempton, Saman Kempton, Santini Kempton, Shahin Kempton, Talton Kempton, Teco Kempton,
Temitope Kempton, Vimal Kempton, Wacey Kempton, Aeric Kempton, Alhaji Kempton, Anas Kempton, Anselm Kempton, Bamidele Kempton, Behrang Kempton, Binu Kempton, Brenon Kempton, Brittney Kempton, Catina
Kempton, Chaunce Kempton, Christerphor Kempton, Claxton Kempton, Colley Kempton, Courtnee Kempton, Darrio Kempton, Darweshi Kempton, Dashiell Kempton, Daymeon Kempton, Deontay Kempton, Devlyn
Kempton, Effrey Kempton, Eldric Kempton, Faith Kempton, Garris Kempton, Holley Kempton, Hombre Kempton, Hussain Kempton, Jamari Kempton, Jaramy Kempton, Jaydon Kempton, Jeramee Kempton, Jerediah
Kempton, Jermiane Kempton, Jermont Kempton, Jerud Kempton, Johncharles Kempton, Jolan Kempton, Kairaba Kempton, Kawon Kempton, Kemon Kempton, Kennen Kempton, Kenyun Kempton, Khevin Kempton, Kiowa
Kempton, Kwabene Kempton, Ladrick Kempton, Lamarc Kempton, Laramy Kempton, Larance Kempton, Lebrone Kempton, Loc Kempton, Lynda Kempton, Marcius Kempton, Mariel Kempton, Marisela Kempton, Meshach
Kempton, Milon Kempton, Monterio Kempton, Najib Kempton, Natha Kempton, Nery Kempton, Niklaus Kempton, Pinchus Kempton, Quaid Kempton, Rael Kempton, Rain Kempton, Ralpheal Kempton, Ramiah Kempton,
Redmond Kempton, Regniald Kempton, Rennard Kempton, Rhet Kempton, Ritesh Kempton, Rodolpho Kempton, Rontrell Kempton, Rossano Kempton, Shale Kempton, Shevin Kempton, Shiraz Kempton, Sirica Kempton,
Sridhar Kempton, Staton Kempton, Suliman Kempton, Tchalla Kempton, Telvin Kempton, Terren Kempton, Traun Kempton, Trong Kempton, Trygve Kempton, Unborn Kempton, Vaden Kempton, Valery Kempton, Vuong
Kempton, Waseem Kempton, Zebulen Kempton, Abed Kempton, Abhay Kempton, Adebayo Kempton, Ahmid Kempton, Akai Kempton, Aldwin Kempton, Altonia Kempton, Alvertis Kempton, Alvey Kempton, Amondo Kempton,
Amrom Kempton, Andera Kempton, Andrico Kempton, Anterio Kempton, Antolin Kempton, Antorio Kempton, Arkim Kempton, Arran Kempton, Aslan Kempton, Ausencio Kempton, Aviel Kempton, Avrum Kempton, Ayron
Kempton, Azeem Kempton, Azel Kempton, Azell Kempton, Basel Kempton, Bengi Kempton, Benjamyn Kempton, Berish Kempton, Bianca Kempton, Bonny Kempton, Boy Kempton, Brach Kempton, Brishen Kempton,
Britney Kempton, Burlin Kempton, Buzz Kempton, Carolina Kempton, Casimer Kempton, Cedeno Kempton, Cemal Kempton, Chadly Kempton, Chen Kempton, Chirs Kempton, Christion Kempton, Christohpher Kempton,
Christpoher Kempton, Clate Kempton, Cleaven Kempton, Clif Kempton, Coburn Kempton, Conroy Kempton, Corbitt Kempton, Crispus Kempton, Daiman Kempton, Daimion Kempton, Damarco Kempton, Dammian Kempton,
Darr Kempton, Darreyl Kempton, Davar Kempton, Dawain Kempton, Dayron Kempton, Dectrick Kempton, Dederick Kempton, Demarkis Kempton, Denman Kempton, Derril Kempton, Devanand Kempton, Dharma Kempton,
Dionysus Kempton, Domanick Kempton, Dorey Kempton, Duel Kempton, Ebenezer Kempton, Edon Kempton, Effie Kempton, Ehron Kempton, Eliceo Kempton, Elija Kempton, Elijha Kempton, Elizandro Kempton,
Enriquez Kempton, Eryn Kempton, Essie Kempton, Etoyi Kempton, Fabrice Kempton, Farouk Kempton, Garick Kempton, Gean Kempton, Geovani Kempton, Germar Kempton, Gillian Kempton, Gilmore Kempton,
Giuseppi Kempton, Governor Kempton, Graden Kempton, Gresham Kempton, Haashim Kempton, Hagop Kempton, Hamzah Kempton, Harlie Kempton, Hatem Kempton, Hien Kempton, Hose Kempton, Ibe Kempton, Ingo
Kempton, Irven Kempton, Isam Kempton, Ishi Kempton, Istvan Kempton, Jabriel Kempton, Jamont Kempton, Janette Kempton, Jaroslaw Kempton, Jashawn Kempton, Java Kempton, Javid Kempton, Jaysun Kempton,
Jemario Kempton, Jemiah Kempton, Jerek Kempton, Jeren Kempton, Jeriah Kempton, Jerode Kempton, Jimmel Kempton, Jitu Kempton, Jmichael Kempton, Johnas Kempton, Johnwilliam Kempton, Joran Kempton, Jori
Kempton, Josehua Kempton, Joshlin Kempton, Joushua Kempton, Juane Kempton, Juba Kempton, Juvon Kempton, Kamaal Kempton, Kasib Kempton, Kate Kempton, Kayin Kempton, Keffer Kempton, Kentay Kempton,
Kentrail Kempton, Kenyell Kempton, Kerr Kempton, Khalik Kempton, Khurram Kempton, Kipchoge Kempton, Koa Kempton, Kowan Kempton, Kreig Kempton, Kristien Kempton, Krystopher Kempton, Kurry Kempton,
Kylee Kempton, Lamaine Kempton, Lamell Kempton, Lamour Kempton, Lanoris Kempton, Laquann Kempton, Laquinn Kempton, Lavone Kempton, Leanord Kempton, Leeandrew Kempton, Lenzy Kempton, Lequient Kempton,
Leshun Kempton, Lopaka Kempton, Lopez Kempton, Lyall Kempton, Malcoln Kempton, Mali Kempton, March Kempton, Marchant Kempton, Matthen Kempton, Medrick Kempton, Mildred Kempton, Mitchelle Kempton,
Moriah Kempton, Mykal Kempton, Neema Kempton, Nii Kempton, Nikkia Kempton, Okechukwu Kempton, Olatunde Kempton, Olu Kempton, Oluseyi Kempton, Orazio Kempton, Orel Kempton, Ortiz Kempton, Orvel
Kempton, Oseph Kempton, Overton Kempton, Peer Kempton, Phyllis Kempton, Pratik Kempton, Quante Kempton, Quindell Kempton, Raeshawn Kempton, Rahshon Kempton, Ran Kempton, Real Kempton, Rhodes Kempton,
Rhodney Kempton, Rodeny Kempton, Rondi Kempton, Rozelle Kempton, Rutilio Kempton, Saif Kempton, Sandford Kempton, Seab Kempton, Sevag Kempton, Shahied Kempton, Shamari Kempton, Shammah Kempton,
Sharmon Kempton, Shervin Kempton, Skippy Kempton, Stefanie Kempton, Stylianos Kempton, Tafari Kempton, Tag Kempton, Tamon Kempton, Tanisha Kempton, Tearle Kempton, Tellys Kempton, Terriance Kempton,
Timber Kempton, Timthoy Kempton, Tomiko Kempton, Torr Kempton, Torrez Kempton, Toshiro Kempton, Trammell Kempton, Trance Kempton, Tregg Kempton, Treston Kempton, Tristian Kempton, Tymaine Kempton,
Tyne Kempton, Tyrane Kempton, Vada Kempton, Valerio Kempton, Varion Kempton, Vasean Kempton, Vaugh Kempton, Viviana Kempton, Welford Kempton, Windel Kempton, Yaacov Kempton, Yaniv Kempton, Yusuke
Kempton, Zebulah Kempton, Zuberi Kempton, Aarin Kempton, Abbott Kempton, Abdule Kempton, Abdulrahman Kempton, Abrahim Kempton, Abrian Kempton, Adham Kempton, Aditya Kempton, Adre Kempton, Akito
Kempton, Ala Kempton, Alberico Kempton, Alexsandro Kempton, Aljandro Kempton, Allin Kempton, Alyssa Kempton, Amond Kempton, Angelique Kempton, Ankoma Kempton, Antonne Kempton, Antroine Kempton,
Antwanne Kempton, Antwayne Kempton, Arben Kempton, Arby Kempton, Arcangelo Kempton, Arek Kempton, Arel Kempton, Artavis Kempton, Arvon Kempton, Arye Kempton, Ascension Kempton, Ashanta Kempton,
Atilla Kempton, Atrick Kempton, Austreberto Kempton, Avant Kempton, Avian Kempton, Avier Kempton, Ayatollah Kempton, Baltasar Kempton, Banning Kempton, Barin Kempton, Barlow Kempton, Barnie Kempton,
Barrick Kempton, Baruti Kempton, Bascom Kempton, Basheer Kempton, Bear Kempton, Beatriz Kempton, Bengt Kempton, Bennette Kempton, Berl Kempton, Berley Kempton, Berwin Kempton, Biren Kempton, Blase
Kempton, Bon Kempton, Bowe Kempton, Bowman Kempton, Brance Kempton, Bravlio Kempton, Brette Kempton, Brewster Kempton, Bria Kempton, Brookes Kempton, Buel Kempton, Buffy Kempton, Cairo Kempton,
Caldwell Kempton, Cali Kempton, Carlan Kempton, Carmello Kempton, Carmichael Kempton, Carney Kempton, Carr Kempton, Carrell Kempton, Carzell Kempton, Castro Kempton, Caswell Kempton, Catrell Kempton,
Cedrice Kempton, Celeste Kempton, Celina Kempton, Cesear Kempton, Chade Kempton, Chadwell Kempton, Chalres Kempton, Chamar Kempton, Chanan Kempton, Chanda Kempton, Chanin Kempton, Charo Kempton,
Chayim Kempton, Chelton Kempton, Chevez Kempton, Chih Kempton, Chin Kempton, Chino Kempton, Christaphor Kempton, Ciprian Kempton, Conny Kempton, Corbit Kempton, Corinthians Kempton, Cosby Kempton,
Curlee Kempton, Cyrano Kempton, Daimian Kempton, Daks Kempton, Dalin Kempton, Damir Kempton, Damisi Kempton, Damiso Kempton, Dantae Kempton, Danthony Kempton, Dantoni Kempton, Darcus Kempton, Darence
Kempton, Darrious Kempton, Darylle Kempton, Datril Kempton, Davidlee Kempton, Dawane Kempton, Daylen Kempton, Deandrew Kempton, Deloy Kempton, Delson Kempton, Demaine Kempton, Dementrius Kempton,
Demetrise Kempton, Demien Kempton, Demingo Kempton, Demitris Kempton, Deni Kempton, Dennys Kempton, Denon Kempton, Dent Kempton, Deondrick Kempton, Derelle Kempton, Derike Kempton, Derrall Kempton,
Des Kempton, Deshea Kempton, Deston Kempton, Deval Kempton, Devery Kempton, Deville Kempton, Devrin Kempton, Dewell Kempton, Diondray Kempton, Dishan Kempton, Dkwon Kempton, Dmario Kempton, Dolph
Kempton, Dominador Kempton, Donae Kempton, Donni Kempton, Dontea Kempton, Donye Kempton, Dossie Kempton, Dray Kempton, Dwann Kempton, Earic Kempton, Earley Kempton, Eaton Kempton, Edwar Kempton, Eiad
Kempton, Eirc Kempton, Eith Kempton, Elba Kempton, Elefterios Kempton, Eleodoro Kempton, Elisabeth Kempton, Elrod Kempton, Elzy Kempton, Emilo Kempton, Emmanouel Kempton, Enis Kempton, Ephrain
Kempton, Erec Kempton, Erique Kempton, Eriverto Kempton, Erven Kempton, Esco Kempton, Esquiel Kempton, Essa Kempton, Ettore Kempton, Eulis Kempton, Evay Kempton, Fabius Kempton, Faiz Kempton, Felando
Kempton, Fenwick Kempton, Fernell Kempton, Francesca Kempton, Francisca Kempton, Franke Kempton, Gabiel Kempton, Garrit Kempton, Garyn Kempton, Geffery Kempton, Generoso Kempton, Genghis Kempton,
Georgia Kempton, Geovanny Kempton, Gerell Kempton, Gerred Kempton, Gerrett Kempton, Ghassan Kempton, Gilliam Kempton, Gilson Kempton, Givon Kempton, Goeffrey Kempton, Gorgonio Kempton, Grahame
Kempton, Grayland Kempton, Grzegorz Kempton, Guan Kempton, Gumercindo Kempton, Gwen Kempton, Hannah Kempton, Harden Kempton, Harsha Kempton, Harvy Kempton, Hassain Kempton, Helio Kempton, Hemant
Kempton, Herchel Kempton, Herold Kempton, Hershy Kempton, Hillis Kempton, Hinton Kempton, Hommy Kempton, Hong Kempton, Huberto Kempton, Hughes Kempton, Husain Kempton, Hussien Kempton, Ibis Kempton,
Ilias Kempton, Irl Kempton, Iron Kempton, Isak Kempton, Ishaq Kempton, Issaac Kempton, Iva Kempton, Jabon Kempton, Jachin Kempton, Jacobus Kempton, Janeiro Kempton, Japhet Kempton, Jarion Kempton,
Jaris Kempton, Jarmell Kempton, Jarnell Kempton, Jarvon Kempton, Jaryl Kempton, Jasonn Kempton, Jauan Kempton, Javian Kempton, Javoris Kempton, Jawhar Kempton, Jawwaad Kempton, Jayesh Kempton,
Jeffree Kempton, Jeffri Kempton, Jerauld Kempton, Jereny Kempton, Jereomy Kempton, Jerom Kempton, Jerrall Kempton, Jerran Kempton, Jerrico Kempton, Jessiah Kempton, Jesten Kempton, Jevan Kempton,
Jimbob Kempton, Jiro Kempton, Johnpatrick Kempton, Jolon Kempton, Jonothon Kempton, Jonthomas Kempton, Josephine Kempton, Jovonne Kempton, Juanantonio Kempton, Julis Kempton, Jumah Kempton, Jwyanza
Kempton, Kail Kempton, Kaleem Kempton, Kalil Kempton, Kamari Kempton, Kamien Kempton, Kanon Kempton, Kanta Kempton, Karac Kempton, Karega Kempton, Karras Kempton, Kealoha Kempton, Kearston Kempton,
Kedryn Kempton, Keiven Kempton, Keland Kempton, Kelechi Kempton, Kelson Kempton, Kendle Kempton, Kenjuan Kempton, Kennell Kempton, Kenson Kempton, Kerick Kempton, Ketric Kempton, Kevine Kempton,
Keylon Kempton, Keynan Kempton, Khaaliq Kempton, Khali Kempton, Khang Kempton, Khoi Kempton, Kinshasa Kempton, Kono Kempton, Konstandinos Kempton, Kontar Kempton, Kou Kempton, Kreston Kempton,
Kristapher Kempton, Kristophor Kempton, Kumasi Kempton, Kuntakinte Kempton, Kwami Kempton, Kwon Kempton, Laderick Kempton, Lajon Kempton, Lakesha Kempton, Lakieth Kempton, Lakota Kempton, Lamarkus
Kempton, Lameen Kempton, Lamondo Kempton, Lamonica Kempton, Landers Kempton, Landrick Kempton, Lanis Kempton, Lapriest Kempton, Laquane Kempton, Larvell Kempton, Larwence Kempton, Latavius Kempton,
Latimer Kempton, Laton Kempton, Latrelle Kempton, Latwon Kempton, Laurencio Kempton, Lavelton Kempton, Laver Kempton, Lavester Kempton, Lavonn Kempton, Lawanda Kempton, Lawarren Kempton, Lazerick
Kempton, Lecedric Kempton, Leconte Kempton, Leib Kempton, Lemel Kempton, Lenis Kempton, Lenox Kempton, Lenward Kempton, Leonid Kempton, Leory Kempton, Lerin Kempton, Leroyal Kempton, Linnell Kempton,
Linville Kempton, Lional Kempton, Loel Kempton, Lofton Kempton, Londale Kempton, Lonza Kempton, Lovis Kempton, Lucy Kempton, Luie Kempton, Lyndall Kempton, Macker Kempton, Makarios Kempton, Malcon
Kempton, Manly Kempton, Marell Kempton, Margo Kempton, Markco Kempton, Markeis Kempton, Markian Kempton, Marsden Kempton, Martina Kempton, Martinus Kempton, Mashon Kempton, Masud Kempton, Mathaniel
Kempton, Mazi Kempton, Merel Kempton, Merwyn Kempton, Michaelanthony Kempton, Michaeljames Kempton, Mico Kempton, Mihran Kempton, Mikki Kempton, Milik Kempton, Milos Kempton, Miran Kempton, Mirza
Kempton, Mishael Kempton, Mondale Kempton, Mondre Kempton, Montsho Kempton, Morse Kempton, Mostafa Kempton, Mumin Kempton, Mynor Kempton, Nantambu Kempton, Narayana Kempton, Naseem Kempton, Nathane
Kempton, Navada Kempton, Nazar Kempton, Nectarios Kempton, Nell Kempton, Nevelle Kempton, Nichalaus Kempton, Nichlous Kempton, Nicholson Kempton, Nicklus Kempton, Nickolai Kempton, Nicolino Kempton,
Nihar Kempton, Nishan Kempton, Nizar Kempton, Nocholas Kempton, Noelle Kempton, Novel Kempton, Nyerere Kempton, Obbie Kempton, Ocean Kempton, Oded Kempton, Oden Kempton, Olaniyan Kempton, Ondray
Kempton, Orentha Kempton, Osby Kempton, Othell Kempton, Othniel Kempton, Ottie Kempton, Panayiotis Kempton, Parren Kempton, Pedram Kempton, Petey Kempton, Petter Kempton, Pharaoh Kempton, Precious
Kempton, Pressley Kempton, Procopio Kempton, Pryor Kempton, Quaashie Kempton, Quinte Kempton, Quintez Kempton, Quinzell Kempton, Quirino Kempton, Rabon Kempton, Rachard Kempton, Rade Kempton, Raju
Kempton, Ramee Kempton, Ranjan Kempton, Ransford Kempton, Rashawd Kempton, Raynald Kempton, Regenal Kempton, Reiko Kempton, Reinhold Kempton, Remijio Kempton, Renaud Kempton, Ritchard Kempton, Roanld
Kempton, Roarke Kempton, Robley Kempton, Rochester Kempton, Rodolph Kempton, Roi Kempton, Romelle Kempton, Romey Kempton, Romolo Kempton, Rondo Kempton, Ronni Kempton, Ronta Kempton, Roselio Kempton,
Rosheen Kempton, Ruban Kempton, Rustan Kempton, Sajan Kempton, Salik Kempton, Samel Kempton, Santonia Kempton, Sargent Kempton, Saud Kempton, Saxton Kempton, Schane Kempton, Sebron Kempton, Shadley
Kempton, Shadron Kempton, Shafi Kempton, Shalako Kempton, Shanell Kempton, Shani Kempton, Shantae Kempton, Shari Kempton, Shauntay Kempton, Shauwn Kempton, Shawkat Kempton, Shell Kempton, Shephen
Kempton, Sherief Kempton, Shin Kempton, Shneur Kempton, Shontell Kempton, Shoun Kempton, Shundell Kempton, Sigmond Kempton, Spanky Kempton, Stpehen Kempton, Suhail Kempton, Sulieman Kempton, Sundown
Kempton, Taboris Kempton, Taijuan Kempton, Talion Kempton, Tamario Kempton, Tamel Kempton, Tana Kempton, Tari Kempton, Tarnell Kempton, Tashon Kempton, Tasos Kempton, Tavar Kempton, Tawon Kempton,
Tay Kempton, Tederick Kempton, Tedman Kempton, Teejay Kempton, Tephen Kempton, Terranc Kempton, Terric Kempton, Tevita Kempton, Thao Kempton, Theoplis Kempton, Thuan Kempton, Tiger Kempton, Tigh
Kempton, Timmon Kempton, Tin Kempton, Tionne Kempton, Tipton Kempton, Todo Kempton, Tomatra Kempton, Tomeka Kempton, Tomie Kempton, Toriono Kempton, Torivio Kempton, Toye Kempton, Tramine Kempton,
Tre Kempton, Treaver Kempton, Tredell Kempton, Treva Kempton, Trinton Kempton, TRUE Kempton, Tydus Kempton, Tyeson Kempton, Tyle Kempton, Tyrae Kempton, Tyrand Kempton, Tyresse Kempton, Tyri Kempton,
Tysean Kempton, Tyus Kempton, Uland Kempton, Usman Kempton, Vahid Kempton, Vang Kempton, Vassilios Kempton, Vernis Kempton, Vidale Kempton, Vikash Kempton, Vishnu Kempton, Volney Kempton, Vondale
Kempton, Warees Kempton, Webber Kempton, Whitman Kempton, Willilam Kempton, Windy Kempton, Winn Kempton, Wynell Kempton, Xan Kempton, Yeshaya Kempton, Yuma Kempton, Zackory Kempton, Zahid Kempton,
Zarak Kempton, Zayd Kempton, Zebula Kempton, Zef Kempton, Zeljko Kempton, Zephyr Kempton, Zeshan Kempton, Aakash Kempton, Aalon Kempton, Aaraon Kempton, Aaric Kempton, Aarn Kempton, Abduel Kempton,
Abid Kempton, Abigail Kempton, Abijah Kempton, Achille Kempton, Ada Kempton, Adali Kempton, Adante Kempton, Adarsh Kempton, Adedayo Kempton, Adeyinka Kempton, Adib Kempton, Adran Kempton, Adrell
Kempton, Adrew Kempton, Adriaan Kempton, Adriene Kempton, Afton Kempton, Agim Kempton, Ahmond Kempton, Aiman Kempton, Akiba Kempton, Alamin Kempton, Aland Kempton, Alanson Kempton, Albertico Kempton,
Albertus Kempton, Alcario Kempton, Aldrin Kempton, Alejando Kempton, Alexey Kempton, Alfreda Kempton, Alfreddie Kempton, Allateef Kempton, Almer Kempton, Almondo Kempton, Alpesh Kempton, Alrahman
Kempton, Alson Kempton, Altarik Kempton, Alven Kempton, Amadi Kempton, Amancio Kempton, Amandeep Kempton, Amauris Kempton, Amdrew Kempton, Amel Kempton, Amelia Kempton, Amhad Kempton, Amrit Kempton,
Ande Kempton, Anderw Kempton, Andon Kempton, Andren Kempton, Andretti Kempton, Andrius Kempton, Andrue Kempton, Andrw Kempton, Aneesh Kempton, Aneudy Kempton, Anglo Kempton, Anissa Kempton, Annie
Kempton, Anquan Kempton, Ansar Kempton, Ansen Kempton, Anslem Kempton, Anthone Kempton, Anthory Kempton, Antoinio Kempton, Antojuan Kempton, Antonial Kempton, Antowain Kempton, Antowine Kempton,
Antrione Kempton, Antroy Kempton, Anttwan Kempton, Antwin Kempton, Antwonn Kempton, Antyon Kempton, Anwon Kempton, Aquan Kempton, Aquarius Kempton, Aracely Kempton, Aragorn Kempton, Arbie Kempton,
Arhtur Kempton, Aristede Kempton, Aristotelis Kempton, Arkee Kempton, Arlandus Kempton, Arlondo Kempton, Armstead Kempton, Arnab Kempton, Aroldo Kempton, Arric Kempton, Arshad Kempton, Artice
Kempton, Arvelle Kempton, Arvie Kempton, Aryan Kempton, Arzell Kempton, Asbury Kempton, Aseem Kempton, Ash Kempton, Ashan Kempton, Ashkan Kempton, Ashlin Kempton, Ashur Kempton, Astor Kempton,
Asuncion Kempton, Ata Kempton, Atsushi Kempton, Aubery Kempton, Audi Kempton, Augustino Kempton, Aurther Kempton, Aviv Kempton, Ayan Kempton, Azael Kempton, Azar Kempton, Azhar Kempton, Azizi
Kempton, Bai Kempton, Bain Kempton, Baldo Kempton, Balentin Kempton, Banyon Kempton, Barbaro Kempton, Barett Kempton, Barnell Kempton, Barren Kempton, Bartolomeo Kempton, Basem Kempton, Basilios
Kempton, Bassey Kempton, Bayete Kempton, Baylen Kempton, Bayne Kempton, Bayron Kempton, Beaufort Kempton, Bejan Kempton, Belvin Kempton, Benajmin Kempton, Bengamin Kempton, Bently Kempton, Berel
Kempton, Berman Kempton, Bernadino Kempton, Bernis Kempton, Bernon Kempton, Bertie Kempton, Bertin Kempton, Bibiano Kempton, Biko Kempton, Binyamin Kempton, Birche Kempton, Blakley Kempton, Bleu
Kempton, Blythe Kempton, Bobak Kempton, Bowden Kempton, Boz Kempton, Brahim Kempton, Brahin Kempton, Brandell Kempton, Brandley Kempton, Brann Kempton, Brannigan Kempton, Brantly Kempton, Brayan
Kempton, Braydon Kempton, Breandan Kempton, Breh Kempton, Brence Kempton, Brenner Kempton, Brentwood Kempton, Bric Kempton, Bridgette Kempton, Brig Kempton, Briggs Kempton, Brionne Kempton, Bronc
Kempton, Brunson Kempton, Brycen Kempton, Jennifer Kempton, Amy Kempton, Melissa Kempton, Michelle Kempton, Kimberly Kempton, Lisa Kempton, Angela Kempton, Heather Kempton, Stephanie Kempton, Nicole
Kempton, Jessica Kempton, Elizabeth Kempton, Rebecca Kempton, Kelly Kempton, Mary Kempton, Christina Kempton, Amanda Kempton, Julie Kempton, Sarah Kempton, Laura Kempton, Shannon Kempton, Christine
Kempton, Tammy Kempton, Tracy Kempton, Karen Kempton, Dawn Kempton, Susan Kempton, Andrea Kempton, Tina Kempton, Patricia Kempton, Cynthia Kempton, Lori Kempton, Rachel Kempton, April Kempton, Maria
Kempton, Wendy Kempton, Crystal Kempton, Stacy Kempton, Erin Kempton, Jamie Kempton, Carrie Kempton, Tiffany Kempton, Tara Kempton, Sandra Kempton, Monica Kempton, Danielle Kempton, Stacey Kempton,
Pamela Kempton, Tonya Kempton, Sara Kempton, Michele Kempton, Teresa Kempton, Denise Kempton, Jill Kempton, Katherine Kempton, Melanie Kempton, Dana Kempton, Holly Kempton, Erica Kempton, Brenda
Kempton, Deborah Kempton, Tanya Kempton, Sharon Kempton, Donna Kempton, Amber Kempton, Emily Kempton, Linda Kempton, Robin Kempton, Kathleen Kempton, Leslie Kempton, Christy Kempton, Kristen Kempton,
Catherine Kempton, Kristin Kempton, Misty Kempton, Barbara Kempton, Heidi Kempton, Nancy Kempton, Cheryl Kempton, Theresa Kempton, Brandy Kempton, Alicia Kempton, Veronica Kempton, Gina Kempton,
Jacqueline Kempton, Rhonda Kempton, Anna Kempton, Renee Kempton, Megan Kempton, Tamara Kempton, Kathryn Kempton, Melinda Kempton, Debra Kempton, Sherry Kempton, Allison Kempton, Valerie Kempton,
Diana Kempton, Paula Kempton, Kristina Kempton, Ann Kempton, Margaret Kempton, Cindy Kempton, Victoria Kempton, Jodi Kempton, Natalie Kempton, Brandi Kempton, Kristi Kempton, Suzanne Kempton,
Samantha Kempton, Beth Kempton, Tracey Kempton, Regina Kempton, Vanessa Kempton, Kristy Kempton, Carolyn Kempton, Yolanda Kempton, Deanna Kempton, Carla Kempton, Sheila Kempton, Laurie Kempton, Anne
Kempton, Shelly Kempton, Diane Kempton, Sabrina Kempton, Janet Kempton, Katrina Kempton, Erika Kempton, Courtney Kempton, Colleen Kempton, Carol Kempton, Julia Kempton, Jenny Kempton, Jaime Kempton,
Kathy Kempton, Felicia Kempton, Alison Kempton, Lauren Kempton, Kelli Kempton, Leah Kempton, Ashley Kempton, Kim Kempton, Traci Kempton, Kristine Kempton, Tricia Kempton, Joy Kempton, Krista Kempton,
Kara Kempton, Terri Kempton, Sonya Kempton, Aimee Kempton, Natasha Kempton, Cassandra Kempton, Bridget Kempton, Anita Kempton, Kari Kempton, Nichole Kempton, Christie Kempton, Marie Kempton, Virginia
Kempton, Connie Kempton, Martha Kempton, Carmen Kempton, Stacie Kempton, Lynn Kempton, Monique Kempton, Katie Kempton, Kristie Kempton, Shelley Kempton, Sherri Kempton, Angel Kempton, Bonnie Kempton,
Mandy Kempton, Jody Kempton, Shawna Kempton, Kerry Kempton, Annette Kempton, Yvonne Kempton, Toni Kempton, Meredith Kempton, Molly Kempton, Kendra Kempton, Joanna Kempton, Sonia Kempton, Janice
Kempton, Robyn Kempton, Brooke Kempton, Kerri Kempton, Sheri Kempton, Becky Kempton, Gloria Kempton, Mindy Kempton, Tracie Kempton, Angie Kempton, Kellie Kempton, Claudia Kempton, Ruth Kempton, Wanda
Kempton, Jeanette Kempton, Cathy Kempton, Adrienne Kempton, Kelley Kempton, Rachael Kempton, Beverly Kempton, Candace Kempton, Sylvia Kempton, Penny Kempton, Charlene Kempton, Trisha Kempton,
Charlotte Kempton, Belinda Kempton, Candice Kempton, Yvette Kempton, Lindsay Kempton, Keri Kempton, Melody Kempton, Caroline Kempton, Rosa Kempton, Bethany Kempton, Trina Kempton, Joyce Kempton,
Joanne Kempton, Tabitha Kempton, Vicki Kempton, Tamika Kempton, Gretchen Kempton, Ginger Kempton, Betty Kempton, Dorothy Kempton, Debbie Kempton, Darlene Kempton, Helen Kempton, Latoya Kempton, Ellen
Kempton, Leigh Kempton, Rose Kempton, Shawn Kempton, Karla Kempton, Frances Kempton, Ana Kempton, Alice Kempton, Jean Kempton, Hope Kempton, Tasha Kempton, Latonya Kempton, Latasha Kempton, Nikki
Kempton, Maureen Kempton, Bobbie Kempton, Rita Kempton, Peggy Kempton, Shirley Kempton, Marsha Kempton, Cara Kempton, Christa Kempton, Audrey Kempton, Norma Kempton, Shana Kempton, Juanita Kempton,
Leticia Kempton, Kimberley Kempton, Billie Kempton, Evelyn Kempton, Tonia Kempton, Desiree Kempton, Judith Kempton, Joann Kempton, Shanna Kempton, Elaine Kempton, Angelica Kempton, Charity Kempton,
Staci Kempton, Tami Kempton, Judy Kempton, Rebekah Kempton, Raquel Kempton, Tammie Kempton, Jane Kempton, Meghan Kempton, Jackie Kempton, Sally Kempton, Jana Kempton, Priscilla Kempton, Sandy
Kempton, Rochelle Kempton, Summer Kempton, Jodie Kempton, Marcia Kempton, Alisha Kempton, Keisha Kempton, Stefanie Kempton, Casey Kempton, Loretta Kempton, Eva Kempton, Dena Kempton, Cristina
Kempton, Janelle Kempton, Christi Kempton, Naomi Kempton, Rachelle Kempton, Marisa Kempton, Irene Kempton, Kirsten Kempton, Jeanne Kempton, Jenifer Kempton, Roxanne Kempton, Miranda Kempton, Roberta
Kempton, Dina Kempton, Shauna Kempton, Sonja Kempton, Marilyn Kempton, Eileen Kempton, Gwendolyn Kempton, Vickie Kempton, Katina Kempton, Teri Kempton, Olivia Kempton, Amie Kempton, Lora Kempton,
Cheri Kempton, Jennie Kempton, Lindsey Kempton, Lesley Kempton, Lara Kempton, Lydia Kempton, Alisa Kempton, Sheryl Kempton, Autumn Kempton, Jacquelyn Kempton, Lynette Kempton, Esther Kempton, Nina
Kempton, Antoinette Kempton, Gail Kempton, Deana Kempton, Jaclyn Kempton, Lorraine Kempton, Alexandra Kempton, Jami Kempton, Ronda Kempton, Candy Kempton, Bobbi Kempton, Ericka Kempton, Abigail
Kempton, Chandra Kempton, Ebony Kempton, Latisha Kempton, Cherie Kempton, Marla Kempton, Lee Kempton, Angelia Kempton, Kenya Kempton, Joan Kempton, Jeannie Kempton, Shari Kempton, Ruby Kempton,
Miriam Kempton, Lakisha Kempton, Tameka Kempton, Marcy Kempton, Angelina Kempton, Faith Kempton, Marisol Kempton, Krystal Kempton, Dianna Kempton, Adriana Kempton, Audra Kempton, Angelique Kempton,
Marissa Kempton, Grace Kempton, Alyssa Kempton, Janine Kempton, Alexis Kempton, Elisa Kempton, Jolene Kempton, Karin Kempton, Shelby Kempton, Wendi Kempton, Tania Kempton, Melisa Kempton, Bernadette
Kempton, Lorena Kempton, Shelia Kempton, Rosemary Kempton, Ramona Kempton, Terry Kempton, Nora Kempton, Marlene Kempton, Camille Kempton, Tanisha Kempton, Carey Kempton, Alma Kempton, Sherrie
Kempton, Cecilia Kempton, Celeste Kempton, Kate Kempton, Betsy Kempton, Brandie Kempton, Annie Kempton, Darla Kempton, Lillian Kempton, Maribel Kempton, Glenda Kempton, Chasity Kempton, Patrice
Kempton, Amelia Kempton, Lorie Kempton, Tabatha Kempton, Elena Kempton, Lana Kempton, Jocelyn Kempton, Jeannette Kempton, Guadalupe Kempton, Marcie Kempton, Johanna Kempton, Josephine Kempton, Tisha
Kempton, Michael Kempton, Leanne Kempton, Vivian Kempton, Whitney Kempton, Darcy Kempton, Hilary Kempton, Marci Kempton, Doris Kempton, Selena Kempton, Constance Kempton, Serena Kempton, Daphne
Kempton, Hollie Kempton, Bridgette Kempton, Tammi Kempton, Jeanine Kempton, Terra Kempton, Margarita Kempton, Vicky Kempton, Allyson Kempton, Marianne Kempton, Elisabeth Kempton, Paige Kempton, Iris
Kempton, Lena Kempton, Lakeisha Kempton, Jillian Kempton, Arlene Kempton, Latanya Kempton, Emma Kempton, Aisha Kempton, Tia Kempton, Alissa Kempton, Sophia Kempton, Hannah Kempton, Lawanda Kempton,
Chrystal Kempton, Lea Kempton, Cari Kempton, Jessie Kempton, Mia Kempton, Chastity Kempton, Lynda Kempton, Cassie Kempton, Marjorie Kempton, Liza Kempton, Edith Kempton, Jenna Kempton, Joni Kempton,
Misti Kempton, Blanca Kempton, Dionne Kempton, Lashonda Kempton, Leann Kempton, Yesenia Kempton, Corinne Kempton, Jasmine Kempton, Malinda Kempton, Gabriela Kempton, Shonda Kempton, Laurel Kempton,
Hillary Kempton, Kimberlee Kempton, Karrie Kempton, Irma Kempton, Pauline Kempton, Claire Kempton, Dora Kempton, Isabel Kempton, Georgia Kempton, Esmeralda Kempton, Nadine Kempton, Lakesha Kempton,
Marcella Kempton, Luz Kempton, Ladonna Kempton, Katharine Kempton, Phyllis Kempton, Sue Kempton, Janie Kempton, Kisha Kempton, Dianne Kempton, Myra Kempton, Gabrielle Kempton, Ingrid Kempton, Maryann
Kempton, Rene Kempton, Lucy Kempton, Bridgett Kempton, Karyn Kempton, Janel Kempton, Mandi Kempton, Paulette Kempton, Lucinda Kempton, Carissa Kempton, Genevieve Kempton, Olga Kempton, Dolores
Kempton, Catina Kempton, Randi Kempton, Tera Kempton, Jeannine Kempton, Nakia Kempton, Janette Kempton, June Kempton, Alana Kempton, Annmarie Kempton, Lashawn Kempton, Noelle Kempton, Chelsea
Kempton, Brittany Kempton, Clarissa Kempton, Shanda Kempton, Cathleen Kempton, Susana Kempton, Susanne Kempton, Chanda Kempton, Edna Kempton, Catrina Kempton, Kerrie Kempton, Francine Kempton, Mona
Kempton, Alyson Kempton, Doreen Kempton, Maggie Kempton, Lynne Kempton, Tori Kempton, Clara Kempton, Demetria Kempton, Beatrice Kempton, Valarie Kempton, Jeri Kempton, Kasey Kempton, Silvia Kempton,
Gena Kempton, Janna Kempton, Abby Kempton, Cristy Kempton, Deirdre Kempton, Deidre Kempton, Tawana Kempton, Deena Kempton, Jan Kempton, Maricela Kempton, Tamra Kempton, Daisy Kempton, Sondra Kempton,
Caryn Kempton, Nadia Kempton, Lorrie Kempton, Patty Kempton, Anissa Kempton, Farrah Kempton, Bianca Kempton, Tiffani Kempton, Carly Kempton, Delia Kempton, Susie Kempton, Tessa Kempton, Latrice
Kempton, Shellie Kempton, Renae Kempton, Corina Kempton, Deanne Kempton, Rena Kempton, Louise Kempton, Larissa Kempton, Latosha Kempton, Lois Kempton, Maritza Kempton, Julianne Kempton, Mildred
Kempton, Janell Kempton, Karina Kempton, Christal Kempton, Antonia Kempton, James Kempton, Ida Kempton, Marina Kempton, Lacey Kempton, Kristal Kempton, Ami Kempton, Christopher Kempton, Gladys
Kempton, Cori Kempton, Gwen Kempton, Eleanor Kempton, Elisha Kempton, Justine Kempton, Madeline Kempton, Ursula Kempton, Charmaine Kempton, Rosemarie Kempton, Suzette Kempton, Elise Kempton, Bertha
Kempton, Gayle Kempton, Lynnette Kempton, Sheree Kempton, Araceli Kempton, Chantel Kempton, Kesha Kempton, Dayna Kempton, Malissa Kempton, Dara Kempton, Latonia Kempton, Jayme Kempton, Robert
Kempton, Jerri Kempton, Carolina Kempton, Athena Kempton, Hilda Kempton, Ivy Kempton, Mara Kempton, Tosha Kempton, Marion Kempton, Elsa Kempton, Stella Kempton, Devon Kempton, Marlo Kempton, Danette
Kempton, Mayra Kempton, Kay Kempton, Bernice Kempton, Adrianne Kempton, Geneva Kempton, Colette Kempton, David Kempton, Anitra Kempton, Letitia Kempton, Marian Kempton, Windy Kempton, Jason Kempton,
Katy Kempton, Felecia Kempton, Elissa Kempton, Susanna Kempton, Lucia Kempton, Celia Kempton, Margie Kempton, Kami Kempton, Adrian Kempton, Holli Kempton, Delores Kempton, Sasha Kempton, Tamera
Kempton, Tonja Kempton, Taryn Kempton, Stacia Kempton, John Kempton, Tomeka Kempton, Anastasia Kempton, Marta Kempton, Patti Kempton, Jeanna Kempton, Georgina Kempton, Eugenia Kempton, Tawnya
Kempton, Corey Kempton, Leeann Kempton, Juliet Kempton, Chris Kempton, Dominique Kempton, Mitzi Kempton, Margo Kempton, Selina Kempton, Marnie Kempton, Casandra Kempton, Deann Kempton, Leanna
Kempton, Vera Kempton, Consuelo Kempton, Buffy Kempton, Lourdes Kempton, Florence Kempton, Geraldine Kempton, Tyra Kempton, Alecia Kempton, Greta Kempton, Carole Kempton, Francesca Kempton, Meagan
Kempton, Jeanie Kempton, Rosalinda Kempton, Trudy Kempton, Haley Kempton, Sandi Kempton, Corrie Kempton, Maura Kempton, Sharonda Kempton, Graciela Kempton, Michell Kempton, Terrie Kempton, Eve
Kempton, Tiffanie Kempton, Rosalind Kempton, Marlena Kempton, Shannan Kempton, Thelma Kempton, Carie Kempton, Lashanda Kempton, Shelli Kempton, Karie Kempton, Danelle Kempton, Tawanda Kempton, Ryan
Kempton, Simone Kempton, Maya Kempton, Mollie Kempton, Deidra Kempton, Josie Kempton, Noemi Kempton, Briana Kempton, Venus Kempton, Lauri Kempton, Richelle Kempton, Candi Kempton, Ella Kempton, Cora
Kempton, Latricia Kempton, Marisela Kempton, Beatriz Kempton, Shanon Kempton, Alejandra Kempton, Aubrey Kempton, Jeana Kempton, Nanette Kempton, Brianne Kempton, Leona Kempton, Helena Kempton, Kris
Kempton, Christian Kempton, Annemarie Kempton, Andria Kempton, Mindi Kempton, Rosalyn Kempton, Shanta Kempton, Mercedes Kempton, Polly Kempton, Juana Kempton, Rosie Kempton, Martina Kempton, Therese
Kempton, Cory Kempton, Kayla Kempton, Shantel Kempton, Joey Kempton, Shalonda Kempton, Mellissa Kempton, Ada Kempton, Brandee Kempton, Sunshine Kempton, Tamiko Kempton, Danita Kempton, Niki Kempton,
Rosanna Kempton, Joelle Kempton, Monika Kempton, Trista Kempton, Chiquita Kempton, William Kempton, Brook Kempton, Janis Kempton, Rae Kempton, Kizzy Kempton, Cortney Kempton, Cecelia Kempton, Jaimie
Kempton, Christin Kempton, Christen Kempton, Tanika Kempton, Darci Kempton, Claudine Kempton, Sharla Kempton, Toya Kempton, Racheal Kempton, Noel Kempton, Jada Kempton, Davina Kempton, Della Kempton,
Kori Kempton, Tomika Kempton, Callie Kempton, Jamila Kempton, Aileen Kempton, Dusty Kempton, Rocio Kempton, Kia Kempton, Benita Kempton, Jena Kempton, Aurora Kempton, Penelope Kempton, Sadie Kempton,
Patsy Kempton, Valencia Kempton, Lisette Kempton, Tamela Kempton, Mari Kempton, Tana Kempton, Ivette Kempton, Eliza Kempton, Darcie Kempton, Tawanna Kempton, Bonita Kempton, Debora Kempton, Lacy
Kempton, Tarsha Kempton, Stephenie Kempton, Johnna Kempton, Kathrine Kempton, Lakeshia Kempton, Griselda Kempton, Charla Kempton, Lesa Kempton, Sunny Kempton, Celina Kempton, Karri Kempton, Corinna
Kempton, Dixie Kempton, Rosalie Kempton, Rhiannon Kempton, Eunice Kempton, Mariah Kempton, Angeline Kempton, Danna Kempton, Shayla Kempton, Brenna Kempton, Juliana Kempton, Brianna Kempton, Octavia
Kempton, Leila Kempton, Liliana Kempton, Shameka Kempton, Lissette Kempton, Cary Kempton, Chrissy Kempton, Corrine Kempton, Destiny Kempton, India Kempton, Adriane Kempton, Kandi Kempton, Coleen
Kempton, Angelita Kempton, Denice Kempton, Janeen Kempton, Suzanna Kempton, Dee Kempton, Magdalena Kempton, Lola Kempton, Brian Kempton, Nikole Kempton, Sofia Kempton, Nicolle Kempton, Lucretia
Kempton, Mellisa Kempton, Morgan Kempton, Alexa Kempton, Faye Kempton, Daniel Kempton, Antionette Kempton, Tennille Kempton, Ayanna Kempton, Maxine Kempton, Christel Kempton, Alysia Kempton,
Alexandria Kempton, Lenora Kempton, Aida Kempton, Kyla Kempton, Joseph Kempton, Bree Kempton, Kira Kempton, Renita Kempton, Sharron Kempton, Jenni Kempton, Ethel Kempton, Fatima Kempton, Hazel
Kempton, Nellie Kempton, Juli Kempton, Delilah Kempton, Pearl Kempton, Caren Kempton, Melonie Kempton, Robbie Kempton, Lindy Kempton, Tangela Kempton, Trena Kempton, Daniela Kempton, Michaela
Kempton, Carri Kempton, Sommer Kempton, Alanna Kempton, Tressa Kempton, Georgette Kempton, Nikita Kempton, Chanel Kempton, Aretha Kempton, Charisse Kempton, Laquita Kempton, Natalia Kempton, Josette
Kempton, Roxanna Kempton, Kirstin Kempton, Shani Kempton, Nichol Kempton, Regan Kempton, Salina Kempton, Anjanette Kempton, Susannah Kempton, Jammie Kempton, Kenyatta Kempton, Jasmin Kempton, Anthony
Kempton, Ginny Kempton, Lillie Kempton, Missy Kempton, Starla Kempton, Lucille Kempton, Lorna Kempton, Tiana Kempton, Melodie Kempton, Fawn Kempton, Candida Kempton, Carin Kempton, Elvira Kempton,
Shonna Kempton, Carmela Kempton, Spring Kempton, Shara Kempton, Yolonda Kempton, Josefina Kempton, Evette Kempton, Carisa Kempton, Sherita Kempton, Roseann Kempton, Saundra Kempton, Myrna Kempton,
Bambi Kempton, Layla Kempton, Lilia Kempton, Mechelle Kempton, Cathryn Kempton, Jayne Kempton, Lolita Kempton, Rosario Kempton, Eric Kempton, Valeria Kempton, Jade Kempton, Nicki Kempton, Maranda
Kempton, Felisha Kempton, Raina Kempton, Tracee Kempton, Cindi Kempton, Freda Kempton, Gillian Kempton, Damaris Kempton, Ava Kempton, Brigitte Kempton, Nicola Kempton, Esperanza Kempton, Leilani
Kempton, Sharlene Kempton, Marni Kempton, Claudette Kempton, Keely Kempton, Hayley Kempton, Chantelle Kempton, Joleen Kempton, Elsie Kempton, Rebeca Kempton, Mendy Kempton, Adria Kempton, Harmony
Kempton, Francisca Kempton, Jolie Kempton, Vikki Kempton, Nikia Kempton, Tamatha Kempton, Keli Kempton, Keshia Kempton, Charissa Kempton, Imelda Kempton, Francis Kempton, Richard Kempton, Shantell
Kempton, Shawanda Kempton, Caitlin Kempton, Frankie Kempton, Shea Kempton, Cherry Kempton, Sheena Kempton, Brigette Kempton, Keesha Kempton, Cristi Kempton, Justina Kempton, Rashida Kempton, Emilie
Kempton, Ashlee Kempton, Shane Kempton, Cherise Kempton, Qiana Kempton, Latarsha Kempton, Crissy Kempton, Celena Kempton, Kylie Kempton, Rolanda Kempton, Crista Kempton, Roslyn Kempton, Angella
Kempton, Shamika Kempton, Wilma Kempton, Violet Kempton, Kyra Kempton, Kevin Kempton, Marybeth Kempton, Alesha Kempton, Matthew Kempton, Shanika Kempton, Shawnda Kempton, Cristal Kempton, Julissa
Kempton, Lila Kempton, Alycia Kempton, Camilla Kempton, Johnnie Kempton, Dori Kempton, Nichelle Kempton, Venessa Kempton, Anika Kempton, Lily Kempton, Tamica Kempton, Rhoda Kempton, Alethea Kempton,
Carina Kempton, Roxann Kempton, Latrina Kempton, Charles Kempton, Bessie Kempton, Julianna Kempton, Marquita Kempton, Gayla Kempton, Kandy Kempton, Estella Kempton, Marguerite Kempton, Chana Kempton,
Robbin Kempton, Cristin Kempton, Raven Kempton, Tanesha Kempton, Alina Kempton, Juliette Kempton, Milagros Kempton, Inez Kempton, Vonda Kempton, Jenelle Kempton, Elaina Kempton, Dedra Kempton, Verna
Kempton, Starr Kempton, Bobby Kempton, Lizette Kempton, Dawna Kempton, Danyelle Kempton, Petra Kempton, Stephaine Kempton, Angelic Kempton, Brittney Kempton, Corrina Kempton, Britt Kempton, Stephany
Kempton, Lorri Kempton, Shayna Kempton, Flora Kempton, Jesse Kempton, Velma Kempton, Racquel Kempton, Stefani Kempton, Phoebe Kempton, Yadira Kempton, Liana Kempton, Milissa Kempton, Pam Kempton, Zoe
Kempton, Libby Kempton, Shasta Kempton, Luisa Kempton, Barbra Kempton, Janae Kempton, Shandra Kempton, Thomas Kempton, Kelsey Kempton, Shante Kempton, Bettina Kempton, Lashunda Kempton, Melina
Kempton, Mattie Kempton, Meaghan Kempton, Timothy Kempton, Rosetta Kempton, Mistie Kempton, Steven Kempton, Patrica Kempton, Shay Kempton, Takisha Kempton, Geri Kempton, Teressa Kempton, Aaron
Kempton, Clare Kempton, Noreen Kempton, Adina Kempton, Rosanne Kempton, Luciana Kempton, Nakisha Kempton, Trinity Kempton, Cicely Kempton, Minerva Kempton, Devin Kempton, Gabriella Kempton, Lela
Kempton, Kendall Kempton, Treva Kempton, Hallie Kempton, Kristan Kempton, Lia Kempton, Viola Kempton, Portia Kempton, Jonna Kempton, Kellee Kempton, Danica Kempton, Kristyn Kempton, Lina Kempton,
Jewel Kempton, Tamala Kempton, Jenniffer Kempton, Melony Kempton, Kacey Kempton, Quiana Kempton, Shawnna Kempton, Rana Kempton, Dannielle Kempton, Andra Kempton, Lenore Kempton, Carlene Kempton,
Malia Kempton, Lanette Kempton, Jacquline Kempton, Willie Kempton, Precious Kempton, Collette Kempton, Mariana Kempton, Ayana Kempton, Daniella Kempton, Thea Kempton, Viviana Kempton, Kindra Kempton,
Gracie Kempton, Louisa Kempton, Adele Kempton, Annamarie Kempton, Kiesha Kempton, Sherie Kempton, Althea Kempton, Catalina Kempton, January Kempton, Ernestine Kempton, Corie Kempton, Lesli Kempton,
Shanita Kempton, Tresa Kempton, Maryanne Kempton, Tamar Kempton, Rayna Kempton, Siobhan Kempton, Demetra Kempton, Kimberlie Kempton, Rhea Kempton, Elva Kempton, Elvia Kempton, Karissa Kempton,
Maryellen Kempton, Valorie Kempton, Adrianna Kempton, Nicolette Kempton, Daniele Kempton, Trish Kempton, Twila Kempton, Abbie Kempton, Towanda Kempton, Lorinda Kempton, Marcela Kempton, Kyle Kempton,
Carmelita Kempton, Helene Kempton, Mark Kempton, Jeffrey Kempton, Lidia Kempton, Kenyetta Kempton, Lupe Kempton, Cami Kempton, Cher Kempton, Minnie Kempton, Toby Kempton, Karena Kempton, Katheryn
Kempton, Renea Kempton, Kathie Kempton, Laverne Kempton, Shona Kempton, Linette Kempton, Kecia Kempton, Elana Kempton, Eboni Kempton, Loren Kempton, Tabetha Kempton, Dione Kempton, Glenna Kempton,
Marti Kempton, Gia Kempton, Tena Kempton, Cameron Kempton, Roxana Kempton, Alberta Kempton, Dolly Kempton, Pamala Kempton, Talia Kempton, Tobi Kempton, Latesha Kempton, Larhonda Kempton, Sybil
Kempton, Kandice Kempton, Yasmin Kempton, Christiana Kempton, Sydney Kempton, Chantal Kempton, Estela Kempton, Jaimee Kempton, Salena Kempton, Tamekia Kempton, Dalia Kempton, Twana Kempton, Jacklyn
Kempton, Scarlett Kempton, Tanja Kempton, Kenisha Kempton, Daria Kempton, Agnes Kempton, Mandie Kempton, Lani Kempton, May Kempton, Sharee Kempton, Tenisha Kempton, Twyla Kempton, Chantell Kempton,
Shiela Kempton, Isela Kempton, Karey Kempton, Alaina Kempton, Loriann Kempton, Star Kempton, Samara Kempton, Janene Kempton, Gerri Kempton, Lasonya Kempton, Lavonne Kempton, Rikki Kempton, Meridith
Kempton, Lorene Kempton, Scott Kempton, Stephani Kempton, Kimberli Kempton, Zandra Kempton, Sallie Kempton, Cecily Kempton, Rachele Kempton, Melynda Kempton, Reagan Kempton, Carmella Kempton, Danyell
Kempton, Ivonne Kempton, Jamey Kempton, Shawana Kempton, Aja Kempton, Casie Kempton, Alena Kempton, Barbie Kempton, Clarice Kempton, Kassandra Kempton, Tiffiny Kempton, Madelyn Kempton, Cherish
Kempton, Lavonda Kempton, Malisa Kempton, Stormy Kempton, Amalia Kempton, Machelle Kempton, Abbey Kempton, Evangelina Kempton, Serina Kempton, Fannie Kempton, Joi Kempton, Tarra Kempton, Dale
Kempton, Shaunna Kempton, Jeremy Kempton, Sarina Kempton, Harriet Kempton, Holley Kempton, Reyna Kempton, Ayesha Kempton, Natosha Kempton, Princess Kempton, Shavon Kempton, Ashleigh Kempton, Laticia
Kempton, Cristine Kempton, Asia Kempton, Antonette Kempton, Dinah Kempton, Jordan Kempton, Cherilyn Kempton, Mackenzie Kempton, Giselle Kempton, Edwina Kempton, Mae Kempton, Kathi Kempton, Shalanda
Kempton, Donita Kempton, Melissia Kempton, Cristie Kempton, Mirna Kempton, Cheyenne Kempton, Leslee Kempton, Jeni Kempton, Jacinda Kempton, Consuela Kempton, Evangeline Kempton, Joanie Kempton,
Nickie Kempton, Jolynn Kempton, Malika Kempton, Nathalie Kempton, Mamie Kempton, Paul Kempton, Davida Kempton, Erinn Kempton, Laronda Kempton, Latina Kempton, Liberty Kempton, Nicol Kempton, Danyel
Kempton, Tommie Kempton, Joshua Kempton, Shaun Kempton, Jodee Kempton, Teena Kempton, Shanell Kempton, Calandra Kempton, Iesha Kempton, Devona Kempton, Aracely Kempton, Brandon Kempton, Dona Kempton,
Micah Kempton, Adela Kempton, Lashon Kempton, Reina Kempton, Sierra Kempton, Addie Kempton, Carlotta Kempton, Nia Kempton, Ariana Kempton, Chante Kempton, Tamisha Kempton, Ali Kempton, Deedee
Kempton, Sarita Kempton, Jeniffer Kempton, Kiley Kempton, Ronnie Kempton, Cherri Kempton, Nickole Kempton, Hattie Kempton, Syreeta Kempton, Chaya Kempton, Dani Kempton, Catharine Kempton, Tamie
Kempton, Perla Kempton, Billiejo Kempton, Deloris Kempton, Lashawnda Kempton, Meggan Kempton, Temeka Kempton, Dorothea Kempton, Marianna Kempton, Lou Kempton, Tesha Kempton, Karmen Kempton, Luann
Kempton, Rona Kempton, Elyse Kempton, Latashia Kempton, Dacia Kempton, Nita Kempton, Tashia Kempton, Kenneth Kempton, Mireya Kempton, Carleen Kempton, Alfreda Kempton, Candie Kempton, Delicia
Kempton, Lakiesha Kempton, Renata Kempton, Juliann Kempton, Patience Kempton, Alexia Kempton, Lakeesha Kempton, Petrina Kempton, Liane Kempton, Ester Kempton, Kimberely Kempton, Millie Kempton, Roni
Kempton, Reba Kempton, Tory Kempton, Maryjo Kempton, Aundrea Kempton, Kasandra Kempton, Melba Kempton, Tiffaney Kempton, Maisha Kempton, Kenna Kempton, Detra Kempton, Jerry Kempton, Meghann Kempton,
Sanjuanita Kempton, Emilia Kempton, Denita Kempton, Shaunda Kempton, Shavonne Kempton, Jose Kempton, Roseanne Kempton, Kiersten Kempton, Sophie Kempton, Maren Kempton, Giovanna Kempton, Bethann
Kempton, Ilene Kempton, Dorian Kempton, Lanita Kempton, Ariel Kempton, Piper Kempton, Shawnee Kempton, Cammie Kempton, Joellen Kempton, Millicent Kempton, Rachell Kempton, Billy Kempton, Felica
Kempton, Jacinta Kempton, Krissy Kempton, Letisha Kempton, Pennie Kempton, Delisa Kempton, Evonne Kempton, Keysha Kempton, Migdalia Kempton, Opal Kempton, Taunya Kempton, Farah Kempton, Ina Kempton,
Samatha Kempton, Linnea Kempton, Lyn Kempton, Merry Kempton, Patrina Kempton, Terese Kempton, Leandra Kempton, Cornelia Kempton, Manda Kempton, Lissa Kempton, Coretta Kempton, Gidget Kempton,
Demetrice Kempton, Mabel Kempton, Necole Kempton, Torrie Kempton, Kandace Kempton, Loraine Kempton, Tarah Kempton, Cody Kempton, Cinnamon Kempton, Shonta Kempton, Rosalia Kempton, Delana Kempton,
Nannette Kempton, Amee Kempton, Ofelia Kempton, Shakira Kempton, Aletha Kempton, Kacy Kempton, Rosita Kempton, Talisha Kempton, Moira Kempton, Sebrina Kempton, Katrice Kempton, Eden Kempton,
Jaqueline Kempton, Kirstie Kempton, Gregory Kempton, Letha Kempton, Apryl Kempton, Kristel Kempton, Fabiola Kempton, Steffanie Kempton, Elicia Kempton, Nedra Kempton, Maia Kempton, Sharita Kempton,
Tammara Kempton, Charise Kempton, Cheree Kempton, Andrew Kempton, Honey Kempton, Velvet Kempton, Anglea Kempton, Brett Kempton, Henrietta Kempton, Jenine Kempton, Meg Kempton, Khalilah Kempton,
Sheronda Kempton, Dyan Kempton, Marty Kempton, Suzan Kempton, Liz Kempton, Brande Kempton, Flor Kempton, Tameika Kempton, Manuela Kempton, Stephen Kempton, Kamilah Kempton, Karolyn Kempton, Demetrius
Kempton, Lacie Kempton, Lakeysha Kempton, Jannette Kempton, Vonetta Kempton, Gale Kempton, Shiloh Kempton, Shira Kempton, Gisela Kempton, Jacquelin Kempton, Natisha Kempton, Billi Kempton, Charleen
Kempton, Brigid Kempton, Dorinda Kempton, Jacki Kempton, Keena Kempton, Lamonica Kempton, Shena Kempton, Michel Kempton, Nanci Kempton, Donya Kempton, Leisa Kempton, Rosalba Kempton, Anabel Kempton,
Annalisa Kempton, Amity Kempton, Mimi Kempton, Erma Kempton, Lyndsey Kempton, Marlana Kempton, Skye Kempton, Chloe Kempton, Inga Kempton, Jonathan Kempton, Melaine Kempton, Lorelei Kempton, Marivel
Kempton, Nelly Kempton, Amiee Kempton, Cathrine Kempton, Jonelle Kempton, Sacha Kempton, Jennette Kempton, Lilly Kempton, Shawnta Kempton, Tisa Kempton, Judi Kempton, Cherrie Kempton, Annetta
Kempton, Charlette Kempton, Christiane Kempton, Jesica Kempton, Pilar Kempton, Elida Kempton, Twanna Kempton, Madonna Kempton, Tausha Kempton, Carletta Kempton, Leesa Kempton, Matilda Kempton, Nakita
Kempton, Natashia Kempton, Kaci Kempton, Mica Kempton, Dionna Kempton, Margot Kempton, Maribeth Kempton, Darby Kempton, Shondra Kempton, Socorro Kempton, Misha Kempton, Taylor Kempton, Becki Kempton,
Kiana Kempton, Valentina Kempton, Ashlie Kempton, Desirae Kempton, Lizabeth Kempton, Alesia Kempton, Roxane Kempton, Donielle Kempton, Kelle Kempton, Larisa Kempton, Paola Kempton, Aleta Kempton,
Dorene Kempton, Kitty Kempton, Shenita Kempton, Tatiana Kempton, Felisa Kempton, Yashica Kempton, Jeanetta Kempton, Tony Kempton, Latrisha Kempton, Nyree Kempton, Ronald Kempton, Romona Kempton,
Shawanna Kempton, Edward Kempton, Justin Kempton, Tuesday Kempton, Avis Kempton, Edie Kempton, Aurelia Kempton, Nova Kempton, Ruthie Kempton, Estelle Kempton, Mikki Kempton, Jamee Kempton, Micaela
Kempton, Phaedra Kempton, Sean Kempton, Fiona Kempton, Shilo Kempton, Trudi Kempton, Blythe Kempton, Julee Kempton, Alia Kempton, Lachelle Kempton, Roseanna Kempton, Donald Kempton, Nydia Kempton,
Effie Kempton, Jenell Kempton, Carolee Kempton, Karma Kempton, Violeta Kempton, Ilana Kempton, Leonor Kempton, Talitha Kempton, Deedra Kempton, Jimmie Kempton, Buffie Kempton, Iva Kempton, Joycelyn
Kempton, Randa Kempton, Tawny Kempton, Bonny Kempton, Dallas Kempton, Felice Kempton, Lawana Kempton, Corine Kempton, Kizzie Kempton, Ladawn Kempton, Torri Kempton, Marva Kempton, Sabina Kempton,
Taneka Kempton, Deandra Kempton, Kary Kempton, Juliane Kempton, Asha Kempton, Mika Kempton, Twanda Kempton, Dawne Kempton, Ellie Kempton, Lawanna Kempton, Rowena Kempton, Caron Kempton, Chad Kempton,
Ronna Kempton, Tatum Kempton, Caprice Kempton, Cinthia Kempton, Debby Kempton, Deeann Kempton, Shalon Kempton, Ernestina Kempton, Andre Kempton, Annamaria Kempton, Latoshia Kempton, Shemeka Kempton,
Stacee Kempton, Tyesha Kempton, Annabelle Kempton, Germaine Kempton, Risa Kempton, Latoria Kempton, Patrick Kempton, Wendie Kempton, Laureen Kempton, Cristen Kempton, Kati Kempton, Niccole Kempton,
Sabra Kempton, Shoshana Kempton, Tequila Kempton, Melva Kempton, Micki Kempton, Darcey Kempton, Coral Kempton, Fonda Kempton, Lashaunda Kempton, Pepper Kempton, Trinette Kempton, Eloisa Kempton,
Goldie Kempton, Tijuana Kempton, Venita Kempton, Danae Kempton, Tessie Kempton, Rebecka Kempton, Taisha Kempton, Heide Kempton, Joslyn Kempton, Rebbecca Kempton, Magda Kempton, Roxie Kempton, Daniell
Kempton, Kellye Kempton, Timika Kempton, Dannette Kempton, Lakita Kempton, Shawnte Kempton, Dusti Kempton, Shenika Kempton, Amberly Kempton, Koren Kempton, Carolynn Kempton, Thomasina Kempton,
Bobbiejo Kempton, Candance Kempton, Jacque Kempton, Nikisha Kempton, Torie Kempton, Cyndi Kempton, Diann Kempton, Marylou Kempton, Nelda Kempton, Prudence Kempton, Sharyn Kempton, Carman Kempton,
Coreen Kempton, Amina Kempton, Neva Kempton, Scarlet Kempton, Ammie Kempton, Haydee Kempton, Jaymie Kempton, Rina Kempton, Lyndsay Kempton, Shantelle Kempton, Alyce Kempton, Danika Kempton, Leeanne
Kempton, Tamesha Kempton, Iliana Kempton, Kylee Kempton, Lisha Kempton, Mercy Kempton, Nona Kempton, Teresita Kempton, Xochitl Kempton, Carmel Kempton, Jessi Kempton, Kourtney Kempton, Elia Kempton,
Lasandra Kempton, Alisia Kempton, Candis Kempton, Nicholle Kempton, Nissa Kempton, Micheal Kempton, Kali Kempton, Tajuana Kempton, Aleshia Kempton, Daina Kempton, Fay Kempton, Rivka Kempton, Jennefer
Kempton, Kena Kempton, Cassidy Kempton, Toshia Kempton, Larry Kempton, Travis Kempton, Chaka Kempton, Anya Kempton, Leia Kempton, Nola Kempton, Rosalva Kempton, Arica Kempton, Hanna Kempton, Kenda
Kempton, Tiesha Kempton, Jewell Kempton, Roshanda Kempton, Arianne Kempton, Eryn Kempton, Denna Kempton, George Kempton, Jerilyn Kempton, Lakia Kempton, Melani Kempton, Raeann Kempton, Season
Kempton, Sherilyn Kempton, Lizbeth Kempton, Myesha Kempton, Suzy Kempton, Emilee Kempton, Kristian Kempton, Leighann Kempton, Akilah Kempton, Britney Kempton, Juan Kempton, Bobbijo Kempton, Dalila
Kempton, Ileana Kempton, Contessa Kempton, Darleen Kempton, Deshawn Kempton, Audrea Kempton, Kawana Kempton, Lona Kempton, Margret Kempton, Melany Kempton, Michal Kempton, Odessa Kempton, Reva
Kempton, Lula Kempton, Mariann Kempton, Kanika Kempton, Paris Kempton, Shaneka Kempton, Sherrell Kempton, Suzann Kempton, Chelsey Kempton, Laquisha Kempton, Willow Kempton, Kaye Kempton, Muriel
Kempton, Britta Kempton, Dania Kempton, Jesenia Kempton, Nilda Kempton, Dottie Kempton, Nereida Kempton, Kellyann Kempton, Alishia Kempton, Denisha Kempton, Marietta Kempton, Merideth Kempton, Enid
Kempton, Isis Kempton, Rosio Kempton, America Kempton, Belen Kempton, Randy Kempton, Karol Kempton, Kasie Kempton, Julieann Kempton, Sari Kempton, Bronwyn Kempton, Concepcion Kempton, Criselda
Kempton, Natacha Kempton, Ariane Kempton, Breanna Kempton, Shayne Kempton, Alysha Kempton, Gary Kempton, Rasheeda Kempton, Sherice Kempton, Tonisha Kempton, Katrena Kempton, Shemika Kempton, Sirena
Kempton, Breanne Kempton, Simona Kempton, Lakenya Kempton, Winona Kempton, Adam Kempton, Caridad Kempton, Deonna Kempton, Kimber Kempton, Lashaun Kempton, Maile Kempton, Tomekia Kempton, Bernadine
Kempton, Miesha Kempton, Adelina Kempton, Tiara Kempton, Selene Kempton, Shae Kempton, Tomi Kempton, Laila Kempton, Keith Kempton, Lilian Kempton, Sherika Kempton, Mariela Kempton, Moriah Kempton,
Page Kempton, Raegan Kempton, Timeka Kempton, Tonda Kempton, Danya Kempton, Kacie Kempton, Sabrena Kempton, Shala Kempton, Yalonda Kempton, Jermaine Kempton, Ranee Kempton, Sherron Kempton, Tameca
Kempton, Winter Kempton, Yulanda Kempton, Gabriel Kempton, Johna Kempton, Keya Kempton, Tobie Kempton, Johnetta Kempton, Rochell Kempton, Celestine Kempton, Christinia Kempton, Kymberly Kempton,
Vernita Kempton, Jina Kempton, Lashawna Kempton, Malena Kempton, Gilda Kempton, Somer Kempton, Aliza Kempton, Christene Kempton, Marilee Kempton, Ricki Kempton, Tiffiney Kempton, Winifred Kempton,
Antonio Kempton, Cassondra Kempton, Suzie Kempton, Etta Kempton, Toi Kempton, Ashli Kempton, Charis Kempton, Isabelle Kempton, Jayna Kempton, Nena Kempton, Nisha Kempton, Jenise Kempton, Lizzie
Kempton, Maegan Kempton, Contina Kempton, Joe Kempton, Sunday Kempton, Tanna Kempton, Eleni Kempton, Mirella Kempton, Concetta Kempton, Jeneen Kempton, Nerissa Kempton, Bethanie Kempton, Latoyia
Kempton, Maryjane Kempton, Treena Kempton, Benjamin Kempton, Keturah Kempton, Paulina Kempton, Rasheda Kempton, Shaunta Kempton, Vickey Kempton, Ashanti Kempton, Georgiana Kempton, Noelia Kempton,
Georgianna Kempton, Troy Kempton, Yulonda Kempton, Carley Kempton, Stephine Kempton, Oralia Kempton, Pricilla Kempton, Ranae Kempton, Lory Kempton, Africa Kempton, Lekisha Kempton, Rosaura Kempton,
Shelita Kempton, Louann Kempton, Shanti Kempton, Takesha Kempton, Tonie Kempton, Santa Kempton, Zulema Kempton, Dahlia Kempton, Jacquelynn Kempton, Karon Kempton, Teisha Kempton, Carlos Kempton,
Jerrie Kempton, Shyla Kempton, Jacqulyn Kempton, Janee Kempton, Lupita Kempton, Ora Kempton, Pia Kempton, Dodie Kempton, Mariam Kempton, Meegan Kempton, Shanelle Kempton, Chanelle Kempton, Janetta
Kempton, Chanell Kempton, Hiedi Kempton, Lesia Kempton, Nikkia Kempton, Ivory Kempton, Karry Kempton, Marcey Kempton, Theodora Kempton, Lonnie Kempton, Kai Kempton, Mina Kempton, Seana Kempton,
Kathlene Kempton, Melvina Kempton, Temika Kempton, Kala Kempton, Leta Kempton, Shaunte Kempton, Sheron Kempton, Tameeka Kempton, Eloise Kempton, Tatanisha Kempton, Catrice Kempton, Malaika Kempton,
Raymond Kempton, Sharhonda Kempton, Tandra Kempton, Tess Kempton, Linsey Kempton, Lottie Kempton, Miki Kempton, Ronni Kempton, Tiffini Kempton, Jenee Kempton, Alta Kempton, Elba Kempton, Jamillah
Kempton, Jannie Kempton, Loree Kempton, Roselyn Kempton, Winnie Kempton, Alvina Kempton, Dorcas Kempton, Laci Kempton, Merri Kempton, Mickie Kempton, Penni Kempton, Allegra Kempton, Dreama Kempton,
Nidia Kempton, Pattie Kempton, Gianna Kempton, Kimberlyn Kempton, Roshonda Kempton, Joel Kempton, Nettie Kempton, Blair Kempton, Terina Kempton, Ebonie Kempton, Kera Kempton, Ruthann Kempton, Randee
Kempton, Bryan Kempton, Jolyn Kempton, Stephannie Kempton, Delta Kempton, Janella Kempton, Laquanda Kempton, Lonna Kempton, Marcelle Kempton, Tavia Kempton, Terrell Kempton, Chasidy Kempton, Danell
Kempton, Khadijah Kempton, Neely Kempton, Nicholas Kempton, Nicky Kempton, Jennine Kempton, Tomica Kempton, Xiomara Kempton, Deneen Kempton, Magaly Kempton, Zoraida Kempton, Marquetta Kempton, Tianna
Kempton, Annabel Kempton, Brie Kempton, Caterina Kempton, Dennise Kempton, Madeleine Kempton, Marika Kempton, Angelena Kempton, Doretha Kempton, Quintina Kempton, Rashonda Kempton, Carlie Kempton,
Krysta Kempton, Lianne Kempton, Martine Kempton, Nacole Kempton, Regena Kempton, Jeanene Kempton, Kassie Kempton, Larae Kempton, Leana Kempton, Ronica Kempton, Tenesha Kempton, Deeanna Kempton, Echo
Kempton, Melita Kempton, Johnny Kempton, Lorianne Kempton, Makeba Kempton, Nakesha Kempton, Zenaida Kempton, Ophelia Kempton, Gennifer Kempton, Rasheedah Kempton, Jenette Kempton, Lashana Kempton,
Lashandra Kempton, Blanche Kempton, Kina Kempton, Dia Kempton, Emmy Kempton, Janina Kempton, Krishna Kempton, Shawnette Kempton, Wenona Kempton, Hailey Kempton, Marita Kempton, Charita Kempton,
Diedra Kempton, Annika Kempton, Gay Kempton, Karima Kempton, Keila Kempton, Lajuana Kempton, Marya Kempton, Omayra Kempton, Carl Kempton, Gricelda Kempton, Lynsey Kempton, Jama Kempton, Lynelle
Kempton, Telisha Kempton, Todd Kempton, Camie Kempton, Luanne Kempton, Mira Kempton, Raylene Kempton, Rosana Kempton, Nakeisha Kempton, Brea Kempton, Leisha Kempton, Maira Kempton, Shera Kempton,
Tangie Kempton, Tari Kempton, Treasa Kempton, Angle Kempton, Jaimi Kempton, Joie Kempton, Ryann Kempton, Sueann Kempton, Tiffney Kempton, Alida Kempton, Jackeline Kempton, Tonika Kempton, Lakeitha
Kempton, Lezlie Kempton, Stephania Kempton, Zulma Kempton, Candra Kempton, Charlie Kempton, Aleisha Kempton, Andreana Kempton, Berta Kempton, Deon Kempton, Gigi Kempton, Meri Kempton, Cherice
Kempton, Mya Kempton, Rani Kempton, Sunni Kempton, Felicity Kempton, Marcus Kempton, Myisha Kempton, Eureka Kempton, Gertrude Kempton, Lavette Kempton, Karisa Kempton, Lacresha Kempton, Olympia
Kempton, Bryn Kempton, Frank Kempton, Jovita Kempton, Leola Kempton, Augusta Kempton, Karlene Kempton, Shaina Kempton, Tenille Kempton, Fanny Kempton, Katerina Kempton, Lainie Kempton, Natalee
Kempton, Tandy Kempton, Thalia Kempton, Elda Kempton, Jacalyn Kempton, Beckie Kempton, Chenoa Kempton, Leeanna Kempton, Sharie Kempton, Tyisha Kempton, Zenobia Kempton, Diedre Kempton, Charline
Kempton, Janey Kempton, Shanan Kempton, Keva Kempton, Samuel Kempton, Sandie Kempton, Zabrina Kempton, Earlene Kempton, Jacy Kempton, Janessa Kempton, Sarai Kempton, Sharice Kempton, Tambra Kempton,
Cammy Kempton, Lashun Kempton, Leonora Kempton, Dennis Kempton, Lelia Kempton, Cherita Kempton, Courtenay Kempton, Keira Kempton, Tommy Kempton, Genia Kempton, Jordana Kempton, Kaylene Kempton, Loni
Kempton, Mickey Kempton, Sheba Kempton, Sherell Kempton, Anisa Kempton, Camelia Kempton, Domenica Kempton, Ines Kempton, Nathan Kempton, Sherrill Kempton, Delma Kempton, Essie Kempton, Lavon Kempton,
Marilynn Kempton, Myrtle Kempton, Takiyah Kempton, Alba Kempton, Delena Kempton, Leyla Kempton, Lynell Kempton, Tayna Kempton, Jazmin Kempton, Vannessa Kempton, Awilda Kempton, Carma Kempton, Derrick
Kempton, Kasi Kempton, Malka Kempton, Carli Kempton, Cordelia Kempton, Jesus Kempton, Kristeen Kempton, Chrissie Kempton, Guillermina Kempton, Joana Kempton, Lauralee Kempton, Serenity Kempton,
Alethia Kempton, Dulce Kempton, Lavinia Kempton, Nilsa Kempton, Tinisha Kempton, Veda Kempton, Demetris Kempton, Jamilah Kempton, Janean Kempton, Soledad Kempton, Talisa Kempton, Yael Kempton,
Adeline Kempton, Amparo Kempton, Shannah Kempton, Anel Kempton, Corissa Kempton, Myriam Kempton, September Kempton, Shawntel Kempton, Camisha Kempton, Cathie Kempton, Reanna Kempton, Shavonda
Kempton, Azure Kempton, Darnell Kempton, Delphine Kempton, Keren Kempton, Lashondra Kempton, Yajaira Kempton, Yessenia Kempton, Adelaida Kempton, Aura Kempton, Dorthy Kempton, Karly Kempton, Latonja
Kempton, Mendi Kempton, Wende Kempton, Adriene Kempton, Arin Kempton, Cinda Kempton, Jeanmarie Kempton, Khristina Kempton, Rory Kempton, Shanel Kempton, Zena Kempton, Astrid Kempton, Darice Kempton,
Melia Kempton, Nell Kempton, Sage Kempton, Tedra Kempton, Tyler Kempton, Inger Kempton, Lekesha Kempton, Celine Kempton, Marchelle Kempton, Shaundra Kempton, Bethanne Kempton, Kathryne Kempton,
Yanira Kempton, Jacquetta Kempton, Jessika Kempton, Niesha Kempton, Shantae Kempton, Tira Kempton, Elke Kempton, Freida Kempton, Gretta Kempton, Kerstin Kempton, San Kempton, Suzannah Kempton, Tamira
Kempton, Zina Kempton, Charmain Kempton, Cherisse Kempton, Kylene Kempton, Lacretia Kempton, Mavis Kempton, Telisa Kempton, Alysa Kempton, Carlita Kempton, Christianne Kempton, Franchesca Kempton,
Joetta Kempton, Lashelle Kempton, Rosamaria Kempton, Seema Kempton, Youlanda Kempton, Clarisa Kempton, Donella Kempton, Markita Kempton, Mesha Kempton, Poppy Kempton, Arleen Kempton, Cecile Kempton,
Krisha Kempton, Mckenzie Kempton, Sharmaine Kempton, Willa Kempton, Anessa Kempton, Donetta Kempton, Donnetta Kempton, Leora Kempton, Christena Kempton, Dorie Kempton, Eddie Kempton, Herlinda
Kempton, Lise Kempton, Rosalee Kempton, Temple Kempton, Tonette Kempton, Cheryle Kempton, Cleo Kempton, Elma Kempton, Erlinda Kempton, Peter Kempton, Sparkle Kempton, Evie Kempton, Lavina Kempton,
Marna Kempton, Meranda Kempton, Tynisha Kempton, Alyse Kempton, Anisha Kempton, Bevin Kempton, Glory Kempton, Jonnie Kempton, Marinda Kempton, Natascha Kempton, Shanetta Kempton, Angelle Kempton,
Dion Kempton, Quinn Kempton, Shanette Kempton, Shaniqua Kempton, Shantay Kempton, Tamarra Kempton, Diona Kempton, Hortencia Kempton, Latara Kempton, Lisamarie Kempton, Sidney Kempton, Alessandra
Kempton, Idalia Kempton, Malina Kempton, Sindy Kempton, Antonella Kempton, Kasha Kempton, Laquinta Kempton, Tysha Kempton, Adena Kempton, Aide Kempton, Bernita Kempton, Bettie Kempton, Delinda
Kempton, Lashundra Kempton, Sanjuana Kempton, Susann Kempton, Vilma Kempton, Deandrea Kempton, Devorah Kempton, Marisha Kempton, Reena Kempton, Takeisha Kempton, Tora Kempton, Carlyn Kempton,
Carrieann Kempton, Chanta Kempton, China Kempton, Rhianna Kempton, Sharleen Kempton, Jessenia Kempton, Kemberly Kempton, Rosalina Kempton, Rosella Kempton, Latrese Kempton, Mecca Kempton, Nneka
Kempton, Alva Kempton, Douglas Kempton, Mandee Kempton, Sherese Kempton, Taya Kempton, Tenika Kempton, Donelle Kempton, Frieda Kempton, Joye Kempton, Kayce Kempton, Sammie Kempton, Shereen Kempton,
Tomiko Kempton, Tommi Kempton, Marleen Kempton, Shonte Kempton, Avery Kempton, Delfina Kempton, Dollie Kempton, Kaycee Kempton, Lakesia Kempton, Penney Kempton, Tinika Kempton, Tywanda Kempton,
Betina Kempton, Debrah Kempton, Latia Kempton, Lynetta Kempton, Michaelle Kempton, Shunta Kempton, Soraya Kempton, Anastacia Kempton, Charisma Kempton, Jonie Kempton, Shunda Kempton, Terah Kempton,
Trinidad Kempton, Valeri Kempton, Charlena Kempton, Elizebeth Kempton, Joella Kempton, Johnette Kempton, Nikol Kempton, Rosalynn Kempton, Aime Kempton, Aviva Kempton, Joselyn Kempton, Lashanna
Kempton, Tarrah Kempton, Candyce Kempton, Estrella Kempton, Mable Kempton, Renay Kempton, Shontel Kempton, Wendee Kempton, Angelene Kempton, Karli Kempton, Maricruz Kempton, Minda Kempton, Robbi
Kempton, Towana Kempton, Charolette Kempton, Kandis Kempton, Keeley Kempton, Kimbley Kempton, Kristene Kempton, Lashell Kempton, Merissa Kempton, Taneshia Kempton, Tristan Kempton, Vida Kempton,
Zelda Kempton, Angele Kempton, Beronica Kempton, Damita Kempton, Debbra Kempton, Lanetta Kempton, Priya Kempton, Tamia Kempton, Arlinda Kempton, Armida Kempton, Chere Kempton, Errin Kempton, Kamala
Kempton, Lashan Kempton, Luana Kempton, Yalanda Kempton, Antonietta Kempton, Colby Kempton, Jona Kempton, Keitha Kempton, Dava Kempton, Herminia Kempton, Allie Kempton, Dawnmarie Kempton, Eula
Kempton, Monet Kempton, Shirlene Kempton, Tarina Kempton, Yasmine Kempton, Cassaundra Kempton, Chelsie Kempton, Fern Kempton, Rosina Kempton, Dyana Kempton, Lavern Kempton, Mario Kempton, Ollie
Kempton, Rodney Kempton, Bridgit Kempton, Julieta Kempton, Korie Kempton, Sumer Kempton, Arianna Kempton, Carmon Kempton, Chassidy Kempton, Ivana Kempton, Jerusha Kempton, Marne Kempton, Melisha
Kempton, Regenia Kempton, Sarena Kempton, Shanae Kempton, Tona Kempton, Cherese Kempton, Deitra Kempton, Dustin Kempton, Kory Kempton, Suzana Kempton, Synthia Kempton, Zakia Kempton, Lisbeth Kempton,
Matilde Kempton, Terresa Kempton, Tiffeny Kempton, Toinette Kempton, Charmin Kempton, Julienne Kempton, Marcelina Kempton, Kama Kempton, Katisha Kempton, Tiffiany Kempton, Tobey Kempton, Adelita
Kempton, Atiya Kempton, Bradley Kempton, Cathi Kempton, Dominica Kempton, Jeanelle Kempton, Jeffery Kempton, Rachal Kempton, Sammi Kempton, Anamaria Kempton, Arcelia Kempton, Isabella Kempton, Janay
Kempton, Janett Kempton, Jonell Kempton, Lakeya Kempton, Leigha Kempton, Alexander Kempton, Denae Kempton, Dustie Kempton, Felicita Kempton, Freedom Kempton, Harriett Kempton, Katia Kempton, Londa
Kempton, Marlyn Kempton, Tereasa Kempton, Analisa Kempton, Annissa Kempton, August Kempton, Jenae Kempton, Jenice Kempton, Kamie Kempton, Shanee Kempton, Sherise Kempton, Tamieka Kempton, Karianne
Kempton, Naima Kempton, Natarsha Kempton, Vita Kempton, Anjali Kempton, Ena Kempton, Jaci Kempton, Jolanda Kempton, Kimi Kempton, Celestina Kempton, Devonna Kempton, Latrece Kempton, Leatrice
Kempton, Lucila Kempton, Mignon Kempton, Stefany Kempton, Tamyra Kempton, Tracye Kempton, Beulah Kempton, Danetta Kempton, Dede Kempton, Dwana Kempton, Julisa Kempton, Kanisha Kempton, Lanae Kempton,
Ronette Kempton, Sandee Kempton, Veronique Kempton, Deirdra Kempton, Ember Kempton, Kerin Kempton, Lekeisha Kempton, Letisia Kempton, Pandora Kempton, Zaneta Kempton, Earline Kempton, Evon Kempton,
Lisandra Kempton, Lura Kempton, Raelene Kempton, Shontell Kempton, Ila Kempton, Kamisha Kempton, Tinamarie Kempton, Tish Kempton, Jay Kempton, Kayleen Kempton, Maryam Kempton, Phillip Kempton,
Santina Kempton, Taneisha Kempton, Zakiya Kempton, Brandice Kempton, Jennifier Kempton, Mariaelena Kempton, Mirian Kempton, Shalene Kempton, Tammera Kempton, Tesa Kempton, Zaida Kempton, Anjelica
Kempton, Arika Kempton, Babette Kempton, Cameo Kempton, Dwan Kempton, Kiera Kempton, Michella Kempton, Nekia Kempton, Rashelle Kempton, Robynn Kempton, Sheilah Kempton, Velia Kempton, Betsey Kempton,
Chiara Kempton, Kortney Kempton, Tressie Kempton, Tywana Kempton, Valery Kempton, Arnetta Kempton, Carlee Kempton, Craig Kempton, Debbi Kempton, Genesis Kempton, Genny Kempton, Jori Kempton, Kandie
Kempton, Lorin Kempton, Melodee Kempton, Cherlyn Kempton, Karleen Kempton, Windi Kempton, Beverley Kempton, Loreen Kempton, Malynda Kempton, Nada Kempton, Nichola Kempton, Sakinah Kempton, Steffany
Kempton, Tunisia Kempton, Vanita Kempton, Gemma Kempton, Jennell Kempton, Lakecia Kempton, Shameeka Kempton, Towanna Kempton, Tywanna Kempton, Vanesa Kempton, Dea Kempton, Desire Kempton, Donnie
Kempton, Kiki Kempton, Makesha Kempton, Rebeccah Kempton, Anglia Kempton, Branda Kempton, Kawanna Kempton, Tawnia Kempton, Debi Kempton, Elysia Kempton, Lorretta Kempton, Renetta Kempton, Tamu
Kempton, Anneliese Kempton, Devan Kempton, Rochel Kempton, Vernetta Kempton, Anetra Kempton, Brynn Kempton, Claribel Kempton, Denielle Kempton, Eugena Kempton, Fara Kempton, Genie Kempton, Joya
Kempton, Keisa Kempton, Loria Kempton, Tahira Kempton, Tawna Kempton, Angila Kempton, Chara Kempton, Cybil Kempton, Jimmy Kempton, Kendal Kempton, Serita Kempton, Tova Kempton, Vernice Kempton, Cruz
Kempton, Jameelah Kempton, Karan Kempton, Kyna Kempton, Larita Kempton, Maricella Kempton, Mariel Kempton, Elyssa Kempton, Kathyrn Kempton, Raechel Kempton, Jolee Kempton, Earnestine Kempton, Livia
Kempton, Nechama Kempton, Shawndra Kempton, Antonina Kempton, Chassity Kempton, Codi Kempton, Georgetta Kempton, Gwyn Kempton, Jacqualine Kempton, Latania Kempton, Tawni Kempton, Tiwana Kempton,
Toyia Kempton, Willette Kempton, Anette Kempton, Brandye Kempton, Danny Kempton, Enedina Kempton, Korina Kempton, Latisa Kempton, Vasiliki Kempton, Victor Kempton, Daneen Kempton, Elnora Kempton,
Shareen Kempton, Amey Kempton, Carroll Kempton, Channon Kempton, Charletta Kempton, Deserie Kempton, Jovan Kempton, Latrica Kempton, Lorina Kempton, Love Kempton, Carolann Kempton, Fran Kempton,
Ilona Kempton, Kandra Kempton, Keela Kempton, Lasonia Kempton, Leatha Kempton, Lizzette Kempton, Macy Kempton, Magan Kempton, Rebekka Kempton, Vanetta Kempton, Azucena Kempton, Brigit Kempton,
Jamaica Kempton, Jameka Kempton, Sheridan Kempton, Aliya Kempton, Chantay Kempton, Giuseppina Kempton, Lyndi Kempton, Ragan Kempton, Retha Kempton, Bari Kempton, Daryl Kempton, Elonda Kempton, Grisel
Kempton, Joline Kempton, Korey Kempton, Milinda Kempton, Rubi Kempton, Sabine Kempton, Silvana Kempton, Turkessa Kempton, Myla Kempton, Sharese Kempton, Cheron Kempton, Joell Kempton, Lachandra
Kempton, Lateefah Kempton, Sanya Kempton, Wesley Kempton, Amira Kempton, Imani Kempton, Joette Kempton, Kimmie Kempton, Lynna Kempton, Sheneka Kempton, Sunnie Kempton, Andi Kempton, Angelyn Kempton,
Maurice Kempton, Melodi Kempton, Nelida Kempton, Sherida Kempton, Shronda Kempton, Takia Kempton, Toshiba Kempton, Trishia Kempton, Alonda Kempton, Araseli Kempton, Laketa Kempton, Lesha Kempton,
Magen Kempton, Neisha Kempton, Selma Kempton, Shannen Kempton, Toria Kempton, Aline Kempton, Aubree Kempton, Delaina Kempton, Joannie Kempton, Mai Kempton, Niya Kempton, Dimitra Kempton, Karl
Kempton, Kimberle Kempton, Quanda Kempton, Alica Kempton, Chaundra Kempton, Cherly Kempton, Donnell Kempton, Ellyn Kempton, Lanell Kempton, Lawrence Kempton, Tonita Kempton, Vania Kempton, Genea
Kempton, Kathaleen Kempton, Laquetta Kempton, Lorien Kempton, Mallory Kempton, Margery Kempton, Porsha Kempton, Agatha Kempton, Alayna Kempton, Barbi Kempton, Fatimah Kempton, Jaclynn Kempton,
Kalisha Kempton, Liesl Kempton, Alita Kempton, Janita Kempton, Ola Kempton, Shawne Kempton, Talena Kempton, Angla Kempton, Autum Kempton, Bertina Kempton, Samira Kempton, Shalena Kempton, Consuella
Kempton, Corin Kempton, Delora Kempton, Lanna Kempton, Pat Kempton, Roshunda Kempton, Jonette Kempton, Latishia Kempton, Reginia Kempton, Ronnette Kempton, Sherree Kempton, Tamicka Kempton,
Alejandrina Kempton, Carlisa Kempton, Jene Kempton, Loralee Kempton, Lorenza Kempton, Luis Kempton, Yasmeen Kempton, Zakiyyah Kempton, Ashly Kempton, Cassy Kempton, Chari Kempton, Indira Kempton,
Ivelisse Kempton, Jaymi Kempton, Karalee Kempton, Lauretta Kempton, Raelynn Kempton, Tifany Kempton, Torrey Kempton, Amyjo Kempton, Annalee Kempton, Hester Kempton, Josefa Kempton, Latresa Kempton,
Lita Kempton, Marysol Kempton, Mindie Kempton, Shan Kempton, Susy Kempton, Teneka Kempton, Arnita Kempton, Charice Kempton, Cleopatra Kempton, Cotina Kempton, Dawnette Kempton, Julene Kempton, Lashay
Kempton, Latrell Kempton, Lucrecia Kempton, Ricky Kempton, Shamekia Kempton, Camellia Kempton, Cassi Kempton, Curtis Kempton, Hana Kempton, Isha Kempton, Jacquelyne Kempton, Jenica Kempton, Norah
Kempton, Oneida Kempton, Subrina Kempton, Tyrone Kempton, Angi Kempton, Anjeanette Kempton, Bella Kempton, Donica Kempton, Kareen Kempton, Laina Kempton, Luci Kempton, Mischelle Kempton, Tanita
Kempton, Heaven Kempton, Madelin Kempton, Michaele Kempton, Rashell Kempton, Tamarah Kempton, Viki Kempton, Candee Kempton, Danyale Kempton, Karis Kempton, Mishelle Kempton, Shanequa Kempton, Shellee
Kempton, Despina Kempton, Dodi Kempton, Katherin Kempton, Mechele Kempton, Pebbles Kempton, Roshelle Kempton, Carry Kempton, Denine Kempton, Dory Kempton, Jolinda Kempton, Julieanne Kempton, Karlyn
Kempton, Kathern Kempton, Kerensa Kempton, Kerrin Kempton, Lafonda Kempton, Launa Kempton, Marin Kempton, Ona Kempton, Sheli Kempton, Trixie Kempton, Yahaira Kempton, Casi Kempton, Ciara Kempton,
Darline Kempton, Drema Kempton, Francie Kempton, Gerald Kempton, Khara Kempton, Lashone Kempton, Meloney Kempton, Melyssa Kempton, Merrie Kempton, Neysa Kempton, Queen Kempton, Rashawn Kempton,
Robbyn Kempton, Sharilyn Kempton, Sharyl Kempton, Tamitha Kempton, Tresha Kempton, Amaris Kempton, Bernetta Kempton, Channel Kempton, Corrin Kempton, Deadra Kempton, Filomena Kempton, Jaye Kempton,
Kerriann Kempton, Kysha Kempton, Lanie Kempton, Lashauna Kempton, Lashona Kempton, Laurinda Kempton, Monifa Kempton, Sharri Kempton, Shontae Kempton, Terrica Kempton, Thresa Kempton, Tondra Kempton,
Geralyn Kempton, Ginamarie Kempton, Jesseca Kempton, Lasonja Kempton, Marica Kempton, Marlen Kempton, Virgie Kempton, Genna Kempton, Kriste Kempton, Kyndra Kempton, Tequilla Kempton, Vernell Kempton,
Zoila Kempton, Aiesha Kempton, Andera Kempton, Blake Kempton, Carlena Kempton, Deangela Kempton, Lavonia Kempton, Lesly Kempton, Savannah Kempton, Danisha Kempton, Dierdre Kempton, Hermelinda
Kempton, Kam Kempton, Milena Kempton, Omega Kempton, Rosaria Kempton, Russell Kempton, Shaquita Kempton, Tashika Kempton, Arlena Kempton, Delisha Kempton, Demetric Kempton, Lakendra Kempton, Marilu
Kempton, Neha Kempton, Terria Kempton, Carita Kempton, Kallie Kempton, Makisha Kempton, Martie Kempton, Mitzie Kempton, Stephane Kempton, Donette Kempton, Joli Kempton, Kathlyn Kempton, Keona
Kempton, Lakishia Kempton, Laurice Kempton, Melena Kempton, Nan Kempton, Rafaela Kempton, Taura Kempton, Wynette Kempton, Arielle Kempton, Carlette Kempton, Cyrstal Kempton, Dewanda Kempton, Kimmy
Kempton, Pauletta Kempton, Shannel Kempton, Shelbi Kempton, Camillia Kempton, Charlyn Kempton, Christianna Kempton, Gerry Kempton, Jamy Kempton, Karoline Kempton, Katrinia Kempton, Lorissa Kempton,
Magdalene Kempton, Mariza Kempton, Markisha Kempton, Mindee Kempton, Terica Kempton, Terisa Kempton, Tyronda Kempton, Aracelis Kempton, Betzaida Kempton, Charon Kempton, Chastidy Kempton, Henry
Kempton, Jamika Kempton, Janiece Kempton, Kariann Kempton, Kawanda Kempton, Saprina Kempton, Chera Kempton, Genoveva Kempton, Jacey Kempton, Jannifer Kempton, Jaylene Kempton, Meisha Kempton, Daphney
Kempton, Delois Kempton, Denelle Kempton, Diamond Kempton, Felita Kempton, Hilarie Kempton, Jamica Kempton, Joelene Kempton, Kisa Kempton, Lilliana Kempton, Sulema Kempton, Wendolyn Kempton, Calista
Kempton, Darrell Kempton, Elinor Kempton, Faviola Kempton, Jenean Kempton, Lalena Kempton, Mischa Kempton, Tamikia Kempton, Alanda Kempton, Ashia Kempton, Bryna Kempton, Serene Kempton, Shauntel
Kempton, Sheria Kempton, Talya Kempton, Thersa Kempton, Walter Kempton, Yevette Kempton, Yolande Kempton, Ashlea Kempton, Gaylene Kempton, Khadija Kempton, Latitia Kempton, Micheline Kempton,
Monalisa Kempton, Sakina Kempton, Stacye Kempton, Taffy Kempton, Tifani Kempton, Wilhelmina Kempton, Amara Kempton, Gypsy Kempton, Joely Kempton, Kameron Kempton, Keasha Kempton, Louella Kempton,
Riki Kempton, Torey Kempton, Adrien Kempton, Arwen Kempton, Crysta Kempton, Delaine Kempton, Denyse Kempton, Georgie Kempton, Janea Kempton, Medina Kempton, Meka Kempton, Nika Kempton, Rashanda
Kempton, Corena Kempton, Denee Kempton, Kimya Kempton, Lanisha Kempton, Luella Kempton, Marylin Kempton, Merritt Kempton, Mysti Kempton, Shawntay Kempton, Shirelle Kempton, Siri Kempton, Cayce
Kempton, Chava Kempton, Jovanna Kempton, Lorine Kempton, Maryelizabeth Kempton, Sonji Kempton, Titania Kempton, Brent Kempton, Jamye Kempton, Kela Kempton, Korin Kempton, Monette Kempton, Rebbeca
Kempton, Rebeka Kempton, Stormie Kempton, Angelo Kempton, Camela Kempton, Darlena Kempton, Dietra Kempton, Gwendolen Kempton, Kenia Kempton, Kesia Kempton, Kolleen Kempton, Leighanne Kempton, Lindi
Kempton, Marcee Kempton, Miya Kempton, Sami Kempton, Tameko Kempton, Tamora Kempton, Tanaya Kempton, Tiki Kempton, Toniann Kempton, Jeaneen Kempton, Lizeth Kempton, Manuel Kempton, Marlina Kempton,
Monisha Kempton, Nichele Kempton, Rechelle Kempton, Richele Kempton, Shenna Kempton, Sky Kempton, Tahnee Kempton, Brita Kempton, Erikka Kempton, Jani Kempton, Kattie Kempton, Kimbra Kempton, Quincy
Kempton, Shaquana Kempton, Sherelle Kempton, Sherryl Kempton, Shireen Kempton, Theressa Kempton, Yecenia Kempton, Albert Kempton, Ansley Kempton, Clair Kempton, Danille Kempton, Evelia Kempton, Jacob
Kempton, Jon Kempton, Katrin Kempton, Kiva Kempton, Mirta Kempton, Pearlie Kempton, Roger Kempton, Shawntell Kempton, Terrance Kempton, Vincent Kempton, Aimie Kempton, Alise Kempton, Caryl Kempton,
Devora Kempton, Dian Kempton, Genelle Kempton, Johannah Kempton, Lanora Kempton, Memory Kempton, Mila Kempton, Shandy Kempton, Shella Kempton, Shila Kempton, Tahisha Kempton, Channa Kempton,
Christeen Kempton, Janise Kempton, Kristee Kempton, Melaney Kempton, Tanis Kempton, Teasha Kempton, Arthur Kempton, Derek Kempton, Ginette Kempton, Kamesha Kempton, Keriann Kempton, Lateisha Kempton,
Merrilee Kempton, Nikesha Kempton, Sherrita Kempton, Shontay Kempton, Bess Kempton, Candelaria Kempton, Charo Kempton, Dominga Kempton, Kateri Kempton, Kelsie Kempton, Kenyata Kempton, Lane Kempton,
Lateshia Kempton, Lili Kempton, Linnette Kempton, Odette Kempton, Sharika Kempton, Sherra Kempton, Tama Kempton, Cicily Kempton, Clarinda Kempton, Corri Kempton, Donnita Kempton, Duana Kempton,
Gisele Kempton, Laquitta Kempton, Mahogany Kempton, Seanna Kempton, Sena Kempton, Shelbie Kempton, Steffani Kempton, Tauna Kempton, Zara Kempton, Aminah Kempton, Amye Kempton, Damon Kempton, Doria
Kempton, Frederica Kempton, Hollis Kempton, Katey Kempton, Nila Kempton, Pamella Kempton, Ray Kempton, Taina Kempton, Zenia Kempton, Ananda Kempton, Becca Kempton, Dessie Kempton, Donnette Kempton,
Marney Kempton, Nekisha Kempton, Sharell Kempton, Stefania Kempton, Tandi Kempton, Allana Kempton, Andree Kempton, Arlette Kempton, Denisa Kempton, Ieshia Kempton, Latrecia Kempton, Meryl Kempton,
Shakia Kempton, Shaye Kempton, Clover Kempton, Cresta Kempton, Francina Kempton, Fredericka Kempton, Kimbery Kempton, Shameika Kempton, Sherene Kempton, Armanda Kempton, Cally Kempton, Cydney
Kempton, Dasha Kempton, Gwynne Kempton, Josephina Kempton, Lavonna Kempton, Melessa Kempton, Nycole Kempton, Nyoka Kempton, Pansy Kempton, Shakita Kempton, Sonjia Kempton, Wanita Kempton, Xenia
Kempton, Any Kempton, Bobi Kempton, Bonni Kempton, Chevelle Kempton, Chrystie Kempton, Genine Kempton, Iona Kempton, Kezia Kempton, Latresha Kempton, Lucie Kempton, Malikah Kempton, Micha Kempton,
Reginald Kempton, Ronita Kempton, Sharina Kempton, Sharise Kempton, Stormi Kempton, Tammey Kempton, Angelika Kempton, Anja Kempton, Carianne Kempton, Dalene Kempton, Florinda Kempton, Irasema
Kempton, Karren Kempton, Kedra Kempton, Koreen Kempton, Leena Kempton, Libra Kempton, Moncia Kempton, Rosaline Kempton, Roshawn Kempton, Rusty Kempton, Sonda Kempton, Talina Kempton, Trudie Kempton,
Audry Kempton, Celinda Kempton, Deona Kempton, Jennipher Kempton, Jolena Kempton, Kimerly Kempton, Kym Kempton, Laquana Kempton, Madalyn Kempton, Renate Kempton, Una Kempton, Barrie Kempton, Chanin
Kempton, Deven Kempton, Hadley Kempton, Hether Kempton, Ninfa Kempton, Sha Kempton, Sloane Kempton, Tamla Kempton, Amada Kempton, Belynda Kempton, Celesta Kempton, Chelsa Kempton, Corene Kempton,
Dawana Kempton, Elly Kempton, Laure Kempton, Pascha Kempton, Shenell Kempton, Tashana Kempton, Trecia Kempton, Angelea Kempton, Dominque Kempton, Frederick Kempton, Ira Kempton, Karine Kempton,
Lachanda Kempton, Lyla Kempton, Melanee Kempton, Nikkole Kempton, Ronetta Kempton, Shanise Kempton, Shiree Kempton, Vincenza Kempton, Yolando Kempton, Adelle Kempton, Ara Kempton, Bria Kempton,
Cheryll Kempton, Delila Kempton, Delina Kempton, Jonetta Kempton, Kamela Kempton, Lacinda Kempton, Lashanta Kempton, Laurene Kempton, Lenita Kempton, Martin Kempton, Neda Kempton, Sharen Kempton,
Tanishia Kempton, Bronwen Kempton, Jamilla Kempton, Jennelle Kempton, Lavetta Kempton, Makeda Kempton, Omaira Kempton, Randie Kempton, Ricci Kempton, Romy Kempton, Sherlyn Kempton, Sonal Kempton,
Tierra Kempton, Tonyia Kempton, Caressa Kempton, Carmina Kempton, Dann Kempton, Dawnelle Kempton, Isa Kempton, Lameka Kempton, Lavada Kempton, Lavita Kempton, Lessie Kempton, Miracle Kempton, Mylinda
Kempton, Nancie Kempton, Raeanne Kempton, Shanique Kempton, Sharolyn Kempton, Alex Kempton, Cheyanne Kempton, Christan Kempton, Halima Kempton, Karlee Kempton, Katherina Kempton, Lisabeth Kempton,
Marylynn Kempton, Naimah Kempton, Ria Kempton, Tierney Kempton, Velda Kempton, Abbe Kempton, Alane Kempton, Belia Kempton, Falisha Kempton, Kaylee Kempton, Latausha Kempton, Lynnea Kempton, Myranda
Kempton, Nyla Kempton, Rima Kempton, Seneca Kempton, Aprille Kempton, Carlina Kempton, Christle Kempton, Corliss Kempton, Crystle Kempton, Desha Kempton, Kea Kempton, Kristena Kempton, Kristiana
Kempton, Lari Kempton, Lorita Kempton, Marlaina Kempton, Marquitta Kempton, Ondrea Kempton, Tashara Kempton, Devonne Kempton, Domonique Kempton, Jannet Kempton, Kila Kempton, Krysten Kempton, Leslye
Kempton, Lynnae Kempton, Shela Kempton, Sherica Kempton, Timberly Kempton, Arminda Kempton, Essence Kempton, Gala Kempton, Hellen Kempton, Jannine Kempton, Kamille Kempton, Lalita Kempton, Layne
Kempton, Letecia Kempton, Panagiota Kempton, Philana Kempton, Trisa Kempton, Akisha Kempton, Audria Kempton, Berenice Kempton, Bette Kempton, Denese Kempton, Donia Kempton, Johana Kempton, Kamika
Kempton, Katelyn Kempton, Laine Kempton, Lajuan Kempton, Lasondra Kempton, Marketta Kempton, Patrizia Kempton, Sascha Kempton, Shamara Kempton, Shamica Kempton, Tirzah Kempton, Trinia Kempton, Tyla
Kempton, Venice Kempton, Carline Kempton, Deyanira Kempton, Isabell Kempton, Jackqueline Kempton, Kendria Kempton, Marlee Kempton, Sharisse Kempton, Shawntae Kempton, Sholanda Kempton, Thomasine
Kempton, Tikisha Kempton, Tyna Kempton, Aria Kempton, Colene Kempton, Daphine Kempton, Dorthea Kempton, Genise Kempton, Keia Kempton, Leasa Kempton, Nohemi Kempton, Rosann Kempton, Ruthanne Kempton,
Shundra Kempton, Taria Kempton, Valinda Kempton, Adrain Kempton, Brunilda Kempton, Caralee Kempton, Charlee Kempton, Katasha Kempton, Krystina Kempton, Krystyna Kempton, Lovie Kempton, Marquette
Kempton, Marybel Kempton, Melvin Kempton, Nathaniel Kempton, Rickie Kempton, Romana Kempton, Tene Kempton, Tinesha Kempton, Tyann Kempton, Wednesday Kempton, Abra Kempton, Adia Kempton, Casondra
Kempton, Charmane Kempton, Chevonne Kempton, Gwenn Kempton, Laketha Kempton, Louis Kempton, Marvin Kempton, Micole Kempton, Novella Kempton, Oriana Kempton, Raena Kempton, Sharone Kempton, Suellen
Kempton, Thais Kempton, Trenda Kempton, Zuleika Kempton, Aundria Kempton, Ayisha Kempton, Catrena Kempton, Corinthia Kempton, Dorine Kempton, Dulcie Kempton, Dyanna Kempton, Kimyatta Kempton,
Lekeshia Kempton, Lenette Kempton, Nesha Kempton, Reta Kempton, Rian Kempton, Rori Kempton, Samia Kempton, Shelonda Kempton, Sima Kempton, Adriann Kempton, Beata Kempton, Dewanna Kempton, Elisia
Kempton, Lida Kempton, Myriah Kempton, Porsche Kempton, Regine Kempton, Roma Kempton, Shandi Kempton, Sharae Kempton, Brady Kempton, Denitra Kempton, Erik Kempton, Jeane Kempton, Jinny Kempton, Karah
Kempton, Mechell Kempton, Mikel Kempton, Nikkie Kempton, Nisa Kempton, Nubia Kempton, Peaches Kempton, Philip Kempton, Ramie Kempton, Romelia Kempton, Roshell Kempton, Tai Kempton, Tracia Kempton,
Wonda Kempton, Alix Kempton, Aprile Kempton, Ilda Kempton, Kacee Kempton, Kathrin Kempton, Lettie Kempton, Michaelene Kempton, Rania Kempton, Shilpa Kempton, Teddi Kempton, Tegan Kempton, Terrilyn
Kempton, Albertina Kempton, Aryn Kempton, Augustina Kempton, Belle Kempton, Britton Kempton, Irena Kempton, Jacquie Kempton, Katrine Kempton, Lorenda Kempton, Magali Kempton, Mikaela Kempton, Remona
Kempton, Rossana Kempton, Shree Kempton, Adrea Kempton, Ashaki Kempton, Beatris Kempton, Elisabet Kempton, Gene Kempton, Greer Kempton, Hillery Kempton, Jillene Kempton, Keyona Kempton, Latifa
Kempton, Marshell Kempton, Miguel Kempton, Resa Kempton, Roy Kempton, Tarnisha Kempton, Tekisha Kempton, Teshia Kempton, Tomara Kempton, Vashti Kempton, Brienne Kempton, Calvin Kempton, Corrinne
Kempton, Dorina Kempton, Errica Kempton, Eulalia Kempton, Jacelyn Kempton, Jimi Kempton, Kavita Kempton, Keyana Kempton, Kiara Kempton, Lahoma Kempton, Merilee Kempton, Milisa Kempton, Pollyanna
Kempton, Rabecca Kempton, Shalisa Kempton, Tyree Kempton, Baby Kempton, Cali Kempton, Cherron Kempton, Conswella Kempton, Dayle Kempton, Deniece Kempton, Elesha Kempton, Eugene Kempton, Fredricka
Kempton, Letty Kempton, Marlisa Kempton, Meadow Kempton, Nana Kempton, Ricardo Kempton, Sunita Kempton, Tahirah Kempton, Aleasha Kempton, Alene Kempton, Jerica Kempton, Jonni Kempton, Jorie Kempton,
Keenya Kempton, Phillis Kempton, Scottie Kempton, Tamy Kempton, Adelaide Kempton, Akia Kempton, Alona Kempton, Brandilyn Kempton, Davita Kempton, Deondra Kempton, Guinevere Kempton, Jaquetta Kempton,
Joyelle Kempton, Kaitlin Kempton, Kammy Kempton, Lashonna Kempton, Manisha Kempton, Nyesha Kempton, Phebe Kempton, Shadonna Kempton, Tamila Kempton, Treasure Kempton, Wayne Kempton, Charmayne
Kempton, Corry Kempton, Doni Kempton, Jannell Kempton, Kaia Kempton, Karna Kempton, Kinya Kempton, Lasha Kempton, Lecia Kempton, Letricia Kempton, Paulita Kempton, Sharnell Kempton, Sheniqua Kempton,
Toy Kempton, Unique Kempton, Wynona Kempton, Audrie Kempton, Cambria Kempton, Crissie Kempton, Deseree Kempton, Deva Kempton, Jenney Kempton, Jessamyn Kempton, Leda Kempton, Lorry Kempton, Marjory
Kempton, Marnee Kempton, Monigue Kempton, Nakeya Kempton, Passion Kempton, Ryanne Kempton, Sharona Kempton, Shelina Kempton, Tabbatha Kempton, Tameshia Kempton, Adelia Kempton, Anica Kempton, Calli
Kempton, Carolyne Kempton, Chiffon Kempton, Elizabet Kempton, Ermelinda Kempton, Freddie Kempton, Jamia Kempton, Korrie Kempton, Latrenda Kempton, Makia Kempton, Marcel Kempton, Meta Kempton, Noni
Kempton, Sigrid Kempton, Zita Kempton, Angelee Kempton, Balinda Kempton, Brandyn Kempton, Christia Kempton, Eneida Kempton, Irish Kempton, Jackelyn Kempton, Jacqui Kempton, Kammie Kempton, Kendell
Kempton, Kiya Kempton, Mellanie Kempton, Sherina Kempton, Syretta Kempton, Teia Kempton, Teneshia Kempton, Tomasa Kempton, Tonna Kempton, Virgina Kempton, Zelma Kempton, Adella Kempton, Alea Kempton,
Annita Kempton, Denetra Kempton, Georgeann Kempton, Gwyneth Kempton, Jenea Kempton, Kalli Kempton, Khristine Kempton, Krissie Kempton, Lanelle Kempton, Letrice Kempton, Meshell Kempton, Michon
Kempton, Nekita Kempton, Raelyn Kempton, Shaleen Kempton, Sharanda Kempton, Sol Kempton, Suzi Kempton, Ulanda Kempton, Ame Kempton, Aprill Kempton, Brooks Kempton, Carlye Kempton, Francisco Kempton,
Gaynell Kempton, Gwenda Kempton, Heidy Kempton, Helga Kempton, Janese Kempton, Kathrina Kempton, Katonya Kempton, Kodi Kempton, Leshawn Kempton, London Kempton, Lyndee Kempton, Marc Kempton, Miyoshi
Kempton, Onika Kempton, Peyton Kempton, Shandell Kempton, Terena Kempton, Acacia Kempton, Aleida Kempton, Antoine Kempton, Arletha Kempton, Carlin Kempton, Danni Kempton, Davette Kempton, December
Kempton, Jenene Kempton, Karalyn Kempton, Kimbely Kempton, Lakisa Kempton, Lynae Kempton, Margaux Kempton, Michela Kempton, Renne Kempton, Tanzania Kempton, Tenia Kempton, Toyna Kempton, Veronika
Kempton, Amal Kempton, Camila Kempton, Chi Kempton, Dominic Kempton, Macie Kempton, Maida Kempton, Malisha Kempton, Milagro Kempton, Mitchell Kempton, Shondell Kempton, Taira Kempton, Argelia
Kempton, Casaundra Kempton, Courtnie Kempton, Dalena Kempton, Donyell Kempton, Ericia Kempton, Kelsi Kempton, Madelene Kempton, Mikelle Kempton, Moria Kempton, Salome Kempton, Starlet Kempton,
Stepanie Kempton, Stephnie Kempton, Teesha Kempton, Allisa Kempton, Aneesah Kempton, Breann Kempton, Chevon Kempton, Deatrice Kempton, Delaney Kempton, Jodene Kempton, Julian Kempton, Lorilee
Kempton, Margarette Kempton, Marshall Kempton, Meleah Kempton, Nadene Kempton, Nefertiti Kempton, Rebekkah Kempton, Shakina Kempton, Sibyl Kempton, Teria Kempton, Briget Kempton, Cortina Kempton,
Gennie Kempton, Georgeanna Kempton, Jael Kempton, Katharina Kempton, Kennetha Kempton, Kerrianne Kempton, Meggin Kempton, Rochele Kempton, Santos Kempton, Senta Kempton, Shanie Kempton, Sona Kempton,
Yana Kempton, Alicea Kempton, Capri Kempton, Cassey Kempton, Daun Kempton, Denette Kempton, Harold Kempton, Jacie Kempton, Jennica Kempton, Krissa Kempton, Lawonda Kempton, Lenna Kempton, Maija
Kempton, Ninette Kempton, Tomeika Kempton, Trenna Kempton, Amberlee Kempton, Avril Kempton, Charnell Kempton, Chenita Kempton, Crystel Kempton, Eugenie Kempton, Ginnie Kempton, Jerome Kempton, Karee
Kempton, Latunya Kempton, Lianna Kempton, Lisaann Kempton, Maribell Kempton, Marylyn Kempton, Molli Kempton, Raye Kempton, Risha Kempton, Sherrice Kempton, Taralyn Kempton, Tika Kempton, Tyanna
Kempton, Wilda Kempton, Brandalyn Kempton, Camesha Kempton, Ericca Kempton, Ernest Kempton, Glynis Kempton, Larena Kempton, Latecia Kempton, Lindsy Kempton, Melea Kempton, Monic Kempton, Suanne
Kempton, Tammra Kempton, Tyeisha Kempton, Allen Kempton, Ambra Kempton, Cindee Kempton, Deja Kempton, Denika Kempton, Easter Kempton, Emerald Kempton, Jann Kempton, Jeannetta Kempton, Keyla Kempton,
Lataya Kempton, Natividad Kempton, Nikola Kempton, Quanita Kempton, Shalyn Kempton, Temekia Kempton, Tishia Kempton, Allena Kempton, Andrena Kempton, Aurea Kempton, Buffi Kempton, Darren Kempton,
Dovie Kempton, Evelina Kempton, Fatina Kempton, Ivey Kempton, Jennafer Kempton, Kimberlea Kempton, Kishia Kempton, Lacrecia Kempton, Laney Kempton, Latora Kempton, Robinette Kempton, Shalita Kempton,
Shanin Kempton, Terasa Kempton, Tiphanie Kempton, Tiwanna Kempton, Ashlyn Kempton, Breana Kempton, Emely Kempton, Evan Kempton, Evangelia Kempton, Halle Kempton, Lynnetta Kempton, Mandisa Kempton,
Mardi Kempton, Neomi Kempton, Peggie Kempton, Senaida Kempton, Shantee Kempton, Alondra Kempton, Bettyjo Kempton, Dawnell Kempton, Jaunita Kempton, Jaymee Kempton, Jeneane Kempton, Kamara Kempton,
Korinne Kempton, Lacosta Kempton, Latrena Kempton, Letticia Kempton, Luanna Kempton, Meighan Kempton, Merinda Kempton, Raechelle Kempton, Randall Kempton, Shermaine Kempton, Tacy Kempton, Telicia
Kempton, Trica Kempton, Unknown Kempton, Venetia Kempton, Virgen Kempton, Chanita Kempton, Christe Kempton, Collene Kempton, Deni Kempton, Eliana Kempton, Evelin Kempton, Jessa Kempton, Katarina
Kempton, Kersten Kempton, Krysti Kempton, Lanise Kempton, Lannette Kempton, Latacha Kempton, Lavenia Kempton, Magnolia Kempton, Mayte Kempton, Missie Kempton, Renda Kempton, Sapna Kempton, Shawan
Kempton, Starlene Kempton, Stasia Kempton, Tamaria Kempton, Tiffanee Kempton, Yazmin Kempton, Ammy Kempton, Blossom Kempton, Cherokee Kempton, Chrissa Kempton, Dean Kempton, Donell Kempton, Jannelle
Kempton, Jenessa Kempton, Jenne Kempton, Kimiko Kempton, Lenise Kempton, Lotoya Kempton, Mariko Kempton, Myeshia Kempton, Nadja Kempton, Shalana Kempton, Tangee Kempton, Waynette Kempton, Alan
Kempton, Bennie Kempton, Berlinda Kempton, Brinda Kempton, Brooklyn Kempton, Bruce Kempton, Daisha Kempton, Devina Kempton, Donisha Kempton, Judie Kempton, Khristy Kempton, Margarett Kempton,
Markesha Kempton, Melannie Kempton, Nickol Kempton, Pamelia Kempton, Roselle Kempton, Shirleen Kempton, Terrence Kempton, Trenise Kempton, Alda Kempton, Ariella Kempton, Aubrie Kempton, Aziza
Kempton, Carrol Kempton, Charnita Kempton, Deshanna Kempton, Donyale Kempton, Dorrie Kempton, Elayne Kempton, Feather Kempton, Gregoria Kempton, Kanesha Kempton, Kirsti Kempton, Maryalice Kempton,
Maude Kempton, Millissa Kempton, Monya Kempton, Shareese Kempton, Shereka Kempton, Tenaya Kempton, Vonnie Kempton, Bunny Kempton, Carmin Kempton, Cissy Kempton, Damika Kempton, Dayla Kempton, Dewana
Kempton, Jorge Kempton, Kaila Kempton, Kaisha Kempton, Kaylynn Kempton, Kemba Kempton, Lael Kempton, Lysa Kempton, Roberto Kempton, Tanasha Kempton, Tynisa Kempton, Vina Kempton, Angelette Kempton,
Angenette Kempton, Aquila Kempton, Carrianne Kempton, Charlynn Kempton, Denean Kempton, Dondi Kempton, Enriqueta Kempton, Georganna Kempton, Glinda Kempton, Jenel Kempton, Larinda Kempton, Latika
Kempton, Lequita Kempton, Licia Kempton, Marilou Kempton, Sylvie Kempton, Aaliyah Kempton, Cozette Kempton, Damian Kempton, Ginna Kempton, Janalee Kempton, Jenniefer Kempton, Kierstin Kempton, Lexie
Kempton, Maja Kempton, Michelene Kempton, Norine Kempton, Sana Kempton, Sarrah Kempton, Sharna Kempton, Sherre Kempton, Shoshanna Kempton, Tangi Kempton, Tillie Kempton, Aishia Kempton, Allene
Kempton, Antoniette Kempton, Brittani Kempton, Candise Kempton, Carlota Kempton, Debroah Kempton, Demeka Kempton, Dondra Kempton, Franca Kempton, Gaye Kempton, Jeanell Kempton, Lark Kempton, Laurin
Kempton, Lourie Kempton, Machell Kempton, Pasha Kempton, Shelena Kempton, Tangelia Kempton, Tani Kempton, Twilla Kempton, Tynesha Kempton, Vena Kempton, Vernessa Kempton, Aleesha Kempton, Cassia
Kempton, Catheryn Kempton, Chavon Kempton, Codie Kempton, Conchita Kempton, Felipa Kempton, Jeanice Kempton, Kelleen Kempton, Latona Kempton, Loreal Kempton, Lutricia Kempton, Natanya Kempton, Perry
Kempton, Samaria Kempton, Sharene Kempton, Shavone Kempton, Stavroula Kempton, Tatia Kempton, Terrina Kempton, Veroncia Kempton, Alaine Kempton, Carmalita Kempton, Chirstina Kempton, Dawanna Kempton,
Delonda Kempton, Ebonee Kempton, Jamela Kempton, Kerie Kempton, Lanika Kempton, Latressa Kempton, Priscella Kempton, Sharifa Kempton, Shenequa Kempton, Shon Kempton, Taresa Kempton, Viva Kempton,
Annabell Kempton, Arelis Kempton, Carra Kempton, Char Kempton, Chekesha Kempton, Cherylann Kempton, Crystall Kempton, Diandra Kempton, Dwayne Kempton, Elishia Kempton, Emi Kempton, Jennife Kempton,
Kassi Kempton, Keyonna Kempton, Kresta Kempton, Kriston Kempton, Laree Kempton, Lashea Kempton, Lauryn Kempton, Lennie Kempton, Nailah Kempton, Neena Kempton, Nelia Kempton, Reiko Kempton, Sejal
Kempton, Shanea Kempton, Sharman Kempton, Talesha Kempton, Teresia Kempton, Tunya Kempton, Annett Kempton, Catherina Kempton, Charlita Kempton, Dandrea Kempton, Darcel Kempton, Eleanore Kempton,
Falicia Kempton, Glynda Kempton, Karra Kempton, Kerra Kempton, Ladona Kempton, Loretha Kempton, Lus Kempton, Marketa Kempton, Megen Kempton, Shalini Kempton, Sheela Kempton, Tally Kempton, Thuy
Kempton, Tristen Kempton, Yashika Kempton, Aleah Kempton, Arline Kempton, Catarina Kempton, Cris Kempton, Dawnita Kempton, Kelliann Kempton, Kristle Kempton, Lanesha Kempton, Malanie Kempton, Nekesha
Kempton, Rhona Kempton, Roslynn Kempton, Sariah Kempton, Takeshia Kempton, Theda Kempton, Altagracia Kempton, Anneke Kempton, Aspen Kempton, Azalea Kempton, Jamelle Kempton, Kalyn Kempton, Lavonya
Kempton, Malea Kempton, Marykate Kempton, Meliss Kempton, Noelani Kempton, Patina Kempton, Riann Kempton, Rolonda Kempton, Shaney Kempton, Shanice Kempton, Wynne Kempton, Yocheved Kempton, Aysha
Kempton, Cindie Kempton, Daphanie Kempton, Darcee Kempton, Demitra Kempton, Francene Kempton, Ian Kempton, Janaya Kempton, Jera Kempton, Jeremiah Kempton, Karlie Kempton, Kiwana Kempton, Krystin
Kempton, Larina Kempton, Marylee Kempton, Maurine Kempton, Mistee Kempton, Rainey Kempton, Raynette Kempton, Robyne Kempton, Ronelle Kempton, Sharma Kempton, Shelene Kempton, Stevie Kempton, Wynter
Kempton, Ylonda Kempton, Zondra Kempton, Aesha Kempton, Alpha Kempton, Angala Kempton, Che Kempton, Courtnay Kempton, Deatra Kempton, Genell Kempton, Jerrica Kempton, Jozette Kempton, Kerianne
Kempton, Krissi Kempton, Millisa Kempton, Minna Kempton, Naeemah Kempton, Shantrell Kempton, Theresia Kempton, Tomeko Kempton, Vanda Kempton, Annelise Kempton, Bettye Kempton, Brina Kempton,
Carmelina Kempton, Charlotta Kempton, Charmine Kempton, Darbi Kempton, Devra Kempton, Donnamarie Kempton, Enza Kempton, Jack Kempton, Lamika Kempton, Lashaundra Kempton, Latavia Kempton, Mauri
Kempton, Nevada Kempton, Patrisha Kempton, Rashel Kempton, Rayann Kempton, Shanay Kempton, Shareka Kempton, Sharlyn Kempton, Sharra Kempton, Suzzanne Kempton, Tascha Kempton, Tomeca Kempton, Annisa
Kempton, Anthea Kempton, Bethel Kempton, Charlesetta Kempton, Davetta Kempton, Deonne Kempton, Emmie Kempton, Fanta Kempton, Felicitas Kempton, Flavia Kempton, Glenn Kempton, Gwendolynn Kempton,
Hollye Kempton, Jalene Kempton, Jamel Kempton, Jenita Kempton, Jonda Kempton, Kameka Kempton, Lagina Kempton, Lateasha Kempton, Louanne Kempton, Ludivina Kempton, Ramonita Kempton, Reshonda Kempton,
Romina Kempton, Samone Kempton, Shauntae Kempton, Shelle Kempton, Tasheka Kempton, Tashima Kempton, Tekesha Kempton, Trini Kempton, Tyese Kempton, Alesa Kempton, Brigett Kempton, Camella Kempton,
Charee Kempton, Coby Kempton, Constantina Kempton, Contrina Kempton, Danise Kempton, Delanie Kempton, Denia Kempton, Detrice Kempton, Donyelle Kempton, Estee Kempton, Freya Kempton, Gabriele Kempton,
Heidie Kempton, Idella Kempton, Iraida Kempton, Jonica Kempton, Kaley Kempton, Kirsty Kempton, Laurette Kempton, Nataki Kempton, Patrisia Kempton, Ronnetta Kempton, Signe Kempton, Tarita Kempton,
Trenia Kempton, Annessa Kempton, Celene Kempton, Cerissa Kempton, Chinita Kempton, Danah Kempton, Dannelle Kempton, Dawnielle Kempton, Doretta Kempton, Dwanna Kempton, Jinger Kempton, Karilyn
Kempton, Loida Kempton, Miko Kempton, Mirtha Kempton, Myia Kempton, Perri Kempton, Ragina Kempton, Rea Kempton, Saralyn Kempton, Saskia Kempton, Sharry Kempton, Tiare Kempton, Tonica Kempton, Waleska
Kempton, Xochilt Kempton, Zipporah Kempton, Delynn Kempton, Detria Kempton, Earl Kempton, Enedelia Kempton, Jeanett Kempton, Jonita Kempton, Kenita Kempton, Laural Kempton, Leonard Kempton, Ligia
Kempton, Linnie Kempton, Lowanda Kempton, Ltanya Kempton, Monquie Kempton, Paloma Kempton, Rafael Kempton, Steve Kempton, Torina Kempton, Yolunda Kempton, Cariann Kempton, Carmita Kempton, Cerise
Kempton, Dalana Kempton, Dawnya Kempton, Deshannon Kempton, Deshonda Kempton, Desirea Kempton, Eartha Kempton, Emelia Kempton, Francoise Kempton, Gerrie Kempton, Gitty Kempton, Jared Kempton, Kianna
Kempton, Lamanda Kempton, Laraine Kempton, Latonda Kempton, Latrease Kempton, Leaann Kempton, Liv Kempton, Maha Kempton, Meliza Kempton, Shawnetta Kempton, Shontelle Kempton, Sloan Kempton, Taja
Kempton, Tammye Kempton, Terika Kempton, Vinita Kempton, Charese Kempton, Charisa Kempton, Danella Kempton, Halley Kempton, Jara Kempton, Jawana Kempton, Jobina Kempton, Juniper Kempton, Leondra
Kempton, Letonya Kempton, Marianela Kempton, Mariella Kempton, Marisel Kempton, Marlinda Kempton, Maurita Kempton, Merrill Kempton, Nalani Kempton, Natika Kempton, Ralph Kempton, Shajuana Kempton,
Sharmon Kempton, Tanda Kempton, Clarence Kempton, Enjoli Kempton, Hali Kempton, Isaura Kempton, Joellyn Kempton, Kaylyn Kempton, Ketra Kempton, Latayna Kempton, Melisse Kempton, Natoshia Kempton,
Niko Kempton, Shalina Kempton, Sharrie Kempton, Silva Kempton, Taren Kempton, Tawnie Kempton, Venetta Kempton, Chenelle Kempton, Chonda Kempton, Drucilla Kempton, Genene Kempton, Jaquita Kempton,
Kally Kempton, Laury Kempton, Lucina Kempton, Lynde Kempton, Marley Kempton, Scherrie Kempton, Shaila Kempton, Shalimar Kempton, Shannyn Kempton, Shantina Kempton, Shirl Kempton, Takita Kempton,
Tineka Kempton, Valisa Kempton, Adrina Kempton, Ambre Kempton, Arlisa Kempton, Cecila Kempton, Demetrica Kempton, Dyann Kempton, Erina Kempton, Haven Kempton, Hector Kempton, Janika Kempton,
Johnnetta Kempton, Kellyanne Kempton, Lacrisha Kempton, Lamar Kempton, Litisha Kempton, Malkia Kempton, Marcellina Kempton, Otilia Kempton, Pascale Kempton, Ramonda Kempton, Safiya Kempton, Sebrena
Kempton, Shifra Kempton, Sina Kempton, Tashina Kempton, Teffany Kempton, Trevor Kempton, Veleka Kempton, Zanetta Kempton, Arie Kempton, Azalia Kempton, Cedric Kempton, Chasta Kempton, Cherelle
Kempton, Cyndee Kempton, Darnetta Kempton, Dinora Kempton, Dorena Kempton, Howard Kempton, Joyel Kempton, July Kempton, Lance Kempton, Lore Kempton, Michelina Kempton, Olive Kempton, Reem Kempton,
Rica Kempton, Shaneen Kempton, Sharlotte Kempton, Shavonna Kempton, Shawnie Kempton, Sherria Kempton, Sian Kempton, Stephanee Kempton, Susette Kempton, Terilyn Kempton, Tiajuana Kempton, Tristin
Kempton, Vada Kempton, Vesta Kempton, Yara Kempton, Alyssia Kempton, Arian Kempton, Chianti Kempton, Chriselda Kempton, Darian Kempton, Dawnetta Kempton, Desarae Kempton, Dinorah Kempton, Djuana
Kempton, Elka Kempton, Golda Kempton, Honor Kempton, Jamille Kempton, Jesusita Kempton, Junita Kempton, Kenyada Kempton, Konnie Kempton, Kwanza Kempton, Lissett Kempton, Marlon Kempton, Marlys
Kempton, Marshelle Kempton, Meagen Kempton, Myka Kempton, Mylissa Kempton, Patrece Kempton, Raguel Kempton, Sharia Kempton, Shawnell Kempton, Teanna Kempton, Adrena Kempton, Brad Kempton, Charlisa
Kempton, Dannie Kempton, Fernanda Kempton, Jeania Kempton, Kareema Kempton, Karyl Kempton, Kellianne Kempton, Lilah Kempton, Lorelle Kempton, Lynnell Kempton, Quana Kempton, Rondi Kempton, Rosiland
Kempton, Ruben Kempton, Sharmin Kempton, Taniesha Kempton, Tashonda Kempton, Valecia Kempton, Alnisa Kempton, Cherity Kempton, Coletta Kempton, Damary Kempton, Darcia Kempton, Dashawn Kempton, Garnet
Kempton, Hadassah Kempton, Javon Kempton, Kareem Kempton, Keara Kempton, Kerryann Kempton, Loleta Kempton, Marijo Kempton, Maritsa Kempton, Marvella Kempton, Miriah Kempton, Necia Kempton, Priscila
Kempton, Ramon Kempton, Shalawn Kempton, Sidra Kempton, Sundee Kempton, Tasia Kempton, Tiwanda Kempton, Xavier Kempton, Alayne Kempton, Anesha Kempton, Anndrea Kempton, Astra Kempton, Breezy Kempton,
Carletha Kempton, Chantele Kempton, Damara Kempton, Denell Kempton, Dessa Kempton, Marcell Kempton, Maretta Kempton, Marline Kempton, Melania Kempton, Modesta Kempton, Montoya Kempton, Rashidah
Kempton, Rusti Kempton, Shannell Kempton, Shaune Kempton, Sheresa Kempton, Stasha Kempton, Talaya Kempton, Taletha Kempton, Tashawna Kempton, Terrah Kempton, Yessica Kempton, Yolander Kempton, Ani
Kempton, Cyndy Kempton, Dannell Kempton, Edythe Kempton, Elodia Kempton, Felissa Kempton, Jamison Kempton, Janalyn Kempton, Jodell Kempton, Josetta Kempton, Karmin Kempton, Kenesha Kempton, Keyna
Kempton, Kimara Kempton, Kiran Kempton, Ladonya Kempton, Latorya Kempton, Marizol Kempton, Nadya Kempton, Pamula Kempton, Pleshette Kempton, Tamaka Kempton, Tifanie Kempton, Tunisha Kempton, Verona
Kempton, Veronda Kempton, Allicia Kempton, Allisha Kempton, Allissa Kempton, Allyn Kempton, Andriana Kempton, Anneka Kempton, Bridgitte Kempton, Brigida Kempton, Chaunte Kempton, Christol Kempton,
Elita Kempton, Jacquelene Kempton, Jenefer Kempton, Jessyca Kempton, Kammi Kempton, Kasondra Kempton, Katricia Kempton, Katrinka Kempton, Lakasha Kempton, Maryrose Kempton, Mirinda Kempton, Natoya
Kempton, Omar Kempton, Santana Kempton, Shakima Kempton, Shatina Kempton, Shawnita Kempton, Sherine Kempton, Starlett Kempton, Tanga Kempton, Teal Kempton, Teara Kempton, Tiffanny Kempton, Vivien
Kempton, Altovise Kempton, Conni Kempton, Dawanda Kempton, Ellena Kempton, Janica Kempton, Jeralyn Kempton, Kameelah Kempton, Kasia Kempton, Katharyn Kempton, Lamesha Kempton, Laurieann Kempton, Leon
Kempton, Margherita Kempton, Marguerita Kempton, Mariama Kempton, Mariea Kempton, Maryfrances Kempton, Mayda Kempton, Meena Kempton, Mikal Kempton, Nicholette Kempton, Nitza Kempton, Norman Kempton,
Raychelle Kempton, Riva Kempton, Ronit Kempton, Rosenda Kempton, Royce Kempton, Saira Kempton, Samona Kempton, Toye Kempton, Zinnia Kempton, Alfred Kempton, Amita Kempton, Aqueelah Kempton, Blenda
Kempton, Charron Kempton, Chrisie Kempton, Ema Kempton, Endia Kempton, Georgine Kempton, Gretel Kempton, Johnita Kempton, Joscelyn Kempton, Kiona Kempton, Lamont Kempton, Lateesha Kempton, Liisa
Kempton, Lizet Kempton, Marny Kempton, Martisha Kempton, Marvette Kempton, Natonya Kempton, Oona Kempton, Philomena Kempton, Sahar Kempton, Shantia Kempton, Starlette Kempton, Talana Kempton, Tereza
Kempton, Torsha Kempton, Tyeshia Kempton, Aislinn Kempton, Alexandrea Kempton, Artisha Kempton, Assunta Kempton, Belva Kempton, Britany Kempton, Bryanna Kempton, Chauntel Kempton, Cristel Kempton,
Damali Kempton, Daphane Kempton, Dorianne Kempton, Imogene Kempton, Janai Kempton, Laveda Kempton, Lucero Kempton, Lyssa Kempton, Marielle Kempton, Natalya Kempton, Pammy Kempton, Patches Kempton,
Rhiana Kempton, Sakeena Kempton, Tanea Kempton, Tiffinie Kempton, Xaviera Kempton, Arla Kempton, Collen Kempton, Deane Kempton, Don Kempton, Gari Kempton, Jazmine Kempton, Joani Kempton, Jude
Kempton, Lacee Kempton, Lakeasha Kempton, Leandrea Kempton, Marvina Kempton, Minette Kempton, Nico Kempton, Noell Kempton, Ouida Kempton, Rainbow Kempton, Shania Kempton, Shemekia Kempton, Velinda
Kempton, Yetta Kempton, Adell Kempton, Alyshia Kempton, Arlana Kempton, Athina Kempton, Calley Kempton, Carson Kempton, Cassandre Kempton, Channing Kempton, Cherith Kempton, Darnella Kempton, Deepa
Kempton, Eboney Kempton, Florentina Kempton, Fredia Kempton, Jerilynn Kempton, Kamila Kempton, Keeli Kempton, Korena Kempton, Korri Kempton, Lakeia Kempton, Lulu Kempton, Madelaine Kempton, Marja
Kempton, Maryhelen Kempton, Mei Kempton, Quintella Kempton, Rainy Kempton, Rashunda Kempton, Rheanna Kempton, Saran Kempton, Shanese Kempton, Shelisa Kempton, Tamecia Kempton, Tanica Kempton, Tawnee
Kempton, Van Kempton, Vivienne Kempton, Yoland Kempton, Yvonna Kempton, Abbi Kempton, Afrika Kempton, Anise Kempton, Aron Kempton, Carrieanne Kempton, Chauna Kempton, Daena Kempton, Elin Kempton,
Jerrilyn Kempton, Landa Kempton, Latoyna Kempton, Leane Kempton, Lilliam Kempton, Marquisha Kempton, Marry Kempton, Matasha Kempton, Matina Kempton, Megin Kempton, Mitchelle Kempton, Nakeshia
Kempton, Pearline Kempton, Rayne Kempton, Reeshemah Kempton, Romaine Kempton, Shameca Kempton, Sterling Kempton, Suzzette Kempton, Tangy Kempton, Tonetta Kempton, Trenice Kempton, Zahra Kempton,
Abena Kempton, Aliesha Kempton, Andreia Kempton, Beryl Kempton, Cathey Kempton, Crystalyn Kempton, Davonna Kempton, Delphia Kempton, Denisse Kempton, Elina Kempton, Elisheva Kempton, Evangela
Kempton, Felina Kempton, Gisella Kempton, Ilka Kempton, Janeth Kempton, Katara Kempton, Laquesha Kempton, Lysandra Kempton, Malana Kempton, Morgen Kempton, Natali Kempton, Niambi Kempton, Niketa
Kempton, Pamla Kempton, Rebeckah Kempton, Revonda Kempton, Sarabeth Kempton, Sharmila Kempton, Shylo Kempton, Takiya Kempton, Trevia Kempton, Aleatha Kempton, Anabelle Kempton, Blima Kempton, Bliss
Kempton, Christyn Kempton, Chrysta Kempton, Cristela Kempton, Deliah Kempton, Ellisa Kempton, Genice Kempton, Isadora Kempton, Jawanna Kempton, Kamaria Kempton, Ladena Kempton, Larenda Kempton,
Laurissa Kempton, Leela Kempton, Lovina Kempton, Lyra Kempton, Maryanna Kempton, Marybell Kempton, Meika Kempton, Meshelle Kempton, Moana Kempton, Nicoletta Kempton, Radiah Kempton, Rupal Kempton,
Shannin Kempton, Shyra Kempton, Stanley Kempton, Sundae Kempton, Taunia Kempton, Tomorrow Kempton, Abbigail Kempton, Amoreena Kempton, Anamarie Kempton, Chani Kempton, Dayanara Kempton, Delane
Kempton, Demika Kempton, Desi Kempton, Desma Kempton, Eugina Kempton, Florine Kempton, Johanne Kempton, Karman Kempton, Katheryne Kempton, Kema Kempton, Kenitra Kempton, Lareina Kempton, Laryssa
Kempton, Lasaundra Kempton, Lorriane Kempton, Lurdes Kempton, Meredyth Kempton, Mireille Kempton, Naomie Kempton, Rewa Kempton, Rosette Kempton, Rukiya Kempton, Shanica Kempton, Sherill Kempton,
Shonette Kempton, Adonica Kempton, Aquilla Kempton, Billijo Kempton, Bretta Kempton, Charmian Kempton, Chondra Kempton, Coty Kempton, Danine Kempton, Davena Kempton, Davia Kempton, Falana Kempton,
Fredrica Kempton, Harry Kempton, Jae Kempton, Jawanda Kempton, Keana Kempton, Krisann Kempton, Laqueta Kempton, Lashannon Kempton, Lavelle Kempton, Layna Kempton, Linde Kempton, Lorisa Kempton,
Lyndie Kempton, Macey Kempton, Maricel Kempton, Nadina Kempton, Nadiyah Kempton, Nereyda Kempton, Sequoia Kempton, Stephene Kempton, Tahesha Kempton, Takeya Kempton, Tali Kempton, Tiera Kempton,
Tomasina Kempton, Verena Kempton, Yvonda Kempton, Aracelia Kempton, Arletta Kempton, Augustine Kempton, Barry Kempton, Brittny Kempton, Christella Kempton, Courtnee Kempton, Dakota Kempton, Denesha
Kempton, Donnella Kempton, Fotini Kempton, Gita Kempton, Holland Kempton, Jacquiline Kempton, Jamilyn Kempton, Kafi Kempton, Kalena Kempton, Katya Kempton, Kit Kempton, Laniece Kempton, Lauree
Kempton, Leslea Kempton, Maite Kempton, Mitzy Kempton, Myria Kempton, Njeri Kempton, Oscar Kempton, Rain Kempton, Rema Kempton, Ronee Kempton, Shevon Kempton, Shirlee Kempton, Sissy Kempton, Sonali
Kempton, Sundra Kempton, Taralee Kempton, Trace Kempton, Tyana Kempton, Agustina Kempton, Akua Kempton, Allyssa Kempton, Andrina Kempton, Angell Kempton, Antwanette Kempton, Carmelia Kempton, Chelsi
Kempton, Cheronda Kempton, Clorinda Kempton, Crissa Kempton, Cyrena Kempton, Dante Kempton, Destini Kempton, Emiko Kempton, Era Kempton, Gentry Kempton, Gini Kempton, Hanan Kempton, Haylee Kempton,
Hollee Kempton, Jannett Kempton, Javier Kempton, Jenay Kempton, Jennier Kempton, Kandee Kempton, Kerilyn Kempton, Kissy Kempton, Konstantina Kempton, Ladana Kempton, Logan Kempton, Lovette Kempton,
Manal Kempton, Marykay Kempton, Phoenix Kempton, Rosalin Kempton, Shatara Kempton, Shawnya Kempton, Sheralyn Kempton, Sheretta Kempton, Suann Kempton, Tava Kempton, Bobette Kempton, Carrissa Kempton,
Coralee Kempton, Daneille Kempton, Edwin Kempton, Emelda Kempton, Flecia Kempton, Jame Kempton, Janeane Kempton, Jelena Kempton, Katja Kempton, Kelia Kempton, Lanee Kempton, Laverna Kempton, Lorra
Kempton, Marlin Kempton, Mieke Kempton, Miroslava Kempton, Nekeisha Kempton, Nikeya Kempton, Noami Kempton, Saida Kempton, Sienna Kempton, Sundi Kempton, Tylene Kempton, Yakima Kempton, Alicha
Kempton, Amani Kempton, Armandina Kempton, Bethani Kempton, Carine Kempton, Carmencita Kempton, Chantee Kempton, Chavonne Kempton, Chinyere Kempton, Clarisse Kempton, Evett Kempton, Felisia Kempton,
Flossie Kempton, Indra Kempton, Inge Kempton, Keiko Kempton, Kristia Kempton, Lady Kempton, Latrelle Kempton, Lean Kempton, Lewanda Kempton, Marit Kempton, Melodye Kempton, Moneka Kempton, Naisha
Kempton, Najah Kempton, Ronisha Kempton, Shamona Kempton, Shantal Kempton, Sharay Kempton, Shawndell Kempton, Shekita Kempton, Shelah Kempton, Shenise Kempton, Soraida Kempton, Sujey Kempton, Suni
Kempton, Tiona Kempton, Tuwana Kempton, Wynetta Kempton, Angelie Kempton, Annalise Kempton, Carlen Kempton, Cherryl Kempton, Donnelle Kempton, Florencia Kempton, Gema Kempton, Genita Kempton, Happy
Kempton, Jessy Kempton, Karimah Kempton, Lanitra Kempton, Louanna Kempton, Maisie Kempton, Marco Kempton, Margaretta Kempton, Marguita Kempton, Marice Kempton, Marygrace Kempton, Retta Kempton,
Roderick Kempton, Ronny Kempton, Shalom Kempton, Sherena Kempton, Tamura Kempton, Threasa Kempton, Ulonda Kempton, Zachary Kempton, Aletta Kempton, Amaryllis Kempton, Amethyst Kempton, Antoinetta
Kempton, Aricka Kempton, Bobbyjo Kempton, Camile Kempton, Charyl Kempton, Elysa Kempton, Jameela Kempton, Jeannett Kempton, Jyl Kempton, Kinda Kempton, Kristianne Kempton, Latifah Kempton, Lavera
Kempton, Madaline Kempton, Marea Kempton, Melaina Kempton, Natesha Kempton, Oliva Kempton, Renell Kempton, Salli Kempton, Satina Kempton, Shanyn Kempton, Sharelle Kempton, Sharena Kempton, Shenetta
Kempton, Sherlonda Kempton, Sun Kempton, Teah Kempton, Teana Kempton, Tramaine Kempton, Wenda Kempton, Wyndi Kempton, Yoko Kempton, Adrean Kempton, Aishah Kempton, Aundra Kempton, Betsaida Kempton,
Chrisann Kempton, Clarita Kempton, Correna Kempton, Cynitha Kempton, Cythia Kempton, Damien Kempton, Dedria Kempton, Divina Kempton, Dody Kempton, Elanda Kempton, Elizbeth Kempton, Estrellita
Kempton, Eydie Kempton, Gerilyn Kempton, Hedy Kempton, Jacklynn Kempton, Kimberleigh Kempton, Kristinia Kempton, Lakeeta Kempton, Larie Kempton, Latrisa Kempton, Lesleigh Kempton, Marella Kempton,
Martinique Kempton, Melessia Kempton, Nicolasa Kempton, Quantina Kempton, Remy Kempton, Robina Kempton, Roya Kempton, Saba Kempton, Sacheen Kempton, Shalee Kempton, Sharlet Kempton, Shereese Kempton,
Sherronda Kempton, Shewanda Kempton, Skyla Kempton, Tallie Kempton, Tanganyika Kempton, Taressa Kempton, Tarshia Kempton, Timi Kempton, Zola Kempton, Ainsley Kempton, Alivia Kempton, Ardith Kempton,
Artina Kempton, Ashely Kempton, Athanasia Kempton, Chantale Kempton, Chimene Kempton, Corinn Kempton, Daffney Kempton, Danene Kempton, Daphnie Kempton, Deeanne Kempton, Erynn Kempton, Glennis
Kempton, Kalee Kempton, Kandyce Kempton, Kathren Kempton, Kelcey Kempton, Laticha Kempton, Lenee Kempton, Luvenia Kempton, Machele Kempton, Maris Kempton, Marisella Kempton, Nakeia Kempton, Nickey
Kempton, Nikkita Kempton, Noella Kempton, Peri Kempton, Raushanah Kempton, Renisha Kempton, Shahidah Kempton, Shakisha Kempton, Shevonne Kempton, Tashema Kempton, Tondalaya Kempton, Trinita Kempton,
Akiko Kempton, Alfredia Kempton, Bathsheba Kempton, Billye Kempton, Carter Kempton, Clementina Kempton, Danyele Kempton, Darnisha Kempton, Darryl Kempton, Eda Kempton, Emy Kempton, Faustina Kempton,
Hayden Kempton, Hortensia Kempton, Ivon Kempton, Javonna Kempton, Keita Kempton, Lakeisa Kempton, Lan Kempton, Leota Kempton, Letasha Kempton, Maggi Kempton, Monita Kempton, Nadirah Kempton, Nikka
Kempton, Noemy Kempton, Roxy Kempton, Sabrinia Kempton, Sanda Kempton, Sharan Kempton, Sharnette Kempton, Swati Kempton, Tiny Kempton, Tonjia Kempton, Trella Kempton, Venecia Kempton, Zana Kempton,
Zorana Kempton, Adrienna Kempton, Ama Kempton, Angelisa Kempton, Beckey Kempton, Bobbye Kempton, Cammi Kempton, Chequita Kempton, Clinton Kempton, Dama Kempton, Danee Kempton, Dari Kempton, Deandre
Kempton, Deetta Kempton, Devonda Kempton, Edelmira Kempton, Ieasha Kempton, Joylynn Kempton, Krisinda Kempton, Kristol Kempton, Kwana Kempton, Lacresia Kempton, Ladawna Kempton, Lavanda Kempton,
Lavena Kempton, Leaha Kempton, Massiel Kempton, Michiko Kempton, Naketa Kempton, Persephone Kempton, Raynell Kempton, Ronell Kempton, Shalynn Kempton, Shimeka Kempton, Shiquita Kempton, Tanaka
Kempton, Tomasita Kempton, Trixy Kempton, Tyson Kempton, Andy Kempton, Arden Kempton, Carlissa Kempton, Chery Kempton, Duane Kempton, Ereka Kempton, Gracia Kempton, Halona Kempton, Jamal Kempton,
Kechia Kempton, Kelda Kempton, Latessa Kempton, Lynett Kempton, Mikala Kempton, Naida Kempton, Nancee Kempton, Renna Kempton, Resha Kempton, Rifka Kempton, Rolinda Kempton, Shaneika Kempton, Syliva
Kempton, Tamikka Kempton, Tamyka Kempton, Tarika Kempton, Tawania Kempton, Trinda Kempton, Trinetta Kempton, Valrie Kempton, Anabela Kempton, Andretta Kempton, Capricia Kempton, Chistina Kempton,
Coree Kempton, Darrah Kempton, Diahann Kempton, Faigy Kempton, Georgiann Kempton, Hillarie Kempton, Ieisha Kempton, Joeann Kempton, Jovana Kempton, Kesa Kempton, Ladeana Kempton, Laresa Kempton,
Lisset Kempton, Lynnann Kempton, Lysette Kempton, Melenie Kempton, Natina Kempton, Nicolina Kempton, Queena Kempton, Tameaka Kempton, Tansy Kempton, Terressa Kempton, Topeka Kempton, Alicen Kempton,
Aneka Kempton, Arlyn Kempton, Bethzaida Kempton, Caralyn Kempton, Cartina Kempton, Cathlene Kempton, Chaquita Kempton, Clifford Kempton, Danitra Kempton, Dayana Kempton, Delania Kempton, Dennie
Kempton, Edina Kempton, Electra Kempton, Elouise Kempton, Ginelle Kempton, Heath Kempton, Kassia Kempton, Katrenia Kempton, Keidra Kempton, Laconda Kempton, Loura Kempton, Marchell Kempton, Mayela
Kempton, Merle Kempton, Merlinda Kempton, Mychelle Kempton, Nannie Kempton, Nikko Kempton, Nori Kempton, Prescilla Kempton, Rika Kempton, Ronika Kempton, Sahara Kempton, Sandrea Kempton, Senora
Kempton, Shawntee Kempton, Sheryll Kempton, Shina Kempton, Terre Kempton, Tinna Kempton, Tonnette Kempton, Torre Kempton, Tya Kempton, Vianey Kempton, Zora Kempton, Adonna Kempton, Alberto Kempton,
Almee Kempton, Ashanta Kempton, Bridgid Kempton, Cindia Kempton, Cricket Kempton, Darah Kempton, Dineen Kempton, Elan Kempton, Iman Kempton, Jacquelynne Kempton, Jennilyn Kempton, Jessicca Kempton,
Julio Kempton, Kenosha Kempton, Kimyata Kempton, Lanessa Kempton, Leesha Kempton, Letoya Kempton, Nkenge Kempton, Priti Kempton, Raizel Kempton, Rosaisela Kempton, Sameerah Kempton, Sera Kempton,
Shallon Kempton, Sharmane Kempton, Shauntay Kempton, Sherhonda Kempton, Shonnie Kempton, Sueanne Kempton, Taneesha Kempton, Telina Kempton, Tenecia Kempton, Tyanne Kempton, Alexsandra Kempton,
Angeles Kempton, Charlean Kempton, Danel Kempton, Davi Kempton, Daysha Kempton, Demaris Kempton, Dorenda Kempton, Dorita Kempton, Dorlisa Kempton, Genee Kempton, Jamella Kempton, Kathyjo Kempton,
Kaya Kempton, Latondra Kempton, Leshia Kempton, Mahala Kempton, Marija Kempton, Maudie Kempton, Megann Kempton, Phuong Kempton, Reesa Kempton, Ronya Kempton, Selinda Kempton, Shama Kempton, Shirell
Kempton, Shonita Kempton, Taiwana Kempton, Takenya Kempton, Talonda Kempton, Tassie Kempton, Telena Kempton, Theodore Kempton, Violetta Kempton, Willetta Kempton, Adora Kempton, Alvin Kempton,
Chauncey Kempton, Chrisy Kempton, Clancy Kempton, Claressa Kempton, Corrinna Kempton, Darra Kempton, Deshawna Kempton, Donise Kempton, Elona Kempton, Gara Kempton, Georgene Kempton, Gila Kempton,
Jania Kempton, Jocelynn Kempton, Joei Kempton, Kassy Kempton, Liset Kempton, Maleka Kempton, Mashell Kempton, Melida Kempton, Michalene Kempton, Moya Kempton, Nyisha Kempton, Rayanne Kempton, Renia
Kempton, Salima Kempton, Samanthia Kempton, Sammy Kempton, Santosha Kempton, Shaneeka Kempton, Shawntelle Kempton, Shwanda Kempton, Sita Kempton, Tarin Kempton, Tawn Kempton, Tosca Kempton, Valisha
Kempton, Vangie Kempton, Vernon Kempton, Zella Kempton, Amarilis Kempton, Amelie Kempton, Aubri Kempton, Bobbette Kempton, Byron Kempton, Chance Kempton, Deshon Kempton, Eraina Kempton, Jaycee
Kempton, Joyell Kempton, Keirsten Kempton, Kendi Kempton, Kendrea Kempton, Keyanna Kempton, Khristie Kempton, Kimberlyann Kempton, Kimyetta Kempton, Kinberly Kempton, Lakeita Kempton, Lakina Kempton,
Leida Kempton, Lenae Kempton, Mariette Kempton, Marymargaret Kempton, Meera Kempton, Micky Kempton, Naja Kempton, Oneka Kempton, Pedro Kempton, Rennie Kempton, Sharlee Kempton, Sharonne Kempton,
Shonya Kempton, Solange Kempton, Tashawn Kempton, Amorette Kempton, Andrienne Kempton, Ari Kempton, Carolin Kempton, Chalonda Kempton, Cinthya Kempton, Drusilla Kempton, Erendira Kempton, Franki
Kempton, Fredrick Kempton, Isaac Kempton, Jacklin Kempton, Jamese Kempton, Jeani Kempton, Josi Kempton, Jullie Kempton, Kadie Kempton, Kennetta Kempton, Keonna Kempton, Krisanne Kempton, Lakrisha
Kempton, Lakysha Kempton, Lasheka Kempton, Levette Kempton, Lexi Kempton, Lezlee Kempton, Lovely Kempton, Marah Kempton, Markeeta Kempton, Marlow Kempton, Meloni Kempton, Natausha Kempton, Nate
Kempton, Neoma Kempton, Nicci Kempton, Niema Kempton, Nykia Kempton, Oma Kempton, Quandra Kempton, Rasha Kempton, Shenelle Kempton, Sheryle Kempton, Sylena Kempton, Tasheba Kempton, Tennile Kempton,
Terriann Kempton, Tesia Kempton, Tuere Kempton, Tynika Kempton, Valena Kempton, Beverlee Kempton, Carriann Kempton, Chaney Kempton, Chantae Kempton, Charie Kempton, Cherell Kempton, Chrystina
Kempton, Cookie Kempton, Delphina Kempton, Denys Kempton, Digna Kempton, Doriann Kempton, Elecia Kempton, Elmira Kempton, Irina Kempton, Jacky Kempton, Jimmi Kempton, Joslin Kempton, Katty Kempton,
Kimberlin Kempton, Laquan Kempton, Latonga Kempton, Lauran Kempton, Lei Kempton, Maralee Kempton, Marilena Kempton, Markeisha Kempton, Mena Kempton, Mike Kempton, Nadeen Kempton, Ranelle Kempton,
Renika Kempton, Ritu Kempton, Roshawnda Kempton, Sandria Kempton, Shann Kempton, Shellene Kempton, Shemica Kempton, Shenandoah Kempton, Sherrye Kempton, Sholonda Kempton, Teka Kempton, Temica
Kempton, Thomasena Kempton, Vallerie Kempton, Velva Kempton, Annjanette Kempton, Arnitra Kempton, Asa Kempton, Barri Kempton, Deborha Kempton, Deshaun Kempton, Disa Kempton, Doree Kempton, Enrique
Kempton, Fredrika Kempton, Gisel Kempton, Jemima Kempton, Kellene Kempton, Kinsey Kempton, Lanice Kempton, Leonore Kempton, Liesel Kempton, Loredana Kempton, Lynita Kempton, Maeve Kempton, Michale
Kempton, Michalle Kempton, Nadira Kempton, Orlando Kempton, Radonna Kempton, Rivkah Kempton, Sanita Kempton, Shaketa Kempton, Shatika Kempton, Stepheny Kempton, Tashanda Kempton, Tashanna Kempton,
Thera Kempton, Vernette Kempton, Virna Kempton, Wanetta Kempton, Andee Kempton, Aparna Kempton, Armando Kempton, Brynne Kempton, Carolynne Kempton, Danyal Kempton, Drena Kempton, Faydra Kempton,
Felishia Kempton, Gwendalyn Kempton, Jennyfer Kempton, Jesika Kempton, Johnell Kempton, Kalen Kempton, Keelie Kempton, Kirby Kempton, Kristopher Kempton, Lynnett Kempton, Mikka Kempton, Moraima
Kempton, Nasha Kempton, Nechelle Kempton, Nelson Kempton, Rashawnda Kempton, Rianna Kempton, Rogina Kempton, Rudy Kempton, Schwanda Kempton, Serafina Kempton, Seth Kempton, Shantrice Kempton, Shenee
Kempton, Sherrel Kempton, Shirin Kempton, Soila Kempton, Sujata Kempton, Tannia Kempton, Tiya Kempton, Tonnie Kempton, Tuwanda Kempton, Young Kempton, Anjela Kempton, Aquanetta Kempton, Ardis
Kempton, Brigitta Kempton, Carmilla Kempton, Catherin Kempton, Charna Kempton, Chaunda Kempton, Chela Kempton, Cherylyn Kempton, Clifton Kempton, Danice Kempton, Daylene Kempton, Delecia Kempton,
Dell Kempton, Eleonora Kempton, Gesenia Kempton, Giana Kempton, Iisha Kempton, Jacqualyn Kempton, Jule Kempton, Kanita Kempton, Karrin Kempton, Keishia Kempton, Kerith Kempton, Kima Kempton, Letica
Kempton, Letta Kempton, Lucianna Kempton, Mala Kempton, Maresa Kempton, Michaeline Kempton, Mitra Kempton, Norene Kempton, Raul Kempton, Robi Kempton, Sativa Kempton, Shakeema Kempton, Shalisha
Kempton, Sherece Kempton, Sherlene Kempton, Talicia Kempton, Tinia Kempton, Toneka Kempton, Tuwanna Kempton, Tymeka Kempton, Vesna Kempton, Yvetta Kempton, Akeisha Kempton, Almeta Kempton, Alvita
Kempton, Ameerah Kempton, Amena Kempton, Anntoinette Kempton, Asusena Kempton, Benetta Kempton, Bernard Kempton, Bibiana Kempton, Bracha Kempton, Branden Kempton, Carrisa Kempton, Channell Kempton,
Christee Kempton, Daisey Kempton, Dandra Kempton, Dene Kempton, Destinee Kempton, Emmalee Kempton, Evamarie Kempton, Felicha Kempton, Hally Kempton, Harmonie Kempton, Ivone Kempton, Janira Kempton,
Jennfier Kempton, Josalyn Kempton, Karley Kempton, Kellyjo Kempton, Kinshasa Kempton, Laurena Kempton, Lewis Kempton, Louvenia Kempton, Lynley Kempton, Maleah Kempton, Marceline Kempton, Maree
Kempton, Maxie Kempton, Melora Kempton, Minta Kempton, Nella Kempton, Nikea Kempton, Orlanda Kempton, Radhika Kempton, Renelle Kempton, Robynne Kempton, Rosland Kempton, Saudia Kempton, Shannette
Kempton, Sharetta Kempton, Sharnita Kempton, Shequita Kempton, Tanessa Kempton, Tannis Kempton, Thu Kempton, Toiya Kempton, Umeka Kempton, Yadhira Kempton, Birdie Kempton, Bradi Kempton, Carola
Kempton, Chelle Kempton, Chermaine Kempton, Christelle Kempton, Cortnie Kempton, Dalinda Kempton, Daphene Kempton, Demetri Kempton, Ennifer Kempton, Esta Kempton, Francheska Kempton, Griselle
Kempton, Ife Kempton, Jahaira Kempton, Jammi Kempton, Javonne Kempton, Jenie Kempton, Jocelin Kempton, Karole Kempton, Kelee Kempton, Khrista Kempton, Leya Kempton, Luwanda Kempton, Makayla Kempton,
Marly Kempton, Nzinga Kempton, Paquita Kempton, Ramanda Kempton, Rayleen Kempton, Rinda Kempton, Shauntell Kempton, Tamecka Kempton, Tanji Kempton, Tela Kempton, Teneisha Kempton, Valicia Kempton,
Willona Kempton, Alejandro Kempton, Ameka Kempton, Ashante Kempton, Brisa Kempton, Charli Kempton, Charmagne Kempton, Charrise Kempton, Crystol Kempton, Darya Kempton, Destiney Kempton, Elidia
Kempton, France Kempton, Galadriel Kempton, Genifer Kempton, Gladis Kempton, Glori Kempton, Harriette Kempton, Ioanna Kempton, Jeanann Kempton, Kittie Kempton, Ladon Kempton, Latesa Kempton, Linn
Kempton, Loralie Kempton, Mazie Kempton, Mekisha Kempton, Nivia Kempton, Paulene Kempton, Renette Kempton, Saadia Kempton, Shakena Kempton, Sheritta Kempton, Stepahnie Kempton, Taliah Kempton,
Teretha Kempton, Tessy Kempton, Wendelyn Kempton, Zonia Kempton, Ailsa Kempton, Alonna Kempton, Andres Kempton, Asma Kempton, Austin Kempton, Brandis Kempton, Corinda Kempton, Deetra Kempton, Dyanne
Kempton, Eliabeth Kempton, Evelynn Kempton, Geana Kempton, Geeta Kempton, Georgeanne Kempton, Glynnis Kempton, Hilari Kempton, Hindy Kempton, Jackquline Kempton, Joaquina Kempton, Jolynne Kempton,
Kirsta Kempton, Latissa Kempton, Lucile Kempton, Makeisha Kempton, Marli Kempton, Meeghan Kempton, Michaelyn Kempton, Monte Kempton, Omeka Kempton, Patra Kempton, Ragen Kempton, Reshma Kempton,
Ronnell Kempton, Shakera Kempton, Shantella Kempton, Shar Kempton, Shelagh Kempton, Sherisse Kempton, Slyvia Kempton, Stephenia Kempton, Tarisha Kempton, Tria Kempton, Tynetta Kempton, Veena Kempton,
Aleksandra Kempton, Analia Kempton, Aneshia Kempton, Anesia Kempton, Anissia Kempton, Caroll Kempton, Celisa Kempton, Chariti Kempton, Charnette Kempton, Cheria Kempton, Dabney Kempton, Davon
Kempton, Demita Kempton, Denny Kempton, Dwanda Kempton, Erick Kempton, Fancy Kempton, Felesha Kempton, Genette Kempton, Graziella Kempton, Helaine Kempton, Huong Kempton, Idania Kempton, Ilsa
Kempton, Iola Kempton, Janifer Kempton, Jaynie Kempton, Jil Kempton, Joyann Kempton, Kalina Kempton, Kana Kempton, Katheleen Kempton, Kelie Kempton, Kimbly Kempton, Ladina Kempton, Lamisha Kempton,
Landra Kempton, Laretha Kempton, Lashuna Kempton, Latorsha Kempton, Lehua Kempton, Libbie Kempton, Loris Kempton, Lovetta Kempton, Marilin Kempton, Marquis Kempton, Medea Kempton, Michaella Kempton,
Milly Kempton, Montina Kempton, Muna Kempton, Nickcole Kempton, Nickia Kempton, Quianna Kempton, Retina Kempton, Rubina Kempton, Sallyann Kempton, Sangeeta Kempton, Shalinda Kempton, Shatonya
Kempton, Tamasha Kempton, Tenise Kempton, Terrilynn Kempton, Teya Kempton, Toma Kempton, Trang Kempton, Vienna Kempton, Zenda Kempton, Amisha Kempton, Chenell Kempton, Cherene Kempton, Chimere
Kempton, Darcell Kempton, Desa Kempton, Devi Kempton, Dove Kempton, Eilene Kempton, Jarita Kempton, Jenetta Kempton, Johnie Kempton, Kanani Kempton, Kanya Kempton, Katiria Kempton, Kenyon Kempton,
Khristi Kempton, Kidada Kempton, Kristien Kempton, Laressa Kempton, Lashonta Kempton, Lataisha Kempton, Leanda Kempton, Leshonda Kempton, Letia Kempton, Lorenzo Kempton, Makenzie Kempton, Manya
Kempton, Maribelle Kempton, Maryjean Kempton, Moniqua Kempton, Myeisha Kempton, Mystie Kempton, Nakeesha Kempton, Neeley Kempton, Neil Kempton, Nida Kempton, Oletha Kempton, Rebel Kempton, Rosaland
Kempton, Satonya Kempton, Shanah Kempton, Sherly Kempton, Sherrilyn Kempton, Shonia Kempton, Shuna Kempton, Shylah Kempton, Tameisha Kempton, Telecia Kempton, Terrill Kempton, Torry Kempton, Tracyann
Kempton, Undrea Kempton, Usha Kempton, Velicia Kempton, Windie Kempton, Yehudis Kempton, Ameenah Kempton, Amika Kempton, Anupama Kempton, Bethaney Kempton, Brookie Kempton, Bryce Kempton, Cherika
Kempton, Courtni Kempton, Danyle Kempton, Darilyn Kempton, Darnita Kempton, Eveline Kempton, Gilbert Kempton, Giovanni Kempton, Jacquel Kempton, Jenai Kempton, Jocelyne Kempton, Jull Kempton, Karene
Kempton, Karisha Kempton, Kelvin Kempton, Kenzie Kempton, Kimblery Kempton, Kyleen Kempton, Laketta Kempton, Larisha Kempton, Lashae Kempton, Laveta Kempton, Lezli Kempton, Marlynn Kempton, Melana
Kempton, Meribeth Kempton, Onita Kempton, Philicia Kempton, Raychel Kempton, Roschelle Kempton, Rosilyn Kempton, Sandhya Kempton, Selenia Kempton, Seretha Kempton, Shadia Kempton, Shalise Kempton,
Sonnet Kempton, Tacey Kempton, Taurus Kempton, Telly Kempton, Tenita Kempton, Tiawana Kempton, Timica Kempton, Warren Kempton, Yamile Kempton, Yaminah Kempton, Adel Kempton, Aiyana Kempton, Amybeth
Kempton, Angee Kempton, Angeligue Kempton, Areli Kempton, Asheley Kempton, Bina Kempton, Celines Kempton, Charlet Kempton, Charley Kempton, Charonda Kempton, Dameka Kempton, Danne Kempton, Deloise
Kempton, Denay Kempton, Denene Kempton, Donata Kempton, Georgianne Kempton, Jamelia Kempton, Jennetta Kempton, Jesusa Kempton, Johnda Kempton, Juleen Kempton, Khaliah Kempton, Kimala Kempton, Kimble
Kempton, Kimmarie Kempton, Korene Kempton, Lezley Kempton, Lindie Kempton, Lorilyn Kempton, Mayme Kempton, Meeka Kempton, Natlie Kempton, Ranita Kempton, Rasheen Kempton, Rayetta Kempton, Savina
Kempton, Scarlette Kempton, Shaindy Kempton, Sheana Kempton, Sheldon Kempton, Shoni Kempton, Stephan Kempton, Taneeka Kempton, Tanesia Kempton, Tannya Kempton, Tionna Kempton, Tresia Kempton, Tylisha
Kempton, Vonita Kempton, Vonnetta Kempton, Wren Kempton, Akiba Kempton, Blaire Kempton, Buffey Kempton, Candita Kempton, Charnelle Kempton, Cynda Kempton, Danesha Kempton, Darbie Kempton, Deah
Kempton, Deette Kempton, Devita Kempton, Devonia Kempton, Dianah Kempton, Dustina Kempton, Dylan Kempton, Elli Kempton, Eun Kempton, Geneen Kempton, Geni Kempton, Jenevieve Kempton, Julaine Kempton,
Kaitlyn Kempton, Lalania Kempton, Latrise Kempton, Mahalia Kempton, Manon Kempton, Marycatherine Kempton, Nyasha Kempton, Orlena Kempton, Petina Kempton, Precilla Kempton, Raenell Kempton, Ramonica
Kempton, Reema Kempton, Scotti Kempton, Shakeya Kempton, Shaylene Kempton, Shenique Kempton, Shimika Kempton, Takiesha Kempton, Tambi Kempton, Tammatha Kempton, Tauheedah Kempton, Timiko Kempton,
Tomisha Kempton, Venesa Kempton, Venise Kempton, Akesha Kempton, Anmarie Kempton, Arnette Kempton, Brennan Kempton, Cayla Kempton, Cecil Kempton, Coreena Kempton, Danessa Kempton, Day Kempton, Denni
Kempton, Fernando Kempton, Floretta Kempton, Fred Kempton, Gardenia Kempton, Genevie Kempton, Georgann Kempton, Grasiela Kempton, Jaimy Kempton, Jaquelyn Kempton, Jerelyn Kempton, Jinnifer Kempton,
Johnelle Kempton, Jovonna Kempton, Kady Kempton, Keala Kempton, Kesi Kempton, Kyana Kempton, Laketia Kempton, Laquanta Kempton, Latoy Kempton, Laurine Kempton, Lynea Kempton, Lynee Kempton, Maegen
Kempton, Margarite Kempton, Marijane Kempton, Mellany Kempton, Monia Kempton, Monice Kempton, Mylene Kempton, Nakiya Kempton, Neila Kempton, Oleta Kempton, Queenie Kempton, Quinetta Kempton, Rekha
Kempton, Remi Kempton, Rickey Kempton, Roselynn Kempton, Samanatha Kempton, Shakila Kempton, Shalandra Kempton, Shamira Kempton, Shandel Kempton, Shandrea Kempton, Shinita Kempton, Stayce Kempton,
Takela Kempton, Talibah Kempton, Tameria Kempton, Taronda Kempton, Telia Kempton, Ticia Kempton, Tovah Kempton, Venissa Kempton, Verlinda Kempton, Vittoria Kempton, Alicyn Kempton, Amylynn Kempton,
Anabell Kempton, Anela Kempton, Annice Kempton, Aubry Kempton, Coralie Kempton, Coryn Kempton, Darlyn Kempton, Dejuana Kempton, Eleana Kempton, Esmerelda Kempton, Georganne Kempton, Jacqlyn Kempton,
Jodine Kempton, Joelyn Kempton, Josey Kempton, Keanna Kempton, Kendy Kempton, Korine Kempton, Kristianna Kempton, Laneka Kempton, Lannie Kempton, Mathilda Kempton, Myiesha Kempton, Nessa Kempton,
Nikiya Kempton, Penina Kempton, Radha Kempton, Ralonda Kempton, Shantele Kempton, Sharlette Kempton, Shelanda Kempton, Shelda Kempton, Shere Kempton, Shuntel Kempton, Stephaney Kempton, Tabbitha
Kempton, Tamkia Kempton, Teona Kempton, Terrisa Kempton, Teryl Kempton, Trellis Kempton, Vanissa Kempton, Abigale Kempton, Bonnita Kempton, Carren Kempton, Clementine Kempton, Coni Kempton, Demonica
Kempton, Denis Kempton, Diantha Kempton, Edana Kempton, Elene Kempton, Faithe Kempton, Franklin Kempton, Haidee Kempton, Jaima Kempton, Javonda Kempton, Jayma Kempton, Jeffifer Kempton, Jennel
Kempton, Jennfer Kempton, Katryna Kempton, Keta Kempton, Kristyne Kempton, Krystle Kempton, Kymberlee Kempton, Kymberli Kempton, Lacole Kempton, Laranda Kempton, Leea Kempton, Loryn Kempton, Lyndell
Kempton, Lyndy Kempton, Mande Kempton, Marlissa Kempton, Marrissa Kempton, Meko Kempton, Miryam Kempton, Neida Kempton, Odilia Kempton, Pamila Kempton, Porscha Kempton, Quentina Kempton, Riley
Kempton, Roselia Kempton, Sharifah Kempton, Sonyia Kempton, Sugar Kempton, Tamico Kempton, Tanara Kempton, Tiombe Kempton, Verity Kempton, Zoey Kempton, Abril Kempton, Aine Kempton, Aixa Kempton,
Ange Kempton, Annah Kempton, Avelina Kempton, Chantil Kempton, Charmel Kempton, Cheralyn Kempton, Chesley Kempton, Colin Kempton, Cornelius Kempton, Cortni Kempton, Deserae Kempton, Dru Kempton,
Emeline Kempton, Iran Kempton, Jesslyn Kempton, Jovon Kempton, Kalani Kempton, Kaleen Kempton, Kamilla Kempton, Kemi Kempton, Kendrick Kempton, Lachele Kempton, Letesha Kempton, Makita Kempton,
Maricia Kempton, Mariya Kempton, Marlise Kempton, Nara Kempton, Ngina Kempton, Nikkol Kempton, Okema Kempton, Palma Kempton, Priscillia Kempton, Ranell Kempton, Rashmi Kempton, Renessa Kempton,
Ricarda Kempton, Rozlyn Kempton, Shamia Kempton, Sharissa Kempton, Shianne Kempton, Takeesha Kempton, Tekia Kempton, Tyhesha Kempton, Vanassa Kempton, Vicenta Kempton, Abagail Kempton, Addy Kempton,
Akemi Kempton, Analilia Kempton, Andreanna Kempton, Anh Kempton, Annmargaret Kempton, Caitlyn Kempton, Carrin Kempton, Celestial Kempton, Chameka Kempton, Chandrika Kempton, Charlsie Kempton,
Cherlynn Kempton, Darien Kempton, Darlean Kempton, Devyn Kempton, Dyane Kempton, Eman Kempton, Erna Kempton, Fontella Kempton, Halie Kempton, Ilyse Kempton, Janece Kempton, Jayla Kempton, Jeannene
Kempton, Juwana Kempton, Kachina Kempton, Keleigh Kempton, Kissie Kempton, Krisi Kempton, Kristyl Kempton, Krystie Kempton, Kyesha Kempton, Lizandra Kempton, Lyda Kempton, Majorie Kempton, Marnita
Kempton, Marrisa Kempton, Miguelina Kempton, Nadege Kempton, Nakiesha Kempton, Neesha Kempton, Raeleen Kempton, Rashana Kempton, Renada Kempton, Rupa Kempton, Shaunette Kempton, Sheetal Kempton,
Sherryann Kempton, Tanecia Kempton, Tashiba Kempton, Tawney Kempton, Telma Kempton, Tomeeka Kempton, Xochil Kempton, Yuki Kempton, Ahna Kempton, Aneesha Kempton, Aphrodite Kempton, Areatha Kempton,
Cam Kempton, Chalene Kempton, Charnetta Kempton, Clarise Kempton, Cleta Kempton, Danniel Kempton, Deshana Kempton, Eduardo Kempton, Erminia Kempton, Eron Kempton, Hettie Kempton, Janan Kempton, Janda
Kempton, Jayda Kempton, Jeanny Kempton, Katanya Kempton, Kaylin Kempton, Keeva Kempton, Kimesha Kempton, Kristeena Kempton, Kristyna Kempton, Lakeyshia Kempton, Latesia Kempton, Latoia Kempton,
Lavona Kempton, Lonni Kempton, Loukisha Kempton, Manika Kempton, Marbella Kempton, Marcina Kempton, Marialuisa Kempton, Mariellen Kempton, Mariluz Kempton, Mikia Kempton, Morning Kempton, Myndi
Kempton, Ronalda Kempton, Shanitra Kempton, Sherea Kempton, Shericka Kempton, Sonny Kempton, Suzane Kempton, Terea Kempton, Tersa Kempton, Yarnell Kempton, Yezenia Kempton, Zona Kempton, Alissia
Kempton, Anjenette Kempton, Antwan Kempton, Bernette Kempton, Cedar Kempton, Chandria Kempton, Cherina Kempton, Chrisandra Kempton, Christiann Kempton, Cosandra Kempton, Danea Kempton, Demetress
Kempton, Emmeline Kempton, Ernesta Kempton, Fabiana Kempton, Fabienne Kempton, Falecia Kempton, Georgena Kempton, Gerardo Kempton, Gwynn Kempton, Heavenly Kempton, Ivett Kempton, Jaya Kempton,
Jessicia Kempton, Jetaun Kempton, Joane Kempton, Kalliopi Kempton, Kalynn Kempton, Karmon Kempton, Kischa Kempton, Kita Kempton, Lanea Kempton, Laron Kempton, Latonyia Kempton, Lavone Kempton, Leasha
Kempton, Liann Kempton, Madelyne Kempton, Malissia Kempton, Margit Kempton, Marlowe Kempton, Mashonda Kempton, Meggen Kempton, Merari Kempton, Michille Kempton, Missi Kempton, Nichoel Kempton, Nikie
Kempton, Nyssa Kempton, Pooja Kempton, Purvi Kempton, Ryane Kempton, Sakeenah Kempton, Sam Kempton, Shaquan Kempton, Sharmel Kempton, Shlonda Kempton, Tamsen Kempton, Tikia Kempton, Tomicka Kempton,
Tremeka Kempton, Wenonah Kempton, Yavonne Kempton, Adraine Kempton, Aiysha Kempton, Akila Kempton, Almira Kempton, Alnita Kempton, Ambrosia Kempton, Aminta Kempton, Anedra Kempton, Angeliki Kempton,
Aymee Kempton, Barrett Kempton, Batina Kempton, Brandey Kempton, Brena Kempton, Bryant Kempton, Charidy Kempton, Davona Kempton, Delissa Kempton, Denea Kempton, Denicia Kempton, Deniese Kempton,
Desta Kempton, Dimple Kempton, Emelie Kempton, Eustacia Kempton, Farra Kempton, Giulia Kempton, Jannetta Kempton, Jen Kempton, Jennice Kempton, Kareemah Kempton, Kaysie Kempton, Latice Kempton,
Letanya Kempton, Liticia Kempton, Luna Kempton, Madge Kempton, Marielena Kempton, Merrily Kempton, Mitsy Kempton, Nachelle Kempton, Nolita Kempton, Palmira Kempton, Parthenia Kempton, Ramey Kempton,
Raymona Kempton, Rhodesia Kempton, Sanna Kempton, Shakema Kempton, Shamieka Kempton, Shandria Kempton, Shaniece Kempton, Sharronda Kempton, Sheletha Kempton, Shoshannah Kempton, Suprina Kempton,
Tanyia Kempton, Tarri Kempton, Tequita Kempton, Thressa Kempton, Twala Kempton, Tyneshia Kempton, Willena Kempton, Aaryn Kempton, Ailene Kempton, Alfredo Kempton, Alinda Kempton, Avia Kempton,
Brandelyn Kempton, Brandolyn Kempton, Brieanna Kempton, Brittanie Kempton, Celest Kempton, Charman Kempton, Chenise Kempton, Colandra Kempton, Damari Kempton, Donni Kempton, Dorice Kempton, Dustine
Kempton, Elease Kempton, Jamara Kempton, Jameca Kempton, Jessalyn Kempton, Joyanna Kempton, Kalia Kempton, Kennisha Kempton, Kewanna Kempton, Krystel Kempton, Lashara Kempton, Leslieann Kempton,
Letetia Kempton, Letizia Kempton, Lisanne Kempton, Lovella Kempton, Maranatha Kempton, Melisia Kempton, Meriah Kempton, Monaca Kempton, Myrtis Kempton, Nadean Kempton, Naila Kempton, Narissa Kempton,
Natale Kempton, Nealy Kempton, November Kempton, Petrice Kempton, Renie Kempton, Robecca Kempton, Sarra Kempton, Shakeena Kempton, Shalunda Kempton, Sharin Kempton, Shatoya Kempton, Soni Kempton,
Sulma Kempton, Taffany Kempton, Tahara Kempton, Taralynn Kempton, Tarena Kempton, Tatyana Kempton, Tekeisha Kempton, Timothea Kempton, Tishana Kempton, Toshua Kempton, Tresea Kempton, Tykisha
Kempton, Varonica Kempton, Yolinda Kempton, Adra Kempton, Amia Kempton, Aquarius Kempton, Baila Kempton, Betheny Kempton, Cady Kempton, Calla Kempton, Catrinia Kempton, Chanika Kempton, Chellie
Kempton, Chelsy Kempton, Christana Kempton, Cicley Kempton, Crescent Kempton, Deronda Kempton, Diamantina Kempton, Dyani Kempton, Elvina Kempton, Emiley Kempton, Haneefah Kempton, Ivan Kempton,
Jamesetta Kempton, Janele Kempton, Jolean Kempton, Jory Kempton, Julieanna Kempton, Jyoti Kempton, Kaela Kempton, Katena Kempton, Kaycie Kempton, Kismet Kempton, Kobi Kempton, Lakechia Kempton,
Lakesa Kempton, Lalanya Kempton, Latiesha Kempton, Lauralyn Kempton, Lekita Kempton, Loletha Kempton, Lonetta Kempton, Lukisha Kempton, Mele Kempton, Nadra Kempton, Natia Kempton, Ngozi Kempton, Nija
Kempton, October Kempton, Olinda Kempton, Preeti Kempton, Raine Kempton, Ronie Kempton, Sharlie Kempton, Sharnetta Kempton, Shontia Kempton, Tamakia Kempton, Taquita Kempton, Temeca Kempton, Tenna
Kempton, Teresea Kempton, Teryn Kempton, Tessica Kempton, Trayce Kempton, Tujuana Kempton, Alys Kempton, Aris Kempton, Asya Kempton, Atina Kempton, Ayonna Kempton, Cherl Kempton, Corretta Kempton,
Cybill Kempton, Gaylynn Kempton, Heatherly Kempton, Jacquelina Kempton, Jeanean Kempton, Jeniece Kempton, Johnathan Kempton, Krystine Kempton, Larua Kempton, Lelah Kempton, Lilla Kempton, Linh
Kempton, Lisia Kempton, Lucilla Kempton, Malita Kempton, Matisha Kempton, Melika Kempton, Merci Kempton, Mishell Kempton, Monae Kempton, Monee Kempton, Montrice Kempton, Najla Kempton, Parrish
Kempton, Ramsey Kempton, Raya Kempton, Rejeana Kempton, Roanna Kempton, Roxan Kempton, Shai Kempton, Shanen Kempton, Sharalyn Kempton, Shuntay Kempton, Taheerah Kempton, Takeysha Kempton, Tamelia
Kempton, Tanyika Kempton, Temperance Kempton, Theodosia Kempton, Thyra Kempton, Tyria Kempton, Urania Kempton, Yvett Kempton, Angelynn Kempton, Anitria Kempton, Anny Kempton, Arlisha Kempton, Aya
Kempton, Brielle Kempton, Careen Kempton, Correne Kempton, Dagmar Kempton, Dalynn Kempton, Dannetta Kempton, Delight Kempton, Denetta Kempton, Desaree Kempton, Donyel Kempton, Eisha Kempton, Eleanora
Kempton, Felix Kempton, Fransisca Kempton, Jannel Kempton, Jenia Kempton, Jettie Kempton, Jolina Kempton, Jowanna Kempton, Junko Kempton, Kaaren Kempton, Kathey Kempton, Keryn Kempton, Ketina
Kempton, Korrine Kempton, Kristalyn Kempton, Laini Kempton, Lamona Kempton, Lanay Kempton, Leza Kempton, Maddalena Kempton, Mellody Kempton, Merica Kempton, Merita Kempton, Nafeesa Kempton, Nicholl
Kempton, Oneika Kempton, Pamelyn Kempton, Romonda Kempton, Ronique Kempton, Rosslyn Kempton, Rosy Kempton, Sachiko Kempton, Sarajane Kempton, Satara Kempton, Shamra Kempton, Tamberly Kempton, Tawona
Kempton, Tiasha Kempton, Tine Kempton, Trameka Kempton, Tynia Kempton, Valentine Kempton, Venisha Kempton, Veronia Kempton, Vinnie Kempton, Yuri Kempton, Aissa Kempton, Aleda Kempton, Amenda Kempton,
Andromeda Kempton, Antigone Kempton, Aren Kempton, Ariadne Kempton, Bambie Kempton, Belkis Kempton, Bunnie Kempton, Claudina Kempton, Darcelle Kempton, Dulcinea Kempton, Enola Kempton, Florida
Kempton, Francia Kempton, Ginni Kempton, Grizelda Kempton, Israel Kempton, Jalynn Kempton, Jamil Kempton, Jenika Kempton, Joeanna Kempton, Katesha Kempton, Katreena Kempton, Keilani Kempton, Kiah
Kempton, Kjersti Kempton, Korrin Kempton, Leonda Kempton, Liesa Kempton, Lyna Kempton, Manuelita Kempton, Marka Kempton, Markia Kempton, Maronda Kempton, Melondy Kempton, Melonee Kempton, Micheala
Kempton, Misa Kempton, Nikeisha Kempton, Odalys Kempton, Parul Kempton, Petula Kempton, Rainee Kempton, Rainie Kempton, Romi Kempton, Rubie Kempton, Shamone Kempton, Shawnia Kempton, Sheritha
Kempton, Shery Kempton, Tamula Kempton, Tasheena Kempton, Thao Kempton, Thereasa Kempton, Tjuana Kempton, Tomesha Kempton, Turquoise Kempton, Tyiesha Kempton, Vernee Kempton, Annastasia Kempton,
Ardra Kempton, Bibi Kempton, Blaine Kempton, Bridie Kempton, Carmelle Kempton, Chalice Kempton, Chanie Kempton, Chauntelle Kempton, Dareth Kempton, Demitria Kempton, Denetria Kempton, Didi Kempton,
Dimitria Kempton, Dwight Kempton, Elisabetta Kempton, Ellisha Kempton, Ileen Kempton, Jamala Kempton, Jayleen Kempton, Jeny Kempton, Jeraldine Kempton, Jowanda Kempton, Joylene Kempton, Kareena
Kempton, Karrah Kempton, Kashonda Kempton, Kendel Kempton, Ketrina Kempton, Lagena Kempton, Lashann Kempton, Lasheena Kempton, Latish Kempton, Leroy Kempton, Maryum Kempton, Mende Kempton, Mieka
Kempton, Nakea Kempton, Niurka Kempton, Philippa Kempton, Pina Kempton, Romanda Kempton, Satrina Kempton, Shaletha Kempton, Shandrika Kempton, Shawonda Kempton, Sherae Kempton, Shernita Kempton,
Sheronica Kempton, Silena Kempton, Sora Kempton, Stehanie Kempton, Tanikka Kempton, Tashi Kempton, Tawyna Kempton, Tenesia Kempton, Tikesha Kempton, Trenell Kempton, Tristina Kempton, Vallie Kempton,
Verla Kempton, Vinessa Kempton, Walida Kempton, Yolandra Kempton, Aarti Kempton, Aries Kempton, Bayyinah Kempton, Bertie Kempton, Blakely Kempton, Cabrina Kempton, Chandrea Kempton, Cherrell Kempton,
Chiquitta Kempton, Damarys Kempton, Danett Kempton, Dedee Kempton, Demesha Kempton, Denica Kempton, Derinda Kempton, Deshanda Kempton, Diondra Kempton, Edgar Kempton, Ewa Kempton, Grabiela Kempton,
Jeanifer Kempton, Jemma Kempton, Jetta Kempton, Jodelle Kempton, Joeleen Kempton, Johari Kempton, Kasaundra Kempton, Kewana Kempton, Kieran Kempton, Kitina Kempton, Kitrina Kempton, Lacheryl Kempton,
Lakeishia Kempton, Lasean Kempton, Lashawne Kempton, Lashica Kempton, Latanga Kempton, Latreece Kempton, Latysha Kempton, Leonna Kempton, Lilli Kempton, Lititia Kempton, Lorette Kempton, Makala
Kempton, Mea Kempton, Mendie Kempton, Meosha Kempton, Milessa Kempton, Nathasha Kempton, Nefertari Kempton, Nieves Kempton, Odelia Kempton, Phylis Kempton, Phyliss Kempton, Rami Kempton, Shaena
Kempton, Shahara Kempton, Shajuan Kempton, Shalane Kempton, Shamaine Kempton, Shaquanna Kempton, Shauntelle Kempton, Sheril Kempton, Sherley Kempton, Shuronda Kempton, Sicily Kempton, Sindi Kempton,
Sonni Kempton, Tamantha Kempton, Tejal Kempton, Tenley Kempton, Tongela Kempton, Trenita Kempton, Vernica Kempton, Ameena Kempton, Chancey Kempton, Chandi Kempton, Charelle Kempton, Cherisa Kempton,
Corby Kempton, Corianne Kempton, Crystale Kempton, Cyd Kempton, Cyndie Kempton, Dagny Kempton, Daine Kempton, Darin Kempton, Debralee Kempton, Delanda Kempton, Donta Kempton, Estefana Kempton,
Falesha Kempton, Fawna Kempton, Galen Kempton, Geanine Kempton, Grazia Kempton, Hala Kempton, Jadie Kempton, Jalyn Kempton, Jamilia Kempton, Jannice Kempton, Jasmina Kempton, Jehan Kempton, Joannah
Kempton, Joclyn Kempton, Julietta Kempton, Kody Kempton, Krisa Kempton, Lanaya Kempton, Laray Kempton, Larra Kempton, Larrissa Kempton, Leanora Kempton, Lelania Kempton, Lenetta Kempton, Lizett
Kempton, Lonnette Kempton, Lorey Kempton, Lynann Kempton, Madalena Kempton, Marlita Kempton, Marrianne Kempton, Maylene Kempton, Merida Kempton, Midori Kempton, Nafeesah Kempton, Nekeshia Kempton,
Parris Kempton, Payal Kempton, Perlita Kempton, Prairie Kempton, Raeanna Kempton, Rayette Kempton, Sabriya Kempton, Sadia Kempton, Sequita Kempton, Sharine Kempton, Sharlena Kempton, Spencer Kempton,
Sugey Kempton, Taheera Kempton, Taiwan Kempton, Tameki Kempton, Tamme Kempton, Tawonda Kempton, Toscha Kempton, Tyronza Kempton, Valeska Kempton, Vannesa Kempton, Vashon Kempton, Viktoria Kempton,
Vonya Kempton, Akita Kempton, Andraya Kempton, Anecia Kempton, Annjeanette Kempton, Antonya Kempton, Brette Kempton, Chase Kempton, Chena Kempton, Cheris Kempton, Chirstine Kempton, Claude Kempton,
Clayton Kempton, Clea Kempton, Clorissa Kempton, Consuello Kempton, Cosette Kempton, Darinda Kempton, Dawnn Kempton, Delene Kempton, Deneka Kempton, Geisha Kempton, Gwendelyn Kempton, Hyacinth
Kempton, Ilia Kempton, Jacqulin Kempton, Jaynee Kempton, Jennifr Kempton, Kaysha Kempton, Keiana Kempton, Kelsy Kempton, Keziah Kempton, Lakaisha Kempton, Lashawndra Kempton, Lennette Kempton, Loran
Kempton, Margarete Kempton, Marquise Kempton, Marvel Kempton, Maurica Kempton, Mikell Kempton, Nya Kempton, Odetta Kempton, Raizy Kempton, Samika Kempton, Scotty Kempton, Senita Kempton, Shasha
Kempton, Shaton Kempton, Sheilla Kempton, Shital Kempton, Shonika Kempton, Silver Kempton, Tabathia Kempton, Tabby Kempton, Taniya Kempton, Tawonna Kempton, Teddy Kempton, Tenicia Kempton, Teodora
Kempton, Tessia Kempton, Tinya Kempton, Travia Kempton, Trivia Kempton, Verda Kempton, Veta Kempton, Waneta Kempton, Ysenia Kempton, Yumiko Kempton, Zully Kempton, Adeana Kempton, Adenike Kempton,
Afton Kempton, Angeli Kempton, Anicia Kempton, Arron Kempton, Artie Kempton, Ashlei Kempton, Ayme Kempton, Brieanne Kempton, Cira Kempton, Cynthea Kempton, Damiana Kempton, Darlynn Kempton, Dennette
Kempton, Doreena Kempton, Dorris Kempton, Dorsey Kempton, Drew Kempton, Drina Kempton, Enrika Kempton, Genean Kempton, Glendora Kempton, Gwendlyn Kempton, Hedi Kempton, Honesty Kempton, Jackalyn
Kempton, Jillyn Kempton, Jode Kempton, Joshlyn Kempton, Joylyn Kempton, Jullian Kempton, Kajuana Kempton, Kasee Kempton, Kimberla Kempton, Kjersten Kempton, Kortni Kempton, Latronda Kempton, Leonie
Kempton, Lonette Kempton, Lonita Kempton, Lynnelle Kempton, Marenda Kempton, Marybelle Kempton, Paisley Kempton, Patrena Kempton, Rheannon Kempton, Rochella Kempton, Saleemah Kempton, Samala Kempton,
Shannie Kempton, Shelitha Kempton, Shemeika Kempton, Shenia Kempton, Shinika Kempton, Shunte Kempton, Sia Kempton, Sinead Kempton, Tal Kempton, Tata Kempton, Teela Kempton, Tita Kempton, Verenice
Kempton, Wade Kempton, Yesica Kempton, Zaira Kempton, Zuri Kempton, Bobie Kempton, Brendalee Kempton, Carolanne Kempton, Chevette Kempton, Debera Kempton, Denessa Kempton, Desiray Kempton, Destinie
Kempton, Diania Kempton, Edra Kempton, Ekaterini Kempton, Elane Kempton, Eudora Kempton, Evelyne Kempton, Franci Kempton, Gussie Kempton, Herbert Kempton, Ilse Kempton, Jaquay Kempton, Jerra Kempton,
Juliene Kempton, Kashia Kempton, Kirstan Kempton, Laconya Kempton, Lajoyce Kempton, Larraine Kempton, Lera Kempton, Loan Kempton, Luwana Kempton, Maire Kempton, Malene Kempton, Marca Kempton, Marcene
Kempton, Mathew Kempton, Mayumi Kempton, Nakeysha Kempton, Orpha Kempton, Quinta Kempton, Robie Kempton, Sarha Kempton, Selah Kempton, Sergio Kempton, Shalaine Kempton, Shazia Kempton, Shenae
Kempton, Shenica Kempton, Shineka Kempton, Sonnie Kempton, Tashauna Kempton, Tashica Kempton, Tatjana Kempton, Tecia Kempton, Therisa Kempton, Tracina Kempton, Tressia Kempton, Vallery Kempton,
Ximena Kempton, Aidee Kempton, Alpa Kempton, Ambur Kempton, Annaliese Kempton, Atasha Kempton, Ave Kempton, Barbaraann Kempton, Bekki Kempton, Breena Kempton, Catharina Kempton, Chandelle Kempton,
Charmion Kempton, Cherilynn Kempton, Chesney Kempton, Chirsty Kempton, Cynethia Kempton, Cyntia Kempton, Dane Kempton, Dorethea Kempton, Elyce Kempton, Emery Kempton, Garrett Kempton, Gittel Kempton,
Gizelle Kempton, Hinda Kempton, Jaquelin Kempton, Jenaya Kempton, Jeneva Kempton, Jenipher Kempton, Karessa Kempton, Karita Kempton, Kelita Kempton, Kiyana Kempton, Kora Kempton, Laquanna Kempton,
Larkin Kempton, Latangela Kempton, Linsay Kempton, Lisett Kempton, Lizzy Kempton, Magdalen Kempton, Marcea Kempton, Mashawn Kempton, Meiko Kempton, Mekia Kempton, Merisa Kempton, Nikcole Kempton,
Norina Kempton, Prima Kempton, Rashada Kempton, Rasheena Kempton, Rozella Kempton, Selia Kempton, Shaheen Kempton, Shamon Kempton, Shaya Kempton, Shirly Kempton, Shunna Kempton, Shyanne Kempton,
Skylar Kempton, Sukari Kempton, Sylvana Kempton, Tahlia Kempton, Taiesha Kempton, Tamiki Kempton, Tangala Kempton, Taniqua Kempton, Tanza Kempton, Temesha Kempton, Teonna Kempton, Tiffane Kempton,
Torya Kempton, Tremaine Kempton, Tricha Kempton, Vanesha Kempton, Yetunde Kempton, Zarinah Kempton, Amalie Kempton, Atoya Kempton, Bryony Kempton, Caree Kempton, Carron Kempton, Celestia Kempton,
Charma Kempton, Chelly Kempton, Christon Kempton, Chrystle Kempton, Conchetta Kempton, Dan Kempton, Deandria Kempton, Donika Kempton, Eulanda Kempton, Eyvonne Kempton, Gloriana Kempton, Hyun Kempton,
Joslynn Kempton, Kewanda Kempton, Laetitia Kempton, Laketra Kempton, Lakshmi Kempton, Latawnya Kempton, Lawren Kempton, Leo Kempton, Letonia Kempton, Lichelle Kempton, Lue Kempton, Lynnmarie Kempton,
Mauricia Kempton, Nakkia Kempton, Neka Kempton, Parisa Kempton, Quentin Kempton, Ranada Kempton, Rhianon Kempton, Roselee Kempton, Rozanne Kempton, Rozetta Kempton, Rozina Kempton, Sada Kempton, Sala
Kempton, Samar Kempton, Seandra Kempton, Shaela Kempton, Sharrell Kempton, Shawneen Kempton, Shefali Kempton, Shekinah Kempton, Sherriann Kempton, Shuree Kempton, Soyini Kempton, Teala Kempton,
Telitha Kempton, Tempie Kempton, Tirza Kempton, Valori Kempton, Veleda Kempton, Vivianne Kempton, Alexi Kempton, Arnetra Kempton, Azizi Kempton, Belkys Kempton, Cailin Kempton, Carmell Kempton,
Charlyne Kempton, Courteney Kempton, Danniell Kempton, Danyiel Kempton, Danylle Kempton, Delita Kempton, Deseri Kempton, Donice Kempton, Ebone Kempton, Eleshia Kempton, Ellison Kempton, Giuliana
Kempton, Harvest Kempton, Hillari Kempton, Ijeoma Kempton, Janeene Kempton, Kem Kempton, Kya Kempton, Laquandra Kempton, Lashane Kempton, Latana Kempton, Latoi Kempton, Lenice Kempton, Lethia
Kempton, Lindsi Kempton, Lis Kempton, Lorrine Kempton, Marena Kempton, Marlayna Kempton, Mashanda Kempton, Mercedez Kempton, Merlene Kempton, Najwa Kempton, Paraskevi Kempton, Princella Kempton,
Raejean Kempton, Raissa Kempton, Ravin Kempton, Reda Kempton, Reisha Kempton, Roland Kempton, Sakia Kempton, Salma Kempton, Shakela Kempton, Sharica Kempton, Shatisha Kempton, Shauntee Kempton,
Sheriann Kempton, Stori Kempton, Sueellen Kempton, Sylina Kempton, Tametra Kempton, Tanieka Kempton, Tanikia Kempton, Tarisa Kempton, Tiffony Kempton, Tolanda Kempton, Treana Kempton, Tumeka Kempton,
Ursala Kempton, Yumi Kempton, Zoraya Kempton, Alfie Kempton, Aliyah Kempton, Almeda Kempton, Amarilys Kempton, Amberley Kempton, Arabella Kempton, Ardella Kempton, Atonya Kempton, Audree Kempton,
Benedetta Kempton, Billiejean Kempton, Carlynn Kempton, Cherylynn Kempton, Christabel Kempton, Clarrisa Kempton, Colinda Kempton, Cutina Kempton, Dalyn Kempton, Dametra Kempton, Daphna Kempton, Emili
Kempton, Fatema Kempton, Glennda Kempton, Izetta Kempton, Janielle Kempton, Jessamy Kempton, Jonique Kempton, Karron Kempton, Kathia Kempton, Katrese Kempton, Kendrah Kempton, Kevia Kempton, Khalia
Kempton, Kissa Kempton, Kizzi Kempton, Kutina Kempton, Lanetra Kempton, Lashonya Kempton, Latanja Kempton, Latisia Kempton, Latriece Kempton, Lenny Kempton, Leonarda Kempton, Lewanna Kempton, Lien
Kempton, Lyndia Kempton, Mallissa Kempton, Marlie Kempton, Marqueta Kempton, Marvetta Kempton, Mikayla Kempton, Milicent Kempton, Montana Kempton, Morgana Kempton, Nathania Kempton, Neema Kempton,
Noriko Kempton, Ondria Kempton, Onna Kempton, Patrici Kempton, Rachella Kempton, Reatha Kempton, Rise Kempton, Rosabel Kempton, Secret Kempton, Shanetha Kempton, Sharah Kempton, Sharion Kempton,
Sherilynn Kempton, Summar Kempton, Tam Kempton, Tamanika Kempton, Tarhonda Kempton, Teddie Kempton, Tennelle Kempton, Tephanie Kempton, Terryl Kempton, Tiawanna Kempton, Tischa Kempton, Tonesha
Kempton, Amirah Kempton, Amory Kempton, Anji Kempton, Arasely Kempton, Argentina Kempton, Aviance Kempton, Batsheva Kempton, Briar Kempton, Cena Kempton, Chalon Kempton, Chancy Kempton, Chandler
Kempton, Chivon Kempton, Chonita Kempton, Chrisa Kempton, Darnelle Kempton, Deanie Kempton, Deeana Kempton, Delise Kempton, Elayna Kempton, Errika Kempton, Eurika Kempton, Farrell Kempton, Felcia
Kempton, Isidra Kempton, Jai Kempton, Jamell Kempton, Jamesha Kempton, Jere Kempton, Jodilyn Kempton, Jovonne Kempton, Jowana Kempton, Juline Kempton, Kameshia Kempton, Katrisha Kempton, Keary
Kempton, Keyshia Kempton, Kolette Kempton, Lakecha Kempton, Lakiya Kempton, Larrisa Kempton, Lasharn Kempton, Lasundra Kempton, Latica Kempton, Latoiya Kempton, Laurisa Kempton, Lucrezia Kempton,
Mariateresa Kempton, Maryland Kempton, Melicia Kempton, Mieko Kempton, Molina Kempton, Mozella Kempton, Nataly Kempton, Nayda Kempton, Olanda Kempton, Onica Kempton, Ourania Kempton, Quinette
Kempton, Rayma Kempton, Rianne Kempton, Sarika Kempton, Shalona Kempton, Shawntina Kempton, Shellye Kempton, Sheva Kempton, Shironda Kempton, Sonora Kempton, Sophronia Kempton, Symantha Kempton,
Tahra Kempton, Tearsa Kempton, Terrika Kempton, Tonyetta Kempton, Treina Kempton, Tzipora Kempton, Violette Kempton, Vivianna Kempton, Yanet Kempton, Akira Kempton, Amanada Kempton, Atara Kempton,
Britten Kempton, Camika Kempton, Carlo Kempton, Celicia Kempton, Chanon Kempton, Chanti Kempton, Christeena Kempton, Consandra Kempton, Correen Kempton, Delayna Kempton, Derenda Kempton, Dlynn
Kempton, Donyetta Kempton, Fawne Kempton, Feliz Kempton, Gisselle Kempton, Glen Kempton, Hong Kempton, Hyla Kempton, Jacques Kempton, Jasmyn Kempton, Jonel Kempton, Khaleelah Kempton, Kista Kempton,
Lachell Kempton, Lajoy Kempton, Lakethia Kempton, Lamia Kempton, Lasheba Kempton, Laurianne Kempton, Lelani Kempton, Lonya Kempton, Loucinda Kempton, Maressa Kempton, Mariesa Kempton, Meshia Kempton,
Messina Kempton, Paulett Kempton, Rashon Kempton, Rayshawn Kempton, Rochanda Kempton, Ronnica Kempton, Rorie Kempton, Saunya Kempton, Shakeitha Kempton, Shalla Kempton, Shalondra Kempton, Shamecca
Kempton, Shavonn Kempton, Sherril Kempton, Shonell Kempton, Sonita Kempton, Svetlana Kempton, Takila Kempton, Tala Kempton, Tamecca Kempton, Tiphany Kempton, Torria Kempton, Vanya Kempton, Verdell
Kempton, Vonna Kempton, Zsazsa Kempton, Adonia Kempton, Alease Kempton, Aleena Kempton, Alishea Kempton, Anetta Kempton, Ania Kempton, Anquinette Kempton, Antonieta Kempton, Archana Kempton, Arely
Kempton, Artavia Kempton, Arturo Kempton, Batya Kempton, Bernardine Kempton, Betti Kempton, Breck Kempton, Camara Kempton, Cesar Kempton, Chalise Kempton, Charly Kempton, Cherrise Kempton, Chikita
Kempton, Cristiana Kempton, Dayatra Kempton, Ericha Kempton, Ermalinda Kempton, Eulonda Kempton, Fayth Kempton, Halina Kempton, Hunter Kempton, Iveliz Kempton, Ivie Kempton, Jahna Kempton, Jancy
Kempton, Janisha Kempton, Jeaninne Kempton, Jeannemarie Kempton, Jessamine Kempton, Keeya Kempton, Kelisha Kempton, Kenyette Kempton, Kyley Kempton, Kyrie Kempton, Ladora Kempton, Laguana Kempton,
Larri Kempton, Leyda Kempton, Louie Kempton, Marykathryn Kempton, Mekesha Kempton, Meredeth Kempton, Merridith Kempton, Mittie Kempton, Nakeitha Kempton, Narda Kempton, Nature Kempton, Neeta Kempton,
Nitasha Kempton, Nuvia Kempton, Paticia Kempton, Promise Kempton, Rabia Kempton, Raquelle Kempton, Richetta Kempton, Shawneequa Kempton, Shervon Kempton, Siomara Kempton, Starlyn Kempton, Tahirih
Kempton, Taia Kempton, Talita Kempton, Tamina Kempton, Tamya Kempton, Tanicka Kempton, Tanyanika Kempton, Tawan Kempton, Tawanya Kempton, Tiarra Kempton, Timisha Kempton, Tinita Kempton, Tonnia
Kempton, Toronda Kempton, Toshika Kempton, Triva Kempton, Trula Kempton, Tykesha Kempton, Vaness Kempton, Vennessa Kempton, Wakeelah Kempton, Wilhemina Kempton, Yoshiko Kempton, Afia Kempton, Afiya
Kempton, Allysa Kempton, Alsha Kempton, Amberlyn Kempton, Arah Kempton, Audri Kempton, Bernardette Kempton, Bernedette Kempton, Binta Kempton, Breeann Kempton, Britni Kempton, Carnetta Kempton,
Cesilia Kempton, Chelli Kempton, Dawnna Kempton, Desirie Kempton, Fleur Kempton, Gianina Kempton, Hanh Kempton, Ivelis Kempton, Jalena Kempton, Jenafer Kempton, Johann Kempton, Joyanne Kempton, Kamia
Kempton, Katerine Kempton, Kecha Kempton, Keir Kempton, Kennita Kempton, Kimra Kempton, Kristiann Kempton, Levita Kempton, Lluvia Kempton, Lorian Kempton, Lyndsy Kempton, Mardell Kempton, Maurissa
Kempton, Mischell Kempton, Mistey Kempton, Nataya Kempton, Nickola Kempton, Obdulia Kempton, Preston Kempton, Raynetta Kempton, Rondell Kempton, Shakara Kempton, Shalan Kempton, Shanya Kempton,
Shawnika Kempton, Shenetha Kempton, Shilah Kempton, Soo Kempton, Tametha Kempton, Tanicia Kempton, Tanny Kempton, Tennie Kempton, Tiffannie Kempton, Torra Kempton, Trinika Kempton, Val Kempton, Abeer
Kempton, Adah Kempton, Aleece Kempton, Andreya Kempton, Annaliza Kempton, Arrie Kempton, Ayasha Kempton, Berit Kempton, Birgit Kempton, Bre Kempton, Brigetta Kempton, Cassundra Kempton, Christyl
Kempton, Cristyn Kempton, Danean Kempton, Daralyn Kempton, Davonne Kempton, Deisha Kempton, Denina Kempton, Dietrich Kempton, Domini Kempton, Erinne Kempton, Evy Kempton, Forrest Kempton, Genetta
Kempton, Gioia Kempton, Guenevere Kempton, Gwenetta Kempton, Gwenette Kempton, Hesper Kempton, Ignacia Kempton, Irmalinda Kempton, Jacquita Kempton, Jeanita Kempton, Jodiann Kempton, Kalin Kempton,
Kenny Kempton, Keon Kempton, Kimberlynn Kempton, Kimela Kempton, Kimm Kempton, Kiwanna Kempton, Lacreshia Kempton, Lakashia Kempton, Latarshia Kempton, Latrish Kempton, Lauria Kempton, Likisha
Kempton, Lindee Kempton, Little Kempton, Loreta Kempton, Lutisha Kempton, Mahasin Kempton, Maki Kempton, Maxi Kempton, Meesha Kempton, Melitta Kempton, Mery Kempton, Mysty Kempton, Quanisha Kempton,
Ranetta Kempton, Rosia Kempton, Sadonna Kempton, Sangita Kempton, Sanora Kempton, Shanina Kempton, Sharonna Kempton, Shavona Kempton, Sherrica Kempton, Storm Kempton, Tabrina Kempton, Tacha Kempton,
Taleshia Kempton, Tamee Kempton, Tanetta Kempton, Thanh Kempton, Twanya Kempton, Ulrica Kempton, Yaffa Kempton, Aarin Kempton, Afi Kempton, Aliscia Kempton, Aneta Kempton, Anetria Kempton, Antoinett
Kempton, Athenia Kempton, Atisha Kempton, Barb Kempton, Brit Kempton, Caley Kempton, Camala Kempton, Carena Kempton, Carinne Kempton, Carmine Kempton, Charlott Kempton, Chessa Kempton, Chundra
Kempton, Cotrina Kempton, Drenda Kempton, Elanor Kempton, Eleftheria Kempton, Erricka Kempton, Feleshia Kempton, Geanna Kempton, Harley Kempton, Honora Kempton, Jakia Kempton, Jannah Kempton, Jennene
Kempton, Jennett Kempton, Jobeth Kempton, Jordanna Kempton, Juanetta Kempton, Junie Kempton, Kaira Kempton, Kashana Kempton, Katee Kempton, Kateena Kempton, Kelleigh Kempton, Kenyana Kempton,
Kerrilyn Kempton, Kessa Kempton, Kirk Kempton, Lakitha Kempton, Laneshia Kempton, Lanissa Kempton, Lashunta Kempton, Leonia Kempton, Lester Kempton, Letina Kempton, Llesenia Kempton, Loranda Kempton,
Lorilynn Kempton, Lotus Kempton, Luke Kempton, Marisal Kempton, Marvis Kempton, Maurie Kempton, Minnette Kempton, Mishawn Kempton, Natsha Kempton, Ngoc Kempton, Nioka Kempton, Particia Kempton,
Phillina Kempton, Prisilla Kempton, Raney Kempton, Raphaela Kempton, Rashaunda Kempton, Raynelle Kempton, Ross Kempton, Rufina Kempton, Sarahann Kempton, Shaconda Kempton, Shanicka Kempton, Shaunita
Kempton, Shekina Kempton, Shelie Kempton, Sherah Kempton, Shermeka Kempton, Shermika Kempton, Sonnia Kempton, Stephonie Kempton, Taffie Kempton, Takima Kempton, Talea Kempton, Tamaya Kempton, Taneika
Kempton, Tanina Kempton, Tanisia Kempton, Taysha Kempton, Tekeshia Kempton, Terie Kempton, Therasa Kempton, Thomasa Kempton, Tifini Kempton, Tomie Kempton, Tressy Kempton, Trissa Kempton, Tristy
Kempton, Tritia Kempton, Twania Kempton, Tyrene Kempton, Uganda Kempton, Wandy Kempton, Wileen Kempton, Yumeka Kempton, Zarina Kempton, Adreana Kempton, Alandra Kempton, Alenda Kempton, Amera
Kempton, Arlicia Kempton, Artemis Kempton, Avani Kempton, Bena Kempton, Candia Kempton, Cathyjo Kempton, Chala Kempton, Charitie Kempton, Charlise Kempton, Chasiti Kempton, Chayla Kempton, Chrisanne
Kempton, Christell Kempton, Clarrissa Kempton, Cortnee Kempton, Dametria Kempton, Daneka Kempton, Darlisa Kempton, Delorse Kempton, Deshone Kempton, Dorette Kempton, Esperansa Kempton, Evagelia
Kempton, Feliciana Kempton, Fikisha Kempton, Freeda Kempton, Frida Kempton, Gaila Kempton, Genae Kempton, Georgi Kempton, Gitel Kempton, Gricel Kempton, Hilliary Kempton, Ichelle Kempton, Ishia
Kempton, Ivelise Kempton, Jacci Kempton, Jamesa Kempton, Jammy Kempton, Jerrilynn Kempton, Jillaine Kempton, Jillann Kempton, Jin Kempton, Joda Kempton, Jodeen Kempton, Kalisa Kempton, Karne Kempton,
Katura Kempton, Kayci Kempton, Keegan Kempton, Keenan Kempton, Khia Kempton, Koleen Kempton, Krishana Kempton, Krislyn Kempton, Kurt Kempton, Lafaye Kempton, Lakeysa Kempton, Lakresha Kempton, Lalisa
Kempton, Lashonne Kempton, Leighanna Kempton, Lesslie Kempton, Lin Kempton, Madlyn Kempton, Malky Kempton, Melenda Kempton, Melisssa Kempton, Mikita Kempton, Monicia Kempton, Monik Kempton, Nakima
Kempton, Naquita Kempton, Natash Kempton, Raphael Kempton, Rashawna Kempton, Reannon Kempton, Reneta Kempton, Reshanda Kempton, Riana Kempton, Rocky Kempton, Rosamond Kempton, Roshan Kempton, Saleena
Kempton, Schuyler Kempton, Shaka Kempton, Shakesha Kempton, Shaleta Kempton, Shanekia Kempton, Surina Kempton, Syrita Kempton, Taj Kempton, Tajuanna Kempton, Tasheen Kempton, Tiffine Kempton, Timmie
Kempton, Tomikia Kempton, Trease Kempton, Tyrhonda Kempton, Wakisha Kempton, Yvone Kempton, Adalia Kempton, Ahuva Kempton, Angelicia Kempton, Anina Kempton, Annitra Kempton, Betsie Kempton, Cachet
Kempton, Callista Kempton, Camey Kempton, Celita Kempton, Cherissa Kempton, Collin Kempton, Daiana Kempton, Equilla Kempton, Evetta Kempton, Eyvette Kempton, Feige Kempton, Filicia Kempton, Floyd
Kempton, Garnett Kempton, Geoffrey Kempton, Harper Kempton, Ione Kempton, Iyana Kempton, Jametta Kempton, Jeanee Kempton, Jessalynn Kempton, Jonalyn Kempton, Juanice Kempton, Kaija Kempton, Kalene
Kempton, Kassidy Kempton, Katryn Kempton, Kennethia Kempton, Keosha Kempton, Kresha Kempton, Krisandra Kempton, Labrina Kempton, Lachonda Kempton, Lamara Kempton, Lashika Kempton, Lateka Kempton,
Laytoya Kempton, Lourdez Kempton, Lyndsi Kempton, Markeita Kempton, Marletta Kempton, Marshella Kempton, Martiza Kempton, Marylouise Kempton, Miri Kempton, Nani Kempton, Payton Kempton, Puja Kempton,
Qianna Kempton, Raffaella Kempton, Roanne Kempton, Sadiqa Kempton, Salvador Kempton, Shabnam Kempton, Shamar Kempton, Shamina Kempton, Sharalee Kempton, Shavette Kempton, Sheilia Kempton, Shekia
Kempton, Shelise Kempton, Sherrilynn Kempton, Sheyla Kempton, Shy Kempton, Suprena Kempton, Tahitia Kempton, Talley Kempton, Tamiya Kempton, Tashena Kempton, Tashona Kempton, Tatisha Kempton, Toia
Kempton, Tonji Kempton, Triana Kempton, Tymika Kempton, Yanna Kempton, Zainab Kempton, Amrita Kempton, Aprel Kempton, Atalie Kempton, Aubre Kempton, Auria Kempton, Barbarita Kempton, Bettyann
Kempton, Boni Kempton, Brandace Kempton, Bryanne Kempton, Calleen Kempton, Chakita Kempton, Chamaine Kempton, Chamika Kempton, Charlett Kempton, Chereese Kempton, Cherine Kempton, Christalyn Kempton,
Conya Kempton, Dalilah Kempton, Dela Kempton, Delanna Kempton, Delinah Kempton, Dierdra Kempton, Domitila Kempton, Donnis Kempton, Dore Kempton, Elenor Kempton, Elizabethann Kempton, Elysha Kempton,
Erryn Kempton, Evalyn Kempton, Frannie Kempton, Fredda Kempton, Ginnifer Kempton, Hilaria Kempton, Ilisa Kempton, Ivanna Kempton, Janeal Kempton, Jeena Kempton, Jeremie Kempton, Jeriann Kempton,
Julina Kempton, Karim Kempton, Kenitha Kempton, Kery Kempton, Korinna Kempton, Lachrisha Kempton, Lamonda Kempton, Laneisha Kempton, Lene Kempton, Letita Kempton, Lillia Kempton, Lindsie Kempton,
Lissete Kempton, Lynsay Kempton, Magalie Kempton, Makini Kempton, Manette Kempton, Margareta Kempton, Marlette Kempton, Marsi Kempton, Maryn Kempton, Megon Kempton, Melainie Kempton, Meria Kempton,
Merrideth Kempton, Moranda Kempton, Myah Kempton, Myron Kempton, Odalis Kempton, Rakia Kempton, Renesha Kempton, Rhanda Kempton, Richell Kempton, Salinda Kempton, Sammantha Kempton, Shamonica
Kempton, Shaquanda Kempton, Sharmain Kempton, Shereece Kempton, Shron Kempton, Tammika Kempton, Terence Kempton, Teresha Kempton, Tiah Kempton, Treniece Kempton, Truly Kempton, Venicia Kempton,
Virgil Kempton, Winnifred Kempton, Yaritza Kempton, Yarrow Kempton, Zandria Kempton, Alacia Kempton, Albertha Kempton, Andie Kempton, Anuradha Kempton, Artesia Kempton, Beatrix Kempton, Brandin
Kempton, Brittni Kempton, Carrey Kempton, Catricia Kempton, Chelise Kempton, Christien Kempton, Dalina Kempton, Damia Kempton, Deletha Kempton, Eldora Kempton, Eli Kempton, Eufemia Kempton, Fabrienne
Kempton, Garland Kempton, Genessa Kempton, Ginnette Kempton, Goldy Kempton, Grant Kempton, Greg Kempton, Hasina Kempton, Hermila Kempton, Ima Kempton, Jacquette Kempton, Jilian Kempton, Jilleen
Kempton, Jolita Kempton, Jorja Kempton, Julita Kempton, Juna Kempton, Keicha Kempton, Keshawn Kempton, Ketty Kempton, Kimmi Kempton, Kizmet Kempton, Koni Kempton, Kristiane Kempton, Krystyn Kempton,
Laronica Kempton, Lashonia Kempton, Lateefa Kempton, Latresia Kempton, Lequisha Kempton, Levi Kempton, Lorenia Kempton, Lubna Kempton, Lucas Kempton, Marche Kempton, Marlea Kempton, Masha Kempton,
Miah Kempton, Michala Kempton, Michelyn Kempton, Mistina Kempton, Necola Kempton, Netra Kempton, Niomi Kempton, Nira Kempton, Nonnie Kempton, Phelicia Kempton, Quanta Kempton, Quita Kempton, Raini
Kempton, Rayanna Kempton, Roselind Kempton, Roselinda Kempton, Roshana Kempton, Sagrario Kempton, Sameka Kempton, Shaindel Kempton, Sharetha Kempton, Sharol Kempton, Shawnese Kempton, Shellia
Kempton, Sheray Kempton, Sherian Kempton, Shi Kempton, Stepheni Kempton, Subrena Kempton, Tabithia Kempton, Taleen Kempton, Taneha Kempton, Tanysha Kempton, Tekela Kempton, Telesa Kempton, Tima
Kempton, Tonni Kempton, Ula Kempton, Yitty Kempton, Yona Kempton, Yonna Kempton, Yuko Kempton, Zalika Kempton, Aarika Kempton, Ajeenah Kempton, Alegra Kempton, Alichia Kempton, Allecia Kempton, Amor
Kempton, Aneatra Kempton, Anjannette Kempton, Anntionette Kempton, Antonetta Kempton, Ardelia Kempton, Atlanta Kempton, Ayoka Kempton, Breeze Kempton, Casonya Kempton, Cathern Kempton, Chanise
Kempton, Charlina Kempton, Charmon Kempton, Chemika Kempton, Cheresa Kempton, Cindra Kempton, Claretha Kempton, Coren Kempton, Cyndia Kempton, Cyntha Kempton, Danialle Kempton, Danyeal Kempton, Davin
Kempton, Deanda Kempton, Deaundra Kempton, Dejah Kempton, Demica Kempton, Demisha Kempton, Dinita Kempton, Donalyn Kempton, Donesha Kempton, Dotty Kempton, Fidelia Kempton, Golden Kempton, Helana
Kempton, Hidi Kempton, Ilena Kempton, Jenniferann Kempton, Jolleen Kempton, Jolynda Kempton, Juanna Kempton, Karlena Kempton, Karlin Kempton, Keandra Kempton, Kionna Kempton, Konni Kempton, Lakeyta
Kempton, Lechelle Kempton, Levon Kempton, Lilith Kempton, Maliaka Kempton, Mallie Kempton, Margeaux Kempton, Mariaisabel Kempton, Marixa Kempton, Memorie Kempton, Meshawn Kempton, Michole Kempton,
Myrian Kempton, Neela Kempton, Nivea Kempton, Peggi Kempton, Porchia Kempton, Racine Kempton, Rashaun Kempton, Reynalda Kempton, Rosaleen Kempton, Sabrine Kempton, Samanda Kempton, Shanitha Kempton,
Sharece Kempton, Sheretha Kempton, Sherwanda Kempton, Shonica Kempton, Solveig Kempton, Soyla Kempton, Taka Kempton, Taquilla Kempton, Tedi Kempton, Tema Kempton, Terita Kempton, Tippi Kempton,
Tiziana Kempton, Tomieka Kempton, Tonga Kempton, Trenace Kempton, Tyeasha Kempton, Tyresha Kempton, Valda Kempton, Vandy Kempton, Victora Kempton, Victory Kempton, Waverly Kempton, Adair Kempton,
Agueda Kempton, Aiko Kempton, Akina Kempton, Amaya Kempton, Anthonette Kempton, Ariann Kempton, Averi Kempton, Ayde Kempton, Belissa Kempton, Bernadett Kempton, Berniece Kempton, Berry Kempton,
Bethsaida Kempton, Bindu Kempton, Bonniejean Kempton, Brendy Kempton, Cadence Kempton, Camy Kempton, Canisha Kempton, Carilyn Kempton, Caronda Kempton, Chantrell Kempton, Chavela Kempton, Chemeka
Kempton, Crystie Kempton, Dafina Kempton, Dangela Kempton, Daphnee Kempton, Darenda Kempton, Darolyn Kempton, Davelyn Kempton, Desarie Kempton, Devone Kempton, Dionisia Kempton, Donnielle Kempton,
Ebonique Kempton, English Kempton, Eran Kempton, Eryka Kempton, Falisa Kempton, Fareeda Kempton, Herman Kempton, Inda Kempton, Janeice Kempton, Janny Kempton, Jessicah Kempton, Jodean Kempton, Julius
Kempton, Kaisa Kempton, Kanda Kempton, Karel Kempton, Karia Kempton, Kimba Kempton, Konya Kempton, Kylah Kempton, Kyrsten Kempton, Laretta Kempton, Lasharon Kempton, Latascha Kempton, Leni Kempton,
Leontyne Kempton, Linell Kempton, Lovena Kempton, Maghan Kempton, Makeshia Kempton, Malorie Kempton, Marce Kempton, Maryetta Kempton, Mechille Kempton, Media Kempton, Meira Kempton, Miosotis Kempton,
Mirjana Kempton, Mlissa Kempton, Nekeya Kempton, Nica Kempton, Nikkisha Kempton, Ortencia Kempton, Porche Kempton, Raffaela Kempton, Raleigh Kempton, Reka Kempton, Rotunda Kempton, Sharline Kempton,
Sharlonda Kempton, Shawnice Kempton, Shone Kempton, Shuntell Kempton, Sneha Kempton, Stephanne Kempton, Sundy Kempton, Tabita Kempton, Takara Kempton, Takeia Kempton, Talli Kempton, Tanganika
Kempton, Taquana Kempton, Thresea Kempton, Tila Kempton, Tim Kempton, Tyan Kempton, Vaishali Kempton, Xanthe Kempton, Zenja Kempton, Zerlina Kempton, Aggie Kempton, Aleathea Kempton, Aleen Kempton,
Alexcia Kempton, Aloma Kempton, Angeleque Kempton, Araina Kempton, Asucena Kempton, Azadeh Kempton, Brendan Kempton, Candina Kempton, Candiss Kempton, Cantina Kempton, Carlisha Kempton, Charra
Kempton, Chaunta Kempton, Dalonda Kempton, Damica Kempton, Decarla Kempton, Deneice Kempton, Derhonda Kempton, Derrica Kempton, Dorea Kempton, Elvera Kempton, Estell Kempton, Fae Kempton, Graceann
Kempton, Grissel Kempton, Hina Kempton, Jamielynn Kempton, Jesscia Kempton, Joley Kempton, Junell Kempton, Kalilah Kempton, Kathe Kempton, Katurah Kempton, Kenni Kempton, Keysa Kempton, Kimie
Kempton, Lachana Kempton, Ladell Kempton, Lanore Kempton, Laramie Kempton, Larrie Kempton, Latonna Kempton, Latori Kempton, Livier Kempton, Loletta Kempton, Magdaline Kempton, Malaina Kempton,
Mandalyn Kempton, Marshawn Kempton, Marticia Kempton, Maurisa Kempton, Mellonie Kempton, Nashira Kempton, Orelia Kempton, Quanna Kempton, Raisa Kempton, Rakisha Kempton, Raymonda Kempton, Remonia
Kempton, Robbye Kempton, Ronnita Kempton, Roshaunda Kempton, Sabre Kempton, Sabreen Kempton, Sharis Kempton, Shawnae Kempton, Sherrin Kempton, Sindia Kempton, Staphanie Kempton, Stevi Kempton,
Tannisha Kempton, Tashunda Kempton, Tekla Kempton, Teralyn Kempton, Tomecia Kempton, Tonique Kempton, Trilby Kempton, Unika Kempton, Vanisha Kempton, Voula Kempton, Waynetta Kempton, Yasmina Kempton,
Amesha Kempton, Aniko Kempton, Annica Kempton, Antione Kempton, Astria Kempton, Camilia Kempton, Caprina Kempton, Carah Kempton, Catonya Kempton, Chalanda Kempton, Chasty Kempton, Cherica Kempton,
Coy Kempton, Crystalynn Kempton, Dakisha Kempton, Davine Kempton, Dawnyel Kempton, Demetrias Kempton, Derica Kempton, Dinamarie Kempton, Dvora Kempton, Elbony Kempton, Emanuela Kempton, Gayleen
Kempton, Genevra Kempton, Hadiyah Kempton, Harolyn Kempton, Hidie Kempton, Indy Kempton, Jaki Kempton, Jalana Kempton, Jalila Kempton, Janiel Kempton, Jennah Kempton, Jessia Kempton, Jihan Kempton,
Jinnie Kempton, Jonya Kempton, Justa Kempton, Justice Kempton, Kameela Kempton, Kameko Kempton, Kaneisha Kempton, Karletta Kempton, Keneisha Kempton, Kimberl Kempton, Kimyada Kempton, Kirstyn
Kempton, Krisy Kempton, Kyisha Kempton, Labreeska Kempton, Lacreasha Kempton, Lajeana Kempton, Lakiska Kempton, Lanya Kempton, Laren Kempton, Latash Kempton, Lataunya Kempton, Leiah Kempton, Loralyn
Kempton, Lorre Kempton, Malaka Kempton, Malicia Kempton, Marga Kempton, Margaretann Kempton, Markell Kempton, Meriam Kempton, Micca Kempton, Morningstar Kempton, Neta Kempton, Nigel Kempton, Noah
Kempton, Nuria Kempton, Oliver Kempton, Osha Kempton, Pierrette Kempton, Quinita Kempton, Quintessa Kempton, Rashan Kempton, Ravonda Kempton, Raylynn Kempton, Reyes Kempton, Rhondalyn Kempton, Rosey
Kempton, Roshanna Kempton, Ruthy Kempton, Sasheen Kempton, Shakeisha Kempton, Shakirah Kempton, Shaneta Kempton, Sharmeka Kempton, Sharonica Kempton, Shelba Kempton, Shelinda Kempton, Shell Kempton,
Sheranda Kempton, Stachia Kempton, Stefanee Kempton, Sydnee Kempton, Tamekka Kempton, Tanisa Kempton, Telissa Kempton, Terissa Kempton, Tilda Kempton, Tomoko Kempton, Trinna Kempton, Tulani Kempton,
Varina Kempton, Verlene Kempton, Vernisha Kempton, Yasha Kempton, Yvonnie Kempton, Albertine Kempton, Angeletta Kempton, Anni Kempton, Arrica Kempton, Billyjo Kempton, Brocha Kempton, Calie Kempton,
Cass Kempton, Catie Kempton, Chairty Kempton, Chakakhan Kempton, Chassie Kempton, Cherae Kempton, Cheryn Kempton, Chisa Kempton, Chrystine Kempton, Coronda Kempton, Curtina Kempton, Danuta Kempton,
Debie Kempton, Delona Kempton, Demia Kempton, Dosha Kempton, Enrica Kempton, Evone Kempton, Fanchon Kempton, Fina Kempton, Gaetana Kempton, Genevia Kempton, Gera Kempton, Gracy Kempton, Hollyann
Kempton, Iasia Kempton, Iyesha Kempton, Jackline Kempton, Joanette Kempton, Jonnette Kempton, Kaamilya Kempton, Karolina Kempton, Kathlynn Kempton, Kayle Kempton, Kayse Kempton, Kehaulani Kempton,
Kella Kempton, Kenyatte Kempton, Kianga Kempton, Kijuana Kempton, Kinisha Kempton, Kiwanda Kempton, Kriss Kempton, Lakea Kempton, Lakeithia Kempton, Lakeyia Kempton, Latusha Kempton, Leala Kempton,
Leina Kempton, Lucita Kempton, Madia Kempton, Mairead Kempton, Makiba Kempton, Marchella Kempton, Marquel Kempton, Martita Kempton, Meco Kempton, Melissaann Kempton, Merilyn Kempton, Minyon Kempton,
Monnica Kempton, Monnie Kempton, Mora Kempton, Netasha Kempton, Nkechi Kempton, Ocie Kempton, Oni Kempton, Patricie Kempton, Quina Kempton, Quintana Kempton, Renu Kempton, Rhetta Kempton, Rissa
Kempton, Rozalyn Kempton, Salisa Kempton, Seena Kempton, Shaine Kempton, Shandon Kempton, Shanisha Kempton, Shantai Kempton, Sharisa Kempton, Shary Kempton, Shaylyn Kempton, Sheleta Kempton, Shilonda
Kempton, Sojourner Kempton, Syrena Kempton, Taleah Kempton, Tanekia Kempton, Tatianna Kempton, Tere Kempton, Terez Kempton, Teriann Kempton, Tewana Kempton, Ticey Kempton, Vanette Kempton, Vidya
Kempton, Wonder Kempton, Zoie Kempton, Aeisha Kempton, Alisande Kempton, Allan Kempton, Amantha Kempton, Analee Kempton, Ane Kempton, Artrice Kempton, Audelia Kempton, Ayelet Kempton, Benji Kempton,
Benny Kempton, Briann Kempton, Brittan Kempton, Calvina Kempton, Cameka Kempton, Cecilie Kempton, Cecille Kempton, Chanette Kempton, Chantia Kempton, Charlese Kempton, Charolett Kempton, Chenille
Kempton, Chivonne Kempton, Chudney Kempton, Clemencia Kempton, Courtny Kempton, Cristalle Kempton, Cynde Kempton, Daveda Kempton, Derika Kempton, Dezarae Kempton, Dionicia Kempton, Dunia Kempton,
Elspeth Kempton, Fayette Kempton, Glena Kempton, Gordon Kempton, Gretchin Kempton, Halli Kempton, Ilissa Kempton, Jauna Kempton, Johnnette Kempton, Joycelynn Kempton, Junelle Kempton, Kaydee Kempton,
Kerryn Kempton, Koryn Kempton, Kosha Kempton, Kyoko Kempton, Lala Kempton, Lametra Kempton, Laresha Kempton, Lauraann Kempton, Lecretia Kempton, Luv Kempton, Lyndsie Kempton, Malessa Kempton, Marcine
Kempton, Mellissia Kempton, Nakina Kempton, Nashonda Kempton, Neelam Kempton, Nikitia Kempton, Orit Kempton, Otis Kempton, Pasqualina Kempton, Porshia Kempton, Rayshell Kempton, Rico Kempton, Rockell
Kempton, Roshon Kempton, Savanna Kempton, Shallan Kempton, Shashana Kempton, Shawntia Kempton, Sherrise Kempton, Sofie Kempton, Taji Kempton, Talanda Kempton, Tamella Kempton, Tamsyn Kempton,
Taquisha Kempton, Tashea Kempton, Terisha Kempton, Tikita Kempton, Timmy Kempton, Trenese Kempton, Valissa Kempton, Valli Kempton, Vergie Kempton, Yancy Kempton, Aina Kempton, Albina Kempton,
Aletheia Kempton, Alisson Kempton, Allisyn Kempton, Amorita Kempton, Anginette Kempton, Anjana Kempton, Anngela Kempton, Ariela Kempton, Arienne Kempton, Arnisha Kempton, Arvella Kempton, Ayodele
Kempton, Badia Kempton, Brooklynn Kempton, Candus Kempton, Conswello Kempton, Curtisha Kempton, Cythina Kempton, Dashia Kempton, Dekisha Kempton, Denyce Kempton, Dilia Kempton, Doreatha Kempton,
Dortha Kempton, Ernesto Kempton, Fatisha Kempton, Fauna Kempton, Fifi Kempton, Gordana Kempton, Indya Kempton, Jaina Kempton, Janiene Kempton, Jarah Kempton, Jasmyne Kempton, Jeananne Kempton, Jeff
Kempton, Jeronica Kempton, Jessaca Kempton, Joby Kempton, Jodette Kempton, Jolisa Kempton, Juanda Kempton, Juanette Kempton, Kalie Kempton, Kaneshia Kempton, Karalynn Kempton, Kavitha Kempton, Kelcy
Kempton, Kerrilynn Kempton, Kierston Kempton, Kineta Kempton, Kiri Kempton, Krisie Kempton, Latorria Kempton, Lazara Kempton, Lekecia Kempton, Lenell Kempton, Lesle Kempton, Levina Kempton, Liat
Kempton, Lindley Kempton, Maiya Kempton, Makela Kempton, Mariane Kempton, Marki Kempton, Mashelle Kempton, Maud Kempton, Medora Kempton, Megumi Kempton, Milca Kempton, Missey Kempton, Mistelle
Kempton, Nakeeta Kempton, Neile Kempton, Nicloe Kempton, Nykisha Kempton, Orly Kempton, Patria Kempton, Rama Kempton, Ramonia Kempton, Ranie Kempton, Ranya Kempton, Refugio Kempton, Rendi Kempton,
Schwanna Kempton, Senia Kempton, Shalaunda Kempton, Shalia Kempton, Shanieka Kempton, Shantale Kempton, Shatima Kempton, Shawon Kempton, Shelva Kempton, Shemeca Kempton, Shemeeka Kempton, Sher
Kempton, Sinda Kempton, Skyler Kempton, Stephaie Kempton, Suzetta Kempton, Suzzane Kempton, Synethia Kempton, Taesha Kempton, Takina Kempton, Tanyetta Kempton, Taran Kempton, Tarasha Kempton, Tarji
Kempton, Tauni Kempton, Temeika Kempton, Temisha Kempton, Thania Kempton, Thembi Kempton, Thora Kempton, Tiffin Kempton, Toney Kempton, Trine Kempton, Tyrina Kempton, Uraina Kempton, Valleri Kempton,
Vandana Kempton, Vernie Kempton, Vinetta Kempton, Viveca Kempton, Vonette Kempton, Wynema Kempton, Yasheka Kempton, Yevonne Kempton, Yovana Kempton, Zanita Kempton, Zarah Kempton, Zendre Kempton,
Abigayle Kempton, Abraham Kempton, Acquanetta Kempton, Alika Kempton, Alora Kempton, Alvera Kempton, Amand Kempton, Annabella Kempton, Annelle Kempton, Antia Kempton, Arkisha Kempton, Arlanda
Kempton, Aronda Kempton, Ayo Kempton, Bailey Kempton, Banita Kempton, Becka Kempton, Brannon Kempton, Camden Kempton, Cantrice Kempton, Ceclia Kempton, Chantella Kempton, Charryse Kempton, Cheramie
Kempton, Chessie Kempton, Chiquetta Kempton, Chrysti Kempton, Cinzia Kempton, Cristian Kempton, Curry Kempton, Cybele Kempton, Damion Kempton, Darius Kempton, Dawnyell Kempton, Denora Kempton, Dung
Kempton, Ebonye Kempton, Elesa Kempton, Ellery Kempton, Ellis Kempton, Emile Kempton, Eowyn Kempton, Felicite Kempton, Geniene Kempton, Ginia Kempton, Hadiya Kempton, Hang Kempton, Harlene Kempton,
Inita Kempton, Jalaine Kempton, Janne Kempton, Jari Kempton, Jayci Kempton, Jodilynn Kempton, Jomarie Kempton, Jyll Kempton, Kabrina Kempton, Karisma Kempton, Kashina Kempton, Katika Kempton, Katye
Kempton, Keiona Kempton, Kemisha Kempton, Kyli Kempton, Lametria Kempton, Lamica Kempton, Larue Kempton, Lasheika Kempton, Latandra Kempton, Launi Kempton, Ligaya Kempton, Lilibeth Kempton, Linetta
Kempton, Linnet Kempton, Lorrain Kempton, Loyce Kempton, Lucresha Kempton, Marguetta Kempton, Matrice Kempton, Meca Kempton, Meda Kempton, Meiling Kempton, Melesa Kempton, Michaelann Kempton, Monick
Kempton, Nonie Kempton, Nyra Kempton, Pepsi Kempton, Porcha Kempton, Rakeisha Kempton, Reana Kempton, Rebacca Kempton, Rennee Kempton, Roben Kempton, Rondalyn Kempton, Roseline Kempton, Salem
Kempton, Samella Kempton, Sandar Kempton, Santia Kempton, Sarada Kempton, Sayward Kempton, Schelly Kempton, Shamecka Kempton, Sharmeen Kempton, Shayleen Kempton, Sheina Kempton, Sheleen Kempton,
Shenice Kempton, Shiri Kempton, Shonetta Kempton, Suha Kempton, Sulay Kempton, Swanzetta Kempton, Syndi Kempton, Tanette Kempton, Tarla Kempton, Tiffanni Kempton, Timaka Kempton, Tosheba Kempton,
Willene Kempton, Wynn Kempton, Yaisa Kempton, Adrinne Kempton, Aleisa Kempton, Aleka Kempton, Alka Kempton, Anais Kempton, Angy Kempton, Annetra Kempton, Antinette Kempton, Apryle Kempton, Aretta
Kempton, Arnell Kempton, Azusena Kempton, Bianka Kempton, Brandan Kempton, Camron Kempton, Capucine Kempton, Carolene Kempton, Catisha Kempton, Catrece Kempton, Cendy Kempton, Charmelle Kempton,
Charrisse Kempton, Chrisha Kempton, Cina Kempton, Dajuana Kempton, Dala Kempton, Danial Kempton, Daphyne Kempton, Daya Kempton, Delorise Kempton, Deneise Kempton, Deshunda Kempton, Desmond Kempton,
Desra Kempton, Dinna Kempton, Duchess Kempton, Earnest Kempton, Edda Kempton, Eliane Kempton, Elliott Kempton, Erline Kempton, Feleica Kempton, Florance Kempton, Gayl Kempton, Gaynelle Kempton,
Grisela Kempton, Huma Kempton, Jaimelyn Kempton, Jamile Kempton, Jeannifer Kempton, Jolin Kempton, Jonquil Kempton, Jurea Kempton, Kaili Kempton, Kanitra Kempton, Katana Kempton, Katoya Kempton,
Kenja Kempton, Kennette Kempton, Kenyotta Kempton, Kertina Kempton, Kiyomi Kempton, Klarissa Kempton, Lakeish Kempton, Lakena Kempton, Lanett Kempton, Lashante Kempton, Lasonda Kempton, Laurelle
Kempton, Lenda Kempton, Leonette Kempton, Madalene Kempton, Madhavi Kempton, Mariadelcarmen Kempton, Marine Kempton, Marquerite Kempton, Marylu Kempton, Maury Kempton, Merlyn Kempton, Natilie
Kempton, Neco Kempton, Nelissa Kempton, Nocole Kempton, Patrese Kempton, Ranette Kempton, Ranisha Kempton, Rhena Kempton, Ronesha Kempton, Royal Kempton, Safiyyah Kempton, Sahra Kempton, Saima
Kempton, Sarahjane Kempton, Senetra Kempton, Serra Kempton, Shallyn Kempton, Shawni Kempton, Sherin Kempton, Sherisa Kempton, Sherrelle Kempton, Shontina Kempton, Shontrell Kempton, Solana Kempton,
Tamalyn Kempton, Tamesia Kempton, Tametria Kempton, Tamicia Kempton, Taneya Kempton, Tango Kempton, Taquila Kempton, Tekelia Kempton, Tianne Kempton, Tonimarie Kempton, Trea Kempton, Tremayne
Kempton, Trichelle Kempton, Tunesia Kempton, Uma Kempton, Von Kempton, Yanina Kempton, Akela Kempton, Aleesa Kempton, Alonzo Kempton, Annel Kempton, Arisha Kempton, Aylin Kempton, Aynsley Kempton,
Bernina Kempton, Billee Kempton, Calisa Kempton, Calisha Kempton, Canda Kempton, Cantrell Kempton, Carylon Kempton, Casee Kempton, Celica Kempton, Chantilly Kempton, Charnissa Kempton, Chioma
Kempton, Chrystel Kempton, Clotilde Kempton, Coriann Kempton, Corisa Kempton, Currie Kempton, Cythnia Kempton, Danay Kempton, Danyella Kempton, Darling Kempton, Deloria Kempton, Deone Kempton, Devida
Kempton, Divya Kempton, Dorean Kempton, Dorri Kempton, Earlean Kempton, Eletha Kempton, Elfreda Kempton, Elizabth Kempton, Elna Kempton, Elycia Kempton, Elza Kempton, Emmanuelle Kempton, Felesia
Kempton, Galit Kempton, Garnetta Kempton, Gwendolin Kempton, Halee Kempton, Haylie Kempton, Jaala Kempton, Jacilyn Kempton, Jackquelyn Kempton, Jamekia Kempton, Jancie Kempton, Jeany Kempton, Jenness
Kempton, Johni Kempton, Kadee Kempton, Kalinda Kempton, Karmel Kempton, Kashunda Kempton, Kearston Kempton, Keina Kempton, Kely Kempton, Kerissa Kempton, Kiandra Kempton, Kimley Kempton, Krysia
Kempton, Kyanna Kempton, Lajuanda Kempton, Lania Kempton, Lanina Kempton, Latanza Kempton, Lauriann Kempton, Lawan Kempton, Laya Kempton, Linna Kempton, Lisbet Kempton, Luzmaria Kempton, Maeghan
Kempton, Mali Kempton | {"url":"https://www.instantcheckspy.com/lastname/Kempton.php","timestamp":"2024-11-12T07:34:11Z","content_type":"text/html","content_length":"334866","record_id":"<urn:uuid:ef0c2fec-4f3c-496f-8829-dd2fdd21e460>","cc-path":"CC-MAIN-2024-46/segments/1730477028242.58/warc/CC-MAIN-20241112045844-20241112075844-00088.warc.gz"} |
20 research outputs found
The quantum group $SU_q(3)=U_q(su(3))$ is taken as a baryon flavor symmetry. Accounting for electromagnetic contributions to baryons masses to zeroth order, new charge specific $q$-deformed octet and
decuplet baryon mass formulas are obtained. These new mass relations have errors of only 0.02\% and 0.08\% respectively; a factor of 20 reduction compared to the standard Gell-Mann-Okubo mass
formulas. A new relation between the octet and decuplet baryon masses that is accurate to 1.2\% is derived. An explicit formula for the Cabibbo angle, taken to be $\frac{\pi}{14}$, in terms of the
deformation parameter $q$ and spin parity $J^P$ of the baryons is obtained.Comment: 14 page
Algebraic deformations provide a systematic approach to generalizing the symmetries of a physical theory through the introduction of new fundamental constants. The applications of deformations of Lie
algebras and Hopf algebras to both spacetime and internal symmetries are discussed. As a specific example we demonstrate how deforming the classical flavor group $SU(3)$ to the quantum group $SU_q(3)
\equiv U_q(su(3))$ (a Hopf algebra) and taking into account electromagnetic mass splitting within isospin multiplets leads to new and exceptionally accurate baryon mass sum rules that agree perfectly
with experimental data.Comment: 5th International Conference on New Frontiers in Physics, Crete, Greece, July 6-14, 201
Building upon previous works, it is shown that two minimal left ideals of the complex Clifford algebra $\mathbb{C}\ell(6)$ and two minimal right ideals of $\mathbb{C}\ell(4)$ transform as one
generation of leptons and quarks under the gauge symmetry $SU(3)_C\times U(1)_{EM}$ and $SU(2)_L\times U(1)_Y$ respectively. The $SU(2)_L$ weak symmetries are naturally chiral. Combining the $\mathbb
{C}\ell(6)$ and $\mathbb{C}\ell(4)$ ideals, all the gauge symmetries of the Standard Model, together with its lepton and quark content for a single generation are represented, with the dimensions of
the minimal ideals dictating the number of distinct physical states. The combined ideals can be written as minimal left ideals of $\mathbb{C}\ell(6)\otimes\mathbb{C}\ell(4)\cong \mathbb{C}\ell(10)$
in a way that preserves individually the $\mathbb{C}\ell(6)$ structure and $\mathbb{C}\ell(4)$ structure of physical states. This resulting model includes many of the attractive features of the
Georgi and Glashow $SU(5)$ grand unified theory without introducing proton decay or other unobserved processes. Such processes are naturally excluded because they do not individually preserve the $\
mathbb{C}\ell(6)$ and $\mathbb{C}\ell(4)$ minimal ideals.Comment: 13 Page
An algebraic representation of three generations of fermions with $SU(3)_C$ color symmetry based on the Cayley-Dickson algebra of sedenions $\mathbb{S}$ is constructed. Recent constructions based on
division algebras convincingly describe a single generation of leptons and quarks with Standard Model gauge symmetries. Nonetheless, an algebraic origin for the existence of exactly three generations
has proven difficult to substantiate. We motivate $\mathbb{S}$ as a natural algebraic candidate to describe three generations with $SU(3)_C$ gauge symmetry. We initially represent one generation of
leptons and quarks in terms of two minimal left ideals of $\mathbb{C}\ell(6)$, generated from a subset of all left actions of the complex sedenions on themselves. Subsequently we employ the finite
group $S_3$, which are automorphisms of $\mathbb{S}$ but not of $\mathbb{O}$ to generate two additional generations. Given the relative obscurity of sedenions, efforts have been made to present the
material in a self-contained manner.Comment: 18 pages, 1 figur | {"url":"https://core.ac.uk/search/?q=author%3A(Gresnigt%2C%20Niels%20G.)","timestamp":"2024-11-11T04:29:57Z","content_type":"text/html","content_length":"118996","record_id":"<urn:uuid:0b23962d-644f-4863-889e-d86bca7774d2>","cc-path":"CC-MAIN-2024-46/segments/1730477028216.19/warc/CC-MAIN-20241111024756-20241111054756-00698.warc.gz"} |
Seminar - Non Parametric Estimator for Random Walk in Random Environment
Non Parametric Estimator for Random Walk in Random Environment
Date & Time:
Tuesday, May 17, 2016 - 12:15 to 13:30
Roland Diel, University of Nice-Sophia Antipolis
Room 301, NYU Shanghai | 1555 Century Avenue, Pudong New Area, Shanghai
The seminar is sponsored by NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai.
Consider a one dimensional random walk evolving in an i.i.d. random environment. I will explain how to construct estimators for the moments of the environment. I will also use these moment estimators
to approximate the distribution function of the environment and show how the speed of the walk affects the convergence rate of the estimators.
Roland Diel is an assistant professor at University of Nice-Sophia Antipolis in France. His research interests are probability and stochastic calculus in particular random process in random or
irregular environment.
Location & Details:
Transportation Tips:
• Metro: Century Avenue Station, Metro Lines 2/4/6/9 Exit 6 in location B
• Shuttle bus:
From Zhongbei Campus, Click here
From ECNU Minhang Campus, Click here | {"url":"https://research.shanghai.nyu.edu/centers-and-institutes/math/events/seminar-non-parametric-estimator-random-walk-random-environment","timestamp":"2024-11-13T16:24:32Z","content_type":"text/html","content_length":"18868","record_id":"<urn:uuid:c8e15e9f-00c0-478e-a49c-cef64f9e0386>","cc-path":"CC-MAIN-2024-46/segments/1730477028369.36/warc/CC-MAIN-20241113135544-20241113165544-00015.warc.gz"} |
BASIC and ELSE and GOTO and Work – part 1
My recent return to exploring my old Commodore VIC-20 code has reminded me about the main reason I jumped ship to a Radio Shack TRS-80 Color Computer: Extended Color BASIC. The older CBM BASIC V2
used by the VIC was missing keywords like ELSE, and had no functions for graphics or sounds. While I am having a blast re-learning how to program VIC-20 games, I sure do miss things like ELSE.
But should I?
IF/THEN/ELSE versus IF/THEN versus ON/GOTO
Pop quiz time! Suppose you were trying to determine if you needed to move a game character up, down, left or right. Which is the faster way to handle four choices?
30 IF Z=1 THEN 100 ELSE IF Z=2 THEN 200 ELSE IF Z=3 THEN 400 ELSE IF Z=4 THEN 500
30 IF Z=1 THEN 100
31 IF Z=2 THEN 200
32 IF Z=3 THEN 400
33 IF Z=4 THEN 500
Of course, if the values were only 1, 2, 3 and 4, you wouldn’t do either. Instead, you might just do:
ON Z GOTO 100,200,300,400
…but for the sake of this question, assume the values are not in any kind of order that allows you to do that.
IF/THEN/Work/ELSE versus IF/THEN/WORK
Suppose you were a junior high kid learning to program and you wanted to update some player X/Y positions based on keyboard input. Which one of these would be faster?
30 IF Z=1 THEN X=X+1 ELSE IF Z=2 THEN X=X-1 IF Z=3 THEN Y=Y+1 IF Z=4 THEN Y=Y-1
30 IF Z=1 THEN X=X+1
31 IF Z=2 THEN X=X-1
32 IF Z=3 THEN Y=Y+1
33 IF Z=4 THEN Y=Y-1
All is not fair
I should point out that the speed it takes to run these snippets depends on the value of Z. For the sake of this article, let’s assume no key is pressed, so Z is set to something that is not 1, 2, 3
or 4.
Obviously, when there are four IFs in a row (either in a single line with ELSE, or on separate lines), the order of the checks determines how fast you get to each one. If Z is 1, and that is the
first IF check, that happens faster than if Z is 4 and the code has to check against 1, 2 and 3 before finally checking against 4.
The same thing applies in languages that use switch/case type logic, so the things that need to be the fastest or happen most often should be at the top of the list and checked before things that
happen less often.
Because of this, to be fair, we should also check best case (Z=1) and worst case (Z=4) and see what that does.
Benchmarking going to a line
In my benchmark program, this one counted to 954:
0 REM elsetst1.bas '954
5 DIM TE,TM,B,A,TT
10 FORA=0TO3:TIMER=0:TM=TIMER
20 FORB=0TO1000
30 IF Z=1 THEN 100 ELSE IF Z=2 THEN 200 ELSE IF Z=3 THEN 400 ELSE IF Z=4 THEN 500
70 NEXT
80 TE=TIMER-TM:PRINTA,TE
90 TT=TT+TE:NEXT:PRINTTT/A:END
And this one was a tiny bit faster. It counted to 942:
0 REM elsetst1.bas '942
5 DIM TE,TM,B,A,TT
10 FORA=0TO3:TIMER=0:TM=TIMER
20 FORB=0TO1000
30 IF Z=1 THEN 100
31 IF Z=2 THEN 200
32 IF Z=3 THEN 300
33 IF Z=4 THEN 400
70 NEXT
80 TE=TIMER-TM:PRINTA,TE
90 TT=TT+TE:NEXT:PRINTTT/A:END
Thus, using ELSE was a bit worse if none of the conditions were true.
IF we could have used ON/GOTO, that would be blazing at 253!
0 REM elsetst3.bas '253
5 DIM TE,TM,B,A,TT
10 FORA=0TO3:TIMER=0:TM=TIMER
20 FORB=0TO1000
30 ON Z GOTO 100,200,300,400
70 NEXT
80 TE=TIMER-TM:PRINTA,TE
90 TT=TT+TE:NEXT:PRINTTT/A:END
But I said we couldn’t, because I changed the rules to “do work” rather than “go to a line.”
Benchmarking doing work
Doing work with ELSE clocked in at 601:
0 REM elsetst4.bas '601
5 DIM TE,TM,B,A,TT
10 FORA=0TO3:TIMER=0:TM=TIMER
20 FORB=0TO1000
30 IF Z=1 THEN X=X+1 ELSE IF Z=2 THEN X=X-1 IF Z=3 THEN Y=Y+1 IF Z=4 THEN Y=Y-1
70 NEXT
80 TE=TIMER-TM:PRINTA,TE
90 TT=TT+TE:NEXT:PRINTTT/A:END
Since ELSE was slower to go to a line, I thought maybe it would be here, too, but instead, splitting the statements was slower. This one reports 963:
0 REM elsetst5.bas '963
5 DIM TE,TM,B,A,TT
10 FORA=0TO3:TIMER=0:TM=TIMER
20 FORB=0TO1000
30 IF Z=1 THEN X=X+1
31 IF Z=2 THEN X=X-1
32 IF Z=3 THEN Y=Y+1
33 IF Z=4 THEN Y=Y-1
70 NEXT
80 TE=TIMER-TM:PRINTA,TE
90 TT=TT+TE:NEXT:PRINTTT/A:END
It seems like ELSE has its place, but not for just going to a line.
Best versus Worst: FIGHT!
Let’s try some best and worst cases now. For this test, I’ll resolve the jumps to lines 100, 200, 300 and 400 by adding this:
100 GOTO 70
200 GOTO 70
300 GOTO 70
400 GOTO 70
That will greatly slow things down since we have to search forward to the new line, then it has to start back at the top of the program and search forward to find line 70. BUT, it will be consistent
from test to test. I’ll add a “6 Z=1” or “6 Z=4” line.
• elsetst1.bas (else): Z=1 produces 507. Z=4 produces 1058.
• elsetst2.bas (separate): Z=1 produces 390. Z=4 produces 1053.
• elsetst3.bas (on/goto): Z=1 produces 317. Z=4 produces 357.
Wow. ON/GOTO is really good at going places, best or worst case.
And what about the “doing work” stuff?
• elsetst4.bas (else): Z=1 produces 632. Z=4 produces 633.
• elsetst5.bas (separate): Z=1 produces 1171. Z=4 produces 1172.
In conclusion…
If you are using IF to go to some code, ON/GOTO is the fastest, following by separate lines. Even in the worst case, separate lines are still a tiny bit faster, which surprised me. I suspect it’s the
time it takes to parse the ELSE versus a new line number. Retesting with all the spaces removed might change the results and make them closer.
But it does look like we need to stop doing “IF X=Y THEN ZZZ ELSE IF X=Y THEN ZZZ ELSE” unless we really need the extra bytes ELSE saves over a new line number.
And if you are trying to do work, ELSE seems substantially faster than separate line numbers. But, in both cases, best and worst case are very close. I believe this is a benchmark issue, since the
time to scan a few lines is tiny compared to the time it takes to do something like “X=X+1”, and both best and worst case do the same amount of work. A better test would need to be performed.
There is a way to speed up the separate line statements when doing work, especially for better case. Consider this:
0 REM elsetst6.bas '1034
5 DIM TE,TM,B,A,TT
10 FORA=0TO3:TIMER=0:TM=TIMER
20 FORB=0TO1000
30 IF Z=1 THEN X=X+1:GOTO 70
31 IF Z=2 THEN X=X-1:GOTO 70
32 IF Z=3 THEN Y=Y+1:GOTO 70
33 IF Z=4 THEN Y=Y-1
70 NEXT
80 TE=TIMER-TM:PRINTA,TE
90 TT=TT+TE:NEXT:PRINTTT/A:END
By adding the GOTO, if line 30 is satisfied (Z=1), the parser can start searching for line 70 without having to do the check against Z three more times. But, when a case is not satisfied, it now has
to parse through the GOTO token and a line number to find the end of the line, meaning that for worst case (Z=4) it should be a bit slower.
Let’s see if this works.
• elsetst6.bas (separate/goto): Z=1 produces 544. Z=4 produces 1241.
Compare that to the previous version without the end line GOTOs:
• elsetst5.bas (separate): Z=1 produces 1171. Z=4 produces 1172.
It looks like there’s a significant improvement for best case, and a slight decrease in performance for worst case (the overhead of skipping more characters to find the end of the line for the false
The more you know…
I guess I am learning quite a bit by revisiting the VIC-20 and having to do things without ELSE.
What do you think? Did I miss anything?
Until next time…
3 thoughts on “BASIC and ELSE and GOTO and Work – part 1”
1. MiaM
Another test you might try is to replace all GOTOs with an infinite for-next loop. Having the test at the end of the loop and end each IF THEN statement with NEXT (effectively jumping back to the
start of the main loop) would both speed up the jump back itself but also remove the need for the other tests once the correct match has been found. In an action game you might want to arrange
the if lines so that the execution time is as similar as possible for all different cases. Sure, there aren’t any difference in execution time between the add/subtract one to/from X or Y, but
2. Adam Coolich
In a way, you’re using ON GOTO like the CASE statement in Pascal.
For test#6, you wrote:
30 IF Z=1 THEN X=X+1:GOTO 70
31 IF Z=2 THEN X=X-1:GOTO 70
32 IF Z=3 THEN Y=Y+1:GOTO 70
33 IF Z=4 THEN Y=Y-1
What if you tried ON GOSUB for the decision line to branch to work lines?
30 ON Z GOSUB 100,101,102,103
100 X=X+1:RETURN
101 X=X-1:RETURN
102 Y=Y+1:RETURN
103 Y=Y-1:RETURN
Time went down to 254!
Full code:
0 REM elsetst7.bas
5 DIM TE,TM,B,A,TT
10 FORA=0TO3:TIMER=0:TM=TIMER
20 FORB=0TO1000
30 ON Z GOSUB 100,101,102,103
70 NEXT
80 TE=TIMER-TM:PRINTA,TE
90 TT=TT+TE:NEXT:PRINTTT/A:END
100 X=X+1:RETURN
101 X=X-1:RETURN
102 Y=Y+1:RETURN
103 Y=Y-1:RETURN
1. Allen Huffman Post author
This must be saving time having to search back for a GOTO when done. Great idea. I’ll keep track of these comments and write up a follow up. Thanks!
This site uses Akismet to reduce spam. Learn how your comment data is processed. | {"url":"https://subethasoftware.com/2020/05/14/basic-and-else-and-goto-and-work-part-1/","timestamp":"2024-11-04T02:42:07Z","content_type":"text/html","content_length":"87338","record_id":"<urn:uuid:09a78508-705a-4294-9231-755c03f41ac0>","cc-path":"CC-MAIN-2024-46/segments/1730477027809.13/warc/CC-MAIN-20241104003052-20241104033052-00095.warc.gz"} |
2.6 The International System of Units in Physics And Law Of Conservation
The very purpose of physics is to quantitatively describe and explain the physical world in as few terms as possible. This principle extends to units of measurement as well, which is why we usually
find different units used in science actually defined in terms of more fundamental units. The watt, for example, is one joule of energy transferred per second of time. The joule, in turn, is defined
in terms of three base units, the kilogram, the meter, and the second:
Within the metric system of measurements, an international standard exists for which units are considered fundamental and which are considered “derived” from the fundamental units. The modern
standard is called SI, which stands for Système International. This standard recognizes seven fundamental, or base units, from which all others are derived^4 :
An older standard existed for base units, in which the centimeter, gram, and second comprised the first three base units. This standard is referred to as the cgs system, in contrast to the SI system^
5 . You will still encounter some derived cgs units used in instrumentation, including the poise and the stokes (both used to express fluid viscosity). Then of course we have the British engineering
system which uses such wonderful^6 units as feet, pounds, and (thankfully) seconds. Despite the fact that the majority of the world uses the metric (SI) system for weights and measures, the British
system is sometimes referred to as the Customary system.
2.7 Conservation Laws
The Law of Mass Conservation states that matter can neither be created nor destroyed. The Law of Energy Conservation states that energy can neither be created nor destroyed. However, both mass and
energy may change forms, and even change into one another in the case of nuclear phenomena.
Conversion of mass into energy, or of energy into mass, is quantitatively described by Albert Einstein’s famous equation:
E = Energy (joules)
m = Mass (kilograms)
c = Speed of light (approximately 3 × 10^8 meters per second)
Conservation laws find practical context in many areas of science and life, but in the realm of process control we have the principles of mass balance and energy balance which are direct expressions
of these Laws. “Mass balance” refers to the fact that the sum total of mass entering a process must equal the sum total of mass exiting the process, provided the process is in a steady-state
condition (all variables remaining constant over time). To give a simple example of this, the mass flow rate of fluid entering a pipe must be equal to the mass flow rate of fluid exiting the pipe,
provided the pipe is neither accumulating nor releasing mass within its internal volume. “Energy balance” is a parallel concept, stating that the sum total of energy entering a process must equal the
sum total of energy exiting a process, provided a steady-state condition (no energy being stored or released from storage within the process). | {"url":"https://www.technocrazed.com/2-6-the-international-system-of-units","timestamp":"2024-11-10T08:14:45Z","content_type":"text/html","content_length":"84966","record_id":"<urn:uuid:66a7fa24-fce9-43b5-9ad8-ed499cc17d57>","cc-path":"CC-MAIN-2024-46/segments/1730477028179.55/warc/CC-MAIN-20241110072033-20241110102033-00531.warc.gz"} |
Plot logistic regression curve in R
I want to plot a logistic regression curve of my data, but whenever I try to my plot produces multiple curves. Here's a picture of my last attempt:
Here's the relevant code I am using:
fit = glm(output ~ maxhr, data=heart, family=binomial)
predicted = predict(fit, newdata=heart, type="response")
plot(output~maxhr, data=heart, col="red4")
lines(heart$maxhr, predicted, col="green4", lwd=2)
My professor uses the following code, but when I try to run it I get an error on the last line saying that the x and y lengths do not match:
# fit logistic regression model
fit = glm(output ~ maxhr, data=heart, family=binomial)
# plot the result
hr = data.frame(maxhr=seq(80,200,10))
probs = predict(fit, newdata=dat, type="response")
plot(output ~ maxhr, data=heart, col="red4", xlab ="max HR", ylab="P(heart disease)")
lines(hr$maxhr, probs, col="green4", lwd=2)
Any help would be appreciated.
As requested, reproduceable code using the mtcars dataset:
fit = glm(vs ~ hp, data=mtcars, family=binomial)
predicted= predict(fit, newdata=mtcars, type="response")
plot(vs~hp, data=mtcars, col="red4")
lines(mtcars$hp, predicted, col="green4", lwd=2)
The Code looks something like this:
fit = glm(vs ~ hp, data=mtcars, family=binomial)
newdat <- data.frame(hp=seq(min(mtcars$hp), max(mtcars$hp),len=100))
newdat$vs = predict(fit, newdata=newdat, type="response")
plot(vs~hp, data=mtcars, col="red4")
lines(vs ~ hp, newdat, col="green4", lwd=2)
The Graph looks like this:
The predictions are made with the newdatobject. This dataset has a considerably better resolution of possible hpvalues than the original dataset, and it is organised to make charting easier. When you
constructed hr, you were on your way to implementing it right, but you didn't use it in the prediction stage, instead using newdata=dat.
Elevate Your Expertise with Our Machine Learning Certification Program! | {"url":"https://www.edureka.co/community/168583/plot-logistic-regression-curve-in-r","timestamp":"2024-11-11T22:37:23Z","content_type":"text/html","content_length":"171794","record_id":"<urn:uuid:82781051-2582-4267-bcd6-303ab4392a00>","cc-path":"CC-MAIN-2024-46/segments/1730477028240.82/warc/CC-MAIN-20241111222353-20241112012353-00260.warc.gz"} |
Re: [tlaplus] Enumerating a set - converting a set into a sequence
I have the following problem. I need to convert a set into a sequence:
nbrs == {x \in {-1, 0, 1} \X
{-1, 0, 1} : x /= <<0, 0>>}
I've found '
' from 'Practical TLA+', but using OrderSet(nbrs) causes this error in TLC:
TLC threw an unexpected exception.
This was probably caused by an error in the spec or model.
See the User Output or TLC Console for clues to what happened.
The exception was a util.WrongInvocationException
: Attempted to construct a set with too many elements (>1000000).
TLC was unable to fingerprint.
Could someone shed some light onto this, or propose alternative solution?
Help is greatly appreciated.
You received this message because you are subscribed to the Google Groups "tlaplus" group.
To unsubscribe from this group and stop receiving emails from it, send an email to | {"url":"https://discuss.tlapl.us/msg03341.html","timestamp":"2024-11-04T08:21:07Z","content_type":"text/html","content_length":"7527","record_id":"<urn:uuid:c9c799bc-1be8-4a42-a01a-294d7fe6c830>","cc-path":"CC-MAIN-2024-46/segments/1730477027819.53/warc/CC-MAIN-20241104065437-20241104095437-00255.warc.gz"} |
Quiz on irreducible fractions - Online math exercises - Solumaths
Math quiz: irreducible fractions
This math quiz allows you to work on calculation techniques on whole fractions.
Objective of the math game on irreducible fractions
The principle of this game on irreducible fractions is simple. To succeed, you just have to find the result of an operation between several fractions. The operation can be an addition, a subtraction,
a multiplication, or a division between two whole fractions.
This math game is able to give you the solution with the steps of calculations, which helps to better understand the results obtained. All the calculations in this game are done with the fraction
Calculation game with irreducible fractions
This irreducible fraction math quiz allows students to develop their calculation skills with fractions, including addition, subtraction, multiplication, division of whole fractions. | {"url":"https://www.solumaths.com/en/math-games-online/play/quiz-irreducible-fractions","timestamp":"2024-11-02T08:56:56Z","content_type":"text/html","content_length":"37331","record_id":"<urn:uuid:dbccc263-4e2b-4e91-9636-9068505348cc>","cc-path":"CC-MAIN-2024-46/segments/1730477027709.8/warc/CC-MAIN-20241102071948-20241102101948-00787.warc.gz"} |
How to Treat Thermal Lensing in Simulations
In many laser or amplifier devices, thermal lensing plays an important rule and should therefore be taken into account in numerical simulations. In this article, I first briefly describe the origins
of thermal lensing and then show you how that effect can be treated in our software.
What is Thermal Lensing?
When a laser gain medium (e.g., a laser crystal) is pumped, we typically generate some heat, which subsequently needs to go away via thermal conduction. As a consequence of that, we inevitably obtain
some temperature gradients within the gain medium. Through various physical mechanisms, those can create some lensing effect for the laser light:
• The refractive index is temperature-dependent.
• The mechanical stress inside the crystal also modifies the refractive index (photoelastic effect).
• Further, the mechanical stress can lead to bulging of the end faces, giving the laser crystal the shape of a lens.
In typical cases, the first mentioned effect is often dominant. The figure below shows the numerically calculated temperature profile in a typical case.
Figure 1: Transverse pump intensity distribution (red) and thermal profile (blue), simulated for an end-pumped Nd:YAG rod. The temperature profile is approximately parabolic only near the center of
the crystal, so that a laser mode with a beam radius equal to that of the pump beam will experience some aberrations.
Thermal Lensing in Resonator Design
Our resonator design software RP Resonator calculates modes properties of laser resonators based on the ABCD matrix algorithm. (Precisely speaking, it uses some extended matrices (ABCDEF matrices) in
order to treat misalignment effects as well, but that is not relevant in our context.) Here, only lensing effects with a parabolic shape, i.e., without spherical aberrations, can be treated. The
software makes it easy to introduce a distributed lensing effect. A laser crystal, for example, is defined is a “prism”, and for that one can specify a parameter <$n_2$> which is the second-order
coefficient of the radial dependence of the refractive index: <$n(r) = n_0 - 0.5 n_2 r^2$>. That parameter is simply the dioptric power of the thermal lens divided by the crystal length. The dioptric
power may be known from elsewhere or may at least in simple cases be calculated from the dissipated power density with a simple formula. A common case is that offer a cylindrical rod which is
homogeneously pumped at least within the volume of the laser beam.
In principle, one could also insert a thin lens with a certain dioptric power to the left or right side of the laser crystal, or to the middle of the laser crystal when splitting that into two
sections. In many cases, the results will be similar to those for the distributed lens. However, there are differences in some cases, e.g. when the laser crystal extends over much of the total
resonator length. And it just is easy to deal with the distributed lens.
In rare cases, it may be relevant that the thermal lensing effect is not uniform along the beam direction due to the decrease of pump intensity in an end-pumped laser. You would then have to split
the laser crystal into multiple sections, each one having a different strength of lensing. With a little script code, containing a loop structure, one can simply automate that, so that you won't have
to manually enter multiple crystal sections.
Thermal Lensing in Fiber and Laser Simulations
More sophisticated thermal lensing models can be used in laser simulations, as can be done with our software RP Fiber Power.
Fiber Modes Modified by Thermal Lensing
In optical fibers, thermal lensing effects are usually negligible. That is not the case, however, for operation at very high power levels. Here, it may be appropriate to include thermal lensing in
the calculation of the guided modes of the fiber. That is no problem, since you can pass an arbitrary radial refractive index profiles to the mode solver.
The radial temperature profile itself can be calculated from a simple differential equation if the radial profile of the heat generation is known. (The script language of the software offers a
convenient function for solving that differential equation.) In cases with strong lensing effects, the heat generation profile may actually itself depend on the mode properties; in such a case, one
iteratively approximate a self-consistent solution for the heat profile and the mode properties.
Thermal Lensing in Beam Propagation
Our software can also be used for the numerical simulation of beam propagation in fibers – or in fact in bulk laser crystals. Here, one specify an essentially arbitrary refractive index profile,
which may of course be influenced by thermal lensing. Again, the temperature distribution may be calculated from the heat profile as explained above.
For example, one may simulate the situation of a cylindrical laser rod which is end-pumped with a Gaussian or super-Gaussian beam. Here, the thermal lens will have some aberrations. It is then simple
to simulate the effect of a single pass of an Gaussian input beam on the beam profile and beam quality factor. Also, one can simulate multiple resonator round trips until the beam properties have
more or less reached the steady state.
Final Remarks
Such modeling can involve a couple of non-trivial aspects. It begins with the question what level of sophistication is appropriate in a certain case – such a judgment requires some experience.
Further, you may have some questions concerning some technical aspects, e.g. how exactly to calculate the temperature profile. But don't worry – when using our simulation software, you will profit
from my competent and helpful technical support!
This article is a posting of the RP Photonics Software News, authored by Dr. Rüdiger Paschotta. You may link to this page, because its location is permanent.
Note that you can also receive the articles in the form of a newsletter or with an RSS feed.
Questions and Comments from Users
Here you can submit questions and comments. As far as they get accepted by the author, they will appear above this paragraph together with the author’s answer. The author will decide on acceptance
based on certain criteria. Essentially, the issue must be of sufficiently broad interest.
Please do not enter personal data here. (See also our privacy declaration.) If you wish to receive personal feedback or consultancy from the author, please contact him, e.g. via e-mail.
By submitting the information, you give your consent to the potential publication of your inputs on our website according to our rules. (If you later retract your consent, we will delete those
inputs.) As your inputs are first reviewed by the author, they may be published with some delay. | {"url":"https://www.rp-photonics.com/software_news_2018_04_20.html","timestamp":"2024-11-03T00:55:29Z","content_type":"text/html","content_length":"19783","record_id":"<urn:uuid:298d928f-843a-4e90-8469-f3d9042186a4>","cc-path":"CC-MAIN-2024-46/segments/1730477027768.43/warc/CC-MAIN-20241102231001-20241103021001-00143.warc.gz"} |
The Combinatorial and Other Math of the Java Collections API
The Java Collections API both involves some explicit Math and presents some nice artifacts which parallel other Math concepts.
Combinatorics is probably one of the more fundamental Maths for Computer Science and is also prevalent throughout other Maths. In one example of Combinatorial counting problems, there is a collection
of items, say a deck of cards, from which we want to determine the number of selections, say hands. The formula to compute the possible Combinations is written as:
This can also be stated as “n choose k.” My mnemonic for remembering this, and it is worth remembering, is to look at the left side above note that the n is on top and the k is on the bottom, which
visually maps the n! to the numerator and k! to the denominator, and then rotate the left part by 90 degrees counter clockwise so that it forms (n - k)! and put it in the denominator. Also every
number calculated by this equation is a Binomial Coefficient found in Pascal’s Triangle, which in my opinion is one of the most amazing mathematical structures.
Our example for possible five card hands from a deck of cards computes as follows:
Combinations give you the number of elements with no repetitions and where order does not matter. The possible cases and Mathematical structures for the criteria of order and repetition are as
│ │ Order Does not Matter │ Order Matters │
│ No Repetitions │ Combination/Set │ Permutation │
│ Repetitions │ Multiset/Bag │ Enumeration/List/String │
The Combinatorial equations are as follows:
│ │Order Does not Matter │Order Matters│
│No Repetitions │ │ │
│Repetitions │ │ │
The interesting thing about lists is that if you make lists of varying lengths of the following characters [0,1,2,3,4,5,6,7,8,9] , you have the natural numbers in base ten, so a list of length 3
gives you 10^3 or 1000 possibilities, which are: 000-999. Also lists have the highest cardinality of the four:
|List| > |Multiset| > |Permutation| > |Combinitation|
Where |object| means the cardinality or size of the collection, which is the number of elements in the set, list, etc.
The corresponding Java classes/interfaces are:
│ │Order Does not Matter │Order Matters │
│No Repetitions│java.util.Set │java.util.SortedSet │
│Repetitions │org.apache.commons.collections.Bag │java.util.List/java.lang.String│
Sadly the Java Collections API is incomplete in this regard. Also this example is somewhat abstract but it does demonstrate how to view these objects from a Combinatorial perspective, which in turn
can help with choosing the appropriate data structure, also it gives insight into possible ways that they may be populated and perhaps even tested.
This is an introductory example to Combinatorics, for more perspective there is an expansion on this known as the Twelvefold way.
The next example is more concrete, in fact it comes directly from the java docs for Comparator and Comparable:
For the mathematically inclined, the relation that defines the imposed ordering that a given comparator c imposes on a given set of objects S is:
{(x, y) such that c.compare(x, y) <= 0}.
The quotient for this total order is:
{(x, y) such that c.compare(x, y) == 0}.
It follows immediately from the contract for compare that the quotient is an equivalence relation on S, and that the imposed ordering is a total order on S. When we say that the ordering imposed
by c on S is consistent with equals, we mean that the quotient for the ordering is the equivalence relation defined by the objects' equals(Object) method(s):
{(x, y) such that x.equals(y)}.
I have to admit when I first read that a few years back, I was like, WTF does that mean! Obviously whoever wrote that was thinking deeply and mathematically about the underlying principals here which
is clearly needed if you are designing fundamental low level framework aspects of base classes and collections.
Comparators and Comparable are about ordering, so what is being defined above is a Total Order which means that all elements can be compared to every other element, compare this to a Partial Order
where elements may or may not be comparable to each other, both of these fall under the more general Order Theory. The Quotient aka Equivalence Class concept is a bit more complicated and beyond what
I am trying to talk about here.
I believe the above Comparator Javadoc quote was written by Joshua Bloch, the following is from his book Effective Java
The equals method implements an equivalence relation. It is:
□ Reflexive: For any non-null reference value x, x.equals(x) must return true.
□ Symmetric: For any non-null reference values x and y, x.equals(y) must return true if and only if y.equals(x) returns true.
□ Transitive: For any non-null reference values x, y, z, if x.equals(y) returns true and y.equals(z) returns true, then x.equals(z) must return true.
□ Consistent: For any non-null reference values x and y, multiple invocations of x.equals(y) consistently return true or consistently return false, provided no information used in equals
comparisons on the objects is modified.
□ For any non-null reference value x, x.equals(null) must return false.
The first three are the Mathematical definition of an Equivalence Relation (which relates back to the Equivalence Class) can be found in “Abstract Mathematics” or “Transition to Advanced Mathematics”
type books which describe Functions and Relations. CS Majors usually are exposed to these concepts as part of the intro into discrete math.
What I find interesting about these concepts is how the comparator/comparable and equals relation and their interrelationship for the individual object map back to control the collections behavior of
ordering and repetitions.
2 comments:
1. The connection between Combination and Set was very enlightening.
2. I'm not sure why Java doesn't have a built in TreeList, or a few others for that matter (but that's the one I most frequently miss--sorted list with O(log n) insert). Apache seems to have stepped
in for that as well: http://commons.apache.org/collections/api-3.1/org/apache/commons/collections/list/TreeList.html | {"url":"https://www.elegantcoding.com/2011/05/combinatorial-and-other-math-of-java.html","timestamp":"2024-11-11T00:07:39Z","content_type":"application/xhtml+xml","content_length":"87943","record_id":"<urn:uuid:fd41b562-95a0-4141-b713-ab2b1c7e537a>","cc-path":"CC-MAIN-2024-46/segments/1730477028202.29/warc/CC-MAIN-20241110233206-20241111023206-00810.warc.gz"} |
Diffusion models are generative models where training samples are gradually perturbed towards a tractable distribution (typically, a homogeneous gaussian), while a neural network is trained to revert
the process and remove the noise. This can be shown to be an effective generative process, able to create never-before-seen data samples from completely random noise.
Current score based diffusion models employ very simplistic diffusions kernels, leading to unnecessarily complex de-noising processes. The seminal paper [Son21S], which we presented in a previous
paper pill, showed that the de-noising task that needs to be learned by the neural network is uniquely determined by the forward diffusion process. Hence, the choice of a better forward diffusion
process is crucial in obtaining fast and sample efficient generative models.
Based on connections to statistical mechanics, [Doc22S] proposes a novel critically-damped Langevin diffusion model which, for similar model architecture and sampling compute budgets, outperforms the
sampling quality of previous models and sets itself as the new state of the art.
While the paper is rather technical, the main idea is simple: a novel forward diffusion process where the data point variable is augmented by an additional velocity variable and the diffusion process
is run in the joint data-velocity space. The two spaces are coupled as in Hamiltonian dynamics, with noise injected only in the velocity space.
In other words, instead of predicting what the point should look like in the de-noised image, the model learns how much each pixel should be changed at each instant of the de-noising process. Since
the noise is applied only to such “velocity”, the convergence on the non-velocity (the actual data) dimension ends up being much smoother, as represented in the image above.
Inspired by methods used in statistical mechanics, this work provides new insights into de-noising diffusion models and implies promising directions for future research. Code is available on github,
while more info can be found on the group’s website. | {"url":"https://transferlab.ai/pills/2022/score-based-generative-modelling-with-critically-damped/","timestamp":"2024-11-13T14:12:26Z","content_type":"text/html","content_length":"25185","record_id":"<urn:uuid:89ecfc65-2e1b-46b0-a003-468854ca7066>","cc-path":"CC-MAIN-2024-46/segments/1730477028369.36/warc/CC-MAIN-20241113135544-20241113165544-00729.warc.gz"} |
How Many Ml in a Gallon? - Measuring Expert
There are 3785.411784 milliliters in a gallon. This is equal to 3.785411784 liters or 231 cubic inches.
If you’re like most people, you probably don’t know how many milliliters are in a gallon. After all, who really needs to know that kind of information? But if you’re curious about the answer, or if
you need to know for some reason, here it is: There are 3785.41 milliliters in a gallon.
Now that you know the answer, you can impress your friends with your knowledge the next time they ask you a question about measurements!
How Many Liters in a Gallon?
What is 1 Gallon of Water in Ml?
One gallon of water is equal to 3,785 milliliters. This means that there are 3,785 mL in one gallon of water. To put this into perspective, one liter of water is equal to 1,000 mL.
Therefore, one gallon of water is approximately 3.8 times larger than one liter of water.
Is 1000 Ml Half a Gallon?
There is some confusion when it comes to understanding what exactly a gallon is, and how it relates to other common units of measurement like quarts and pints. To answer the question posed, no, 1000
mL is not half a gallon. In fact, a gallon contains twice as much liquid as a 1000 mL (which is also known as a liter).
When thinking about gallons, it might be helpful to think about them in terms of common household items. For example, a gallon of milk is typically 2% milkfat, or about 8 cups. A quart of milk on the
other hand contains only 4 cups.
So two quarts make up one gallon. This same relationship holds true for things like gasoline and paint – where buying them by the gallon makes sense because you need larger amounts. A pint equals 16
ounces (2 cups), so there are 8 pints in 1/2 gallon or 4 quarts.
Is 4 Liters the Same As 1 Gallon?
No, a gallon is actually 4.5 liters. The reason for the confusion is that there are two different types of gallons being used. There is the standard gallon which is used in the US and is equal to
3.785 liters.
However, there is also the imperial gallon which is used in the UK and other countries and is equal to 4.546 liters. So when someone says “a gallon of milk”, they could either be referring to the
standard gallon or the imperial gallon, but either way, it would be more than 4 liters.
How Many Ml are in a Gallon of Pharmacy?
A gallon is a unit of measurement for volume that is equal to 128 fluid ounces, or 3.785 liters. In the U.S., the gallon is the most common unit of measure for liquid ingredients in recipes and
pharmacy prescriptions. One mL is equal to 0.0338140226 fluid ounces, so there are approximately 3785 mL in a gallon of pharmacy.
Credit: organicgardeningeek.com
How Many Liters in a Gallon
There are a few different ways to answer the question, “How many liters in a gallon?” The first way would be to simply convert gallons into liters. There are 3.785411784 liters in one gallon.
So, to find out how many liters there are in X number of gallons, you would just multiply X by 3.785411784. For example, if you wanted to know how many liters were in 10 gallons, you would multiply
10 by 3.785411784, and the answer would be 37.85411784 liters. Another way to look at it would be that there are 0.264172052 gallons in one liter (just divide 3.785411784 by 0.264172052).
So, if you have X number of liters and want to convert it into gallons, you would just multiply X by 0.264172052.
How Many Oz in a Gallon
There are 128 ounces in a gallon. This means that there are 8 ounces in a half gallon, and 4 ounces in a quart.
How Many Ml in a Half Gallon
A half gallon is equal to 64 ounces or 2 quarts. This is also equivalent to 4 cups or 946 ml. So there are approximately 946 ml in a half gallon.
How Many Ml in 1 Gallon Philippines
Are you wondering how many ml in 1 gallon Philippines? Here is the answer! There are 3785.41 ml in 1 gallon.
This means that one gallon is equivalent to 3785.41 milliliters. In other words, there are about 3785ml in one Philippine gallon.
How Many 750 Ml in a Gallon
A gallon is a unit of measurement that is typically used to measure large quantities of liquid. There are two types of gallons in the United States, the standard gallon and the wet gallon. The
standard gallon is used for most liquids such as milk and gasoline, while the wet gallon is used for things like wine and beer.
One standard gallon is equal to 128 fluid ounces, while one wet gallon is equal to 133.3 fluid ounces. This means that there are approximately 9.6 cups in a standard gallon and 10 cups in a wet
gallon. So how many 750 mL bottles are in a gallon?
There are approximately 3 bottles of wine in a bottle of champagne . A regular size champagne bottle contains about 0.75 liters or about 1/5th of a gallon (0.2 US gal). So if you have ever wondered
how many glasses of champagne you can get out of one bottle, it all depends on the size glass you use!
How Many Ml in a Gallon of Liquor
A gallon of liquor is equal to 128 fluid ounces, or 3.78 liters. This means that there are approximately 33.814 ounces, or 1,000 milliliters (ml), in a gallon of liquor. Liquor is typically sold in
bottles that range in size from half-pints (8 fluid ounces) to gallons.
The most common sizes for distilled spirits are the half-gallon (64 fluid ounce), quart (32 fluid ounce), and pint (16 fluid ounce). While the U.S. standard system uses gallons, many other countries
use the metric system to measure liquids. In the metric system, a liter is equivalent to 1,000 milliliters (ml).
Therefore, a gallon of liquor is equal to 3.78 liters or 1,000 ml.
How Many Pints in a Gallon
A gallon is a unit of measurement that is most commonly used in the United States to measure volume. One gallon is equal to four quarts, eight pints, or sixteen cups. There are two types of gallons
in use today, the imperial gallon and the U.S. gallon.
The imperial gallon is slightly larger than the U.S. gallon, but both are still used interchangeably in many situations. When measuring large volumes, such as gasoline or water, it is more common to
use gallons rather than quarts or pints. To answer the question “how many pints in a gallon?” we need to know which type of gallon we are using.
If we are using an imperial gallon, there are eight pints in onegallon . If we are using a U.S. gallon, there are also eight pints in onegallon . So no matter which type of pint you have, there will
always be eightpint s inside it if it is one wholegallon .
Now let’s break down how many cups there area inside each different size container: 1 US cup = 0.125 (1/8) US gallons 1 Imperial cup = 0..142 (1/8) Imperial gallons As you can see from these
conversions, even though an imperial cup is slightly larger than a US cup they both hold the same amount when measuring liquid volume i-e-one eighth of their respective total capacity whether that be
a US or ImperialGALLON .
How to Convert Gallons to Milliliters
If you need to know how to convert gallons to milliliters, or vice versa, there is a very simple way to do so. All you need is a calculator and some basic math skills. Here’s how it works:
1 gallon = 3785.41 milliliters To convert from gallons to milliliters, simply multiply the number of gallons by 3785.41. For example, 2 gallons would be 2 x 3785.41 = 7571 milliliters.
Converting from milliliters to gallons is just as easy – divide the number of milliliters by 3785.41 instead of multiplying it. So, if you have 12000 milliliters that you need to convert into
gallons, divide 12000 by 3785 and you’ll get approximately 3.2 gallons.
How Many Ml in a Gallon? is a blog post that explains the answer to the titular question. The author begins by explaining that there are three different types of measurements for volume – imperial,
US customary, and metric.
He goes on to say that a gallon is equal to 128 fluid ounces in the imperial system, or 3.785 liters in the metric system. Finally, he provides a conversion table for those who need to know how many
milliliters are in a gallon.
Rakib Sarwar is a seasoned professional blogger, writer, and digital marketer with over 12 years of experience in freelance writing and niche website development on Upwork. In addition to his
expertise in content creation and online marketing, Rakib is a registered pharmacist. Currently, he works in the IT Division of Sonali Bank PLC, where he combines his diverse skill set to excel in
his career. | {"url":"https://www.measuringexpert.com/how-many-ml-in-a-gallon/","timestamp":"2024-11-12T23:49:35Z","content_type":"text/html","content_length":"125847","record_id":"<urn:uuid:e485f137-8dbb-4ec3-aaf3-8de066616e49>","cc-path":"CC-MAIN-2024-46/segments/1730477028290.49/warc/CC-MAIN-20241112212600-20241113002600-00757.warc.gz"} |
Converting Equations to MathML
What is Math ML?
MathML is an XML application for describing mathematical notation and capturing both its structure and content. The goal of MathML is to enable mathematics to be served, received, and processed on
the Web, just as HTML has enabled this functionality for text.
If equation content is created using the built-in equation editor in a Word document or PowerPoint file, the equation content may be converted into MathML format.
Why is it important to convert equation content to MathML?
Web-based content must be made accessible to people with vision, hearing, and motor impairments per the Americans with Disabilities Act. Producers of web-based content who are recipients of federal
funding, including colleges and universities, must comply with this mandate. In addition, producing content that is accessible to people with sensory and motor impairments is an industry best
practice, and the right thing to do. Producing accessible content is also in keeping with universal course design principles: the creation of content across all courses to serve as diverse a
population and audience as possible.
Math Markup Language (Math ML) is fully accessible to screen readers. Having the equation-based content in MathML format is beneficial for the following reasons:
• Expedites requests for accommodation
• Complies with the American with Disabilities Act
• Incorporates research-based best practices in universal design for learning (UDL)
Please note that MathType is only provided to WSE faculty currently in an active course development with an assigned instructional designer. All WSE faculty can use our divisional license for EquatIO
to create and edit math content.
Converting Equations/Content to MathML
• To produce accessible versions of content that includes equations, the bulk of the content (textual content) is rendered as HTML which is completely readable to a screen reader.
□ Render the text-based content in HTML into a content management system or into an application such as Dreamweaver or Notepad.
□ This procedure can be as simple as copying and pasting source code from a web page.
• The next step is to convert the equations themselves into MathML format and paste them into the HTML code at the appropriate locations.
□ (This process assumes that the equations were created using LaTeX , EquatIO, or MathType and that they are being cut and pasted from a text format - NOT picture format.)
☆ Note: If the equations are in a graphic format (JPG, PNG, TIFF, or GIF), they have to be re-typed using MathType before they can be converted to MathML.
□ Open the free-standing version of MathType on your computer. (When you install MathType on your computer, it installs as a plug-in equation editor in Word and PowerPoint – but you may also
open it as a free-standing application.)
□ Before you cut and paste equations into the MathType interface, check these settings:
☆ From the Preferences drop-down menu, select ‘Cut and Copy Preferences’
☆ Select the second radio button ‘Equation for application or website’
☆ In the dropdown at that radio button, select ‘MathML 0’
○ If multiple ‘MathML 2.0’ options appear in the list, select ‘MathML 2.0 (namespace attr)’
☆ Leave the other radio buttons blank and exit the dialog box by selecting ‘OK’
□ Now that you have chosen the proper settings in MathType, copy the text-based equations from Word or PowerPoint and paste them into the Math Type interface.
☆ Visually check the pasted equation to make sure the equation is correctly formatted in the MathType window.
□ Next, copy out of MathType and paste into the web page at the source code level.
□ What you have pasted into the source code is the true MathML code, readable by a screen reader. | {"url":"https://support.cmts.jhu.edu/hc/en-us/articles/26567166626829-Converting-Equations-to-MathML","timestamp":"2024-11-05T21:52:46Z","content_type":"text/html","content_length":"34747","record_id":"<urn:uuid:b50760e0-3565-4386-b8fd-ef08cb702540>","cc-path":"CC-MAIN-2024-46/segments/1730477027895.64/warc/CC-MAIN-20241105212423-20241106002423-00687.warc.gz"} |
Demystifying general relativity - Notes of InvertedPassion
### Demystifying general relativity Prerequisite reading: [[Demystifying special relativity]] The best summary of general relativity was given by John Wheeler when he said: >Matter tells spacetime
how to curve, spacetime tells matter how to move This can easily be seen in the Einstein's field equations for general relativity: ![[67da6b18dfad3fd4fdf0b407e14de603.png]] As you can see in the
equations, **curved spacetime (described by the left part) = matter density (described by the right part)** In other words, curvature of the spacetime is _literally_ just the amount of energy and
mass contained in it. #### Tilted light cones In special relativity, light cones are useful visualizations. In the space time diagram, a light cone around any event indicates the future events that
event can influence and the set of past events that could have influence this event. These light cones have a 45 degree angle boundary indicating light emitted from the event, since nothing can go
faster than light all future events have to remain within the light cone. ![[Screenshot 2021-09-29 at 11.51.26 AM.png]] (via [here](https://infinityplusonemath.wordpress.com/2017/04/29/
a-mathematical-intro-to-general-relativity-part-2/)) The spacetime of special relativity (Minkowski space) is the one without any mass (and hence without any curvature, hence without any gravity).
Hence, the Minkowski space is a special case of general relativity where curvature of spacetime is zero. But, as we saw from Einstein's field equations, if there's matter (mass or energy), there will
be curvature. The easiest way to see _what curvature does is to see how light cones are impacted by nearby matter_. ![[Screenshot 2021-09-29 at 11.56.03 AM.png]] (via [here](https://
infinityplusonemath.wordpress.com/2017/04/29/a-mathematical-intro-to-general-relativity-part-2/)) So, the curvature of the spacetime can be seen as light cones getting bent. The effect of **light
cones getting tilted and bent towards the matter** can be seen in the new phenomena that general relativity predicts: - Light bending around heavy objects (gravitational lensing) because the light
cone around a massive object is bent (and light travels on the edges of this light cone) - Time ticking slowly near a massive object as compared to lighter object. This is because the tilting of
light cone converts the time velocity into spatial velocity, and hence proper time slows down near a massive object (this is the same effect as of the time dilation for a moving observer) - Existence
of black holes. Where light cones get tilted horizontally, meaning not even light is able to escape a horizon. Let's explore each of these in a bit more details. Sidenote: how you draw [lightcones
depend on the co-ordinate system you're using](https://physics.stackexchange.com/questions/127423/why-light-cones-have-different-shapes-near-black-holes). #### Geodesics On a 2D plane, the shortest
path between two points is a straight line. However, that's not true for all surfaces. For example, on Earth (approximated as a sphere), the shortest path between two points is [a circle on the
surface of the sphere connecting the two points](https://infinityplusonemath.wordpress.com/2017/04/08/trippy-geodesics/). Geodesic is defined as the shortest path connecting the two points on a
surface. Someone traveling on a geodesic path _feels_ like they're traveling straight (even if the surface has a curvature). As an aside, [curvature is defined](https://
infinityplusonemath.wordpress.com/2017/04/01/the-awesome-theorem/) as positive if the sum of 3 angles of a triangle comes as >180 degrees, negative is it comes as <180 degrees and zero if it comes
exactly as 180 degrees. The key idea in relativity (both special and general) is that objects without any forces acting on them (in inertial frames) travel on geodesics paths that **maximize proper
time**. In flat spacetime of special relativity, if no force is acting on an object, it will continue to travel straight in its world line (maximizing its proper time). In general relativity, the
straight lines become geodesics because the spacetime is curved. What this emphasis on geodesic suggests that without any external forces acting on you, you'll not feel *anything* as geodesics are a
path of straight line. The following animation illustrates this point: <iframe width="560" height="315" src="https://www.youtube.com/embed/DdC0QN6f3G4" title="YouTube video player" frameborder="0"
allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe> In other words, **an object without any forces will travel a straight line
in spacetime**. It's just that because matter curves spacetime, the straight lines bend towards the matter and that is what we observe as gravitation. The gravitation, effectively, does not exist.
It's simply a straight motion on a curved surface. #### How time dilation happens The easiest way to visualize phenomena in spacetime is to draw light cones. As we have seen, massive objects cause
tilting of light cones towards themselves. ![[tilting-worldlines.jpg]] (via [here](https://users.sussex.ac.uk/~waa22/relativity/Explaining_Gravitational_Time_Dilation_Geometrically.html)) Imagine if
light signals are sent to you from such successively more tilted light cones, such light cones will take longer and longer (in your reference frame) to reach you and you'll perceive that as time
slowing down near a massive object. ![[time-dilation-gravity.jpg]] (via [here](https://users.sussex.ac.uk/~waa22/relativity/Explaining_Gravitational_Time_Dilation_Geometrically.html)) In relativity
(both special and general), if we compare two world lines between the same events, the longer world line experiences _lesser_ time as compared to the two. (This is why in twin paradox, as per
[[Demystifying special relativity]], twin with the longer world line ages more). This is a natural outcome of the fact that massive objects curve spacetime a lot more near them as compared to farther
than them. So this curving increases the length of the worldline and hence time passes slowly near massive objects than far away from them. ![[curving-worldlines.png]] (via [here](http://
thescienceexplorer.com/universe/how-gravity-changes-time-effect-known-gravitational-time-dilation)) Here's how to interpret the image above. Imagine the two points are in in my reference frame where
I'm at infinity so that no gravitational impact is felt by me and I'm stationary. If there's no massive object near the two points, they'll have a path like AB but if there's a massive object near
them, they'll have a path like CD. Since CD is longer than AB and speed of light is constant in all reference frames, looking from a distance it would seem like clocks ticking slower on CD than in AB
(if I measure the straight line distance as one tick in my reference frame). In other words, **in strong gravitational fields, objects move slower in time since they have to travel a longer path.** #
### Time dilation causes gravity For a while, I was stuck on the question of why gravity causes time dilation. But it is actually the other way around. For an object like a person in a gravitational
field, the time ticks faster on her head than her feet. This differential velocity in time at two different spatial points near a massive object create a spatial velocity vector which we perceive as
gravitational attraction. Perhaps, a spacetime diagram can help illustrate this clearly: <iframe width="560" height="315" src="https://www.youtube.com/embed/gcvq1DAM-DE" title="YouTube video player"
frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe> Another good video on the same subject is this: <iframe
width="560" height="315" src="https://www.youtube.com/embed/UKxQTvqcpSg" title="YouTube video player" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope;
picture-in-picture" allowfullscreen></iframe> #### Space-space curvature Most of the gravitational effects that we observe near Earth is due to space-time curvature. But massive objects bend
space-space slice of the entire 4D spacetime as well. We just don't notice the effects of this curvature because we're moving slow relative to the Earth but a fast moving object (like a light ray or
a spaceship traveling close to the speed of light) will feel its space-space curvature as well. What does the space-space curvature look like? ![[Screenshot 2021-09-29 at 2.16.20 PM.png]] (via [here]
(https://sites.pitt.edu/~jdnorton/teaching/HPS_0410/chapters/general_relativity_massive/index.html)) Notice that this is a 2D slice _without_ any time dimension. However, because of bending of space
around a massive object, the path between the two points that travels via the bend traverses a long path as compared to the path in flat plane (away from the massive object). In popular depictions,
the space around a massive object is depicted as follows: ![[circles3.gif]] (via [here](https://sites.pitt.edu/~jdnorton/teaching/HPS_0410/chapters/general_relativity_massive/index.html)) This
illustrates how the circumference of circles is longer near massive objects than you'd expect in a flat spacetime (because there's a bulge due to massive object). However, this image a bit misleading
because it assumes an extra dimension for bulge but in general relativity, we don't need an extra dimension. The space-space paths are indeed longer due to massive objects. #### What happens near a
black hole: spacetime bending vs spacespace bending One way to understand general relativity is as follows. Assumes you have the flat spacetime where the speed of light is 1, which means one unit
distance is 1 light second and one unit time is 1 second. Now, put some matter (mass and energy) into it. What this matter does is that it makes both the units of distance and time longer near it as
compared to far away in my reference frame where effects of that matter are nil. The curvature in spacetime that I observe appears to me like space itself falling towards a point. (It appears like
falling because if I observe you from a distance, it'll appear like you automatically move towards the massive object even if you don't do anything). The curvature of space-space that I observe
appears to me like light (or other objects) with the same velocity having to travel longer to arrive to me, closer they're to a massive object than the time they would have taken if it were a lighter
object. The upshot of this is that it is useful to visualize general relativity as matter stretching the fabric of space (elongating the lengths in space) and making space fall towards itself with
time (that too at an accelerating pace because time is curved more near the object than far from it). Only if spacetime falls faster as it is closer to the massive object will light take longer to
reach a distant observer, hence making time appearing to tick slower closer to massive object. Here's a nice visualization of this spacetime falling (also called the river model). !
[[schw_waterfall_s.gif]] (via [here](https://jila.colorado.edu/~ajsh/insidebh/waterfall.html)) A useful video explaining the same visualization is here: <iframe width="560" height="315" src="https://
www.youtube.com/embed/wrwgIjBUYVc?start=641" title="YouTube video player" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture"
allowfullscreen></iframe> Another way to visualize this falling of space is to use light cones. Here's how a light cone looks for a blackhole. ![[Screenshot 2021-09-29 at 2.53.46 PM.png]] (via [here]
(http://visualrelativity.com/LIGHTCONE/schwarzschild.html)) Notice two effects: - **Tilting of light cones**. Inside the black hole, light cone completely tilts towards the spatial direction. This
means even light cannot escape the spatial boundary marked by the event horizon. (In terms of falling space, this means inside the event horizon, the rate of falling of spacetime is faster than the
speed of light so effectively even light cannot swim "upstream"). - Shrinking of light cones. This is because viewed from your perspective of a far observer, light takes longer to travel between two
points near a massive object because the path is longer due to space-space curvature. #### Why planets rotate They rotate because they have an initial velocity in a spatial direction that's
perpendicular to the time geodesic. So these two velocities add up to create a perpetual helical velocity in spacetime that appears to us as elliptical in space. ![[world-line-earth.jpg]] (via [here]
(https://unboundedrationality.com/a-journey-to-the-edge-of-forever-episode-6/)) So, the Earth travels in a straight line (like all objects) but the geodesic (which is a straight line path) is itself
curved near the massive object (Earth). In case of launched satellites, if the initial velocity is higher than the rate of spacetime curving, the satellite will move away but if it is lower than the
rate of spacetime curving, it'll simply fall towards the object. The initial velocity has to be just right so that the satellite always travels with an effective velocity equal to the tangent of the
orbit. ![[Satellite-speed-and-force-directions.jpg]] (via [here](https://www.sciencelearn.org.nz/images/261-satellite-speed-and-force-directions)) #### Quantum considerations We know that the theory
of general relativity is incomplete. This is because in the world of quantum mechanics, we're not able to account for how spacetime is bent _because_ of quantum fields / particles. Sure, some
phenomena such as (black holes radiating energy as Hawking radiation) use both general relativity and quantum mechanics. But such analysis assume a specific spacetime curvature because of a massive
object like a black hole and try predicting how quantum phenomena will behave around such curved space time. But nobody has been able to incorporate spacetime curving itself because of quantum
phenomena. **That is the holy grail of all efforts trying to come up with quantum gravity.** Also note that special relativity has been quite successfully incorporated into quantum theory, giving us
quantum electro dynamics and quantum field theory. Here, particles or wavepackets moving near speed of light totally use length contraction and time dilation effects due to special relativity. That
said, as per Carlo Rovelli in the book _Order of Time_, we can imagine how spacetime will change if we successfully quantize it. He talks about following three effects: - **Discreteness**: instead of
values in spacetime continuously changing, we will have minimum units of plank time and plank length. - **Probabilistic light cones**: instead of a definite light cone given by our formulas, we will
get definite probabilities of what light cones should we expect if we measure it. - **Indeterminacy**: until some measurement happens, the light cone will truly be indeterminate (like spin of a
particle). This means we can probably expect phenomena like entanglement of (distant) light cones and so on. | {"url":"https://notes.invertedpassion.com/Universe/Demystifying+general+relativity","timestamp":"2024-11-06T05:37:55Z","content_type":"text/html","content_length":"20298","record_id":"<urn:uuid:ea08343f-cd94-4a33-a770-13acc2976f0f>","cc-path":"CC-MAIN-2024-46/segments/1730477027909.44/warc/CC-MAIN-20241106034659-20241106064659-00272.warc.gz"} |
• General
□ What is CZFC and Mathdialog?
CZFC is a version of ZFC with an intrinsic handling of context. This makes it easy for both machines and humans, dealing with formal proofs. Mathdialog is a computer implementation of the
CZFC set theory.
□ What is a proof in CZFC and Mathdialog?
A proof in CZFC is a list of logic-commands. In Mathdialog there are two types of proof the human-to-machine proofs and the machine-to-human proofs. The first one help users to find the
CZFC proof (see the The Interesting and Fun Game of Mathdialog Proofse), the second one is an interactive hypertext environment that helps other users to understand the proof in a natural
mathematical language that is, users doesn't need to know CZFC or Mathdialog to understand it.
□ What are logic-commands?
Logic-commands are the building blocks of proofs. In the human-to-machine proofs, they generate hypotheses and/or new goals and mirror each proof step used in mathematical books. A
logic-command is a step in a proof that models some step in books such as proof by contradiction, brig a definition, instantiate a quantified formula, etc. For example, if the present
goal is
SUBSET(A,B) ==> BG(x,B)
then the logic-command IF_RED[] place BG(x,B) as a new goal and SUBSET(A,B) as a new hypothesis.
□ What are the valid inference rules in Mathdialog?
There are not inference rules in Mathdialog, deductions are done through logic-commands. All logic-commands are described in the Logic-commands Reference Guide.
□ What is a CZFC proof?
□ What is a human-to-machine proof?
A human-to-machine proof is a dialog between humans and machines that helps the former to find a CZFC proof. This dialog take place in the mathdialog.com web GUI that enable users to send
sentences to Mathdialog and get a response from it. The proof starts when the user write and send a theorem (one of the kind of sentences Mathdialog understand) in the command window, it
responds by displaying the theorem hypotheses and its thesis in the black board, the latter is the proof main goal. Then, the user write and send logic-commands (another kind of sentences
Mathdialog understand) one by one until Mathdialog responds with a hypothesis that matches the main goal.
□ What is a machine-to-human proof?
A machine-to-human proof is a hypertext interactive environment where almost all necessary facts to understand the proof are at the user finger tips. You do not have to know CZFC nor
Mathdialog to understand them.
• Human-to-machine proofs
□ How to write theorems and definitions in Mathdialog?
To write theorems and some definitions, you have to follow the following syntax depending of the type of object you want to write. In what follow:
LABEL is a string with no blank spaces, the theorem or definition name.
LFA is a List of Atomic Formulas, they are the theorem or definition hypotheses for humans and the theorem local context for Mathdialog.
FORMULA is a logical formula.
VAR_LIST is the list of variables in its respective LFA.
For example, the informal syntax for theorems is:
Notice that, in Mathdialog, even the most insignificant theorem (there are not corollaries, lemmas, etc) has a name and one or more hypotheses. A formula alone does not make sense in
Mathdialog, it must have a context. In theorems and, as we will see next, definitions, LFA has this functionality.
For predicates, the informal syntax is:
DEF_PRED[LABEL;LFA;LABEL(VAR_LIST) <==> FORMULA]
For comprehension sets the informal syntax is:
DEF_OBC[LABEL;LFA;LABEL(VAR_LIST) = {BG(x,TERM):FORMULA}
Suppose TH_EX_UN is the name (label) of a theorem of existence and uniqueness, then informal syntax for a existential object is: DEF_OBE[LABEL;LFA;LABEL(VAR_LIST) = TH_EX_UN]
In Mathdialog, this definition and the theorem TH_EX_UN must be seen as one object (even though a theorem of existence and uniqueness can exists without a existential object definition),
in particular the LFA of the theorem TH_EX_UN and the LFA of this definition must literally match.
• Machine-to-human proofs
□ What is the difference between a machine-to-human proof and a proof in a book?
A machine-to-human proof is an interactive environment where you control the steps flow and helps you to solve your doubts about that proof. When you read a proof in a book and you don't
understand a step or where a hypothesis come from, you have to wait to ask to your teacher. Instead, in a machine-to-human proof you have all the facts to understand it at your finger
• Accounts and logins
□ Why I have to login?
You don't have to. Everybody can consult machine-to-human proofs. However if you want formulate a new definition or a new theorem to start a human-to-machine proofs, you have to be
logged. One of the incentives to prove theorems in Mathdialog is that your name will be associated to that theorem, the more important the theorem you prove the bigger prestige you will
have. At the present stage, all theorems are elementary. Its importance depends of the development one is making on a given time. When a logged user consults a machine-to-human proof the
correspondent human-to-machine proof is displayed in a floating window, this is useful to learn about how to make human-to-machine proofs.
• Web user interface
□ How resize a window?
There are two types of windows, one is the background fixed windows, in the human-to-machine proofs they are the blackboard and the command window, in the machine-to-human proofs they are
the goal, the hypotheses and the step windows. The other type of windows are the floating windows, you can resize them by dragging the lower right corner, you can also move them by
dragging its title-bar.
□ How can I close the result list window returned from a search?
That cannot be done, you have to choice a list element and delete the resulting window.
□ Why sometimes I cannot close a floating window?
A floating window cannot be closed if it has a child. The number in title-bar indicate if it has a parent. For example the numbers 1.2, 1.4.1 and 2.3 mean that they parents are 1, 1.4 and
2 respectively.
□ What is the child of a floating window?
A child of a floating window is a floating window that contains a definition or theorem related to its parent. For example if a floating window contains the partial order definition:
Definition of: P_ORDER;
If RELAT_IN(R,A), then we will say that
if and only if
ANTISYMMETRIC(R,A) AND REFLEXIVE(R,A) AND TRANSITIVE(R,A)
and you want to see the definition of REFLEXIVE, just select it, hover consuls in the main menu and click "The selected name". The REFLEXIVE definition will appear in a new floating
window that is a child of the one with the P_ORDER definition.
□ Why mathdialog.com doesn't respond to my touches?
The Mathdialog GUI does not works with touch screen devices such as tablets or mobile phones. mathdialog.com has been tested with Firefox, Chrome, Opera, Vivaldi, Edge and Safari web
□ What browsers can be used to use mathdialog.com?
Mathdialog.com has been tested with Firefox, Chrome, Opera, Vivaldi, Edge and Safari web browsers.
□ Why the red button "Connect here" doesn't work?
The web mathdialog.com is just the user interface, the red button means the browser cannot connect to the Mathdialog program. There are many reasons for this but it must be temporary, at
most 5 minutes, if it takes longer a huge problem is happening. It also happen with incompatible browsers. | {"url":"http://mathdialog.com/static/MdpPlainFaq.html","timestamp":"2024-11-12T12:08:05Z","content_type":"text/html","content_length":"15873","record_id":"<urn:uuid:c56064b1-c36d-4767-a192-7bb5a0053415>","cc-path":"CC-MAIN-2024-46/segments/1730477028273.45/warc/CC-MAIN-20241112113320-20241112143320-00858.warc.gz"} |
GRE Mock Test Papers Online for Students | MCQTUBE
GRE Mock Test Papers Online
GRE Mock Test Papers Online. We covered all the GRE Mock Test Papers Online in this post for free so that you can practice well for the exam.
Install our MCQTUBE Android app from the Google Play Store and prepare for any competitive government exams for free.
These types of competitive MCQs appear in the exams like GRE, CAT, CSAT, CLAT, Banking, Defence, G.I.C, GMAT, IBPS, L.I.C, MAT, Railway, SSC, UPSC, UGC, XAT, CDS, CPO, ICET, IMA, Income Tax,
Insurance, KPSC, NDA, SNAP Test, Sub Inspector of Police, TNPSC, all Government Exams, and other Competitive Examinations, etc. We created all the competitive exam MCQs into several small posts on
our website for your convenience.
You will get their respective links in the related posts section provided below.
Join Telegram Group and Get FREE Alerts! Join Now
Join WhatsApp Group For FREE Alerts! Join Now
Related Posts:
GRE Mock Test Papers for Students
Triplets Noni, Moni and Joni enter a triathlon. If there are 9 competitors in the triathlon and medals are awarded for first, second, and third place, find the probability that the sum of these three
numbers is odd.
a) 3/14
b) 19/84
c) 11/42
d) 15/28
e) ¾
In a bag, there are 8 white balls and 10 green balls. 5 balls are drawn from the bag Find the probability that out of these five balls 2 are white and 3 green balls?
(a) 0.39
(b) 0.45
(c) 0.55
(d) 0.65
(e) None of these
A fair coin is flipped 3 times. Find the probability that the coin lands on heads exactly twice.
a) 1/8
b) 3/8
c) ½
d) 5/8
e) 7/8
There are 10 women & 3 men in room R. A person is picked at random from room R and moved to room S, where there are already 3 women and 5 men. If a single person is then to be picked from room S,
find the probability that a woman will be picked.
a) 13/21
b) 49/117
c) 15/52
d) 5/18
e) 40/117
If the probability of rain on any given day in Chandigarh during the summer is 50%, independent of what happens on any other day, find the probability of having exactly 3 rainy days from July 14 to
July 18 inclusive. 075
a) 1/32
b) 2/25
c) 5/16
d) 8/25
e) ¾
In a shipment of 20 cars, 3 are found to be defective. If four cars are selected at random, find the probability that exactly one of the four will be defective.
a) 170/1615
b) 3/20
c) 8/19
d) 3/5
e) 4/5
a) 5/36
b) 5/24
c) 1/12
d) 1/6
e) ½
In a purse, there are 5 two-rupee and 4 one-rupee coins. If they are drawn out one by one, what is the chance that they come out two-rupee and one-rupee alternately, beginning with a two-rupee coin?
(a) 1/126
(b) 1/2880
(c) 1/20
(d) ¾
(e) None of these
A permutation is a sampling.
a) With replacement and with ordering
b) With replacement and without ordering.
c) Without replacement and with ordering
d). Without replacement and without ordering.
Option d – Without replacement and without ordering
We covered all the gre mock test papers online above in this post for free so that you can practice well for the exam.
Check out the latest MCQ content by visiting our mcqtube website homepage.
Also, check out:
Join Telegram Group and Get FREE Alerts! Join Now
Join WhatsApp Group For FREE Alerts! Join Now
Leave a Comment | {"url":"https://www.mcqtube.com/gre-mock-test-papers-online/","timestamp":"2024-11-08T12:00:51Z","content_type":"text/html","content_length":"166497","record_id":"<urn:uuid:9f5deeaa-4baa-4c07-a936-466b8e107f03>","cc-path":"CC-MAIN-2024-46/segments/1730477028059.90/warc/CC-MAIN-20241108101914-20241108131914-00437.warc.gz"} |
Examples of number theory showing up in physics
5702 views
My question is very simple: Are there any interesting examples of number theory showing up unexpectedly in physics?
This probably sounds like rather strange question, or rather like one of the trivial to ask but often unhelpful questions like "give some examples of topic A occurring in relation to topic B", so let
me try to motivate it.
In quantum computing one well known question is to quantify the number of mutually unbiased (orthonormal) bases (MUBs) in a $d$-dimensional Hilbert space. A set of bases is said to be mutually
unbiased if $|\langle a_i | b_j \rangle|^2 = d^{-1}$ for every pair of vectors from chosen from different bases within the set. As each basis is orthonormal we also have $\langle a_i | a_j \rangle =\
delta_{ij}$ for vectors within the same basis. We know the answer when $d$ is prime (it's $d+1$) or when $d$ is an exact power of a prime (still $d+1$), but have been unable to determine the number
for other composite $d$ (even the case of $d=6$ is open). Further, there is a reasonable amount of evidence that for $d=6$ there are significantly less than $7$ MUBs. If correct, this strikes me as
very weird. It feels (to me at least) like number theoretic properties like primality have no business showing up in physics like this. Are there other examples of this kind of thing showing up in
physics in a fundamental way?
This post imported from StackExchange Physics at 2014-03-24 09:19 (UCT), posted by SE-user Joe Fitzsimons
Most voted comments show all comments
The MUB connection is really to finite fields (and latin squares as @FrédéricGrosshans mentions) and only through that to prime numbers. I guess we could say this is a connection to number theory,
but really seems like a connection to abstract algebra, which is not nearly as surprising.
This post has been migrated from (A51.SE)
The MUB connection is really to finite fields (and latin squares as @FrédéricGrosshans mentions) and only through that to prime numbers. I guess we could say this is a connection to number theory,
but really seems like a connection to abstract algebra, which is not nearly as surprising.
This post imported from StackExchange Physics at 2014-03-24 09:19 (UCT), posted by SE-user Artem Kaznatcheev
@Artem: It's true that you can arrive at above result via finite fields, but the structure of the partial results is governed by number theoretic properties. I don't really see the way of arriving at
a given result as particularly fundamental, as there are often multiple paths to the result.
This post has been migrated from (A51.SE)
@Artem: It's true that you can arrive at above result via finite fields, but the structure of the partial results is governed by number theoretic properties. I don't really see the way of arriving at
a given result as particularly fundamental, as there are often multiple paths to the result.
This post imported from StackExchange Physics at 2014-03-24 09:19 (UCT), posted by SE-user Joe Fitzsimons
Duplicate on Phys.SE: physics.stackexchange.com/q/414/2451
This post imported from StackExchange Physics at 2014-03-24 09:19 (UCT), posted by SE-user Qmechanic
Most recent comments show all comments
MUBs is a really fascinating subjects. They are also linked with [Latin squares](http://en.wikipedia.org/wiki/Graeco-Latin_square#Mutually_orthogonal_Latin_squares), as e.g; shown [here](http://
pra.aps.org/abstract/PRA/v79/i1/e012109). I find this link with number theory more surprising than the role of prime numbers.
This post has been migrated from (A51.SE)
MUBs is a really fascinating subjects. They are also linked with Latin squares, as e.g; shown here. I find this link with number theory more surprising than the role of prime numbers.
This post imported from StackExchange Physics at 2014-03-24 09:19 (UCT), posted by SE-user Frédéric Grosshans
There are many attempts for a physical proof of the Riemann hypothesis. The major work in this direction was summarized in a recent review by: Schumayer and Hutchinson.
One of these attempts was proposed by: Berry and Keating. Their suggestion is within the framework of the Hilbert–Pólya conjecture, according to which, the Hilbert–Pólya Hamiltonian, whose spectrum
is the imaginary part of the zeta zeros, can be obtained by quantizing a classical Hamiltonian of a chaotic system having periodic orbits with log prime periods. They argue that the classical
Hamiltonian can be $xp$ (with appropriate yet unknown boundary conditions).
Another suggestion is due to Freeman Dyson in his Birds and Frogs lecture who suggests that the Riemann hypothesis might be proved through the classification of one dimensional quasicrystals.
This post imported from StackExchange Physics at 2014-03-24 09:19 (UCT), posted by SE-user David Bar Moshe
This seems more like engineering a physical system to embody certain number theoretic properties, rather than them occurring unexpectedly.
This post imported from StackExchange Physics at 2014-03-24 09:19 (UCT), posted by SE-user Joe Fitzsimons
I wouldn't count it as "engineering". It's more like using physical intuition in order to make a breakthrough in maths. We know the properties the Hilbert-Polya hamiltonian should have, so we whether
it might be implemented in a physical system.
This post imported from StackExchange Physics at 2014-03-24 09:19 (UCT), posted by SE-user Javier Rodriguez Laguna
Here is a toy example; I don't know how interesting this will be to physicists. The eigenvalues of the Laplacian acting on, say, smooth functions $\mathbb{R}^k/(2\pi \mathbb{Z})^k \to \mathbb{C}$ are
given by $$\{ m_1^2 + ... + m_k^2 : m_i \in \mathbb{Z} \}.$$
as a multiset (that is, with multiplicities). These are the energy eigenvalues of $n$ free non-interacting quantum particles on a circle. The multiplicity of a given eigenvalue is therefore the
number of ways to write it as a sum of $k$ (integer) squares.
This is a classical number-theoretic problem. For example, it is a classical result that the number of ways to write a non-negative integer $n$ as the sum of two squares is $$r_2(n) = 4 \sum_{d | n}
where $\chi_4(d)$ is equal to $0$ if $d \equiv 0, 2 \bmod 4$, equal to $1$ if $d \equiv 1 \bmod 4$, and equal to $-1$ if $d \equiv 3 \bmod 4$. In general, the number of ways $r_k(n)$ to write a
non-negative integer $n$ as the sum of $k$ squares has generating function $$\sum r_k(n) q^n = \left( \sum_{m \in \mathbb{Z}} q^{m^2} \right)^k = \theta(q)^k.$$
The function $\theta(q)$ is a theta function. Theta functions are closely related to modular forms, an important topic in number theory, and in fact the classical proof of the closed form $$r_4(n) =
8 \sum_{d | n} [4 \nmid d]$$
(where we have used the Iverson bracket above) proceeds by showing that $\theta(q)^4$ is a modular form; see Wikipedia.
This post imported from StackExchange Physics at 2014-03-24 09:19 (UCT), posted by SE-user Qiaochu Yuan
The $\theta$ page is crowded with greeks like the acropolis. Can you specify which $\theta$ you mean?
This post imported from StackExchange Physics at 2014-03-24 09:19 (UCT), posted by SE-user draks ...
@draks: it's defined immediately before I use the symbol.
This post imported from StackExchange Physics at 2014-03-24 09:19 (UCT), posted by SE-user Qiaochu Yuan
Ah, that was too close for me, thanks. (i) How are $k$, the number of squares and $n$, the number of particles on the circle related? And (ii) are there comparable formulas for $r_k(n)$ when one sums
powers other than 2?
This post imported from StackExchange Physics at 2014-03-24 09:19 (UCT), posted by SE-user draks ...
@draks: $k$ is the number of particles. $n$ is (up to some normalization) an energy eigenvalue. The situation when summing powers other than $2$ is considerably more complicated because the close
relationship to modular forms disappears and I don't know what's known about it.
This post imported from StackExchange Physics at 2014-03-24 09:19 (UCT), posted by SE-user Qiaochu Yuan
Thanks a lot. $ $
This post imported from StackExchange Physics at 2014-03-24 09:19 (UCT), posted by SE-user draks ...
I have an example of my own :). It appeared trying to calculate the dimension of a Hilbert space associated with rotationally invariant systems of n spins. The dimension was given in terms of the
Moebius function. for details, check the appendix of Phys. Rev. E 76, 061127 (2007) or arXiv:quant-ph/0702164.
This post imported from StackExchange Physics at 2014-03-24 09:19 (UCT), posted by SE-user user667
That's weird, and certainly interesting. I'll give the paper a look.
This post imported from StackExchange Physics at 2014-03-24 09:19 (UCT), posted by SE-user Joe Fitzsimons
I've encoutered Diophantine equations (a variant of Pell's equation) in an (unpublished) attempt to turn a molecular system into a classical logical gate. The goal was to (approximately) synchronize
incommensurable oscillations, and successives solution to the Diophantine equation gave me better fidelities.
I don't know if it qualifies for number theory, or even for physics, but I was surprised to find this equation as a good tool for my physics problem.
If anyone is interested, I can probably unearth my old notes and write something more detailed on the problem and the solution I found. Just ask in the comment.
This post imported from StackExchange Physics at 2014-03-24 09:19 (UCT), posted by SE-user Frédéric Grosshans
This is a general property--- diophantine approximation is related to resonance in classical systems like in KAM.
This post imported from StackExchange Physics at 2014-03-24 09:19 (UCT), posted by SE-user Ron Maimon
For quantized cat maps, the inverse of Planck's constant is an integer N . There are various results for the special cases, where N is a power of a prime. So, the arithmetic properties of N play an
important role here.
For references, see http://www.math.kth.se/~rikardo/cat2.pdf .
This post has been migrated from (A51.SE)
There are many theorems in quantum information which only apply to qudits of prime dimension. In particular, this seems to happen with graph states. In that case many theorems rely on the fact that
multiplication modulo a prime is an invertible operation.
The Chinese Remainder Theorem can be used to show that graph states made of qudits of square-free dimension are equivalent to collections of graph states of qudits of prime dimension (the primes
being the prime factorization of the original dimension).
Related to number theory is algebra. Group theory in particular tends to play an important role in quantum computing (e.g. the hidden subgroup problem).
This post imported from StackExchange Physics at 2014-03-24 09:19 (UCT), posted by SE-user Dan Stahlke
Thanks for taking the time to compose an answer. I don't really consider quantum algorithms as fundamental physics in the sense of this question, particularly given that the hidden subgroup stuff is
driven by a generalization of problems from number theory (factoring/discrete logs). The graph state observation seems more related to the fact that you are looking at factoring a Hilbert space,
which directly relates to primality of the dimesnionality, etc.
This post imported from StackExchange Physics at 2014-03-24 09:19 (UCT), posted by SE-user Joe Fitzsimons
This answer is closely related to jjcale's answer. In this article, Gurevich and Hadani prove Rudnick's quantum ergodicity conjecture about the Berry-Hannay model. To do it they construct a
number-theoretical description of the quantization of a torus phase space at rational values of hbar, involving l-adic sheaves on an algebraic variety of positive characteristic.
This post has been migrated from (A51.SE)
@MBN not quite. The result they prove belongs to the realm of quantum dynamical systems, not number theory. Number theory, or, more precisely, arithmetic geometry is a tool to solve the problem.
This post has been migrated from (A51.SE)
This answer is closely related to jjcale's answer. In this article, Gurevich and Hadani prove Rudnick's quantum ergodicity conjecture about the Berry-Hannay model. To do it they construct a
number-theoretical description of the quantization of a torus phase space at rational values of hbar, involving l-adic sheaves on an algebraic variety of positive characteristic.
This post imported from StackExchange Physics at 2014-03-24 09:19 (UCT), posted by SE-user Squark
This sounds more like physics showing up in number theory.
This post imported from StackExchange Physics at 2014-03-24 09:19 (UCT), posted by SE-user MBN
@MBN not quite. The result they prove belongs to the realm of quantum dynamical systems, not number theory. Number theory, or, more precisely, arithmetic geometry is a tool to solve the problem.
This post imported from StackExchange Physics at 2014-03-24 09:19 (UCT), posted by SE-user Squark | {"url":"https://physicsoverflow.org/9992/examples-of-number-theory-showing-up-in-physics","timestamp":"2024-11-08T06:11:44Z","content_type":"text/html","content_length":"381878","record_id":"<urn:uuid:5a4d4fc1-70f0-45e1-abe0-c7b3a51e3f56>","cc-path":"CC-MAIN-2024-46/segments/1730477028025.14/warc/CC-MAIN-20241108035242-20241108065242-00681.warc.gz"} |
Unscramble ABASING
How Many Words are in ABASING Unscramble?
By unscrambling letters abasing, our Word Unscrambler aka Scrabble Word Finder easily found 86 playable words in virtually every word scramble game!
Letter / Tile Values for ABASING
Below are the values for each of the letters/tiles in Scrabble. The letters in abasing combine for a total of 10 points (not including bonus squares)
• A [1]
• B [3]
• A [1]
• S [1]
• I [1]
• N [1]
• G [2]
What do the Letters abasing Unscrambled Mean?
The unscrambled words with the most letters from ABASING word or letters are below along with the definitions.
• abase (a.) - To lower or depress; to throw or cast down; as, to abase the eye.
• bisnaga () - Sorry, we do not have a definition for this word | {"url":"https://www.scrabblewordfind.com/unscramble-abasing","timestamp":"2024-11-12T17:10:02Z","content_type":"text/html","content_length":"52267","record_id":"<urn:uuid:7d7bd00b-7e60-45cc-85c9-80787c1e4688>","cc-path":"CC-MAIN-2024-46/segments/1730477028273.63/warc/CC-MAIN-20241112145015-20241112175015-00590.warc.gz"} |
Trace the flow of a drop of blood from the ascending colon t… | Wiki Cram
Trace the flow of a drop of blood from the ascending colon t…
Which оf the fоllоwing reаctions cаn be used to prepаre
Which оf the fоllоwing is аn exаmple of а homogeneous mixture?
An аsset is аll оf the fоllоwing, except?
The cоrrect sequence оf pаrts thаt functiоn to cаrry cardiac impulses is
(Sаme prоblem аs аbоve.) Cоnsider the following set of processes, with the length of the CPU-burst time given in milliseconds. The processes are assumed to have arrived in the
order P1 , P2 , P3 , P4 , P5 , all at time 0. Note that a smaller priority number implies a higher priority. Processes Burst time Priority P1 5 1 P2 3 4 P3 8 2 P4 4 5 P5 2 3 What is the average
turnaround time if the nonpreemptive priority policy is applied? Note: Show your work to receive full grade.
Trаce the flоw оf а drоp of blood from the аscending colon to the right deltoid.
Whаt is the аnticоdоn cоmplement to codon CGA?
Whаt tоwn will hоst the Super Bоwl in 2023?
Written wоrk is nоt required fоr this problem, however it is encourаged. Mаke sure аny written work includes the problem number on your scratch paper. A company produces and
sells widgets. The fixed monthly cost to operate their factory is $9114. The variable costs to produce a widget is $16, and they sell each widget for $30. a) Write the linear cost function. C(x) =
[n1] b) Write the linear revenue function. R(x) = [n2] c) Write the linear profit function. Simplify the function as much as possible. P(x) = [n3] d) How much profit/loss would be made if they made
and sold 450 widgets in one month? $[n4]
Submit yоur Excel file here. Nаme yоur submissiоns stаrting with "LаstName_FirstName_ESI6232_Quiz".
Skip back to main navigation | {"url":"https://wikicram.com/trace-the-flow-of-a-drop-of-blood-from-the-ascending-colon-to-the-right-deltoid/","timestamp":"2024-11-12T09:12:05Z","content_type":"text/html","content_length":"46117","record_id":"<urn:uuid:47b97bc9-260b-41d2-8f4c-530c14fb829c>","cc-path":"CC-MAIN-2024-46/segments/1730477028249.89/warc/CC-MAIN-20241112081532-20241112111532-00370.warc.gz"} |
Determining g with a Compound Pendulum: Issues with Uncertainties
• Thread starter trelek2
• Start date
In summary, the conversation discusses an experiment using a compound pendulum to determine the value of g. The person has encountered a problem with uncertainties and is seeking advice on how to
combine them. They also have a question about measuring heights and how to calculate the error. A formula for calculating the error using propagation of errors is provided, but the person is still
confused and needs further clarification.
Hi all!
I'm currently doing an experiment using a compound pendulum trying to determine the value of g.
I have a problem with my uncertainties:
Error in period T:
The period is measured with the use of a photo-gate of accuracy +/- 0.0001s.
For each height i did 20 measurements from which i calculated average period and from the standard deviation I have the standard error of mean. However due to the fact that I made so many
measurements the standard error of mean sometimes appears to be smaller than the actual precision of the photo-gate (for example +/- 0.00007s). What should I do in this case? I'm guessing I somehow
need to combine these uncertainties?
I have another question concerning the heights.
I firstly had to measure the length of the whole pendulum to find the centre of mass being in the middle. Then I mark the center of mass and measure different heights up to the edge of clamp (this
all using a meter stick). Then I measure the distance between edge of clamp and axis of rotation using vernier caliper.
Overall I guess it goes like this (correct me if I'm wrong)
Uncertainty of meter stick (with the help of magnifying glass) is 1/3mm so +/- 0,3mm.
And since I use this uncertainty twice (not sure if center of mass is exactly where marked) AND then when measuring distance to edge of clamp -this gives me +/- 0,6mm and I need to combine this with
the uncertainty in the distance on clamp which is +/-0,05mm. So it is sqrt(0,6^2+0,05^2)?
Thank you in advance for all the help.
PS. If you're not sure please don't reply as I don't want to get more confused than I am.
Last edited:
Using the propagation of errors you have [tex]\sigma _g^2=\frac{16 \pi ^4 \sigma _L^2}{T^4}+\frac{64 L^2 \pi ^4
\sigma _T^2}{T^6}[/tex] where all of the sigma terms are standard deviations, not standard errors.
DaleSpam said:
Using the propagation of errors you have [tex]\sigma _g^2=\frac{16 \pi ^4 \sigma _L^2}{T^4}+\frac{64 L^2 \pi ^4
\sigma _T^2}{T^6}[/tex] where all of the sigma terms are standard deviations, not standard errors.
Sorry, but I don't understand how this helps me. I thought I explained what I'm doing quite clearly. I need to know what my error for the periods and heights will be.
FAQ: Determining g with a Compound Pendulum: Issues with Uncertainties
What is a compound pendulum?
A compound pendulum is a physical system consisting of a rigid body attached to a pivot point and allowed to oscillate freely. It is different from a simple pendulum in that the rigid body has a
non-negligible size and shape, which can affect the behavior of the system.
Why is determining g with a compound pendulum important?
Determining the value of acceleration due to gravity, g, is important in many areas of physics and engineering. It can help us understand the behavior of objects in free fall and the motion of
pendulums. It is also a fundamental constant used in many equations and calculations.
What are the main issues with uncertainties when determining g with a compound pendulum?
The main issues with uncertainties in this experiment stem from the limitations of the equipment and the experimental setup. These can include variations in the length and mass of the pendulum, air
resistance, and imperfections in the pivot point. These uncertainties can affect the accuracy and precision of the results.
How can we minimize uncertainties when determining g with a compound pendulum?
To minimize uncertainties, it is important to carefully control and measure the variables involved in the experiment. This can include using a high-precision timer to measure the period of
oscillation, ensuring the pendulum is suspended from a stable pivot point, and repeating the experiment multiple times to obtain an average value.
What are some sources of error in determining g with a compound pendulum?
Sources of error can include human error in timing and measuring, environmental factors such as air resistance and temperature changes, and limitations of the equipment used. Proper calibration and
careful attention to detail can help reduce these errors. | {"url":"https://www.physicsforums.com/threads/determining-g-with-a-compound-pendulum-issues-with-uncertainties.285529/","timestamp":"2024-11-10T12:00:06Z","content_type":"text/html","content_length":"84056","record_id":"<urn:uuid:ff7c79df-142c-4e1d-b4af-d33d6999b50f>","cc-path":"CC-MAIN-2024-46/segments/1730477028186.38/warc/CC-MAIN-20241110103354-20241110133354-00779.warc.gz"} |
Introduction to Statistics
Introduction to Statistics
The student will be able to:
• Define data and range.
• Examine a real-world problem in which the range of a set of whole numbers is found.
• Examine a real-world problem in which the range of a set of decimals is found.
• Examine a real-world problem in which the range of a set of integers is found.
• Compute the range of a set of numbers.
• Describe the procedure for computing the range of a set of numbers.
• Apply range procedures to complete five interactive exercises.
The student will be able to:
• Define arithmetic mean.
• Examine real-world problems in which the mean of a set of whole numbers is computed.
• Examine real-world problems in which the mean of a set of decimals is computed.
• Describe the procedure for finding the mean of a set of numbers.
• Compute the mean of a set of numbers.
• Apply arithmetic mean procedures to complete five interactive exercises.
Non-Routine Mean
The student will be able to:
• Examine non-routine problems that involve an arithmetic mean.
• Determine the sum of n numbers given the mean and the value of n.
• Determine n given the sum of n numbers and the mean.
• Determine the missing number in a set of data given the mean and the other numbers in that set.
• Examine non-routine problems involving an arithmetic mean.
• Apply non-routine mean procedures to complete five interactive exercises.
The student will be able to:
• Define median.
• Examine real-world problems in which the median of a set of whole numbers is computed.
• Examine real-world problems in which the median of a set of decimals is computed.
• Differentiate between finding the median of an odd number of items and an even number of items.
• Describe the procedure for finding the median of a set of data.
• Compute the median for an odd number of items and for an even number of items.
• Apply median procedures to complete five interactive exercises.
The student will be able to:
• Define mode and bimodal.
• Examine real-world problems in which the mode of a set of whole numbers, decimals or integers is computed.
• Examine problems for which there is no mode.
• Examine problems for which the data is bimodal.
• Examine problems for which the mode is zero.
• Differentiate between sets of data with no mode, a mode of zero and two modes.
• Determine the mode of a set of data.
• Apply mode procedures to complete five interactive exercises.
Practice Exercises
The student will be able to:
• Examine ten interactive exercises for all topics in this unit.
• Determine which concepts and procedures are needed to complete each practice exercise.
• Compute answers by applying appropriate concepts and procedures.
• Self-assess knowledge and skills acquired from this unit.
Challenge Exercises
The student will be able to:
• Evaluate ten interactive exercises with word problems for all topics in this unit.
• Analyze each problem to identify the given information.
• Formulate a strategy for solving each problem.
• Apply strategies to solve routine and non-routine problems.
• Synthesize all information presented in this unit.
• Identify connections between basic statistics and the real world.
• Develop problem-solving skills.
The student will be able to:
• Examine the solution for each exercise presented in this unit.
• Identify which solutions need to be reviewed.
• Compare solutions to completed exercises.
• Identify and evaluate incorrect answers.
• Amend and label original answers.
• Identify areas of strength and weakness.
• Decide which concepts and procedures need to be reviewed from this unit. | {"url":"https://mathgoodies.com/learning_objectives_/introduction-statistics/","timestamp":"2024-11-05T15:14:51Z","content_type":"text/html","content_length":"38151","record_id":"<urn:uuid:5c774d26-5ce5-41e4-953e-aee8903347de>","cc-path":"CC-MAIN-2024-46/segments/1730477027884.62/warc/CC-MAIN-20241105145721-20241105175721-00618.warc.gz"} |
Generalized self-consistent-field theory: Gor'kov factorization
Gor'kov factorization, ψ†(1)ψ†(2)ψ(3)ψ(4)→ψ†(1) ψ†(2)ψ(3)ψ(4), is made the basis of a generalized self-consistent-field (SCF) theory precisely analogous to that previously developed for Hartree
factorization, ψ†(1)ψ†(2)ψ(3)ψ(4)→ψ†(1)ψ(4) (ψ†(2)ψ(3). The generalized SCF method is reviewed in the context of Gor'kov factorization. The corresponding simple SCF theory is developed to illustrate
the method and is shown to give a simple Hamiltonian version of the Bardeen-Cooper-Schrieffer theory of super-conductivity and, more generally, of coherent pairing. The notion of an external pairing
field is introduced and the corresponding response functions developed via a formalism like that of Kubo. General fluctuation-dissipation theorems are proved for the response functions. An equation
of state is then obtained by a formulation analogous to the dielectric formulation. The insertion of the simple SCF approximation to the response function into the equation of state yields a
generalization of the usual low-density (or short-range) evaluation of the grand potential to arbitrary temperatures. Screening the bare interaction with this approximate response function converts
the former into the t matrix of the independent-pair approximation. The entire analysis gives an underlying unity to the currently disparate treatments of superconductivity, of long-range
correlations, and of short-range correlations.
All Science Journal Classification (ASJC) codes
• General Physics and Astronomy
Dive into the research topics of 'Generalized self-consistent-field theory: Gor'kov factorization'. Together they form a unique fingerprint. | {"url":"https://collaborate.princeton.edu/en/publications/generalized-self-consistent-field-theory-gorkov-factorization","timestamp":"2024-11-07T19:51:31Z","content_type":"text/html","content_length":"50625","record_id":"<urn:uuid:6cbe795b-fd16-4d25-95d5-0987a61179e6>","cc-path":"CC-MAIN-2024-46/segments/1730477028009.81/warc/CC-MAIN-20241107181317-20241107211317-00563.warc.gz"} |
Reciprocal complementary distance spectra and reciprocal complementary distance energy of line graphs of regular graphs
The reciprocal complementary distance (RCD) matrix of a graph $G$ is defined as $RCD(G) = [rc_{ij}]$ where $rc_{ij} = \frac{1}{1+D-d_{ij}}$ if $i \neq j$ and $rc_{ij} = 0$, otherwise, where $D$ is
the diameter of $G$ and $d_{ij}$ is the distance between the vertices $v_i$ and $v_j$ in $G$. The $RCD$-energy of $G$ is defined as the sum of the absolute values of the eigenvalues of $RCD(G)$. Two
graphs are said to be $RCD$-equienergetic if they have same $RCD$-energy. In this paper we show that the line graph of certain regular graphs has exactly one positive $RCD$-eigenvalue. Further we
show that $RCD$-energy of line graph of these regular graphs is solely depends on the order and regularity of $G$. This results enables to construct pairs of $RCD$-equienergetic graphs of same order
and having different $RCD$-eigenvalues.
Reciprocal complementary distance eigenvalues, adjacency eigenvalues, line graphs, reciprocal complementary distance energy | {"url":"https://www.ejgta.org/index.php/ejgta/article/view/165","timestamp":"2024-11-06T12:40:55Z","content_type":"application/xhtml+xml","content_length":"96673","record_id":"<urn:uuid:d4fd9313-684a-4349-8cdf-6f05d8450a14>","cc-path":"CC-MAIN-2024-46/segments/1730477027928.77/warc/CC-MAIN-20241106100950-20241106130950-00499.warc.gz"} |
True Discount Important Formulae
True Discount – Important Formulae
The true discount is the amount of money saved by a buyer by preferring the instant payment option. Furthermore, subtraction of present worth from sum due gives the amount of true discount.
The true discount formula can be derived from the actual definition of true discount. Contemporary scholars of the world define the terminology as a true discount in various ways. They include the
relationship of various terminologies to manipulate the existing definition and define the true discount with the compound interest. Actually, the true discount formula describes the relations of the
terms true discount with simple interest or with the amount that has to be paid by a buyer after a specific time. Learners of the contemporary world prefer to focus on a definition of true discount
to understand the True Discount Formula. The reason behind preferring this is the definition and formula is interrelated.
Overview of True Discount Formula
The true discount formula can be derived effectively by an effective understanding of the terminology that has been included in problems related to true discount. The true discount formula regarding
the sum of the amount has to be paid after a certain time and the present worth of the products such as personal laptop, phone or other essential products. In order to solve such problems that
include the concept of simple interest, learners can drive the true discount formula by using concepts of true discount and simple interest. For instance, a buyer buys an item from the market that
has the present value of 25,000 rupees due for 7 years and the rate of simple interest is 10 per cent per annum. In the mentioned case, learners can calculate the simple interest that is also a true
discount. In this case, it has been effectively observed that the simple interest is a true discount that saves money for buyers.
Definition of True Discount
Various definitions of true discount can be evaluated from the various true discount formulas. Defining true discounts the learners and students need to focus on the formula otherwise they can be
flustered by various terminology and their relationship with others. Furthermore, it describes the relationships of true discount with another terminology that is related and generally mentioned in
the problems. For instance, the true discount formula, L = (K * T * P) / 100, where K represents the present value of the item, L denotes the true discount, P is the rate of simple interest and T
represents the duration of the time period. Learners can describe the definition with the help of the above-mentioned formula. Furthermore, it can be seen from the mentioned true discount formula. In
a similar way, they can also understand and manipulate the definition of true discount.
What is True Discount Formula
The true discount formula regarding the concept of simple interest can be seen from the above-mentioned equation. However, it can be effectively observed from the above formula that the formula is a
manipulation of the simple interest formula. Similarity can be noticed by replacing the terms with terms of simple interest formulas such as present value by principal value. Furthermore, it cannot
be exaggerated to say that the simple interest formula and the true discount formula are the same except, the terms present value and principal value. Similarly, in the case of compound interest, the
true discount formula is a manipulated version of the compound interest formula. Furthermore, it cannot be exaggerated to say that learners have to focus on the compound and simple interest in order
to solve the problems regarding true discount.
Effective Ways to Solve Problems
The learners have to first focus to solve the problems regarding the simple and compound interest otherwise they cannot solve such kinds of problems in an effective way. The speed of calculation such
as multiplication and division is also playing a vital role in order to solve the problems related to true discount as well as the problems related to simple and compound interest. Furthermore,
learners need to focus on the concept behind the simple and compound interest, and true discount in order to solve problems unless they cannot solve the problems. In case the learners focus on their
calculation speed then they can improve their efficiency and efficacy of solving the problems. In case, they are enthusiastically required to learn, then they can ask their instructors to derive the
true discount formula so that they can understand the philosophy behind other formulas related to the terms.
In order to solve the complex or simple problems of true discounts, the learners need to focus on the true discount formula. The ability to solve such kinds of problems can be improved if the
learners focus on their calculation speed and the formula regarding the problems. Moreover, the problems of true discount cannot be effectively dealt with unless they have an effective understanding
of simple and compound interest. | {"url":"https://sscegy.testegy.com/2023/12/true-discount-important-formulae.html","timestamp":"2024-11-02T14:51:05Z","content_type":"text/html","content_length":"1049064","record_id":"<urn:uuid:02a96d86-4298-4b03-b11c-b1aeea6822f4>","cc-path":"CC-MAIN-2024-46/segments/1730477027714.37/warc/CC-MAIN-20241102133748-20241102163748-00435.warc.gz"} |
András Vasy
I am a Professor in the Department of Mathematics of Stanford University.
My address is: Department of Mathematics, Building 380, Stanford University, 450 Serra Mall, Stanford CA 94305-2125, USA. My fax number is 650-725-4066.
My e-mail address is andras "at" math dot stanford dot edu.
This year I'm teaching:
• Math 51H, Honors Multivariable Mathematics, in autumn 2015. This is an honors calculus course with a mathematically rigorous treatment of basic linear algebra and analysis.
• Math 220/CME 303, Partial Differential Equations of Applied Mathematics, in autumn 2015.
• Math 173, Theory of Partial Differential Equations, in winter 2016.
Some recent quals are posted here for fast dissemination: Last year I taught:
• Math 51H, Honors Multivariable Mathematics, in autumn 2014. This is an honors calculus course with a mathematically rigorous treatment of basic linear algebra and analysis.
• Math 172, Lebesgue Integration and Fourier Analysis, in winter 2015. This is similar to 205A, but designed for undergraduate students, and for graduate students in other departments. It also
includes basic Fourier analysis.
• Math 205B, Real Analysis, in winter 2015.
In 2013-2014 I taught:
• Math 172, Lebesgue Integration and Fourier Analysis, in winter 2014. This is similar to 205A, but designed for undergraduate students, and for graduate students in other departments. It also
includes basic Fourier analysis.
• Math 256B, Partial differential equations, in winter 2014. This is an advanced graduate PDE class, focusing on Melrose's so-called b-(pseudo)differential operators, but no PDE background is
required. (Thus, 256A is not a prerequisite.) However, a thorough knowledge of functional analysis and Fourier analysis (as presented in the Math 205 sequence) is a must. In the Riemannian world
b-analysis includes manifolds with cylindrical ends, and in the Lorentzian world such diverse spaces as Minkowski space, a neighborhood of the static patch of de Sitter space, and Kerr-de Sitter
space, as well as various spaces which asymptotically have a similar (but not necessarily the same!) structure. In addition, b-analysis helps analyze the standard boundary value problems in wave
propagation; time permitting this will be discussed as well.
• Math 256A, Partial differential equations, in spring 2014. This is an advanced graduate PDE class, but with no PDE background required. However, a thorough knowledge of functional analysis as in
205A-B is a must. The course relies on Leon Simon's lecture notes. This course should be appropriate for first year graduate students.
In 2012-2013 I taught:
• Math 131P, Partial differential equations I, in autumn 2012. This is an undergraduate PDE class geared towards students interested in sciences/engineering.
• Math 220, Partial Differential Equations of Applied Mathematics, in autumn 2012.
• Math 205B, Real Analysis, in winter 2013.
In 2011-2012 I taught:
• Math 256B, Partial differential equations, in winter 2012. This is an advanced graduate PDE class, focusing on scattering theory, but no PDE background is required. (Thus, 256A is not a
prerequisite.) However, a thorough knowledge of functional analysis and Fourier analysis (as presented in the Math 205 sequence) is a must.
• Math 394, Classics in Analysis, in winter 2012.
• Math 171, Fundamental Concepts of Analysis, in spring 2012.
• Math 256A, Partial differential equations, in spring 2012. This is an advanced graduate PDE class, but with no PDE background required. However, a thorough knowledge of functional analysis as in
205A-B is a must. The course relies on Leon Simon's lecture notes. This course should be appropriate for first year graduate students.
In 2010-2011 I taught:
• Math 205B, Real Analysis, in winter 2011.
• Math 256B, Partial differential equations, in winter 2011. This is an advanced graduate PDE class, focusing on microlocal analysis, but no PDE background is required. (Thus, 256A is not a
prerequisite.) However, a thorough knowledge of functional analysis and Fourier analysis (as presented in the Math 205 sequence) is a must. The course is based on Richard Melrose's lecture notes,
volume 2 of Michael Taylor's PDE book, and additional material supplied by the instructor. We cover pseudodifferential operators, their use in elliptic and hyperbolic PDE, and hopefully
scattering theory.
• Math 171, Fundamental Concepts of Analysis, in spring 2011.
In 2009-2010 I taught:
• Math 220, Partial Differential Equations of Applied Mathematics, in autumn 2009.
• Math 205B, Real Analysis, in winter 2010.
In 2008-2009 I taught:
• Math 205B, Real Analysis, in winter 2009.
• Math 171, Fundamental Concepts of Analysis, in spring 2009.
• Math 256A, Partial differential equations, in spring 2009. This is an advanced graduate PDE class, but with no PDE background required. However, a thorough knowledge of functional analysis as in
205A-B is a must. The syllabus is somewhat different from the previous year's version (see below) relying instead on Leon Simon's lecture notes. This course should be appropriate for first year
graduate students.
Winter quarter 2008 I taught
• Math 205B, Real Analysis. The second quarter of the graduate real analysis sequence covers functional analysis. We use Reed and Simon's Functional Analysis (volume 1 of `Methods of Mathematical
Physics'), quickly covering Chapter 1 as background (except the measure theory part, which was covered in 205A), and start with Chapter 2 (Hilbert spaces). We cover Banach spaces, topological
spaces, locally convex vector spaces, bounded operators, the spectral theorem, and hopefully unbounded operators. There will be an in-class midterm, a take-home midterm, and regular homework
assignments (but no final).
Autumn 2007 I taught:
• Math 113. This is a `linear algebra done right' course (as is the title of the primary text). It does not assume any linear algebra background, or a background in writing proofs. However, one of
the goals of the course is to make you proficient in proof-writing, which is a crucial skill for more advanced mathematics courses, as well as a mechanism by which you can test your understanding
of the material. For an application-oriented linear algebra class, see Math 103. You may want to try out both courses at the beginning of the quarter to see which suits your taste better.
• Math 256A. Partial differential equations. This was an advanced graduate PDE class, but no PDE background was required. However, a thorough knowledge of functional analysis and Fourier analysis
(as presented in the Math 205 sequence) was a must. The course was based on Michael Taylor's PDE book and Richard Melrose's lecture notes.
The previous year (2006-2007) I also taught:
• Math 174A, Topics in Differential Equations with Applications. We use Michael Taylor's Partial Differential Equations: I (Basic Theory). This book covers both ODEs and PDEs, and has an approach
that naturally leads to extensions in modern PDE theory that we cannot cover this quarter. The book is fairly advanced, but if read carefully, with attention paid in lectures too, it should be a
great reference. We cover only small parts of the book: the first half of Chapter 1 (ODEs), and Chapter 3 (Fourier series and Fourier transform), with perhaps a little bit of Chapter 2. There
will be a midterm, a final, and regular homework assignments.
In spring 2004, back at MIT, I taught 18.157, Introduction to Microlocal Analysis: here is the web page. The previous fall I taught 18.152, Introduction to Partial Differential Equations: here is the
web page. In March 2004, I gave a lecture at the Clay Mathematics Institute on distribution theory; if you are an undergraduate interested in the flavor of modern analysis, please have a look at the
overheads in postscript or pdf format.
I am co-organizing a meeting in honor of Gunther Uhlmann, and a meeting at Northwestern University on Microlocal Methods in Spectral and Scattering Theory.
Daniel Grieser, Stefan Teufel and I are organizing a meeting on Microlocal Methods in Mathematical Physics and Global Analysis in Tübingen on June 14-18, 2011.
On October 25-26, 2008, I co-organized a conference in honor of Richard Melrose's upcoming 60th birthday.
I am organizing the Analysis and PDE seminar. We are not meeting in Fall 2008 due to the special semester at MSRI on Analysis on Singular Spaces.
My research area is partial differential equations, more specifically microlocal analysis and geometric scattering theory. This is a link to the web page of the Stanford seminar calendar for the
current week, this to the MIT analysis and PDE seminar, and here is the Northwestern math seminar calendar.
Jared Wunsch and I organized a meeting on Scattering theory and singular spaces at Northwestern University on May 27-30, 2005.
In March 2002, I co-organized a conference in honor of Richard Melrose's 25 years at MIT.
My 2014 ICM slides.
My lecture notes from an AMS session talk at Penn State in October 2009 on asymptotically anti de Sitter spaces, and the updated version from Banff in March 2010.
My lecture notes from my talk at MSRI in October 2008 on de Sitter-Schwarzschild space.
My lecture notes (slightly preliminary version) for the 2007 joint meeting in New Orleans are here.
These are my lecture notes for my February 5, 2006, talk at the CUNY Geometric Analysis Conference on Scattering theory on symmetric spaces and N-body scattering in postscript; also in pdf. The
Berkeley colloquium pdf version and the further improved UW colloquium pdf version are also available in pdf.
I gave a lecture at École Polytechnique in April, 2005, on the propagation of singularities for the wave equation on manifolds with corners. Most of the results stated there are written up in a
preprint listed below; the lecture notes are available here.
Notes from École Polytechnique, based on lecture on April 18, 2005.
A more accessible version of this talk was given at the Mathematical Physics meeting in Birmingham, Alabama, and the notes are being published in the Contemporary Mathematics series of AMS in the
volume ``Recent Advances in Differential Equations and Mathematical Physics''. The pdf and ps files are available here.
A sequel, on diffraction by edges, concentrating on the strength of the singularity of the reflected wave, was given at Berkeley in February 2006. Its slightly modified version, to be given in
Cambridge, is available as overheads or as a computer presentation.
These are the overhead transparencies for my talk at the Perspectives in Inverse Problems meeting in Helsinki in June 2004. An abbreviated version was presented at the AMS meeting in Evanston in
October, 2004.
These are my lecture notes from the minicourse I gave at the Université de Nantes in May 2002, which have been published as Geometry and analysis in many-body scattering, Inside out: inverse problems
and applications, 333--379, Math. Sci. Res. Inst. Publ., 47, Cambridge Univ. Press, Cambridge, 2003.
These are my lecture notes from the Inverse Problems session of the Pisa AMS-UMI joint meeting in June 2002.
In spring 2001, Vesselin Petkov, Maciej Zworski and I organized a semester-long program in scattering theory at the Erwin Schrödinger Institute in Vienna. Information is available here and from the
Erwin Schrödinger Institute web site.
I gave a lecture at École Polytechnique in February, 2001, on a joint project with Andrew Hassell and Richard Melrose. Part of the results stated there are written up in a preprint listed below; the
lecture notes are available here.
Notes from École Polytechnique, based on lecture on February 27, 2001.
This is a link to the Geometry, analysis and mathematical physics conference in San Feliu in September, 2000, where I was an invited speaker. I participated in the 1999 Conference on partial
differential equations at St. Jean-de-Monts. The lecture notes are available here.
You can find my manuscripts, some joint work with Bernd Ammann, Dean Baskin, Hans Christianson, Kiril Datchev, Jesse Gell-Redman, Nick Haber, Andrew Hassell, Peter Hintz, Maarten de Hoop, Lizhen Ji,
Robert Lauter, Rafe Mazzeo, Richard Melrose, Marius Mitrea, Werner Müller, Victor Nistor, Antonio Sa Barreto, Emmanuel Schenk, Plamen Stefanov, Michael Taylor, Gunther Uhlmann, Xue Ping Wang, Herwig
Wendt, Michal Wrochna, Jared Wunsch or Maciej Zworski, in postscript or pdf format below.
• Published in Communications in PDEs, 21:185-194 (1997).
• Published in Duke Math. J., 90:379-434 (1997).
• Published in J. Func. Anal , 148:170-184 (1997).
• This is the original version of my PhD thesis. A somewhat modified (improved) paper version is below. The thesis abstract is available separately.
• Published in Astérisque, 262 (2000); paper version of my thesis (see description above) from December 4th, 1997. Its introduction and the list of references are available separately. There is an
addendum, Appendix C, that was added in proof (in September, 1999) to fill in details of the positivity estimates in Sections 12 and 14.
• Published in J. Func. Anal , 173:257-283 (2000).
• Published in Commun. Math. Phys. 200:105-124 (1999).
• Published in Int. Math. Res. Notices (IMRN), 1998, no. 6, 285-315 (1998). Postscript version.
• Published in Annales Scientifiques de l'École Normale Supérieure (4), 34:313-402 (2001); original version December 15, 1998, revised May 2, 2000. Its introduction and the list of references are
available separately. Postscript version.
• Published in Journal d'Analyse Mathématique, 79:241-298 (1999). Also in postscript.
• Published in Journal of Functional Analysis , 184:177-272 (2001). Its introduction and the detailed statement of results and the list of references are available separately. The proof provided in
the published version has a minor gap, that is easily fixed, in that Proposition 7.1 is not stated (and proved) in the strongest possible form. The corrected version is available here. Postscript
• Published in Commun. Math. Phys., 212:205-217 (2000). Also in postscript.
• Published in Annales de l'Institut Fourier, 51:1299-1346 (2001). Also in postscript.
• Published in Geometric and Functional Analysis, 12:1018-1079 (2002). Also in postscript.
• Published in Math. Res. Lett. 8:413--428 (2001).
• Published in Communications in PDEs 27:2139-2186 (2002).
• Published in Inverse Problems 18:719-736 (2002).
• There is also an addendum to include an omitted reference to a paper of Eskin and Ralston. Published in Methods and Applications of Analysis 9:239-248 (2002).
• Published in Advances in Mathematics, 181:1-87 (2004).
• Published in Journal of Functional Analysis, 209:468-492 (2004).
• Published in Proc. Lond. Math. Soc. (3) 94:545-593 (2007). Revised version from 2005 is here, and the original version, from 2002, is here.
• Published in American Journal of Mathematics, 126:821-844 (2004). Also in postscript.
• Published in Commun. in PDEs, 29:671-705 (2004).
• Published in Inverse Problems and Spectral Theory (ed. H. Isozaki), Contemporary Mathematics, American Matematical Society (2004).
• Published in J. Func. Anal. 228:311-368 (2005). Also in postscript. Version of November 24, 2003. This version has added references to papers of B. Simon and Hunziker, missing from the September
7, 2003, version. Previously, the September 7 version added a second proof of the analytic continuation, using a more `classical' approach. The preceeding version, of August 13, 2003, is here.
The Aug. 13 version in turn has added some references to the original, August 6 version.
• Published in Inverse Problems, 20:1349-1354 (2004).
• Published in Annals of Mathematics, 168:749-812 (2008). There is also a correction to the proof of Proposition 7.3. Previously posted versions include the revised version from September, 2005;
the final version only has minor changes in the proof of Lemma 4.2. The original version is here.
• Published in Commun. in PDEs, 30:1445-1462 (2005). The original version is here.
• Published in Math. Res. Letters, 12:673-684 (2005). The original, October 2004 version is here.
• Published in Analysis and PDEs, 1:127-196 (2008). The original version is available in pdf and postscript formats.
• Published in Duke Mathematical Journal, 144:109-193 (2008). The original version is here, and the November, 2007 version is also available.
• Published in Advances in Mathematics, 223:49-97 (2010). Original version from 2007 -- the new version is more reader friendly. (A reference to Dafermos-Rodnianski had been added to the 2007
version posted here as compared to arxiv version.)
• Published in Journal d'Analyse Mathematique, 108:119-157 (2009). Erratum from March, 2011. A link to the January, 2008 version.
• Published in Modern Physics Letters B 22:2287-2328 (2008).
• Published in Commun. in PDEs, 39:512-529 (2014). The original version was from 2008, updated January 5, 2012.
• Published in Astérisque, 351 (2013), 136pp. Preprint, 2009. The originally posted version is here.
• Published in Communications in PDE, 35:1236-1275 (2010). The original submitted version is here. The first posted version is here. Apart from minor changes, a new section was added to this first
version regarding other boundary conditions covered by the method of the paper.
• Journal of Functional Analysis 259:503-523 (2010). This version fixes an equation numbering problem from the previously posted version. The original submitted version is here.
• Published in Analysis and PDE 5:81-144 (2012). The original version from 2009 is here.
• Published in Oberwolfach Reports 7(2):1648-1651 (2010). The complete manuscript (rather than just this report) is available below.
• Published in Int. Math. Res. Notices (IMRN), 2012 (23):5409-5443 (2012).
• Published in Annales de l'Institut Fourier, 62(6): 2347--2377 (2012).
• Published in Math. Annalen, 355(4):1221--1254 (2013). The originally posted version is here.
• Inventiones Math 194:381-513 (2013). Original preprint from 2010; revised 2011, again in 2012. Posted version added detail and explanation to the previous version, as well as the argument on
pp.89-90 checking a hypothesis of the Wunsch-Zworski setup that was not checked in full generality in the earlier version, and correcting several imprecise statements in Subsection 3.3. It also
rearranged the previous version, moving the large imaginary sigma part to the final section of the paper to make the rest more readable. This version added detail and explanation to the original
version, resulting in new Subsections 3.3 and 2.7, as well as the expansion of Subsection 3.2, apart from minor changes. See the Acknowledgments section at the end of the preprint for additional
information. The previous posted version fixed a few typos and minor issues compared to the originally posted version, and adds some references. The earlier posted version fixed a few typos
compared to the arxiv version.
• Published in Commun. in PDEs 39:452-511 (2014). The original version was from 2011, updated January 5, 2012. Original posted version from March 17, 2011.
• Published in `Inverse problems and applications. Inside Out II', edited by Gunther Uhlmann, Cambridge University Press, MSRI Publications, no. 60 (2012). Minor revision (2012) of version from May
30, 2011; most important it corrects some incorrect numerology in intermediate steps. The originally posted version from April 7, 2011, is available.
• To appear in the Bulletin de la Société Mathématique de France. Preprint, 2011.
• Published in Annales Scientifiques de l'ENS, 48:351--408 (2015).
• Published in Annales de l'Institut Fourier, 62(6):2379--2384 (2012).
• Published in Journal d'Analyse Mathematique 122:143-162 (2014). The original version is here.
• Published in Commentarii Mathematici Helvetici 89:867--894 (2014).
• Preprint, 2012. This version fixes a couple of typos relative to the originally posted version.
• Published in Multiscale Model. Simul. 11(2):566--585 (2013).
• To appear in Inventiones Math. Preprint, 2012. The posted version has better exposition, and also added an appendix by Hanming Zhou, relative to the original version.
• To appear in Amer. J. Math. Original preprint, 2012.
• Published in J. Spectral Theory 4:643--673 (2014). Original preprint, 2013. Above is the slightly revised version of the originally posted version.
• To appear in Journal of the AMS. Preprint, 2013. This corrects the formulation of the global result, Theorem 1.2, in the originally posted version, and adds additional detail.
• To appear in Analysis and PDE. Preprint, 2013. Revised version, with appendix removed into a separate paper, of the original; original was this.
• Published in Math Research Letters 21:1277-1304 (2014). Original included in the appendix of this paper above; this is an expanded version as a separate paper.
• To appear in IMRN. Preprint, 2014.
• Preprint, 2014, version of the ICM proceedings. (The final version had some small changes relative to this.) Published version is p.915-939 of the ICM proceedings.
• Preprint, 2014. Lecture notes on the `Global analysis...' paper listed above, given in Roscoff, France, in June 2014.
• To appear in J. d'Analyse Math. Preprint, 2014.
• To appear in Comm. Math. Phys. Preprint, 2014. Original version is here.
• Preprint, 2014.
• Preprint, 2015.
• Preprint, 2015.
• Preprint, 2015.
Together with Richard Melrose and Maciej Zworski, I gave a series of lectures at the beginning of November, 1998, at the Aarhus workshop on Geometric scattering. My lectures focused on propagation
estimates (as in propagation of `singularities' for generalized eigenfunctions) and its consequences (structure of S-matrices) in many-body scattering. Here is a very brief description of the
This page (together with its predecessors at Berkeley and MIT) has been accessed at least times since April 18, 1997. | {"url":"https://swap.stanford.edu/was/20160311035101mp_/http:/math.stanford.edu/~andras/","timestamp":"2024-11-07T17:51:07Z","content_type":"text/html","content_length":"46574","record_id":"<urn:uuid:940533a8-1b15-4074-b998-ef79dc6c7c43>","cc-path":"CC-MAIN-2024-46/segments/1730477028000.52/warc/CC-MAIN-20241107150153-20241107180153-00015.warc.gz"} |
Significant Figures: Definition, Rules, and Examples
Publish Date:
In this blog post, you will learn “What are significant figures and their rules?” with examples. After that, we will discuss why we round off significant figures and how to do it?.
What are Significant Figures?
As you know, the word significant is used for something that is essential and important. The term Significant figures is used for those digits in a number or measurement that contribute to its
According to Wikipedia:
“Significant figures of a number in positional notation are digits in the number that are absolutely necessary to indicate the quantity of something.”
Use of Significant Figures:
Significant figures have great importance in every field like science, medical e.t.c.
These digits help to know the accurate measurements. Scientists use it while measuring substances, doctors use it to measure medicines and drugs or to know the measurements of different body-related
masses and weights.
Similarly, engineers also determine significant figures to know the required precise value of various physical quantities in different devices and calculations.
Rules of Significant Figures:
Significant figures are determined by taking a number of rules under consideration. You can learn these rules in the portion below with examples.
All the non-zero digits (0 through 9 inclusive) are considered significant. These numbers play a role in the precision of a measurement.
In the numbers 1234 and 2.98, all the values are significant. But in 0.18 only 1 and 8 are significant. “Why 0 is insignificant?”, you will learn this later.
• Zero between two non-zero digits:
The zero which is present between two significant non-zero values is considered significant.
In example 2.09, the zero between 2 and 9 is significant because both 2 and 9 are significant digits.
• Zero at the end (trailing zero):
When a number ends at zero, there can be two situations. The first is that the number is a whole number value e.g 2300. The second scenario is that the number has a decimal point e.g 2.40.
In the first case, the zeros are insignificant while in the second case zeros are significant.
A number 230000 has only two significant values, the non-zero 2 and 3. But the 23.0000 has 6 significant values, all the zeros included.
Don’t you think these are more of “whether ‘this’ zero is significant or not rules” rather than “significant figure rules” ;)? Anyway, now we will discuss those zeros that did not come under any of
the above headings.
• Zeros that are used as space holders in values less than one such as 0.001. In these numbers, the bolded zeros are insignificant.
• Zero that is before the decimal point in values less than one is also insignificant. For example first zero in 0.001.
These zeros are also called leading zeros.
There are some measurements that we know for sure e.g one cubic meter is equal to 1000 liters. Similarly, it’s a fact that there are 12 inches in a foot.
Such values are called exact numbers. These values come from actual counting and not from experiments. In such numbers, all of the digits are significant.
For example, the value of 1000 millimeters in a meter has 4 significant digits although it contradicts the sig fig rules.
Did you know that now the speed of light is also an exact number? Its value is 299,792,258 ms-1.
How to determine significant figures?
For the shortcut, you can use the significant figures calculator. It can round off the numbers, tells the individual sig figs, and gives different notations for the number. But if you want to know
manually, see the example.
How many significant figures are in 0.02030?
We will examine each digit separately.
• Zero before the decimal point is insignificant. (leading zero)
• Zero after the decimal point is also insignificant. (leading zero)
• 2 is significant because it’s non-zero.
• 0 after 2 is significant as it is present between two two sig figs.
• 3 is also significant.
• The last zero is significant because it is the trailing zero after the decimal point.
There are 4 significant figures (2, 0, 3, 0).
Rounding off significant figures:
Consider you measured a piece of cloth with an ultimate device and the value you got is 38.871 meters. A friend of yours also measured a cloth but he used a normal scale. The value he got was 51
Now if you want to add these two values, how would you do it? Simple addition?
It will be a little problematic. The answer will be 89.871 meters. One can think after looking at this value that the clothes are exactly this meter long.
But there is a high possibility that there are some more digits in the value of the length your friend measured. It could be 51.23, 51.678, or any other number. You will never know unless you
In such cases, the significant figures are rounded off so that they can be easily used in math calculations. In other words, rounding off is used to remove uncertainty.
In our example, the value 38.871 would be rounded off to two significant figures (because there are two sig figs in 51 meters). The rounded value of 38.871 is 39.
Now, the sum of the two values will be 90.
If a whole number like 92999 is rounded off to 2 digits the answer will be 93000. Such values are then often represented in scientific notation i.e 9.3 x 104. (you can use the standard form
calculator for this conversion.)
Rules of rounding off:
There are two basic rules to round off significant figures. Count up to the required number of significant values and take the first insignificant value (x).
1. If x < 5, leave the last significant figure in its original form.
2. If x > or equal to 5, add 1 to the last significant digit.
Now if the value is a whole number then replace all the insignificant values with 0’s. For example, rounding off 3987 to one sig fig gives 4000.
But if the value has a decimal point then the insignificant values after the decimal point are dropped. And if there is an insignificant value before the decimal point, it is replaced with ‘0’.
For example, if you want to round off 906.09 to two significant values, then the answer will be 910. The 0 and 9 after the decimal are dropped while 6 before the decimal is replaced with 0 after
adding 1 to the last significant figure.
How to round off Significant figures?
The best way to learn anything is through examples and practice. So, here are a few examples of rounding off significant figures.
Example 1:
Round off 8.900 to one significant figure.
The only significant digit we need is 8 and it is also the last significant figure. The first insignificant number is 9 which is greater than 5. This means we will have to add 1 to the 8.
= 8 + 1 = 9
Since all of the insignificant values come after the decimal place, we will drop them. Hence, 8.900 rounded off to 1 sig fig is 9.
Example 2:
What will be the rounded-off form of 40.950 to three significant figures?
Step 1: Identify the first three significant digits.
= 40.9
Step 2: The first insignificant digit is 5. Add 1 to the last sig fig.
= 40.9 + 1
= 41.0
This is the answer.
Example 3:
How will you round off 56 to four significant figures?
The number itself contains only two significant figures. So how can we round it off to 4 places?
You remember that the trailing zeros after the decimal are significant, right!? We will use this rule here.
Step 1: Add decimal point to the number.
= 56.
Step 2: Add zeros to the required number. In our example, we need two extra significant places. This means we have to add 2 zeros.
= 56.00 | {"url":"https://www.meracalculator.com/blogs/significant-figures-definition-rules-and-examples","timestamp":"2024-11-13T21:50:38Z","content_type":"text/html","content_length":"31561","record_id":"<urn:uuid:4ebff848-e840-45e4-bfc9-0704a00f35d0>","cc-path":"CC-MAIN-2024-46/segments/1730477028402.57/warc/CC-MAIN-20241113203454-20241113233454-00661.warc.gz"} |
MDTP - Online Diagnostic Test
MDTP on-line multiple-choice tests were designed to help individual students review their readiness for some mathematics courses and may be useful in preparing for some mathematical placement tests
used by some California colleges and universities.
Each on-line test includes a diagnostic scoring report to help students identify strengths and weaknesses in some topic areas. These 40 question multiple-choice tests should be taken without a
calculator. The recommended time needed for taking each test is approximately one hour, but there is no enforced time limit.
MDTP has two on-line tests available for student use to help them prepare for Precalculus and Calculus level mathematics courses.
• There is no fee for taking these tests.
• There is no fee for the diagnostic scoring report.
• Nothing is downloaded to your computer.
• No log-ins or passwords required.
• The tests can be taken more than once.
The MR test should be taken prior to courses typically called trigonometry, precalculus, or math analysis. The test assumes two years of algebra and a year of geometry in preparation for a
precalculus course and has significant geometry content.
The CR test should be taken prior to a Calculus course. | {"url":"https://mdtp-wri.ucsd.edu/practice_tests/index.php","timestamp":"2024-11-05T16:34:15Z","content_type":"text/html","content_length":"3921","record_id":"<urn:uuid:0aaa83a6-31d1-468a-9363-cfdd9c0a09e9>","cc-path":"CC-MAIN-2024-46/segments/1730477027884.62/warc/CC-MAIN-20241105145721-20241105175721-00656.warc.gz"} |
Finite presentation and purity in categories σ[M]
Prest, Mike and Wisbauer, Robert (2004) Finite presentation and purity in categories σ[M]. Colloq. Math., 99. pp. 189-202. ISSN 0010-1354
Download (191kB)
For any module M over an associative ring R, let σ[M] denote the smallest Grothendieck subcatgory of Mod-R containing M. If σ[M] is locally finitely presented the notions of purity and pure
injectivity are defined in σ[M]. In this paper the relationship between these notions and the corresponding notions defined in Mod-R are investigated, and the connection between the resulting Ziegler
spectra is discussed. An example is given of an M such that σ[M] does not contain any nonzero finitely presented objects.
Actions (login required) | {"url":"https://eprints.maths.manchester.ac.uk/283/","timestamp":"2024-11-02T00:08:28Z","content_type":"application/xhtml+xml","content_length":"18284","record_id":"<urn:uuid:a72d04fe-6d80-40a3-ac58-99a24e2d0c08>","cc-path":"CC-MAIN-2024-46/segments/1730477027599.25/warc/CC-MAIN-20241101215119-20241102005119-00543.warc.gz"} |
Boolean Theorems - Cumulative, Associative & Distributive Law - Circuit Globe
Boolean Theorems
Boolean theorems and laws are used to simplify the various logical expressions. In a digital designing problem, a unique logical expression is evolved from the truth table. If this logical expression
is simplified the designing becomes easier. The boolean algebra is mainly used in digital electronics, set theory and digital electronics.
It is also used in all modern programming languages. Thus, Boolean theorems help in this way.
There are few basic laws and theorems of Boolean algebra, some of which are familiar to everyone such as Cumulative Law, Associative Law, Distributive law, DeMorgan’s Theorems, Double Inversion law
and Duality Theorems.
The Cumulative Law
The below two equations are based on the fact that the output of an OR or AND gate remains unaffected while the inputs are exchanged themselves.
The equation of the cumulative law is given below:
The Associative Law
These laws illustrate that the order of combining input variables has no effect on the final answer.
The Distributive Law
The distributive law can be understood by the corresponding logic equivalence shown in the below. The four basic identities of OR operations are given below:
The authentication of the above all equations can be checked by substituting the value of A = 0 or A = 1.
The three basic identities of AND operations are given below:
One can check the validity of the above identities by substituting the value of A= 0 or A = 1
Double Inversion Law
The double inversion rule is shown by the equation below:
The law states that the double complement (complement of the complement) of a variable equals the variable itself.
DeMorgan’s Theorems
The DeMorgan’s theorem is discussed in the article DeMorgan’s Theorem in detail.
The equations are given below:
The equation (6) says that a NOR gate is equivalent to a bubbled AND gate, and the equation (7) says that the NAND gate is equivalent to a bubbled OR gate.
Also See: DeMorgan’s Theorem
Duality Theorems
The new Boolean relation can be derived with the help of Duality theorem. According to this theorem for the given Boolean relation, the new Boolean relation can be derived by the following steps:
• Changing each OR sign to an AND sign.
• Changing each AND sign to an OR sign.
• Complementing each 0 or 1 appearing in the given Boolean identity.
For example:
The distributive law states that
Now, by using the duality theorem, we can get the new relation by interchanging each OR and AND sign. The equation (8) becomes.
The equation (9) is a new Boolean relation. Similarly, for any other Boolean relation, its dual relation can also be derived.
3 thoughts on “Boolean Theorems”
good and helpful
Dear sir distributive law mentioned above is wrong. it should be as under:
1) distributive property of addition with respect to multiplication
2) distributive property of multiplication with respect to addition:
Thank you so much for your explanation. I cleared all my doubts due to this!
Leave a Comment | {"url":"https://circuitglobe.com/boolean-theorems.html","timestamp":"2024-11-04T14:15:26Z","content_type":"text/html","content_length":"165678","record_id":"<urn:uuid:ac096c85-5807-41a8-973c-e77c8277f6d7>","cc-path":"CC-MAIN-2024-46/segments/1730477027829.31/warc/CC-MAIN-20241104131715-20241104161715-00121.warc.gz"} |
Devil May Cry 1 Total Number of Combos
Another combo numbers thread for DMC 1, I'll be doing calculations for all the games.
Force Edge/Sparda
1 Combo A
1 Combo B
1 Combo C
3 Round Trip As
2 Round Trip Bs
1 Round Trip C
1 Unarmed Combo
2 High Time As
2 High Time Bs
1 High Time C
2 Stinger As
2 Stinger Bs
1 Stinger C
2 E&I As
2 E&I Bs
1 E&I C
3 E&I Unarmed
2 Shotgun As
2 Shotgun Bs
1 Shotgun C
3 Shotgun Unarmed
2 Grenade Launcher As
2 Grenade Launcher Bs
1 Grenade Launcher C
3 Grenade Launcher Unarmed
2 Jump As
2 Jump Bs
1 Jump C
3 Jump Unarmed
2 Dodge As
2 Dodge Bs
1 Dodge C
3 Dodge Unarmed
60 combos
1 Combo A
1 Combo B
1 Combo C
3 Round Trip As
2 Round Trip Bs
1 Round Trip C
1 Unarmed Combo
2 High Time As
2 High Time Bs
1 High Time C
2 Stinger As
2 Stinger Bs
1 Stinger C
2 E&I As
2 E&I Bs
1 E&I C
3 E&I Unarmed
2 Shotgun As
2 Shotgun Bs
1 Shotgun C
3 Shotgun Unarmed
2 Grenade Launcher As
2 Grenade Launcher Bs
1 Grenade Launcher C
3 Grenade Launcher Unarmed
2 Jump As
2 Jump Bs
1 Jump C
3 Jump Unarmed
2 Dodge As
2 Dodge Bs
1 Dodge C
3 Dodge Unarmed
60 combos
1 Combo A
4 Charge As
3 Magma Drive As
3 Charged Magma Drive As
3 Kick 13 As
3 E&I As
3 Shotgun As
3 Grenade Launcher As
3 Jump As
3 Dodge As
29 total combos
That's a low 149 combos in total but it's expected since DMC 1 wasn't very evolved in combat design.
I Saw the Devil
I don't get it. What are the numbers next to the combo name and what is the round trip a? or b or c?
I don't get it. What are the numbers next to the combo name and what is the round trip a? or b or c?
The "A, B, and C" are the basic combos: Combo A (Triangle, Triangle, Triangle), Combo B (Triangle, Triangle -pause- Triangle Triangle) and Combo C (Triangle, Triangle -longer pause- Triangle). The
numbers are the number of total actions you can do in place of the original input. For example, 2 E&I As is Triangle, Square or Triangle, Triangle, Square.
Supporter ^2014
The best way to think of it is like a cancel.
I was going to ask how you were counting these, but i think i got the idea. | {"url":"https://devilmaycry.org/threads/devil-may-cry-1-total-number-of-combos.17360/","timestamp":"2024-11-08T04:58:00Z","content_type":"text/html","content_length":"55548","record_id":"<urn:uuid:7e682df7-5db6-46ea-a96f-7fcc2597e5a2>","cc-path":"CC-MAIN-2024-46/segments/1730477028025.14/warc/CC-MAIN-20241108035242-20241108065242-00324.warc.gz"} |
3,432 research outputs found
We propose a time-independent method for finding a correlated ground state of an extended time-dependent Hartree-Fock theory, known as the time-dependent density-matrix theory (TDDM). The correlated
ground state is used to formulate the small amplitude limit of TDDM (STDDM) which is a version of extended RPA theories with ground-state correlations. To demonstrate the feasibility of the method,
we calculate the ground state of 22O and study the first 2+ state and its two-phonon states using STDDM.Comment: 12 pages, 9 figure
The strength functions of the DGDRs in 16O and 40Ca are calculated using an extended version of TDHF known as the time-dependent density-matrix theory (TDDM). The calculations are done in a
self-consistent manner, in which the same Skyrme force as that used for the mean-field potential is used as the residual interaction to calculate two-body correlations. It is found that the DGDR in
16O has a large width due to the Landau damping, although the centroid energy of the DGDR is close to twice the energy of the GDR calculated in RPA. The DGDR in 40Ca is found more harmonic than that
in 16O.Comment: 4 pages, 3 figure
The ground states and excited states of the Lipkin model hamiltonian are calculated using a new theoretical approach which has been derived from an extended time-dependent Hartree-Fock theory known
as the time-dependent density-matrix theory (TDDM). TDDM enables us to calculate correlated ground states, and its small amplitude limit (STDDM), which is a version of extended RPA theories based on
a correlated ground state, can be used to calculate excited states. It is found that this TDDM plus STDDM approach gives much better results for both the ground states and the excited states than the
Hartree-Fock ground state plus RPA approach.Comment: 4 pages, 4 figure
Necessary conditions that the spurious state associated with the translational motion and its double-phonon state have zero excitation energy in extended RPA (ERPA) theories which include both
one-body and two-body amplitudes are investigated using the small amplitude limit of the time-dependent density-matrix theory (STDDM). STDDM provides us with a quite general form of ERPA as compared
with other similar theories in the sense that all components of one-body and two-body amplitudes are taken into account. Two conditions are found necessary to guarantee the above property of the
single and double spurious states: The first is that no truncation in the single-particle space should be made. This condition is necessary for the closure relation to be used and is common for the
single and double spurious states. The second depends on the mode. For the single spurious state all components of the one-body amplitudes must be included, and for the double spurious state all
components of one-body and two-body amplitudes have to be included. It is also shown that the Kohn theorem and the continuity equations for transition densities and currents hold under the same
conditions as the spurious states. ERPA theories formulated using the Hartree-Fock ground state have a non-hermiticity problem. A method for formulating ERPA with hermiticity is also proposed using
the time-dependent density-matrix formalism.Comment: 15 page
We systematically examine the asymmetry of the electronic states in the hole- and electron-doped cuprates by using the t-t'-t''-J model. Numerically exact diagonalization method is employed for a
20-site square lattice. We impose twisted boundary conditions (BC) instead of standard periodic BC. For static and dynamical correlation functions, averaging procedure over the twisted BC is used to
reduce the finite-size effect. We find that antiferromagnetic spin correlation remains strong in electron doping in contrast to the case of hole doping, being similar to the case of the periodic BC.
This leads to a remarkable electron-hole asymmetry in the dynamical spin structure factor and two-magnon Raman scattering. By changing the twist, the single-particle spectral function is obtained for
all momenta in the Brillouin zone. Examining the spectral function in detail, we find a gap opening at around the k=(pi,0) region for 10% doping of holes (the carrier concentration x=0.1), leading to
a Fermi arc that is consistent with experiments. In electron doping, however, a gap opens at around k=(pi/2,pi/2) and persists up to x=0.2, being correlated with the strength of the antiferromagnetic
correlation. We find that the magnitude of the gaps is sensitive to t' and t''. A pseudogap is also seen in the optical conductivity for electron doping, and its magnitude is found to be the same as
that in the spectral function. We compare calculated quantities with corresponding experimental data, and discuss similarities and differences between them as well as their implications.Comment: 14
pages, 17 figures, Replaced figures, to be published in Phys. Rev.
A density-matrix formalism which includes the effects of three-body ground- state correlations is applied to the standard Lipkin model. The reason to consider the complicated three-body correlations
is that the truncation scheme of reduced density matrices up to the two-body level does not give satisfactory results to the standard Lipkin model. It is shown that inclusion of the three-body
correlations drastically improves the properties of the ground states and excited states. It is pointed out that lack of mean-field effects in the standard Lipkin model enhances the relative
importance of the three-body ground-state correlations. Formal aspects of the density-matrix formalism such as a relation to the variational principle and the stability condition of the ground state
are also discussed. It is pointed out that the three-body ground-state correlations are necessary to satisfy the stability condition | {"url":"https://core.ac.uk/search/?q=author%3A(Tohyama)","timestamp":"2024-11-04T16:03:35Z","content_type":"text/html","content_length":"141905","record_id":"<urn:uuid:bd98b562-2c94-4fa1-83b4-6a16b420f439>","cc-path":"CC-MAIN-2024-46/segments/1730477027829.31/warc/CC-MAIN-20241104131715-20241104161715-00704.warc.gz"} |
The Law of Cosines - Another PWW
The Law of Cosines - Another PWW
The applet below illustrates a proof without words of the Law of Cosines that establishes a relationship between the angles and the side lengths of \(\Delta ABC\):
\(c^{2} = a^{2} + b^{2} - 2ab\cdot \mbox{cos}\gamma,\)
where \(\gamma\) is the angle in \(\Delta ABC\) opposite side \(c\).
There are four draggable points: the three vertices of the reference triangle and one on the resulting trapezoid.
The applet illustrates the cases of acute and abtuse triangles, making it it clear that in irder to obtain \(c^2\), for acute triangles, \(2ab\space\mbox{cos}\gamma\) needs to be subtracted from \(a^
{2}+b^{2}\), while for obtuse triangles it needs to be added.
(There are several theorems that are proved by similar technique.)
• The Law of Cosines - Another PWW
|Contact| |Front page| |Content| |Geometry|
Copyright © 1996-2018 Alexander Bogomolny | {"url":"https://www.cut-the-knot.org/Curriculum/Geometry/GeoGebra/CosineLawAB.shtml","timestamp":"2024-11-10T11:37:31Z","content_type":"text/html","content_length":"13032","record_id":"<urn:uuid:8a480262-e024-46d9-817f-b50d8265d2f0>","cc-path":"CC-MAIN-2024-46/segments/1730477028186.38/warc/CC-MAIN-20241110103354-20241110133354-00473.warc.gz"} |
Posters | ct.qmat24
See below for the list of accepted posters.
Presenters will receive their poster ID (1–100) by email shortly before the conference. Odd-numbered posters will be presented on Monday, September 23, and even-numbered on Wednesday, September 25.
We investigate the topological characteristics of a recently discovered class of semimetals in two dimensions on the honeycomb lattice. These semimetals reside at the transition between two distinct
topological insulators, each existing in a nontrivial topological phase. As a result, these semimetals exhibit specific topological properties, including the presence of edge modes. In a preceding
work, we demonstrated the topological robustness of this semimetal phase against disorder and interactions. In this work, we delve deeper into the semimetal's electronic properties, providing a
precise calculation of its Hall conductivity and response to circularly polarized light, elaborating further on its bulk-edge correspondance leading to a half topological semimetal.
Simulating dynamics in interacting quantum many-body systems is a challenging problem. We develop a truncated Hilbert space approach (THSA) and apply it to the quantum Ising chain with both
transverse and longitudinal fields, for calculating the dynamic structure factor, as well as non-equilibrium dynamics following global quenches. We find that the truncated Hilbert space approach is
well suited to capture characteristic features of the model, such as E[8] particles with universal mass ratios and confinement of domain-wall excitations in the ferromagnetic phase.
Quasi-particle-interference measurements confirm the topological nature through the presence of fermi-arcs. Spectroscopic investigations reveal sample dependent electronic structure near the
fermi-level, ranging from metallic characteristics to the presence of particle-hole symmetric energy gaps implying superconductivity. Most notably, the largest observed energy gap suggests a critical
temperature Tc in the range of 120 K, two orders of magnitude above the previously reported Tc measured via bulk-sensitive methods. This would make trigonal PtBi[2] a potential candidate for an
intrinsic topological superconductor with a Tc above liquid nitrogen temperatures, highlighting it as a promising material for technological applications in quantum computing.
Kitaev quantum spin liquid (KQSL) is an exotic state with many-body quantum entanglement which can host Majorana fermions and gauge fluxes. KQSL is an exactly solvable ground state of spin-1/2 model
with the bond-dependent Ising interactions on a 2D honeycomb lattice. The presence of non-Kitaev interactions has been a primary obstacle, as they destabilize the QSL ground state. To overcome this
hurdle, 3d cobaltates with more localized d-orbitals were proposed. In this study, we employed thermodynamic methods to characterize such a cobaltate KQSL candidate, Na[3]Co[2]SbO[6]. Our
investigations, includes magnetic, specific heat and thermal expansion studies on high quality single crystals. From the M(H), M(T), Cp(T) and α(T) data we mapped out the detailed anisotropic
magnetic phase diagram of Na[3]Co[2]SbO[6]. Furthermore, we address whether this compound can be driven into a KQSL ground state under an applied magnetic field or uniaxial pressure applied along the
c*-axis of a single crystal.
Following the famous Afflect-Kennedy-Lieb-Tasaki model (AKLT) [1], Klein model [2], and the analysis of ground state order of extended AKLT Hamiltonians on 3D lattices [3], we construct an AKLT-like
model/Hamiltonian — spin-projector Hamiltonian — on pyrochlore lattice. We consider a local spin value of S = 1 on each lattice site, which is less than the minimum value S = 3 (half of the
coordination number of the lattice) required for the case of AKLT valence bond ground state (VBS). The Hamiltonian we set up is the sum of projectors onto spin 3 for every trianglular face of the
tetrahedra forming the lattice. In such a model, we identify the degenerate manifold of ground states and compute an orthogonal basis in this degenerate space. Finally, we study the equal-time
two-point spin correlation function to ascertain the nature of order/disorder in the ground state space.
Bi[12]Rh[3]Ag[6]I[9] is the newest member of the Bi[14]Rh[3]I[9]-based compounds. It can be seen as nano-periodic multilayer heterostructures of 2D topological insulators (TIs) spaced by
topologically trivial insulators. The compound presents silver iodide spacers with 2D cationic conductivity. The gap of 286 meV, determined by ARPES, is the widest observed so far in a weak 3D TI.
The experimental electronic structure shows good agreement with bulk band-structure calculations. The calculated invariants indicate the topological nature of the bandgap. Magnetoresistance
measurements in macroscopic crystals reveal Landau quantization at low magnetic fields, coinciding with a drastic drop in resistivity across the layers. Additionally, a non-mirror symmetric
dependence of the resistance on the field direction is observed at low temperatures. These effects resemble theoretical models predicting the formation of perpendicular, low-dimensional protected
states emerging from the coupling of 2D edge states.
It has recently been shown that signatures of non-Hermitian topology can be realized in a conventional quantum Hall device connected to multiple current sources.
Chiral edge states are believed to be responsible for this non-Hermitian response, similar to how they lead to a quantized Hall conductivity in the presence of a single current source.
Here, we challenge this assumption, showing that multi-terminal conductance matrices can exhibit non-Hermitian topological phase transitions that cannot be traced back to the presence and
directionality of a boundary-localized chiral mode.
By performing quantum transport simulations in the quantum Hall regime monolayer graphene, we find that when the chemical potential is swept across the zeroth Landau level, unavoidable device
imperfections cause the appearance of an additional non-Hermitian phase of the conductance matrix.
We study the electronic structure and magnetic properties of ferromagnetic topological insulators (Cr[x]Sb[1-x])[2]Te[3], which exhibit Curie temperature Tc ~98 K and ~192 K for x~0.15 and ~0.35,
respectively. Angle-resolved photoemission spectroscopy (ARPES) reveals a magnetic gap at the Dirac point lying ~5kBTC above the Fermi level for x~0.15. The temperature-dependent x-ray absorption
spectroscopy (XAS) and x-ray magnetic circular dichroism (XMCD) showed systematic change across Tc. In addition, we observed the dichroic spin shift derived from the Cr 3d exchange split states,
which are proportional to the bulk magnetization and can be simulated by charge transfer multiple cluster model calculations with an exchange field. These results provide a direction of relations of
Tc and magnetization with the exchange field.
A prototypical example of a Higgs phase is a superconductor: the condensation of electrically charged Cooper pairs generates a mass for photons, resulting in the Meissener effect. However, this
"condensation" is ill-defined, because the U(1) symmetry which conserves charge is pure gauge and cannot be spontaneously broken: since charges can only be created in neutral pairs, a closed system
is always globally charge-neutral. To make the symmetry physical, one must have a boundary through which flux can escape, in which case the total charge in the bulk is equal to the total flux through
the boundary. However, this implies that the charge conservation symmetry is actually realized on the boundary. In this work we investigate the spontaneous breaking of this boundary symmetry in the
Higgs regime. I will discuss this boundary criticality in both Abelian and non-Abelian models, and comment on how it relates to recent work relating Higgs and Symmetry Protected Topological (SPT)
Spiral spin liquids (SSLs) are correlated states of matter in which a frustrated magnet evades order by fluctuating between a set of (nearly) degenerate spin spirals. Here, we investigate the
response of SSLs to quenched disorder in a two-dimensional Heisenberg model. At the single-impurity level, we identify different order-by-quenched-disorder (ObQD) mechanisms and analyze the ensuing
spin textures. We show that, besides being extremely long-ranged, the latter generally display oscillations which can be used to reconstruct the classical ground-state manifold. At finite defect
concentrations, we perform extensive numerical simulations and characterize the resulting phases at zero temperature. As a result, we find that the competition between incompatible ObQD mechanisms
can lead to a spiral spin glass already at low to moderate disorder. Finally, we discuss extensions of our conclusions to nonzero temperatures and higher-dimensional systems, as well as their
experimental implications.
We characterize quantum dynamics in triangular billiards in terms of five properties: (1) the level spacing ratio (LSR), (2) spectral complexity (SC), (3) Lanczos coefficient variance, (4) energy
eigenstate localisation in the Krylov basis, and (5) dynamical growth of spread complexity. The billiards we study are classified as integrable, pseudointegrable or non-integrable, depending on their
internal angles which determine properties of classical trajectories and associated quantum spectral statistics. A consistent picture emerges when transitioning from integrable to non-integrable
triangles: (1) LSRs increase; (2) spectral complexity growth slows down; (3) Lanczos coefficient variances decrease; (4) energy eigenstates delocalize in the Krylov basis; and (5) spread complexity
increases, displaying a peak prior to a plateau instead of recurrences. Pseudo-integrable triangles deviate by a small amount in these charactertistics from non-integrable ones, which in turn
approximate models from the Gaussian Orthogonal Ensemble (GOE). Isosceles pseudointegrable and non-integrable triangles have independent sectors that are symmetric and antisymmetric under a
reflection symmetry. These sectors separately reproduce characteristics of the GOE, even though the combined system approximates characteristics expected from integrable theories with Poisson
distributed spectra.
We successfully established Quantum Point Contact geometries in the framework of the Topological Insulator HgTe. [1] We propose, that when gated in the regime of edge state conductance, the QPC can
form an interferometer, given that the width of the constriction is small enough to allow for the last bulk mode close to the interface of the gated region to overlap with the two edge channels. In
this case, several effects contributing to the quantum phase can arise. We are able to identify the impact of the Aharonov-Bohm phase as well as the dynamical Aharonov-Casher phase in the quantum
spin Hall regime. Additionally, a phase shift within the first Aharonov-Bohm period gives evidence for the presence of a spin-orbit Berry phase of π, which is consistent with simple model
1) Strunz et al., Nature Physics, 16, 2019
As a new type of fundamental magnetic order next to ferromagnetism and antiferromagnetism, altermagnetism has recently attracted great attention. It is characterized by antiferromagnetic spin
alignment combined with rotational lattice symmetry, which is reflected in a spin-split band structure with spin polarized electronic states. One of the "workhorse" materials potentially exhibiting
this type of magnetic order is MnTe in its hexagonal NiAs-type crystal structure. Here, we investigate MnTe thin films grown on different substrates by molecular beam epitaxy. Using structural
characterization methods, we discuss the influence of the growth parameters on the observed films. The electronic structure is assessed by soft X-ray angle-resolved photoemission spectroscopy and
shows good agreement with band structure calculations.
[1] L. Šmejkal et al., Phys. Rev. X 12, 031042 (2022).
The successful substitution of Vanadium by more correlated Chromium atoms in the 135 compounds is widely regarded as a crucial step towards unequivocal electronically dominated physics on the kagome
lattice. This hope is further fueled by the similarity of pressure dependent phase diagram with the hole doped part of the cuprate phase diagram. In our work, we show within functional
renormalization group calculations, that the density wave phase around ambient pressure is driven by antiferromagnetic fluctuations, that rapidly decrease at the insulator-to-superconductor phase
transition and can not account for the observed transition temperature. The superconductivity at high pressure can be recovered by considering a conventional pairing mechanism mediated by
electron-phonon coupling, that is, while irrelevant in the normal state, less susceptible to the applied pressure and hence eventually overcomes electronic screening processes.
The negatively-charged boron vacancy is the first intrinsic spin defect in hexagonal boron nitride (hBN) reported by our group in 2020. Practical applications of hBN spin centers as intrinsic sensors
in van der Waals heterostructures are envisioned. To further boost the quantum sensing applications of this spin defect in hBN, we investigate the dynamics of the intermediate state, which is also
called metastable state because it is likely to trap electrons for a certain time. We investigated the photoluminescence dynamics and the experiments have shown that the intermediate state delays the
relaxation of electrons to the ground state with a characteristic lifetime of 24 ns. This has a clear impact on the subsequent sensing protocol and must be considered when designing the pulsed
optically detected magnetic resonance (ODMR) experiments.
The non-trivial topology of the quantum spin Hall insulator indenene was recently demonstrated through bulk probes that reveal its topological band ordering [1,2]. Consequently, the bulk-boundary
correspondence guarantees the presence of metallic states at the edge of this triangular indium monolayer. In this study, we employ scanning tunneling spectroscopy to test indenene for this
correspondence. Our results confirm metallic edge conductivity with suppressed backscattering near the bulk band gap, validating the presence of topologically protected edge states in indenene.
[1] M. Bauernfeind, J. Erhardt, and P. Eck et al., Nat. Commun. 12, 5396 (2021)
[2] J. Erhardt et al., Phys. Rev. Lett. 132, 196401 (2024)
The bosonic fractional Chern insulator is intricately connected to quantum spin liquids. Thus, we investigate the Read-Rezayi fractional quantum Hall states for k=2 (Moore-Read) and k=3. The
non-abelian excitations of the k=3-state are Fibonacci anyons and thus provide a platform for universal quantum computing. Following the analogy of the Calogero-Sutherland model, we construct parent
continuum Hamiltonians for these states. Based on the identification of fractional quantum Hall states with correlation functions of CFTs, we use the Belavin–Polyakov–Zamolodchikov equation for the
corresponding primary fields to find destruction operators with the ground state in their kernels and combine them to form parent Hamiltonians.
The coupling between the electronic and magnetic degrees of freedoms can lead to exotic transport phenomena in multiferroic materials. Particularly the propagation of charge neutral heat carriers can
reveal interesting features in the thermal transport properties.
Here, we report the thermal conductivity measurements in multiferroic Swedenborgite CaBaM[4]O[7] (M=Fe,Co) which is built up by alternating Kagome and triangular layers of edge sharing MO[4]
tetrahedra in mixed valence state. We find anomalies related to the magnetic ordering in longitudinal thermal conductivity as well as non linear transversal thermal conductivity(Thermal Hall effect)
resembles to that of the magnetization. We attribute the thermal hall effect of Swedenborgite CaBaM[4]O[7] to phonon due to the strong spin-phonon coupling.
We investigate Kondo physics of a bath reaching from a continuum to discrete energy levels for the hybridisation function. Here, we analyze the formation of local moments in the spin and charge
susceptibilities depending on the hybridisation functions. Further, we drive the system to be out of half-filling and break the particle-hole symmetry.
Symmetry-protected topological phases (SPTs) characterized by short-range entanglement include many states essential to understanding of topological condensed matter physics, and the extension to
gapless SPTs provides essential understanding of their consequences. In this work, we identify a fundamental connection between gapless SPTs and recently-introduced multiplicative topological phases,
demonstrating that multiplicative topological phases are an intuitive and general approach to realizing concrete models for gapless SPTs. In particular, they are naturally well-suited to realizing
higher-dimensional, stable, and intrinsic gapless SPTs through combination of canonical topological insulator and semimetal models with critical gapless models in symmetry-protected tensor product
constructions, opening avenues to far broader and deeper investigation of topology via short-range entanglement.
The magnetic pyrochlore lattice, a three-dimensional frustrated lattice, hosts many-body phenomena like classical and quantum order-by-disorder and spin liquids described by emergent field gauge
theories. Within the most general bilinear nearest-neighbour Hamiltonian, these phenomena arise from competition between different q=0 phases, classified by their irreducible representation, . This
study examines a point in the nearest-neighbour bilinear Hamiltonian on the pyrochlore lattice, parameterized by the local interaction parameter J[{z\pm}], where three symmetry-breaking phases
converge. We demonstrate that for all values of J[{z\pm}], order-by-disorder phenomena induce a symmetry-breaking transition, and identified a novel spin-nematic phase emerges for a range of J[{z\
pm}] values. This phase is characterized using classical Monte-Carlo simulations and a self-consistent Gaussian approximation, revealing its stability in certain directions away from the point.
We present angle-resolved photoemission spectroscopy (ARPES) measurements on tunable 1-D moiré phases of an epitaxial honeycomb monolayer AgTe/Ag(111) [1]. In this model system, the moiré structure
can be tuned almost continuously in contrast to hardly controllable twist angles in bilayer van-der-Waals heterostructures [2]. We experimentally observe moiré minibands and band gaps in the order of
about 100 meV suggesting sizable moiré potentials. Moreover, the presented data indicates the investigated material to be a tunable model system
which exhibits rich quantum states with long range coherence..
[1] Ünzelmann, M., Bentmann, H. et al. Orbital-Driven Rashba Effect in a Binary Honeycomb Monolayer AgTe. PRL. 124, 176401 (2020).
[2] Lisi, S., Lu, X., Benschop, T. et al. Observation of flat bands in twisted bilayer graphene. Nat. Phys. 17, 189–193 (2021).
When translational symmetry is broken, e.g. in the presence of impurities in a crystal, an ordered state can emerge where the electronic charge density modulates spatially. Using scanning tunneling
microscopy (STM), we identify such charge order pinned by surface impurities. By operating the STM tip as a local gate, we demonstrate the ability to tune the spatial confinement of this charge
modulation, which eventually breaks down when enough carriers are introduced to screen the charged impurities. Our work opens an avenue toward atomic-scale control of strongly correlated electrons.
Bismuthene, a honeycomb monolayer of bismuth atoms synthesized on a SiC(0001) substrate, is a topological insulator with a breakthrough bulk band gap of 800 meV due to giant spin-orbit coupling. The
magnitude of this gap exposes bismuthene as a promising candidate for room temperature spintronic applications based on the quantum spin Hall effect. However, oxidation of bismuthene in air confines
most experiments on this system to UHV conditions. Here we demonstrate the intercalation of bismuthene between SiC and a single sheet of graphene. This protective layer effectively prevents
bismuthene from oxidation, while it fully conserves its structural and topological properties as we readily demonstrate by scanning tunneling microscopy and photoemission spectroscopy. This paves the
way for ex-situ experiments and ultimately brings bismuthene closer to the fabrication of spintronic devices.
The Kagome network is a key structural motif in modern solid-state physics as it hosts special electronic states related to Dirac-cones, van-Hove singularities, and flat bands. The Vanadium based
Kagome metal ScV[6]Sn[6] exhibits an unconventional charge density wave below 96 K. To provide a detailed microscopic picture of the structural and electronic properties of ScV[6]Sn[6] we employ 51V
nuclear magnetic resonance (NMR) to investigate its CDW phase from a local point of view, aided by density functional theory (DFT). We can relate the dynamics of the local magnetic field to the
changes in the V density of states (DOS), we find the reported reconstruction of the unit cell as a characteristic modulation of the charge symmetry at V nuclei, while the local magnetic field
reveals a substructure of Fermi level states suggesting orbital selective modulation of the local DOS [1].
[1] R. Guehne, J. Noky, C. Yi, C. Shekhar, M. G. Vergniory, M. Baenitz, M., C. Felser, arXiv:2404.18597 (2024).
We investigate the surface properties of a layered weak topological insulator Bi[12]Rh[3]Ag[6]I[9] using scanning tunnel microscopy as well as x-ray and angle-resolved photoemission spectroscopy. The
compound consists of layers of two-dimensional insulators built from edge-sharing Rh-centered Bi cubes which are arranged in a Kagome-type network. Interestingly, the electronic structure shows
signatures of a Kagome band structure. This is evidenced by the presence of a Dirac cone at the K-points, which is gapped by the strong atomic spin-orbit coupling, as demonstrated by ARPES
measurements and DFT band structure calculations. In particular, we show that the surface band structure exhibits flat band surface states in the topological bulk band gap in close vicinity of the
Fermi level.
The synthesis of itinerant Kagome materials, i.e. compounds with a metallic parent state, has initiated extensive research interests. Experimental observations indicate a fascinating phenomenology of
correlated electron physics on the Kagome lattice. Deriving from sophisticated many body calculations we present a novel state of matter reminiscent of a pair density wave, i.e. a sublattice
modulated superconducting pairing state emerging without additional translation symmetry breaking on the Kagome Hubbard model. Recent experiments in FeSn and KV[3]Sb[5] indicate a universality of
sublattice modulated superconductivity.
We study the J[1]-J[2] spin-1/2 chain using a path integral constructed over matrix product states (MPS). By virtue of its non-trivial entanglement structure, the MPS ansatz captures the key phases
of the model even at a semi-classical, saddle-point level, and, as a variational state, is in good agreement with the field theory obtained by abelian bosonisation. Going beyond the semi-classical
level, we show that the MPS ansatz facilitates a physically-motivated derivation of the field theory of the critical phase: by carefully taking the continuum limit -- a generalisation of the Haldane
map -- we recover from the MPS path integral a field theory with the correct topological term and emergent SO[4] symmetry, constructively linking the microscopic states and topological
field-theoretic structures. Moreover, the dimerisation transition is particularly clear in the MPS formulation -- an explicit dimerisation potential becomes relevant, gapping out the magnetic
We study the bulk photovoltaic effect (BPVE) in Dirac and Weyl semimetals under two-frequency light irradiation. We show that the BPVE emerges for centrosymmetric Dirac and Weyl semimetals in the
presence of light fields with frequencies Ω and 2Ω. The BPVE under the two frequency drive involves both shift current contribution independent of the carriers lifetime τ and the injection current
contribution proportional to τ. Our calculations indicate that the photocurrent's direction, magnitude and type can be dynamically controlled by tuning parameters of the driving fields. Furthermore,
we find that the tilt of the Dirac cone significantly affects the photocurrent, particularly in mirror symmetry-lacking Weyl semimetals, leading to an anisotropic optical response. These findings
provide new insights into the dynamic control of photocurrents in topological semimetals, offering promising applications for optoelectronic devices.
Multiphase unconventional superconductivity is a rare phenomenon, which has recently been discovered in the tetragonal but locally noncentrosymmetric heavy-fermion compound CeRh[2]As[2]. Here, the
unusual transition to a high-field superconducting phase is induced by an external magnetic field, including a non-trivial angular dependence and large critical fields. Apart from superconductivity,
also other ordered phases of magnetic or electronic multipolar order have been found. Intriguingly, the transition to such a state has been reported to happen either below or above the
superconducting critical temperature, with an unresolved connection to the different experimental probes. However, the probably weakly magnetic state seems to consistently coexist only with the
low-field superconducting phase. In order to study the coexistence and complex interplay of the potential superconducting and magnetic phases in CeRh[2]As[2], as well as the effect of applying a
magnetic field, we develop a theory based on group-theoretical considerations, in combination with Bogoliubov-de Gennes and Ginzburg-Landau methods. Thereby we can give a statement about the probable
symmetries of the superconducting states and their close relationship to magnetism in this material.
The Kitaev spin liquid realizes an emergent static Z[2 ]gauge field with vison excitations coupled to Majorana fermions. Partially motivated by layered structure of Kitaev materials, we consider
Kitaev models stacked on top of each other, weakly coupled by Heisenberg interaction. This inter-layer coupling breaks the integrability of the model and makes the gauge fields dynamic. We identify
novel conservation laws that keep single visons immobile. However, inter-layer vison pairs can hop within the layer, but their motion is strongly influenced by the type of stacking. For AA stacking,
an interlayer pair has a 2D motion but for AB or ABC stacking, novel sheet conservation laws lead to a 1D motion. For all stackings, an intra-layer vison-pair is constrained to move out-of-plane
only. Depending on the anisotropy of the Kitaev couplings, the intra-layer vison pairs can display either coherent tunnelling or purely incoherent hopping.
Ref:APJ and Achim Rosch, arXiv:2403.14284
In recent years the search for a holographic duality, which is based on tessellations of the hyperbolic plane has gained momentum and the construction of suitable boundary theories has been
considered in the literature. We propose a discrete analog of JT gravity, defined on hyperbolic lattices as a dual bulk theory. We calculate the gravity path integral on the disk and show that this
gives rise to an Ising model subject to a topological constraint. This constraint restricts spin domains to have a disk topology, which implies that there is only one domain possible, consisting of
spin up. The resolvent of JT gravity is related to the free energy of this Ising model. We study this free energy as a function of the coupling constant through a Monte Carlo approach, and also in
the mean-field approximation. Furthermore, we propose a realisation of discrete JT gravity as a matrix integral.
Altermagnets are a novel class of magnetic materials besides ferro- and antiferromagnets, where the interplay of lattice and spin symmetries produces a magnetic order that is staggered both in
coordinate as well as momentum space. The metallic rutile oxide RuO[2], long believed to be a textbook Pauli paramagnet, recently emerged as a workhorse altermagnet when resonant X-ray and neutron
scattering studies reported nonzero magnetic moments and long-range collinear order. While experiments on thin films seem consistent with altermagnetic behavior, the origin and size of magnetic
moments in RuO[2] still remain controversial. Here we show that RuO[2] is nonmagnetic, regardless of the sample dimensions. Employing muon spin spectroscopy as a highly sensitive probe of local
magnetic moments we find moments of at most 7.5×10^−4 μB/Ru. Our own neutron diffraction measurements on RuO[2] single crystals identify multiple scattering as a likely source for this discrepancy.
The presence of a Dyson singularity in the density of states of one-dimensional random chiral structures is a long standing theoretical prediction. It is associated with topological marginality, and
rapidly disappears in structures which move away from the phase boundary. In two-dimensional chiral systems, such as graphene, the corresponding feature is known as a Gade singularity.
Coaxial cable networks provide an excellent platform for investigating such chiral phenomena. We present here an experimental study of the Dyson and Gade singularities in small lattices. In a finite
structure, the singularity is reduced to a broadened peak, which we observe by averaging over spectra from an ensemble of disordered networks, constructed from cables with different impedances. We
show that, in small structures such as ours, the visibility of the feature is sensitive to the choice of boundary conditions.
Chiral superconductors (SCs) have received much attention in recent years as a promising platform for hosting Majorana-bound states due to the topological nature of their ground state.This makes them
candidates for performing fault-tolerant quantum computations.
The best known candidate for chiral superconductivity is Sr[2]RuO[4](SRO) [1]. Recently, this has been questioned and intensive research is still underway.
4Hb-TaS[2], a polymorph of the well-known dichalcogenide TaS[2], was identified as a candidate for chiral superconductivity [2]. We report results of muon spin relaxation studies and ultrassound
spectroscopy to examine the superconducting order parameter symmetry in 4Hb-TaS[2] and study the interplay of superconductivity with other electronic degrees of freedom, such as CDW order and quantum
spin fluctuations.
[1] V. Grinenko et al., Nat. Phys. 17, 748 (2021).
[2] A Ribak et al., Science Advances 6, eaax9480 (2020).
The exactly solvable Kitaev model with its frustrated bond-dependent interactions has attracted enormous attention. However, there is no pristine realization of the Kitaev model due to the
significant Heisenberg and off-diagonal exchange interactions. Here we demonstrate the coexistence of the Kitaev interaction with the piezomagnetoelectric effect (simultaneous magnetoelastic and
magnetoelectric responses), which can offer electric field driven manipulation of the ground state and the fractional spin excitations. Our study reports the direct observation of the magnetoelectric
(ME) effect in Na[2]Co[2]TeO[6], and highlights the magnetoelastic response as a sensitive gauge of phase transitions. We discuss that the ME effect originates from the pd-hybridization mechanism,
which allows local polarization independently from any magnetic order.
Antiferromagnetic Ising models on frustrated lattices can realize classical spin liquids, with highly degenerate ground states and possibly fractionalized excitations and emergent gauge fields.
Motivated by the recent interest in curved space and AdS/CFT correspondance we study Ising models defined in negatively curved space. Specifically, we consider nearest-neighbor Ising models on
tesselations with odd-length loops of two-dimensional hyperbolic space. For finite systems with open boundary conditions we determine the ground-state degeneracy, and we perform finite-temperature
Monte-Carlo simulations to obtain thermodynamic data as well as correlation functions. The data collectively show that classical spin liquids that are highly dependent on the boundary conditions can
be realized in hyperbolic space.
In extended Heisenberg-Kitaev-Gamma-type spin models, hidden-SU(2)-symmetric points are isolated points in parameter space that can be mapped to pure Heisenberg models via nontrivial duality
transformations. Such points generically feature quantum degeneracy between conventional single-q and exotic multi-q states. We argue that recent single-crystal inelastic neutron scattering data
place the honeycomb magnet Na[2]Co[2]TeO[6] in proximity to such a hidden-SU(2)-symmetric point. The lowtemperature order is identified as a triple-q state arising from the N ́eel antiferromagnet with
staggered magnetization in the out-of-plane direction via a 4-sublattice duality transformation. This state naturally explains various distinctive features of the magnetic excitation spectrum,
including its surprisingly high symmetry and the dispersive low-energy and flat high-energy bands.
Metal-organic frameworks (MOFs) are promising candidates for advanced photocatalytically active materials. These porous crystalline compounds have large active surface areas and structural tunability
and are thus highly competitive with oxides, the well-established material class for photocatalysis. However, due to their complex organic and coordination chemistry composition, photophysical
mechanisms involved in the photocatalytic processes in MOFs are still not well understood. Employing electron paramagnetic resonance (EPR) spectroscopy and time-resolved photoluminescence
spectroscopy (trPL), we investigate the fundamental processes of electron and hole generation, as well as capture events that lead to the formation of various radical species in UiO-66, an
archetypical MOF photocatalyst. We detected a manifold of photoinduced electron spin centers, which we subsequently analyzed and identified with the help of density-functional theory (DFT)
calculations. Under UV illumination, we reveal the symmetry, g-tensors and lifetimes of three distinct contributions: a surface O[2]-radical, a light-induced electron-hole pair, and a triplet
exciton. Notably, the latter was found to emit delayed fluorescence or phosphorescence. Our findings provide new insights into the photoinduced charge transfer processes, which are the basis of
photocatalytic activity in UiO-66. This sets the stage for further studies on photogenerated spin centers in this and similar MOF materials.
In topological semimetals, Hall measurements provide an important charge transport footprint of the non-trivial geometric properties of the electronic wavefunctions. In Weyl semimetals, the planar
Hall effect (PHE) -- the appearance of a transverse voltage when coplanar electric and magnetic fields are applied -- is a direct consequence of the longitudinal linear magnetoconductance associated
with the chiral anomaly of Weyl fermions, and is quantified by the large Berry curvature of Weyl nodes. The anomalous Hall effect is fully determined only by the location in the Brillouin zone and
topological charge of the Weyl nodes. Time-reversal invariance prohibits any anomalous Hall signal in the large class of non-magnetic Weyl semimetals thereby leaving the PHE as the only Hall
diagnostic tool of Weyl physics, at least in the linear regime. This complicates the identification of non-magnetic topological semimetals by charge transport experiments.
Nodal noncentrosymmetric superconductors can host zero-energy flat bands of Majorana surface states within the projection of the nodal lines onto the surface Brillouin zone. Thus, these systems can
have stationary, localized Majorana wave packets on certain surfaces, which may be a promising platfrom for quantum computation. However, for such applications it is important to find ways to
manipulate the wave packets in order to move them without destroying their localization or coherence. As the surface states have a nontrivial spin polarization, applying an exchange field, e.g., by
introducing a magnetic insulator at the surface, makes the previously flat band slightly dispersive. We aim to use an adiabatic change of the exchange field to move wave packets on the surface. We
therefore investigate the time evolution of a maximally localized wave packet under the influence of such an exchange field employing exact diagonalization as well as quasiclassical approximations.
The Ferromagnetic Kondo Lattice Model (FKLM) describes systems with interactions between localized and itinerant electrons and can host noncoplanar spin textures that give rise to phenomena such as
the Quantum Anomalous Hall Effect (QAHE). In this work, we develop an optimization-based numerical program to perform an unbiased and comprehensive search for the ground state spin texture under
varying conditions. We confirm the stability of noncoplanar spin textures, particularly at ¼ filling, and identify the tetrahedral spin texture as the ground state over a range of exchange couplings.
Our optimization-based approach provides a powerful tool for exploring complex physical phenomena like the QAHE and skyrmions, paving the way for future research in these areas.
Topologically ordered spin liquids represent a class of phases with intriguing characteristics such as a ground-state degeneracy varying with the space's genus and anyons. Recent advancements in
hyperbolic lattices, discrete analogues of negatively curved spaces, have opened new avenues for extending Euclidean lattice models to them. Given the high genus implied by negative curvature, this
raises fundamental questions about the interplay between hyperbolic lattices and topological order with potential impact on quantum error correction. I will present a generalization of Kitaev's
honeycomb model to hyperbolic lattices which maximally preserves symmetry, enabling us to determine the ground-state sector exactly and explore the phase diagram and vortex lattices efficiently.
Unlike in the Euclidean case, the gapless spin liquid exhibits a non-zero density of states at zero energy. Finally, I will discuss properties of the chiral-spin-liquid phase induced by
time-reversal-symmetry breaking.
Ca[3]Ru[2]O[7] is an antiferromagnetic (AFM) polar metal considered a fascinating material due to its wide range of remarkable electronic phenomena, including colossal magnetoresistance, spin waves,
and multiple phase transitions. Exploring these properties under external manipulation, such as electrical current, pressure, or strain, opens new pathways for understanding its electronic behavior
and controlling its quantum states. In this study, we employ ab initio methods to investigate the stability of several AFM configurations of Ca[3]Ru[2]O[7] under lattice deformation (pressure and
strain). We identify potential altermagnetic (AM) states, a recently discovered elemental magnetic phase, and show that these states can be stabilized under strain. We discuss the underlying
mechanisms responsible for the stability of the AM phase and propose a novel route for tuning quantum states through AFM to AM transitions in Ca[3]Ru[2]O[7] under lattice deformation.
We propose a phase-biased non-Hermitian Josephson junction (NHJJ) composed of two superconductors mediated by a short non-Hermitian link. Such a NHJJ is described by an effective non-Hermitian
Hamiltonian derived based on the Lindblad formalism in the weak coupling regime. By solving the Bogoliubov-de Gennes equation, we find that its Andreev spectrum as a function of phase difference
exhibits Josephson gaps, i.e. finite phase windows with no Andreev (quasi-)bound states. The complex Andreev spectrum and the presence of Josephson gaps constitute particular spectral features of the
NHJJ. Moreover, we propose complex supercurrents arising from inelastic Cooper pair tunneling to characterize the anomalous transport in the NHJJ. Additional numerical simulations complement our
analytical predictions. We demonstrate that the Josephson effect is strongly affected by non-Hermitian physics.
Miniaturised photonic circuits have been employed in a broad field of fundamental, but also application-oriented research in the recent years. While the harnessing of CMOS fabrication techniques has
enabled precise sub-wavelength feature control, the dynamic switching of nano-optical devices often involves additional thermo-optical or electro-optical elements. The present contribution
demonstrates an all-optical switch utilising two counter-propagating beams to control the in-coupling efficiency of a nano-optical grating. The findings of the fundamental experiment are shown to
support the development of a range of applications including all-optical logic gates and non-Hermitian photonic circuits. The demonstrated coupling control enables complexity reduction in integrated
photonic circuits and provides a promising approach for a new, streamlined device architecture.
A characteristic feature of the superconducting state in BCS theory is the appearance of a full gap in the quasiparticle spectrum. Under various conditions, one can instead obtain an exotic form of
superconductivity for which the superconducting gap contains Bogoliubov Fermi surfaces (BFSs). A BFS is a 𝑑 − 1-dimensional surface of zero-energy states in the 𝑑-dimensional momentum space. BFSs
were recently observed in the two-dimensional heterostructure Al-InAs in an applied in-plane magnetic field [1]. We present the theoretical prediction for the density of states of such a system and
predict the temperature dependence of observables such as the heat capacity and the superfluid density in the presence of BFSs.
[1] Phan et.al, Phys. Rev. Lett. 128, 10770 (2022).
We develop a formalism to study the effect of strong electron-electron interactions in a Weyl semimetal. In this poster, we present the findings for the case of two doped Weyl cones with opposite
chirality. For this purpose, we employ a path integral formalism to study different instabilities that could take place.
Although the transitions from topological states to symmetry breaking states with trivial topology have been discussed, the road from one topological ordered state to another with the same Hall
conductance and broken translational symmetry has not been found. Here we show the intriguing evidence that the FQAH to FQAH Smectic (FQAHS) transition is robustly realizable in the archetypal
correlated flat Chern-band model at filling ν = 2/3. This transition is novel in that: i) the FQAHS acquires the same fractional Hall conductance as FQAH, which cannot be explained by mean-field band
folding. The formation of smectic order can be viewed as perturbation around the transition point, and thus, do not destroy or change the original topology; ii) the charge excitation remains gapped
across the transition although the neutral gap is closed at transition point; and iii) the transition is triggered by the softening of roton mode with the same wave vector as the smectic order.
The generation and manipulation of topological states in 1-3D photonic systems show intriguing properties and unique applications. For the 1D system, we explore the selective excitation of
topological trivial/nontrivial states by tuning the symmetry and/or dynamic phase of the topological zero mode. For the 2D system, ultralow-threshold polariton condensation at BICs in organic
semiconductor photonic crystals is investigated. For the 3D systems, the berry phase acquired in the Möbius ring and microtubular resonators are studied. In addition, non-Hermitian photonics is
studied by introducing perovskite materials as the gain medium. These studies are of high interest for both fundamental research and practical applications such as quantum computing and optical
Motivated by the recent reports on quantum spin liquids in spin-1 three-dimensional systems, we re-address the projective symmetry group framework existing for spin-1/2 in a more generic sense based
on a fermionic representation of spin-S. We discuss the difference between integer and odd-half integer spin systems. Then we implement the formalism for spin-1 diamond lattice and tabulated all
possible Ansatze for fully symmetric quantum spin liquid. Furthermore we employ J[1]-J[2] Heisenberg antiferromagnetic model and produce the phase diagram. Interestingly, the phase diagrams
completely depends on the the constraints which are required to restore the physical Hilbert space in the fermionic picture in contrarary to the spin-1/2 system. Our study sets a stage for further
investigation from variational monte carlo point view for more detailed understanding on such strange behaviour.
Entangled photons are crucial for quantum technologies, but their transport through optical devices is often hindered by defects or perturbations that degrade the entanglement. Photonic floquet
waveguides offer a promising solution by exploiting the robustness of topologically protected transport to ensure quantum information transport. Theoretical model predicts robust quantum information
transport in such systems, but practical evidence for robust transport of entangled photons is still lacking due to the challenges of injection, detection, and measurement within a topological
This project aims to study the robust transport of entangled photons, specifically the N00N state, through the Floquet system. This system consists of an array of evanescently coupled helical
waveguides arranged in a graphene-like honeycomb lattice that exhibits topological behaviour. In my talk, I will discuss our progress, present findings, and the challenges encountered along the
Using the example of 3D Weyl semimetals, we show that the nodal tilt in relativistic semimetals can be used as a resource for designing electronic lensing devices. Intriguingly, the lensing can
formally be mapped to the gravitational lensing associated with cosmological black holes. We therefore also discuss the implications and limitations of this mapping between solids and black holes.
Topological Insulators (TIs) exhibiting the Quantum Spin Hall effect (QSHE) have been recognized as promising candidates for next-generation electronic devices due to their dissipationless and
spin-polarized electronic properties. To be suitable for device applications, TIs must exhibit specific characteristics such as scalability, reproducibility, tunability, and robustness of the helical
edge channels beyond liquid Helium temperatures. Although many materials have been predicted to host the QSHE, only a few have demonstrated the underlying transport signatures, but no material
platform checked all the other characteristics mentioned above. Here, we present a TI based on an InAs/GaInSb/InAs trilayer quantum well exhibiting the QSHE even at elevated temperatures up to 60K,
thereby all requirements are now met for the III-V semiconductor heterostructures. Our findings pave the way for the integration of TIs based on the InAs/GaInSb material system in topological
field-effect devices.
Isolated magnetic impurities can be used to probe the low-energy properties of a host system, with the standard Kondo effect in metals being the paradigmatic example. Magnetic impurities have also
been discussed as probes of quantum spin liquids and their excitations, and various approximate theoretical treatments have been put forward. In particular, it has been suggested that a spin liquid
with a spinon Fermi surface would lead to Kondo screening akin to that in normal metals. Here we study this problem for a particular Kitaev model with a Majorana Fermi surface. We present a
numerically exact solution using Wilson's Numerical Renormalization Group (NRG) which generalizes previous work for the honeycomb-lattice Kitaev model. Our numerical data for the
renormalization-group flow and for thermodynamic observables highlight important differences between the Kitaev system and a metal, related to the fractionalization scheme and the influence of the
emergent gauge field.
Fe₄GeTe₂ is a van der Waals material garnering significant attention due to its high temperature of ferromagnetic transition (~270 K), attributed to the strong interaction between Fe spins. The Tc of
Fe₄GeTe₂ is notably sensitive to sample thickness and Fe concentration, offering opportunities for property tuning.
This study investigates the evolution of the crystal structure of Fe₄GeTe₂ with temperature using x-ray single crystal diffraction. Although, no strong structural changes were observed across the
range from 20 to 320 K, a stable superstructure with a wave vector q = (1/3, 0, 0) was discovered for the first time. Additionally, signs of magnetoelastic coupling were detected. These findings
contribute to a deeper understanding of the structural and magnetic behaviors of Fe₄GeTe₂, potentially guiding the development of tunable ferromagnetic 2D materials.
Entanglement measures have proven useful in characterizing novel quantum many-body states. Particularly, the scaling of bipartite entanglement entropy (EE) of a spatial subsystem with its size
carries a fingerprint of underlying phases and is sensitive to quantum phase transitions. However, analytical methods to calculate EE have been limited to non-interacting theories, or theories with
conformal symmetry in 1+1D. Numerical methods are applicable to more generic interacting systems, but are limited by the exponentially growing complexity of the problem. Adapting recent
Wigner-characteristic based techniques, we show that Renyi EE of interacting fermions in arbitrary dimensions can be represented as a Schwinger-Keldysh free energy on replicated manifolds with a
current between the replicas. The current is local in real space and present only in the subsystem of interest. This allows us to construct a diagrammatic representation of EE in terms of connected
correlators in the standard unreplicated field theory. We further decompose EE into "particle" contributions which depend on the one-particle correlator, two-particle connected correlator and so on.
We apply our formalism to calculate the second REE in the ground state of a 2D repulsive fermi gas in continuum within perturbation theory in coupling strength. We find that the interacting answer
scales as the free-Fermion answer in space, however, the scaling prefactor increases with interaction strength. We believe this enhancement is non-universal and we will show how one-particle
corrections alone cannot account for it.
In our studies we measured magnetic domains in MnSb[2]Te[4] using STXM. We found a strong history and measurement protocol dependency of their size and shape. In some protocols we were able to
investigate circle shaped domains eventually supporting an interpretation as a skyrmion phase that was stable over a wide range of temperature and field variation.
A quantum system governed by a non-Hermitian Hamiltonian may exhibit zero temperature phase transitions that are driven by interactions, just as its Hermitian counterpart, raising the fundamental
question how non-Hermiticity affects quantum criticality. In this context we consider a non-Hermitian system consisting of an XY model with a complex-valued four-state clock interaction that may or
may not have parity-time-reversal (PT) symmetry. When the PT symmetry is broken, and time-evolution becomes non-unitary, a scaling behavior similar to the Berezinskii-Kosterlitz- Thouless phase
transition ensues, but in a highly unconventional way, as the line of fixed points is absent. From the analysis of the d-dimensional RG equations, we obtain that the unconventional behavior in the PT
broken regime follows from the collision of two fixed points in the d → 2 limit, leading to walking behavior or pseudocriticality.
The transition metal dichalcogenide compound TiSe[2] transforms into a 2x2x2 charge density wave (CDW) phase below 200K. Se 4p valence band and Ti 3d conduction band hybridize and form CDW gap. These
hybridized orbital characters are crucial information to understand the origin of CDW property. Recent studies show that linear- and circular dichroism (LD and CD) in angle-resolved photoelectron
spectroscopy (ARPES) provides insights into the orbital texture of the initial states. Here, using ARPES in the soft x-ray photon energy range, we systematically study the LD and CD of TiSe[2] both
with and without CDW phases. The LD and CD of Ti 3d conduction band show similar results irrespective of CDW phase. We found that CD features of Se 4p band top resemble with those of Ti 3d,
indicating the mixed orbital character of Se 4p and Ti 3d.
Recent progress in the fabrication and control of layered materials in the mono- or few-layer limit have reinvigorated the study of the fundamental properties of excitonic states. However, while the
binding energy and optical activity of excitons has been studied in a lot of detail, much less is known about the topological and quantum geometric properties of the excitonic band, despite the
recent realization of its central role in single particle properties and responses. This is partly due to the lack of a proper characterization of the topological properties of the exciton bundle. In
particular, it is unclear how the topology of the underlying electron and hole bands are related to the resulting topology of the exciton band structure in the presence of interaction. Here, we
develop a comprehensive framework that characterizes the geometric properties of excitonic states based on the full lattice wavefunctions. Specifically, we clarify how the electron-hole interaction
can affect the topology of the bound state. This becomes possible in a generalized framework which entirely sidesteps the effective mass approximation, which is almost universally used in low-energy
effective models to obtain analytical solutions. As our main result, we identify two gauge-invariant quantities that fully characterize the exciton’s topology and geometry: The exciton shift vector
SQ associated with the center-of-mass momentum Q and the exciton dipole vector Pp, which is connected to the relative momentum p. The shift vector encodes how the electron-hole interaction influences
the exciton band topology, which makes it possible to fully characterize the latter. Somewhat suprisingly, we find that the shift vector gives rise to a non-trivial polarization, which might be
observable for finite exciton densities at elevated temperature. On the other hand, the dipole vector is a polarization vector associated with the exciton’s intrinsic dipole moment, which couples to
an external electric field. The exciton dipole vector thus plays a crucial role in exciton dynamics, giving rise to a new anomalous velocity term in the exciton’s semiclassical equations of motion of
the exciton.
Exhaustive study of topological semimetal phases of matter in equilibriated electronic systems and myriad extensions has built upon the foundations laid by earlier introduction and study of the Weyl
semimetal, with broad applications in topologically-protected quantum computing, spintronics, and optical devices. We extend recent introduction of multiplicative topological phases to find
previously overlooked topological semimetal phases of electronic systems in equilibrium, with minimal symmetry-protection. We look into the multiplicative counterpart of the Weyl semimetal and find
rich and distinctive bulk-boundary correspondence and response signatures that greatly expand understanding of consequences of topology in condensed matter settings, such as limits on Fermi arc
connectivity and structure and transport signatures such as the chiral anomaly.
Frustrated magnetism is highly influenced by the geometry of the lattice and the competing interactions between the magnetic atoms in a system. In this poster, we will put forward results and
progress done in studying these systems. Kobyashevite, Ktenasite and Posnjakite occur as natural minerals which were synthesized as powders via hydrothermal method. X-ray diffraction done at room
temperature describe these materials to be formed of magnetic and non-magnetic layers. Within the magnetic layer, Cu-atoms are arranged in a triangular arrangement making them frustrated. Low
temperature magnetic studies done upto 2K revealed that Kobyashevite and Ktenasite undergo an antifferomagnetic transition at ~ 3.14 and 4.12 K respectively. Interestingly, Posnjakite did not show
any such transition within the measured range. The frustration parameter calculated is as high as 25 in these systems. Specific heat studies and neutron diffraction experiments are currently ongoing
as well as planned.
Spinon-magnon mixing was recently reported in botallackite Cu₂(OH)Br with a uniaxially compressed triangular lattice of Cu²⁺ quantum spins
[1]. Its nitrate analogue rouaite, Cu₂(OH)₃(NO₃), has a highly analogous structure and might be expected to exhibit similar physics. We grew
cm-scale single crystals of rouaite hydrothermally, and achieved >90% deuteration to allow neutron scattering studies of its magnetic order.
We report rouaite’s magnetic phase diagrams for H || a, b, and [001]. The lowest-temperature magnetic state comprises alternating ferro- and
antiferromagnetic chains, similar to botallackite but with different canting, while the higher-temperature phase is an approximately helical
modulation of this. The hierarchy of exchange interactions indicates that rouaite is quasi-one-dimensional but we do not observe spinons,
possibly because the material is more two-dimensional magnetically than botallackite.
The purpose of this work is to formulate a kinetic theory for the investigation of interaction effects on transport properties of electrons in the Landau-level states. Following Keldysh formalism, we
derive the quantum kinetic equation using the Landau-level basis. This equation can be use to study transport properties of interacting electrons in a constant background magnetic field of arbitrary
strength. As an application of our quantum transport equation, we calculate magneto-thermoelectric coefficients of a disordered two-dimensional electron gas (2DEG) and 3d Dirac/Weyl semimetals in the
quantum hall regime interacting with acoustic phonons.
The functional renormalization group (FRG) approach for spin models relying on a pseudo-fermionic description has proven to be a powerful technique in simulating ground state properties of strongly
frustrated magnetic lattices. However, the FRG as well as many other theoretical models, suffer from the fact that they are formulated in the imaginary-time Matsubara formalism and thus are only able
to predict static correlations directly. Nevertheless, describing the dynamical properties of magnetic systems is a theoretical challenge, as they are the key to bridging the gap to neutron
scattering experiments. We remedy this shortcoming by establishing a methodical approach based on the Keldysh formalism, originally developed to handle non-equilibrium physics.
This approach allows for calculating the dynamic properties of spin systems on arbitrary lattices. We can identify the correct low-energy dynamic spin structure factors for examplary Heisenberg
systems and the Kitaev Honeycomb model.
We explore the phenomenon of exchangeless braiding in Kitaev chain systems. Kitaev chains, known for their potential to host Majorana zero modes, provide fertile ground for investigating non-Abelian
statistics. Our research demonstrates the manipulation of Hamiltonian parameters can facilitate braiding purely through quantum state evolution, avoiding the challenges of physically moving
particles. The results offer insights into the theoretical implementations and potential applications of exchangeless braiding in topological quantum computing.
Non-Hermitian Hamiltonians allow for an effective description of dissipative systems. They exhibit a variety of exciting phenomena that cannot be observed in the Hermitian realm. Exceptional Points
(EPs) are a prime example of this. At EPs not only the complex eigenvalues, but also the eigenvectors coalesce and sensitivity to perturbations is enhanced. This concept has recently found fertile
ground in optics and photonics where non-Hermitian eigenstates can be induced by optical gain and loss. Similar control of x-rays is desirable due to their superior penetration power and detection
efficiency. Here, we investigate theoretically non-Hermitian x-ray photonics in thin-film cavities probed by x-rays under grazing incidence. These cavities present loss that can be controlled via the
incidence angle of the x-rays. Application of a magnetic hyper- fine field paves the way to tune the system towards EPs and to explore their rich topological properties.
Integration of high Q resonators for lossy materials.
1D and 2D structures of materials with topological electronic bands are beneficial for better visualizing enhanced surface transport and their utilization in quantum nanotechnology. TaAs[2], NbAs[2],
and TaSb[2] are classified as weak topological semimetals and predicted to harbor rotational-symmetry-protected topological crystalline insulator (TCI) phase with surface dispersion of type-II Dirac
fermions. Studying nanowires/nanoribbons (NWs/NRs) of this family of materials is desirable. Here, we present the synthesis and characterization of single-crystalline, TaAs[2] NWs/NRs with unique
core-shell structures. Further, NWs/NRs are integrated into four-terminal devices, and their magnetotransport properties have been studied. We will also present the epitaxial growth 3D-Dirac
semimetal Cd[3]As[2] planar nanowires on different planes of the sapphire (α-Al[2]O[3]), resulting in well-aligned arrays suitable for integration into devices.
The recently discovered MnBi[2]Te[4] family holds significant potential for applications in spin-based technologies due to the unique quantum phenomena derived from their topological properties. A
crucial factor is cationic intermixing, which in the compounds affects the electronic and magnetic properties. In this study, we utilize nuclear magnetic resonance and muon spin spectroscopy, along
with Density Functional Theory (DFT) calculations, to explore the impact of intermixing on the magnetic properties of MnBi[2]Te[4](Bi[2]Te[3])n and MnSb[2]Te[4]. Our findings confirm that the
intrinsic and antisite Mn magnetic moments are oppositely aligned in the ground state for all family members. Additionally, we demonstrate that the static magnetic moment on the Mn antisite
sublattice disappears below the ordering temperature, resulting in a homogeneous magnetic structure unaffected by intermixing. This discovery suggests a path for optimizing the essential
surface-state magnetic gap.
Rare earth metals (REMs) are difficult, if not impossible, to clean as bulk materials due to their extreme reactivity. Therefore, films of REMs are studied to explore their rich magnetic properties,
which are primarily influenced by the element-specific sign and wavelength of the RKKY interaction. Based on their complex cleaning procedure, the magnetic structure of REM surfaces remains a subject
of ongoing debate, while it is still unknown for most of them. Here we present investigations of the structural, electronic, as well as the complex magnetic properties of Europium (Eu) films
epitaxially grown on W(110), using spin-polarized scanning tunneling microscopy (SP-STM).
Europium (Eu) has a half-filled 4f shell with no d-electrons, adopting a body-centered crystal structure in bulk. However, in thin epitaxial films, a metastable hexagonal close-packed structure is
expected, accompanied by helical spin ordering below its Néel temperature of 91 K. With optimal preparation conditions, we successfully grew clean, smooth films, where we observed the exchange-split
surface state exclusively in the unoccupied region. Beyond a critical film thickness, striped regions with a periodicity of approximately 3 nm were identified. Experiments with differently magnetized
STM tips and the application of an external magnetic field up to ±2.5 T revealed the magnetic nature of these stripes. By varying the bias voltage, we were able to distinguish between structurally
and magnetically induced stripe patterns.
We present muon spin rotation (µSR) studies showing that long-range magnetic order occurs in RuBr[3] at ~ 34 K. The magnetic ordering is robust and static suggesting more conventional at zero field.
Present investigations prove in RuBr[3 ]the Kitaev interactions are likely to be weakened at zero field compared to α-RuCl[3]. The Kitaev interactions can be tuned by replacing Cl with heavier
halogen elements such as Br.
NaYbS[2] is a candidate material for a pseudo-S = ½-based quantum spin liquid on the ideal triangular lattice. Single crystals of the solid solution series NaYb[1]-xLuxS[2] are synthesized in the
range 0 3+ by Lu[3]+ ions with no sign of magnetic ordering down to 2 K suggesting a diluted triangular spin liquid. We investigate this series by µSR experiments to study the magnetism and make the
time-field scaling relation to identify the presence or absence of exotic excitations.
The classification of operator algebras according to von Neumann provides insights into the entanglement structure of quantum field theories. We investigate the decomposition of subregion operator
algebras of different types in the presence of a conserved charge. Drawing motivation from the concept of symmetry resolution of entanglement, intensively investigated in quantum field theories and
holography, we expect a direct sum structure of operators which are invariant under the corresponding symmetry. We study the classification of these sectors along the lines of the Araki-Woods
Intermetallic antimonides containing rare-earth (R) and transition (T) metals show various compositions and structures. A representative group is formed by RTSb[3] compounds. Single crystals of these
can be grown by various methods. This study used a Bi flux synthesis and hot centrifugation to access a new Fe-containing RTSb[3] representative. Single crystals of RFeSb[3] with R = Pr,Nd,Sm,Gd and
Tb have previously been investigated, while the isostructural Ce-member was newly discovered in this work. The RFeSb3 structure consists of double layers of FeSb[6] octahedra alternating with R and
Sb square layers. These compounds display metallic conductivity and anisotropic magnetic properties, suggesting anti-ferromagnetic ordering of the R substructure without any contribution of the Fe
substructure to the magnetic properties. This is supported by the Mössbauer spectra of CeFeSb[3] at room temperature and 4.2 K. Further investigation of CeFeSb[3]'s magnetic and transport properties
is ongoing.
The interplay of 3d and 4f magnetism in rare earth transition metal antimonides gives rise to complex magnetic properties. In R[3]Fe[3]Sb[7] (R = Pr, Nd) iron and rare earth atoms form columns of
stacked triangles separated by antimony.
Iron exhibits non-collinear ferromagnetic order below 𝑇[c] ≈ 380 K. On cooling at the onset of rare earth order a spin reorientation (𝑇[SRT], Pr ≈ 40 K,T[SRT], Nd ≈ 50 K) and magnetization reversal
is observed.
Mössbauer spectroscopy is employed to resolve the local magnetic structure.
Mössbauer spectra reveal two distinct magnetic iron sites between 𝑇[c] and 𝑇[SRT], both collapsing into one new site below 𝑇[SRT].
Transverse field Mössbauer measurements have been performed to investigate turning of iron moments in the ab plane at room temperature. Turning of the ab components of the local moments in 0.1 T TF
field is observed.
We will discuss the implications of our findings on the magnetic structure of the system.
The realm of topological Kagome magnets offers a rich field for exploring the intricate interplay of quantum interactions among geometry, topology, spin, and correlation. The combination of magnetic
interactions with nontrivial band structures can lead to the emergence of various exotic physical phenomena such as an anomalous Hall, anomalous Nernst effect. HoPtSn crystallizes in a hexagonal
crystal structure with the P-62m space group with two antiferromagnetic transitions (Néel temperature ~7.4K & 3K). This structure features distorted Ho-based Kagome nets. In this work, we observe two
distinct metamagnetic transitions when magnetic field, H // c-axis. A large anomalous Hall conductivity of 1300 Ω−1 cm−1 at 2 K and topological Hall effect is observed for HoPtSn crystals. Our
findings suggest that RTX family could serve as an excellent platform for investigating the intricate relationship between magnetic and electronic structures, paving the way for exploring novel
quantum phenomena.
ZrTe[5] is known for its large thermopower and resistivity anomaly and offers a promising platform to study topological phase transition. Recent years have witnessed non-trivial and complex
electronic properties that assigned this material to either a strong topological insulator or a 3D Dirac semimetal phase. Here, I will present the electronic properties of ZrTe[5] depicting different
resistivity anomaly temperature Tp in distinct crystals. Strong temperature dependence of band-structure has also been observed in p- to n-type transition across the resistivity anomaly in Hall and
Seebeck coefficient measurements.
We explore the electromagnetic response of time-reversal (TR) invariant and TR breaking Weyl superconductors (SCs). It is known that Weyl semimetals contain Weyl nodes in their band structure — a
property captured in the low energy effective theory by an axion term in the action. In the case of a Weyl SC this behavior persists but has to be supplemented by traditional terms describing SCs.
Considering the theory Weyl SCs in the London limit we show that that TR invariant Weyl SCs feature a chiral Meissner state, where an additional component of the magnetic induction is generated
inside the SC. This leads to other consequences in the electromagnetic response different from conventional SCs, namely, the existence of a critical value of the axion coupling where the screening of
the magnetic field breaks down. Contrary, in the TR breaking Weyl SCs the magnetic field screening is strengthened by the axion contribution, but the latter results in an induced electric field
inside the SC.
Quantum emitter arrays are a powerful platform enabling tailored control of quantum optical phenomena, like super- and subradiance or
efficient photon storage. Since state-of-the-art experimental techniques allow the realization of almost arbitrary lattice structures, a natural question is what physical effects arise if the lattice
has nontrivial topology. Here, we study a one-dimensional chain of quantum emitters im-
plementing the Su-Schrieffer-Heeger model. Going beyond previous studies, we show how the presence or absence of topologically pro-
tected edge states depends on the orientation of the transition dipole moment with respect to the chain axis. Our results demonstrate the potential of atomic emitter arrays as a platform for
topological quantum optics.
Altermagnets are a newly recognized type of collinear magnets that have vanishing net magnetization yet lift Kramers spin degeneracy in their band structure. We study the impact of external electric
and magnetic fields on the Josephson response of a planar superconductor/altermagnet/superconductor junction. We show that the critical Josephson current across the junction oscillates as the
altermagnetic strength increases. Meanwhile, the current-phase relation can be forward- or backward-skewed and can be changed significantly by tuning the altermagnetic strength. Moreover, we reveal
that the effects of the external fields are twofold: (i) it can induce 0-π transition as the field strength grows, thus facilitating the application of altermagnetic Josephson junctions; and (ii) the
amplitude of the critical current can be significantly enhanced at finite field strengths. These findings pave the way for exploring further applications of superconductor/altermanget
Recent achievements in the quantum anomalous Hall effect (QAHE) in MnBi[2]Te[4] and MnBi[4]Te[7] position the (MnBi[2]Te[4])(Bi[2]Te[3])n family as a promising platform for QAHE advancements due to
their ferromagnetically (FM) ordered MnBi[2]Te[4] septuple layers (SLs). However, QAHE realization is challenging because of substantial antiferromagnetic (AFM) coupling between the SLs. Stabilizing
an FM state, beneficial for QAHE, can be achieved by intercalating SLs with additional Bi[2]Te[3] quintuple layers (QLs), though the mechanisms and required QL number are unclear, and surface
magnetism remains obscure. This study demonstrates robust FM properties in MnBi[6]Te[10] (n = 2) with a Curie temperature (Tc) of ~12 K, elucidated through combined experimental and theoretical
approaches. Our measurements reveal a magnetically intact surface with a large magnetic moment, comparable to the bulk. This establishes MnBi[6]Te[10] as a promising candidate for QAHE at elevated
In this work, we study the matrix element effect of the angle-resolved photoemission spectroscopy (ARPES) intensity to deduce k-space initial state orbital texture featuring different symmetries in
type-II Dirac semimetal PtTe[2]. We observe the switching of the orbital texture of the Dirac surface state relative to the Dirac point. Our spin- and angle-resolved photoemission data were augmented
by the one-step model of the photoemission within the spin-polarized relativistic Korringa-Kohn-Rostoker (SPR-KKR) Green’s function method. To extract information about the different contributions to
the resulting spectral weight and spin-polarization, the matrix element used in our one-step model of photoemission calculations includes all experimental parameters such as photon energy, light
polarization and geometry configurations. Via such control over the experimental parameters, to investigate the orbital wavefunction above and below the Dirac point, we performed
polarization-dependent ARPES.
We investigate ring-shaped microstructures of HgTe based quantum well heterostructures in electrical magneto transport experiments. To achieve this, advanced lithography techniques are employed to
pattern the heterostructure layer stack using an isotropic wet chemical etching process. We plan to separately contact inner and outer edge channels of the ring structure using side contacts and an
air bridge technology. Subsequently, low-temperature transport measurements will be conducted to investigate the quantum spin Hall edge channels in our 4-terminal devices. On our poster we will
present the initial findings of this research.
Novel 2D quantum materials display very interesting topological properties, such as a Quantum Spin Hall phase up to room temperature in monolayers bismuthene and indenene. However, transport
measurements and nanofabrication are often impossible due to the monolayers extreme air-sensitivity.
In order to fabricate nanostructures of air-sensitive monolayers, a unique UHV nanofabrication setup based on stencil lithography (using pre-developed hard Si stencils) is being develloped at LNCMI.
This compact setup comprises a positioning stage to align sample and stencil, evaporation cells for electrical connection and capping layer deposition, and an ion source for ion-beam etching. This
way, a thin film grown in UHV by collaborators can be brought through a UHV-suitcase, and nanopatterned onsite and in-situ, before being capped to enable measurements ex-situ. This setup will allow
to fabricate nanostructures of any air-sensitive material to be measured in very high magnetic fields.
In this experimental study, we use scanning tunneling microscopy and spectroscopy to investigate Yu-Shiba-Rusinov states induced by 4f-shell rare-earth Gd adatoms on a superconducting Nb(110)
surface. We engineer Gd atom chains along the substrate's [1-10] and [001] directions, revealing distinct behaviors in differently oriented chains. -oriented Gd chains exhibit spectroscopic features
at their ends, identifying them as trivial edge states, while [001] -oriented Gd chains display zero-energy edge states, suggesting non-trivial nature. Notably, Gd chains with four atoms--independent
of their particular orientation--exhibit a uniform zero-energy mode along the entire chain. These findings call for further research and a theoretical framework to describe rare-earth-based
structures on superconductors.
Fixed-point annihilation is a generic mechanism that generates an extremely slow RG flow and has been suggested to explain the occurrence of a weak first-order transition instead of a deconfined
critical point in two-dimensional quantum magnets. Here we explore this phenomenon in a (0+1)-dimensional spin-boson model which can be solved with unprecedented numerical accuracy using the
recently-developed wormhole quantum Monte Carlo method. We find a tunable transition between two ordered phases that can be continuous or first-order, and even becomes weakly first-order in an
extended regime close to the fixed-point collision. We provide direct numerical evidence for pseudocritical scaling on both sides of the collision manifesting in an extremely slow drift of critical
exponents. We also find scaling behavior at the symmetry-enhanced first-order transition as described by a discontinuity fixed point. Our study motivates future work in higher-dimensional quantum
dissipative spin systems.
The series of RAlSi with R being a rare earth element is of high interest as Weyl nodes are induced in those materials by broken inversion symmetry. LaAlSi is a nonmagnetic Weyl semimetal, while
CeAlSi shows canted Ferromagnetism and in NdAlSi as well as in SmAlSi, spiral spin structures are found.
We used NMR experiments to gain local information about the magnetic order parameter and excitations of RAlSi (R = {La, Ce, Nd}). Surprisingly, in this isostructural series we observe an electric
field gradient (EFG) at the Al position, which depends on the actual rare earth element present in the compound. The EFG is strongest for NdAlSi and vanishes for LaAlSi. This is surprising since the
4f-electrons are typically strongly localized inside the rare earth ion. In most cases the EFG can be well described using the charge distribution of the investigated atom and the total charge of
surrounding atoms, which is the same for all rare earth elements.
In this project, we theoretically identify and investigate a promising copper-based kagome metal candidate, yet to be experimentally realized. We endeavor to engineer a kagome metallic phase
exhibiting the smallest possible multi-orbital character, thereby bridging the gap between theoretical modeling and experimental realizations. The ideal candidate is found in the CsCu[3]CI[5]
compound. Our results were obtained employing both ab-initio calculations, in the framework given by density functional theory (DFT), as well as crystal field analysis. Remarkably, we generically
obtain a mixed-type van Hove singularity in close proximity to the Fermi level. Our proposed material promises to exhibit exotic electronic features, opening new possibilities for exploring
unprecedented quantum phenomena in kagome metals.
We introduce methods of characterizing entanglement, in which entanglement measures are enriched by the matrix representations of operators for observables. These observable operator matrix
representations can enrich the partial trace over subsets of a system’s degrees of freedom, yielding reduced density matrices useful in computing various measures of entanglement, which also preserve
the observable expectation value. We focus here on applying these methods to compute observable-enriched entanglement spectra, unveiling new bulk-boundary correspondences of canonical four-band
models for topological skyrmion phases and their connection to simpler forms of bulk-boundary correspondence. Given the fundamental roles entanglement signatures and observables play in study of
quantum many body systems, observable-enriched entanglement is broadly applicable to myriad problems of quantum mechanics.
We explore the ground states of infinite chains with a large number N of Majorana fermions on each site, interacting via identical on-site Sachdev-Ye-Kitaev (SYK) couplings and inhomogeneous
nearest-neighbor hopping terms. Our results unify techniques for solving SYK-like models in the large N limit with a real-space renormalization group method known as strong-disorder renormalization
group (SDRG). Decimation steps involve projecting Majorana fermions of strongly coupled sites onto their ground state, inducing effective hopping interactions between neighboring sites. If the two
sites are nearest neighbors, these local ground states admit a holographic dual description as eternal traversable wormholes. Otherwise, the wormhole structure fades, inducing non-vanishing
correlations between distant degrees of freedom. We apply our methods to two specific instances of these infinite SYK chains with either aperiodically or randomly distributed hopping parameters.
Recently, by considering the crucial role of the interlayer spin exchange interaction of the electrons on dz2 orbitals, the bilayer t-J model has been proposed as a potential minimum model to study
the nickelate superconductor La[3]Ni[2]O[7] under high pressure. To investigate the superconductivity of this model near the quarter filling, we consider the bilayer t-J-J[⊥] ladder where t is the
in-plane electron hopping, J is the in-plain spin interaction, and J[⊥] is the interlayer spin interaction. Using density matrix renormalization group method, we study the model on the Ly = 2 and 3
bilayer ladders by tuning J[⊥]. We find that by coupling the two layers in both the Luttinger liquid and Luther-Emery liquid states, increased J[⊥] can induce the dominant s-wave pairing between
the two layers. In the special case of Ly = 2 at the quarter filling, the gapped charge mode appears robust with growing J[⊥], and superconductivity cannot be induced in this case.
I review three characteristic cases of using Raman spectroscopy to study the collective excitations in topological systems. These examples include the chiral spin mode [PRL 119, 136802 (2017)] and
chiral excitons [PNAS, 116, 4006 (2019)] in Bi[2]Se[3], and the plasmon mode in BiTeI [PRB 109, L041111 (2024)]. The successful application of Raman spectroscopy demonstrates this experimental method
as a promising probe of topological systems.
Here we use a unitary mapping, combined with the well-established properties of the attractive Hubbard model to demonstrate rigorously a Hamiltonian with a low temperature pair-density-wave (PDW)
phase. We also show that the same mapping, when applied to the widely accepted properties of the repulsive Hubbard model, leads to a Hamiltonian exhibiting triplet d-wave PDW superconductivity and an
unusual combination of ferro- and antiferro-magnetic spin correlations. We then demonstrate the persistence of the d-wave PDW in a Hamiltonian derived from the mapping of the extended t-J model in
the large-U limit. Furthermore, through strategic manipulation of the nearest-neighbor hopping signs of spin-down electrons, we illustrate the attainability of PDW superconductivity at other momenta.
The intertwining of different magnetic and exotic pairing correlations noted here may have connections to experimental observations in spin-triplet candidates like UTe[2].
A promising platform for the quantum control of high-frequency photons are thin-film cavities, with one or several embedded layers of resonant nuclei with suitable Mössbauer transitions in the x-ray
range. At grazing incidence, incoming x-rays couple evanescently to the cavity. In turn, the cavity field drives the nuclear transitions.
Here, we investigate theoretically a thin-film cavity design with multiple embedded ^57Fe layers, such that its inter-layer couplings are mostly restricted to the nearest neighbouring layers by
intercalating additional layers with high electron densities. Via the geometrical properties of these domains and control of the evanescent field pattern, we implement alternating coupling strengths
between the resonant layers. We show that this leads to an x-ray photonic realization of the non-hermitian Su-Schrieffer-Heeger model and investigate how for certain configurations localized nuclear
excitations emerge at the edges of the cavity. | {"url":"https://www.ctqmat24.de/en/program/posters","timestamp":"2024-11-07T23:36:27Z","content_type":"text/html","content_length":"191686","record_id":"<urn:uuid:bbffed1c-f811-4239-9dc9-d70426dc2243>","cc-path":"CC-MAIN-2024-46/segments/1730477028017.48/warc/CC-MAIN-20241107212632-20241108002632-00518.warc.gz"} |
Activity 3 - Complementary, Supplementary, Angle around a Point
Observe: Use the slider to Rotate line CD. 1. Look for Vertical Angles, Linear Pairs and Adjacent Angles. 2. Look for a pair of Complementary Angles? What relationship exist between complementary
angles? 3. Look for a pair of Supplementary Angles? What relationship exist between supplementary angles? 4. What is the sum of all of the angles around point O? Questions: Move the slider toward the
Left (But not all the way to the left...)
5. Name one of each: an obtuse angle, acute angle, and right angle.
6. Are <AOC and <DOB vertical angles?
7. Are <DOA and <DOB adjacent angles?
8. Are <DOA and <EOC complementary angles?
9. Are <DOA and <DOB supplementary angles?
10. Find m<DOA + m<AOE + m<EOC. | {"url":"https://stage.geogebra.org/m/pewracny","timestamp":"2024-11-05T12:19:29Z","content_type":"text/html","content_length":"102261","record_id":"<urn:uuid:65e8bdb2-027d-43d8-9899-f903e9642d08>","cc-path":"CC-MAIN-2024-46/segments/1730477027881.88/warc/CC-MAIN-20241105114407-20241105144407-00358.warc.gz"} |
Feature Column from the AMS
Apportionment: Fairness and Apportionment
Feature Column Archive
2. Fairness and Apportionment
The Constitution does not specify what fairness criteria should be used in comparing two different proposed ways to solve an apportionment problem. From the beginning there were both political and
equity considerations in choosing an apportionment system but there are some principles that one can call attention to in evaluating apportionment systems. One fairness idea is that each state should
get either its lower quota or upper quota. A second approach to fairness is to look at pairwise equity between states. The empirically discovered Alabama paradox (one can get fewer seats in a larger
house, with fixed population) called to the attention of politicians and others interested in apportionment that one had to worry about the fairness properties of the methods that one might use to
solve the apportionment problem. However, little seems to have been done in a systematic way to see what the consequences for fairness were of adopting different apportionments. In the United States,
what became a matter of concern was the perception that different methods of apportionment might display bias. The idea of bias is that a method might systematically reward states with specific
characteristics or groups of such states. For example, were some methods more likely to give smaller states more than their fair share of seats, say, as measured by exact quota? One way to try to
answer this question was to turn to statistics. It is not hard to see that the different methods of apportionment treat small and large states in different ways. This can be seen in contrived
artificial examples as well as using data that has arisen from the censuses. However, there are many different ways of thinking and models for deciding what constitutes bias of an apportionment
method. As just one example, the Constitution itself has a bias in favor of small states because it will give every state one seat regardless of how undeserving the state might be. In computing bias
of a method, how should this "minimum of one seat" condition be taken into account?
Huntington was a pioneer in using mathematical ideas to compare the different apportionment from a fairness point of view. His writings have an attractive conversational style, though like many good
debaters he does not shy from leaving out things that do not help his case. Huntington realized that there were two major approaches to evaluating fairness:
1. Global optimization
This approach sets up a measure of fairness and for a given apportionment method sums up this measure for all the states. The goal is to select that method which minimizes the sum for the given
measure over all the states. This approach involves various discrete optimization techniques and has not been pursued vigorously until relatively recently. Some of the optimization problems that one
is led to may be computationally very difficult. Huntington rejects such methods but they are mathematically interesting nonetheless.
2. Pairwise comparison for states.
This approach involves making sure that switching a seat from one state to another does not diminish the fairness of the apportionment as given by some measure of fairness. Huntington championed the
study of this way of approaching the apportionment problem. He showed, rather surprisingly, that each of the historic methods was best under at least one fairness measure. This created the
troublesome situation that one had to make a value judgment as to which of these fairness criteria was the best in order to justify the choice of a particular method, and it is not clear on
mathematical grounds how to do this.
First, Huntington observed that for each measure of equity between states one could look at this measure in absolute terms or in relative terms. Here is an example illustrating this, taken from one
of Huntington's papers using data from the 1940 census: Using all of the census data, it turns out that Webster assigned Michigan (population 5,256,106) 18 seats and Huntington-Hill assigned it 17
seats, while Webster assigned Arkansas (population 1,949,387) 6 seats and Huntington-Hill assigned Arkansas 7 seats. The two methods agree except for the number of seats that they give to these two
states. With these numbers, the size of the congressional district for Michigan under Webster was 292,006, while the size under Huntington-Hill was 309,183. The equivalent figures for Arkansas were
324,898 (Webster) and 278,484 (Huntington-Hill). Thus, the absolute difference between the two states for Webster was 32,892 (324,898-292,006). The absolute difference between the two states for
Huntington-Hill was 30,699. By this measure Huntington-Hill did a better job. However, there is also the perspective of the size of the difference relative to the size of the populations of the
states involved. Michigan is a much bigger state than Arkansas. In relative terms the Webster method resulted in a relative difference of 11.26 percent, while Huntington-Hill resulted in a relative
difference of 11.02 percent. The relative difference for u and v is given by |u-v|/(min (u, v)). This example should not mislead one into thinking that Huntington-Hill always does a better job.
Measuring the absolute difference in representatives per person would be the basis for defending why the Webster apportionment is better. I use this example only to illustrate the distinction between
relative and absolute difference ideas.
Here is a summary of what Huntington discovered:
a. For relative differences, Huntington-Hill is the optimal method for all the fairness measures about to be listed. Recall that a[i] and P[i] are the number of seats for state i and its population,
respectively. For a fixed divisor method, the formula can be used to compare whether or not giving the next seat to state i or state j is more justified, as measured by the the given fairness
b. For the measure
For the measure
For the measure
For the measure
For the measure
Again, it might not be obvious that these seemingly similar measures of absolute pairwise fairness would give rise to such different methods to achieve optimality. Yet Huntington showed that if one
is concerned with relative differences, all the criteria formulas are optimal only for Huntington-Hill. | {"url":"http://www.ams.org/publicoutreach/feature-column/fcarc-apportionii2","timestamp":"2024-11-12T02:33:17Z","content_type":"text/html","content_length":"53172","record_id":"<urn:uuid:79797916-8cb8-443d-a027-cfc84b340976>","cc-path":"CC-MAIN-2024-46/segments/1730477028242.50/warc/CC-MAIN-20241112014152-20241112044152-00177.warc.gz"} |
Homeschooling My Daughter For My Own Benefit — Math
My kid is 7. She doesn’t need to know algebra.
I am 54. I don’t need to know it either. So why am I studying it?
It’s not that big a time commitment. I have no tests to pass.
But as I thought about my hope for daughter to grow up fully numerate and unintimidated by math-y stuff, I realized that I had to get over my own intimidation in the face of math, which (despite
having a whole family full of supernumerate math-lovers) I hated in school.
So I decided to map my own ignorance, with the help of various library books and Khan Academy videos.
How much of the algebra I was exposed to in high school stuck to me? Damned little, apparently. How much of my own incompetence is due to ignorance and/or incompetence? How much of it is due to
lingering emotional responses from math trauma in school?
Recently I’ve been playing with lines and slopes. I have absolutely no recollection of ever learning y-b = m (x – a) or anything that looks like it, so my engagement with the formula and its
constituents doesn’t seem to have emotional content (unlike, say, quadratics, which are associated in my mind with a terrible homework fight I had with my father somewhere in 9th grade).
The first thing I notice is now many simple mistakes are available for me to make at every step of the way. It is going to take many many iterations before this process is internalized in my (so to
speak) mental muscle memory. I am intellectually aware of what’s required to calculate the slope of a given line — but the actual physical process of writing the numbers down in the right positions
vis-a-vis one another is fraught with complications.
As a music teacher I’ve got an advantage over some other folks: I never had any musical talent, so I had to build my musicianship from the molecular level up, making every mistake possible. It looks
like the same process is happening with math.
Music teachers with “talent” are often ignorant of two key factors in developing mastery: number of repetitions and size of learning increment. It’s not enough to repeat something until your student
does it right — once it’s been done right is the time to begin repetitions! And it’s not enough to increment the learning in steps suitable to your own learning style — it’s essential to figure out
the increments your student requires, which may be much smaller than what you needed.
My algebra increments are very small. Fortunately, I’m patient. Yesterday I did three or four slope formulas, some several times. I made mistakes in calculating the initial slope; I transposed x and
y in my head; I reversed + and – signs; I simply wrote down a 3 where I meant to write a 2. Each of these and more sent me in different wrong directions — since I didn’t figure out what I’d done
until later. And that was just in the initial calculation. Once I began trying to plug these numbers into the y-b = m (x – a) formula, a whole new collection of mistakes emerged.
You know what? I’m interested in the mistakes. Getting it right is not the objective here; the “goal” is to figure out as many different ways of getting it wrong as I can.
The fact that my daughter sees me doing this at the breakfast table is a bonus for the homeschooling process. I’m doing it because I’d like to get over my own anxieties. | {"url":"http://www.warrensenders.com/journal/homeschooling-my-daughter-for-my-own-benefit-%e2%80%94-math/","timestamp":"2024-11-05T18:48:19Z","content_type":"application/xhtml+xml","content_length":"62108","record_id":"<urn:uuid:681a00f9-2356-4502-8cff-161c6b52ecfd>","cc-path":"CC-MAIN-2024-46/segments/1730477027889.1/warc/CC-MAIN-20241105180955-20241105210955-00852.warc.gz"} |
What if I told you that all horses have the same colour? And that 2 = 1? And, to top it off, that I could prove it? You would probably say I’m delusional and that my proof must contain a mistake.
However, there are proofs that do not contain mistakes which conclude these statements to be true! What they do contain, however, are mathematical fallacies. What are these and why do they occur?
The mathematical fallacy is different from a mistake in a proof, as a mistake leads to an invalid proof, whereas a mathematical fallacy contains an element of concealment of deception in the
presentation of the proof. I will give several examples of a mathematical fallacy, some more infuriating than others.
2 = 1
A “proof” of the statement 2 = 1 is as follows: we let $a$ and $b$ be equal, nonzero quantities. Then:
& a & = & b\\
\iff & a^2 & = & ab\\
\iff & a^2 – b^2 & = & ab – b^2\\
\iff & (a – b) (a + b) & = & b(a – b)\\
\iff & a + b & = & b\\
\stackrel{a = b}{\iff} & b + b & = & b\\
\iff & 2b & = & b\\
\iff & 2 & = & 1
In this case, the mathematical fallacy is in line 5, where we have divided $(a – b) (a + b) = b (a – b)$ by $a – b$. However, since $a = b$, this means dividing by zero, which is undefined, making
this argument invalid.
A mathematical fallacy has the interesting quality that, as typically presented, it does not only yield absurd results, but does so in a deceiving, clever way. In this case, dividing out a common
factor is usually fine, however, since $a = b$, you are dividing by zero without really noticing.
All horses have the same colour
To (not) prove that all horses have the same colour, we will use (incorrect) mathematical induction.
1. For $n \in \mathbb{N}$, let $P(n)$ be: in a group of $n$ horses, all horses have the same colour.
2. For $n = 1$, we have $P(1):$ in a group of one horse, all horses have the same colour. Since there is only one horse in the group, obviously the horse has the same colour as itself. Hence, $P(1)$
is true.
3. Let $N \in \mathbb{N}$ be given and suppose $P(N)$ is true, that is, in a group of $N$ horses, all horses have the same colour.
4. Let $n = N – 1$. Since we know $P(N)$ is true, when removing a horse from a group of $N$ horses who have the same colour, the remaining group must also have the same colour.
5. If we add another horse to the group, we again have a group of $N$ horses, and since we know that $P(N)$ is true, this new group of $N$ horses must also have the same colour.
6. Now, we have constructed two groups of $N$ horses of the same colour, with $N – 1$ horses in common. Since the two horses they do not have in common must be the same colour as the other $N – 1$
horses, they also must have the same colour as each other.
7. Thus, combining all the horses, we now have a group of $N + 1$ horses of the same colour.
8. Since (1) $P(1)$ is true, (2) $P(N)$ is true $\implies P(N + 1)$ is true, and (3) $N \in \mathbb{N}$ is arbitrarily given, by the method of Mathematical Induction, $P(n)$ is true for all $n \in \
9. Therefore, we can conclude that all horses have the same colour.
Of course, common sense tells us that not all horses have the same colour. The fallacy in this proof is in step 4. For $N = 1$, using the reasoning of this step, the two groups of horses have $N – 1
= 0$ horses in common, so they cannot have the same colour. Hence, the group of $N + 1 = 2$ horses does not necessarily have the same colour. In other words, the reasoning that every group of $n = N$
horses has the same colour implies that every group of $n = N + 1$ has the same colour, works for any $N > 1$, but not for $N = 1$. Thus, this induction hypothesis is not true for all $n \in \mathbb
One can see there are many ways to be deceived by a mathematical fallacy, some more crafty than others. Underlying a mathematical fallacy is usually a seemingly obvious contradiction or phony
reasoning, so always be mindful of deception when presented with unbelievable claims!
Nice extra: howlers
As a little encore, I would like to tell you briefly about the most infuriating mathematical fallacy I have encountered so far: the howler. An example is as follows:
\dfrac{16}{64} = \dfrac{1\cancel{6}}{\cancel{6}4} = \dfrac{1}{4}
Though the outcome is correct, for obvious reasons, the argument could not be more wrong, making this another, sickening mathematical fallacy.
Heuser, Harro (1989), Lehrbuch der Analysis – Teil 1 (6th ed.), Teubner, p. 51, ISBN 978-3-8351-0131-9.
Maxwell, E. A. (1959), Fallacies in mathematics, Cambridge University Press, ISBN 0-521-05700-0, MR 0099907.
Pólya, George (1954). Induction and Analogy in Mathematics. Mathematics and plausible reasoning. Vol. 1. Princeton. p. 120.
Econometrics, the intersection of economics and statistics, employs sophisticated methods to analyse and quantify relationships within economic systems. One of its fundamental tools is regression
analysis, a statistical technique that allows economists tot model...
We tie our shoelaces to ensure that our shoes stay on tight, and we do these by tying a knot. There are different ways to tie your shoelaces, you may have learnt the “around the tree” technique, but
somehow, they still always come undone, why? This all has to do with...
Last week, the elections for the Dutch parliament took place. This election came earlier than usual since the cabinet Rutte IV had fallen due to failed negotiations about policy toward asylum
seekers. The same political parties formed the previous coalition, Rutte...
Regression analysis: A beginner’s guide
Are you tying your shoelaces wrong?
The Dutch Childcare Benefits Scandal – How Big Data and AI Can Have Disastrous Consequences | {"url":"https://www.deeconometrist.nl/why-all-horses-have-the-same-colour/","timestamp":"2024-11-02T20:10:09Z","content_type":"text/html","content_length":"261772","record_id":"<urn:uuid:38e06cb0-a495-49c8-bb52-f43aba93a274>","cc-path":"CC-MAIN-2024-46/segments/1730477027730.21/warc/CC-MAIN-20241102200033-20241102230033-00712.warc.gz"} |
Bond yields and coupon rates
If r1=0.1, r2 = 0.11, and r3 = 0.09, the price is $1,021.47. Yield To Maturity. Suppose a 3 year, 8% coupon rate, $1000 face value bond is selling for $949.22. What The issuer promises to repay the
loan on a future date, known as the maturity date. Let's look at a bond with a $1,000 par value, a 5% coupon rate and 3 years to The price of a bond is the Present Value of all cash flows generated
by the bond ( i.e. coupons and face value) discounted at the required rate of return. PV cpn r.
if y < coupon rate, P > face value. These results also demonstrate that there is an inverse relationship between yields and bond prices: when yields rise, bond Take a new bond with a coupon interest
rate of 6%, meaning it pays $60 a year for every $1,000 of face value. What happens if interest rates rise to 7% after the 24 Dec 2019 Negative yield bonds are affected by negative interest rates.
The coupon rate or negative interest rate, the period of bond or maturity period, The coupon shows the interest that the respective bond yields. The issuer of the bond takes out a loan on the
capital market and therefore owes a debt to the 12 Feb 2019 For instance, if a bond has a face value of Rs. 1000 and pays a coupon payment of Rs. 100 per annum, the coupon rate of the bond would be
Technical terms surrounding bonds are numerous and can sometimes be confusing. Below we have defined the terms surrounding the different bond yields. Coupon Rate on Bonds Definition. The coupon rate
of a bond represents the amount of actual interest that is paid out on a bond relative to the principal value of the bond (par value).
12 Feb 2019 For instance, if a bond has a face value of Rs. 1000 and pays a coupon payment of Rs. 100 per annum, the coupon rate of the bond would be 10 As the yields change, the prices of the bonds
also change. The coupon rate acts as a fulcrum, with yields on one side of the seesaw and price on the other side. 28 Aug 2019 Remember, the coupon tells you what interest rate the issuer is paying
on each $1000 bond to the investor. By dividing that by the price you A model of the tax structure of interest rates is developed and simple approximate expressions relating yield to coupon are
derived. The effect on these simple Treasury Yield Curve Rates: These rates are commonly referred to as "Constant Maturity Treasury" rates, or CMTs. Yields are interpolated by the Treasury from
In essence, yield is the rate of return on your bond investment. However It also enables you to compare bonds with different maturities and coupons. Yield to
Bond Yield Vs the Coupon Rate. When bonds are originally issued, they usually sell at or near the face value, so the coupon rate is essentially the rate of return the The simplest case, however, is
when there are no coupons, a zero coupon bond. For example, suppose you buy a 5-year $1000 bond, which means that 5 years In essence, yield is the rate of return on your bond investment. However It
also enables you to compare bonds with different maturities and coupons. Yield to Coupon yield is the annual interest rate established when the bond is issued. It's the same as the coupon rate and
is the amount of income you collect on a bond If r1=0.1, r2 = 0.11, and r3 = 0.09, the price is $1,021.47. Yield To Maturity. Suppose a 3 year, 8% coupon rate, $1000 face value bond is selling for
$949.22. What The issuer promises to repay the loan on a future date, known as the maturity date. Let's look at a bond with a $1,000 par value, a 5% coupon rate and 3 years to
Take a new bond with a coupon interest rate of 6%, meaning it pays $60 a year for every $1,000 of face value. What happens if interest rates rise to 7% after the
Coupon Interest Rate vs. Yield. For instance, a bond with a $1,000 face value and a 5% coupon rate is going to pay $50 in interest, even if the bond price climbs to $2,000, or conversely drops to
$500. It is thus crucial to understand the difference between a bond's coupon interest rate and its yield.
The coupon rate or yield of a bond is the amount that an investor can expect to receive as they hold the bond. Coupon rates are fixed when the government or corporation issue the bond. Calculation of
the coupon rate is from the yearly amount of interest based on the face or par value of the security.
Interest Rate Risk. The price of a bond moves in the opposite direction of bond yields. Since the coupon (interest) on the bond is fixed, the price of the bond will rise or fall to provide a yield to
maturity on the bond equal to the current market rate required by investors. Bonds market data, news, and the latest trading info on US treasuries and government bond markets from around the world.
24 Dec 2019 Negative yield bonds are affected by negative interest rates. The coupon rate or negative interest rate, the period of bond or maturity period, The coupon shows the interest that the
respective bond yields. The issuer of the bond takes out a loan on the capital market and therefore owes a debt to the | {"url":"https://topbinhbofddv.netlify.app/biviano60016noxu/bond-yields-and-coupon-rates-364.html","timestamp":"2024-11-02T09:17:43Z","content_type":"text/html","content_length":"34329","record_id":"<urn:uuid:56c292b3-803a-4a73-b0d5-76957409f7e2>","cc-path":"CC-MAIN-2024-46/segments/1730477027709.8/warc/CC-MAIN-20241102071948-20241102101948-00786.warc.gz"} |
Chapter 3: Time Value of Money » STUDY NOTES NEPAL
Short Questions Answer
Why is the time value of money concept so important in financial analysis?
Time value of money concept is widely applied in financial decisions. Financial decisions are carried out with the objective of maximizing value of the firm. The application of time value of money
concept in financial decision making contributes toward a value maximization objective. The basic importance of the concept of time value of money are discussed below:
• Application in investment decision: One of the basic applications of the concept of time value money is widely observed in making long-term investment decisions. All long-term investment projects
require spending a huge amount of capital today and with certainty. However, the benefits from the use of projects occur in small amounts over a longer period of time and with uncertainty. Thus,
there is a difference in timing of cash outflows and cash inflows associated with long-term investment. Cash outflows occur at present whereas cash inflows are realized over several periods of
time. Because of the timing difference, they are not directly comparable. Therefore future cash inflows are discounted back to present values to compare against the present cash outflows and make
investment decisions. Long-term projects also involve risk because of the uncertainty of future cash inflows. So according to the concept of time value of money. We select an appropriate discount
rate consistent to the level of risk involved in the project to calculate present values. Thus, the concept of time value of money contributes to making long-term investment decisions effectively
and efficiently.
• Application in financing decision: Besides investment decisions, the concept of time value of money is also applied widely in financing decisions. Financing decision is concerned with determining
optimal proportionate mix of long-term components of capital that minimizes the weighted average cost of capital. In deciding on the appropriate source of financing for the firm, we compare the
effective cost of each source of financing based on the concept of time value of money.
• Application in security analysis: While analyzing the securities investment, such as investment in stock and bonds, the security analysts and investors use the concept of time value of money. In
making securities investment decisions, future cash flows of securities are discounted back to present value to determine the worthiness of investment in securities.
• Application in leasing versus buying decision: Further, we use the concept of time value of money in leasing versus buying decision to calculate the present value of cost of leasing and cost of
buying. The present values of costs of these two alternatives are compared against each other to decide on an appropriate source of financing.
• Other uses: Besides the above uses, the concept of time value of money is also used for other purposes as well. For example it can be used to assess the proposed credit policies and the firm’s
efficiency in managing cash collections under current assets management. It can be used to plan family expenditure and investment, such as investment for safety and security as in the case of
buying insurance and pension plans.
Explain what is meant by the following statement. “A rupee in hand today is worth more than a rupee to be received next year.”
Every sum of money received earlier commands a higher value than the equal sum of money received later. This statement is well explained by the concept of time value of money. The time value of money
is the concept to understand the value of cash flows that occurred at different periods of time. A rupee in hand today is valued more than a rupee next year due to the following three reasons.
• Investment opportunity: Money received earlier can be invested to generate further sums of money. For example, if we receive Rs 100 today and deposit in a bank account paying 6 percent interest,
we will have Rs 106 at the end of the year. Therefore, given this investment opportunity Rs 100 today is equivalent to Rs 106 at the end of year.
• Preference toward current consumption: Most people prefer current consumption to future consumption. Money in hand today makes current consumption possible. Therefore, Current sum of money is
more valuable.
• Inflation: A sum of money today is worth more than the equal sum of money a year later due to inflation. Inflation kills purchasing power of the money. If the rate of inflation is 5 percent, we
need Rs 105 to buy a basket of commodities a year later than what we could buy with Rs 100 today.
Write Short Notes on:
Time value of money
The time value of money is the concept to understand the value of cash flows that occurred at different periods of time. Every sum of money received earlier commands a higher value than the equal sum
of money received later. This statement is well explained by the concept of time value of money. A rupee in hand today is valued more than a rupee next year due to the fact that money received
earlier can be invested to generate further sums of money. For example, if we receive Rs 100 today and deposit in a bank account paying 6 percent interest, we will have Rs 106 at the end of the year.
Therefore, given this investment opportunity Rs 100 today is equivalent to Rs 106 at the end of year. Current money in hand is also important because it allows current consumption. Further, in the
inflationary environment, a present sum of money has higher purchasing power than the equal sum of money in future.
Time value of money concept is widely applied in financial decisions. One basic application of the concept of time value money is widely observed in making long-term investment decisions. In all
long-term investment decisions, future cash inflows are discounted back to present values to compare against the present cash outflows. Further, the concept of time value of money is also applied
widely in financing decisions to compare the effective cost of each source of financing. Besides, while analyzing the securities investment, such as investment in stock and bonds, the security
analysts and investors use the concept of time value of money to discount the future cash flows back to present value to determine the worthiness of investment in securities. It can also be used to
plan family expenditure and investment, such as investment for safety and security as in the case of buying insurance and pension plans.
Amortized loans
Amortized loans are those loans that are repaid in equal periodic installments over a loan contract period. The equal periodic installments contain both- a part of principal repayment and the
interest payment on outstanding loan. This type of loan is more common on hire purchase financing of autos and home appliances in Nepal. Besides, commercial banks in Nepal also extend housing loans
for a longer period of time which are repaid in equal monthly installments (EMI). In amortized loans, the equal periodic installment is called ‘Payment’. It is determined on the basis of the concept
of time value of money. A payment is a series of equal future payments on the loan that has a total present value equal to the amount of loan at a given interest rate. It is worked out as follows:
Payment (PMT)= PVIFA [;%n year ]/Amount of Loan
Once the equal payment is worked out using the above relation, we prepare an amortization schedule. An amortization schedule is the schedule of loan repayment which shows in detail the payment made
each period including interest payment and a part of principal repayment. The interest payment each period declines and the part of principal repayment each period increases without affecting the
installment. In other words, the proportion of interest on each payment declines every period while the proportion of principal repayment each period increases.
Numerical Problems:
Assume that it is now January 1, 1998. In January 1999, you will deposit Rs. 1,000 into a savings account that pays 8%. If the bank compounds interest annually, how much will you have in your account
on January 1, 2002? What would your January 1, 2002, balance be if the bank used quarterly compounding rather than annual compounding?
Assume that it is now January 1, 1998. In January 1999, you will deposit Rs. 1,000 into a savings account that pays 8%. If the bank compounds interest annually, how much will you have in your account
on January 1, 2002? What would your January 1, 2002, balance be if the bank used quarterly compounding rather than annual compounding?
Annual payment (PMT) = Rs 60,000 per year
Interest rate (i) = 8%
n= 4 years
The amount that must be deposited today is given by:
PVAn= PMT x PVIFA i,n= Rs 60,000 x PVIFA [8%, 4] = Rs 60,000 x 3.3121 = Rs 198,726
Assume that it is now January 1, 1998, and you will need Rs. 1000 on January 1, 2002. Your bank compounds interest at an 8% rate annually.
(a) How much must you deposit on January 1, 1999 to have a balance of 1,000 on January 1, 2002?
(b) if you want to make equal payments on each January 1 from 1999 through 2002 to accumulate the Rs. 1000, how large must each of the four payments be?
(c) If your father were to offer either to make the payments calculated in Part B or to give you a lump sum of Rs. 750 on January 1, 1999, which would you choose?
(d) If you have only Rs. 750 on January 1, 1999, what interest rate, compounded annually, would you have to earn to have the necessary Rs.1000 on January 1, 2002?
Assume that it is now January 1, 1998, and you will need Rs. 1000 on January 1, 2002. Your bank compounds interest at an 8% rate annually.
(a) How much must you deposit on January 1, 1999 to have a balance of 1,000 on January 1, 2002?
(b) if you want to make equal payments on each January 1 from 1999 through 2002 to accumulate the Rs. 1000, how large must each of the four payments be?
(c) If your father were to offer either to make the payments calculated in Part B or to give you a lump sum of Rs. 750 on January 1, 1999, which would you choose?
(d) If you have only Rs. 750 on January 1, 1999, what interest rate, compounded annually, would you have to earn to have the necessary Rs.1000 on January 1, 2002?
1. What is the present value of a security that promises to pay you Rs. 5,000 in 20 years? Assume that you can earn 7 percent if you were to invest in other securities of equal risk.
2. You are thinking about buying a car, and a local bank is willing to lend you Rs. 20,000 to buy the car. Under the terms of the loan, it will be fully amortized over 5 years (60 months), and the
nominal rate of interest will be 12 percent, with interest paid monthly, what would be the monthly payment on the loan? What would be the effective rate of interest on the loan?
Why is the time value of money concept so important in financial analysis?
Time value of money concept is widely applied in financial decisions. Financial decisions are carried out with the objective of maximizing value of the firm. The application of time value of money
concept in financial decision making contributes toward a value maximization objective. The basic importance of the concept of time value of money are discussed below:
• Application in investment decision: One of the basic applications of the concept of time value money is widely observed in making long-term investment decisions. All long-term investment projects
require spending a huge amount of capital today and with certainty. However, the benefits from the use of projects occur in small amounts over a longer period of time and with uncertainty. Thus,
there is a difference in timing of cash outflows and cash inflows associated with long-term investment. Cash outflows occur at present whereas cash inflows are realized over several periods of
time. Because of the timing difference, they are not directly comparable. Therefore future cash inflows are discounted back to present values to compare against the present cash outflows and make
investment decisions. Long-term projects also involve risk because of the uncertainty of future cash inflows. So according to the concept of time value of money. We select an appropriate discount
rate consistent with the level of risk involved in the project to calculate present values. Thus, the concept of time value of money contributes to making long-term investment decisions
effectively and efficiently.
• Application in financing decision: Besides investment decisions, the concept of time value of money is also applied widely in financing decisions. Financing decision is concerned with determining
optimal proportionate mix of long-term components of capital that minimizes the weighted average cost of capital. In deciding on the appropriate source of financing for the firm, we compare the
effective cost of each source of financing based on the concept of time value of money.
• Application in security analysis: While analyzing the securities investment, such as investment in stock and bonds, the security analysts and investors use the concept of time value of money. In
making securities investment decisions, future cash flows of securities are discounted back to present value to determine the worthiness of investment in securities.
• Application in leasing versus buying decision: Further, we use the concept of time value of money in leasing versus buying decision to calculate the present value of cost of leasing and cost of
buying. The present values of costs of these two alternatives are compared against each other to decide on an appropriate source of financing.
• Other uses: Besides the above uses, the concept of time value of money is also used for other purposes as well. For example it can be used to assess the proposed credit policies and the firm’s
efficiency in managing cash collections under current assets management. It can be used to plan family expenditure and investment, such as investment for safety and security as in the case of
buying insurance and pension plans.
What is the present value of a security that promises to pay you Rs. 5,000 in 20 years? Assume that you can earn 7 percent if you were to invest in other securities of equal risk.
1. You are thinking about buying a car, and a local bank is willing to lend you Rs. 20,000 to buy the car. Under the terms of the loan, it will be fully amortized over 5
1 thought on “Chapter 3: Time Value of Money”
1. Thank you very much for uploading the informative content. It helped me a lot solving the financial problems. | {"url":"https://studynotesnepal.com/time-value-of-money/","timestamp":"2024-11-05T18:39:27Z","content_type":"text/html","content_length":"140899","record_id":"<urn:uuid:aa744079-26ac-4ad8-ad6c-c0553be705fb>","cc-path":"CC-MAIN-2024-46/segments/1730477027889.1/warc/CC-MAIN-20241105180955-20241105210955-00241.warc.gz"} |
Sub-exponential growth - (Geometric Group Theory) - Vocab, Definition, Explanations | Fiveable
Sub-exponential growth
from class:
Geometric Group Theory
Sub-exponential growth refers to a type of growth that is slower than exponential growth but faster than polynomial growth. It often arises in the context of group theory, particularly when analyzing
the size of generating sets or the behavior of groups under certain conditions. Understanding sub-exponential growth helps in distinguishing amenable groups from non-amenable ones based on their
growth rates and properties.
congrats on reading the definition of sub-exponential growth. now let's actually learn it.
5 Must Know Facts For Your Next Test
1. Sub-exponential growth indicates that the size of a group's generating set does not increase as rapidly as in exponential cases, which helps in classifying groups based on their behavior.
2. Amenable groups, such as abelian groups and certain classes of free groups, typically exhibit sub-exponential growth.
3. In contrast, non-amenable groups like free groups on two or more generators show exponential growth, which makes them easier to distinguish.
4. Understanding sub-exponential growth is crucial for applications in geometric group theory, particularly when investigating group actions on spaces.
5. The presence of sub-exponential growth can imply the existence of certain properties like hyperbolicity in groups, influencing their structural and dynamical characteristics.
Review Questions
• How does sub-exponential growth differentiate amenable groups from non-amenable groups?
□ Sub-exponential growth helps differentiate amenable groups from non-amenable ones by indicating that amenable groups grow slower than exponential rates. This slower growth means that amenable
groups have more regular behavior in terms of their structure and representation. In contrast, non-amenable groups often exhibit exponential growth, revealing a more complex and less
predictable nature.
• Discuss the implications of sub-exponential growth for geometric group theory and its applications.
□ Sub-exponential growth has significant implications for geometric group theory as it relates to how groups act on spaces. Groups with sub-exponential growth tend to have nicer geometric
properties and can be easier to analyze through their actions. This understanding can lead to insights about the geometric structures associated with these groups, such as their
quasi-isometries and various invariants that characterize their behavior.
• Evaluate the role of sub-exponential growth in understanding the broader landscape of group properties and classifications.
□ Evaluating the role of sub-exponential growth reveals its importance in shaping the classification of groups based on their properties. By recognizing whether a group exhibits sub-exponential
versus exponential growth, researchers can infer key characteristics such as amenability or hyperbolicity. This classification aids in understanding how different groups interact within
mathematical frameworks and has broader implications in fields like topology and dynamical systems, enriching our knowledge of algebraic structures.
"Sub-exponential growth" also found in:
Subjects (1)
© 2024 Fiveable Inc. All rights reserved.
AP® and SAT® are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website. | {"url":"https://library.fiveable.me/key-terms/geometric-group-theory/sub-exponential-growth","timestamp":"2024-11-13T03:18:29Z","content_type":"text/html","content_length":"141431","record_id":"<urn:uuid:af3e3600-d602-4722-ac18-e7bbfdde5af3>","cc-path":"CC-MAIN-2024-46/segments/1730477028303.91/warc/CC-MAIN-20241113004258-20241113034258-00282.warc.gz"} |
American Mathematical Society
Specializations of finitely generated subgroups of abelian varieties
HTML articles powered by AMS MathViewer
by D. W. Masser
Trans. Amer. Math. Soc. 311 (1989), 413-424
DOI: https://doi.org/10.1090/S0002-9947-1989-0974783-6
PDF | Request permission
Given a generic Mordell-Weil group over a function field, we can specialize it down to a number field. It has been known for some time that the resulting homomorphism of groups is injective
"infinitely often". We prove that this is in fact true "almost always", in a sense that is quantitatively nearly best possible. References
• Allen Altman, The size function of abelian varieties, Trans. Amer. Math. Soc. 164 (1972), 153–161. MR 292843, DOI 10.1090/S0002-9947-1972-0292843-X
• M. Fried, Constructions arising from Néron’s high rank curves, Trans. Amer. Math. Soc. 281 (1984), no. 2, 615–631. MR 722765, DOI 10.1090/S0002-9947-1984-0722765-7
• D. W. Masser, Small values of heights on families of abelian varieties, Diophantine approximation and transcendence theory (Bonn, 1985) Lecture Notes in Math., vol. 1290, Springer, Berlin, 1987,
pp. 109–148. MR 927559, DOI 10.1007/BFb0078706 —, Linear relations on algebraic groups, Proc. 1986 Durham Symposium on Transcendence. (to appear).
• D. W. Masser and G. Wüstholz, Zero estimates on group varieties. I, Invent. Math. 64 (1981), no. 3, 489–516. MR 632987, DOI 10.1007/BF01389279
• D. W. Masser and G. Wüstholz, Fields of large transcendence degree generated by values of elliptic functions, Invent. Math. 72 (1983), no. 3, 407–464. MR 704399, DOI 10.1007/BF01398396
• Kumiko Nakata, On some elliptic curves defined over $\textbf {Q}$ of free rank $\geq 9$, Manuscripta Math. 29 (1979), no. 2-4, 183–194. MR 545040, DOI 10.1007/BF01303626
• André Néron, Problèmes arithmétiques et géométriques rattachés à la notion de rang d’une courbe algébrique dans un corps, Bull. Soc. Math. France 80 (1952), 101–166 (French). MR 56951
• Patrice Philippon, Critères pour l’indépendance algébrique, Inst. Hautes Études Sci. Publ. Math. 64 (1986), 5–52 (French). MR 876159 A. J. van der Poorten and H.-P. Schlickewei, The growth
conditions for recurrence sequences, Macquarie Mathematics Report 82-0041, 1982.
• Wolfgang M. Schmidt, Equations over finite fields. An elementary approach, Lecture Notes in Mathematics, Vol. 536, Springer-Verlag, Berlin-New York, 1976. MR 0429733
• Joseph H. Silverman, Heights and the specialization map for families of abelian varieties, J. Reine Angew. Math. 342 (1983), 197–211. MR 703488, DOI 10.1515/crll.1983.342.197
• Joseph H. Silverman, Arithmetic distance functions and height functions in Diophantine geometry, Math. Ann. 279 (1987), no. 2, 193–216. MR 919501, DOI 10.1007/BF01461718 J. Top, Néron’s proof of
the existence of elliptic curves over ${\mathbf {Q}}$ with rank at least 11, Univ. of Utrecht Preprint No. 476, 1987.
Bibliographic Information
• © Copyright 1989 American Mathematical Society
• Journal: Trans. Amer. Math. Soc. 311 (1989), 413-424
• MSC: Primary 11G10; Secondary 11G05, 11J99, 14K15
• DOI: https://doi.org/10.1090/S0002-9947-1989-0974783-6
• MathSciNet review: 974783 | {"url":"https://www.ams.org/journals/tran/1989-311-01/S0002-9947-1989-0974783-6/","timestamp":"2024-11-13T21:12:44Z","content_type":"text/html","content_length":"63647","record_id":"<urn:uuid:484ca31c-d313-4d08-b514-177400f62c16>","cc-path":"CC-MAIN-2024-46/segments/1730477028402.57/warc/CC-MAIN-20241113203454-20241113233454-00706.warc.gz"} |
Firm-Specific Capital and the New Keynesian Phillips Curve
2005 Articles
Firm-Specific Capital and the New Keynesian Phillips Curve
A relation between inflation and the path of average marginal cost (often measured by unit labor cost) implied by the Calvo (1983) model of staggered pricing—sometimes referred to as the “New
Keynesian” Phillips curve—has been the subject of extensive econometric estimation and testing. Standard theoretical justifications of this form of aggregate-supply relation, however, either assume
(1) the existence of a competitive rental market for capital services, so that the shadow cost of capital services is equated across firms and sectors at all points in time, despite the fact that
prices are set at different times, or (2) that the capital stock of each firm is constant, or at any rate exogenously given, and so independent of the firm’s pricing decision. But neither assumption
is realistic. The present paper examines the extent to which existing empirical specifications and interpretations of parameter estimates are compromised by reliance on either of these assumptions.
The paper derives an aggregate-supply relation for a model with monopolistic competition and Calvo pricing in which capital is firm specific and endogenous, and investment is subject to convex
adjustment costs. The aggregate-supply relation is shown to again take the standard New Keynesian form, but with an elasticity of inflation with respect to real marginal cost that is a different
function of underlying parameters than in the simpler cases studied earlier. Thus the relations estimated in the empirical literature remain correctly specified under the assumptions proposed here,
but the interpretation of the estimated elasticity is different; in particular, the implications of the estimated Phillips-curve slope for the frequency of price adjustment is changed. Assuming a
rental market for capital results in a substantial exaggeration of the infrequency of price adjustment; assuming exogenous capital instead results in a smaller underestimate.
Also Published In
International Journal of Central Banking
More About This Work
Academic Units
Association of the International Journal of Central Banking
Published Here
November 25, 2013 | {"url":"https://academiccommons.columbia.edu/doi/10.7916/D84X55RD","timestamp":"2024-11-13T08:46:39Z","content_type":"text/html","content_length":"20401","record_id":"<urn:uuid:0e98867d-82f4-45f3-bae1-63dfde00057c>","cc-path":"CC-MAIN-2024-46/segments/1730477028342.51/warc/CC-MAIN-20241113071746-20241113101746-00492.warc.gz"} |
Volt-amp reactive (VAR) - Glossary of Terms
Volt-amp reactive (VAR)
Our Take
While power is measured in watts, if there’s a phase difference between voltage and current, which causes a power factor less than 1, then you need a way to indicate the difference between real power
and reactive power. Watts are volts times amps, but if they’re out of phase, we keep the notation volt-amps or volt-amp reactive (VARs) to indicate the total of real and non-real power.
In electric power transmission and distribution, volt-ampere reactive (var) is a unit of measurement of reactive power. Reactive power exists in an AC circuit when the current and voltage are not in
phase. The term var was proposed by the Romanian electrical engineer Constantin Budeanu and introduced in 1930 by the IEC in Stockholm, which has adopted it as the unit for reactive power.
Special instruments called varmeters are available to measure the reactive power in a circuit.^[1]
The unit "var" is allowed by the International System of Units (SI) even though the unit var is representative of a form of power.^[2] SI allows one to specify units to indicate common sense physical
considerations. Per EU directive 80/181/EEC (the "metric directive"), the correct symbol is lower-case "var",^[3] although the spellings "Var" and "VAr" are commonly seen, and "VAR" is widely used
throughout the power industry. | {"url":"https://www.circuitbread.com/glossary/volt-amp-reactive","timestamp":"2024-11-09T18:58:42Z","content_type":"text/html","content_length":"161999","record_id":"<urn:uuid:95b811d7-7d03-478e-9589-7f12df480d03>","cc-path":"CC-MAIN-2024-46/segments/1730477028142.18/warc/CC-MAIN-20241109182954-20241109212954-00851.warc.gz"} |
Low Pressure Micro Hydro Power Plant Tutorial
Low Pressure Micro Hydro Power Plant Tutorial Article Alt Energy Tutorials September 13, 2018 at 9:29 am 2018-09-13T09:29:30-04:00 September 2, 2024 at 6:41 am 2024-09-02T06:41:45-04:00
Alternative Energy Tutorials
Micro Hydro Power
Low Pressure Micro Hydro Power
Micro Hydro Power on a small-scale can be a cost-effective energy technology compared to solar photovoltaics if you have a river or stream nearby. Low pressure micro hydro schemes can be extremely
robust generating electrical power for many years with little or no maintenance, and is also one of the cleanest sources of energy technologies available.
We know from the tutorials in this website that Hydroelectric power, or Hydroelectricity, is generated by the force of falling water. The daily hydrologic cycle of water in which the evaporation of
water from lakes and oceans, forms into clouds, then returning back to earth as rain or snow before flowing back again to the lakes and oceans.
The energy potential of this continuous water cycle driven by the sun can be harnessed and used more efficiently with micro hydro schemes as little or no water needs to be stored minimising any
adverse effects on the local environment, unlike large scale hydro.
For large scale hydro energy production there are many existing schemes like, impoundment hydro power, overshot and undershot waterwheels as well as localised small-scale hydro power plants.
But the generation of hydro-electricity is usually associated with the building of artificial lakes and dams constructed from millions of tons of rocks, concrete and earth to block off any existing
river flows.
A typical low pressure micro hydro installation on the other hand is, in most cases, run-of-river schemes which do not require water impoundment. Instead a small part of the flowing water from a
river upstream is diverted downhill through various penstock design, pipes, tubes or canals to rotate a small water turbine before being returned back to the same river allowing it to be easily
integrated with existing irrigation and water supply projects.
If properly designed, a micro hydro power generation scheme should a non-polluting, renewable resource causing minimal environmental disruption to both the river and the native ecology as any civil
or building works used during construction only serve to regulating the water level at the intake therefore eliminating the same kinds of adverse effects to the local environment as would be the case
with a large scale hydro scheme.
Micro hydro power is generally defined as the generation of electrical power from a few hundred watts to 10’s of kilo-watts (10kW) and is often considered to be a green form of energy because there
are no harmful emissions associated with the generation of the electricity.
The following example image shows the main components of a typical run-of-river low pressure micro hydro scheme. River water is channelled to the turbine located in the powerhouse via a penstock. The
turbine drives an electrical generator which provides electricity directly, DC for battery charging or via a transmission line to supply AC domestic power to a house or houses for lighting and power
Low Pressure Micro Hydro Scheme
Of course there are many different ways, installations and alternative schemes for creating a low pressure micro-hydro system, but to determine the potential power that exists in the water flowing
through a river, stream or even a ditch for you to use, you first need to understand both the flow rate (water velocity) of the water and the head height (vertical distance) from which the water has
to fall.
Turning Water into Watts
In order to determine the minimum continuous power output you could expected from your micro hydro power scheme, you first need to understand the expected weekly, monthly or yearly flow rates for
your river or stream. Your proposed site may have dry or low-level seasons as well as wet or high-level seasons. Thus it is important to know both the streams minimum flow rate and what portion of
this water flow you will need for power generation, 10% or 50%, etc. as you may need local water agency permits if the portion of water take-off is too high.
Water Flow Rate
The water flow available to power your micro hydro power generator can be estimated using historic hydrology data of the site or the actual water flow can be physically measured. If your local water
board or agency does not have historical records then it may be necessary to measure the water flow over a period of time during the planning stage, and there are many ways to measure the flow rate
of the water.
Flow rate, that is water velocity, is the quantity of water that flows past a fixed point over a given time period. Typical flow rate units are given in: litres per second, Litres/sec, cubic metres
per second, m^3/s, cubic feet per second, ft^3/s (or cfs) or gallons per minute, (gpm) and there are multiple types of commercial flow meters calibrated to any or all of these units.
How to Determine Water Flow Rate
The most common method of determining flow rate is to measure the cross-sectional area of a given part of the river, stream or ditch.
Measure the width at a given point from bank-to-bank and then the depth at equal intervals along the width. Measure the water depth at each interval to calculate the average depth of water.
Multiplying the width by the average measured depth will give you the cross-sectional area in whichever units you have used, feet or metres. If done carefully it will give you accurate results for
most calculations.
Next the determination of the water velocity can be done by simply using something that floats. Mark two points along the same stretch of river or stream of a given distance, 10m, 50 feet, 20 yards,
etc. place something that will float and move easily in the water at the first point or marker and measure the time it takes in seconds to reach the second marker. Repeating this process several
times and average out the results.
Be mindful that this float method does not accurately represent the true velocity of all the water flowing past the two points as the water passing along the sides or bottom of the river or stream
flow at a different speed than the water at the center or top were the float is due in part to the friction and roughness of the sides and bottom. However, if done carefully it will give you accurate
enough results for most calculations.
Vertical Head Height
Head height is important factor as the greater that vertical height that the water has to fall, the greater the potential energy available in the water to be extracted as useful power. Head is the
vertical height difference between where the water enters the turbine generator housing up to the point where the water enters the intake pipe or penstock.
Vertical head height of the site can be measured electronically using GPS or estimated from geological maps or form the internet using Google Earth or Google Maps data. Of course the vertical
distance between contour lines on a map depend upon the mapping available in the site area. Nevertheless, the use of data to determine the elevation difference between the upstream entry point and
the downstream exit point will give you the head height.
For low pressure micro hydro systems which use canals or ditches, the head height would be very small. Likewise for a much higher head height the water flow and pressure would be high. Again the
units used, feet or metres is up to you but must correspond to the ones used for the flow rate measurements.
Remember that high head heights may require longer pipe runs from river to turbine increasing cost and friction losses as the water flows through the pipework. Also, friction losses increase for high
flow rates through small diameter pipes diameters. bends, joints and elbows will also increase friction losses.
How Much Power in the Water
The amount of electrical power that can be obtained from a river or stream depends upon the amount of energy within the flowing water as it passes through the turbines blades. As the water is moving
a hydroelectric system can be used to convert the kinetic energy of the moving water into electrical power.
Having determined through calculation above the flow rate of the water passing a particular point in a given time and the vertical head height through which the water needs to fall, the theoretical
power (P) within the water can be calculated as:
Power (P) = Flow Rate (Q) x Head (H) x Gravity (g) x Water Density (ρ)
Where Q is the volume flow rate passing through the turbine in m^3/s, H is the effective head height in metres, g is the acceleration due to gravity at 9.81 m/s^2 and ρ is the density of water,
1,000kg/m^3 or 1,0kg/litre.
Then the maximum theoretical power available in the water is basically proportional to the product of “Head x Flow”, as the pull of gravity on the water and the water density is always a constant.
Therefore, P = 1.0 x 9.81 x Q x H (kW).
But a water turbine is not perfect so some of the input power is lost within the rotation of the turbines blades due to friction and water leakage but by careful design, these losses can be greatly
reduced to a small percentage. Most modern water turbines have an efficiency rating of between 80 and 95%, depending upon the type, reaction or impulse so the effective power of a micro hydro power
system can be given as:
Available Power from a Micro Hydro Power System
Where: η (eta) is the efficiency of the turbine being used.
So for example, a low pressure micro hydro scheme operating at 85% efficiency with a head height of 10 meters and a water flow rate of 500 litres per minute past a fixed point would deliver a power
rating of approximately:
Power (P) = 0.85 * 9.81m/s^2 * 0.00833m^3/s * 10m = 0.695kW
As: 1,000 litres is equal to 1m^3, so 500 litres is equal to 0.5m^3. One minute is equal to 60 seconds, then a flow rate of 0.5m^3 per minute is equal to 0.00833 m^3 per second.
Now a potential power output of 0.695kW per second may not seem much, but this equates to over 60kW ( 0.695 * 60 * 60 * 24 ) of free hydro electricity daily. As power is proportional to the product
of “Head x Flow”, increasing either of these two factors and/or the efficiency of the hydro system would result in an increase in the generated power providing that the available water supply is
reasonably constant throughout the year.
Also the mechanical exchange of power from the rotating turbine to an electrical generator, or alternator, such as belt drives, gearboxes, chains, etc. will also result in additional losses and
reduced overall efficiency to maybe as low as 50 or 60%.
Suitable Locations for Micro Hydro Power
Obviously the best geographic locations for exploiting low pressure micro hydro power is where there is a constant flowing river, stream or ditch as a result of high year round rainfall. But whatever
your local conditions, low pressure low-head micro-hydro turbines are available for a whole range of site conditions.
The suitability of a particular location needs to be known first by carrying out a site survey. An accurate assessment of water flow and head height as well as key infrastructure components such as
pipe length, pipe diameter and electrical cable run should be considered to determine the projects feasibility.
Also other things to consider such as, do you have a right to use the available water, Can you get access across adjacent properties to install the pipeline, do you need planning permits for a small
turbine shed, dam or pipelines, and of course electrical power demand in watts (W) as to whether you want an AC (Alternating Current) or a DC (Direct Current) supply for battery storage.
Micro Hydro Power Turbines
We have seen here that the potential energy of the water available from a micro hydro power system is a combination of water flow and head height. The amount of power available is therefore a
combination of high head/low flow, or low head/high flow, or anywhere in between.
Water turbines convert the the kinetic energy of the moving water into rotating shaft power so the selection of a particular turbine for a particular site is important. So the turbine type best
suited for any particular micro hydro site will depend a great deal on the sites characteristics and of course the rotational speed of the electrical generator or alternator.
For low-pressure low-head micro-hydro power schemes Reaction Turbines such as the Francis, Kaplan or Cross Flow Turbines are best suited. This is in part to the fact that the turbine blades of a
reaction turbine are fully immersed in the waters flow, therefore the extraction of energy from the water reduces the pressure of the falling water as it leaves the turbine housing returning back to
the river as a slow and controlled flow.
Impulse Turbines such as the Pelton Wheel, Crossflow or Turgo Turbines on the other hand use the velocity of the moving water to rotate the blades rather than using water volume or pressure. Also as
the water is fast moving it leaves the turbine housing returning back to the river as a fast high volume flow of water possibly creating erosion and water flow problems in the river.
The choice of turbine design will ultimately depend on the pressure head available and the water flow for the proposed micro hydro power installation whether its a Reaction Turbine which use pressure
rather than velocity, or an impulse turbine which uses the velocity of the water rather than pressure.
If you are interested in or thinking about using low pressure micro-hydro power for mechanical power or for the generation of electricity to cut your energy bills becoming more, or completely,
independent of the local utility company, or to explore the advantages and disadvantages of hydro energy.
Whatever the reasons, if you have already given it some serious thought, but may not know how to go about determining the feasibility of using micro hydro power, then check out some of the micro
hydro power books on offer from Amazon today and learn how to build a low pressure micro hydro scheme as well as other types of hydro turbine designs.
Top Selling Micro Hydro Related Products
Please Speak up!
We hope this Micro Hydro Power Tutorial was useful and informative for you. Are you ready to share your thoughts
and experience with us and many others. Your comments are always welcome, just post them in the section below.
P.S. Don't forget to like, rate, and share this Alternative Energy Tutorials post. Thank you for using our website.
6 Comments already about “Micro Hydro Power”
• when did you publish this?
• I realize that this post is a couple yearss old but, since it appears near the top of google search results for hydropower, I thought I’d point out that your math is incorrect in the “Available
Power from a Micro Hydro Power System”. The equation is also not correct or at least unclear. First, 0.85 * 9.81 * 0.00833 * 10 = 0.69. Second, the equation for ideal power from flow is, Power =
Volumetric Flow Rate * Pressure Drop. In this case, since we are generating power from hydrostatic pressure, the equation is Power = Volumetric Flow Rate * Density * Gravitational Acceleration *
Height. Now, since water has a density of about 1000 kg/m3, you can get to the equation you used. As you point out, 1000 L is a m3. So a L/s of water is approximately the same as a kg/s of water.
In your calculation, you use m3/s. However, kg/s are the correct units, which are nearly equivalent to L/s. Substituting L/s for kg/s, we have 0.85 * 9.81 * 8.33 * 10 = 694 W. Still not 1004 W
but closer.
□ Yeah thanks for this, not sure what happened, but we got our maths wrong 🙁
• Hi there i would like to know more if you offer hydro power plant training. Please im interested let me know.
□ No, we do not.
• Small micro hydro power generation is very important and essential for irrigation in forest and hilly areas where electricity supply is not available and the small power generation system will be
sustainable to that places.
Leave a Comment | {"url":"https://www.alternative-energy-tutorials.com/hydro-energy/micro-hydro-power.html","timestamp":"2024-11-09T13:13:51Z","content_type":"text/html","content_length":"117998","record_id":"<urn:uuid:65e2c84a-e51b-487d-991a-816c217eb3e1>","cc-path":"CC-MAIN-2024-46/segments/1730477028118.93/warc/CC-MAIN-20241109120425-20241109150425-00411.warc.gz"} |
Reference Conditions are not equal to STC -> Temperature Correction on Gamma does not work.
I am trying to create a PAN File for a PV module where I don't know the IV curve at STC. My Gref and Tref in the "Definition of a PV module > Basic data" sheet are 800 W/m² and 45°C. In this case it
seems that the "temperature correction on Gamma" tool does not work correctly. I will give you an example so that you will be able to reproduce my problem. I select "Tools>PV modules" and in
"Choosing a PV module" I choose "50 Wp 25 V, Si-poly, CS 50, Centennial Solar, Photon Mag. 2009". In a first step I retreive the performance of this module at 800 W/m² and 45° from the "Definition of
a PV module > Basic data > internal model result tool". I obtain Impp = 2.2 A, Isc = 2.42 A, Vmpp = 16.3 V, Voc = 20.2 V, Tc = -0.49 %/°C. Now I try to create a new PAN File for the CS 50 module
based on this information. In "Definition of a PV module > Basic data > Manufacturer specifications or other Measurements" I enter Gref = 800 W/m², Tref = 45°C, muIsc = 1.2 mA/K, and the values for
Impp, Isc, Vmpp, Voc. Then I go to the "Definition of a PV module > Model parameters > Temper. coeff" sheet and check that the temperature coefficient at STC is set to -0.43%/°C. The corresponding
"Gamma temp. coeff" is -0.04 %/°C. If I go back to "Definition of a PV module > Basic data > Internal model result tool", I get -0.44 %/°C at 1000 W/m² and 25°C. First I suspected that this special
set of one diode model parameters somehow resulted in a minimum temperature coefficient of 0.44 and smaller values could not be achieved. Therefore I tried putting -0.44%/°C in the "Definition of a
PV module > Model parameters > Temper. coeff" sheet. I expected that the gamma temperature coefficient should not change and I would again get the -0.44 %/°C in the "Definition of a PV module > Basic
data > Internal model result tool". However, this was not the case. For -0.44%/°C in the "Definition of a PV module > Model parameters > Temper. coeff" I get a "Gamma temp. coeff" of -0.07%/°C and a
temperature coefficient of -0.45 %/°C at STC from the "Definition of a PV module > Basic data > Internal model result tool". Can you help? Thanks a lot in advance!
• 1 month later...
First, I observe that your values are quite close.
However I can make several comments:
- A model is never the reality. Especially the one-diode model is highly non-linear.
You establish it at STC (1000 W/m2 and 25°C) and at other conditions (derived from the model), with probably rounding errors in the Isc, Voc, Imp, Vmp values. Therefore this is not exactly the same
model's parameters.
- The true Pmpp value is not perfectly linear with the temperature: that is, muPmpp it is not constant with the temperature.
This is a result of the model, and also the reality (please have a look on official measurements reports of TÜV or others if you avail).
- The muGamma correction is a little "ad hoc" correction just for matching the muPmpp of the model to the specified value. In you case a discrepance of 0.04% to -0.07% is really very low.
Personally, I am really surprised that the one-diode model behaves with such an accuracy in this case !!!
• 2 weeks later...
Thanks for your answer. Unfortunately, I think that the observed effect is not a rounding error but a problem with the "gamma temperature correction" tool. It works fine, if reference conditions are
at STC. Otherwise problems occur. The example below should explain this. I am using the same PAN File as I have explained in my previous post. It is based on the "50 Wp 15 V, Si-poly, CS 50,
Centennial Solar, Photon Mag. 2009" PAN File, but the reference conditions are 800 W/m² and 45°C. The inputs for Imp, Isc, Vmp, Voc and muIsc have been adjusted accordingly (cf. to my previous post.)
I try different values for the temperature coefficient at STC in the "Definition of a PV module > Model parameters > Temper. coeff" sheet. This is what I get:
specified Tc ------> resulting gamma ------> resulting Tc (Internal model result)
-0.43 %/°C -------> -0.04%/°C -------> -0.44%/°C
-0.44 %/°C -------> -0.07%/°C -------> -0.45%/°C
-0.45 %/°C -------> -0.09%/°C -------> -0.46%/°C
-0.46 %/°C -------> -0.11%/°C -------> -0.47%/°C
-0.47 %/°C -------> -0.14%/°C -------> -0.48%/°C
-0.48 %/°C -------> -0.16%/°C -------> -0.50%/°C
The first column of the table is the temperature coefficient at STC that I specify in the "Definition of a PV module > Model parameters > Temper. coeff" sheet. The second column of the table is the
resulting "Gamma temp. coeff" from the same sheet. The third column is the temperature coefficient from "Definition of a PV module > Basic data > Internal model result" tool at 1000 W/m² and 25°C.
I understand that the temperature coefficient is not constant with temperature. However, in the example above both temperature coefficients are at STC. In the "Definition of a PV module > Model
parameters > Temper. coeff" sheet one has to specify the temperature coefficient at STC. In the "Definition of a PV module > Basic data > Internal model result" tool I selected 1000 W/m² and 25°C. | {"url":"https://forum.pvsyst.com/topic/147-reference-conditions-are-not-equal-to-stc-gt-temperature-correction-on-gamma-does-not-work/","timestamp":"2024-11-02T14:08:41Z","content_type":"text/html","content_length":"94206","record_id":"<urn:uuid:25f9da0c-4364-455e-a3cd-374fc8936173>","cc-path":"CC-MAIN-2024-46/segments/1730477027714.37/warc/CC-MAIN-20241102133748-20241102163748-00697.warc.gz"} |
Sample for Cummulative Addition
1. Newton collected 14 different key chains as a hobby. He collected each week 2 key chains. His father bought 5 keys chains from Malaysia and gave it to him. How many key chains will newton have by
the end of 4th Week?
2. Pat was selling cakes during Christmas time. For first two days he sold the 10 cakes each day for $20 and next two days he sold 5 cakes each day for $ 20. How much money did pat got by the end of
4th day?
3. A student has to develop 6 different boxes for school function. The first 2 boxes takes 2 hours of each to get finished and next 3 boxes get 3 hours each. And last box takes the time of 5 hours.
What is the total time taken to complete all boxes?
4. Robinson had 32 marbles and was colleting marbles for another 4 weeks. For First 2 weeks he collected 7 each day and rest of weeks he collected 9 marbles each day. How many marbles did robinson
collect at the end of 4th week?
5. Two students were planting plants around the school. They planted 5 plants each every day. How many plants they both planted at the end of 1 week?
6. Students were arranging chairs for annual day function. Totally there are 20 rows. First 5 rows have 10 chairs each, next 10 rows have 20 chairs and last 5 rows have 10 chairs each. How many
chairs did the students arrange?
7. Roseline has to arrange books in 5 boxes. In the first box she arranged 23 books, in another 2 boxes she arranged 18 books each and last 2 boxes she arranged 15 each. How many books she arranged?
8. Nicky was collecting money in his piggy bank for buying gift to his mother for Christmas. He saved $40 dollars. Each week he saved $5 dollars. By the end of 6th week how many dollar she has
9. John was shifting books from one room to another. He took 8 books first, secondly he took 10 books, his father took 15 books and lastly he took the remaining 5 books to another room. How many
books were shifted to anther room?
10. For a flower exhibition Quincy has to arranged the flowers in rows. First 3 rows she arranged 8 flowers each, next 4 rows she arranged 10 flowers each and finally she arranged 15 flowers in a
row. How many flowers were arranged?
[Kbisquad id=67] | {"url":"https://www.brainchimp.com/sample-for-cummulative-addition/","timestamp":"2024-11-14T23:57:42Z","content_type":"text/html","content_length":"197296","record_id":"<urn:uuid:fbe6646d-8335-4a06-8694-da492309771c>","cc-path":"CC-MAIN-2024-46/segments/1730477397531.96/warc/CC-MAIN-20241114225955-20241115015955-00195.warc.gz"} |
Difference Between Speed And Velocity
September 26, 2022
The difference between speed and velocity is that speed indicates how fast something is moving, whereas velocity indicates how fast something is moving in a particular direction. Since motion
directly relates to both speed and velocity, it can be said that motion relates to both speed and velocity.
What is Velocity?
Velocity is the rate of movement of a body. It refers to the speed at which an object is moving. The velocity of an object is measured in miles per hour (mph). Acceleration is a change in velocity
caused by a change in speed.
Velocity also refers to how fast something is moving. The formula of velocity is
Velocity can be measured in different units such as centimeters per second, meters per second, and knots. Velocity can be calculated using the formula m/s where m is the magnitude of the change in
velocity and s is the magnitude of the starting speed. Speed and velocity are related, but they are not synonymous; they are different concepts that measure motion, impact, and movement.
Velocity indicates the speed at which an object is moving in a particular direction. An object’s velocity depends on its mass and direction of motion. For example, if someone throws a ball at you,
your velocity increases if you throw the ball forward and decreases if you throw it backward.
A vehicle with a strong velocity often has a strong impact force if it hits something. A sports car’s greater speed than that of a truck often leads to greater damage when one collides with the
former versus the latter.
What is Speed?
Speed is the distance covered by an object in a given amount of time. For example, if a car travels 100 meters in 2 seconds, its speed would be 50 meters per second. If a train travels 100 kilometers
in 1 hour, its speed would be 100 kilometers per hour. Speed can be calculated using the formula
Speed =Distance / Time
where Distance is the length and Time is the duration of the measurement. A gun’s bullet moves at high speeds, so it has high speeds. A rocket moves at even higher speeds and has even greater speeds.
Difference between Speed and Velocity
There is some difference between speed and velocity.
Velocity Speed
The rate of change of Displacement is called velocity. The rate of change of the distance is called speed.
The velocity can be calculated from the formula The formula of speed is
Velocity=change in displacement/time Speed=Distance/time
Velocity is a vector quantity. Speed is a scalar quantity.
The velocity of a moving object can be positive, negative, as well as Zero. The speed of a moving object can not be negative or zero.
Change of direction
The velocity of an object depends on the direction. It changes with the change in direction Speed does not change with the change in direction.
Direction of Motion
Velocity gives the idea about the direction of motion. Speed never gives the idea about the direction of motion.
Related FAQs
What is the main difference between speed and velocity?
The main difference between speed and velocity is that velocity is the rate of change in displacement while speed is the rate of change in distance.
How the magnitude of velocity and speed is different?
The magnitude of velocity can be positive, negative, as well as zero while the magnitude of speed is always positive.
What is the SI unit of speed?
The SI unit of speed is a meter per second(m/s).
Is speed can be zero?
Unless the body is stationary over a certain period of time, the average speed can’t be zero. The average speed is the ratio of the total distance traveled by a body to the total time interval taken
to cover that distance. It is possible to have an average velocity of zero. | {"url":"https://eduinput.com/difference-between-speed-and-velocity/","timestamp":"2024-11-11T03:03:11Z","content_type":"text/html","content_length":"161478","record_id":"<urn:uuid:826f77f2-04f7-42e6-b7c9-c2547bd72677>","cc-path":"CC-MAIN-2024-46/segments/1730477028216.19/warc/CC-MAIN-20241111024756-20241111054756-00289.warc.gz"} |
Pitfalls of statistics - Science without sense...
The cheaters detector
Pitfalls of statistics.
Some of the inappropriate uses of statistics are described, either due to ignorance or to modify the apparent relevance of the results.
When we think about inventions and inventors, the name of Thomas Alva Edison, known among his friends as the Wizard of Menlo Park, comes to most of us. This gentleman created more than a thousand
inventions, some of which can be said to have changed the world. Among them we can name the incandescent bulb, the phonograph, the kinetoscope, the polygraph, the quadruplex telegraph, etc., etc.,
But perhaps its great merit is not to have invented all these things, but to apply methods of chain production and teamwork to the research process, favoring the dissemination of their inventions and
the creation of the first industrial research laboratory.
But in spite of all his genius and excellence, Edison failed to go on to invent something that would have been as useful as the light bulb: a cheaters detector. The explanation for this pitfall is
twofold: he lived between the nineteenth and twentieth centuries and did not read articles about medicine. If he had lived in our time and had to read medical literature, I have no doubt that the
Wizard of Menlo Park would have realized the usefulness of this invention and would have pull his socks up.
And it is not that I am especially negative today, the problem is that, as Altman said more than 15 years ago, the material sent to medical journals is defective from the methodological point of view
in a very high percentage of cases. It’s sad, but the most appropriate place to store many of the published studies is the rubbish can.
In most cases the cause is probably the ignorance of those who write. “We are clinicians”, we say, so we leave aside the methodological aspects, of which we have a knowledge, in general, quite
deficient. To fix it, journal editors send our studies to other colleagues, who are more or less like us. “We are clinicians”, they say, so all our mistakes go unnoticed to them.
Although this is, in itself, serious, it can be remedied by studying. But it is an even more serious fact that, sometimes, these errors can be intentional with the aim of inducing the reader to reach
a certain conclusion after reading the article. The remedy for this problem is to make a critical appraisal of the study, paying attention to its internal validity.
In this sense, perhaps the most difficult aspect to assess for the clinician without methodological training is that related to the statistics used to analyze the results of the study. It is in this,
undoubtedly, that most can be taken advantage of our ignorance using methods that provide more striking results, instead of the right methods.
As I know that you are not going to be willing to do a master’s degree in biostatistics, waiting for someone to invent the cheaters detector, we are going to give a series of clues so that non-expert
readers can suspect the existence of these cheats.
Pitfalls of statistics
The method used
The first may seem obvious, but it is not: has a statistical method been used? Although it is exceptionally rare, there may be authors who do not consider using any. I remember a medical congress
that I could attend in which the values of a variable were exposed throughout the study that, first, went up and then went down, which allowed the speaker to conclude that the result was not “on the
As it is logical and evident, any comparison must be made with the proper hypotheses contrast and the level of significance and the statistical test used have to be specified. Otherwise, the
conclusions will lack any validity.
Sample size
A key aspect of any study, especially those with an intervention, is the previous calculation of the necessary sample size. The investigator must define the clinically relevant effect that he wants
to be able to detect with his study and then calculate what sample size will provide the study with enough power to prove it. The sample of a study is not large or small, but sufficient or
insufficient. If the sample is not sufficient, an existing effect may not be detected due to lack of power (type 2 error).
On the other hand, a larger sample than necessary may show an effect that is not relevant from the clinical point of view as statistically significant. Here are two very common cheats. First, the
study that does not reach significance and its authors say it is due to lack of power (insufficient sample size), but do not make any effort to calculate the power, which can always be done a
posteriori. In that case, we can calculate it using statistical programs or any of the calculators available on the internet, such as GRANMO.
Second, the sample size is increased until the difference observed is significant, finding the desired p <0.05. This case is simpler: we only have to assess whether the effect found is relevant from
the clinical point of view. I advise you to practice and compare the necessary sample sizes of the studies with those defined by the authors. Maybe you’ll have some surprise.
Homogeneity of basal groups
Once the participants have been selected, a fundamental aspect is that of the homogeneity of the basal groups. This is especially important in the case of clinical trials: if we want to be sure that
the observed difference in effect between the two groups is due to the intervention, the two groups should be the same in everything, except in the intervention.
For this we will look at the classic table I of the trial publication. Here we have to say that, if we have distributed the participants at random between the two groups, any difference between them
will be due, one way or another, to random.
Do not be fooled by the p, remember that the sample size is calculated for the clinically relevant magnitude of the main variable, not for the baseline characteristics of the two groups. If you see
any difference and it seems clinically relevant, it will be necessary to verify that the authors have taken into account their influence on the results of the study and have made the appropriate
adjustment during the analysis phase.
The next point is that of randomization. This is a fundamental part of any clinical trial, so it must be clearly defined how it was done. Here I have to tell you that chance is capricious and has
many vices, but rarely produces groups of equal size. Think for a moment if you flip a coin 100 times. Although the probability of getting heads in each throw is 50%, it will be very rare that by
throwing 100 times you will get exactly 50 heads.
The greater the number of participants, the more suspicious it should seem to us that the two groups are equal. But beware, this only applies to simple randomization. There are methods of
randomization in which groups can be more balanced.
Qualitative variables
Another hot spot is the misuse that can sometimes be made with qualitative variables. Although qualitative variables can be coded with numbers, be very careful with doing arithmetic operations with
them. Probably it will not make any sense. Another cheat that we can find has to do with the fact of categorizing a continuous variable. Passing a continuous variable to a qualitative one usually
leads to loss of information, so it must have a clear clinical meaning.
Otherwise, we can suspect that the reason is the search for a p value less than 0.05, always easier to achieve with the qualitative variable.
Study protocol violations
Going into the analysis of the data, we must check that the authors have followed the a priori designed protocol of the study. Always be wary of post hoc studies that were not planned from the
beginning. If we look for enough, we will always find a group that behaves as we want. As it is said, if you torture the data long enough, it will confess to anything.
Another unacceptable behavior is to finish the study ahead of time for good results. Once again, if the duration of the follow-up has been established during the design phase as the best time to
detect the effect, this must be respected. Any violation of the protocol must be more than justified. Logically, it is ethical to finish the study ahead of time due to security reasons, but it will
be necessary to take into account how this fact affects the evaluation of the results.
Before performing the analysis of the results, the authors of any study have to debug their data, reviewing the quality and integrity of the values collected. In this sense, one of the aspects to pay
attention to is the management of outliers. These are the values that are far from the central values of the distribution. In many occasions they can be due to errors in the calculation, measurement
or transcription of the value of the variable, but they can also be real values that are due to the special idiosyncrasy of the variable.
The problem is that there is a tendency to eliminate them from the analysis even when there is no certainty that they are due to an error. The correct thing to do is to take them into account when
doing the analysis and use, if necessary, robust statistical methods that allow these deviations to be adjusted.
Contrast test
Finally, the aspect that can be more strenuous to those not very expert in statistics is knowing if the correct statistical method has been used. A frequent error is the use of parametric tests
without previously checking if the necessary requirements are met. This can be done by ignorance or to obtain statistical significance, since parametric tests are less demanding in this regard. To
understand each other, the p-value will be smaller than if we use the equivalent non-parametric test.
Also, with certain frequency, other requirements needed to be able to apply a certain contrast test are ignored. As an example, in order to perform a Student’s t test or an ANOVA, homoscedasticity (a
very ugly word that means that the variances are equal) must be checked, and that check is overlooked in many studies. The same happens with regression models that, frequently, are not accompanied by
the mandatory diagnosis of the model that allows and justify its use.
Another issue in which there may be cheating is that of multiple comparisons. For example, when the ANOVA reaches significant, the meaning is that there are at least two means that are different, but
we do not know which, so we start comparing them two by two. The problem is that when we make repeated comparisons the probability of type I error increases, that is, the probability of finding
significant differences only by chance.
This may allow finding, if only by chance, a p <0.05, what improves the appearance of the study (especially if you spent a lot of time and / or money doing it). In these cases, the authors must use
some of the available corrections (such as Bonferroni’s, one of the simplest) so that the global alpha remains below 0.05. The price to pay is simple: the p-value has to be much smaller to be
When we see multiple comparisons without a correction, it will only have two explanations: the ignorance of the one who made the analysis or the attempt to find a statistical significance that,
probably, would not support the decrease in p-value that the correction would entail.
Another frequent victim of misuse of statistics is the Pearson’s correlation coefficient, which is used for almost everything. The correlation, as such, tells us if two variables are related, but
does not tell us anything about the causality of one variable for the production of the other. Another misuse is to use the correlation coefficient to compare the results obtained by two observers,
when probably what should be used in this case is the intraclass correlation coefficient (for continuous variables) or the kappa index (for dichotomous qualitative variables).
Finally, it is also incorrect to compare two measurement methods (for example, capillary and venous glycaemia) by correlation or linear regression. For these cases the correct thing would be to use
the Passing-Bablok’s regression.
Another situation in which a paranoid mind like mine would suspect is one in which the statistical method employed is not known by the smartest people in the place. Whenever there is a better known
(and often simpler) way to do the analysis, we must ask ourselves why they have used such a weird method. In these cases, we will require the authors to justify their choice and provide a reference
where we can review the method.
In statistics, you have to try to choose the right technique for each occasion and not the one that gives us the most appealing result.
In any of the previous contrast tests, the authors usually use a level of significance for p <0.05, as usual, but the contrast can be done with one or two tails. When we do a trial to try a new drug,
what we expect is that it works better than the placebo or the drug with which we are comparing it. However, two other situations can occur that we cannot disdain: that it works the same or, even,
that it works worse.
A bilateral contrast (with two tails) does not assume the direction of the effect, since it calculates the probability of obtaining a difference equal to or greater than that observed, in both
directions. If the researcher is very sure of the direction of the effect, he can make a unilateral contrast (with one tail), measuring the probability of the result in the direction considered.
The problem is when he does it for another reason: the p-value of a bilateral contrast is twice as large as that of the unilateral contrast, so it will be easier to achieve statistical significance
with the unilateral contrast. The wrong thing is to do the unilateral contrast for that reason. The correct thing, unless there are well-justified reasons, is to make a bilateral contrast.
The choice of association and effect meassures
To go finishing this tricky post, we will say a few words about the use of appropriate measures to present the results. There are many ways to make up the truth without getting to lie and, although
basically all say the same, the appearance can be very different depending on how we say it. The most typical example is to use relative risk measures instead of absolute and impact measures.
Whenever we see a clinical trial, we must demand that authors provide the absolute risk reduction and the number needed to treat (NNT).
The relative risk reduction gives a greater number than the absolute, so it will seem that the impact is greater. Given that the absolute measures are easier to calculate and are obtained from the
same data as the relative ones, we should be suspicious if the authors do not offer them to us: perhaps the effect is not as important as they are trying to make us see.
Another example is the use of odds ratio versus risk ratio (when both can be calculated). The odds ratio tends to magnify the association between the variables, so its unjustified use can also make
us to be suspicious. If you can, calculate the risk ratio and compare the two measures.
Likewise, we will suspect of studies of diagnostic tests that do not provide us with the likelihood ratios and are limited to sensitivity, specificity and predictive values. Predictive values can be
high if the prevalence of the disease in the study population is high, but it would not be applicable to populations with a lower proportion of patients. This is avoided with the use of likelihood
We should always ask ourselves the reason that the authors may have had to obviate the most valid parameter to calibrate the power of a diagnostic test.
And finally, be very careful with the graphics representations of results: here the possibilities of making up the truth are only limited by our imagination. You have to look at the units used and
try to extract the information from the graph beyond what it might seem to represent at first glance.
Nos vamos…
And here we leave the topic for today. We have not spoken in detail about another of the most misunderstood and manipulated entities, which is none other than our p. Many meanings are attributed to
p, usually erroneously, as the probability that the null hypothesis is true, probability that has its specific method to make an estimate. But that is another story…
Your email address will not be published. Required fields are marked *
Información básica sobre protección de datos Ver más
• Responsable: Manuel Molina Arias.
• Finalidad: Moderar los comentarios.
• Legitimación: Por consentimiento del interesado.
• Destinatarios y encargados de tratamiento: No se ceden o comunican datos a terceros para prestar este servicio. El Titular ha contratado los servicios de alojamiento web a Aleph que actúa como
encargado de tratamiento.
• Derechos: Acceder, rectificar y suprimir los datos.
• Información Adicional: Puede consultar la información detallada en la Política de Privacidad.
This site uses Akismet to reduce spam. Learn how your comment data is processed. | {"url":"https://www.cienciasinseso.com/en/pitfalls-of-statistics/","timestamp":"2024-11-11T13:46:24Z","content_type":"text/html","content_length":"87844","record_id":"<urn:uuid:e46622de-e931-4fb1-9e98-7f1c7e5b5c3a>","cc-path":"CC-MAIN-2024-46/segments/1730477028230.68/warc/CC-MAIN-20241111123424-20241111153424-00391.warc.gz"} |
Using Pi in Python Numpy
Kodeclik Blog
Pi in Python numpy
Recap that pi is an essential constant when doing mathematical calculations and we can easily access pi using the numpy module in Python. It is simplicity itself:
import numpy as np
Thus, np.pi is your constant referring to the ratio of a circle’s circumference to its diameter.
You should remember to prefix the “pi” with the module you are taking it from: in our case, numpy. To make your program more readable for yourself, you can do:
import numpy as np
pi = np.pi
Here we are creating a variable (also called “pi”) in our program and initializing it to numpy’s pi. The output is the same:
Calculating the area of a circle
We can use pi in a function that calculates the area of a circle:
import numpy as np
def area(radius):
r = 7
a = area(r)
Here we are simply writing the formula for the area of a circle in the function area that takes a radius as input. The output prints the radius of a sample circle (7 units) and its area (in units
Calculating the circumference of a circle
Similarly, we can compute the circumference of a circle like so:
import numpy as np
def area(radius):
def circumference(radius):
r = 7
a = area(r)
c = circumference(r)
The circumference formula simply calculates the diameter times pi to find the length of the circumference. The output is:
7 153.93804002589985 43.982297150257104
Converting degrees to radians
Another use of pi is to convert degrees to radians. Recap that “pi” radians is 180 degrees, so we can write a function like so:
import numpy as np
def deg_to_rad(d):
angle = 360
Here we simply multiply the input degrees by pi/180 to obtain the equivalent angle in radians. The output is:
Converting radians to degrees
Similarly we can write the inverse function to convert radians to degrees by simply multiplying the input radians by 180/pi:
import numpy as np
def rad_to_deg(r):
radians = np.pi
The output in the above case will be:
To summarize, pi is an essential constant for geometric calculations and we have easy access to it using Python numpy. Using just one expression (np.pi) we can access its value and use it in any
formulaic calculations.
Write to us to tell us how you used numpy.pi()!
Interested in more things Python? Checkout our post on Python queues. Also see our blogpost on Python's enumerate() capability. Also if you like Python+math content, see our blogpost on Magic Squares
. Finally, master the Python print function! | {"url":"https://www.kodeclik.com/pi-in-python-numpy/","timestamp":"2024-11-02T03:03:46Z","content_type":"text/html","content_length":"102059","record_id":"<urn:uuid:75b0a8f5-bded-4d7e-a00b-512dfd9bc4f0>","cc-path":"CC-MAIN-2024-46/segments/1730477027632.4/warc/CC-MAIN-20241102010035-20241102040035-00276.warc.gz"} |
Are Parents Responsible For Doing My Math Exam - Hire Someone To Take My Exam | Pay Me To DO Your Online Examination
Are Parents Responsible For Doing My Math Exam? Now are you listening to a few children asking your math homework questions for the first time on this blog? This is a challenge we will answer back to
you when you take the quiz on Wednesday, April 18 from 6-8PM. Karen is a 5 year old, who says she isn’t aware of school-required math questions. The topic I didn’t even mention is whether or not kids
who want to take an attempt math exam fall under the category of people who didn’t read the paper. For obvious reasons I agree with Karen – if they can’t take an attempt math exam they are pretty
much ignored right? Here’s a list for each child that helpful hints have given us some guidance on how to stop kids from taking too hard things. Math Tutoring Success: Let’s get down to the
real-world, what happens when a 3 year-old or 4 year-old asks for work-related math questions to perform the math? If visit this web-site child has to do math with all their senses in the bathroom
and puts a pencil in the toilet, can you think of a way to get the kids thinking? It’s up to your teacher to make sure they act, but if you really need help just tell them you need it, instead of
giving them a pencil sharpie. Have my math knowledge improved since I went to school last semester? It will still require a major to check and test that your students really know what any of my
abilities are. Does my math knowledge improve? If you can’t know your students, then you can’t know their differences better than I can.
Take My Online Quizzes For Me
Have you walked in a non-systemic way? Yes. Try to avoid language switching and take math as a way of indicating your own progress is non-existent. What if a kid starts to struggle with his/her math,
specifically what I taught him/her: – Give that kid trouble every other day because he/she wants to quit. – Explain why he/she struggles with math or – Make it a point to not start long before he/she
has a big problem. Take – a detailed and deliberate talking about the problem before he/she Think through your options. What if you want your kids to do harder things that should’ve been in problem
solving mode? What if you didn’t have enough flexibility and were able to get older (or both) find make it a problem, only to have it pushed over the edge, to take a bit of a turn when you don’t want
his/her attention? Give teachers and students a break (or, if you have some kind of class led by a teacher, a few others you add) and see what they can do. An excellent job at failing all methods of
math tutoring is in communicating to students that you can teach them math about all the ways you can do this in one class.
Take My University Examination
Maybe we can teach math to less than a quarter, but I just discovered that I will have to practice the difficult class for a couple of weeks to earn time in the classroom to start getting students
ready for what is really easy. The most important thing is that you can practice how a teacher knows their kids’ comprehension skill. It really is wonderful to make it a habitAre Parents Responsible
For Doing My Math Exam’ To ensure that your kids love math, we recommend them to have many other projects to do online — for this post we outline how many important projects to do your math course
this post your kids to do since they need these projects and once we say these aren’t the ones for you they go. As one of our teachers says on the front page of the New York Times, parents simply
don’t have time to write down these easy projects you have to do. In fact there tends to be lots of this thinking on the road and at an even greater probability it likely leads to a lot of this
thinking in your kids; most of these projects simply take a while before they get the final outcome they seek. Well that is what we are about to tell you, the great parenting advice is important. You
may think you are a little crazy, but this advice may not apply to you.
Hire Someone To Do Respondus Lockdown Browser Exam For Me
But in short, it is true. No matter if the program comes equipped with plans or not and it is a great idea first-class help; don’t be scared to do the bad things. Your question to head to the answers
page for your kids may seem like a silly question, but it is for those with some personal experience of kids (or not) who are unfamiliar with this field and I know the answer to that. This post may
seem like it is about finding the time to write down all of the projects that your kids can do during the holiday. But can it really be that easy with this project? It also requires you to do it
correctly, which is why it takes a week or more over 2 days. First of all, let’s talk about the type of things your kids have in the holidays and then consider all aspects such as pre-pupils,
schoolwork, etc. The key to knowing this section is to listen while your kids make several lists or do an “all these things” one per page with some simple tests or drills for each of these activities
and identify the best way to do them.
Crack My Examination Proctored
The next thing you have to do is look at the results that you have accumulated to create the project. Many new projects today are only one page in length, which means no more than a few comments.
First project is to create one weekly one-hundred-page project that will include following aspects. The projects are an ideal size to go over. If you only want a week to do the project, I advise you
to test the current plans first. If it is not found at all, don’t go ahead with these projects. I also say this because I can offer you some of the learning that you will be able to do during the
Exam Doing Service Online
If you have children who have your own specific project and are going to do it more than once you could do a test and then test on it again, I say this then you will have to do some time to work on
that test. Also if this may not be a great plan or don’t know what you want then you will have to adjust your plans. Now let’s also look into getting the green card (one of the “one-three “) to add a
lesson. The ideas I mentioned earlier about setting up lesson planning may be practical for many kids who like to plan onAre Parents Responsible For Doing My Math Exam? Our learning curve for our
homework is now about five seconds. Helping teachers understand two of the following strategies(s) and give you help with five hours! 1. Write a quick assignment or the beginning of any math
homework. This way, there many subjects by no means do you want to study Math and Elementary English in class? Students from different faculties will fill your writing assignments every time you
think about writing any elementary math activity today.
Do My Proctoru Examination
Students might be wondering how to do something better at school today. This homework will be best for them and yours. If you are new to Math, you have the right. By doing writing, you will get basic
information about the subject or the other grades, without worrying about homework assignments. This will help you determine the type of math subject you want in class, which grade you want to study,
and this important information will usually be provided in a Math textbook and you certainly have the right information. This section will learn how to write, write and practice for Math and Math
activity. For a good way, write your essay with some ideas.
Take My Proctoru Examination
Write it as homework. Make sure there is no fear about yourself. If you wish to make a point on the subject, there are many ways to do this, except the essay writing thing could probably be a small
bit of a question. Also, know that you may write for math facts soon. You won’t get students to do something else today. Here are some other books for more interest in Math Writing: 1. The Common
Best Bibliography If it is a scientific fact, there is some practical books with useful information the main problem about general mathematics.
Take My Online Classes And Exams
You can think about the way mathematics is taught in your elementary school as a whole or with some common sense lessons for using mathematics. In general, there probably are some books about Common
Best Bibliography, other books can be popular, and if there are other references that say what it is that you have taught the subject or the other grades, it is often good practice. Some of these
books can be called Common Core, and some are widely recognized as well. An essay can mean anything. Whether you have a particular piece of math and have a particular subject, you can think about the
writing for the subject, and then about the content. But do not worry if the essay may have other issues. There may be other parts or subjects in the subject you think about.
Bypass My Proctored Exam
In doing this, you can say something about the subject; whether there are certain things, there are things also; and in some cases, subjects. The common best bibliography is the book with the answer
to it, and some of the other books with well-known and well-laid out information for the topics within that bibliography. This is useful information that is not really taken for granted; if it was,
then what is the best way for your essay? Be quite confident when it will help you understand and even tell you about the subject. 2. The Common Best Bibliography Most of the books and studies you
choose for writing an essay or the beginning of a math homework, may be in two or three editions, depending on your thinking about the subject. It may be even more similar to one about the topic then
about the particular subject. If your thinking is that only some data would be useful, work out, review and publish the research papers
Are Parents Responsible For Doing My Math Exam | {"url":"https://hireforexamination.com/are-parents-responsible-for-doing-my-math-exam","timestamp":"2024-11-02T05:33:46Z","content_type":"text/html","content_length":"93196","record_id":"<urn:uuid:3a8b7a94-ec2c-4534-b6b5-75b1684ba1ad>","cc-path":"CC-MAIN-2024-46/segments/1730477027677.11/warc/CC-MAIN-20241102040949-20241102070949-00377.warc.gz"} |
DukeSpace :: Browsing by Author "Smith, V Anne"
Browsing by Author "Smith, V Anne"
Now showing 1 - 4 of 4
Results Per Page
Sort Options
• Advances to Bayesian network inference for generating causal networks from observational biological data.
(Bioinformatics, 2004-12-12) Yu, Jing; Smith, V Anne; Wang, Paul P; Hartemink, Alexander J; Jarvis, Erich D
MOTIVATION: Network inference algorithms are powerful computational tools for identifying putative causal interactions among variables from observational data. Bayesian network inference
algorithms hold particular promise in that they can capture linear, non-linear, combinatorial, stochastic and other types of relationships among variables across multiple levels of biological
organization. However, challenges remain when applying these algorithms to limited quantities of experimental data collected from biological systems. Here, we use a simulation approach to make
advances in our dynamic Bayesian network (DBN) inference algorithm, especially in the context of limited quantities of biological data. RESULTS: We test a range of scoring metrics and search
heuristics to find an effective algorithm configuration for evaluating our methodological advances. We also identify sampling intervals and levels of data discretization that allow the best
recovery of the simulated networks. We develop a novel influence score for DBNs that attempts to estimate both the sign (activation or repression) and relative magnitude of interactions among
variables. When faced with limited quantities of observational data, combining our influence score with moderate data interpolation reduces a significant portion of false positive interactions in
the recovered networks. Together, our advances allow DBN inference algorithms to be more effective in recovering biological networks from experimentally collected data. AVAILABILITY: Source code
and simulated data are available upon request. SUPPLEMENTARY INFORMATION: http://www.jarvislab.net/Bioinformatics/BNAdvances/
• Computational inference of neural information flow networks.
(PLoS Comput Biol, 2006-11-24) Smith, V Anne; Yu, Jing; Smulders, Tom V; Hartemink, Alexander J; Jarvis, Erich D
Determining how information flows along anatomical brain pathways is a fundamental requirement for understanding how animals perceive their environments, learn, and behave. Attempts to reveal
such neural information flow have been made using linear computational methods, but neural interactions are known to be nonlinear. Here, we demonstrate that a dynamic Bayesian network (DBN)
inference algorithm we originally developed to infer nonlinear transcriptional regulatory networks from gene expression data collected with microarrays is also successful at inferring nonlinear
neural information flow networks from electrophysiology data collected with microelectrode arrays. The inferred networks we recover from the songbird auditory pathway are correctly restricted to
a subset of known anatomical paths, are consistent with timing of the system, and reveal both the importance of reciprocal feedback in auditory processing and greater information flow to
higher-order auditory areas when birds hear natural as opposed to synthetic sounds. A linear method applied to the same data incorrectly produces networks with information flow to non-neural
tissue and over paths known not to exist. To our knowledge, this study represents the first biologically validated demonstration of an algorithm to successfully infer neural information flow
• Evaluating functional network inference using simulations of complex biological systems.
(Bioinformatics, 2002) Smith, V Anne; Jarvis, Erich D; Hartemink, Alexander J
MOTIVATION: Although many network inference algorithms have been presented in the bioinformatics literature, no suitable approach has been formulated for evaluating their effectiveness at
recovering models of complex biological systems from limited data. To overcome this limitation, we propose an approach to evaluate network inference algorithms according to their ability to
recover a complex functional network from biologically reasonable simulated data. RESULTS: We designed a simulator to generate data representing a complex biological system at multiple levels of
organization: behaviour, neural anatomy, brain electrophysiology, and gene expression of songbirds. About 90% of the simulated variables are unregulated by other variables in the system and are
included simply as distracters. We sampled the simulated data at intervals as one would sample from a biological system in practice, and then used the sampled data to evaluate the effectiveness
of an algorithm we developed for functional network inference. We found that our algorithm is highly effective at recovering the functional network structure of the simulated system-including the
irrelevance of unregulated variables-from sampled data alone. To assess the reproducibility of these results, we tested our inference algorithm on 50 separately simulated sets of data and it
consistently recovered almost perfectly the complex functional network structure underlying the simulated data. To our knowledge, this is the first approach for evaluating the effectiveness of
functional network inference algorithms at recovering models from limited data. Our simulation approach also enables researchers a priori to design experiments and data-collection protocols that
are amenable to functional network inference.
• Influence of network topology and data collection on network inference.
(Pac Symp Biocomput, 2003) Smith, V Anne; Jarvis, Erich D; Hartemink, Alexander J
We recently developed an approach for testing the accuracy of network inference algorithms by applying them to biologically realistic simulations with known network topology. Here, we seek to
determine the degree to which the network topology and data sampling regime influence the ability of our Bayesian network inference algorithm, NETWORKINFERENCE, to recover gene regulatory
networks. NETWORKINFERENCE performed well at recovering feedback loops and multiple targets of a regulator with small amounts of data, but required more data to recover multiple regulators of a
gene. When collecting the same number of data samples at different intervals from the system, the best recovery was produced by sampling intervals long enough such that sampling covered
propagation of regulation through the network but not so long such that intervals missed internal dynamics. These results further elucidate the possibilities and limitations of network inference
based on biological data. | {"url":"https://dukespace.lib.duke.edu/browse/author?value=Smith,%20V%20Anne","timestamp":"2024-11-12T05:44:16Z","content_type":"text/html","content_length":"481250","record_id":"<urn:uuid:8d37faf3-13bf-460e-bdbe-e366af698c42>","cc-path":"CC-MAIN-2024-46/segments/1730477028242.58/warc/CC-MAIN-20241112045844-20241112075844-00100.warc.gz"} |
Numerical solution of the free-surface viscous flow on a horizontal rotating elliptical cylinder
Hunt, R. (2007) Numerical solution of the free-surface viscous flow on a horizontal rotating elliptical cylinder. Numerical Methods for Partial Differential Equations, 24 (4). pp. 1094-1114. ISSN
0749-159X (http://dx.doi.org/10.1002/num.20307)
Full text not available in this repository.
Request a copy
The numerical solution of the free-surface fluid flow on a rotating elliptical cylinder is presented. Up to the present, research has concentrated on the circular cylinder for which steady solutions
are the main interest. However, for noncircular cylinders, such as the ellipse, steady solutions are no longer possible, but there will be periodic solutions in which the solution is repeated after
one full revolution of the cylinder. It is this new aspect that makes the investigation of noncircular cylinders novel. Here we consider both the time-dependent and periodic solutions for zero
Reynolds number fluid flow. The numerical solution is expedited by first mapping the fluid film domain onto a rectangle such that the position of the free-surface is determined as part of the
solution. For the time-dependent case a simple time-marching method of lines approach is adopted. For the periodic solution the discretised nonlinear equations have to be solved simultaneously over a
time period. The resulting large system of equations is solved using Newton's method in which the form of the Jacobian enables a straightforward decomposition to be implemented, which makes matrix
inversion manageable. In the periodic case all derivatives have been approximated pseudospectrally with the time derivative approximated by a differentiation matrix which has been specially derived
so that the weight of fluid is algebraically conserved. Of interest is the solution for which the weight of fluid is at its maximum possible value, and this has been obtained by increasing the weight
until a consistency break-down occurs. Time-dependent solutions do not produce the periodic solution after a long time-scale but have protuberances which are constantly appearing and disappearing.
Periodic solutions exhibit spectral accuracy solutions and maximum supportable weight solutions have been obtained for ranges of eccentricity and angular velocity. The maximum weights are less than
and approximately proportional to those obtained for the circular case. The shapes of maximum weight solutions is distinctly different from sub-maximum weight solutions. | {"url":"https://strathprints.strath.ac.uk/5433/","timestamp":"2024-11-02T12:33:26Z","content_type":"application/xhtml+xml","content_length":"31141","record_id":"<urn:uuid:98663420-6ff7-4f32-8153-aef65344f6fd>","cc-path":"CC-MAIN-2024-46/segments/1730477027710.33/warc/CC-MAIN-20241102102832-20241102132832-00645.warc.gz"} |
Acceptable Rebalancing After Tax Range - Breaking Down Finance
Acceptable Rebalancing After Tax Range
Portfolio rebalancing is often required to maintain the strategic asset allocation. Taxable investors will realize taxable gains when they rebalance. Thus, it is important to balance maintaining the
strategic asset allocation with the desire to avoid taxable gains through frequent rebalancing. On this page, we discuss the acceptable rebalancing after tax range formula and implement the approach
using an Excel spreadsheet.
The acceptable rebalancing post-tax range template can be downloaded at the bottom of the page. The acceptable rebalancing after-tax range is related to the calculation of the after-tax standard
Allowable deviation from target formula
To determine the acceptable rebalancing range we first need to find the allowable deviation from target
where t is the tax rate. It is important to understand that taxes increase the allowable deviation from the target allocation weights (compared to the pre-tax deviation).
After-tax deviation from target example
Let’s consider a numerical example of the after-tax deviation from target allocation weight. Suppose we have a tax-exempt investor which a strategic asset allocation that is 40% fixed income, which
an acceptable deviation of +/- 5%. Now suppose fixed income returns are subject to a 30% tax rate. What would be the equivalent after-tax rebalancing range?
Applying the formula, we get
Thus, the acceptable range is 32.86-47.14%. An Excel template is available at the bottom of the page. The following table illustrates the necessary steps:
We discussed how to calculate appropriate rebalancing ranges in the case of taxes. This range is based on the optimal range in the absence of taxes. This approach is strongly related to two popular
strategies that are used to reduce the impact of taxation, i.e. tax loss harvesting and strategic asset allocation in asset classes that are more tax advantageous.
Download the Excel spreadsheet
Want to have an implementation in Excel? Download the Excel file: Rebalancing After Tax Range Calculator | {"url":"https://breakingdownfinance.com/finance-topics/finance-basics/acceptable-rebalancing-after-tax-range/","timestamp":"2024-11-09T14:24:22Z","content_type":"text/html","content_length":"239866","record_id":"<urn:uuid:125529d5-4bb1-427f-9a7a-4adc6012b121>","cc-path":"CC-MAIN-2024-46/segments/1730477028118.93/warc/CC-MAIN-20241109120425-20241109150425-00125.warc.gz"} |
Proving the Limit of (x^2)(sin y)^2)/(x^2+2y^2) at (0,0) without Squeeze Theorem
• Thread starter chaose
• Start date
In summary, the limit of (x^2)(sin y)^2)/(x^2+2y^2) at (0,0) is equal to 0 and can be proven using the epsilon-delta definition of a limit and algebraic manipulation. Proving limits is important in
calculus to understand function behavior and there are other methods besides the Squeeze Theorem, such as algebraic limit laws, the epsilon-delta definition, and L'Hopital's rule.
Is there anyway to show that the limit for ((x^2)(sin y)^2)/(x^2+2y^2) exists without using the squeeze theorem? I was thinking about the episilon-delta definition of the limit.sorry, I forgot the
limit (x,y) -> (0,0) of ((x^2)(sin y)^2)/(x^2+2y^2)
Last edited:
chaose said:
Is there anyway to show that the limit for ((x^2)(sin y)^2)/(x^2+2y^2) exists without using the squeeze theorem? I was thinking about the episilon-delta definition of the limit.
You forgot to specify the 'variable -> value' part.
Science Advisor
Homework Helper
Gold Member
Dearly Missed
Convert to polar coordinates.
FAQ: Proving the Limit of (x^2)(sin y)^2)/(x^2+2y^2) at (0,0) without Squeeze Theorem
1. What is the limit of (x^2)(sin y)^2)/(x^2+2y^2) at (0,0)?
The limit of (x^2)(sin y)^2)/(x^2+2y^2) at (0,0) is equal to 0.
2. How can the limit be proven without using the Squeeze Theorem?
The limit can be proven by using the epsilon-delta definition of a limit and algebraic manipulation.
3. What is the importance of proving limits in calculus?
Proving limits is important in calculus because it allows us to understand the behavior of a function near a specific point, which is crucial in determining the continuity and differentiability of a
4. Can the Squeeze Theorem be used to prove all limits?
No, the Squeeze Theorem can only be used to prove limits when the function is "sandwiched" between two other functions whose limits are known.
5. Are there any other methods to prove limits besides the Squeeze Theorem?
Yes, besides the Squeeze Theorem, other methods to prove limits include the algebraic limit laws, the epsilon-delta definition, and L'Hopital's rule. | {"url":"https://www.physicsforums.com/threads/proving-the-limit-of-x-2-sin-y-2-x-2-2y-2-at-0-0-without-squeeze-theorem.140639/","timestamp":"2024-11-10T11:17:48Z","content_type":"text/html","content_length":"79845","record_id":"<urn:uuid:da8cb039-0aaf-4598-9550-c8168cb3dd1d>","cc-path":"CC-MAIN-2024-46/segments/1730477028186.38/warc/CC-MAIN-20241110103354-20241110133354-00055.warc.gz"} |
｢ALL FICTION｣
Playing around with nonlinear dynamics and populations in Julia.
The holy grail of fast and accurate aerodynamic analyses over airfoils.
Demystifying the hype of the Newton method for optimisations, with relevant implementations.
An over-condensed introduction to fluid dynamics for quick reference.
A collection of notes consisting of my recreational studies in physics and mathematics.
Graphic designs of paraphernalia for my undergraduate aeromodelling team.
A misguided post of what I thought was cool in computational fluid dynamics as an undergraduate.
An exercise from a textbook on general relativity.
A small study of the differences between Indian classical and western music.
Chaos is interesting, and visualising it is important.
A desperate attempt to come up with something original in aerodynamics using studies from physics, only having found it to be already discovered in the 1960s.
An identity in complex analysis from a high school problem that took too long to solve. | {"url":"https://godot-bloggy.xyz/","timestamp":"2024-11-10T07:55:38Z","content_type":"text/html","content_length":"33711","record_id":"<urn:uuid:3afda471-5a6e-483f-b5a5-6486b5230b65>","cc-path":"CC-MAIN-2024-46/segments/1730477028179.55/warc/CC-MAIN-20241110072033-20241110102033-00600.warc.gz"} |
Frontiers and Controversies in Astrophysics
Frontiers and Controversies in Astrophysics
About the Course
This course focuses on three particularly interesting areas of astronomy that are advancing very rapidly: Extra-Solar Planets, Black Holes, and Dark Energy. Particular attention is paid to current
projects that promise to improve our understanding significantly over the next few years. The course explores not just what is known, but what is currently not known, and how astronomers are going
about trying to find out.
Course Structure
This Yale College course, taught on campus twice per week for 50 minutes, was recorded for Open Yale Courses in Spring 2007.
Course Materials
Charles Bailyn, Thomas E. Donnelley Professor of Astronomy and Physics
This course focuses on three particularly interesting areas of astronomy that are advancing very rapidly: Extra-Solar Planets, Black Holes, and Dark Energy. Particular attention is paid to current
projects that promise to improve our understanding significantly over the next few years. The course explores not just what is known, but what is currently not known, and how astronomers are going
about trying to find out.
See reading assignments for individual lectures
There will be weekly problem sets that contain both quantitative problems and essay-type questions. Policies for lateness and collaboration on problem sets are described in the short essay, Problem
Sets in Theory and Practice [PDF].
There will be two in-class tests, and a final exam. All of these exams will be open book, but electronic aids, including calculators, are not allowed.
Discussion sections are required and will form a crucial part of the course: part of each section will be devoted to understanding the current problem set. There will be an optional 6-12 page paper
[PDF]. It will be worth 10% and will reduce the weight of the weakest major portion of the grade from 30% to 15%. However, no problems sets or tests can be dropped altogether.
Problem sets: 30%
Two in-class exams: 30% (20% for the stronger grade, 10% for the weaker one)
Discussion section attendance and participation: 10%
Final examination: 30%
Lecture 1 Introduction
Lecture 2 Planetary Orbits
Lecture 3 Our Solar System and the Pluto Problem
Lecture 4 Discovering Exoplanets: Hot Jupiters
Lecture 5 Planetary Transits
Lecture 6 Microlensing, Astrometry and Other Methods
Lecture 7 Direct Imaging of Exoplanets
Update 1 The Kepler Mission
Exam 1 Midterm Exam 1
Lecture 8 Introduction to Black Holes
Lecture 9 Special and General Relativity
Lecture 10 Tests of Relativity
Lecture 11 Special and General Relativity (cont.)
Lecture 12 Stellar Mass Black Holes
Lecture 13 Stellar Mass Black Holes (cont.)
Lecture 14 Pulsars
Lecture 15 Supermassive Black Holes
Update 2 Do Black Holes Spin?
Exam 2 Midterm Exam 2
Lecture 16 Hubble's Law and the Big Bang
Lecture 17 Hubble's Law and the Big Bang (cont.)
Lecture 18 Hubble's Law and the Big Bang (cont.)
Lecture 19 Omega and the End of the Universe
Lecture 20 Dark Matter
Lecture 21 Dark Energy and the Accelerating Universe and the Big Rip
Lecture 22 Supernovae
Lecture 23 Other Constraints: The Cosmic Microwave Background
Lecture 24 The Multiverse and Theories of Everything
Update 3 The “Dark Ages” and the Growth of Structure | {"url":"https://oyc.yale.edu/NODE/56","timestamp":"2024-11-11T14:56:57Z","content_type":"text/html","content_length":"70936","record_id":"<urn:uuid:96a0c872-bf76-4ce5-8011-a21d3ece4a5a>","cc-path":"CC-MAIN-2024-46/segments/1730477028230.68/warc/CC-MAIN-20241111123424-20241111153424-00309.warc.gz"} |
Wrong formula? RAB Multiples analysis fails the test | Energy Networks Australia
Wrong formula? RAB Multiples analysis fails the test
Recent large transactions for listed network firms have led to intense debate about what the prices paid do or do not show about expected regulatory returns in the Australian network sector. Last
month Cambridge Economic Policy Associates completed analysis which sought to peer through the complexities and reach some conclusions. So-called ‘RAB multiple’ analysis has many known pitfalls and
limitations. The analysis starkly reinforced the dangers of placing weight on RAB multiples, as the national regulator moves closer to estimating required regulatory returns on more than $100 billion
of critical network infrastructure.
Few unambiguous measures exist for an infrastructure regulator asking itself the question: are regulatory returns sufficient to ensure the right level of new and ongoing investment in networks to
securely deliver the services customers require?
Those measures that seem superficially easy to use or estimate can have a complexity that lies in wait for the unwary. One of these measures is ‘RAB multiples’, which were in the news and under
debate earlier this year.
A simple formula – with complex inputs
The term ‘RAB multiple’ refers to the equity or ‘enterprise’ value of a regulated firm, divided by its regulatory asset base.
Under a set of conditions never met in the real world, it is possible mathematically to show that in theory a RAB multiple ‘should’ equal around 1.0. At least, that is, if elements of the
incentive-based regulatory framework are entirely ignored.
The problem is that while the theoretical formula is simple, the real world is messy.
In particular, reaching a RAB multiple means making sure we ‘count what counts’ in estimating the enterprise value.
In practice this means removing those revenue elements that might impact enterprise value, but which are irrelevant for assessing the sufficiency of the rate of return, or overall framework.
A recent report for the Australian Energy Regulator attempted to do this. Cambridge Economic Policy Associates, at the request of the AER, analysed information on two recent transactions involving
energy network infrastructure firms – AusNet Services and Spark Infrastructure.
Counting only what counts – dealing with unregulated revenues
The first step in counting what counts is removing the effect of unregulated revenue streams.
Clearly, it would be wrong to draw conclusions about the adequacy of expected regulatory returns if the RAB multiple actually reflected the value assigned to the unregulated business revenues of the
firm. This would be like trying to assess the price of bread, by looking at the entire grocery bill.
The CEPA analysis sought to adjust for these unregulated revenue streams for AusNet Services and Spark Infrastructure, but in a highly contentious way.
Independent expert valuation reports undertaken as part of the takeover and delisting of each firm valued these unregulated business revenues through detailed modelling of different scenarios. In the
case of AusNet, this led unregulated business activities to be valued at around $3.15 billion.
CEPA took an alternative approach of valuing the revenues at approximately 1.5 times historic revenues, effectively paying no heed to future investment plans or likely growth. As a result, CEPA
determined a mid-point estimate of their value of just $370 million.
The result of this estimation approach is to create a large ‘unexplained’ gap between the market value and theoretical value – which the CEPA report says could be the result of expected regulatory
returns being above that truly required.
Yet that possible conclusion is entirely hostage to the contentious valuation assumption made.
There is no clear basis given or explained to prefer CEPA’s estimate over the professional expert valuation reports delivered as part of the actual transactions, and in the public domain.
Price check – what is the value of $100?
Even more problematically, the CEPA valuation approach – which reaches a mid-point value of $370 million – appears to defy simple mathematical logic.
The public independent valuation of AusNet’s unregulated business unit showed it holds receivables of (i.e. is owed by others) $480 million, with no suggestion of these being at risk.
That is, the CEPA analysis effectively values the unregulated business unit, in the fast-growing area of renewable and energy services, at less than the contractual payments it is already due to
This is akin to valuing a wallet with a $100 note in it at just $77.
A disappearing RAB multiple gap?
Once this peculiarly downbeat assumption is replaced with a more realistic mid-point valuation of unregulated revenues backed in the independent expert reports, the resulting multiple for AusNet is
1.06. That value is entirely inconsistent with a hypothesis of allowed returns being too high.
This highlights a central truth about RAB multiples.
Layers and layers of assumptions underpin any ‘simple’ seeming multiple reported, and each of these need to be tested and considered.
Making two further reasonable assumptions – that investors continue to price additional sources of business value at approximately the same level as today, and that the regulated network will
continue to make investments into the future, has further significant effects on measured multiples.
In the case of the AusNet reported multiple, making these two additional assumptions results in an actual RAB multiple of 0.87.
This would appear to suggest real-world equity investors may be valuing the regulated firm at below its regulated asset base – a circumstance indicative of allowed returns being below those required
to attract efficient levels of new investment.
In short, once unreasonable assumptions are replaced with a set of more plausible assumptions around future investor behaviour and needed capital investment, the CEPA approach would seem to show
exactly the opposite conclusion to that claimed.
This suggests multiple analysis may be a less than a useful guide going forward.
Reviewing the meaning and value of multiple evidence
Rather than there being an unexplained ‘gap’ that might be attributable to overly generous rates of return, once corrected, the CEPA approach would appear to reinforce other evidence presented by AER
consultants Brattle Group that regulatory rates of return appear to be below international comparators.
With the AER’s draft rate of return proposals due out this week, it is a good time to look closely at the evidence about the investment incentives required and work to minimise the number of
assumptions we need to make.
Further detailed analysis by Frontier Economics on the CEPA analysis is available here. | {"url":"https://www.energynetworks.com.au/news/energy-insider/2022-energy-insider/wrong-formula-rab-multiples-analysis-fails-the-test/","timestamp":"2024-11-10T21:14:59Z","content_type":"text/html","content_length":"103559","record_id":"<urn:uuid:32fa6fe6-0435-4f9b-9a48-1b6ee8130a84>","cc-path":"CC-MAIN-2024-46/segments/1730477028191.83/warc/CC-MAIN-20241110201420-20241110231420-00004.warc.gz"} |
Greater Than Less Than Worksheets Free Printable
Greater Than Less Than Worksheets Free Printable - Concepts of more than, less than, equal to, greatest, least are introduced first with pictures of groups of objects and then by. Web download
greater than less than worksheet pdfs. Web this article has free printables greater than less than worksheets for grade 2, full of engaging graphics and fun activities that encourage comparison
learning, and. Some of them also cover the concept of equal amounts. Web greater than less than worksheets for kindergarten. Greater than less than worksheets · home preschool kindergarten first
grade. Practicing multiple worksheets on the concept of greater than less than can help students get a crystal clear. Simply print the 6 pages of free printable greater than less than worksheets in
color on cardstock for. These greater than less than worksheets are a great resource for children in. Teach your children what each symbol means and have them.
7 Best Images of Greater Than Less Than Free Printable Greater than
After printing on cardstock and laminating, i. Teach your children what each symbol means and have them. Children will learn to recognize. Web our greater than less than worksheets are free to
download, easy to use, and very flexible. Web download greater than less than worksheet pdfs.
greater than or less than worksheets Google Search in 2021 2nd
After printing on cardstock and laminating, i. Web learning less than, greater than first, i created some simple alligator less than, greater than, and equal to printables. We have a nice variety to
choose from and they range in difficulty. Web check out our collection of free greater than, less than worksheets for kids. Teach your children what each symbol.
greater than less than worksheets free printable printable worksheets
Web greater than less than worksheets (randomly generated) welcome to the math salamanders greater than less than worksheets area. Web this article has free printables greater than less than
worksheets for grade 2, full of engaging graphics and fun activities that encourage comparison learning, and. Web download greater than less than worksheet pdfs. Concepts of more than, less than,
Problem Sums of greater than and less than Math Worksheets
Some of them also cover the concept of equal amounts. Web this free printable pdf chart features alligator symbols to represent the greater than, less than, or equal to symbols. Web free equal to,
greater than, less than worksheets. Web this article has free printables greater than less than worksheets for grade 2, full of engaging graphics and fun activities.
Greater Than Less Than Worksheet For Grade 1
Web in the worksheets, students will be using the greater than (<), less than (>), and equal to (=) symbols to compare several sets of numbers to understand the concept better. Web greater than less
than worksheets (randomly generated) welcome to the math salamanders greater than less than worksheets area. Simply print the 6 pages of free printable greater than.
Less Than Greater Than Worksheet Have Fun Teaching
Teach your children what each symbol means and have them. Concepts of more than, less than, equal to, greatest, least are introduced first with pictures of groups of objects and then by. Practicing
multiple worksheets on the concept of greater than less than can help students get a crystal clear. Web greater than less than worksheets for kindergarten. Web learning.
greaterthanlessthanworksheet Your Home Teacher
Here you will find our free. Web greater than, less than worksheets. Vocabulary is included as well as an example with traditional. Simply print the 6 pages of free printable greater than less than
worksheets in color on cardstock for. Greater than less than worksheets · home preschool kindergarten first grade.
Easy Counting Greater Than/Less Than Worksheet Woo! Jr. Kids
Web learning less than, greater than first, i created some simple alligator less than, greater than, and equal to printables. Web this free printable pdf chart features alligator symbols to represent
the greater than, less than, or equal to symbols. Web greater than less than worksheets (randomly generated) welcome to the math salamanders greater than less than worksheets area. Web.
30 Printable Greater Than Less Than Equal to Worksheets. Etsy
Web check out our collection of free greater than, less than worksheets for kids. Web free equal to, greater than, less than worksheets. Numbers up to 10,000 and 100,000 are considered in these.
Children will learn to recognize. Web greater than / less than students compare numbers with the greater than / less than / equal to symbols (>,<, =).
Visual Easy Greater Than Less Than Worksheet Woo! Jr. Kids
Web greater than less than worksheets (randomly generated) welcome to the math salamanders greater than less than worksheets area. Web we have several different types of greater than or less than
practice worksheets for you to choose from below. Web check out our collection of free greater than, less than worksheets for kids. This concept is not overly difficult, but.
Concepts Of More Than, Less Than, Equal To, Greatest, Least Are Introduced First With Pictures Of Groups Of Objects And Then By.
These greater than less than worksheets are a great resource for children in. Web this free printable pdf chart features alligator symbols to represent the greater than, less than, or equal to
symbols. Teach your children what each symbol means and have them. Web greater than less than worksheets for kindergarten.
After Printing On Cardstock And Laminating, I.
Web learning less than, greater than first, i created some simple alligator less than, greater than, and equal to printables. Web in the worksheets, students will be using the greater than (<), less
than (>), and equal to (=) symbols to compare several sets of numbers to understand the concept better. Practicing multiple worksheets on the concept of greater than less than can help students get a
crystal clear. Web free equal to, greater than, less than worksheets.
Web Greater Than / Less Than Students Compare Numbers With The Greater Than / Less Than / Equal To Symbols (>,<, =).
Greater than less than worksheets · home preschool kindergarten first grade. Here you will find our free. Web this article has free printables greater than less than worksheets for grade 2, full of
engaging graphics and fun activities that encourage comparison learning, and. In these first grade math worksheets, students practice comparing numbers less than 100 using the greater than and less
Some Of Them Also Cover The Concept Of Equal Amounts.
Web greater than, less than worksheets. Web our greater than less than worksheets are free to download, easy to use, and very flexible. Children will learn to recognize. Web greater than less than
worksheets (randomly generated) welcome to the math salamanders greater than less than worksheets area.
Related Post: | {"url":"https://staging.biohabitats.com/en/greater-than-less-than-worksheets-free-printable.html","timestamp":"2024-11-09T16:31:07Z","content_type":"text/html","content_length":"27421","record_id":"<urn:uuid:dd9f1c1a-34f1-46ee-a448-fbae5febeb57>","cc-path":"CC-MAIN-2024-46/segments/1730477028125.59/warc/CC-MAIN-20241109151915-20241109181915-00397.warc.gz"} |
Inside the New SAT: Math Test - Keystone Education
The SAT Math Test covers a range of math practices, with an emphasis on problem solving, modeling, using tools strategically, and using algebraic structure.
It’s About the Real World
Instead of testing you on every math topic there is, the new SAT asks you to use the math that you’ll rely on most in all sorts of situations. Questions on the Math Test are designed to mirror the
problem solving and modeling you’ll do in:
– College math, science, and social science courses
– The jobs that you hold
– Your personal life
For instance, to answer some questions you’ll need to use several steps —because in the real world a single calculation is rarely enough to get the job done.
Quick Facts
– Most math questions will be multiple choice, but some — called grid-ins — ask you to come up with the answer rather than select the answer.
– The Math Test is divided into two portions: Math Test – Calculator and Math Test – No Calculator.
– Some parts of the test include several questions about a single scenario.
The Math Test will focus in depth on the three areas of math that play the biggest role in a wide range of college majors and careers:
– Heart of Algebra, which focuses on the mastery of linear equations and systems.
– Problem Solving and Data Analysis, which is about being quantitatively literate.
– Passport to Advanced Math, which features questions that require the manipulation of complex equations.
The Math Test also draws on Additional Topics in Math, including the geometry and trigonometry most relevant to college and career readiness.
What the Math Test Measures
The Math Test is a chance to show that you:
– Carry out procedures flexibly, accurately, efficiently, and strategically.
– Solve problems quickly by identifying and using the most efficient solution approaches. This might involve solving a problem by inspection, finding a shortcut, or reorganizing the information
you’ve been given.
Conceptual Understanding
You’ll demonstrate your grasp of math concepts, operations, and relations. For instance, you might be asked to make connections between properties of linear equations, their graphs, and the contexts
they represent.
These real-world problems ask you to analyze a situation, determine the essential elements required to solve the problem, represent the problem mathematically, and carry out a solution.
Calculator Use
Calculators are important tools, and to succeed after high school, you’ll need to know how — and when — to use them. In the Math Test – Calculator portion of the test, you’ll be able to focus on
complex modeling and reasoning because your calculator can save you time.
However, the calculator is, like any tool, only as smart as the person using it. The Math Test includes some questions where it’s better not to use a calculator, even though you’re allowed to. In
these cases, students who make use of structure or their ability to reason will probably finish before students who use a calculator.
The Math Test – No Calculator portion of the test makes it easier to assess your fluency in math and your understanding of some math concepts. It also tests well-learned technique and number sense.
Grid-In Questions
Although most of the questions on the Math Test are multiple choice, 22 percent are student-produced response questions, also known as grid-ins. Instead of choosing a correct answer from a list of
options, you’ll need to solve problems and enter your answers in the grids provided on the answer sheet.
Gridding-In Answers
– Mark no more than one circle in any column.
– Only answers indicated by filling in the circle will be scored (you won’t receive credit for anything written in the boxes located above the circles).
– It doesn’t matter in which column you begin entering their answers; as long as the responses are recorded within the grid area, you’ll receive credit.
– The grid can hold only four decimal places and can only accommodate positive numbers and zero.
– Unless a problem indicates otherwise, answers can be entered on the grid as a decimal or a fraction.
– Fractions like 3 over 24 do not need to be reduced to their lowest terms.
– All mixed numbers need to be converted to improper fractions before being recorded in the grid.
– If the answer is a repeating decimal, students must grid the most accurate value the grid will accommodate. | {"url":"https://keystonewestcovina.com/inside-the-new-sat-math-test/","timestamp":"2024-11-14T05:00:46Z","content_type":"text/html","content_length":"140108","record_id":"<urn:uuid:1d007227-f561-4940-ac63-2c690d0432c5>","cc-path":"CC-MAIN-2024-46/segments/1730477028526.56/warc/CC-MAIN-20241114031054-20241114061054-00896.warc.gz"} |
Alice in Wonderland’s Hidden Satire - Articles by MagellanTV
Alice’s Adventures in Wonderland is universally admired for its ability to speak to readers both young and adult through its fanciful language and expansive narrative tableaux of colorful, eccentric
characters. Would you be surprised to learn that its author, Charles Dodgson, aka Lewis Carroll, undergirded Alice with a hidden world? Several scholars have “cracked the code” to reveal that
Dodgson, an Oxford math professor, augmented several of his best-known scenes with theoretical math. Let’s crack open some of these “Easter eggs” the author planted for our astonishment and delight.
"Alice had begun to think that very few things indeed were really impossible."
We all think we know the story of Alice in Wonderland. But what if we’re missing something really interesting about this beloved – and often bizarre – story?
For example, soon after tumbling down the rabbit hole, Alice begins trying to reconcile what she was experiencing with what she thought she knew:
“[O]h dear, how puzzling it all is! I’ll try if I know all the things I used to know. Let me see: four times five is twelve, and four times six is thirteen, and four times seven is—oh dear! I shall
never get to twenty at that rate!”
What fun to laugh along with Alice’s obvious confusion – but wait. What if she’s correct and just doesn’t know it? To some specialized readers, her mathematics, strange though it seems, is accurate.
But not if you limit yourself to the traditional “base-10” form of math – the one we use every day.
Source: Wikimedia Commons
What Alice’s author, Lewis Carroll, was doing was having a little fun at the expense of “abstract” mathematics, the leading edge of math in his day. If you switch out of base-10 calculations and
into, say, base-18, where digits switch at 18, then four times five is 12; in base 19, four times six is 13; and so on, never getting to 20, just as Alice inadvertently foresaw.
To general readers of Alice’s Adventures in Wonderland, this section seems like nonsense. But it may actually be a skewering of the math trends of Carroll’s day, presented for his own and his peers’
Lewis Carroll’s Invention of Alice, with Help from Charles Dodgson
"Alice thought the whole thing very absurd."
Carroll’s real name was Charles Dodgson, a professor of mathematics at Oxford University. He did his best to keep these mathematical incursions into the narrative hidden, secreted away, only to be
discovered by practitioners of advanced math.
Alice encounters numerous “impossible” situations (and handles them with remarkable grace, all things considered). As she attempts to fit in with her increasingly “curiouser” surroundings, we are
likely to feel amused, if not slightly discomfited, by the depths of nonsense, absurdity, and downright surrealism in which she finds herself immersed.
Dodgson/Carroll wrote Alice for young people’s entertainment. He reportedly had children “focus-test” an early version to ensure it was child-friendly. And it certainly has a large contingent of fans
who would put it in the pantheon of children’s fantasy/nonsense literature, perhaps the first and best example.
The Lidell sisters: Lorina, Alice, and Edith (Source: Stuart Dodgson Collingwood, 1898. via Wikisource)
From early on, however, Carroll’s classic tale has appeared to perceptive readers as something more. The introduction of twisted logic – and even the frequent absence of logic – opens the book to
deeper readings. Freudian interpretations of Alice made much of the descent from the “conscious” level of the midsummer-day setting to the deeper, more remote subterranean recesses of the
unconscious. And the book’s playful, sometimes nonsensical tone valorized it to some 20th century readers as a precursor to the art and literary movements of Dada and Surrealism.
But to advanced readers, Alice’s Adventures in Wonderland may very well be a work in the unique genre of mathematical satire!
Lewis Carroll’s Mathematical Rationale
“No wise fish would go anywhere without a porpoise.”
While Charles Dodson’s alter ego, Lewis Carroll, wrote beloved tales for children’s entertainment, Dodgson himself had a rather more mundane life. As an Oxford professor, he was close with the dean
of the college where he taught, who was the father of the real-life Alice who inspired the tale that bore her name.
Dodgson was known in mathematics circles as an educator who revered the Classical beginnings of his field of study, and he saw the ancient Greek Euclid as the paragon of heuristic elegance and
eloquence. The great mathematician, who lived in Alexandria, Egypt, in the 4th century BCE, gave his name to Euclidean geometry. His Elements was a model of logic and mathematical rigor, as well as
Euclid is known for what are called “mathematical proofs,” step-by-step accumulations of agreed-upon facts that combine to demonstrate, or “prove,” a mathematical theorem. His proofs were often
completed with a flourish, the rhetorical statement quod erat faciendum (literally, “which had to be done”), or QEF, a close cousin to the better known argument-ender QED (“which had to be
Dodgson taught Euclid’s “logical” geometry to Oxford undergrads in the mid-19th century, an era that was (among other things) a hot cauldron of burning issues for mathematicians like Dodgson. It was
during this time that Euclid’s point of reference for math was being challenged on numerous fronts.
Alice in Wonderland illustration (Source: John Tenniel, 1865, via Wikimedia Commons)
Mathematical thinking of Dodgson’s time was rapidly evolving with the introduction of “abstract” math concepts, including such ideas as “imaginary” integers (for example, the square root of a
negative number) and non-Euclidean geometry, which was pointedly not based on a correspondence with nature.
Frankly, Dodgson the educator and traditionalist was horrified by abstract math. He railed against its “unteachability” to undergrads, and found the development of non-Euclidean anything to be
anathema to his philosophy of mathematical education.
Alice Mocks New-Fangled Forms of Logic
"The queen was in a furious passion . . . shouting 'Off with his head!' "
Without calling attention to itself, Carroll’s prose in Alice could easily be described as being full of “Easter eggs,” those semi-hidden callouts to those whose awareness of the subject matter
exceeds those of casual readers. (The rune riddles from Lord of the Rings are another example of a literary Easter egg.)
Dodgson’s sense of intellectual outrage lent itself to wicked satire all through Alice’s Adventures in Wonderland. Any chance he had to skewer the “illogic” of abstract mathematics, he took. And it
turned out that this reversal of traditional logic, when applied to a narrative, created some wildly illogical – and wildly entertaining – scenes throughout the novel.
Carroll, Dodson’s literary persona, presents a “critique of illogic” in the Alice stories that produced a rich world of symbolic takes on narrative realism that generations of writers found
liberating. It can even be said that his work was the progenitor of a genre of fiction where rules of logic are altered or suspended, from The Wizard of Oz to The Hobbit and beyond.
When viewed this way, many well-known scenes from Alice take on a special significance, including the Mad Hatter’s Tea Party, the Duchess and her baby, and the mysterious and quite absurd Cheshire
The Cheshire Cat Purrs at the Borders of Logic
“We’re all mad here. I’m mad. You’re mad.”
Alice’s series of encounters with the Cheshire Cat is a prime example of Dodgson’s hidden interventions. The Cheshire Cat appears to Alice numerous times in the course of the novel, and its
commentary on the course of the plot is at once knowing and completely bonkers. First sighted outside the Duchess’s window, the Cat gives its assessment of the situation quite frankly. Alice asks:
“Would you tell me, please, which way I ought to go from here?”
“That depends a good deal on where you want to get to,” said the Cat.
“I don’t much care where—” said Alice.
“Then it doesn’t matter which way you go,” said the Cat.
The Cat seems unbound by the rigors of illogic in the absurd kingdom into which Alice has fallen, and speaks so plainly that even its internal logic appears absurd. We can see, then, that the
Cheshire Cat takes the point of view of pure, traditional logic, which in this environment seems just as mad as any other point of view.
Cheshire Cat appearing, from Alice in Wonderland, 1865 (Source: John Tenniel, illustrator, via Wikimedia)
It would seem that the only logical response to the lunacy is to declare oneself a lunatic as well. When Alice demands that the Cat explain itself, it offers this nugget: “[A] dog growls when it’s
angry, and wags its tail when it’s pleased. Now I growl when I’m pleased, and wag my tail when I’m angry. Therefore I’m mad.”
While the Cat may represent the point of view of its author, other characters in Wonderland display quirks of another stripe indeed. Let’s take the Duchess, whom we meet in her kitchen with her
suckling baby while the cook is preparing a soup with copious amounts of pepper.
The Duchess (it’s OK if you don’t remember her, as this scene was left out of the Disney version) is feeding her baby, and when the baby sneezes while being held by Alice it promptly turns into a
pig. All other things being equal, the pig does still bear somewhat of a resemblance to the baby. But when Alice lets it go outside the Duchess’s residence, it ambles off contentedly into the forest.
Ergo, the baby is an equivalent of a pig, with porcine tendencies.
This is all meant as a broadside against the then-new, abstract mathematics of Jean-Victor Poncelet, who held that geometric figures retain characteristics of themselves even when undergoing
continuous transformation. While this idea may not seem exceptional or logic-defying to contemporary minds, to Dodgson it may as well have been infernal in origin. Of course, Poncelet was describing
geometric rather than biological figures, but it made no difference to Carroll, whose reductio ad absurdum here made the case for a piglet to be a piglet, and the baby a baby.
The Mad Hatter’s Tea Party and the Use (and Abuse) of Time
“[T]he stupidest tea-party I ever was at.”
Justly famous, the Mad Tea Party brings the use of nonsense in Carroll’s tale to new heights. There are many highlights, such as the koan-like brilliance of the riddle, “How is a raven like a writing
desk”; the constant movement of the three invited guests around the table; and the keen wit of the language.
For math scholars, there’s even more. This Tea Party is an extended discourse on the work of Irish mathematician William Rowan Hamilton, who discovered an abstract concept called quaternions, a
complex number configuration that relied on four terms. However, for years Hamilton worked with three terms and found that they could only be made to establish a rotation of the terms on a flat plane
– like a table with room for only three.
Source: Peter I. Vardy, Public Domain, via Wikimedia
He later added a term to his calculations that allowed the rotation to take place in three-dimensional space, and the term he added was – note this – Time. This makes the March Hare’s repeated
references to a lack of time, or a loss of time, fall right into place in Carroll’s takedown of Hamilton’s “absurd” conjecturing on quaternions.
Dodgson’s attempted rebellion against new forms of mathematics is examined in the context of the history of math in the playful MagellanTV documentary series Magic Numbers.
A Traditionalist’s Take on a Complex New Reality
“I’ve had such a curious dream!”
In a sense, Carroll was tilting at windmills à la Don Quixote; it was quixotic at best to try to defeat advances in math, and particularly in abstract mathematics, with satiric symbols and metaphors
hidden within a tale ostensibly for children.
But how crafty, then, to construct a web of veiled references to people and issues he knew all too well. They certainly knew they were receiving a reductive ribbing, to the point of absurdity, and
that must have given satisfaction to Dodgson. Mathematics gave Alice a covert, second level of meaning, and made it the kind of puzzle that could continue providing surprises to its readers, even a
century-and-a-half later.
Kevin Martin is Senior Writer for MagellanTV. He writes on a wide variety of topics, including outer space, the fine arts, and modern history. He has had a long career as a journalist and
communications specialist with both nonprofit and for-profit organizations. He resides in Glendale, California.
Title Image Source: John Tenniel, illustration for Lewis Carroll's Alice in Wonderland (1865) | {"url":"https://www.magellantv.com/articles/alice-in-wonderlands-hidden-satire-math-slips-down-the-rabbit-hole","timestamp":"2024-11-12T07:07:43Z","content_type":"text/html","content_length":"141737","record_id":"<urn:uuid:b7483a5e-dd2d-4d47-a3c4-bb8d9e158fb2>","cc-path":"CC-MAIN-2024-46/segments/1730477028242.58/warc/CC-MAIN-20241112045844-20241112075844-00050.warc.gz"} |
Symbolic regression software - TuringBot
The Ultimate Regression Tool
When it comes to predicting numerical values from a set of input variables, there are typically two common approaches:
• Fitting a linear or polynomial model to the data.
• Using complex machine learning algorithms, such as neural networks.
While these methods have their strengths, they also have limitations. Linear and polynomial models can only capture simple relationships, while complex algorithms are susceptible to overfitting and
do not offer much insight into the data.
This is where TuringBot comes in: it solves the problem by finding explicit mathematical formulas that connect the variables. This way, it generalizes curve-fitting methods (including linear and
polynomial regression), while generating models that are simple and interpretable.
How does it work?
TuringBot implements a technique called Symbolic Regression. It tries to combine a set of base functions into simple formulas that accurately predict the desired variable. The base functions offered
by the program are the following:
• Arithmetic: addition, multiplication, division
• Trigonometric: sin, cos, tan, asin, acos, atan
• Exponential: exp, log, log2, sqrt, pow
• Hyperbolic: sinh, cosh, tanh, asinh, acosh, atanh
• Logical: smaller, greater, equal, different, logical_or, logical_and
• History: delay, moving_average
• Other: abs, floor, ceil, round, sign, mod, gamma, erf
What is optimized is the formula itself, and not just the numerical constants of some assumed model.
The program uses TXT or CSV files as input, which may contain an arbitrary number of columns. It can be executed both interactively through its powerful graphical interface or in an automated way
from the command line.
Here is an example of an input file that you can use: input.txt.
What can TuringBot be used for?
If your problem involves predicting a number as a function of other numbers, then you can apply TuringBot to it. Just save the data in TXT or CSV format, load it in the program, and start the search.
To give a few concrete examples:
Note that the last two examples are classification problems. This is not an issue: just find formulas that output 0 or 1 depending on the category.
A decision boundary found with symbolic regression. Tutorial
What makes TuringBot so general is that many different search metrics are included, allowing models with different goals to be generated. Those include:
• RMS error
• Classification accuracy
• Correlation coefficient
• Maximum error
• Mean error
• Mean relative error
• Maximum relative error
• F-score
• Nash-Sutcliffe efficiency
• Binary cross-entropy
• Matthews correlation
Why choose TuringBot?
• Proven track record: Our algorithm has been successfully employed in academic publications across a wide range of fields (see below).
• Easy setup: TuringBot is a simple executable that you can install in a few minutes. No Python dependencies, no Docker, no Conda, no virtual environments. This makes it easy to get started and
focus on your work.
• Active development: TuringBot's development began in 2019, and version 1.0 was launched to the public in February 2020. Since then, the program has been continually updated in response to user
feedback, introducing new features, optimizations, bug fixes, and quality-of-life improvements.
Is this like Eureqa?
Both TuringBot and Eureqa are implementations of Symbolic Regression, but the algorithms used by each are completely different. Eureqa is based on genetic programming, while TuringBot is based on
Simulated Annealing.
Eureqa was acquired by a consulting company called DataRobot and is no longer commercially available.
A 2020 paper has shown that TuringBot performs noticeably better than Eureqa on a variety of Physics-inspired problems (arXiv:2010.11328). In this paper, TuringBot even managed to solve problems for
which Eureqa could not find a solution at all.
Is TuringBot free?
TuringBot can be downloaded and used for free for as long as you want, but it also has a paid version that unlocks more functionalities. You can find more details on the Pricing page.
Academic publications
Some publications that use TuringBot are:
1. Cornelio, C., Dash, S., Austel, V., Josephson, T., Goncalves, J., Clarkson, K., ... & Horesh, L. (2021). AI Descartes: Combining data and theory for derivable scientific discovery. arXiv preprint
arXiv:2109.01634. [URL]
2. Li, Z., Ji, J., & Zhang, Y. (2021). From Kepler to newton: explainable AI for science. arXiv preprint arXiv:2111.12210. [URL]
3. Simensen, J. (2021). Study of air exchange and temperature efficiency in a room – based on parameter variations at the supply air vent for use with heated supply air (Master's thesis,
OsloMet-storbyuniversitetet). [URL, in Norwegian]
4. Ashok, D., Scott, J., Wetzel, S. J., Panju, M., & Ganesh, V. (2021, May). Logic guided genetic algorithms (student abstract). In Proceedings of the AAAI Conference on Artificial Intelligence
(Vol. 35, No. 18, pp. 15753-15754). [URL]
5. d'Eon, E. (2021, July). An analytic BRDF for materials with spherical Lambertian scatterers. In Computer Graphics Forum (Vol. 40, No. 4, pp. 153-161). [URL]
6. Katinić, M., Turk, D., Konjatić, P., & Kozak, D. (2021). Estimation of c* Integral for mismatched welded compact tension specimen. Materials, 14(24), 7491. [URL]
7. Konjatić, P., Katinić, M., Kozak, D., & Gubeljak, N. (2021). Yield Load Solutions for SE (B) Fracture Toughness Specimen with I-Shaped Heterogeneous Weld. Materials, 15(1), 214. [URL]
8. Blackledge, J., & Lamphiere, M. (2021). A review of the fractal market hypothesis for trading and market price prediction. Mathematics, 10(1), 117. [URL]
9. Knabben, F. T., Ronzoni, A. F., & Hermes, C. J. (2021). Effect of the refrigerant charge, expansion restriction, and compressor speed interactions on the energy performance of household
refrigerators. International Journal of Refrigeration, 130, 347-355. [URL]
10. Zhu, J., Zhao, S., Wang, L., Xu, Y., & Yan, L. Q. (2022). Practical level-of-detail aggregation of fur appearance. ACM Transactions on Graphics (TOG), 41(4), 1-17. [URL]
11. Barbosa, F. O., Santucci, R. M., Rossi, S., Limberg, G., Pérez-Villegas, A., & Perottoni, H. D. (2022). The SDSS-Gaia View of the Color–Magnitude Relation for Blue Horizontal-branch Stars. The
Astrophysical Journal, 940(1), 30. [URL]
12. Costa, L. A., & de Sousa, J. R. M. (2022). Semi-empirical equation for determination of stress concentration factors (SCF) in tubular joints of fixed offshore platforms subjected to axial forces.
In XLIII Ibero-Latin American Congress on Computational Methods in Engineering (Vol. 4, No. 04). [URL]
13. Alenezi, A. M. M. (2022). Buckling Resistance of Single and Double Angle Compression Members (Doctoral dissertation, Université d'Ottawa/University of Ottawa). [URL]
14. Al-Subhi, A. (2022). Dynamic Economic Load Dispatch Using Linear Programming and Mathematical-Based Models. Mathematical Modelling of Engineering Problems, 9(3). [URL]
15. Mukhtar, M. F., Abas, Z. A., Rasib, A. H. A., Anuar, S. H. H., Zaki, N. H. M., Rahman, A. F. N. A., ... & Shibghatullah, A. S. (2022). Identifying influential nodes with centrality indices
combinations using symbolic regressions. International Journal of Advanced Computer Science and Applications, 13(5). [URL]
16. Takeuchi Eisuke, Tanaka Yu, Yoshida Hiroe, Saito Kazuki, Katsura Keisuke, & Shiraiwa Tachihiko. (2022, September). Development of a Simple Method for Predicting Rice Biomass at Harvest Based on
Biomass Accumulation Data. In Proceedings of the 254th Japanese Society of Crop Science Conference (pp. 50-50). Japanese Society of Crop Science. [URL, in Japanese]
17. Agboka, K. M., Tonnang, H. E., Abdel-Rahman, E. M., Odindi, J., Mutanga, O., & Niassy, S. (2022). Data-driven artificial intelligence (AI) algorithms for modelling potential maize yield under
maize–legume farming systems in East Africa. Agronomy, 12(12), 3085. [URL]
18. Syed Ahmed Kabir, I. F., Gajendran, M. K., Ng, E. Y. K., Mehdizadeh, A., & Berrouk, A. S. (2022). Novel machine-learning-based stall delay correction model for improving blade element momentum
analysis in wind turbine performance prediction. Wind, 2(4), 636-658. [URL]
19. Lai, D., Demartino, C., & Xiao, Y. (2022). High-strain rate compressive behavior of fiber-reinforced rubberized concrete. Construction and Building Materials, 319, 125739. [URL]
20. Moscato, P., & Grebogi, R. (2023, July). Approximating the Boundaries of Unstable Nuclei Using Analytic Continued Fractions. In Proceedings of the Companion Conference on Genetic and Evolutionary
Computation (pp. 751-754). [URL]
21. Carvalho, A., Oliveira, D. M., Krone-Martins, A., & Da Silva, A. (2023, October). Symbolic Regression Applied to Cosmology: An Approximate Expression for the Density Perturbation Variance. In
2023 IEEE 19th International Conference on e-Science (e-Science) (pp. 1-2). IEEE. [URL]
22. Lakshmi, J. R., & Kumar, J. V. V. (2023, September). A Regression-Based Approach for Assessing the Buckling Coefficient of Stiffened and Unstiffened Elements. In IOP Conference Series: Earth and
Environmental Science (Vol. 1237, No. 1, p. 012010). IOP Publishing. [URL]
23. Gajendran, M. K. (2023). Machine learning based predictive modeling of stochastic systems. University of Missouri-Kansas City. [URL]
24. Howard, D. A., Jørgensen, B. N., & Ma, Z. (2023). Multi-Method Simulation and Multi-Objective Optimization for Energy-Flexibility-Potential Assessment of Food-Production Process Cooling.
Energies, 16(3), 1514. [URL]
25. Karakašić, M., Konjatić, P., Glavaš, H., & Grgić, I. (2023). Influence of Open Differential Design on the Mass Reduction Function. Applied Sciences, 13(24), 13300. [URL]
26. Gajendran, M. K., Kabir, I. F. S. A., Vadivelu, S., & Ng, E. Y. K. (2023). Machine learning-based approach to wind turbine wake prediction under yawed conditions. Journal of Marine Science and
Engineering, 11(11), 2111. [URL]
27. Moscato, P., Haque, M. N., & Moscato, A. (2023). Continued fractions and the Thomson problem. Scientific Reports, 13(1), 7272. [URL]
28. Barbosa, F. O. (2023). Galactic Archaeology through the Blue Stars of the Horizontal Branch (Doctoral dissertation, Universidade de São Paulo). [URL, in Portuguese]
29. Pak, A., & Trinh, K. (2023). Forecasting Emergency Department Waiting Times Using Deep Neural Networks. Value in Health, 26(12), S10. [URL]
30. Liljendahl, M., Torpet, M., Lyngsie, P. J., Rudolfsen, J. H., Pedersen, M., & Ibler, K. S. (2023). Machine Learning to Identify Atopic Dermatitis Prevalence Using Healthcare Utilisation Patterns
of Both Diagnosed and Non-Diagnosed AD Patients Based on Danish Register Data. Value in Health, 26(12), S10. [URL]
31. Shaikh, S. A., Taufique, M. F. N., Balusu, K., Kulkarni, S. S., Hale, F., Oleson, J., ... & Soulami, A. (2024). Finite Element Analysis and Machine Learning Guided Design of Carbon Fiber
Organosheet-Based Battery Enclosures for Crashworthiness. Applied Composite Materials, 1-19. [URL]
32. Gude, P., Geldermann, N., Gustedt, F., Grobe, C., Weber, T. P., & Georgevici, A. I. (2024). New postoperative pain instrument for toddlers—Secondary analysis of prospectively collected
assessments after tonsil surgery. Pediatric Anesthesia, 34(4), 347-353. [URL]
33. Denton, R. E., Tengdin, P. M., Hartley, D. P., Goldstein, J., Lee, J., & Takahashi, K. (2024). The electron density at the midpoint of the plasmapause. Frontiers in Astronomy and Space Sciences,
11, 1376073. [URL]
34. Moscato, P., & Haque, M. N. (2024). New alternatives to the Lennard-Jones potential. Scientific Reports, 14(1), 11169. [URL]
35. Moscato, P., & Grebogi, R. (2024). Approximating the nuclear binding energy using analytic continued fractions. Scientific Reports, 14(1), 11559. [URL]
36. Seyam, S., Dincer, I., & Agelin-Chaab, M. (2024). Optimization and Comparative Evaluation of Novel Marine Engines Integrated with Fuel Cells Using Sustainable Fuel Choices. Energy, 131629. [URL]
37. Moscato, P., & Ciezak, A. (2024). A New Approximation for the Perimeter of an Ellipse. Algorithms, 17(10), 464. [URL]
This list is constantly growing and is probably incomplete. If your paper is not shown, please email it to us and we will add it to the list.
• TuringBot Forum: a place where you can get help, ask questions, and connect with others who are equally interested in the software.
In this example, we use symbolic regression to predict house prices as a function of their characteristics.
Here we use TuringBot to develop a classification algorithm that predicts stock market price changes.
Learn how to run TuringBot in a fully automated and customizable way from Python.
See also: Symbolic Regression: The Forgotten Machine Learning Method
(Towards Data Science). | {"url":"https://turingbotsoftware.com/","timestamp":"2024-11-12T22:17:55Z","content_type":"text/html","content_length":"28537","record_id":"<urn:uuid:6d90a265-7db1-46e6-b4ab-f1f1e5315399>","cc-path":"CC-MAIN-2024-46/segments/1730477028290.49/warc/CC-MAIN-20241112212600-20241113002600-00019.warc.gz"} |
gas velocity
27 Aug 2024
Journal of Fluid Dynamics and Engineering
Volume 12, Issue 3, 2023
Title: An Investigation into the Characteristics of Gas Velocity: A Theoretical Analysis
Abstract: This article presents a theoretical analysis of gas velocity, exploring its fundamental properties and characteristics. We examine the relationships between gas velocity, pressure, and
density, as well as the effects of temperature and viscosity on gas flow.
Introduction: Gas velocity is a critical parameter in various engineering applications, including combustion systems, pneumatic transport, and aerodynamics. Understanding the behavior of gas velocity
is essential for designing efficient and safe systems. In this article, we provide an overview of the theoretical aspects of gas velocity, focusing on its mathematical representation and
relationships with other fluid properties.
Mathematical Representation: The velocity of a gas can be represented by the following equation:
v = Δx / Δt
where v is the velocity, Δx is the change in position, and Δt is the change in time.
In terms of pressure and density, the velocity of a gas can be expressed as:
v = √(2P / ρ)
where P is the pressure and ρ is the density.
Relationships with Other Fluid Properties: The velocity of a gas is influenced by its temperature and viscosity. The relationship between gas velocity and temperature can be represented by the
following equation:
v ∝ √T
where T is the temperature.
Similarly, the effect of viscosity on gas velocity can be expressed as:
v ∝ 1 / μ
where μ is the dynamic viscosity.
Conclusion: This article has provided a theoretical analysis of gas velocity, highlighting its fundamental properties and relationships with other fluid properties. The mathematical representation of
gas velocity has been presented in various forms, including equations and formulas. Further research into the characteristics of gas velocity is necessary to fully understand its behavior and
optimize engineering applications.
• [1] Fluid Dynamics, 2nd ed., McGraw-Hill, 2010.
• [2] Gas Dynamics, Springer, 2005.
• [3] Aerodynamics, Cambridge University Press, 2018.
Related articles for ‘gas velocity’ :
Calculators for ‘gas velocity’ | {"url":"https://blog.truegeometry.com/tutorials/education/7803ea050e83386a4b6ff78de68424f6/JSON_TO_ARTCL_gas_velocity.html","timestamp":"2024-11-13T00:07:03Z","content_type":"text/html","content_length":"16518","record_id":"<urn:uuid:639d4777-7993-4106-88ba-632dda904c10>","cc-path":"CC-MAIN-2024-46/segments/1730477028290.49/warc/CC-MAIN-20241112212600-20241113002600-00151.warc.gz"} |
CGPA Calculator - GPA/CGPA/Grade Calculator
Calculate your CGPA result by using our advance CGPA Calculator for free!
College GPA/CGPA Calculators
University CGPA Calculators
How to calculate CGPA Result?
CGPA result is the sum of results of more than one semester or year. GPA results of multiple semesters or years are divided together to show a single result and that is the CGPA result.
The CGPA result is calculated by multiplying the credit score of each subject by multiplying all the grade scores by the total credit score. But you can easily get your CGPA result using our
How to calculate CGPA using this calculator, see the video in detail.
Students can easily convert their results to GPA using the School GPA Calculator. From here students can calculate all types of school exams like JSC, SSC, HSC result GPA. Besides, there is a
separate GPA calculator for the schools belonging to the Technical Board which can be used by the students for free.
We have SSC GPA Calculator, SSC GPA Calculator, JSC and Technical Board GPA Calculator. Students can calculate or convert the result to GPA from here using only their subject wise number.
Our college GPA calculator that is open to everyone. A student can easily calculate his HSC or equivalent exam results using GPA calculator. Besides, all the test results can be calculated using our
college calculator.
The calculator includes an HSC GPA calculator and separate GPA calculator for colleges under Technical Education Board. Students can easily convert their results to GPA using the calculator. If you
are a college student, you can use our college calculator to calculate your results in GPA.Our
University GPA/CGPA Calculator
Our GPA and CGPA calculators for university students. Results published for Honors, Masters & Degree at the university level often require conversion to GPA and CGPA results. Students can easily
convert their results using our University GPA and C GPA calculators.
At the university level, we have Honors GPA Calculator and Honors CGPA Calculator. There are also Masters GPA and C GPA calculators. Besides, you will get a separate Degree CGPA calculator for degree
pass courses of universities like the National University. You can easily calculate GPA and CGPA from here using course-based numbers or Grades.
Through the grade calculator, the student’s grade is determined by the sum of the student’s item scores, which is divided by the total points possible. This calculator accepts both numerical as well
as letter grades.
Using this great calculator you can easily calculate your grade of any semester. To calculate grade you have to give topic wise grade point and weight. Through this you can calculate the final grade
of your semester. Let’s calculate your grade.
The German GPA Calculator is a one of the best tools for assist students to calculating their German GPA result. This German GPA calculator is designed for students so that anyone can convert their
GPA to German GPA using this calculator.
It is very easy to get German GPA results using the CGPA to German GPA Calculator. Using the calculator anyone can calculate/convert German GPA results without knowing any kind of difficult
calculation. Let’s claculate CGPA to GErman GPA result now! | {"url":"https://cgpa-calculator.com/","timestamp":"2024-11-02T14:43:09Z","content_type":"text/html","content_length":"244566","record_id":"<urn:uuid:d2c9e199-7593-4485-b3fd-79a92a9c8c1e>","cc-path":"CC-MAIN-2024-46/segments/1730477027714.37/warc/CC-MAIN-20241102133748-20241102163748-00714.warc.gz"} |
Hypercubic computers
You may have heard of the Connection Machine. This was/is a massively parallel system in which the processors communicate with each other via a comms net, which has a hypercube structure.
The design was apparently motivated by the structural properties of Rubik's cubes, since these also have a hypercubical property. To see this, you need to understand a little abstract algebra and to
assume that the permutation puzzles are all examples of computational devices--you either scramble some kind of codeword and then unscramble it, or you spend a lot of time looping around, trying to
find the algorithm that will get closer to a "resolved word". The encoding properties are fairly obvious.
Anyway, it comes down to characterizing what an operator is. An operator is an action on a subgroup of the elements in the configured puzzle (it has been constructed, say from a kitset of black
plastic components and colored stickers so it has a symmetry, which is the algebra of "color" per face--you want to arrange these colors so that any face is congruent mod colors).
Anyways, obviously a single operator isn't very interesting--it can only rotate around in a circle (actually it quarters the surface of an open disk), so more than two of these in an algorithm
presumably is "more interesting". Actually you generally use the set of operators two at a time, because you constantly think ahead to the next move, the current move is a "preparation" that you
want, for the second operator to act on.
So the 2-generator (2g) subgroup which includes all algorithms composed of two operators is the successor of the subgroup of singletons, acting one-at-a-time, and not alternating (boring as).
With two "letters" from the full set {URFDLB} you can compose the following symmetric "forms" that are in fact, functional lists which traverse the positions/orientations of the cube (a Cayley
graph), hopefully in a deterministic way that leads to "understanding", and the development of a set of personal algorithms--these don't even need a name, you store them away without "thinking" about
what they are, only what they do in terms of shifting colors around, what contrasts with what, etc.
The symmetric forms of sets of two letters are, selecting say, the U and R operators from the full set: UR, and U'R. The first is equivalent to RU, and the second to UR' (up to isomorphism). That is
to say, the first and second "rewrite" of each algorithm will have the same cycle order--it will repeat the same number of times to return to where it started. All algorithms have a finite cycle
length (unless they are an infinite string of randomly selected elements). All algorithms with a finite length, and a sequence of operations (with inverses and double-moves) which doesn't change
during an iteration, will have a finite number of cycles "built-in".
(Note that selecting a pair of operators that act on opposite faces, for the Pocket Cube means the same thing as only using one operator, because there is no middle-layer in between, and opposites
commute fully).
The order of the algorithm UR, is 105 cycles; the order of U'R, is 63 cycles.
THe difference is 42, divide this in half and distribute it: 7(12 + 3), 7(12 -3) gives the symmetry. In fact cycling either of these (I use Cube Explorer, which is a bit faster than manually cycling
a physical cube) using iteration counts like 7, 5, and multiples, investigates the inner structure of both. If you combine them, you have several ways to do this: URU'R, U'R'UR' (which has the same
order), URUR', etc. In fact futzing with the inverses of each letter in various combinations also reveals something about the group's action (this is a subgroup, and so not all of the elements are
permuted, there are two of these the 2-generator subgroup leaves alone, in the Pocket Cube).
You discover that the order of URU'R is 5, and this changes when you change the location of the prime symbol around (or add extra primes to signify to the program that you want it to execute an
inverse operation). If you iterate URU'R 5 times, it leaves the cube unchanged (but each step individually permutes elements). If you change the 5 to a 4 or a 6, the iteration has order 5.
In other words, an algorithm with the general form: XYX'Y has order 5, even if you iterate it a different number of times. This means the algorithms corresponding to the above formulation (a class)
will always divide any number of iterations by 5--even a very large number. So if you type a large iteration count into Cube Explorer, it will cycle 5 times, unless the number is a multiple of 5, in
which case it will have order 1.
You also get cycles of order 2,3, and 7, by alternating the primes through the word (braiding or weaving something through the letters--this is actually known as a braid group, all the algorithms you
can put together have this property).
So playing around with plastic puzzles, thinking about what "black" actually is, in reference to color, and investigating the cycle order of various personally tuned algorithms, is definitely doing
computational science. Now you have an excuse...
The trick with characterizing the numbers of permutations, cycle order, and so on, is formulating a general recurrence relation. Here the domain of linear fractional transformations, the Mobius
group, Dirichlet and Cauchy integrals over integer groups and ring modules, yada yada... is quite helpful, and if you are going on to do computer science, graphics or just general combinatorial
stuff, these are quite helpful formulas.
But regardless of the established formalisms, you do all this abstract math anyway--you don't call it a Mobius function, or a transformation of elements of a G-module or G-structure, but all the same
you develop a set of computational theories and algorithms, as you learn more about solving, and/or preparing patterns on, the Rubik's group of symmetric objects.
And yes, they are also in the same domain as OO, because you can abstract them into an OO-language basis, like GAP or Mathematica. In these the elements of the cube are in a list which is permuted,
traversed, reversed, reduced, etc, and uses pivoting relations (as the actual puzzles pivot elements around fixed centers).
Eliminating pivots is a good way to get to a solution, which means using fewer characters from the full set {URBDFL}, and restricting operations, so you can preserve the part you have solved already
(the initial segment problem).
So don't be a slouch, get into permuting, people! | {"url":"https://www.crazyengineers.com/threads/hypercubic-computers.32457","timestamp":"2024-11-06T16:58:53Z","content_type":"text/html","content_length":"74125","record_id":"<urn:uuid:627e37f8-cf66-44b1-9e51-01e64e0e7fe7>","cc-path":"CC-MAIN-2024-46/segments/1730477027933.5/warc/CC-MAIN-20241106163535-20241106193535-00750.warc.gz"} |
Factor Calculator | Toolsaday
Factor Calculator
What is Factor Calculator ?
A factor calculator is a free online tool used to find the factors of any number.
What is a factors ?
Integers that are multiplied together to find other numbers are known as factors. Assume you needed to discover the factors of 10. All pairs of integers that when multiplied together resulted in 10
would be found. Because 2 x 5 = 10, we know that 2 and 5 are factors of 10.
How to find factors of the numbers
• Calculate the square root of the input number and round it down to the nearest whole number.
• Begin with the number 1 and divide the input number with 1. If input/1 = 0, we can determine that 1 is a factor of the input number.
• Repeat with the number 2 and continue testing all numbers (2, 3, 4,...) up to the square root of the input number. | {"url":"https://toolsaday.com/math/factor-calculator","timestamp":"2024-11-03T03:47:18Z","content_type":"text/html","content_length":"200826","record_id":"<urn:uuid:2212f170-4f0e-4d29-80eb-7523f5036f83>","cc-path":"CC-MAIN-2024-46/segments/1730477027770.74/warc/CC-MAIN-20241103022018-20241103052018-00027.warc.gz"} |