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Python libraries and packages for Data Scientists (Top 5)
Did you know that Python wasn’t originally built for Data Science? And yet today it’s one of the best languages for statistics, machine learning, and predictive analytics as well as simple data
analytics tasks. How come? It’s an open-source language, and data professionals started creating tools for it to complete data tasks more efficiently. Here, I’ll introduce the most important Python
libraries and packages that you have to know as a Data Scientist.
In my previous article, I introduced the Python import statement and the most important modules from the Python Standard Library. In this one, I’ll focus on the libraries and packages that are not
coming with Python 3 by default. In the first half of the article, I’ll list and showcase them. And then, at the end of the article, I’ll also show you how to get (download, install and import) them.
Before we start
If you haven’t done so yet, I recommend going through these articles first:
Top 5 most important Python libraries and packages for Data Science
These are the five most essential Data Science libraries you have to know.
Let’s see them one by one!
How to Become a Data Scientist
(free 50-minute video course by Tomi Mester)
Just subscribe to the Data36 Newsletter here (it’s free)!
Numpy will help you to manage multi-dimensional arrays very efficiently. Maybe you won’t do that directly, but since the concept is a crucial part of data science, many other libraries (well, almost
all of them) are built on Numpy. Simply put: without Numpy you won’t be able to use Pandas, Matplotlib, Scipy or Scikit-Learn. That’s why you need it on the first hand.
3-dimensional numpy array
But on the other hand, it also has a few well-implemented methods. I quite often use Numpy’s random function, which I found slightly better than the random module of the standard library. And when it
comes to simple predictive analytics tasks like linear or polynomial regression, Numpy’s polyfit function is my favorite. (More about that in another article.)
prediction with numpy’s polyfit
To analyze data, we like to use two-dimensional tables – like in SQL and in Excel. Originally, Python didn’t have this feature. Weird, isn’t it? But that’s why Pandas is so important! I like to say,
Pandas is the “SQL of Python.” (Eh, I can’t wait to see what I will get for this sentence in the comment section… ;-)) Okay, to be more precise: Pandas is the library that will help us to handle
two-dimensional data tables in Python. In many senses it’s really similar to SQL, though.
a pandas dataframe
With pandas, you can load your data into data frames, you can select columns, filter for specific values, group by values, run functions (sum, mean, median, min, max, etc.), merge dataframes and so
on. You can also create multi-dimensional data-tables.
That’s a common misunderstanding, so let me clarify: Pandas is not a predictive analytics or machine learning library. It was created for data analysis, data cleaning, data handling and data
discovery… By the way, these are the necessary steps before you run machine learning projects, and that’s why you will need pandas for every scientific project, too.
If you start with Python for Data Science and you learned the basics of Python, I recommend that you focus on learning Pandas next. These short article series of mine will help you: Pandas for Data
I hope I don’t have to detail why data visualization is important. Data visualization helps you to better understand your data, discover things that you wouldn’t discover in raw format and
communicate your findings more efficiently to others.
The best and most well-known Python data visualization library is Matplotlib. I wouldn’t say it’s easy to use… But usually if you save for yourself the 4 or 5 most commonly used code blocks for basic
line charts and scatter plots, you can create your charts pretty fast.
matplotlib dataviz example
Here’s another article that introduces Matplotlib more in-depth: How to use matplotlib.
Without any doubt the fanciest things in Python are Machine Learning and Predictive Analytics. And the best library for that is Scikit-Learn, which simply defines itself as “Machine Learning in
Python.” Scikit-Learn has several methods, basically covering everything you might need in the first few years of your data career: regression methods, classification methods, and clustering, as well
as model validation and model selection. You can also use it for dimensionality reduction and feature extraction.
(Get started with my machine learning tutorials here: Linear Regression in Python using sklearn and numpy!)
a simple classification with a random forest model in Scikit Learn
Note: You will see that machine learning with Scikit-Learn is nothing but importing the right modules and running the model fitting method of them… That’s not the challenging part – it’s rather the
data cleaning, the data formatting, the data preparation, and finding the right input values and the right model. So before you start using Scikit-Learn, I suggest two things. First – as I already
said – master your basic Python and pandas skills to become great at data preparation. Secondly, make sure you understand the theory and the mathematical background of the different prediction and
classification models, so you know what happens with your data when you apply them.
This is kind of confusing, but there is a Scipy library and there is a Scipy stack. Most of the libraries and packages I wrote about in this article are part of the Scipy stack (that is for
scientific computing in Python). And one of these components is the Scipy library itself, which provides efficient solutions for numerical routines (the math stuff behind machine learning models).
These are: integration, interpolation, optimization, etc.
Just like Numpy, you most probably won’t use Scipy itself, but the above-mentioned Scikit-Learn library highly relies on it. Scipy provides the core mathematical methods to do the complex machine
learning processes in Scikit-learn. That’s why you have to know it.
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More Python libraries and packages for data science…
What about image processing, natural language processing, deep learning, neural nets, etc.? Of course, there are numerous very cool Python libraries and packages for these, too. In this article, I
won’t cover them because I think, for a start, it’s worth taking time to get familiar with the above mentioned five libraries. Once you get fluent with them, then and only then you can go ahead and
expand your horizons with more specific data science libraries.
How to get Pandas, Numpy, Matplotlib, Scikit-Learn and Scipy?
First of all, you have to set up a basic data server by following my original How to install Python, R, SQL and bash to practice data science article. Once you have that, you can install these tools
additionally, one by one. Just follow these five steps:
1. Login to your data server!
2. Install numpy using this command:
sudo -H pip3 install numpy==1.19.5
3. Install pandas using this command:
sudo apt-get install python3-pandas
4. Upgrade some additional tools of pandas using these two commands:
sudo -H pip3 install --upgrade beautifulsoup4
sudo -H pip3 install --upgrade html5lib
5. Upgrade Scipy:
sudo -H pip3 install --upgrade scipy
6. Install scikit-learn using this command:
sudo -H pip3 install scikit-learn
Important! During the installation process, you might see warnings, like this one below. (Lot of yellow text.) Don’t worry about them, you can just ignore them for now:
Once you have everything installed, import these new libraries (or specific modules of them) into your Jupyter notebook by using the right import statements. For instance:
import numpy as np
import pandas as pd
import matplotlib
import matplotlib.pyplot as plt
%matplotlib inline
from sklearn.linear_model import LinearRegression
After this you can even test pandas and matplotlib together by running these few lines:
df = pd.DataFrame({'a':[1,2,3,4,5,6,7],
If you see this, you’ve done everything correctly! Great job!
The five most essential Data Science libraries and packages are:
• Numpy
• Pandas
• Matplotlib
• Scikit-Learn
• Scipy
Get them, learn them, use them and they will open a lot of new doors in your data science career!
Tomi Mester
Tomi Mester | {"url":"https://data36.com/python-libraries-packages-data-scientists/","timestamp":"2024-11-13T14:54:05Z","content_type":"text/html","content_length":"166279","record_id":"<urn:uuid:2a4057e3-01d3-44ed-86e9-7f482b29b914>","cc-path":"CC-MAIN-2024-46/segments/1730477028369.36/warc/CC-MAIN-20241113135544-20241113165544-00639.warc.gz"} |
4th Grade Math Worksheets | Equivalent Fractions - Thinkster Math
Equivalent Fractions
Identifying the equivalent fraction of given fraction.
Mapped to CCSS Section# 4.NF.A.1, 3.NF.A.3b, 4.NF.A.2, 4.NF.C.5, 4.NF.B.4b
Explain why a fraction a/b is equivalent to a fraction (n x a)/(n x b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions
themselves are the same size. Use this principle to recognize and generate equivalent fractions.,Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3. Explain why the
fractions are equivalent, e.g., by using a visual fraction model.,Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or
by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <,
and justify the conclusions, e.g., by using a visual fraction model.,Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions
with respective denominators 10 and 100.2 For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100.,Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply
a fraction by a whole number. For example, use a visual fraction model to express 3 x (2/5) as 6 x (1/5), recognizing this product as 6/5. (In general, n x (a/b) = (n x a)/b.)
Try Sample Question | {"url":"https://hellothinkster.com/curriculum-us/grade-4/fractions-grade-4/equivalent-fractions-2/","timestamp":"2024-11-14T14:26:11Z","content_type":"text/html","content_length":"340319","record_id":"<urn:uuid:edd023e4-41cd-4a29-b124-f2884606f158>","cc-path":"CC-MAIN-2024-46/segments/1730477028657.76/warc/CC-MAIN-20241114130448-20241114160448-00101.warc.gz"} |
Calculates the optimal steady-state feedback gain matrix K.
[K, X, E] = lqry(SYS, Q, R)
[K, X, E] = lqry(SYS, Q, R, N)
[K, X, E] = lqry(A, B, C, D, Q, R)
[K, X, E] = lqry(A, B, C, D, Q, R, N)
A continuous or discrete-time linear time-invariant model.
The output weighting matrix (q x q), where q is the number of outputs.
The input weighting matrix (p x p), where p is the number of inputs.
The output/state cross product weighting matrix, such that (Q-N*inv(R)*N') is positive semi-definite.
The state matrix (n x n), where n is the number of states.
The input matrix (n x p), where p is the number of inputs.
The output matrix (q x n), where q is the number of outputs.
The direct transmission matrix (q x p).
The gain matrix. K = inv(R)*(B'X+N').
The symmetric, positive semi-definite solution to the Discrete Algebraic Riccati Equation.
The closed-loop pole locations; the eigenvalues of the matrix A-BK.
Gain matrix obtained from the state-space model:
A = [0.9, 0.25; 0, 0.8];
B = [0; 1];
C = [1, 0];
D = 0;
sys = ss(A, B, C, D);
Q = 2;
R = 1;
[K, X, e] = lqry(sys, Q, R)
K = [Matrix] 1 x 2
12.73999 3.44764
X = [Matrix] 2 x 2
89.05966 12.73999
12.73999 3.44764
e = [Matrix] 2 x 1
-0.87382 + 0.19637i
-0.87382 - 0.19637i
Gain matrix obtained from the transfer function model:
sys_tf=tf([1],[1 6 1]);
Q = 2;
R = 1;
[K, X, e] = lqry(sys.a, sys.b, sys.c, sys.d, Q, R)
K = [Matrix] 1 x 2
0.12079 0.73205
X = [Matrix] 2 x 2
0.12079 0.73205
0.73205 4.60152
e = [Matrix] 2 x 1
The function calculates the optimal steady-state feedback gain matrix K that minimizes a quadratic cost function for a linear state-space system model. The cost function weights the model outputs. | {"url":"https://help.altair.com/twinactivate/help/en_us/topics/reference/oml_language/ControlSystem/lqry.htm","timestamp":"2024-11-10T09:06:24Z","content_type":"application/xhtml+xml","content_length":"93110","record_id":"<urn:uuid:f6bb3303-e987-4bdc-b26c-2791bff918bd>","cc-path":"CC-MAIN-2024-46/segments/1730477028179.55/warc/CC-MAIN-20241110072033-20241110102033-00856.warc.gz"} |
K Means Report Options
Each K Means report contains the following options:
Shows a plot of the points and clusters in the first two principal components of the data, along with a legend identifying the cluster colors. Circles are drawn around the cluster centers and the
size of the circles is proportional to the count inside the cluster. The shaded area is the density contour around the mean. By default, this area indicates where 90% of the observations in that
cluster would fall (Mardia et al. 1980). Use the list below the plot to change the plot axes to other principal components. Alternatively, use the arrow button to cycle through all possible axes
combinations. An option to save the cluster colors to the data table is also located below the plot. See Save Colors to Table. The eigenvalues are shown in decreasing order.
Note: If Columns Scaled Individually is checked in the launch window, the biplot uses a correlation matrix. If Columns Scaled Individually is not checked, the biplot uses a covariance matrix.
Biplot Options
Contains the following options for controlling the appearance of the Biplot:
Show Biplot Rays
Shows the biplot rays. The labeled rays show the directions of the covariates in the subspace defined by the principal components. They represent the degree of association of each variable with each
principal component.
Biplot Ray Position
Enables you to specify the position and radius scaling of the biplot rays. By default, the rays emanate from the point (0,0). In the plot, you can drag the rays or use this option to specify
coordinates. You can also adjust the scaling of the rays to make them more visible with the radius scaling option.
Biplot Contour Density
Enables you to specify the confidence level for the density contours. The default confidence level is 90%.
Mark Clusters
Assigns markers that identify the clusters to the rows of the data table.
Biplot 3D
Shows a three-dimensional biplot of the data. Available only when there are three or more variables.
Parallel Coord Plots
Creates a parallel coordinate plot for each cluster. The plot report has options for showing and hiding the data and means. See Parallel Plots in Essential Graphing.
Scatterplot Matrix
Creates a scatterplot matrix using all of the Y variables.
Save Colors to Table
Assigns colors that identify the clusters to the rows of the data table. If there is a Biplot in the report window, the colors saved to the data table match the colors of the clusters in the Biplot.
If the colors are changed in the Biplot and the Save Colors To Table option is selected again, the colors in the table update to match those in the Biplot.
Note: When any of the Save options are selected, each saved column contains a Notes column property that specifies the number of clusters for that particular column’s data. This enables you to save
columns from more than one cluster fit and use the column property to identify which clustering fit the saved column is from.
Save Clusters
Saves the following two columns to the data table:
– The Cluster column contains the number of the cluster to which the given row is assigned.
– (Not available for Self Organizing Maps.) The Distance column contains the squared Euclidean distance between the given observation and its cluster mean. For each variable, the difference between
the observation’s value and the cluster mean on that variable is divided by the overall standard deviation for the variable. These scaled differences are squared and summed across the variables.
Save Cluster Distance
(Not available for Self Organizing Maps.) Saves a Distance column to the data table. This column is the same as the Distance column obtained from the Save Clusters option.
Save Cluster Formula
Saves a formula column called Cluster Formula to the data table. This is the formula that identifies cluster membership for each.
Save Distance Formula
(Not available for Self Organizing Maps.) Saves a formula column called Distance Formula to the data table. This is the formula that calculates the distance to the assigned cluster.
Save K Cluster Distances
(Not available for Self Organizing Maps.) Saves k columns containing the squared Euclidean distances to each cluster center.
Save K Distance Formulas
(Not available for Self Organizing Maps.) Saves k columns containing the formulas for the squared Euclidean distances to each cluster center.
Publish Cluster Formulas
Publishes to the Formula Depot the same scoring code used in the Save Cluster Formula option.
Simulate Clusters
Creates a new data table containing simulated cluster observations on the Y variables, using the cluster means and standard deviations.
Removes the clustering report. | {"url":"https://www.jmp.com/support/help/en/16.2/jmp/k-means-report-options.shtml","timestamp":"2024-11-12T07:18:36Z","content_type":"application/xhtml+xml","content_length":"12284","record_id":"<urn:uuid:431dba6f-1ae3-4b40-968a-d9dd11e31d5a>","cc-path":"CC-MAIN-2024-46/segments/1730477028242.58/warc/CC-MAIN-20241112045844-20241112075844-00568.warc.gz"} |
Symbolic Differential Computation [SFB F1304-3] - RISC - Johannes Kepler University
Symbolic Differential Computation [SFB F1304-3]
Project Lead
Project Duration
01/04/2004 - 30/09/2008
Project URL
Go to Website
Rational General Solutions of Systems of First-Order Partial Differential Equations
Georg Grasegger, Alberto Lastra, J. Rafael Sendra, Franz Winkler
Journal of Computational and Applied Mathematics 331, pp. 88-103. 2018. ISSN: 0377-0427.
author = {Georg Grasegger and Alberto Lastra and J. Rafael Sendra and Franz Winkler},
title = {{Rational General Solutions of Systems of First-Order Partial Differential Equations}},
language = {english},
journal = {Journal of Computational and Applied Mathematics},
volume = {331},
pages = {88--103},
isbn_issn = {ISSN: 0377-0427},
year = {2018},
refereed = {yes},
length = {16}
A decision algorithm for rational general solutions of first-order algebraic ODEs
G. Grasegger, N.T. Vo, F. Winkler
In: Proceedings XV Encuentro de Algebra Computacional y Aplicaciones (EACA 2016), Universidad de la Rioja, J. Heras and A. Romero (eds.) (ed.), pp. 101-104. 2016. 978-84-608-9024-9.
author = {G. Grasegger and N.T. Vo and F. Winkler},
title = {{A decision algorithm for rational general solutions of first-order algebraic ODEs}},
booktitle = {{Proceedings XV Encuentro de Algebra Computacional y Aplicaciones (EACA 2016)}},
language = {english},
pages = {101--104},
isbn_issn = {978-84-608-9024-9},
year = {2016},
editor = {Universidad de la Rioja and J. Heras and A. Romero (eds.)},
refereed = {yes},
length = {4}
Computation of Dimension in Filtered Free Modules by Gröbner Reduction
Christoph Fuerst, Guenter Landsmann
In: Proceedings of the International Symposium on Symbolic and Algebraic Computation, ACM (ed.), Proceedings of ISSAC '15, pp. 181-188. 2015. 978-1-4503-3435-8. [doi]
author = {Christoph Fuerst and Guenter Landsmann},
title = {{Computation of Dimension in Filtered Free Modules by Gröbner Reduction}},
booktitle = {{Proceedings of the International Symposium on Symbolic and Algebraic Computation}},
language = {english},
pages = {181--188},
isbn_issn = {978-1-4503-3435-8},
year = {2015},
editor = {ACM},
refereed = {yes},
length = {8},
conferencename = {ISSAC '15},
url = {http://doi.acm.org/10.1145/2755996.2756680}
Three Examples of Gröbner Reduction over Noncommutative Rings
Christoph Fuerst, Guenter Landsmann
Technical report no. 15-16 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online). October 2015. [pdf]
author = {Christoph Fuerst and Guenter Landsmann},
title = {{Three Examples of Gröbner Reduction over Noncommutative Rings}},
language = {english},
abstract = {In this report three classes of noncommutative rings are investigated withemphasis on their properties with respect to reduction relations. TheGröbner basis concepts in these rings, being
developed in the literature byseveral authors, are considered and it is shown that the reduction relationscorresponding to these Gröbner bases obey the axioms of a general theoryof Gröbner
number = {15-16},
year = {2015},
month = {October},
sponsor = {partially supported by the Austrian Science Fund (FWF): W1214-N15, project DK11},
length = {31},
type = {RISC Report Series},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
address = {Altenberger Straße 69, 4040 Linz, Austria},
issn = {2791-4267 (online)}
Rational general solutions of systems of autonomous ordinary differential equations of algebro-geometric dimension one
A. Lastra, J.R. Sendra, L.X.C. Ngô, F. Winkler
Publ.Math.Debrecen(86/1-2), pp. 49-69. 2015. 0033-3883.
author = {A. Lastra and J.R. Sendra and L.X.C. Ngô and F. Winkler},
title = {{Rational general solutions of systems of autonomous ordinary differential equations of algebro-geometric dimension one}},
language = {english},
journal = {Publ.Math.Debrecen},
number = {86/1-2},
pages = {49--69},
isbn_issn = {0033-3883},
year = {2015},
refereed = {yes},
length = {21}
Birational transformations preserving rational solutions of algebraic ordinary differential equations
L.X.C. Ngô, J.R. Sendra, F. Winkler
J. Computational and Applied Mathematics(286), pp. 114-127. 2015. 0377-0427.
author = {L.X.C. Ngô and J.R. Sendra and F. Winkler},
title = {{Birational transformations preserving rational solutions of algebraic ordinary differential equations}},
language = {english},
journal = {J. Computational and Applied Mathematics},
number = {286},
pages = {114--127},
isbn_issn = {0377-0427},
year = {2015},
refereed = {yes},
length = {14}
Algebraic General Solutions of First Order Algebraic ODEs
N. T. Vo, F. Winkler
In: Computer Algebra in Scientific Computing, Vladimir P. Gerdt et. al. (ed.), Lecture Notes in Computer Science 9301, pp. 479-492. 2015. Springer International Publishing, ISSN 0302-9743. [url]
author = {N. T. Vo and F. Winkler},
title = {{Algebraic General Solutions of First Order Algebraic ODEs}},
booktitle = {{Computer Algebra in Scientific Computing}},
language = {english},
abstract = {In this paper we consider the class of algebraic ordinary differential equations (AODEs), the class of planar rational systems, and discuss their algebraic general solutions. We establish
for each parametrizable first order AODE a planar rational system, the associated system, such that one can compute algebraic general solutions of the one from the other and vice versa. For the class
of planar rational systems, an algorithm for computing their explicit algebraic general solutions with a given rational first integral is presented. Finally an algorithm for determining an algebraic
general solution of degree less than a given positive integer of parametrizable first order AODEs is proposed.},
series = {Lecture Notes in Computer Science},
volume = {9301},
pages = {479--492},
publisher = {Springer International Publishing},
isbn_issn = {ISSN 0302-9743},
year = {2015},
editor = {Vladimir P. Gerdt et. al.},
refereed = {yes},
length = {14},
url = {http://link.springer.com/content/pdf/10.1007%2F978-3-319-24021-3_35.pdf}
The Concept of Gröbner Reduction for Dimension in filtered free modules
Christoph Fuerst, Guenter Landsmann
Technical report no. 14-12 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online). October 2014. [pdf]
author = {Christoph Fuerst and Guenter Landsmann},
title = {{The Concept of Gröbner Reduction for Dimension in filtered free modules}},
language = {english},
abstract = {We present the concept of Gröbner reduction that is a Gröbner basistechnique on filtered free modules. It allows to compute the dimensionof a filtered free module viewn as a K-vector
space. We apply the de-veloped technique to the computation of a generalization of Hilbert-typedimension polynomials in K[X] as well as in finitely generated difference-differential modules. The
latter allows us to determine a multivariatedimension polynomial where we partition the set of derivations and theset of automorphism in a difference-differential ring in an arbitrary way.},
number = {14-12},
year = {2014},
month = {October},
length = {13},
type = {RISC Report Series},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
address = {Altenberger Straße 69, 4040 Linz, Austria},
issn = {2791-4267 (online)}
Rational general solutions of higher order algebraic ODEs
Y. Huang, L.X.C. Ngo, F. Winkler
J. Systems Science and Complexity (JSSC) 26/2, pp. 261-280. 2013. 1009-6124.
author = {Y. Huang and L.X.C. Ngo and F. Winkler},
title = {{Rational general solutions of higher order algebraic ODEs}},
language = {english},
journal = {J. Systems Science and Complexity (JSSC)},
volume = {26/2},
pages = {261--280},
isbn_issn = {1009-6124},
year = {2013},
refereed = {yes},
length = {20}
Rational general solutions of trivariate rational systems of autonomous ODEs
Y. Huang, L.X.C. Ngo, F. Winkler
Mathematics in Computer Science 6/4, pp. 361-374. 2013. 1661-8270.
author = {Y. Huang and L.X.C. Ngo and F. Winkler},
title = {{Rational general solutions of trivariate rational systems of autonomous ODEs}},
language = {english},
journal = {Mathematics in Computer Science},
volume = {6/4},
pages = {361--374},
isbn_issn = {1661-8270},
year = {2013},
refereed = {yes},
length = {14}
Computer algebra methods for pattern recognition: systems with complex order
F. Winkler, M. Hudayberdiev, G. Judakova
In: Proceedings INTELS 2012 (Moscow), - (ed.), Proceedings of INTELS 2012, pp. 148-150. 2012. 978-5-93347-432-6.
author = {F. Winkler and M. Hudayberdiev and G. Judakova},
title = {{Computer algebra methods for pattern recognition: systems with complex order}},
booktitle = {{Proceedings INTELS 2012 (Moscow)}},
language = {english},
pages = {148--150},
isbn_issn = {978-5-93347-432-6},
year = {2012},
editor = {-},
refereed = {yes},
length = {3},
conferencename = {INTELS 2012}
Classification of algebraic ODEs with respect to rational solvability
L.X.C. Ngo, J.R. Sendra, F. Winkler
Computational Algebraic and Analytic Geometry, Contemporary Mathematics(572), pp. 193-210. 2012. AMS, 0271-4132.
author = {L.X.C. Ngo and J.R. Sendra and F. Winkler},
title = {{Classification of algebraic ODEs with respect to rational solvability}},
language = {english},
journal = {Computational Algebraic and Analytic Geometry, Contemporary Mathematics},
number = {572},
pages = {193--210},
publisher = {AMS},
isbn_issn = {0271-4132},
year = {2012},
refereed = {yes},
length = {18}
The role of Symbolic Computation in Mathematics
F. Winkler
In: Proceedings XIII Encuentro de Algebra Computacional y Aplicaciones (EACA 2012), J.R. Sendra and C. Villarino (ed.), pp. 33-34. 2012. 978-84-8138-770-4.
author = {F. Winkler},
title = {{The role of Symbolic Computation in Mathematics}},
booktitle = {{Proceedings XIII Encuentro de Algebra Computacional y Aplicaciones (EACA 2012)}},
language = {english},
pages = {33--34},
isbn_issn = {978-84-8138-770-4},
year = {2012},
editor = {J.R. Sendra and C. Villarino},
refereed = {yes},
length = {2}
Discrete wave turbulence of rotational capillary water waves
A. Constantin, E. Kartashova, E. Wahlen
Phys. Fluids submitted, pp. 1-13. 2010. AIP, isbn. [pdf]
author = {A. Constantin and E. Kartashova and E. Wahlen},
title = {{Discrete wave turbulence of rotational capillary water waves}},
language = {english},
abstract = {We study the discrete wave turbulent regime of capillarywater waves with constant non-zero vorticity. The explicitHamiltonian formulation and the corresponding couplingcoefficient are
obtained. We also present the constructionand investigation of resonance clustering. Some physicalimplications of the obtained results are discussed.},
journal = {Phys. Fluids},
volume = {submitted},
pages = {1--13},
publisher = {AIP},
isbn_issn = {isbn},
year = {2010},
refereed = {yes},
length = {13}
Capillary freak waves in He-II as a manifestation of discrete wave turbulent regime
E. Kartashova
In: Geophysical Research Abstracts, E. Pelinovsky, C. Kharif (ed.), Proceedings of EGU 2010 (European Geosciences Union, General Assembly 2010),12, pp. 1889-1889. 2010. issn. [pdf]
author = {E. Kartashova},
title = {{Capillary freak waves in He-II as a manifestation of discrete wave turbulent regime}},
booktitle = {{Geophysical Research Abstracts}},
language = {english},
abstract = {Two fundamental findings of the modern theory of wave turbulence are 1) existence of Kolmogorov-Zakharov power energy spectra (KZ-spectra) in $k$-space, \cite{zak2}, and 2) existence of
``gaps" in KZ-spectra corresponding to the resonance clustering, \cite{K06-1}. Accordingly, three wave turbulent regimes can be singled out - \emph{kinetic} (described by wave kinetic equations and
KZ-spectra, in random phase approximation, \cite{ZLF92}); \emph{discrete} (described by a few dynamical systems, with coherent phases corresponding to resonance conditions, \cite{K09b}) and \emph
{mesoscopic} (where kinetic and discrete evolution of the wave field coexist, \cite{zak4}).We present an explanation of freak waves appearance in capillary waves in He-II, \cite{ABKL09}, as a
manifestation of discrete wave turbulent regime. Implications of these results for other wave systems are briefly discussed.},
volume = {12},
pages = {1889--1889},
isbn_issn = {issn},
year = {2010},
editor = { E. Pelinovsky and C. Kharif },
refereed = {yes},
length = {1},
conferencename = {EGU 2010 (European Geosciences Union, General Assembly 2010),}
Towards a Theory of Discrete and Mesoscopic Wave Turbulence
E.Kartashova, V. Lvov, S. Nazarenko, I. Procaccia
Submitted to the RISC Report Series. Technical report no. 10-04 in RISC Report Series, February 2010. [pdf]
author = {E.Kartashova and V. Lvov and S. Nazarenko and I. Procaccia},
title = {{Towards a Theory of Discrete and Mesoscopic Wave Turbulence}},
language = {english},
abstract = {This is WORK IN PROGRESS carried out in years 2008-2009 and partly supported by Austrian FWF-project P20164-N18 and 6 EU Programme under the project SCIEnce, Contract No.
026133).Abstract:\emph{Discrete wave turbulence} in bounded media refers to the regular and chaotic dynamics of independent (that is, discrete in $k$-space) resonance clusters consisting of finite
(often fairly big) number of connected wave triads or quarters, with exact three- or four-wave resonances correspondingly. "Discreteness" means that for small enough amplitudes there is no energy
flow among the clusters. Increasing of wave amplitudes and/or of system size opens new channels of wave interactions via quasi-resonant clusters. This changes statistics of energy exchange between
waves and results in new, \emph{mesoscopic} regime of \emph{wave turbulence}, where \emph{discrete wave turbulence} and \emph{kinetic wave turbulence} in unbounded media co-exist, the latter well
studied in the framework of wave kinetic equations. We overview in systematic manner and from unified viewpoint some preliminary results of studies of regular and stochastic wave behavior in bounded
media, aiming to shed light on their relationships and to clarify their role and place in the structure of a future theory of discrete and mesoscopic wave turbulence, elucidated in this paper. We
also formulate a set of yet open questions and problems in this new field of nonlinear wave physics, that awaits for comprehensive studies in the framework of the theory. We hope that the resulting
theory will offer very interesting issues both from the physical and the methodological viewpoints, with possible important applications in environmental sciences, fluid dynamics, astronomy and
plasma physics.},
year = {2010},
month = {February},
howpublished = {Technical report no. 10-04 in RISC Report Series},
length = {42},
type = {RISC Report Series},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
address = {Altenberger Straße 69, 4040 Linz, Austria},
issn = {2791-4267 (online)}
Resonance clustering in wave turbulent regimes: Integrable dynamics
E. Kartashova, M. Bustamante
Physica A: Stat. Mech. Appl. submitted, pp. 1-31. 2010. Elsevier, ISSN: 0378-4371. [pdf]
author = {E. Kartashova and M. Bustamante},
title = {{Resonance clustering in wave turbulent regimes: Integrable dynamics}},
language = {english},
abstract = {Two fundamental facts of the modern wave turbulence theory are1) existence of power energy spectra in $k$-space, and 2) existence of ``gaps" in this spectra corresponding to the resonance
clustering. Accordingly, three wave turbulent regimes are singled out: \emph{kinetic}, described by wave kinetic equations and power energy spectra; \emph{discrete}, characterized by resonance
clustering; and \emph{mesoscopic},where both types of wave field time evolution coexist. In this paper we study integrable dynamics of resonance clusters appearing in discrete and mesoscopic wave
turbulent regimes. Usinga novel method based on the notion of dynamical invariant we establish that some of the frequently met clusters areintegrable in quadratures for arbitrary initial conditions
and some others -- only for particular initial conditions. Wealso identify chaotic behaviour in some cases. Physical implications of the results obtained are discussed.},
journal = {Physica A: Stat. Mech. Appl.},
volume = {submitted},
pages = {1--31},
publisher = {Elsevier},
isbn_issn = {ISSN: 0378-4371},
year = {2010},
refereed = {yes},
length = {31}
Turbulence of capillary waves revisited
E. Kartashova, A. Kartashov
EPL submitted, pp. 1-6. 2010. isbn. [url]
author = {E. Kartashova and A. Kartashov},
title = {{Turbulence of capillary waves revisited}},
language = {english},
abstract = {Kinetic regime of capillary wave turbulence is classically regarded in terms of three-wave interactions with the exponent of power energy spectrum being $\nu=-7/4$ (two-dimensional case).
We show that a number of assumptions necessary for this regime to occur can not be fulfilled. Four-wave interactions of capillary waves should be taken into account instead, which leads to exponents
$\nu=-13/6$ and $\nu=-3/2$ for one- and two-dimensional wavevectors correspondingly. It follows that for general dispersion functions of decay type, three-wave kinetic regime need not prevail and
higher order resonances may play a major role.},
journal = {EPL},
volume = {submitted},
pages = {1--6},
isbn_issn = {isbn},
year = {2010},
refereed = {yes},
length = {6},
url = {http://arxiv.org/abs/1005.2067}
Nonlinear Resonance Analysis
E. Kartashova
Cambridge edition, 2010. Cambridge University Press, ISBN-13: 9780521763608. [url]
author = {E. Kartashova},
title = {{Nonlinear Resonance Analysis}},
language = {english},
publisher = {Cambridge University Press},
isbn_issn = {ISBN-13: 9780521763608},
year = {2010},
edition = {Cambridge},
translation = {0},
length = {250},
url = {http://www.cambridge.org/catalogue/catalogue.asp?isbn=9780521763608}
Algorithms in Symbolic Computation
Peter Paule, Bruno Buchberger, Lena Kartashova, Manuel Kauers, Carsten Schneider, Franz Winkler
In: Hagenberg Research, Bruno Buchberger et al. (ed.), Chapter 1, pp. 5-62. 2009. Springer, 978-3-642-02126-8. [doi] [pdf]
author = {Peter Paule and Bruno Buchberger and Lena Kartashova and Manuel Kauers and Carsten Schneider and Franz Winkler},
title = {{Algorithms in Symbolic Computation}},
booktitle = {{Hagenberg Research}},
language = {english},
chapter = {1},
pages = {5--62},
publisher = {Springer},
isbn_issn = {978-3-642-02126-8},
year = {2009},
annote = {2009-00-00-C},
editor = {Bruno Buchberger et al.},
refereed = {no},
length = {58},
url = {https://doi.org/10.1007/978-3-642-02127-5_2} | {"url":"https://www1.risc.jku.at/pj/symbolic-differential-computation-sfb-f1304-3/","timestamp":"2024-11-08T06:19:25Z","content_type":"text/html","content_length":"60443","record_id":"<urn:uuid:654f49b1-e70f-4560-8f87-f20b4075b01f>","cc-path":"CC-MAIN-2024-46/segments/1730477028025.14/warc/CC-MAIN-20241108035242-20241108065242-00518.warc.gz"} |
SAT Prep Math - Proportional Reasoning & Relationships | Fiveable
SAT Math: Guide to Proportional Reasoning & Relationships
tl;dr: The SAT Math section is broken up into two parts: one 25-minute section completed without the use of a calculator and one 55-minute section that allows the use of a graphing calculator.
The questions test you on four major content areas: the Heart of Algebra, Problem Solving, Data Analysis, and Passport to Advanced Math. You should be able to change/convert to common units,
understand percentages, read data from charts, graphs, or tables, and determine whether data is linear or exponential. Practice example questions and explanations are provided below!
Overview of the SAT Math Section 🗺️
How long is the SAT Math section?
The Math section of the SAT will be the third and fourth sections and will look like the following:
• one 25-minute section completed without the use of a calculator (of any kind, no exception), followed by
• one 55-minute section that allows the use of a graphing calculator, even though the technology is not always necessary.
SAT Math Topics
These questions (both with-calculator and no-calculator) test on four major content areas: the Heart of Algebra, Problem Solving, Data Analysis, and the Passport to Advanced Math.
• Each section of the Math portion of the SAT begins with multiple-choice questions, each with four choices.
• Following the multiple-choice questions will be questions that do not have choices. Instead, students will bubble in their answers; these questions are often called "grid-in" questions.
• The reference sheet will be available for ALL Math sections of the SAT, regardless of whether calculators are allowed on that section or not.
Breakdown of the Two SAT Math Sections 🧩
• On the calculator portion, some of the grid-ins will relate to one another as part of an Extended Thinking question.
Topics Related to “Proportional Reasoning & Relationships” 📖
• Reading and adjusting for different units of measurement
• Percentage problems
• Change in percentages
• Read data from charts, graphs, or tables
• Determine whether data is linear or exponential
What You Need to Know 🧠
• Be able to change/convert to common units.
• A percentage is a part of 100
• Change in percentage is the difference in % divided by total * 100
• Interpret data from charts, graphs, or tables
• How to find and interpret line of best fit to given data
• If there is a common difference in data values, the relationship is linear
• If there is a common product between data, the relationship is exponential
SAT Math Sample Questions + Explanations 📚
Non-Calculator Practice Problems 🚫🖩
General directions for this section that should be expected:
• The use of a calculator is not allowed at all in this section.
• All variables and expressions represent real numbers unless otherwise specified.
• Figures are drawn to scale unless otherwise specified.
• Assume that all figures lie in a plane.
• Assume that the domain of a given function is the set of all real numbers unless otherwise specified.
1. Let’s start with a medium-difficulty problem:
AP college board SAT practice problems
The correct answer is A:
Looking at the original problem, multiply both sides by the other denominator (get common denominators). This will simplify to 2y=4a-4. Solving for y will then give y=2a-2.
2. This example is considered medium difficulty:
AP college board SAT practice problems
The correct answer is B:
Simplify the numerators and then cross multiply, which will result in 45k+27=54+6k. Solving for k will give you 9/13.
3. This example is considered “hard” difficulty, with reading thrown in as well:
AP college board SAT practice problems
The correct answer is B:
⅕ is the part of the job that two printers can complete in one hour, and each part on the left is the part of the ⅕ that each machine does. Since one printer is twice as fast as the other, 2/x is the
part of the job completed by the faster printer, and 1/x is the slow printer contribution.
Calculator section practice problems 🖩
General directions for this section you should expect to see:
• A graphing calculator is allowed for this section, although not often necessary. (use the calculator as a tool, not as a crutch!)
• All variables and expressions represent real numbers unless otherwise specified.
• Given pictures or figures are drawn to scale unless otherwise specified.
• Assume that all figures lie in a plane.
• Assume that the domain of a given function is the set of all real numbers unless otherwise specified.
1. The following question is considered easy in difficulty, but still requires reading and a solid understanding of the percent relationship.
AP college board SAT practice problems
The correct answer is B:
Aaron’s total stay will be the fixed-rate or $99.95 plus the tax, which is found by multiplying 0.08*99.95… this per x days, added to the one time charge of $5… combining, this will give (99.95 +
0.08*99.95)*x + 5, which simplifies to choice B.
2. The following sample question is considered medium difficulty:
AP college board SAT practice problems
The correct answer is B:
The number of gallons of gas used per hour is 50/21, or (50/21)*t hours.
Since the car’s gas tank has 17 gallons of gas at the start of the trip, and the resulting function will be the starting 17 minus the amount of gas used each hour, giving 17 - (50/21)*t.
3. The following example is considered “medium” in difficulty. Conversion between megabytes and gigabytes and converting between hours, minutes, and seconds is necessary for success on this problem.
AP college board SAT practice problems
The correct answer is B:
1 hour = 3600 seconds.
1 gigabit = 1024 megabits.
3*3600*11 = 118,800 megabits.
Dividing this by 1024 will give 118,800/1024=116.015625 gigabits each day.
If each image is 11.2 gigabits, then 116.0156/11.2=10.3585, which is approximately 10 images per day (round down).
4. This example is considered “hard” in difficulty. It is a proportional relationship, also probability. The key is to recall that information about a random sample can be extrapolated to estimate a
population parameter.
AP college board SAT practice problems
The correct answer is 7212:
d/7500 = exchange rate for dollars to rupees.
Rupees to dollars = (d/7500)*r
Using Traveler card would cost 1.04*(d/7500)*r dollars
To figure out how many rupees need to be spent to make the Traveler card a better option, think:
1.04*(d/7500)*r ≥ d and solve for r…. 1.04r ≥ 7500, which gives r ≥ 7211.53846 → 7212.
Closing 🌟
Congratulations! You’ve made it to the end of SAT Math - Statistics and Data Analysis prep 🙌 You should have a better understanding of the Math sections for the SAT© , topic highlights, what you will
have to be able to do in order to succeed, as well as have seen some practice questions that put the concepts in action. Good luck studying for the SAT Math section 👏
Need more resources? Check out our complete SAT Math Study Guide w/ Practice Problems. Pressed on time? Access our SAT cram sessions and watch the Night Before the SAT cram session. You got this 🥳.
Helpful SAT Math Resources | {"url":"https://fiveable.me/guides/sat-math-proportional-reasoning-relationships","timestamp":"2024-11-12T10:23:48Z","content_type":"text/html","content_length":"68465","record_id":"<urn:uuid:4e74fb93-af5d-47f8-895e-a5e79315b3e9>","cc-path":"CC-MAIN-2024-46/segments/1730477028249.89/warc/CC-MAIN-20241112081532-20241112111532-00859.warc.gz"} |
How to Use Hierarchical Clustering For Customer Segmentation in Python
Have you ever found yourself wondering how you can better understand your customer base and target your marketing efforts more effectively? One solution is to use hierarchical clustering, a method of
grouping customers into clusters based on their characteristics and behaviors. By dividing your customers into distinct groups, you can tailor your marketing campaigns and personalize your marketing
efforts to meet the specific needs of each group. This can be especially useful for businesses with large customer bases, as it allows them to target their marketing efforts to specific segments
rather than trying to appeal to everyone at once. Additionally, hierarchical clustering can help businesses identify common patterns and trends among their customers, which can be useful for
targeting future marketing efforts and improving the overall customer experience. In this tutorial, we will use Python and the scikit-learn library to apply hierarchical (agglomerative) clustering to
a dataset of customer data.
The rest of this tutorial proceeds in two parts. The first part will discuss hierarchical clustering and how we can use it to identify clusters in a set of customer data. The second part is a
hands-on Python tutorial. We will explore customer health insurance data and apply an agglomerative clustering approach to group the customers into meaningful segments. Finally, we will use a
tree-like diagram called a dendrogram, which is helpful for visualizing the structure of the data. The resulting segments could inform our marketing strategies and help us better understand our
customers. So let’s get started!
Customer segmentation is a typical use case for clustering. Image generated with Midjourney.
What is Hierarchical Clustering?
So what is hierarchical clustering? Hierarchical clustering is a method of cluster analysis that aims to build a hierarchy of clusters. It creates a tree-like diagram called a dendrogram, which shows
the relationships between clusters. There are two main types of hierarchical clustering: agglomerative and divisive.
1. Agglomerative hierarchical clustering: This is a bottom-up approach in which each data point is treated as a single cluster at the outset. The algorithm iteratively merges the most similar pairs
of clusters until all data points are in a single cluster.
2. Divisive hierarchical clustering: This is a top-down approach in which all data points are treated as a single cluster at the outset. The algorithm iteratively splits the cluster into smaller and
smaller subclusters until each data point is in its own cluster.
Agglomerative Clustering
In this article, we will apply the agglomerative clustering approach, which is a bottom-up approach to clustering. The idea is to initially treat each data point in a dataset as its own cluster and
then combine the points with other clusters as the algorithm progresses. The process of agglomerative clustering can be broken down into the following steps:
1. Start with each data point in its own cluster.
2. Calculate the similarity between all pairs of clusters.
3. Merge the two most similar clusters.
4. Repeat steps 2 and 3 until all the data points are in a single cluster or until a predetermined number of clusters is reached.
There are several ways to calculate the similarity between clusters, including using measures such as the Euclidean distance, cosine similarity, or the Jaccard index. The specific measure used can
impact the results of the clustering algorithm.
For details on how the clustering approach works, see the Wikipedia page.
Hierarchical clustering is an unsupervised technique to classify things based on patterns in their data. Image created with Midjourney.
Hierarchical Clustering vs. K-means
In a previous article, we have already discussed the popular clustering approach k-means. So how are k-means and hierarchical clustering different? Hierarchical clustering and k-means are both
clustering algorithms that can be used to group similar data points together. However, there are several key differences between these two approaches:
1. The number of clusters: In k-means, the number of clusters must be specified in advance, whereas in hierarchical clustering, the number of clusters is not specified. Instead, hierarchical
clustering creates a hierarchy of clusters, starting with each data point as its own cluster and then merging the most similar clusters until all data points are in a single cluster.
2. Cluster shape: K-means produces clusters that are spherical, while hierarchical clustering produces clusters that can have any shape. This means that k-means is better suited for data that is
well-separated into distinct, spherical clusters, while hierarchical clustering is more flexible and can handle more complex cluster shapes.
3. Distance measure: K-means uses a distance measure, such as the Euclidean distance, to calculate the similarity between data points, while hierarchical clustering can use a variety of distance
measures. This means that k-means is more sensitive to the scale of the features, while hierarchical clustering is less sensitive to the feature scale.
4. Computational complexity: K-means is generally faster than hierarchical clustering, especially for large datasets. This is because k-means only requires a single pass through the data to assign
data points to clusters, while hierarchical clustering requires multiple passes to merge clusters.
5. Visualization: Hierarchical clustering produces a tree-like diagram called a “dendrogram.” The dendrogram shows the relationships between clusters. This can be useful for visualizing the
structure of the data and understanding how clusters are related.
Next, let’s look at how we can implement a hierarchical clustering model in Python.
Customer Segmentation using Hierarchical Clustering in Python
In this comprehensive guide, we explore the application of hierarchical clustering for effective customer segmentation using a customer dataset. This data-driven segmentation method enables
businesses to identify distinct customer clusters based on various factors, including demographics, behaviors, and preferences.
Customer segmentation is a strategic approach that splits a customer base into smaller, more manageable groups with similar characteristics. It aims to better understand the diverse needs and wants
of different customer segments to enhance marketing strategies and product development.
Applying customer segmentation through hierarchical clustering allows businesses to personalize their marketing messages, design targeted campaigns, and tailor products to meet the unique needs of
each segment. This proactive approach can stimulate increased customer loyalty and sales.
We begin by loading the customer data and selecting the relevant features we want to use for clustering. We then standardize the data using the StandardScaler from scikit-learn. Next, we apply
hierarchical clustering using the AgglomerativeClustering method, specifying the number of clusters we want to create. Finally, we add the predictions to the original data as a new column and view
the resulting segments by calculating the mean of each feature for each segment.
The code is available on the GitHub repository.
The future of healthcare will see a tight collaboration between humans and AI. Image generated using Midjourney
About the Customer Health Insurance Dataset
In this tutorial, we will work with a public dataset on health_insurance_customer_data from kaggle.com. Download the CSV file from Kaggle and copy it into the following path, starting from the folder
with your python notebook: data/customer/
The dataset is relatively simple and contains 1338 rows of insured customers. It includes the insurance charges, as well as demographic and personal information such as Age, Sex, BMI, Number of
Children, Smoker, and Region. The dataset does not have any undefined or missing values.
Before we start the coding part, ensure that you have set up your Python 3 environment and the required packages. If you don’t have an environment, follow this tutorial to set up the Anaconda
environment. Also, make sure you install all required packages. In this tutorial, we will be working with the following standard packages:
• pandas
• NumPy
• matplotlib
• scikit-learn
You can install packages using console commands:
pip install <package name>
conda install <package name> (if you are using the anaconda packet manager)
Step #1 Load the Data
To begin, we need to load the required packages and the data we want to cluster. We will load the data by reading the CSV file via the pandas library.
# import necessary libraries
import matplotlib.pyplot as plt
from sklearn.preprocessing import StandardScaler
from sklearn.cluster import AgglomerativeClustering
from sklearn.preprocessing import LabelEncoder
from pandas.api.types import is_string_dtype
import pandas as pd
import math
import seaborn as sns
# load customer data
customer_df = pd.read_csv("data/customer/customer_health_insurance.csv")
age sex bmi children smoker region charges
0 19 female 27.90 0 yes southwest 16884.9240
1 18 male 33.77 1 no southeast 1725.5523
2 28 male 33.00 3 no southeast 4449.4620
Step #2 Explore the Data
Next, it is a good idea to explore the data and get a sense of its structure and content. This can be done using a variety of methods, such as examining the shape of the dataframe, checking for
missing values, and plotting some basic statistics. For example, the following plots will explore the relationships between some of the variables. We won’t go into too much detail here.
def make_kdeplot(df, column_name, target_name):
fig, ax = plt.subplots(figsize=(10, 6))
sns.kdeplot(data=df, hue=column_name, x=target_name, ax = ax, linewidth=2,)
ax.tick_params(axis="x", rotation=90, labelsize=10, length=0)
ax.set_xlim(0, df[target_name].quantile(0.99))
# make kde plot for ext_color
make_kdeplot(customer_df, 'smoker', 'charges')
# make kde plot for ext_color
make_kdeplot(customer_df, 'sex', 'charges')
sns.lmplot(x="charges", y="age", hue="smoker", data=customer_df, aspect=2)
def make_boxplot(customer_df, x,y,h):
fig, ax = plt.subplots(figsize=(10,4))
box = sns.boxplot(x=x, y=y, hue=h, data=customer_df)
make_boxplot(customer_df, "smoker", "charges", "sex")
make_boxplot(customer_df, "region", "charges", "sex")
make_boxplot(customer_df, "children", "bmi", "sex")
Next, let’s prepare the data for model training.
Step #3 Prepare the Data
Before we can train a model on the data, we must prepare it for modeling. This typically involves selecting the relevant features, handling missing values, and scaling the data. However, we are using
a very simple dataset that already has good data quality. Therefore we can limit our data preparation activities to encoding the labels and scaling the data.
To encode the categorical values, we will use label encoder from the scikit-learn library.
# encode categorical features
label_encoder = LabelEncoder()
for col_name in customer_df.columns:
if (is_string_dtype(customer_df[col_name])):
customer_df[col_name] = label_encoder.fit_transform(customer_df[col_name])
Next, we will scale the numeric variables. While scaling the data is an essential preprocessing step for many machine learning algorithms to work effectively, it is generally not necessary for
hierarchical clustering. This is because hierarchical clustering is not sensitive to the scale of the features. However, when you use certain distance measures, such as Euclidean distance, scaling
the data might still be useful when performing hierarchical clustering. Scaling the data can help to ensure that all of the features are given equal weight. This can be useful if you want to avoid
giving more weight to features with larger scales.
# select features
X = customer_df # we will select all features
# standardize the data
scaler = StandardScaler()
X_scaled = scaler.fit_transform(X)
array([[-1.43876426, -1.0105187 , -0.45332 , ..., 1.34390459,
0.2985838 , 1.97058663],
[-1.50996545, 0.98959079, 0.5096211 , ..., 0.43849455,
-0.95368917, -0.5074631 ],
[-0.79795355, 0.98959079, 0.38330685, ..., 0.43849455,
-0.72867467, -0.5074631 ],
[-1.50996545, -1.0105187 , 1.0148781 , ..., 0.43849455,
-0.96159623, -0.5074631 ],
[-1.29636188, -1.0105187 , -0.79781341, ..., 1.34390459,
-0.93036151, -0.5074631 ],
[ 1.55168573, -1.0105187 , -0.26138796, ..., -0.46691549,
1.31105347, 1.97058663]])
Step #4 Train the Hierarchical Clustering Algorithm
To train a hierarchical clustering model using scikit-learn, we can use the AgglomerativeClustering or Ward class. The main parameters for these classes are:
• n_clusters: The number of clusters to form. This parameter is required for AgglomerativeClustering but is not used for Ward.
• affinity: The distance measure used to calculate the similarity between pairs of samples. This can be any of the distance measures implemented in scikit-learn, such as the Euclidean distance or
the cosine similarity.
• linkage: The method used to calculate the distance between clusters. This can be one of “ward,” “complete,” “average,” or “single.”
• distance_threshold: The maximum distance between two clusters that allows them to be merged. This parameter is only used in the AgglomerativeClustering class.
To train the model, we specify the desired parameters and fit the model to the data using the fit_predict method. This method will fit the model to the data and generate predictions in one step.
# apply hierarchical clustering
model = AgglomerativeClustering(affinity='euclidean')
predicted_segments = model.fit_predict(X_scaled)
Now we have a trained clustering model also predicted the segments for our data.
Step #5 Visualize the Results
After the model is trained, we can visualize the results to get a better understanding of the clusters that were formed. There is a wide range of plots and tools to visualize clusters. In this
tutorial, we will use a scatterplot and a dendrogram.
5.1 Scatterplot
For this, we can use the lmplot function in Seaborn. The lmplot creates a 2D scatterplot with an optional overlay of a linear regression model. The plot visualizes the relationship between two
variables and fits a linear regression model to the data that can highlight differences. In the following, we use this linear regression model to highlight the differences between our two cluster
segments and the age of the customers.
# add predictions to data as a new column
customer_df['segment'] = predicted_segments
# create a scatter plot of the first two features, colored by segment
sns.lmplot(x="charges", y="age", hue="segment", data=customer_df, aspect=2)
We can see that our model has determined two clusters in our data. The clusters seem to correspond well with the smoker category, which indicates that this attribute is decisive in forming relevant
5.2 Dendrogram
The hierarchical clustering approach lets us visualize relationships between different groups in our dataset in a dendrogram. A dendrogram is a graphical representation of a hierarchical structure,
such as the relationships between different groups of objects or organisms. It is typically used in biology to show the relationships between different species or taxonomic groups, but it can also be
used in other fields to represent the hierarchical structure of any set of data. In a dendrogram, the objects or groups being studied are represented as branches on a tree-like diagram. The branches
are usually labeled with the names of the objects or groups, and the lengths of the branches represent the distances or dissimilarities between the objects or groups. The branches are also arranged
in a hierarchical manner, with the most closely related objects or groups being placed closer together and the more distantly related ones being placed farther apart.
# Visualize data similarity in a dendogram
def plot_dendrogram(model, **kwargs):
# create the counts of samples under each node
counts = np.zeros(model.children_.shape[0])
n_samples = len(model.labels_)
for i, merge in enumerate(model.children_):
current_count = 0
for child_idx in merge:
if child_idx < n_samples:
current_count += 1 # leaf node
current_count += counts[child_idx - n_samples]
counts[i] = current_count
linkage_matrix = np.column_stack(
[model.children_, model.distances_, counts]
# Plot the corresponding dendrogram
dendrogram(linkage_matrix, orientation='right',**kwargs)
plt.title("Hierarchical Clustering Dendrogram")
# plot the top three levels of the dendrogram
plot_dendrogram(cluster_model, truncate_mode="level", p=4)
plt.xlabel("Euclidean Distance")
plt.ylabel("Number of points in node (or index of point if no parenthesis).")
Source: This code block is based on code from the scikit-learn page
In conclusion, hierarchical clustering is a powerful tool for customer segmentation that can help businesses better understand their customer base and target their marketing efforts more effectively.
By grouping customers into clusters based on their characteristics and behaviors, companies can create targeted campaigns and personalize their marketing efforts to better meet the needs of each
group. Using Python and the scikit-learn library, we were able to apply an agglomerative clustering approach to a dataset of customer data and identify two distinct segments. We can then use these
segments to inform our marketing strategies and get a better understanding of our customers.
By the way, customer segmentation is an area where real-world data can be prone to bias and unfairness. If you’re concerned about this, check out our latest article on addressing fairness in machine
learning with fairlearn.
I hope this article was useful. If you have any feedback, please write your thoughts in the comments.
Sources and Further Reading
• Images generated with OpenAI Dall-E and Midjourney.
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The Right Way to Solve Asset Management
I have written many articles pointing out that the current approach to investment management doesn’t actually work. The theory is all single-point-in-time. This is absurd for a process of investment,
saving, and spending that takes place over the long term and aims at goals that are often far in the future. To extend the single-point-in-time theory to a continuing process over time, applications
of the theory simply assume that the single-point-in-time solution applies to every moment or interval in time in the future.
That this approach is inapplicable has been made obvious by the need for “target-date funds” with their “glide paths,” which do not apply the same solution at every point in time. Yet the supposedly
brilliant concept has nothing to offer that would provide an appropriate glide path for a particular set of future needs. Hence, glide paths are derived by rudimentary rule of thumb with no sound
theoretical basis and little or no relationship to the single-point-in-time theory.
The current theory, which is taught in schools, and tested in CFA institute exams for certification purposes, has as its bedrock the mean-variance optimization model. In a truly appalling 2010 book,
The Endowment Model of Investing: Return, Risk, and Diversification, the authors admitted that the model had to be “tortured” – by which they meant rigged – to produce acceptable outputs. They then
went ahead and “applied” the model throughout the entirety of their 352-page book, quite openly manipulating the model to get the results on which their conclusions depend. It should be no wonder
that the endowment model has failed so badly.
As I have shown before, most of the articles on investment management in financial journals are deeply flawed. They rest on performative mathematical exercises which are then interpreted by the
authors to support their own preconceived non-mathematical conclusions, even when, which is very often the case, they do not actually support them. | {"url":"https://www.advisorperspectives.com/articles/2024/09/30/right-way-solve-asset-management?topic=retirement-income","timestamp":"2024-11-14T05:31:24Z","content_type":"text/html","content_length":"114397","record_id":"<urn:uuid:8824183c-4490-4b12-affc-84d458124541>","cc-path":"CC-MAIN-2024-46/segments/1730477028526.56/warc/CC-MAIN-20241114031054-20241114061054-00142.warc.gz"} |
Modal DIKWP Semantic Mathematics（初学者版）
Modal DIKWP Semantic Mathematics
Yucong Duan
International Standardization Committee of Networked DIKWP for Artificial Intelligence Evaluation(DIKWP-SC)
World Artificial Consciousness CIC(WAC)
World Conference on Artificial Consciousness(WCAC)
(Email: duanyucong@hotmail.com)
This document provides an in-depth explanation of the new version of the Data-Information-Knowledge-Wisdom-Purpose (DIKWP) Semantic Mathematics framework, as proposed by Prof. Yucong Duan. Building
upon previous investigations and addressing identified limitations and paradoxes, this enhanced framework expands its capability to model and represent the full spectrum of natural language semantics
and human cognition. The updated framework aims to construct a comprehensive Cognitive Semantic Space that encapsulates human expressions and provides mechanisms for resolving paradoxes and proving
conjectures within its structure. This detailed explanation covers the framework's foundational principles, enhancements, formal definitions, implementation strategies, and potential applications.
1. Introduction1.1. Background
The DIKWP Semantic Mathematics framework was initially developed to model and represent natural language semantics using fundamental concepts derived from the DIKWP hierarchy:
• Data: Raw facts and figures.
• Information: Data processed to be meaningful.
• Knowledge: Information applied or put into action.
• Wisdom: Insight derived from knowledge over time.
• Purpose: The overarching goals or intentions guiding actions.
The original framework focused on the explicit manipulation of three fundamental semantics:
• Sameness (Data): Recognizing shared attributes or identities between entities.
• Difference (Information): Identifying distinctions or disparities between entities.
• Completeness (Knowledge): Integrating all relevant attributes and relationships to form holistic concepts.
1.2. Motivation for the New Version
Despite its strengths, the initial framework faced challenges:
• Paradoxes: Issues such as Russell's Paradox revealed limitations in handling self-referential constructs.
• Incompleteness: Gödel's incompleteness theorems highlighted potential limitations in the framework's ability to prove all truths within its system.
• Cognitive Limits: The complexity of human cognition and the infinite expressiveness of natural language presented scalability challenges.
The new version addresses these issues by introducing enhancements that increase the framework's robustness, expressive power, and applicability.
2. Overview of the New Version
The new version introduces several key enhancements:
1. Hierarchical Semantic Levels: Organizing semantics into hierarchical levels to prevent paradoxes and improve structure.
2. Integration of Type Theory: Applying type theory to enforce consistency and prevent invalid semantic constructions.
3. Expanded Fundamental Semantics: Incorporating additional fundamental semantics—Contextuality, Temporality, and Modality—to capture more nuances of natural language.
4. Formal Logical Systems: Integrating formal logic systems (e.g., Modal Logic, Temporal Logic) to enhance reasoning capabilities.
5. Mechanisms for Handling Incompleteness and Undecidability: Acknowledging and providing strategies for dealing with undecidable statements.
6. Construction of the Cognitive Semantic Space: Developing a comprehensive space that encapsulates all evolved semantics.
3. Detailed Explanation of the Enhancements3.1. Hierarchical Semantic Levels3.1.1. Purpose and Rationale
• Avoidance of Paradoxes: By organizing semantics into hierarchical levels, self-referential paradoxes like Russell's Paradox are prevented.
• Structured Organization: Hierarchical levels facilitate better management and understanding of complex semantic relationships.
3.1.2. Hierarchical Levels Defined
• Level 0: Primitive Semantics
□ Definition: The most basic semantic elements that cannot be broken down further.
□ Examples: Existence (∃), identity (=), basic logical constants (∧, ∨, ¬).
• Level 1: Constructed Semantics
□ Definition: Semantics constructed from Level 0 primitives using defined operations.
□ Examples: Concepts like "cat," "tree," "red," formed by combining primitives.
• Level 2: Meta-Semantics
□ Definition: Semantics about semantics; statements that describe or reference Level 1 constructs.
□ Examples: "The concept of 'justice' is abstract," "Definitions of 'number' vary across contexts."
• Level n: Higher-Order Semantics
□ Definition: Additional layers for more abstract or complex semantics, where n > 2.
□ Examples: Discussions about the nature of meta-semantics, philosophical analyses.
3.1.3. Formal Representation
Let S_n represent the set of semantics at level n.
• Level 0 (S_0): Contains primitives {p_1, p_2, ..., p_k}.
• Level 1 (S_1): Constructed using operations O on elements of S_0.
S1={O(s0i,s0j,...)∣s0i,s0j∈S0}S_1 = \{ O(s_{0_i}, s_{0_j}, ...) \mid s_{0_i}, s_{0_j} \in S_0 \}
• Level 2 (S_2): Meta-statements about S_1.
S2={M(s1i)∣s1i∈S1}S_2 = \{ M(s_{1_i}) \mid s_{1_i} \in S_1 \}
• Higher Levels: Similarly defined, ensuring no circular references within the same level.
3.1.4. Benefits
• Preventing Self-Reference within the Same Level: By restricting self-reference to higher levels, paradoxes are avoided.
• Clear Separation of Semantics: Improves clarity and manageability.
3.2. Integration of Type Theory3.2.1. Purpose
• Consistency Enforcement: Types prevent invalid operations between incompatible semantics.
• Error Detection: Type mismatches highlight potential semantic errors.
3.2.2. Type Assignments and Rules
• Type System: Define a set of types T = {T_1, T_2, ..., T_n}.
• Assignment Function: A function τ: S \rightarrow T assigns a type to each semantic element.
• Type Rules: Operations are permitted only if the types of operands are compatible.
For operation O:
If τ(si)=Ta and τ(sj)=Tb, then O(si,sj) is valid only if Ta and Tb are compatible under O.\text{If } τ(s_i) = T_a \text{ and } τ(s_j) = T_b, \text{ then } O(s_i, s_j) \text{ is valid only if }
T_a \text{ and } T_b \text{ are compatible under } O.
3.2.3. Example3.2.4. Benefits
• Avoids Paradoxical Constructions: By enforcing type rules, constructs that could lead to paradoxes are disallowed.
• Enhances Clarity: Types make the role and nature of each semantic element explicit.
3.3. Expanded Fundamental Semantics3.3.1. Contextuality3.3.2. Temporality3.3.3. Modality3.4. Formal Logical Systems3.4.1. Purpose
• Enhanced Expressiveness: Formal logics allow precise expression of complex semantics.
• Rigorous Reasoning: Enables formal proofs and deductions within the framework.
3.4.2. Integrated Logics
• Propositional Logic: Basic logical operators and propositions.
• Predicate Logic: Quantifiers and predicates for more detailed expressions.
• Modal Logic: Addresses necessity and possibility.
• Temporal Logic: Handles time-dependent statements.
• Deontic Logic: Deals with obligation and permission (e.g., ethics, law).
3.4.3. Example of Formal Reasoning
• Statement: "All humans are mortal."
• Predicate Logic Representation:
∀x(Human(x)→Mortal(x))\forall x (\text{Human}(x) \rightarrow \text{Mortal}(x))
• Deduction:
□ Given Socrates is a human: \text{Human}(\text{Socrates})
□ Therefore, \text{Mortal}(\text{Socrates}) follows.
3.5. Mechanisms for Handling Incompleteness and Undecidability3.5.1. Recognizing Undecidable Statements3.5.2. External Augmentation and Meta-Reasoning3.5.3. Benefits
• Acknowledgment of Limits: The framework accepts that not all truths are provable within itself.
• Flexibility: Allows for growth and adaptation by incorporating new knowledge or systems.
3.6. Construction of the Cognitive Semantic Space3.6.1. Purpose
• Comprehensive Representation: To encompass all evolved semantics derived from natural language.
• Accessibility: Provide mechanisms for discovering and retrieving explanations and proofs.
3.6.2. Semantic Mapping3.6.3. Semantic Networks
• Nodes: Represent semantic entities (concepts, properties, events).
• Edges: Represent relationships (e.g., "is a type of," "causes," "belongs to").
• Example:
3.6.4. Search and Retrieval Mechanisms
• Query System: Users can input queries in natural language or formal representation.
• Inference Engine: Uses logical reasoning to find explanations or proofs.
• Example:
□ Identify relevant concepts and relationships.
□ Use inference rules to construct an explanation.
□ Query: "Why is a cat considered a mammal?"
□ Process:
3.6.5. Benefits
• Knowledge Discovery: Facilitates exploration of semantic relationships.
• Problem Solving: Assists in finding proofs or explanations for complex problems.
4. Addressing Previous Paradoxes and Limitations4.1. Russell's Paradox4.1.1. The Paradox Restated4.1.2. Resolution in the Framework
• Hierarchical Levels: By assigning sets to levels, a set cannot contain sets of the same or higher level.
• Type Assignments: Sets are typed, and a set of type T cannot contain itself unless explicitly allowed.
• Result: The paradoxical construction is disallowed, preventing the contradiction.
4.2. Gödel's Incompleteness Theorems4.2.1. Acknowledgment of Incompleteness4.2.2. Handling Strategy
• Meta-System Reasoning: Use higher-level systems to reason about statements undecidable in the original system.
• Continuous Expansion: The framework can be extended with new axioms or rules when justified.
4.2.3. Example
• Statement: "All statements in this system are provable."
• Analysis: Recognized as problematic; the framework avoids asserting such completeness.
4.3. Cognitive Limits4.3.1. Scalability and Complexity
• Modularity: The framework is designed to be modular, allowing for incremental expansion.
• Computational Resources: Acknowledges that practical implementation depends on available computational power.
4.3.2. Adaptability
• Learning Mechanisms: Incorporates machine learning techniques to evolve and adapt the semantic space.
• Human-AI Collaboration: Facilitates cooperation between human cognition and AI to overcome individual limitations.
5. Implications and Applications5.1. Universal Semantic Representation
• Cross-Language Compatibility: The framework can map semantics across different natural languages, aiding in translation and communication.
• Interdisciplinary Integration: Bridges gaps between fields by providing a common semantic foundation.
5.2. Advanced Artificial Intelligence
• Natural Language Understanding (NLU): Improves AI's ability to comprehend context, nuance, and complexity in human language.
• Cognitive Computing: Supports the development of AI systems that simulate human thought processes.
5.3. Knowledge Discovery and Proof Generation
• Automated Theorem Proving: Assists in generating proofs for mathematical conjectures.
• Scientific Research: Aids in hypothesis generation and validation through semantic modeling.
5.4. Philosophical Insights
• Understanding Consciousness: Provides tools to model aspects of human consciousness and cognition.
• Exploring Ontological Questions: Helps in formalizing and analyzing philosophical concepts.
6. Conclusion
The new version of the DIKWP Semantic Mathematics framework represents a significant advancement in modeling natural language semantics and human cognition. By addressing previous limitations through
hierarchical semantic levels, type theory integration, expanded fundamental semantics, and formal logical systems, the framework enhances its robustness and applicability.
The construction of the Cognitive Semantic Space offers a comprehensive environment for knowledge representation, discovery, and reasoning. While recognizing inherent limitations, the framework
provides mechanisms to navigate challenges, making it a valuable tool for advancing artificial intelligence, facilitating universal semantic representation, and deepening our understanding of
cognition and knowledge.
7. Future Work7.1. Implementation and Testing
• Prototype Development: Building software implementations to test the framework's practical viability.
• Performance Evaluation: Assessing computational efficiency and scalability.
7.2. Collaboration Across Disciplines
• Interdisciplinary Research: Engaging experts from linguistics, cognitive science, philosophy, and AI.
• User Feedback: Incorporating insights from practitioners to refine the framework.
7.3. Ethical Considerations
• Responsible AI: Ensuring the framework's applications align with ethical guidelines.
• Data Privacy: Safeguarding sensitive information within the cognitive semantic space.
1. Duan, Y. (2023). The Paradox of Mathematics in AI Semantics. Proposed by Prof. Yucong Duan:" As Prof. Yucong Duan proposed the Paradox of Mathematics as that current mathematics will not reach
the goal of supporting real AI development since it goes with the routine of based on abstraction of real semantics but want to reach the reality of semantics. ".
2. Russell, B. (1908). Mathematical Logic as Based on the Theory of Types. American Journal of Mathematics, 30(3), 222-262.
3. Gödel, K. (1931). On Formally Undecidable Propositions of Principia Mathematica and Related Systems. Monatshefte für Mathematik und Physik.
4. Church, A. (1936). An Unsolvable Problem of Elementary Number Theory. American Journal of Mathematics, 58(2), 345-363.
5. Montague, R. (1974). Formal Philosophy: Selected Papers of Richard Montague. Yale University Press.
6. Barwise, J., & Etchemendy, J. (1999). Language, Proof and Logic. CSLI Publications.
7. Blackburn, P., de Rijke, M., & Venema, Y. (2001). Modal Logic. Cambridge University Press.
8. Fagin, R., Halpern, J. Y., Moses, Y., & Vardi, M. Y. (2003). Reasoning About Knowledge. MIT Press.
I extend sincere gratitude to Prof. Yucong Duan for his pioneering work on the DIKWP Semantic Mathematics framework and for inspiring the development of this new version. Appreciation is also given
to researchers in cognitive science, artificial intelligence, logic, and philosophy for their foundational contributions that have informed and enriched this work.
Author Information
For further discussion on the new version of the DIKWP Semantic Mathematics framework and its applications, please contact [Author's Name] at [Contact Information].
Keywords: DIKWP Model, Semantic Mathematics, Cognitive Semantic Space, Hierarchical Semantics, Type Theory, Sameness, Difference, Completeness, Contextuality, Temporality, Modality, Prof. Yucong
Duan, Artificial Intelligence, Knowledge Representation, Formal Logic
Formal DIKWP Semantic Mathematics（初学者版）
Key: Prof. Yucong Duan\'s DIKWP Semantic Mathematics （初学者版）
0 个评论) | {"url":"https://blog.sciencenet.cn/blog-3429562-1453467.html","timestamp":"2024-11-04T21:12:47Z","content_type":"application/xhtml+xml","content_length":"90033","record_id":"<urn:uuid:37935f10-689b-4e18-a383-d746d7e9bab7>","cc-path":"CC-MAIN-2024-46/segments/1730477027861.16/warc/CC-MAIN-20241104194528-20241104224528-00409.warc.gz"} |
What number must be added to each of the numbers 16, 26 and 40 so that the resulting numbers may be in continued proportion? - Ask TrueMaths!What number must be added to each of the numbers 16, 26 and 40 so that the resulting numbers may be in continued proportion?
This is a basic question from ML aggarwal book of class 10th, chapter 7, ratio and proportion., ICSE board
Here we have three different numbers and we have to find the value of the number that can be added in all of three to make them in continued proportion.
Question 10, exercise 7.2 | {"url":"https://ask.truemaths.com/question/what-number-must-be-added-to-each-of-the-numbers-16-26-and-40-so-that-the-resulting-numbers-may-be-in-continued-proportion/","timestamp":"2024-11-14T01:12:55Z","content_type":"text/html","content_length":"126995","record_id":"<urn:uuid:21548bec-c1db-4234-ad01-f33b80d582e4>","cc-path":"CC-MAIN-2024-46/segments/1730477028516.72/warc/CC-MAIN-20241113235151-20241114025151-00573.warc.gz"} |
Resolution of regional seismic models: Squeezing the iceland anomaly
We present a resolution study of the velocity structure beneath Iceland as constrained by teleseismic traveltime tomography using data from the HOTSPOT seismic network. This temporary PASSCAL network
and the tomographic technique that was used to generate the ICEMAN velocity models are typical of regional seismic studies. Therefore, this study also provides a basis for understanding the
resolution of other regional seismic experiments. A suite of tests is used to constrain the range of velocity models that satisfy the traveltime observations on Iceland. These include ray-theoretical
squeezing experiments, which attempt to force velocity anomalies into specific geometries while still satisfying the data set, and finite-frequency experiments, which use the spectral-element method
(SEM) to simulate full waveform propagation through various 3-D velocity models. The use of the SEM allows the verification of the ray-theoretical ICEMAN models without the assumption of ray theory.
The tests show that the ICEMAN models represent an end-member of the range of velocity models that satisfy the data set. The 200-km-width Gaussian-shaped upwelling beneath Iceland, imaged in the
ICEMAN models, is at the broadest end of the allowed model range; the peak -2 per cent compressional and -4 per cent shear wave perturbations are lower bounds on the amplitude of the velocity model.
Such broadening and lowering of velocity anomalies is the product of data coverage, the ray-theory approximation and regularization of the inversion. Comparison of the traveltime delays produced by a
100-km-diameter conduit as measured at short (1 s) and long (∼20 s) periods demonstrate that such a conduit cannot satisfy the observed traveltime delays. Thus the width of the upwelling conduit
beneath Iceland must lie in the range of 100 to 200 km. Separate tests on the minimum depth extent of the anomaly show that significant low velocities are required to 350 km depth. Should the true
conduit be at the narrower end of the possible range, both compressional and shear wave perturbations greater than 10 per cent would be required to depths of at least 350 km. Mineral physics
experiments indicate that such velocity anomalies would in turn require the presence of partial melt or some other fluids to these depths. These bounds on the allowed velocity structure beneath
Iceland provide a constraint on geodynamic models for the generation of the Iceland hotspot, whether it is the result of a top-down or bottom-up process.
All Science Journal Classification (ASJC) codes
• Geophysics
• Geochemistry and Petrology
• Iceland
• Ray theory
• Resolution
• Seismic tomography
• Spectral-element method
Dive into the research topics of 'Resolution of regional seismic models: Squeezing the iceland anomaly'. Together they form a unique fingerprint. | {"url":"https://collaborate.princeton.edu/en/publications/resolution-of-regional-seismic-models-squeezing-the-iceland-anoma","timestamp":"2024-11-01T22:57:27Z","content_type":"text/html","content_length":"57491","record_id":"<urn:uuid:de69edd4-8753-4214-8937-d90994bd6563>","cc-path":"CC-MAIN-2024-46/segments/1730477027599.25/warc/CC-MAIN-20241101215119-20241102005119-00338.warc.gz"} |
logdet is used to define objective functions in determinant maximization problems.
This command is for specifying an objective function in combination with primarily sdpt3 which supports logdet terms natively.
If you use the exponential cone capable solver mosek, you can use log(geomean(x)) as an equivalent expression.
If you use any other SDP solver, use the geomean operator instead to work with the product of the eigenvalues (and thus the determinant). Note that the operator is concave and thus only can be
maximized (or minimized if negated).
YALMIP will automatically replace the logdet term in an objective with a geomean when you use an SDP solver other than sdpt3, and the objective only contains the negated logdet term. This is valid
since the two functions are monotonically related.
If you have a logdet operator on a variable \(X\), the constraint \(X \succeq 0\) should not be added to the model. It is automatically assumed by the solver.
If you want to work with determinants in a less structured fashion without a logdet capable solver, make sure to read the documentation on the det command. | {"url":"https://yalmip.github.io/command/logdet/","timestamp":"2024-11-09T16:45:58Z","content_type":"text/html","content_length":"29855","record_id":"<urn:uuid:24b62f2b-3b7e-4ef4-95d7-95dab00d55b8>","cc-path":"CC-MAIN-2024-46/segments/1730477028125.59/warc/CC-MAIN-20241109151915-20241109181915-00300.warc.gz"} |
Least Squares Fitting--Exponential -- from Wolfram MathWorld
To fit a functional form
take the logarithm of both sides
The best-fit values are then
This fit gives greater weights to small
Applying least squares fitting gives
Solving for
In the plot above, the short-dashed curve is the fit computed from (◇) and (◇) and the long-dashed curve is the fit computed from (9) and (10). | {"url":"https://mathworld.wolfram.com/LeastSquaresFittingExponential.html","timestamp":"2024-11-01T21:00:46Z","content_type":"text/html","content_length":"59602","record_id":"<urn:uuid:a036ca08-9fb2-4546-aaec-0c9ee08934ad>","cc-path":"CC-MAIN-2024-46/segments/1730477027552.27/warc/CC-MAIN-20241101184224-20241101214224-00070.warc.gz"} |
How to solve linear equation on a ti84
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of Linear Equations From: City 17
Literal Equations &
Equations and
Inequalities with Homuck Posted: Friday 05th of Jan 08:33
Absolute Value I recommend trying out Algebrator. It not only assists you with your math problems, but also displays all the required steps in detail so
Rational Expressions that you can enhance the understanding of the subject.
SOLVING LINEAR AND
Steepest Descent for Registered:
Solving Linear Equations 05.07.2001
The Quadratic Equation From: Toronto,
Linear equations in two Ontario
how to solve linear equation on a ti84
Related topics:
Home online algebra2 calculator | primary gcf worksheets | homework of chapter 18 of abstract algebra + dummit and foote | study of functions in algebra | maple solve
Rational Expressions system of non-linear equations | algebra with pizzazz answers | substitution method | 4th class power engineer cheats | solving nonlinear equations in matlab |
Graphs of Rational online graphing calculator plotting | half-life word problems in algebra | solving nonlinear equations in matlab | history of mathamatics | "ti 83 plus" "linear
Functions equations" solve
Solve Two-Step Equations
Multiply, Dividing;
Exponents; Square Roots; Author Message
and Solving Equations
LinearEquations goebald72 Posted: Friday 29th of Dec 09:04
Solving a Quadratic Hey guys ,I was wondering if someone could explain how to solve linear equation on a ti84? I have a major assignment to complete in a
Equation couple of months and for that I need a thorough understanding of problem solving in topics such as rational equations, side-side-side
Systems of Linear similarity and graphing circles. I can’t start my assignment until I have a clear understanding of how to solve linear equation on a ti84
Equations Introduction since most of the calculations involved will be directly related to it in some form or the other. I have a question set , which if someone
Equations and Registered: can help me solve, would help me a lot.
Inequalities 01.02.2007
Solving 2nd Degree From: Paris (I love
Equations U)
Review Solving Quadratic
System of Equations
Solving Equations & nxu Posted: Saturday 30th of Dec 17:25
Inequalities Sounds like your concepts are not strong. Excelling in how to solve linear equation on a ti84 requires that your concepts be strong . I
Linear Equations know students who actually start tutoring juniors in their first year. Why don’t you try Algebrator? I am quite sure, this program will
Functions Zeros, and help you.
Rational Expressions and Registered:
Functions 25.10.2006
Linear equations in two From: Siberia,
variables Russian Federation
Lesson Plan for
Comparing and Ordering
Rational Numbers
LinearEquations sxAoc Posted: Sunday 31st of Dec 19:34
Solving Equations Hi there! I used Algebrator last year when I was having problems with my college math. This software made solving problems so easy. Since
Radicals and Rational then, I always keep a copy of it on my computer .
Solving Linear Equations
Systems of Linear Registered:
Equations 16.01.2002
Solving Exponential and From: Australia
Logarithmic Equations
Solving Systems of
Linear Equations
DISTANCE,CIRCLES,AND EGdigeCOT Posted: Tuesday 02nd of Jan 10:53
QUADRATIC EQUATIONS I’m going to grab a copy for me program right away. But the question is , where can I get it? Anyone?
Solving Quadratic
Quadratic and Rational
Inequalit Registered:
Applications of Systems 19.06.2006
of Linear Equations in From:
Two Variables
Systems of Linear
Test Description for Dnexiam Posted: Wednesday 03rd of Jan 08:57
RATIONAL EX This one is actually quite unique . I am recommending it only after using it myself. You can find the information about the software at
Exponential and https://rational-equations.com/steepest-descent-for-solving-linear-equations.html.
Logarithmic Equations
Systems of Linear
Equations: Cramer's Rule Registered:
Introduction to Systems 25.01.2003
of Linear Equations From: City 17
Literal Equations &
Equations and
Inequalities with Homuck Posted: Friday 05th of Jan 08:33
Absolute Value I recommend trying out Algebrator. It not only assists you with your math problems, but also displays all the required steps in detail so
Rational Expressions that you can enhance the understanding of the subject.
SOLVING LINEAR AND
Steepest Descent for Registered:
Solving Linear Equations 05.07.2001
The Quadratic Equation From: Toronto,
Linear equations in two Ontario
Rational Expressions
Graphs of Rational
Solve Two-Step Equations
Multiply, Dividing;
Exponents; Square Roots;
and Solving Equations
Solving a Quadratic
Systems of Linear
Equations Introduction
Equations and
Solving 2nd Degree
Review Solving Quadratic
System of Equations
Solving Equations &
Linear Equations
Functions Zeros, and
Rational Expressions and
Linear equations in two
Lesson Plan for
Comparing and Ordering
Rational Numbers
Solving Equations
Radicals and Rational
Solving Linear Equations
Systems of Linear
Solving Exponential and
Logarithmic Equations
Solving Systems of
Linear Equations
Solving Quadratic
Quadratic and Rational
Applications of Systems
of Linear Equations in
Two Variables
Systems of Linear
Test Description for
RATIONAL EX
Exponential and
Logarithmic Equations
Systems of Linear
Equations: Cramer's Rule
Introduction to Systems
of Linear Equations
Literal Equations &
Equations and
Inequalities with
Absolute Value
Rational Expressions
SOLVING LINEAR AND
Steepest Descent for
Solving Linear Equations
The Quadratic Equation
Linear equations in two
how to solve linear equation on a ti84
Related topics:
online algebra2 calculator | primary gcf worksheets | homework of chapter 18 of abstract algebra + dummit and foote | study of functions in algebra | maple solve system of non-linear
equations | algebra with pizzazz answers | substitution method | 4th class power engineer cheats | solving nonlinear equations in matlab | online graphing calculator plotting | half-life
word problems in algebra | solving nonlinear equations in matlab | history of mathamatics | "ti 83 plus" "linear equations" solve
Author Message
goebald72 Posted: Friday 29th of Dec 09:04
Hey guys ,I was wondering if someone could explain how to solve linear equation on a ti84? I have a major assignment to complete in a couple of months and for that I
need a thorough understanding of problem solving in topics such as rational equations, side-side-side similarity and graphing circles. I can’t start my assignment
until I have a clear understanding of how to solve linear equation on a ti84 since most of the calculations involved will be directly related to it in some form or the
other. I have a question set , which if someone can help me solve, would help me a lot.
From: Paris (I love
nxu Posted: Saturday 30th of Dec 17:25
Sounds like your concepts are not strong. Excelling in how to solve linear equation on a ti84 requires that your concepts be strong . I know students who actually
start tutoring juniors in their first year. Why don’t you try Algebrator? I am quite sure, this program will help you.
From: Siberia,
Russian Federation
sxAoc Posted: Sunday 31st of Dec 19:34
Hi there! I used Algebrator last year when I was having problems with my college math. This software made solving problems so easy. Since then, I always keep a copy of
it on my computer .
From: Australia
EGdigeCOT Posted: Tuesday 02nd of Jan 10:53
I’m going to grab a copy for me program right away. But the question is , where can I get it? Anyone?
Dnexiam Posted: Wednesday 03rd of Jan 08:57
This one is actually quite unique . I am recommending it only after using it myself. You can find the information about the software at https://rational-equations.com/
From: City 17
Homuck Posted: Friday 05th of Jan 08:33
I recommend trying out Algebrator. It not only assists you with your math problems, but also displays all the required steps in detail so that you can enhance the
understanding of the subject.
From: Toronto,
Author Message
goebald72 Posted: Friday 29th of Dec 09:04
Hey guys ,I was wondering if someone could explain how to solve linear equation on a ti84? I have a major assignment to complete in a couple of months and for that I need a
thorough understanding of problem solving in topics such as rational equations, side-side-side similarity and graphing circles. I can’t start my assignment until I have a clear
understanding of how to solve linear equation on a ti84 since most of the calculations involved will be directly related to it in some form or the other. I have a question set ,
which if someone can help me solve, would help me a lot.
From: Paris (I love
nxu Posted: Saturday 30th of Dec 17:25
Sounds like your concepts are not strong. Excelling in how to solve linear equation on a ti84 requires that your concepts be strong . I know students who actually start tutoring
juniors in their first year. Why don’t you try Algebrator? I am quite sure, this program will help you.
From: Siberia,
Russian Federation
sxAoc Posted: Sunday 31st of Dec 19:34
Hi there! I used Algebrator last year when I was having problems with my college math. This software made solving problems so easy. Since then, I always keep a copy of it on my
computer .
From: Australia
EGdigeCOT Posted: Tuesday 02nd of Jan 10:53
I’m going to grab a copy for me program right away. But the question is , where can I get it? Anyone?
Dnexiam Posted: Wednesday 03rd of Jan 08:57
This one is actually quite unique . I am recommending it only after using it myself. You can find the information about the software at https://rational-equations.com/
From: City 17
Homuck Posted: Friday 05th of Jan 08:33
I recommend trying out Algebrator. It not only assists you with your math problems, but also displays all the required steps in detail so that you can enhance the understanding
of the subject.
From: Toronto,
Posted: Friday 29th of Dec 09:04
Hey guys ,I was wondering if someone could explain how to solve linear equation on a ti84? I have a major assignment to complete in a couple of months and for that I need a thorough understanding of
problem solving in topics such as rational equations, side-side-side similarity and graphing circles. I can’t start my assignment until I have a clear understanding of how to solve linear equation on
a ti84 since most of the calculations involved will be directly related to it in some form or the other. I have a question set , which if someone can help me solve, would help me a lot.
Posted: Saturday 30th of Dec 17:25
Sounds like your concepts are not strong. Excelling in how to solve linear equation on a ti84 requires that your concepts be strong . I know students who actually start tutoring juniors in their
first year. Why don’t you try Algebrator? I am quite sure, this program will help you.
Posted: Sunday 31st of Dec 19:34
Hi there! I used Algebrator last year when I was having problems with my college math. This software made solving problems so easy. Since then, I always keep a copy of it on my computer .
Posted: Tuesday 02nd of Jan 10:53
I’m going to grab a copy for me program right away. But the question is , where can I get it? Anyone?
Posted: Wednesday 03rd of Jan 08:57
This one is actually quite unique . I am recommending it only after using it myself. You can find the information about the software at https://rational-equations.com/
Posted: Friday 05th of Jan 08:33
I recommend trying out Algebrator. It not only assists you with your math problems, but also displays all the required steps in detail so that you can enhance the understanding of the subject. | {"url":"https://rational-equations.com/in-rational-equations/y-intercept/how-to-solve-linear-equation.html","timestamp":"2024-11-06T05:21:51Z","content_type":"text/html","content_length":"101215","record_id":"<urn:uuid:4517238d-8785-4d47-8822-ebcb050190c5>","cc-path":"CC-MAIN-2024-46/segments/1730477027909.44/warc/CC-MAIN-20241106034659-20241106064659-00292.warc.gz"} |
Oxford and Cambridge Lecture Out-takes
This lecturer seems to have a tautology problem:
• “A mapping is 1-1 and onto if and only if it is 1-1 and onto.”
From a lecturer who knows exactly what he intends to do:
• “….and now we need to increase n. The best way to increase n is to increase n.”
Obviously a student who didn’t like his lecturer:
• “I didn’t think he could live down to his reputation, but he did.”
Another dissatisfied student?:
• “Oh dear, where’s my rifle….”
Referring to exams? I hope not…:
• “…because if you’re dead earlier, you certainly are dead later on…”
Good helpful instruction here:
• “You could sort a sequence by assigning 1,2,3… to it. That’s the fastest sort routine I know of!”
Confused medium?:
• “Please yell out if there are any typing errors”
In the middle of a difficult proof:
• “This is the stage where I start to pray”…
followed by…
“Somebody up there is being kind to me, are they? No.”
followed by…
“I’ve done something silly with a square root of 2.”
Guess which subject:
• “I have a personality disorder: I don’t like to assume things are measurable.”
More Lebesgue Integration quotes:
• “You can sleep if you want.”
• “It’s delicate to get your hands on it.”
• “Will we all agree to shut that one in a cupboard?”
• “Well we can’t quite stop yet – although I am tempted…”
Sounds too good to be true:
• “This is fun: lots of magical ways to solve differential equations!”
Any idea of the context of this one?:
• “If you watch T.V. you see there are such things as Marathons”
A disillusioned lecturer:
• “In the old days, the pure days…”
A weensy big headed, are we?:
• “I’m just showing off, seeing how fast I can do them…”
Some quotes from a statistics lecturer:
• “This is a stupid example – you can see why; it’s an exam question.”
• “We observe approximate approximation to …. “
A hopeful Rings and Groups lecturer:
• “… a cube, so it has 8 faces … “
A lecturer nicknamed ‘Hurricane’:
• “OK? Well, not very ok but you can find the mistake yourself”
followed by…
“Whatever you need to get the answer”
An undergraduate talking about Fermat’s last theorem, so I am told…:
• “A millionth of a second is virtually forever”
• “It doesn’t really make a lot of difference between 8 and 33”
Yet *more* Lebesgue integration quotes:
• “Integration by parts is not economical on paper”
• “I can’t be bothered. Can’t we just go back and……”
• “It’s all so simple it’s hard to remember”
• “I worked it out last night – let’s see if it works in the daylight”
This term’s contradictions prize:
• “I want to stop looking at inhomogeneous equations and start looking at inhomogeneous equations”
Nope, this isn’t ‘Hurricane’:
• “Imagine me running towards you at root-three-over-two c”
Physicists? Thick?:
• ” ‘3+1′ is physicists’ notation for ‘4’ “
You’ll never guess what – we had an incredibly quotable Lebesgue integration lecturer:
• “Has anyone got it out yet? (Pause) You’re not doing it are you?”
• “It looks an incredibly integrable function”
• “Proof’s easy, by the way, provided I keep my act together”
• [to a moving blackboard] “SIT!!!”
• “Sorry about that – I’m teaching this to some engineers…they’d have a fit if they saw” [a Lipschitz condition]
• “My mind’s gone crazy again”
• “I’ll just reassmble the duster”
• “Take the computer and it will do lotsof things while you’re at the pub”
• “In lectures, everywhere you have chaos”
Some quotes from a Rings and Groups lecturer:
• “Examples come in two types: interesting ones and examination ones”
• “This [z->conj(z)] is worse than bad”
• “Now I run down the r’s and up the b’s”
• “Just send one of the 1st years to check…”
A confuddled lecturer:
• “Is this the right lecture theatre?”
Do I really need to tell you where these came from?:
• “The proof is not required for finals, but I’m going to give you it anyway because it’s nice.”
• “multiplied by the stupid derivative dFx”
• “I’d thought we’d spend the rest of the day in light entertainment: Let’s do some schools questions!”
• “Questions are easy, with a bit of luck”
• “Tonelli would tell us…” (undergraduate) “No he wouldn’t, he’s dead”
• “Knock that sign for 6 and use Tonelli somewhere”
• “If you want to cut corners, an intelligent corner to cut is not to learn the proofs of any of these theorems”
• “And that’s the singularity that’s going to save our bacon”
• “I’ll take a special delta when I see what I need”
• “And the Riemann-Lebesgue lemma zaps it again”
• “I am falling into a trap. I assume I know it’s there – I want to fall into it”
• “If x were negative this would go sky-high – it would blast off the map”
• “Can I bring along an elephant and some trumpets to draw your attention…”
• “Pinch yourself, kiss your neighbour, anything to draw attantion to this” (loud kissing sound of student kissing neighbour)
• “Let me make a mistake now”
• “Meanwhile back at the ranch…”
• “It’s my lucky day!” [after a double-cancelling error]
• “I actually like integrating”
• “I love integrating” [Referring to previous lecturer]
• “That woman can’t clean the board. I pay someone to clean the floor at home and then I come here and spend 15 minutes mucking around”
• “We could do it if we could pull the sum sign through and that’s what God gave us the monotone convergence theorem for”
• “…and at this stage your heart should have a slight hiccup”
• “…and at this stage you should go and have a beer”
• “I’ll massage this into a shape you can use the MCT on”
• “Now we go into automatic drive and finish this off”
• “I’m going to use this diagram. It’s not completely silly”
After turning out all the lights:
• “So that’s what these switches do!”
From analysis lectures:
• “The fact they’re called divided differences suggests that they are the difference of 2 things divided by something”
• “10! is fairly small”
A different quotable lecturer:
• “Are you bored?” [Students shout Yes]
• “Are you mega-bored?” [Students shout YES]
• “What a waste of life is coming to Oxford to get bored in lectures.”
A talkative lecturer:
• “No, let me stop gibbering my mouth off without thinking about it beforehand… and I’ve just shot myself in the foot”
Obviously good at making mistakes:
• “I’ve just realised I’ve done something crazy…in the notes this time”
A sad lecturer’s tale:
• “I used to be quite clever – it’s the drink”
Proof technique obviously ok:
• “Well I guess that’s a respectable proof actually”
More of the prolific lecturer:
• “You keep thinking you’ve got over the hiccups and then they come back again”
• “I like it. (referring to a lemma) It looks upside down to me.”
• “…there’s the following delicious little proof”
• “I’ve got two 2’s, the third should be a 3”
• “Let’s fall into the trap – let’s do the obviuos thing”
• “(referring to a function) It looks like a case of Carling Black Label”
• “The trick is not to write anything”
• “Ugh. This is horrid, isn’t it”
• “It will enable you to pull derivavtives through integrals, which you have wanted to do all your life – and some of you have been. This tells you when you can legally do it.”
Who said proofs were legal?:
• “Watch this proof carefully – it looks like a confidence trick”
Remember continuity and differentiablity?:
• “In other words this is going to be a 3 epsilon proof.”
Referring to Lorentz:
• “It’s a garden trellis type transformation”
• “To be consistent, call it *^(-1)”
• “We get our own back by calling rotations in the plane ‘Pseudo-Lorentz’”
From a computing lecture:
• “A degree’s worth more than a monitor”
In a differential equations lecture:
• “As you can see, these equations are very easy to remember – hold on, I’ve missed out a term…”
From a groups lecture:
• “It’s a bit like probability except that it can go negative and the integral is not normally 1”
and “I can’t possibly tell you what this is – it’s a very unpleasant space”
Starting off a course early in the year:
• “The important thing to remember about this course is that it doesn’t actually mean anything.”
My, my! Here’s a helpful topology lecturer:
• “I’ll prove it with a diagram, and next time I’ll translate it into pictures.”
From a respected computation lecturer:
• “I don’t have an I.Q.”
and(in the middle of a lecture):
“What am I doing?”
An energetic lecturer:
• “Note that one must always have his sleeves rolled up for discussing this kind of thing.”
Tautology-of-the-term prize:
• “If you start off with a 72 elements and take away half, you’re left with the other half”
This file contains a list of quotes from people in mathematical or scientific circles at Cambridge.
NOTE: knowing some of my lecturers, this is very probably true! – SRV
Overheard at a supervision :
• Supervisor: Do you think you understand the basic ideas of Quantum Mechanics ?
Supervisee: Ah! Well,what do we mean by “to understand” in the context of Quantum Mechanics?
Supervisor: You mean”No”,don’t you?
Supervisee: Yes.
The Tautology prize goes to the lecturer who uttered the gem:
• “If we complicate things they get less simple.”
This year’s modesty award is given for a phrase spoken by a lecturer after a rather difficult concept had just been introduced.
• “You may feel that this is a little unclear but in fact I am lecturing it extremely well.”
Overheard at last year’s Archimedeans’ Garden Party :
• “Quantum Mechanics is a lovely introduction to Hilbert Spaces !”
A Senior mathematician was asked which language he used for some of his computing. He replied that he used a very high level language: RESEARCH STUDENT
From an algebra lecture:
• “A real gentleman never takes bases unless he really has to.”
From the same lecturer:
• “This book fills a well needed gap in the literature.”
And another encouraging book review:
• “This book is only for the serious enthusiast ; I haven’t read it myself.”
Two quotes from an electrical engineer (but former mathematician):
• “…but the four-colour theorem was sufficiently true at the time.”
• “The whole point of mathematics is to solve differential equations!”
And,as a contrast,a quote from a well known mathematician/physicist:
• “Trying to solve [differential] equations is a youthful aberration that you will soon grow out of.”
While on the subject how about this fundamental law of physics heard in General Relativity this year:
• “Nature abhors second order differential equations.”
A perplexing quote from a theoretical chemist:
• “…but it might be a quasi-infinite set.”
What is a “quasi-infinite set? Answers on a strictly finite postcard, please.
This year’s Modesty Prize is awarded to the lecturer who said :
• “Of course,this isn’t really the best way to do it.But seeing as you’re not quite as clever as I am – in fact none of you are anywhere near as clever as I am – we’ll do it this way.”
From the same lecturer :
• “Now we’ll prove the theorem. In fact I’ll prove it all by myself.”
And from a particle physics course :
• “This course will contain a lot of charm and beauty but very little truth.”
A comparison between the programming languages BCPL and BSPL :
• “Like BCPL you can omit semicolons almost anywhere.”
At the beginning of a course it is important to reassure the audience about how straight-forward the course is and about how good the lectures are going to be. But what about this quote from the
beginning of the Galois Theory course:
• “This is going to be an adventure for you…and for me.”
Or this one from Statistical Physics:
• “At the meeting in August I put my name down for this course becase I knew nothing about it.”
In the middle of the Stochastic Systems course the lecturer offered this piece of careers advice:
• “If you haven’t enjoyed the material in the last few lectures then a career in chartered accountancy beckons.”
A lecturer of Linear Systems found the following on his board when he arrived one morning:
• “Roses are red,
Violets are blue,
Greens’ functions are boring
And so are Fourier transforms. “
An engineer actually gave an answer to the question of “quasi-infinite” sets:
• “It’s one with more than ten elements.”
And they wonder why buildings fall over…
From a supervisor :
• “Any theorem in Analysis can be fitted onto an arbitrarily small piece of paper if you are sufficiently obscure.”
No matter how elegant a course is there will always be occasions when a certain about of arithmetic is called for:
• “I just want you to have a brief boggle at the belly-busting complexity of evaluating this.”
A lecturer recently started to use RUNES in his course! His justification:
• “I need an immediately distinguishable character…so I’ll use something that no-one will recognise.”
From a Special Relativity lecture:
• “…and you find you get masses of energy.”
It’s nice to see the general-purpose ‘nobbling constant’ making a welcome return to Cambridge lectures:
• “This must be wrong by a factor that oughtn’t to be too different from unity.”
A flattering comment by a student for his GR supervisor:
• “She’s the only person in DAMTP who’s a real person rather than an abstract machine for doing tripos questions. “
A worrying thought from the same student:
• “Sex and drugs? They’re nothing compared with a good proof!”
A description of a lecturer:
• “G—-‘s a maniacal pixie!!!”
A less polite description of a famous (and notorious) mathematician:
• “I personally think he’s the greatest fraud since Cyril Burt!!” – any guesses ?
Renormalisation holds no fears for this lecturer of Plasma Physics:
• “…and divergent integrals need really sleazy cutoffs.”
In the true style of Cambridge Maths Tripos we have the following:
• “Proof of Thm. 6.2 is trivial from Thm. 6.9”
Can anybody guess the context in which the following is correct ?
• “This theorem is obviously proved as 13 equals 15.”
Why do mathematicians insist on using words that already have another meaning?
• “It is the complex case that is easier to deal with.”
And from various seminars in the King’s College Research Centre:
• “…the non-uniqueness is exponentially small.”
• “I’m not going to say exactly what I mean because I’m not absolutely certain myself.”
• “It’s dangerous to name your children until you know how many you are going to have.”
• “You don’t want to prove theorems that are false.”
And that last one wins the Sybil Fawlty Prize for “Stating the Bleeding Obvious”.
A slightly more honest version of “The student can easily see that…” :
• “If you play around with your fingers for a while, you’ll see that’s true.”
Suggestions are welcome on the meaning of this:
• “If it doesn’t happen at a corner, but at an edge, it nonetheless happens at a corner.”
– Eh ?
In a Complex Variables course a long, long, LONG time ago a lecturer wanted to swap the order of an integral and an infinite sum…
• “To do this we use a special theorem…the theorem that says that secretly this is an applied maths course.”
I never name my lecturers but he’s now head of the Universities Grant Commission. And a lot of universities would like to swap him for an infinite sum.
From an Algebra III lecturer :
• “If you want to prove it the simplest thing is to prove it.”
This year’s Honesty Prize goes to the natural sciences supervisor, who replied to a question with
• “Don’t ask me. I’m not a mathmo.”
And from Oxford…
• “This does have physical applications. In fact it’s all tied up with strings.”
Good heavens, do I see a lecturer actually noticing the existence of his audience!
• “Was that clear enough? Put up your hand if that wasn’t clear enough. Ah, I thought not.”
Snobbery or what?
• “In the sort of parrot-like way you use to teach stats to biologists, this is expected minus observed.”
• “I too would like to know what a statistician actually does.”
• “We’re not doing mathematics; this is statistics.”
Also from statistics:
• “You could define the subspace topology this way, if you were sufficiently malicious.”
• “You mustn’t be too rigid when doing Fluid mechanics.”
Talk about ulterior motives…
• “This handout is not produced for your erudition but merely so I can practice the TeX word-processor.”
From 1A NatSci “Cells” course:
• “There are two proteins involved in DNA synthasis, they are called DNAsynthase 1 and DNAsynthase 3”
From a Part 2 Quantum Mechanics lecture:
• “Just because they are called ‘forbidden’ transitions does not mean that they are forbidden. They are less allowed than allowed transitions, if you see what I mean.”
From an IBM Assembler lecture:
• “If you find bear droppings around your tent, it’s fairly likely that there are bears in the area.”
A Biochemistry paper included an analysis of a previously undiscovered sugar named by the researchers “godnose” .
From a 1B Electrical Engineering lecture:
• “This isn’t true in practice – what we’ve missed out is Stradivarius’s constant.”
And then the aside:
• “For those of you who don’t know, that’s been called by others the fiddle factor…”
One from a 1A Engineering maths lecture :
• “Graphs of higher degree polynomials have this habit of doing unwanted wiggly things.”
• “Apart from the extra line that’s a one line proof.”
• “This is a one line proof…if we start sufficiently far to the left.”
A slight difficulty occured with geometry in an Engineering lecture one day:
• “This is the maximum power triangle.” said a lecturer, pointing to a rectangle.
This year the Computer Scientists seem to be in the running for the Honesty Award:
• “Sorry, I should have made that completely clear. This is a shambles.”
From a Computer Sciences Protection lecture:
• “Who should be going to this lecture? Everyone…apart from the third year of the two-year CompSci course.”
• “I don’t want to go into this in detail, but I would like to illustrate some of the tedium.”
Oh those poor CompScis….
• “I’m not going to get anything more useful done in this lecture, so I might as well talk.”
later followed by …
“Well there you are, one lecture with no useful content.”
Three from a NatSci Physics lecturer:
• “You don’t have to copy that down — there’s no wisdom in it — it only repeats what I said. “
• “We now wish to show that they are not merely equal but _the same thing_.”
• “And before I leave this subject, I would like to tell you something interesting.”
From a first year chemistry lecture some personal problems of the lecturer:
• “Before I started this morning’s lecture I was going to tell you about my third divorce but on reflection I thought I’d better tell my wife first.”
From a single research seminar at the King’s College Research Centre:
• “I’m sure it’s right whether it’s valid or not.”
• “WARNING: There is no reason to believe this will work.” | {"url":"https://www.invariants.org.uk/a-treasury-of-mathematical-humor/oxford-and-cambridge-lecture-out-takes/","timestamp":"2024-11-06T07:20:19Z","content_type":"text/html","content_length":"99941","record_id":"<urn:uuid:eed30ebb-81af-4e6c-a602-fb6c1d3f5da4>","cc-path":"CC-MAIN-2024-46/segments/1730477027910.12/warc/CC-MAIN-20241106065928-20241106095928-00275.warc.gz"} |
Motion Vocabulary 1
• 1. Motion involves...
A) determined using a reference point
B) change in position
C) speed, veocity and acceleration
D) all of these
• 2. Time involves...
A) volume, milliliters
B) how long, seconds
C) how far, meters
D) temperature, celcius
• 3. Meters are...
A) a measurment of how much, mass
B) a measurement of distance, how far
C) a measurement of time, how long
D) a measurement of volume, liters
• 4. Distance tells us...
A) how quickly in time
B) how much in grams
C) how far in meters
D) how long in seconds
• 5. Speed involves...
A) direction only
B) time only
C) distance and time
D) distance only
• 6. Velocity is...
A) distance only
B) direction only
C) speed and direction
D) time only
• 7. Acceleration is...
A) change in velocity
B) distance only
C) time only
D) change in distance
• 8. The international system of units uses...
A) seconds
B) meters
C) liters
D) all of these
• 9. Average speed is...
A) just time
B) total distance divided by total time
C) just distance
D) your speed at that moment
• 10. Constant speed means...
A) your average speed
B) the amount of time it takes you to cover the same distance does not change
C) distance changes with time
D) your speed at that moment | {"url":"https://www.thatquiz.org/tq/preview?c=vgbx9076&s=jqccdg","timestamp":"2024-11-07T09:26:25Z","content_type":"text/html","content_length":"9745","record_id":"<urn:uuid:e9a960db-cdb9-4d58-b607-67547cef13f6>","cc-path":"CC-MAIN-2024-46/segments/1730477027987.79/warc/CC-MAIN-20241107083707-20241107113707-00360.warc.gz"} |
A "system of measurement" is also known as a "metric". The metric system was officially adopted as a standardised system of measurement by the French in the late 18th century, although it was
‘invented’ over a century earlier. Thus in this system meter, kilogram and seconds are fundamental units of measurement. Measurement Index. The ton, used to measure large masses, is equal to 2,000 lb
(short ton) or 2,240 lb (long ton). Believe it or not, the length of a ‘metre’ was derived from measurements of the earth’s circumference, which at the time aroused much curiosity and suspicion!
Different systems of measurement also developed over time in Asian countries. The Metric System of Measurement; Metric Numbers; US Standard Units. To keep like measurements together, physicists and
mathematicians have grouped them into measurement systems. English system - a system of weights and measures based on the foot and pound and second and pint The metric system is a system of measuring
based on the meter, kilogram and second. 2. The U.S. The US is the only industrialized nation that does not mainly use the metric system in its commercial and standards activities. The two major
systems of measurement in use in the world are the U.S. Customary System of measurement and the International System of Units, commonly known as the metric system. Due to this common heritage, the
two systems are fairly similar, but there are certain … The US fluid gallon was defined as 231 cubic inches. In the avoirdupois system, the most widely used of the three, the pound is divided into 16
ounces (oz) and the ounce into 16 drams. Measuring Capacity. Introduction to the Metric System (with Maggie!) international … There are many systems of measurement. The metric system, also known as
the International System of Units (SI), is a system of measurement that is built on three main units: meters, liters, and grams. Introduction to Measurement SOL 6.9 By: Jennifer Del-Castillo John F.
Kennedy Middle School What you need to know First things first, you need to understand the basics There are two systems of measurement US/Customary System which we use here Then there is the metric
system which is used all over the world Measurement Basics Length: is the distance of something measured Volume/Capacity: … Introduction to US Standard Units (with Maggie!) Measurement definition: A
measurement is a result , usually expressed in numbers , that you obtain by measuring... | Meaning, pronunciation, translations and examples The ENGLISH system of linear measurement is based on
inches, feet, yards; 12 inches in a foot, 3 feet in a yard, 5,280 feet in a mile, etc. Both Imperial and USC units sub-divide a gallon into four quarts, eight … SI system: The SI … The US English
System of measurement grew out of the manner in which people secured measurements using body parts and familiar objects. … It actually consists of two related systems—the U.S. Although use of the
metric system has been sanctioned by law in the US since 1866, it has been slow in displacing the American adaptation of the British Imperial System known as the US Customary System. In China, the
first emperor Shi Huang Di created a system of weights and … There are two main systems for measuring distances and weight, the Imperial System of Measurement and the Metric System of Measurement.
Weight: Weight measures the heaviness of something. dram A dram is about as much liquid as one would take in a dose of medicine (the customary use of the word) or poison (the dramatic use of the
word) or spirituous liquor (the humorous use of the word, since a dram is much too small to be considered a … However, it is the simplicity of the system that led to its rapid adoption throughout …
This system was used in France and number of other European countries. We are one of the few countries … Length or distance units include the inch, foot, yard and mile.. Land units include square
miles (2589998.47032 square meter) and acres (4046.8726 square meter).. Common volume units are the teaspoon, tablespoon (3 teaspoons), … It is also called the International System of Units, or SI..
Units of measure in the metric system include: The units of length or linear size are based on the metre.They include the kilometre (km) which is 1,000 metres, the centimetre (cm), and the millimetre
(mm) which is 1/1,000th of a metre. Since 1959, the avoirdupois pound has been officially defined in most English-speaking countries as 0.45359237 kilograms. ; The unit of volume is the litre.It is
used … The majority of the world uses the metric measuring system. The Imperial System is also called The British Imperial because it came from the British Empire that ruled many parts of the world
from the 16th to the 19th century. In 1824 various different volume units of measurement, in use across the British Empire, were replaced with a single system based on the Imperial gallon. At the
same time, the US Armed Forces and medical and scientific communities … In Great Britain the stone, equal to 14 lb, is also used. Also, NASA accounts both English and Metric system abroad the
International Space Station. The United States Customary System The United States Customary System (USCS) was based on the British Imperial System, and many use the term “imperial system,” or IS, to
describe both of these systems today. The minim, as the name implies, is the smallest liquid measure in the English system — 1 60 of a dram by definition, about as much liquid as will form a drop.
The US continued to use the “obsolete” Winchester measure and formally adopted it in 1836 to define the US dry gallon. U.S customary units is the system of units of measurement used to measure things
in the United States.The system of Imperial units is similar and in some parts identical.. Noun: 1. 2.2 The international system of units 2.3 Measurement of length 2.4 Measurement of mass 2.5
Measurement of time 2.6 Accuracy, precision of instruments and errors in measurement 2.7 Significant figures 2.8 Dimensions of physical quantities 2.9 Dimensional formulae and dimensional equations
2.10Dimensional analysis and its applications Summary Exercises Additional exercises. The NASA (National Aeronautics and Space Administration) has apparently used the metric system of measurements
since about 1990, the statement revealed, but English measurement units are still adopted on some missions, and only a few projects use both. A system of measurement is a set of related measures that
are used to give a numeric value to something. Measurement is finding a number that shows the size or amount of something. Check out the units used in your steep tape measure, most likely they are
inches and centimeters. Metric System of Measurement (Correctly called "SI") The metric system is a system of measuring. Customary System of units, used in the United States and dependencies, and the
British Imperial System. Them are generally the same in both systems, … measurement Index performance, distance... Measurement have historically been important, regulated and defined for the purposes
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system of.. To provide you with relevant advertising … Noun: 1 was defined as 231 inches! Were under its rule countries … to most people in the United States of America number! Of an object, and
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system of measurement also developed over time in Asian countries finding a number that shows the or! | {"url":"http://jakesonline.org/2l962d6/what-is-english-system-of-measurement-dd0faf","timestamp":"2024-11-02T06:15:09Z","content_type":"text/html","content_length":"25721","record_id":"<urn:uuid:55f84d36-dfc7-4d32-b1ae-4519cf4ccfe1>","cc-path":"CC-MAIN-2024-46/segments/1730477027677.11/warc/CC-MAIN-20241102040949-20241102070949-00586.warc.gz"} |
Setting Realistic PPC Goals With Growth Modeling - Theadexperts
Let’s suppose you’re leading the PPC strategy for a new ecommerce client. They’ve tasked you with helping them hit $1m monthly revenue by the end of the year.
You know a bit about their business already: they did $250k in revenue last month, and the average customer spends $100 on their store. This is a good starting point, but now you need to figure out
how to get them to $1m.
The first thing you need to understand is whether this goal is even possible — you need an achievable goal to set the project up for success, and to set realistic expectations for your client.
If the goal is indeed possible, you’ll now want to know whether it’s probable — are you actually likely to hit it?
This is where a growth model can come in handy — a set of numbers and calculations that can help you answer questions like “is this possible?” and “is this probable?”, and help you “show your
workings” to the client so that they understand your plan.
Here’s how you might set up a growth model.
Model A: top-down
Last month, the client had 2,500 customers spending an average of $100 each, for $250k total revenue, and they want to hit $1m in monthly revenue by the end of the year. So, you need to 4x their
business, and you have 6 months to do it.
With a bit of number-crunching, you might end up with a model like this:
To get to $1m, you’ll need to grow their revenue by ~25% per month over the next 7 months.
This is interesting, but not terribly useful —
• 25% MoM growth might be possible for some businesses but not others. Which category does this ecommerce company fall into?
• Where will all these new users actually come from?
• How much will you have to spend to acquire these new users?
This top-down model produces a target — 25% MoM revenue growth. To figure out how to hit it, you’ll need a bottom-up approach.
Model B: bottom-up
A bottom-up model should be centered around the customer’s journey and the points in that journey that you can actually influence. Acquisition and conversion are the important steps for this
ecommerce business.
Here’s what they might look like:
1. Acquisition
□ Organic visitors
□ PPC spend
□ PPC cost per click
2. Conversion
□ Visitor → Cart conversion rate
□ Cart → Checkout conversion rate
□ Order value
Each variable above is granular enough that you can make an effort to directly influence it — if you want to increase paid visitors, you could spend more on ads. If you want to increase Cart →
Checkout conversion, you can try reducing friction. If you want to increase order value, you can experiment with promotions.
By doing some simple calculations, you can create a simple model that represents the variables above. And to figure out the current values for each variable, you can get the latest numbers from the
You’ll know that your model is reasonable if it produces a revenue number close to the actual revenue last month ($250k).
Now that you have a model, you can use it to answer your questions.
Question 1: Is hitting the goal possible?
Your model tells you that if everything carries on unchanged, you’ll stay at $250k per month until the end of the year. It’s your job to work backward from the goal to figure out what inputs will get
you to $1m.
It’ll likely be a combination of things —
• Increasing paid visitors
• Improving conversion rates
• Increasing order value
After playing with those numbers, you find a set of inputs that will let you hit your goal:
• Increase PPC spend from $6,000 to $40,000 per month, maintaining a CPC of $1
• Increase visitor → cart conversion rate from 10% to 17%
• Increase cart → checkout conversion rate from 80% to 94%
The model has done something useful — those inputs don’t seem too crazy, so you know that it’s at least possible to hit the goal.
Possible is a good start, but if it turns out to be possible but very unlikely, then your clients will probably end up disappointed.
Question 2: Is hitting the goal probable?
In reality, there’s a lot of uncertainty around every number in your model:
• The CPC could be anywhere from $0.80 – $1.60
• Conversion rates fluctuate every month
• Customer orders generally range from $10 – $180 ($100 was just an average)
You ideally want a bit of breathing room — even if a few things don’t go according to plan, you still want to be able to hit your goals. To do this, you need your model to account for uncertainty.
Uncertainty with spreadsheets
You can deal with uncertainty manually in a spreadsheet using “best-case”, “base-case”, and “worst-case” scenarios for each variable.
This is very cumbersome, and adds a lot of complexity to your model — each input will have 3 separate cells, and each calculation will have 3 separate values — your spreadsheet will triple in size.
It also only shows you specific best-case, base-case, and worst-case scenarios, which don’t tell you the specific likelihood of hitting a particular number.
Uncertainty with standalone tools
An alternative is to use a modeling tool designed to work with uncertainty, like Causal.
Embedded below is an ecommerce growth model built in Causal. It’s interactive, so you can play with the numbers, and you can easily account for uncertainty by using ranges (“$0.80 to $1.60”) instead
of single numbers (“$1”)
With this model, you can see the full range of possible outcomes for your project, and see the probability of hitting your goal at the end of the year. It’s up to you and the client to decide how
much risk to take on — do you want to be 80% confident in hitting the goal, or 90%, or higher?
Communicating your strategy to the client is important for setting expectations and keeping everyone aligned. Causal makes this easy by giving you an interactive dashboard that you can use with
clients, letting you adjust assumptions and simulate scenarios in real-time:
A solid growth model lets you and your clients set realistic goals, and develop a strategy to hit them. It’s important for your model to account for uncertainty so that you can manage client
expectations and develop winning strategies. And it’s crucial to communicate all of this clearly and transparently so that all parties are on the same page.
Happy growth modeling! | {"url":"https://theadexperts.co.uk/setting-realistic-ppc-goals-with-growth-modeling/","timestamp":"2024-11-06T01:08:36Z","content_type":"text/html","content_length":"99335","record_id":"<urn:uuid:1b68a9f0-969f-4710-b7ad-14ba7f9d7abc>","cc-path":"CC-MAIN-2024-46/segments/1730477027906.34/warc/CC-MAIN-20241106003436-20241106033436-00372.warc.gz"} |
Counting Palindromes
Problem C
Counting Palindromes
A palindrome number is a non-negative number without leading zeroes, that reads the same forward or backward. For example, $12321$, $44$ and $9$ are palindrome numbers, while $010$, $123$ and $100$
are not.
Given a positive integer $n$, a prime number $p$ and a non-negative integer $k$ less than $p$. A palindrome number $x$ is called a good palindrome, iff $x$ is equal to $k$ modulo $p$. In other words,
the remainder when $x$ is divided by $p$ equals $k$.
Please count the number of good palindromes with exactly $n$ digits. As this number can be very large, please calculate the result modulo $10^9 + 7$.
The input contains $3$ integers $n$, $p$ and $k$ $(1 \le n \le 10^{18}, 2 \le p \le 1\, 000, 0 \le k < p)$. It is guaranteed that $p$ is a prime.
Output a single integer — the number of good palindromes with exactly $n$ digits, modulo $10^9 + 7$.
Explanation of Sample input
The good palindromes are $0$, $2$, $4$, $6$ and $8$.
Sample Input 1 Sample Output 1 | {"url":"https://danang19.kattis.com/contests/danang19/problems/countingpalindromes","timestamp":"2024-11-07T01:08:32Z","content_type":"text/html","content_length":"27677","record_id":"<urn:uuid:d2c0f6a8-8dba-4730-9c54-784da4f672c9>","cc-path":"CC-MAIN-2024-46/segments/1730477027942.54/warc/CC-MAIN-20241106230027-20241107020027-00577.warc.gz"} |
On continued fraction expansions of quadratic irrationals in positive characteristic
Let R D F[q][Y ] be the ring of polynomials over a finite field F[q], let K D F[q]((Y -^1) be the field of formal Laurent series over F[q], let f 2 K be a quadratic irrational over F[q].Y / and let P
2 R be an irreducible polynomial. We study the asymptotic properties of the degrees of the coefficients of the continued fraction expansion of quadratic irrationals such as P ^n f as n→+ ∞, proving,
in sharp contrast with the case of quadratic irrationals in R over Q considered in [1], that they have one such degree very large with respect to the other ones. We use arguments of [2] giving a
relationship with the discrete geodesic flow on the Bruhat–Tits building of .PGL[2]; K/ and, with A the diagonal subgroup of PGL[2].K/ ^y , the escape of mass phenomena of [7] for A-invariant
probability measures on the compact A-orbits along Hecke rays in the moduli space PGL[2].R/n PGL[2].K/ ^y
• Artin map
• Bruhat-Tits tree
• Bruhat–Tits tree
• Continued fraction expansion
• Hecke tree
• Positive characteristic
• Quadratic irrational
• continued fraction expansion
• positive characteristic
All Science Journal Classification (ASJC) codes
• Discrete Mathematics and Combinatorics
• Geometry and Topology
Dive into the research topics of 'On continued fraction expansions of quadratic irrationals in positive characteristic'. Together they form a unique fingerprint. | {"url":"https://cris.iucc.ac.il/en/publications/on-continued-fraction-expansions-of-quadratic-irrationals-in-posi","timestamp":"2024-11-13T04:30:36Z","content_type":"text/html","content_length":"50083","record_id":"<urn:uuid:2a8c7c33-a052-44ce-95eb-d3030008027b>","cc-path":"CC-MAIN-2024-46/segments/1730477028326.66/warc/CC-MAIN-20241113040054-20241113070054-00762.warc.gz"} |
Adding An Equal Sign Tool In Excel - ExcelAdept
Key Takeaway:
• The Equal Sign Tool is essential for performing calculations in Excel: It is the primary way to begin any formula in Excel, and without it, calculations cannot be performed.
• Adding the Equal Sign Tool in Excel is a simple process: Users can easily enable the feature by checking the “Use the formula bar to enter formulas” box in the Formulas section under Options.
This will enable the Equal Sign Tool to appear automatically in the formula bar.
• Using the Equal Sign Tool in Excel allows for more efficient and accurate calculations: It ensures that Excel recognizes any input as a formula, eliminating the need to manually type “= ” before
every formula. This helps to reduce errors and speeds up the calculation process.
Are you struggling to add equal signs in Excel? With this simple guide, you’ll learn how to quickly and easily add an equal sign tool to your Excel spreadsheet. Stop wasting precious time clicking
and typing – the solution is just a few steps away!
Why is the Equal Sign Tool important in Excel?
The equal sign tool is a fundamental feature of Excel since it is utilized to define formulas in the software. With this tool, users can create formulas for calculations to generate desired results.
This feature is crucial and saves time in performing arithmetic calculations involved. Moreover, it makes the Excel spreadsheet more efficient by helping users avoid manual computation errors. What’s
more, the software enables users to generate complex calculations and make numerous changes to the data, leading to effective interpretation and analysis of results.
It’s worth noting that using the equal sign tool in combination with other functions like sum, average, and max improves productivity and simplifies computations in the Excel spreadsheet.
Pro Tip: To ensure proper computation without errors, users should use parentheses to organize their calculations and follow the order of operations (PEMDAS) while using the equal sign tool in Excel.
Adding the Equal Sign Tool
Mastering the equal sign tool in Excel is simple! To add it:
1. Step 1 – Open Excel.
2. Step 2 – Click Options.
3. Step 3 – Select Formulas.
4. Step 4 – Check the box for “Use the formula bar to enter formulas”.
5. Step 5 – Press OK.
Then, you’ll be able to work smarter and faster in your spreadsheets.
Step 1: Open Excel
To begin with, the first step in adding an Equal Sign Tool in Excel is to open the Excel application.
Here’s a three-step guide on how to open Excel:
1. Click on the Windows Start menu icon.
2. Look for and click on the Microsoft Office option.
3. Select Microsoft Excel from the list of applications that appear.
It is worth noting that you can also launch Excel directly by searching for it via the search bar in your computer’s operating system.
Another essential detail to consider when opening Excel is ensuring that your device has Microsoft Office installed. If not, you may need to download and install it beforehand through authorized
To make the most out of this process, consider creating a shortcut on your desktop or taskbar for quick access to the application.
Finally, some suggestions for navigating Excel proficiently include utilizing keyboard shortcuts such as Ctrl + C and Ctrl + V for copy-pasting, learning functions such as SUM() and AVERAGE(), and
taking advantage of online tutorials and courses to develop your skills further. By doing so, you’ll be well-equipped to make use of all of Excel’s tools effectively.
Don’t worry, clicking on the options won’t open up a Pandora’s box of Excel nightmares…probably.
Step 2: Click on Options
To access further Excel options, proceed with the next step.
1. On the displayed screen, look for ‘File’ in the top left corner.
2. Select the option ‘Options’ near the bottom left of the window.
3. Locate and select ‘Formulas’ from the several categories listed on the left side of the screen.
4. Choose ‘Formulas AutoCorrect Options’ to open a new window.
5. In this new window, unselect ‘Enable Background Error Checking’ in order to prevent distracting red-underlining when using equal sign formulas.
6. Select OK twice to execute your changes.
One vital detail to keep in mind: Equal signs should be placed precisely where intended as they often repeat down desired cells & columns.
To improve efficiency, press F4 after selecting a cell reference inside an equal sign formula to lock either reference or both if needed. This small shortcut saves a tremendous amount of navigational
clicks and typing when repeating down several rows or columns.
Ready to unleash your inner math nerd? Step 3: Select Formulas.
Step 3: Select Formulas
To access the formulas in Excel, follow the third step and click on the relevant menu. Here are four simple steps to locate the formulas menu:
1. Look for the ‘Formulas’ tab at the top of your Excel sheet.
2. Click on it to expand a range of options, including function library, defined names, and formula auditing.
3. Select ‘Insert Function’ to search for a specific function or formula you want to add using keywords.
4. Alternatively, select ‘More Functions’ to browse through all available functions and formulas alphabetically.
It’s essential to know how to access and use formulas in Excel as they can save time and help optimize your work. With various functions available, you can perform advanced calculations without
having to manually do anything yourself.
Don’t miss out on learning how to use tools like this that could help enhance your productivity and elevate your Excel skills further! Add equal sign tool by selecting Formulas today!
Get ready to formula your way to glory with this one simple checkbox.
Step 4: Check the box for “Use the formula bar to enter formulas”
To enable the equal sign tool in Excel, it is essential to activate the “use formula bar to enter formulas” checkbox.
To enable the formula bar and use it to enter formulas, follow these 4 steps:
1. Click on “File” at the top left corner of Excel.
2. Select “Options” immediately below.
3. In the new window, select “Advanced” from the left side.
4. Look for a section that says “When calculating this workbook.” Check the box next to “Use the formula bar to enter formulas.”
It’s worth noting that this step is necessary for accurately using formulas within cells in Microsoft Excel.
Pro Tip: Activating this feature ensures that entering complex formulas such as ‘balancing multiple cells with various conditions’ or ‘calculating ranges’ won’t be frustrating.
OK, let’s just all agree to click that button and move on with our lives.
Step 5: Click OK
After making necessary changes in the ‘Excel Options’ dialog box, click the ‘OK’ button to apply them. Follow these steps to complete the process successfully:
1. Ensure that all the changes made in the ‘Excel Options’ dialog box are according to your preferences before clicking on the ‘OK’ button.
2. Once you click on the button, Excel will save and apply all of your settings within a few seconds.
3. The new equal sign tool will then appear on your Excel ribbon under ‘Formulas’.
4. You can now use it by selecting any two cells that you want to check for equality and then pressing the equal sign ( = ) tool.
5. If both cells have identical values, Excel will return a true value; otherwise, it will return a false value.
6. That’s it! Now you can use this tool whenever you want to compare two cells within your spreadsheet instantly.
Remember to save any changes that you make in Excel options. You can always modify or remove this feature later by going back into “Excel Options” and changing or disabling from there.
You cannot enter an Excel formula without an equal sign. Therefore, adding an “equal sign tool” can be highly beneficial if you work with spreadsheets frequently. It saves users time and effort while
also reducing errors when manually comparing cell values. Don’t let productivity slip by missing out on using this useful feature. Apply these simple steps today!
Equal sign tool: Because who has time for manual math when you can let Excel do the heavy lifting?
How to use the Equal Sign Tool
Using the Equal Sign Tool in Excel can simplify your work and save time. Here is a quick guide to help you get started.
1. Step 1: Begin by opening the Excel worksheet where you want to use the Equal Sign Tool. Choose the empty cell where you want to put the formula.
2. Step 2: Start the formula by typing “=” in the cell. This tells Excel that you want to insert a formula.
3. Step 3: Complete the formula by typing the desired formula or function. When you press Enter, Excel will calculate the result and display it in the cell.
It is important to note that you can use the Equal Sign Tool for any type of calculation in Excel, whether it is adding, subtracting, multiplying, or dividing. Additionally, you can use Excel’s
built-in functions or create your own formulas.
One user shared that using the Equal Sign Tool in Excel helped them save time and improve accuracy when completing financial reports for their company. They were able to quickly perform calculations
and eliminate manual errors.
Advantages of using the Equal Sign Tool
The Equal Sign Tool in Excel offers various benefits to users seeking to optimize their spreadsheets.
Using the Equal Sign Tool in Excel yields advantages such as simplifying formulas, organizing data, and ensuring accuracy. Additionally, users can easily copy and paste formulas across multiple cells
using this tool. It also aids in minimizing formula errors and streamlining calculation processes.
Additionally, using the Equal Sign Tool in Excel is a practical method for making calculations and creating spreadsheets that are more accessible to others. This tool is especially helpful for
accountants and financial analysts who require accuracy and efficiency in their work.
According to a study conducted by Forbes, an overwhelming majority of businesses (88%) still use Excel in their operations, emphasizing the continued relevance and importance of this tool.
Five Facts About Adding an Equal Sign Tool in Excel:
• ✅ The equal sign tool is used in Excel formulas to indicate a mathematical operation. (Source: Microsoft)
• ✅ Adding an equal sign before a value or formula cell reference turns it into a formula. (Source: Excel Easy)
• ✅ Excel has a library of pre-built formulas that use the equal sign tool for commonly used calculations. (Source: Excel Campus)
• ✅ The equal sign tool can be used for concatenate functions to combine text from multiple cells. (Source: Exceljet)
• ✅ Understanding how to use the equal sign tool is essential for advanced data analysis in Excel. (Source: DataCamp)
FAQs about Adding An Equal Sign Tool In Excel
What is an Equal Sign Tool in Excel and how can I add it?
An Equal Sign tool in Excel helps in writing formulas without the need to remember the syntax. You can add this tool to the Quick Access Toolbar for easier access. Here’s how:
1. Click on the Customize Quick Access Toolbar dropdown arrow.
2. Select More Commands.
3. Choose All Commands from the “Choose commands from” dropdown list.
4. Scroll down and select “Formula AutoComplete” option.
5. Click on the Add button.
6. Click OK to add the tool to the Quick Access Toolbar.
How do I use the Equal Sign Tool in Excel?
The Equal Sign Tool in Excel is quite easy to use. Simply start typing your formula, then type an equal sign (“=”) and the tool will pop up a dropdown list of suggestions. Select the one you need and
move on to the next part of your formula.
Is the Equal Sign Tool in Excel only available for certain versions of Excel?
No, it’s available in all versions of Microsoft Excel, from Excel 2007 to the latest versions.
Can I customize the Equal Sign Tool in Excel?
Unfortunately, you cannot customize the tool itself, but you can customize the Quick Access Toolbar where the tool is added. You can add or remove features, or move the toolbar to a different
Why is the Equal Sign Tool not appearing in my Quick Access Toolbar?
This could be due to a variety of reasons, such as not selecting the “All Commands” option when adding the tool or the Quick Access Toolbar has been customized and the tool has been removed. To add
the tool, follow the steps outlined in the first question.
Can I use the Equal Sign Tool when working with different types of data, such as dates or text?
Yes, you can use the Equal Sign Tool for all types of data. The tool will suggest functions, formulas, and ranges that are relevant to the data type you are working with. | {"url":"https://exceladept.com/adding-an-equal-sign-tool-in-excel/","timestamp":"2024-11-03T21:49:44Z","content_type":"text/html","content_length":"67178","record_id":"<urn:uuid:5bed81eb-e6fb-42c1-8fe4-d4bd8cc6a25e>","cc-path":"CC-MAIN-2024-46/segments/1730477027796.35/warc/CC-MAIN-20241103212031-20241104002031-00441.warc.gz"} |
[QSMS Seminar 20220721] Finding ALL solutions
Speaker : 이경용 (University of Alabama)
Place : 129동406호
Schedule : 7월21일(목) 10:00 ~ 11:00
TiTle : Finding ALL solutions
Abstract :
We introduce two famous (or notorious) open problems from Smale's list and Millennium problems: the Jacobian conjecture and the Birch--Swinnerton-Dyer conjecture.
The Jacobian conjecture states that if the Jacobian of a polynomial map is a nonzero constant, then the map is bijective. The condition of the Jacobian being equal to a constant can be translated to
a system of (too many) polynomial equations. An elementary but promising approach is to find ALL solutions systematically. This is based on joint work with Jacob Gliedwell, William Hurst, Li Li, and
George Nasr.
A special case of the weak BSD conjecture can be translated to counting integer solutions of certain Diophantine equations. Again an elementary but promising approach is to find ALL solutions
systematically. This is based on joint work with Ty Clements, Zach Socha, and Vishak Vikranth.
This talk will be completely elementary and accessible to non-experts, as all my collaborators including myself are non-experts. | {"url":"https://qsms.math.snu.ac.kr/index.php?mid=board_sjXR83&order_type=asc&page=8&document_srl=2332&sort_index=readed_count&listStyle=viewer","timestamp":"2024-11-09T04:12:09Z","content_type":"text/html","content_length":"21686","record_id":"<urn:uuid:dd098b36-62b0-4897-af71-6ed71fdfb6da>","cc-path":"CC-MAIN-2024-46/segments/1730477028115.85/warc/CC-MAIN-20241109022607-20241109052607-00297.warc.gz"} |
Sphere Packings and Magical Functions. A talk in pictures on the Fields medal work of Maryna Viazovska.
Date & Time of the event(s)
Description and practical details
May 2nd, 2024 - at 17:15 in Y03 G85
Sphere Packings and Magical Functions.
A talk in pictures on the Fields medal work of Maryna Viazovska. lecture given by Prof. Claire Burrin (UZH)
Abstract :
What is the most space-efficient way to stack oranges (of same size)? The answer seems clear: stack them in a pyramid just as is done at the fruit stand. But often in mathematics, the gulf between
intuition and proof is large. The sphere packing problem (or Kepler conjecture) remained one of geometry's tantalizing problems for nearly 400 years, until the computer-assisted proof of Thomas Hales
in 1998 (complemented by a formal, i.e., computer-checkable, proof in 2017). Still, the more general problem of packing spheres in n-dimensional space is very poorly understood. Then in 2016 came a
breakthrough; Ukrainian mathematician Maryna Viazovska announced having solved the sphere packing problem in dimension 8, and soon after (in collaboration with Cohn, Kumar, Miller, and Radchenko) in
dimension 24. For this work, she became the second woman in history to be awarded the Fields medal in 2022. At the hand of many pictures (and some formulas), I will describe the history of the sphere
packing problem, the role computers have occupied in it, and some of the wondrous geometric insights leading to Viazovska’s solution. This talk will be accessible to all Bachelor students.
Winterthurerstrasse 190
Institut für Mathematik, Universität Zürich
8057 Zürich
Name of the Organisation
University of Zurich | {"url":"http://may12.womeninmaths.org/node/1145","timestamp":"2024-11-09T09:45:10Z","content_type":"text/html","content_length":"25850","record_id":"<urn:uuid:6ee0a662-73c7-4885-a416-23e4501d41c0>","cc-path":"CC-MAIN-2024-46/segments/1730477028116.75/warc/CC-MAIN-20241109085148-20241109115148-00462.warc.gz"} |
Is logic "universal"? For example, when we say that X is logically impossible, we mean to say that in no possible world is X actually possible. But doesn't this mean that we have to prove that in all
possible worlds logic actually applies? In other words, don't we have to demonstrate that no world can exist in which the laws of logic don't apply or in which some other logic applies? If logic is
not "universal" in this sense, that it applies in all possible words, and we've not shown that it absolutely does apply in all worlds, how can we justify saying that what is logically impossible
means the not possible in any possible world, including our actual world?
Read another response about | {"url":"https://askphilosophers.org/question/4837","timestamp":"2024-11-13T22:01:07Z","content_type":"text/html","content_length":"27719","record_id":"<urn:uuid:765a74dc-5f01-4001-9153-78571610476b>","cc-path":"CC-MAIN-2024-46/segments/1730477028402.57/warc/CC-MAIN-20241113203454-20241113233454-00195.warc.gz"} |
How to Study Physics
"How to Study Physics" by David R. Hubin and Charles Riddell, was published by the Learning Skills Center, Univ. of Texas at Austin, in 1977. This revision is by Lawrence C. Shepley, Physics Dept.,
Univ. of Texas, Austin, TX 78712. (He gratefully acknowledges the advice of Leslie Dickie, John Abbott College, Quebec; Kal Kallison, Learning Skills Center, UT Austin; and John Trimble, English
Department, UT Austin.) It may be found online at http://wwwrel.ph.utexas.edu/~larry/how/how.html. Please feel free to browse Larry Shepley's homepage: http://wwwrel.ph.utexas.edu/~larry, and please
do send him your questions and comments on this document. Version of 7 October 1997.
You, like many students, may view college level physics as difficult. You, again like many students, may seem overwhelmed by new terms and equations. You may not have had extensive experience with
problem-solving and may get lost when trying to apply information from your textbook and classes to an actual physics problem. We hope this pamphlet will help!
It's designed to help you stay out of the difficulties that come when you think small and get too involved in memorizing formulas or other specific details without understanding the underlying
principles. It will guide you in understanding how to apply specific knowledge to the problems, how to start, how to seek help, how to check your answer. In short, it will help you develop the study
skills that are important not just in physics but in all of your courses.
Getting an Overview
Effective Participation in a Physics Class
Reading Your Physics Textbook
Problem Solving in Physics
Examples of the Application of the Problem-Solving Principles
Effective Test Preparation
Weekly Flow Chart for Studying Physics
Getting an Overview
It's important to recognize that physics is a problem-solving discipline. Your physics teacher will stress major themes and principles, and one major goal is that you, the student, will be able to
apply these principles to understand and solve problems. You should focus on this fact, that in a physics course, you are expected to solve problems.
An overview of your course can help you organize your efforts and increase your efficiency. To understand and retain data or formulas, you should see the underlying principles and connecting themes.
It is almost inevitable that you will sometimes forget a formula, and an understanding of the underlying principle can help you generate the formula for yourself.
Take these steps to getting an overview early in the term so that all subsequent material can be integrated into your overview:
1. Examine the course outline (first day handout or syllabus) carefully, and read the official description of the course in the University Catalog. Look for underlying themes or a pattern on which
the course is developed and how this course fits in with your other courses.
2. Preview the textbook:
A. Read the introduction and table of contents.
B. Read any notes to the student (or teacher) that are included and the preface.
C. Check the course outline to see what chapters are assigned and which are omitted. If they are not assigned in the same order as in the table of contents, can you see a reason for your
teacher's decision to alter the order of presentation?
3. As you preview the course from this perspective early in the term, look for important themes and principles. Glance at some of the problems. How are important themes illustrated in these
Effective Participation in a Physics Class
It's important that you be well prepared for class in order to use its potential fully for integrating the course material. To prepare for the class, you should do the following:
Prior to each class:
1. Check the course outline or reading assignment to see what will be covered. Prepare by briefly previewing the sections of the textbook that apply to the subjects to be covered. This preview will
improve your ability to follow the class, for you will have seen the new terminology and will recognize signposts that will help integrate the classes into an overall picture.
2. Read the introduction and the summary of the relevant chapter and look at the section headings and subheadings. Try to formulate questions in your mind about the subjects to be covered. This
question-formulating helps you manipulate and therefore better understand the material.
3. Examine the drawings and pictures. Try to determine what principles they illustrate.
4. Make notes of new words, new units of measure, statements of general laws, and other new concepts.
5. Do not underline or highlight the text, since you do not yet know what will be emphasized by the instructor.
6. Right before the beginning of class, check your notes from the last class. Reading your notes will prepare you to listen to the new physics class as part of an integrated course and will help you
to see the broad development of themes.
During class:
Come to the class on time and stay till the very end. Often teachers give helpful hints in the first and last minutes of the lecture. Unfortunately, these times are when a lot of people are not
1. Take good notes. It's helpful to draw up a set of abbreviations and use them consistently in taking notes. Keep a list of them for later reference. Leave ample margins for later comments and for
questions or write on only one side so that you can use the opposite side for comments and questions (see After Class, below).
2. When you copy drawings, completeness is worth more than careful artwork. You should not only copy what is on the board but also record important points that the teacher makes orally about the
3. If you get behind in your note-taking, leave a space in your notes and go on. You can fill in your notes later with the help of a classmate or your textbook. (Note: The Learning Skills Center can
give you additional information on note-taking.)
4. Ask questions. Don't be embarrassed to ask your teacher questions. Many teachers depend on feedback from students to help them set a proper pace for the class. And of course it can happen that
the teacher does not explain a step he or she takes, or even makes a mistake when writing something on the board.
After class:
1. Immediately after class, or as soon as possible, review and edit your notes. You need not rewrite them. Rather, you should look for important ideas and relationships among major topics. Summarize
these in the margin or on the opposite side if you've taken notes only on one side, and at this time you may want to add an outline to your notes. Also, this would be a good time to integrate
notes from your textbook into your lecture notes; then you will have one set of integrated notes to study by.
2. As you review your notes, certain questions may come to mind. Leave space for recording questions, and then either ask the teacher or even better, try to answer these questions for yourself with
your friends and with the help of the text.
Reading Your Physics Textbook
Reading the text and solving homework problems is a cycle: Questions lead to answers that lead back to more questions. An entire chapter will often be devoted to the consequences of a single basic
principle. You should look for these basic principles. These Laws of Nature give order to the physicists' view of the universe. Moreover, nearly all of the problems that you will be faced with in a
physics course can be analyzed by means of one or more of these laws.
When looking for relationships among topics, you may note that in many instances a specific problem is first analyzed in great detail. Then the setting of the problem is generalized into more
abstract results. When such generalizations are made, you should refer back to the case that was previously cited and make sure that you understand how the general theory applies to the specific
problem. Then see if you can think of other problems to which that general principle applies. Some suggestions for your physics reading:
1. Make use of the preview that you did prior to the class. Again, quickly look at the major points of the chapter. Think back to the points stressed in class and any questions you might have
written down.
2. Read the homework problems first. If specific homework problems have not yet been assigned, select several and look these over. Critically assess what principles seem to be most significant in
the assigned chapter. Based upon your brief review of the class and your examination of the problems, try to generate questions in your mind that you want the chapter to answer.
3. Read actively with questions in mind. A passive approach to reading physics wastes your time. Read with a pencil and paper beside the book to jot down questions and notes. If you find that you
are not reading actively, once again take a look at the problems and the lecture notes. Read to learn, not to cover material.
4. Stop periodically and pointedly recall the material that you have read. It is a good idea to repeat material aloud and especially to add notes from the textbook into the margins of your class
5. During your reading you will notice sections, equations, or ideas that apply directly to assigned problems. After you have read such a section, stop and analyze its application to a homework
problem. The interplay of reading and problem solving is part of the cycle of question --> answer --> question. It helps you gain insights that are not possible by reading alone, even careful
reading alone. Passive reading is simply following the chain of thought in the text. Active reading also involves exploring the possibilities of what is being read. By actively combining the
questions that are inherent in problem solving with your reading, you enhance both your concentration while reading and your ability to recall and to apply the material.
Problem Solving in Physics
You may now be like many students a novice problem solver. The goal of this section is to help you become an expert problem solver. Effective, expert problem solving involves answering five
• What's the problem about?
• What am I asked to find?
• What information am I to use? What principles apply?
• What do I know about similar situations?
• How can I go about applying the information to solve the problem?
• Does my solution make sense?
You, the expert, will decide, "this is an energy problem," or, "this is a Newton 2 problem." A novice is more likely to decide, "this is a pulley problem," or, "this is a baseball problem." The
novice concentrates on the surface features of the problem while you concentrate on the underlying principle. You, an expert problem solver, will answer these questions, play around (briefly)
with the problem, and make drawings and sketches (either in your mind, or even better, on paper) before writing down formulas and plugging in numbers. A novice problem solver, on the other hand,
will try to write down equations and plug in numbers as soon as possible. A novice will make many more mistakes than you will when you become an expert.
In a physics course it's important to remember a couple of things about physicists and physics professors:
□ A physicist seeks those problems that can be modeled or represented by a picture or diagram. Almost any problem you encounter in a physics course can be described with a drawing. Such a
drawing often contains or suggests the solution to the problem.
□ A physicist seeks to find unifying principles that can be expressed mathematically and that can be applied to broad classes of physical situations. Your physics text book contains many
specific formulas, but you must understand the broader Laws of Nature in order to grasp the general overview of physics. This broad understanding is vital if you are to solve problems that
may include several different principles and that may use several different formulas. Virtually all specific formulas in physics are combinations of basic laws.
General outline of how to approach a physics problem:
1. Read the problem. Look up the meanings of any terms that you do not know. Answer for yourself the question, "What's this about?" Make sure you understand what is being asked, what the
question is. It is very helpful if you reexpress the problem in your own words or if you tell a friend what the problem is about.
2. Make a drawing of the problem. Even a poor drawing can be helpful, but for a truly good drawing include the following:
A. Give a title that identifies the quantity you are seeking in the problem or that describes the problem.
B. Label the drawing, including the parameters or variables on which the solution depends and that are given in the problem. Write down the given values of these parameters on the drawing.
C. Label any unknown parameters that must be calculated along the way or obtained from the text in order to find the desired solution.
D. Always give the units of measure for all quantities in the problem. If the drawing is a graph, be sure to give both the units and the scale of the axes.
E. Include on the drawing information that is assumed and not given in the problem (such as g, the value of the acceleration due to gravity), and whether air resistance and friction are
3. Establish which general principle relates the given parameters to the quantity that you are seeking. Usually your picture will suggest the correct techniques and formulas. At times it may be
necessary to obtain further information from your textbook or notes before the proper formulas can be chosen. It often happens that further information is needed when the problem has a
solution that must be calculated indirectly from the given information. If further information is needed or if intermediate quantities must be computed, it is here that they are often
4. Draw a second picture that identifies the coordinate system and origin that will be used in relating the data to the equations. In some situations this second picture may be a graph, free
body diagram, or vector diagram rather than a picture of a physical situation.
5. Even an expert will often use the concrete method of working a problem. In this method you do the calculation using the given values from the start, so that the algebra gives numerical values
at each intermediate step on the way to the final solution. The disadvantage of this method is that because of the large number of numerical calculations involved, mistakes are likely, and so
you should take special care with significant figures. However this method has the advantage that you can see, at every step of the way, how the problem is progressing. It also is more direct
and often makes it easier to locate a mistake if you do make one.
6. As an expert, you will more and more use the formal method of working a problem. In this method, you calculate the solution by doing as much as possible without using specific numbers. In
other words, do as much of the algebra as you can before substituting the specific given values of the data. In long and complicated problems terms may cancel or expressions simplify. Our
advice: gain experience in problem solving by substituting the numbers when you start physics, but gradually adopt the formal approach as you become more confident; many people adopt a
compromise approach where they substitute some values but retain others as symbols (for example, "g" for the acceleration due to gravity).
7. Criticize your solution: Ask yourself, "Does it make sense?" Compare your solution to any available examples or to previous problems you have done. Often you can check yourself by doing an
approximate calculation. Many times a calculation error will result in an answer that is obviously wrong. Be sure to check the units of your solution to see that they are appropriate. This
examination will develop your physical intuition about the correctness of solutions, and this intuition will be very valuable for later problems and on exams.
An important thing to remember in working physics problems is that by showing all of your work you can much more easily locate and correct mistakes. You will also find it easier to read the
problems when you prepare for exams if you show all your work.
8. In an examination, you may have to do problems under a strict time limitation. Therefore, when you are finished with a homework problem, practice doing it again faster, in order to build up
your speed and your confidence.
When you have completed a problem, you should be able, at some later time, to read the solution and to understand it without referring to the text. You should therefore write up the problem so as
to include a description of what is wanted, the principle you have applied, and the steps you have taken. If, when you read your own answer to the problem, you come to a step that you do not
understand, then you have either omitted a step that is necessary to the logical development of the solution, or you need to put down more extensive notes in your write-up to remind you of the
reasons for each step.
It takes more time to write careful and complete solutions to homework problems. Writing down what you are doing and thinking slows you down, but more important it makes you behave more like an
expert. You will be well paid back by the assurance that you are not overlooking essential information. These careful write-ups will provide excellent review material for exam preparation.
Examples of the Application of the Problem-Solving Principles
SAMPLE PROBLEM #1:
This problem is stated and the solution written down as you would work it out for homework.
In 1947 Bob Feller, former Cleveland pitcher, threw a baseball across the plate at 98.6 mph or 44.1 m/s. For many years this was the fastest pitch ever measured. If Bob had thrown the pitch
straight up, how high would it have gone?
1. What does the problem ask for, and what is given? Answer: The speed of the baseball is given, and what is wanted is the height that the ball would reach if it were thrown straight up with the
given initial speed. You should double check that whoever wrote the problem correctly calculated that 98.6 miles/hr is equal to 44.1 m/s. You should state explicitly, in words, that you will
use the 44.1 m/s figure and that you will assume the baseball is thrown from an initial height of zero (ground level). You should also state explicitly what value of g you will use, for
example, g = 9.81 m/s^2. You should also state that you assume that air resistance can be neglected. Since you don't know the mass of the baseball, say that you don't (you won't need it,
2. Make a drawing:
3. The general principles to be applied here are those of uniformly accelerated motion. In this case, the initial velocity v[o] decreases linearly in time because of the gravitational
acceleration. The maximum height y[m] occurs at the time t[m] when the velocity reaches zero. The average velocity during from t = 0 to t = t[m] is the average of the initial velocity v = v
[o] and the final velocity v = 0, or half the initial velocity.
4. Make a second drawing. In this case, try a graph of velocity as a function of time:
Notice that the graph is fairly accurate: You can approximate the value of g as 10 m/s^2, so that the velocity decreases to zero in about 4.5 s. Therefore, even before you use your
calculator, you have a good idea of about the value of t[m].
5. The concrete method can now be applied: An initial velocity of 44.1 m/s will decrease at the rate of 9.81 m/s^2 to zero in a time t[m] given by
t[m] = 44.1 / 9.81 = 4.4954 s .
During that time, the average velocity is v[av] = 44.1 / 2 = 22.05 m/s. Therefore the height is given by
y[m] = v[av] t[m] = 99.12 = 99.1 m .
Notice that for all "internal" calculations, more than the correct number of significant figures were kept; only when the final answer was obtained was it put into the correct number of
significant figures, in this case three.
6. To do this problem in a formal method, use the formula for distance y as a function of t if the acceleration a is constant. Do not substitute numbers, but work only with symbols until the
very end:
y = y[o] + v[o ]t + a t^2 / 2 ,
where y[o] = 0 is the initial position, v[o] = 44.1 m/s is the initial velocity, and a = - g = - 9.81 m/s^2 is the constant acceleration. However, do not use the numerical figures at this
point in the calculation. The maximum value of y is when its derivative is zero; the time t[m] of zero derivative is given by:
dy/dt = v^o + a t[m] = 0 --> t[m] = - v[o] / a .
The maximum height y[m] is given by putting this value of t[m] into the equation for y:
y[m] = y[o] + v[o] ( - v[o] / a ) + a ( - v[o] / a )^2 / 2 = y[o] - v[o]^2 / 2a .
Now substitute: y[o] = 0, v[o] = 44.1, a = - 9.81. The result is
y[m] = 0 + 0.5 (44.1)^2 / 9.81 = 99.1 m .
7. Look over this problem and ask yourself if the answer makes sense. After all, throwing a ball almost 100 m in the air is basically impossible in practice, but Bob Feller did have a very fast
fast ball pitch!
There is another matter: If this same problem had been given in a chapter dealing with conservation of energy, you should not solve it as outlined above. Instead, you should calculate what
the initial and final kinetic energy KE and potential energy PE are in order to find the total energy. Here, the initial PE is zero, and the initial KE is m v[o]^2 / 2. The final PE is m g y
[m] and the final KE is zero. Equate the initial KE to the final PE to see that the unknown mass m cancels from both sides of the equation. You can then solve for y[m], and of course you will
get the same answer as before but in a more sophisticated manner.
8. To prepare for an exam, look over this problem and ask yourself how you can solve it as quickly as possible. You may be more comfortable with the concrete approach or with the formal
approach; practice will tell. On an actual exam, you might not have time for a complete drawing or a complete listing of principles. By working this problem a couple of times, even after
you've gotten the answer once, you will become very familiar with it. Even better, explain the problem to a friend of yours, and that way you really will be an expert!
SAMPLE PROBLEM #2:
Again, this problem is stated and the solution written down as you would work it out for homework. As in Sample Problem #1, we go through the eight steps of the general outline.
A one kilogram block rests on a plane inclined at 27^o to the horizontal. The coefficient of friction between the block and the plane is 0.19. Find the acceleration of the block down the
1. The problem asks for the acceleration, not the position of the block nor how long it takes to go down the plane nor anything else. No mention is made of the difference between static or
kinetic coefficients of friction, so assume they are the same. The mass is given, but you will eventually find that it doesn't matter what the mass is. (If the mass had not been given, that
would be an indication that it doesn't matter, but even in that case you may find it easier to assume a value for the mass in order to guide your thoughts as you do the problem.)
2. Here is the first picture. Note that the angle is labeled a[||] for the acceleration down the plane are defined in the picture.
3. There are two general principles that apply here. The first is Newton's Second Law:
F = m a ,
where F is the net force, a vector, and a is acceleration, another vector; the two vectors are in the same direction. The mass m will eventually be found not to make any difference, and in
that case, you might be tempted to write this law as a = F / m, since a is what you want to find. However, the easiest way to remember Newton's Second Law is F = m a, and so that is the law
to work with.
The second principle is that the frictional force is proportional to the normal force (the component of the force on the block due to the plane that is perpendicular to the plane). The
frictional force is along the plane and always opposes the motion. Since the block is initially at rest but will accelerate down the plane, the frictional force will be up along the plane.
The coefficient of friction, which is used in this proportionality relation, is
4. It is now time to draw the second picture. It helps to redraw the first picture and add information to it. In this case a vector diagram is drawn and various forces are defined.
Note that in the vector diagram, the block has been replaced by a dot at the center of the vectors. The relevant forces are drawn in (all except the net force). Even the value assumed for the
gravitational acceleration has been included. Some effort has been made to draw them to scale: The normal force is drawn equal in magnitude and opposite in direction to the component of the
gravity force that is perpendicular to the plane. Also, the friction force has been drawn in parallel to the plane and opposing the motion; it has been drawn in smaller than the normal force.
The angles of the normal and parallel forces have been carefully drawn in relation to the inclined plane. This sub-drawing has a title and labels, as all drawings should.
5. We will do this problem using the formal approach, leaving the concrete method for a check (see below).
6. Now for calculation using the formal approach, where you work with algebra and symbols rather than with numbers. First state in words what you are doing, and then write down the equation:
☆ Magnitude of gravity force = weight = m g.
☆ Resolve gravity force into normal component and parallel component whose magnitudes are:
F[G||] = m g sin [GN] = m g cos
☆ The magnitude of the normal force due to the plane is equal in magnitude (but the direction is opposite) to the magnitude of the normal component of the gravity force:
F[N] = m g cos
☆ The frictional force opposes the motion, and its magnitude is equal to the coefficient of friction times the normal plane force:
F[f] =
☆ The net force (which is along the plane) is the difference between the parallel component of the gravitational force and the friction force; its magnitude is:
F = m g sin
☆ The acceleration is net force over mass:
a[||] = g sin
☆ The numerical answer is (given to two significant figures since the given numbers have two):
a = (9.8 m/s^2) (sin 27^o - 0.19 cos 27^o) = (9.8) (0.454 - 0.19 x 0.891) = 2.79 = 2.8 m/s^2 .
7. When you look over this answer to see if it makes sense, try doing the problem by substituting numbers in at each step (the concrete approach). The weight of a kilogram, for example is 9.8 N.
The normal (perpendicular to the plane) component of the gravitational force is 9.8 times cos 27^o or 8.73 N. This makes sense, for if the angle were very small, the normal component of the
gravitational force would be almost equal to 9.8 itself. Notice that although the final answer should be given to two significant figures, you should keep three in these intermediate
The parallel component of the gravitational force is 9.8 sin 27^o = 4.45 N. The normal force due to the plane is equal in magnitude to the gravitational normal force (but opposite in
direction), and so the frictional force is 0.19 times 8.73 or 1.66 N. The net force is down the plane and equal to the difference 4.45 - 1.66 = 2.79 N. Divide this value by 1 kg to get the
acceleration 2.79 m/s^2 (which is rounded off to 2.8 m/s^2).
Again examine your solution. It says that the block does accelerate down the plane because the final answer is positive. The acceleration is less than g, again a reasonable result. Notice
that if the angle were more than 27^o, then its sine would be larger and its cosine smaller, so the acceleration would be greater. If the angle were less than 27^o then the opposite would be
true, and the acceleration, as calculated above, could become negative. But a negative value for acceleration would be wrong, because that would say that the block would accelerate up the
plane because the frictional force dominates, and that is impossible. Instead, if the calculation had produced a negative value for a, you would have had to change the solution to a = 0,
meaning that the frictional force was enough to prevent sliding.
8. Now anticipate how you'd do this problem on an exam. Is the concrete approach faster and easier for you? Or would you be more comfortable using the formal approach on an exam? It is a good
idea to practice doing this problem when you study for an exam, if you think a similar problem will be asked.
Effective Test Preparation
If you have followed an active approach to study similar to the one suggested in this handout, your preparation for exams will not be overly difficult. If you haven't been very active in
studying, your preparation will be somewhat harder, but the same principles still apply. Always remember: Physics courses, and therefore physics exams, involve problem solving. Hence, your
approach to studying for exams should stress problem solving.
Here are some principles:
□ In the week prior to the exam, follow the three steps below. These steps should give you a reasonably good idea of what has been stressed and on what you can expect to be tested.
☆ Review your notes and recheck the course outline. Your goal at this point is to make sure you know what has been emphasized.
☆ Reread your solutions to the homework problems. Remember that these solutions, if complete, will note underlying principles or laws.
☆ Review the assigned chapters. Once again, your purpose in this early stage of exam preparation is to make sure you know what topics or principles have been emphasized.
□ From this rapid overview, generate a list of themes, principles, and types of problems that you expect to be covered. If samples of previous exams are available, look them over, also, but do
not assume that only previous types of problems will be included. It definitely helps to work with others at this stage.
□ Review actively. Don't be satisfied with simple recognition of a principle. Aim for actual knowledge that you will be able to recall and to use in a test situation. Try to look at all the
possible ways that a principle can be applied. Again, it helps to work with others and to explain things to others (and have them explain things to you).
For example: If velocity and acceleration principles have been emphasized in the course, look over all of your homework problems to see if they illustrate these principles, even partially.
Then if you also can anticipate an emphasis on friction and inertia, once again review all of your homework problems to see if they illustrate those principles.
□ Effective examination preparation involves an interaction among homework problems, the classes, your notes and the text. Review actively, including self-tests in which you create your own
problems which involve a combination of principles. You need to be sure that you can work problems without referring to your notes or to the textbook. Practice doing problems using both the
concrete and the formal approaches, to see which you are more comfortable with.
□ Remember that exams will include a variety of different problems. You want to look back on an exam and say, "I know how to do friction problems so well, that even though they were asked in a
weird way, I could recognize them and solve them."
Weekly Flow Chart for Studying Physics
These tips are based on a list "17 Tips that UT Seniors Wish They'd Known as Freshmen" by Dr. John Trimble, a professor in the English Department. He is a member of The University of Texas's
Academy of Distinguished Professors. These tips have been adapted to fit physics courses, but they are good tips for any university student. I have abbreviated most of these tips but have not
omitted any. You can find the complete version at the Learning Skills Center (and elsewhere).
1. Get to know your professor. Go to his or her office hours early in the semester and often. Get to know your TAs. Go to their office hours early in the semester and often. UT Austin has
faculty and graduate students who are among the best in the world; get to know them.
2. As soon as you can, trade names and phone numbers with at least two classmates. Don't ask the professor what you missed if you happen to miss class; ask your classmates.
3. Make sure you are enrolled in the course you think you are enrolled in. Correct any enrollment mistakes as soon as you can.
4. Read and study your course policy statement (the first day handout or the syllabus). It is a legal contract!
5. Buy and use an appointment book.
6. Keep a notebook of unfamiliar words and phrases. Look them up or ask what they mean. Buy and use a good dictionary.
7. If you haven't yet learned to use a computer, do so. If you don't have a good calculator, which you know how to use easily, buy one and learn to use it. A particular calculator may be
required for class; be sure you get the right one. Study its manual and practice using it until you can do so quickly and accurately.
8. Learn to touch-type. If you hunt-and-peck, you will be at a disadvantage. Learn either through a computer program or at Austin Community College.
9. Bring two calculators to each exam or one calculator and extra batteries. Bring your text book to each exam. Bring extra paper to each exam. Bring two pencils and two pens to each exam. Bring
two blue books if required. Ask which of these you are allowed to use, but of course don't use the items that aren't allowed.
10. Go to each and every class session. Be punctual. Look professional. Don't disturb the class by talking. But do ask questions!
11. Exercise at least every other day.
12. When you write papers, do so in at least two editing stages, with a few hours or a day or two between drafts. Type your papers. When you write up homework problems, do so neatly and
carefully. If possible, ask your professor, TA, or the grader for feedback before you turn in the final version of an assignment.
13. Understand that you are reinventing yourself. You are defining what and who you are for a good many years to come (you may want to reinvent yourself later, at 30 or 40), so be careful about
how you go about it.
14. Hang out with the smartest, most studious people you can find. Watch how they work. Eventually people will be watching you; help them in developing good study habits.
15. Take the teacher, not the course. Shop for the best teachers by asking older students who they are and by reading the Course/Instructor student evaluations at the UGL's Reserve Desk. Try to
meet prospective teachers before enrollment. Keep a "Best Teachers/Best Courses" notebook.
16. Assume responsibility for your own education. Exercise initiative. Learn to love the whole process of education, not just the end-product.
17. Dr. Trimble's seven reasons for going to college:
☆ To meet a lot of interesting people, some of whom will become lifelong friends.
☆ To gain an enlarged view of an enlarged world.
☆ To learn better how to learn. (Most of what you later learn, you'll teach yourself.)
☆ To reinvent yourself -- that is, to discover and explore more of yourself than you normally could at home.
☆ To acquire at least a dilettante's knowledge about a lot of different things, since being informed beats the hell out of being ignorant.
☆ To learn how to handle adult responsibilities while still enjoying a semi-protected environment.
☆ To identify and explore career options. | {"url":"http://physics.csbsju.edu/tk/191/how.html","timestamp":"2024-11-06T20:17:13Z","content_type":"text/html","content_length":"40916","record_id":"<urn:uuid:07913fe2-6f65-4444-b3f0-af10dde6a734>","cc-path":"CC-MAIN-2024-46/segments/1730477027942.47/warc/CC-MAIN-20241106194801-20241106224801-00108.warc.gz"} |
tins ::: Rick Klau's blog – Primes in P
Prof. Manindra Agarwal and two of his students, Nitin Saxena and Neeraj Kayal (both BTech from CSE/IITK who have just joined as Ph.D. students), have discovered a polynomial time deterministic
algorithm to test if an input number is prime or not. Lots of people over (literally!) centuries have been looking for a polynomial time test for primality, and this result is a major breakthrough,
likened by some to the P-time solution to Linear Programming announced in the 70s. [Indian Institute of Technology Kanpur]
Though this breakthrough doesn’t have any short-term impact (current methods for discovering prime numbers are faster), it appears to be foolproof. This is important because many current security
mechanisms (i.e., encryption) depend on prime numbers to remain difficult (if not impossible) to crack. Problems with current methods of picking prime numbers are that the larger the numbers get, the
harder it is to know for certain that the number is a prime. Assuming that Agarwal’s discovery will lead to others who can improve upon it, this bodes well for future cryptographers (which will
necessarily benefit anyone relying on secure communications).
This site uses Akismet to reduce spam. Learn how your comment data is processed. | {"url":"https://tins.rklau.com/2002/08/primes-in-p/","timestamp":"2024-11-10T18:05:09Z","content_type":"text/html","content_length":"65231","record_id":"<urn:uuid:56779872-f829-4256-aece-d7a319268774>","cc-path":"CC-MAIN-2024-46/segments/1730477028187.61/warc/CC-MAIN-20241110170046-20241110200046-00723.warc.gz"} |
Computing a minimum-weight κ-link path in graphs with the concave monge property
Let G be a weighted, complete, directed acyclic graph (DAG) whose edge weights obey the concave Monge condition. We give an efficient algorithm for finding the minimum-weight κ-link path between a
given pair of vertices for any given κ. The algorithm runs in n2O(√logκloglogn) time Our algorithm can be applied to get efficient solutions for the following problems, improving on previous results:
(1) computing length-limited Huffman codes. (2) computing optimal discrete quantization. (3) computing maximum κ-chques of an interval graph. (4) finding the largest κ-gon contained in a given convex
polygon. (5) finding the smallest κ-gon that is the intersection of κ half-planes out of n half-planes defining a convex n-gon.
Original language English (US)
Title of host publication Proceedings of the 6th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 1995
Publisher Association for Computing Machinery
Pages 405-411
Number of pages 7
ISBN (Electronic) 0898713498
State Published - Jan 22 1995
Externally published Yes
Event 6th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 1995 - San Francisco, United States
Duration: Jan 22 1995 → Jan 24 1995
Publication series
Name Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms
Conference 6th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 1995
Country/Territory United States
City San Francisco
Period 1/22/95 → 1/24/95
All Science Journal Classification (ASJC) codes
• Software
• General Mathematics
Dive into the research topics of 'Computing a minimum-weight κ-link path in graphs with the concave monge property'. Together they form a unique fingerprint. | {"url":"https://researchwith.njit.edu/en/publications/computing-a-minimum-weight-%CE%BA-link-path-in-graphs-with-the-concave","timestamp":"2024-11-08T07:27:59Z","content_type":"text/html","content_length":"47716","record_id":"<urn:uuid:6dbd1736-e820-4f3e-ab24-456c6ade1e74>","cc-path":"CC-MAIN-2024-46/segments/1730477028032.87/warc/CC-MAIN-20241108070606-20241108100606-00637.warc.gz"} |
Construction has always been a discipline that requires correct measurements.
Luckily, we have developed plenty of Construction Calculators for your needs.
These calculators were created particularly with construction professionals in mind. Whether you’re a brick layer, roofer, carpenter, or renovator, you’ll find what you need here. If you need to calculate square footage, you can do so easily.
You might need to estimate the amount of materials for a job. Luckily, we have calculators for brick, concrete, and anything else you can possibly think of. Enjoy all these calculators, right at your fingertips. | {"url":"https://thefreecalculator.com/construction","timestamp":"2024-11-03T15:04:09Z","content_type":"text/html","content_length":"31317","record_id":"<urn:uuid:3a408528-9c1d-48f6-a6e1-27f081a2c859>","cc-path":"CC-MAIN-2024-46/segments/1730477027779.22/warc/CC-MAIN-20241103145859-20241103175859-00790.warc.gz"} |
How do you apply gas stoichiometry? | Socratic
How do you apply gas stoichiometry?
1 Answer
${N}_{2}$ + 3${H}_{2}$ ---> 2N${H}_{3}$ What volume of hydrogen is necessary to react with five liters of nitrogen to produce ammonia? (Assume constant temperature and pressure.)
${N}_{2}$ + 3${H}_{2}$ ---> 2N${H}_{3}$ , as per this equation, 1 volume of Nitrogen , needs 3 volumes of Hydrogen. The reaction produces two volumes of ammonia.
Let us write this as equation;
$\text{1 volume of Nitrogen"/"3 volume of Hydrogen}$ (a)
If we start with 5 L of Nitrogen , X volumes of Hydrogen will be needed.
Let us write this as equation;
$\text{5 L of Nitrogen"/"X L of Hydrogen}$ (b)
equate (a) and (b)
$\frac{1}{3}$ = $\frac{5}{X}$
cross multiply $1 \cdot X$ = $3 \cdot 5$ , X=15 L
2CO + ${O}_{2}$ ---> 2C${O}_{2}$ How many liters of carbon dioxide are produced if 75 liters of carbon monoxide are burned in oxygen? How many liters of oxygen are necessary?
As per this equation, 2 volumes of Carbon Monoxide, needs 1 volume of Oxygen. The reaction produces two volumes of Carbon dioxide.
Let us write this as equation;
$\text{2 volume of Carbon Monoxide"/"2 volumes of Carbon Dioxide}$ (a)
If we start with 75 L of Carbon monoxide , X volumes of carbon dioxide will be produced.
Let us write this as equation;
#"75 L of CO"/("X L of "CO_2)# (b)
equate (a) and (b)
$\frac{2}{2}$ = $\frac{75}{X}$
cross multiply $2 \cdot X$ = $2 \cdot 75$ , X= 75 L
$\text{2 volume of Carbon Monoxide"/"1 volumes of Oxygen}$ (a)
If we start with 75 L of Carbon Monoxide , X volumes of Oxygen will be needed.
#"75 L of CO"/("X L of "O_2)# (b)
equate (a) and (b)
$\frac{2}{1}$= $\frac{75}{X}$
$2 \cdot X$ = $75 \cdot 1$
2X =75
X= 37.5 L
Impact of this question
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Using ML.MSBD
ML.MSBD package
This package implements a Maximum Likelihood inference of a multi-state birth-death model on dated phylogenies. It is designed primarily to detect transmission clusters in epidemics such as HIV where
the transmission rate depends on the number of connections between infected and non-infected individuals. However, it can be applied to any situation where sudden jumps in the birth or death rate of
the phylogeny are expected.
Running an inference
The ML inference is run using the ML_MSBD function, which takes a phylogeny in ape format as input. Initial values for all estimated parameters need to be provided: by default these are the state
change rate, the birth rate and the death rate. The time_mode parameter controls where state changes will be placed on the edges of the phylogeny.
tree <- ape::read.tree(text = "((((t3:0.04098955599,(t8:0.03016935301,t10:0.03016935301):0.01082020298):0.06041650538,t2:0.1014060614):0.7530620333,(t1:0.5805635547,(t5:0.2225489503,t7:0.2225489503):0.3580146044):0.2739045399):1.005016052,((t9:0.09730025079,t6:0.09730025079):0.0209186338,t4:0.1182188846):1.741265262);")
ML_MSBD(tree, initial_values = c(0.1, 10, 1), time_mode = "mid")
Sampling through time is supported and sampling proportions can be set differently for extant sampling (rho) and extinct sampling (sigma). It is also possible to treat all tips as extinct samples.
tree_stt <- ape::read.tree(text = "((t6:0.1203204831,t3:0.1251815392):0.527233894,(((t8:0.1153702512,t5:0.2362936393):0.1328287013,((t1:0.6202914508,t4:0.839935567):0.6779029006,t10:0.472941763):0.3049683478):0.1837210727,((t9:0.24675539,t2:0.8737900169):0.6451289295,t7:0.1376576095):0.8951371317):0.5465055171);")
ML_MSBD(tree_stt, initial_values = c(0.1, 10, 1), rho = 0.5, sigma = 0.1, time_mode = "mid")
ML_MSBD(tree_stt, initial_values = c(0.1, 10, 1), rho_sampling = FALSE, sigma = 0.1, time_mode = "mid")
By default the birth rate is constant for a given state. It can also be set to decay exponentially, in which case a step size for the likelihood calculation and an initial value for the birth decay
rate need to be provided.
ML_MSBD(tree, initial_values = c(0.1, 10, 1), c(0.1, 10, 0.5, 1), sigma = 1, stepsize = 0.1, time_mode = "mid")
More details about the options available for the cluster inference and its output can be found using ?ML_MSBD.
Likelihood calculation
The likelihood of a given model configuration on a phylogeny can also be calculated directly. The position of state changes need to be given as a matrix containing the edge and time of the change and
the index of the new state.
likelihood_MSBD(tree, shifts = matrix(c(2,0.8,2), nrow = 1), gamma = 0.05, lambdas = c(10, 6), mus = c(1, 0.5))
## [1] 36.31232
The same sampling and exponential decay options are available as in the ML inference.
likelihood_MSBD(tree_stt, shifts = c(), gamma = 0.05, lambdas = 10, mus = 0.5, sigma = 0.5, rho_sampling = FALSE)
## [1] 64.92664
likelihood_MSBD(tree, shifts = c(), gamma = 0.05, lambdas = 10, mus = 0.5, lambda_rates = 0.1, stepsize = 0.05)
## [1] 32.52058
Another option for sampling is clade-collapsing sampling, where only one lineage per group or family is sampled. In this case the number of distinct tips represented by each lineage and the MRCA age
(s) of the collapsed clades need to be provided.
tree_collapsed = ape::read.tree(text = "((t1:0.379876463,t3:0.379876463):1.668231124,(t2:0.5653793315,t4:0.5653793315):1.482728255);")
likelihood_MSBD_unresolved(tree_collapsed, shifts = matrix(c(2,0.25,2), nrow = 1), gamma = 0.05, lambdas = c(10, 6), mus = c(1, 0.5), lineage_counts = c(5,1,3,6), tcut = 0.1)
## [1] 50.55458
likelihood_MSBD_unresolved(tree_collapsed, shifts = matrix(c(2,0.25,2), nrow = 1), gamma = 0.05, lambdas = c(10, 6), mus = c(1, 0.5), lineage_counts = c(5,1,3,6), tcut = c(0.1,0.0,0.15,0.4))
## [1] 47.845
More details about the available options for likelihood calculation can be found using ?likelihood_MSBD or ?likelihood_MSBD_unresolved. | {"url":"https://cran-r.c3sl.ufpr.br/web/packages/ML.MSBD/vignettes/Using_ML.MSBD.html","timestamp":"2024-11-14T01:58:32Z","content_type":"text/html","content_length":"634578","record_id":"<urn:uuid:360578ad-8b1c-4136-9f05-fe09abbad00f>","cc-path":"CC-MAIN-2024-46/segments/1730477028516.72/warc/CC-MAIN-20241113235151-20241114025151-00014.warc.gz"} |
Control Valve Characteristics | Spirax Sarco
Examples of these and their inherent characteristics are shown in Figures 6.5.1 and 6.5.2.
Fast opening characteristic
The fast opening characteristic valve plug will give a large change in flowrate for a small valve lift from the closed position. For example, a valve lift of 50% may result in an orifice pass area
and flowrate up to 90% of its maximum potential.
A valve using this type of plug is sometimes referred to as having an ‘on/off’ characteristic.
Unlike linear and equal percentage characteristics, the exact shape of the fast opening curve is not defined in standards. Therefore, two valves, one giving a 80% flow for 50% lift, the other 90%
flow for 60% lift, may both be regarded as having a fast opening characteristic.
Fast opening valves tend to be electrically or pneumatically actuated and used for ‘on/off’ control.
The self-acting type of control valve tends to have a plug shape similar to the fast opening plug in Figure 6.5.1. The plug position responds to changes in liquid or vapour pressure in the control
system. The movement of this type of valve plug can be extremely small relative to small changes in the controlled condition, and consequently the valve has an inherently high rangeability. The valve
plug is therefore able to reproduce small changes in flowrate, and should not be regarded as a fast opening control valve.
Linear characteristic
The linear characteristic valve plug is shaped so that the flowrate is directly proportional to the valve lift (H), at a constant differential pressure. A linear valve achieves this by having a
linear relationship between the valve lift and the orifice pass area (see Figure 6.5.3).
For example, at 40% valve lift, a 40% orifice size allows 40% of the full flow to pass.
Equal percentage characteristic (or logarithmic characteristic)
These valves have a valve plug shaped so that each increment in valve lift increases the flowrate by a certain percentage of the previous flow. The relationship between valve lift and orifice size
(and therefore flowrate) is not linear but logarithmic, and is expressed mathematically in Equation 6.5.1:
Example 6.5.1
The maximum flowrate through a control valve with an equal percentage characteristic is 10 m³/h. If the valve has a turndown of 50:1, and is subjected to a constant differential pressure, by using
Equation 6.5.1 what quantity will pass through the valve with lifts of 40%, 50%, and 60% respectively?
The increase in volumetric flowrate through this type of control valve increases by an equal percentage per equal increment of valve movement:
• When the valve is 50% open, it will pass 1.414 m³/h, an increase of 48% over the flow of 0.956 m³/h when the valve is 40% open.
• When the valve is 60% open, it will pass 2.091 m³/h, an increase of 48% over the flow of 1.414 m³/h when the valve is 50% open.
It can be seen that (with a constant differential pressure) for any 10% increase in valve lift, there is a 48% increase in flowrate through the control valve. This will always be the case for an
equal percentage valve with rangeability of 50. For interest, if a valve has a rangeability of 100, the incremental increase in flowrate for a 10% change in valve lift is 58%.
Table 6.5.1 shows how the change in flowrate alters across the range of valve lift for the equal percentage valve in Example 6.5.1 with a rangeability of 50 and with a constant differential pressure.
A few other inherent valve characteristics are sometimes used, such as parabolic, modified linear or hyperbolic, but the most common types in manufacture are fast opening, linear, and equal
Matching the valve characteristic to the installation characteristic
Each application will have a unique installation characteristic that relates fluid flow to heat demand. The pressure differential across the valve controlling the flow of the heating fluid may also
• In water systems, the pump characteristic curve means that as flow is reduced, the upstream valve pressure is increased (refer to Example 6.5.2, and Module 6.3).
• In steam temperature control systems, the pressure drop over the control valve is deliberately varied to satisfy the required heat load.
The characteristic of the control valve chosen for an application should result in a direct relationship between valve opening and flow, over as much of the travel of the valve as possible.
This section will consider the various options of valve characteristics for controlling water and steam systems. In general, linear valves are used for water systems whilst steam systems tend to
operate better with equal percentage valves.
1. A water circulating heating system with three-port valve
In water systems where a constant flowrate of water is mixed or diverted by a three-port valve into a balanced circuit, the pressure loss over the valve is kept as stable as possible to maintain
balance in the system.
- The best choice in these applications is usually a valve with a linear characteristic. Because of this, the installed and inherent characteristics are always similar and linear, and there will be
limited gain in the control loop.
2. A boiler water level control system – a water system with a two-port valve
In systems of this type (an example is shown in Figure 6.5.6), where a two-port feedwater control valve varies the flowrate of water, the pressure drop across the control valve will vary with flow.
This variation is caused by:
• The pump characteristic. As flowrate is decreased, the differential pressure between the pump and boiler is increased (this phenomenon is discussed in further detail in Module 6.3).
• The frictional resistance of the pipework changes with flowrate. The head lost to friction is proportional to the square of the velocity. (This phenomenon is discussed in further detail in Module
• The pressure within the boiler will vary as a function of the steam load, the type of burner control system and its mode of control.
Example 6.5.2 Select and size the feedwater valve in Figure 6.5.6
In a simplified example (which assumes a constant boiler pressure and constant friction loss in the pipework), a boiler is rated to produce 10 tonnes of steam per hour. The boiler feedpump
performance characteristic is tabulated in Table 6.5.2, along with the resulting differential pressure (ΔP) across the feedwater valve at various flowrates at, and below, the maximum flow requirement
of 10 m³/h of feedwater.
Note: The valve ΔP is the difference between the pump discharge pressure and a constant boiler pressure of 10 bar g. Note that the pump discharge pressure will fall as the feedwater flow increases.
This means that the water pressure before the feedwater valve also falls with increased flowrate, which will affect the relationship between the pressure drop and the flowrate through the valve.
It can be determined from Table 6.5.2 that the fall in the pump discharge pressure is about 26% from no-load to full-load, but the fall in differential pressure across the feedwater valve is a lot
greater at 72%. If the falling differential pressure across the valve is not taken into consideration when sizing the valve, the valve could be undersized.
As discussed in Modules 6.2 and 6.3, valve capacities are generally measured in terms of Kv. More specifically, Kvs relates to the pass area of the valve when fully open, whilst Kvr relates to the
pass area of the valve as required by the application.
Consider if the pass area of a fully open valve with a Kvs of 10 is 100%. If the valve closes so the pass area is 60% of the full-open pass area, the Kvr is also 60% of 10 = 6. This applies
regardless of the inherent valve characteristic. The flowrate through the valve at each opening will depend upon the differential pressure at the time.
Using the data in Table 6.5.2, the required valve capacity, Kvr, can be calculated for each incremental flowrate and valve differential pressure, by using Equation 6.5.2, which is derived from
Equation 6.3.2.The Kvr can be thought of as being the actual valve capacity required by the installation and, if plotted against the required flowrate, the resulting graph can be referred to as the
‘installation curve’.
At the full-load condition, from Table 6.5.2:
Required flow through the valve = 10 m³/ h
ΔP across the valve = 1.54 bar
From Equation 6.5.2:
Taking the valve flowrate and valve ΔP from Table 6.5.2, a Kvr for each increment can be determined from Equation 6.5.2; and these are tabulated in Table 6.5.3.
Constructing the installation curve
The Kvr of 8.06 satisfies the maximum flow condition of 10 m3/h for this example.
The installation curve could be constructed by comparing flowrate to Kvr, but it is usually more convenient to view the installation curve in percentage terms. This simply means the percentage of Kvr
to Kvs, or in other words, the percentage of actual pass area relative to the full open pass area.
For this example: The installation curve is constructed, by taking the ratio of Kvr at any load relative to the Kvs of 8.06. A valve with a Kvs of 8.06 would be ‘perfectly sized’, and would describe
the installation curve, as tabulated in Table 6.5.4, and drawn in Figure 6.5.7. This installation curve can be thought of as the valve capacity of a perfectly sized valve for this example.
It can be seen that, as the valve is ‘perfectly sized’ for this installation, the maximum flowrate is satisfied when the valve is fully open.
However, it is unlikely and undesirable to select a perfectly sized valve. In practice, the selected valve would usually be at least one size larger, and therefore have a Kvs larger than the
installation Kvr.
As a valve with a Kvs of 8.06 is not commercially available, the next larger standard valve would have a Kvs of 10 with nominal DN25 connections.
It is interesting to compare linear and equal percentage valves having a Kvs of 10 against the installation curve for this example.
Consider a valve with a linear inherent characteristic
A valve with a linear characteristic means that the relationship between valve lift and orifice pass area is linear. Therefore, both the pass area and valve lift at any flow condition is simply the
Kvr expressed as a proportion of the valve Kvs. For example:
It can be seen from Table 6.5.4, that at the maximum flowrate of 10 m³/h, the Kvr is 8.06. If the linear valve has a Kvs of 10, for the valve to satisfy the required maximum flowrate, the valve will
Using the same routine, the orifice size and valve lift required at various flowrates may be determined for the linear valve, as shown in Table 6.5.5.
An equal percentage valve will require exactly the same pass area to satisfy the same maximum flowrate, but its lift will be different to that of the linear valve.
Consider a valve with an equal percentage inherent characteristic
Given a valve rangeability of 50:1, τ = 50, the lift (H) may be determined using Equation 6.5.1:
Percentage valve lift is denoted by Equation 6.5.3.
As the volumetric flowrate through any valve is proportional to the orifice pass area, Equation 6.5.3 can be modified to give the equal percentage valve lift in terms of pass area and therefore Kv.
This is shown by Equation 6.5.4.
As already calculated, the Kvr at the maximum flowrate of 10 m³/h is 8.06, and the Kvs of the DN25 valve is 10. By using Equation 6.5.4 the required valve lift at full-load is therefore:
Using the same routine, the valve lift required at various flowrates can be determined from Equation 6.5.4 and is shown in Table 6.5.6.
Comparing the linear and equal percentage valves for this application
The resulting application curve and valve curves for the application in Example 6.5.2 for both the linear and equal percentage inherent valve characteristics are shown in Figure 6.5.8.
Note that the equal percentage valve has a significantly higher lift than the linear valve to achieve the same flowrate. It is also interesting to see that, although each of these valves has a Kvs
larger than a ‘perfectly sized valve’ (which would produce the installation curve), the equal percentage valve gives a significantly higher lift than the installation curve. In comparison, the linear
valve always has a lower lift than the installation curve.
The rounded nature of the curve for the linear valve is due to the differential pressure falling across the valve as the flow increases. If the pump pressure had remained constant across the whole
range of flowrates, the installation curve and the curve for the linear valve would both have been straight lines.
By observing the curve for the equal percentage valve, it can be seen that, although a linear relationship is not achieved throughout its whole travel, it is above 50% of the flowrate.
The equal percentage valve offers an advantage over the linear valve at low flowrates. Consider, at a 10% flowrate of 1 m³/h, the linear valve only lifts roughly 4%, whereas the equal percentage
valve lifts roughly 20%. Although the orifice pass area of both valves will be exactly the same, the shape of the equal percentage valve plug means that it operates further away from its seat,
reducing the risk of impact damage between the valve plug and seat due to quick reductions in load at low flowrates.
An oversized equal percentage valve will still give good control over its full range, whereas an oversized linear valve might perform less effectively by causing fast changes in flowrate for small
changes in lift.
Conclusion - In most applications, an equal percentage valve will provide good results, and is very tolerant of over-sizing. It will offer a more constant gain as the load changes, helping to provide
a more stable control loop at all times. However, it can be observed from Figure 6.5.8, that if the linear valve is properly sized, it will perform perfectly well in this type of water application.
3. Temperature control of a steam application with a two-port valve
In heat exchangers, which use steam as the primary heating agent, temperature control is achieved by varying the flow of steam through a two-port control valve to match the rate at which steam
condenses on the heating surfaces. This varying steam flow varies the pressure (and hence temperature) of the steam in the heat exchanger and thus the rate of heat transfer.
Example 6.5.3
In a particular steam-to-water heat exchange process, it is proposed that:
• Water is heated from 10°C to a constant 60°C.
• The water flowrate varies between 0 and 10 L/s (kg/s).
• At full-load, steam is required at 4 bar a in the heat exchanger coils.
• The overall heat transfer coefficient (U) is 1 500 W/m2°C at full-load, and reduces by 4% for every 10% drop in secondary water flowrate.
Using this data, and by applying the correct equations, the following properties can be determined:
• The heat transfer area to satisfy the maximum load. Not until this is established can the following be found:
• The steam temperature at various heat loads.
• The steam pressure at various heat loads.
At maximum load:
Heat load is determined from Equation 2.6.5:
• Find the heat transfer area required to satisfy the maximum load.
The heat transfer area (A) can be determined from Equation 2.5.3:
At this stage, ΔTLM is unknown, but can be calculated from the primary steam and secondary water temperatures, using Equation 2.5.5.
• Find the log mean temperature difference.
ΔTLM may be determined from Equation 2.5.5:
Find the conditions at other heat loads at a 10% reduced water flowrate:
If the water flowrate falls by 10% to 9 kg/s, the heat load reduces to:
Q̇ = 9 kg/s x (60 – 10°C) x 4.19 kJ / kg °C = 1 885.5 kW
The initial ‘U’ value of 1 500 W/m2 °C is reduced by 4%, so the temperature required in the steam space may be calculated from Equation 2.5.3:
• Find the steam temperature at this reduced load.
If ΔTLM = 100°C, and T1, T2 are already known, then Ts may be determined from Equation 2.5.5:
The saturated steam pressure for 137°C is 3.32 bar a (from the Spirax Sarco steam tables).
At 3.32 bar a, hfg = 2 153.5 kJ/kg, consequently from Equation 2.8.1:
Using this routine, a set of values may be determined over the operating range of the heat exchanger, as shown in Table 6.5.7.
If the steam pressure supplying the control valve is given as 5.0 bar a, and using the steam pressure and steam flowrate information from Table 6.5.7; the Kvr can be calculated from Equation 6.5.6,
which is derived from the steam flow formula, Equation 3.21.2.
Using this routine, the Kvr for each increment of flow can be determined, as shown in Table 6.5.8.
The installation curve can also be defined by considering the Kvr at all loads against the ‘perfectly sized’ Kvs of 69.2.
The Kvr of 69.2 satisfies the maximum secondary flow of 10 kg / s.
In the same way as in Example 6.5.2, the installation curve is described by taking the ratio of Kvr at any load relative to a Kvs of 69.2.
Such a valve would be ‘perfectly sized’ for the example, and would describe the installation curve, as tabulated in Table 6.5.8, and drawn in Figure 6.5.9.
The installation curve can be thought of as the valve capacity of a valve perfectly sized to match the application requirement.
It can be seen that, as the valve with a Kvs of 69.2 is ‘perfectly sized’ for this application, the maximum flowrate is satisfied when the valve is fully open.
However, as in the water valve sizing Example 6.5.2, it is undesirable to select a perfectly sized valve. In practice, it would always be the case that the selected valve would be at least one size
larger than that required, and therefore have a Kvs larger than the application Kvr.
A valve with a Kvs of 69.2 is not commercially available, and the next larger standard valve has a Kvs of 100 with nominal DN80 connections.
It is interesting to compare linear and equal percentage valves having a Kvs of 100 against the installation curve for this example.
Consider a valve with a linear inherent characteristic
A valve with a linear characteristic means that the relationship between valve lift and orifice pass area is linear. Therefore, both the pass area and valve lift at any flow condition is simply the
Kvr expressed as a proportion of the valve Kvs. For example.
At the maximum water flowrate of 10 kg/s, the steam valve Kvr is 69.2. The Kvs of the selected valve is 100, consequently the lift is:
Using the same procedure, the linear valve lifts can be determined for a range of flows, and are tabulated in Table 6.5.9.
* The installation curve is the percentage of Kvr at any load to the Kvr at maximum load
Consider a valve with an equal percentage inherent characteristic
An equal percentage valve will require exactly the same pass area to satisfy the same maximum flowrate, but its lift will be different to that of the linear valve.
Given that the valve turndown ratio, τ = 50, the lift (H) may be determined using Equation 6.5.4.
Using the same procedure, the percentage valve lift can be determined from Equation 6.5.4 for a range of flows for this installation.
The corresponding lifts for linear and equal percentage valves are shown in Table 6.5.9 along with the installation curve.
As in Example 6.5.2, the equal percentage valve requires a much higher lift than the linear valve to achieve the same flowrate. The results are graphed in Figure 6.5.10.
There is a sudden change in the shape of the graphs at roughly 90% of the load; this is due to the effect of critical pressure drop across the control valve which occurs at this point.
Above 86% load in this example, it can be shown that the steam pressure in the heat exchanger is above 2.9 bar a which, with 5 bar a feeding the control valve, is the critical pressure value. (For
more information on critical pressure, refer to Module 6.4, Control valve sizing for steam).
It is generally agreed that control valves find it difficult to control below 10% of their range, and in practice, it is usual for them to operate between 20% and 80% of their range.
The graphs in Figure 6.5.10 refer to linear and equal percentage valves having a Kvs of 100, which are the next larger standard valves with suitable capacity above the application curve (the required
Kvr of 69.2), and would normally be chosen for this particular example.
The effect of a control valve which is larger than necessary
It is worth while considering what effect the next larger of the linear or equal percentage valves would have had if selected. To accommodate the same steam loads, each of these valves would have had
lower lifts than those observed in Figure 6.5.10.
The next larger standard valves have a Kvs of 160. It is worth noting how these valves would perform should they have been selected, and as shown in Table 6.5.10 and Figure 6.5.11. | {"url":"https://www.spiraxsarco.com/learn-about-steam/control-hardware-electric-pneumatic-actuation/control-valve-characteristics","timestamp":"2024-11-09T07:56:19Z","content_type":"text/html","content_length":"182188","record_id":"<urn:uuid:7f05ba19-7d48-43c2-a928-d2a83ad8215a>","cc-path":"CC-MAIN-2024-46/segments/1730477028116.30/warc/CC-MAIN-20241109053958-20241109083958-00702.warc.gz"} |
Consider a probability model consisting of randomly drawing two colored balls from a jar containing
Staff member
Consider a probability model consisting of randomly drawing two colored balls from a jar containing 2 red and 1 blue balls. What is the Sample Space of this experiment? (assume B= blue and R=red)
The sample space is the list of all possible events | {"url":"https://www.mathcelebrity.com/community/threads/consider-a-probability-model-consisting-of-randomly-drawing-two-colored-balls-from-a-jar-containing.1361/","timestamp":"2024-11-04T08:55:31Z","content_type":"text/html","content_length":"45933","record_id":"<urn:uuid:17f30abd-4b17-4e2a-b30f-6fa89b468c29>","cc-path":"CC-MAIN-2024-46/segments/1730477027819.53/warc/CC-MAIN-20241104065437-20241104095437-00752.warc.gz"} |
Distributive Property Of Multiplication
These worksheets are specially designed for 3rd graders like you to help you understand and practice a really cool math concept called the distributive property.
So, what is distributive property? It’s a simple rule in math that helps us solve multiplication problems more easily. It says that if we have to multiply a number by the sum of two other numbers, we
can multiply the number with each of the other numbers separately and then add the results together. Sounds interesting, right?
Let me show you an example. Imagine we have a problem like this:
4 × (3 + 2)
According to the distributive property, we can break this down into two smaller multiplication problems:
(4 × 3) + (4 × 2)
Now, we can solve each part:
12 + 8
And finally, we can add the results:
So, 4 × (3 + 2) = 20.
In the Distributive Property of Multiplication Worksheets, you’ll find lots of problems like this to practice. The more you practice, the better you’ll understand the distributive property and the
easier it’ll be for you to solve multiplication problems in the future.
Remember, it’s okay if you don’t get it right away. Keep practicing and asking for help if you need it, and you’ll become a distributive property expert in no time! Good luck, and have fun!
Printable Distributive Property Of Multiplication Worksheets
Answer Key | {"url":"https://www.worksheetsgo.com/distributive-property-of-multiplication/","timestamp":"2024-11-02T07:58:25Z","content_type":"text/html","content_length":"113883","record_id":"<urn:uuid:55e63597-0ee2-4193-9da3-afff01e2c171>","cc-path":"CC-MAIN-2024-46/segments/1730477027709.8/warc/CC-MAIN-20241102071948-20241102101948-00658.warc.gz"} |
Summary - Algebra | Term 3 Chapter 3 | 7th Maths
● The following identities are proved geometrically:
* (x + a)(x +b) = x ^2 + x(a + b) +ab
* (a + b)^2 =a^2 + 2ab +b^2
* (a − b)^2 =a^2 − 2ab +b^2 and
* (a +b)(a − b) = a ^2 −b^2 .
● The factors of an algebraic expression is two or more expressions whose product is the given expression.
● The process of writing an algebraic expression as the product of its factors is called factorisation.
● An algebraic statement that shows two algebraic expression being unequal is known as an algebraic inequation.
● The algebraic expressions are connected with any one of the four signs of inequalities, namely, >, ≥ ,< and ≤.
● When both sides of an inequation are added, subtracted, multiplied and divided by the same non-zero positive number, the inequality remains the same.
● When both sides of an inequation are multiplied or divided by the same non-zero negative number, the sign of inequality is reversed. For example, x < y ⇒ −x >−y .
● The solutions of an inequation can be represented on the number line by marking the true values of solutions with different colour on the number line.
ICT Corner
Expected outcome
Step – 1
Open the Browser and type the URL Link given below (or) Scan the QR Code. GeoGebra work sheet named “(x+a)(x+b)” will open. Drag the sliders to change x, a, b values. Check the steps on right side.
Step - 2
After completing Click on “Inequation” in the left side. Move the slider below to change “a” value.Click on the check boxes to see respective inequations on the number line.
Browse in the link
(x+a)(x+b): https://www.geogebra.org/m/f4w7csup#material/nguv3yey or Scan the QR Code. | {"url":"https://www.brainkart.com/article/Summary_44265/","timestamp":"2024-11-03T10:35:03Z","content_type":"text/html","content_length":"44029","record_id":"<urn:uuid:f372cb39-84e3-45c7-9b73-b82c213f53a0>","cc-path":"CC-MAIN-2024-46/segments/1730477027774.6/warc/CC-MAIN-20241103083929-20241103113929-00625.warc.gz"} |
Two tuning forks that have the same amplitude but slightly
different frequencies are stuck at the...
Two tuning forks that have the same amplitude but slightly different frequencies are stuck at the...
Two tuning forks that have the same amplitude but slightly different frequencies are stuck at the same time to produce a complex wave. What is this called? If the period of the complex wave that they
produce is 0.25s and the period of one of the tuning fork is 0.04s. What is one possible frequency of the other tuning fork? When the sinusoidal waves from the tuning fork are opposite phases, what
happens at those points to the complex wave they produce?
Answers : | {"url":"https://justaaa.com/physics/533692-two-tuning-forks-that-have-the-same-amplitude-but","timestamp":"2024-11-12T06:37:40Z","content_type":"text/html","content_length":"40402","record_id":"<urn:uuid:d3b5b77a-6d7f-4049-a111-88361d47bcb8>","cc-path":"CC-MAIN-2024-46/segments/1730477028242.58/warc/CC-MAIN-20241112045844-20241112075844-00326.warc.gz"} |
perational semantics
2 Introduction to operational semantics. This chapter presents the syntax of a programming language, IMP, a small language of while programs. IMP is called an
We formalize the approach as an operational semantics for a core subset of the with a rigorous simulator based on the operational semantics is described.
« Operational semantics » Patrick Cousot Jerome C. Hunsaker Visiting Professor Massachusetts Institute of Technology Department of Aeronautics and Astronautics Operational Semantics. Pages 13-35.
Cremers, Cas (et al.) Preview Buy Chapter 25,95 Homework Operational Semantics 1. Consider following statement repeat S until b a. Extend the natural operational (“big-step”) semantics of the WHILE
language (Table 2.1 from [1]) by a rule for relation → for the repeat-construct. (The semantics for the repeat-construct should not rely on the existence of a while-construct) Operational semantics
loosely corresponds to interpretation, although again the "implementation language" of the interpreter is generally a mathematical formalism. Operational semantics may define an abstract machine
(such as the SECD machine ), and give meaning to phrases by describing the transitions they induce on states of the machine.
This semantics is inspired by a new denotational semantics proposed in recent related work. operational semantics An approach to the semantics of programming languages that uses the concept of an
“abstract machine” that has a state and some primitive instructions or rules that cause the states to change. The machine is defined by specifying how the components of the state are changed by each
of the instructions or rules. Java: An Operational Semantics Gaurav S. Kc B. Eng. Project nContinued research in Java Semantics nImproved know-how of the Java system. Acknowledgements Natural
Operational Semantics can be easily encoded in formal systems based on λ-calculus type-checking, such as the Edinburgh Logical Framework. An Operational Semantics for Stateflow?
operational semantics An approach to the semantics of programming languages that uses the concept of an “abstract machine” that has a state and some primitive instructions or rules that cause the
states to change. The machine is defined by specifying how the components of the state are changed by each of the instructions or rules. Computations are sequences of state transitions.
Nils Anders Danielsson: Operational semantics using the partiality monad. ICFP 2012: 127-138. [c13]. We formalize the approach as an operational semantics for a core subset of the with a rigorous
simulator based on the operational semantics is described.
Homework Operational Semantics 1. Consider following statement repeat S until b a. Extend the natural operational (“big-step”) semantics of the WHILE language (Table 2.1 from [1]) by a rule for
relation → for the repeat-construct. (The semantics for the repeat-construct should not rely on the existence of a while-construct)
(The semantics for the repeat-construct should not rely on the existence of a while-construct) Operational semantics loosely corresponds to interpretation, although again the "implementation
language" of the interpreter is generally a mathematical formalism.
Since this semantics is not sufficient to cover concurrency, search strategies, or to reason about costs associated to particular computations, we define a "small-step" operational semantics
Contextual Operational Semantics • Can view •as representing the program counter • The advancement rules for •are non-trivial – At each step the entire command is decomposed – This makes contextual
semantics inefficient to implement directly • The major advantage of contextual semantics: allows a mix of local and global reduction 1.1 Operational semantics 3 Some different approaches to
programming language semantics are summarised on Slide 3. This course will be concerned with Operational Semantics. The denotational approach (and its relation to operational semantics) is introduced
in the Part II course on Denotational Semantics. The semantics for type theory that we shall develop isbased on an inductive construction of a system of relations between terms interpreted by an
operational semantics. Since the terminology and notation for the relations that we shall consider are not well-established, we set down our definitions here. An operational semantics is a
mathematical model of programming language execution. It is, in essence, an interpreter defined mathematically.
Coaching online
The machine is defined by specifying how the components of the state are changed by each of the instructions or rules. Java: An Operational Semantics Gaurav S. Kc B. Eng. Project nContinued research
in Java Semantics nImproved know-how of the Java system. Acknowledgements Natural Operational Semantics can be easily encoded in formal systems based on λ-calculus type-checking, such as the
Edinburgh Logical Framework.
1.3 Denotational Semantics The idea behind this semantics is to look at a program as a mathematical function, i.e.
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Types of Operating Systems - There are four main types of operating systems, including RTOS and single-user, multi-tasking as used by Windows. See the types of operating systems. Advertisement By:
Curt Franklin & Dave Coustan Within the bro
We present a formal operational semantics for Stateflow, the graphical Statecharts-like language of the Matlab/Simulink tool suite Denotational vs. Operational. Denotational semantics is similar to
high-level operational semantics, except: Machine is gone Language is mathematics (lamda calculus) The difference between denotational and operational semantics: In operational semantics, the state
changes are defined by coded algorithms for a virtual machine 2004-03-29 · We present a formal operational semantics for Stateflow, the graphical Statecharts-like language of the Matlab/Simulink tool
suite that is widely used in model-based development of embedded systems. | {"url":"https://hurmanblirrikuhgt.firebaseapp.com/73383/84353.html","timestamp":"2024-11-10T21:00:47Z","content_type":"text/html","content_length":"11122","record_id":"<urn:uuid:1dd4dbf8-bdc7-44d0-a654-09bad1de4219>","cc-path":"CC-MAIN-2024-46/segments/1730477028191.83/warc/CC-MAIN-20241110201420-20241110231420-00745.warc.gz"} |
Exercise 5
This exercise requires a little independent work; figuring out how to write a function in Maple, and how to implement a function in Fortran. The actual time required, once you know how to do it, is
quite small. Spend the rest of the time wisely; ie, have fun!
To help you if you get stuck, there are hints, as usual. If you can do without them, the exercise is more useful, but don't be afraid to use ...
... your bonus points! Credits: 4/4
┃ NOTE: ┃
┃ The next lecture covers material that will be part of the first project, so it is a good idea to come to the lecture. ┃
Getting the exercise files [about 1 minute]
To extract the exercise files for this weeks exercise, do
cd ~/ComputerPhysics
cvs update -d
In case of problems, see the CVS update help page.
Using IDL to explore the problem [about 45 minutes]
The integrand from the Lecture Notes is available as the function prof.pro in your 5_Integration directory. In this section, the point is to first look at the shape of the integrand and consider what
happens with the integrand under the substitution of variables discussed in the Lecture Notes, and then explore how the integration error depends on the number of points.
• Start IDLDE as in previous exercises, and try the following. It is possible, but perhaps just disturbing, to copy and paste from these instructions to the IDL command input; why not just type it
in, while actually thinking about what it is that you are doing. Or, if you choose the copy/paste method, use the time you gain to think about the input command, rather than just marching blindly
on to the next one :-!
IDL> n=64 ; even number of pts
IDL> v=100.*(-1.+2.*findgen(n)/(n-1)) ; make equidistant v's
IDL> plot,v,prof(v) ; plot profile as a function of v
IDL> oplot,v,prof(v),psym=1 ; use arrow keys + CTRL-a, CTRL-e to add symbols
IDL> u=atan(100.)*(-1.+2.*findgen(n)/(n-1)) ; construct the u scale
IDL> v=tan(u) ; the corresponding v's
IDL> plot,v,prof(v),psym=-1 ; negative psym value -> line + symbols
IDL> plot,u,prof(v)*(1.+v^2),psym=-1 ; transformed integrand as a function of u
• Use IDL to plot the error in the trapezoidal formula as a function of the number of points used (cf. notes). The first command starts a recording of the IDL commands into a journal file
IDL> journal,'error.jou' ; Start recording
IDL> plot,/xlog,/ylog,[1,3000],[1e-7,10],xstyle=1,/nodata ; empty frame
IDL> exact=5.467382771 ; from Maple
IDL> n=2 ; start small
IDL> n=n*2 & v=100.*(-1.+2.*findgen(n)/(n-1)) ; linear v
IDL> error=abs(trapez(v,prof(v))-exact)/exact ; relative error
IDL> print,n,error & plots,n,error,psym=1 ; print and plot symbol
• Use the arrow keys to repeat the last 3 lines again, until n is equal to 2048. Then reset n and do the case with variable substitution:
IDL> n=2 ; reset n
IDL> n=n*2 & u=atan(100.)*(-1.+2.*findgen(n)/(n-1)) ; linear u
IDL> v=tan(u) ; non-linear v
IDL> error=abs(trapez(u,prof(v)*(1.+v^2))-exact)/exact ; relative error
IDL> print,n,error & plots,n,error,psym=5 ; print and plot symbol
• Use the arrow keys to repeat the last 4 lines again, until the values for the case with variable substitution are filled out (again up to n=2048). The next statement closes the journal file.
IDL> journal ; stop the recording
• How many points are needed for better than 10^-5 precision in the answer for each of the two methods?
For the psym=1 case Credits: 1/-1
For the psym=5 case Credits: 1/-1
• You may now use the journal file (error.jou) to repeat the commands for a PostScript and a png copy. To make the plot more useful edit the journal file removing eventual mistakes and change it
such that the plot includes appropriate labels on the x- and y-axis and add your userid as main title on the figure (if you don't know how to, then check the help on the plot command) and a
horizontal line showing the 10^-5 threshold. Now make a PostScript file with the plot:
IDL> set_plot,'ps' ; PostScript
IDL> @error.jou ; repeat commands from journal file
IDL> device,/close ; close the idl.ps file
And a PNG file:
IDL> set_plot,'z' ; Set the devise to a Z buffer (incl 3D information)
IDL> @error.jou ; repeat commands from journal file
IDL> pic=tvrd() ; reads the graphical to a byte array
IDL> set_plot,'x' ; X windows again
IDL> write_png,'error.png',pic ; saves the image in PNG format
Check that you can see the error.png in the web browser or an image viewer program before submitting it.
Please upload the error.png file Locate and upload your error.png file: Credits: 2/0
Integrals with Maple [about 30 minutes]
Starting Maple
To start maple give the shell command "xmaple". If it is the first time you run xmaple you get a choice btw "worksheet" or "document" -- choose "document".
Evaluating integrals with Maple
To evaluate an indefinite integral, click on "expressions" in the menu list on the left, and then on the first integral symbol. Fill in an expression instead of f, and hit RETURN. Try this with the
expression 1/(1+x^2) (use the hat (caret) sign to make the exponent), which should give you arctan(x).
To evaluate a definite integral, choose instead the next integral symbol in the "expressions" menu, and enter values for the limits. Try for example the interval -100 to 100.
To evaluate a definite integral numerically, just enter the limits in the form of floating point numbers (a number that includes a period), or enclose the expression in evalf(..).
The fact that the integral of 1/(1+x^2) is arctan(x) is precisely the reason for the choice of transformation in the example we are looking at in this exercise. The actual (test) profile is similar
to 1/(1+x^2) (as a real spectral line profile would also be). Hence the transformation of variables u=arctan(x), or x=tan(u), turns the integrand into a nearly constant function.
• To illustrate this further, lets construct the test function from the Lecture Notes (type these lines into the Maple document and hit RETURN after each):
What is the value of the integral? Credits: 2/-2
Substitution of variables in Maple [about 45 minutes]
In this section, we go through the substitution steps in Maple. This is NOT just a repetition of the IDL and Fortran parts; Maple is able to perform analytical differentiation as well as integration,
and in a real situation you might use Maple to try to find a function that is sufficiently "similar" to your complicated integrand, and yet is analytically integrable.
• To perform the variable substitution in Maple, first type and execute a cell with
• With Maple, we can find the transformation "weight function" dv/du with analytic differentiation:
which becomes 1+tan(u)^2
• Given these pieces, write the expression for the transformed integrand (use evalf(Int( )). If you get stuck ...
... use this hint! Credits: -1/-1
Compare this with the formula in the Lecture Notes.
• As before, it is easy to plot the integrand;
Plot(φ (1+v^2),u=atan(-100)..atan(100))
and to evaluate the integral. Check that you get the same answer as before!
• Repeat the plotting from above, but this time plot the graphics to a file that can be included in a report. There are two ways to do this:
□ Click on the graphics window in Maple. Then choose the Plot menu in the top bar of the Maple window and choose one of the few possible choices.
□ Change the plot devise to one of the many available. To do this check the help on plotsetup and look at the examples at the bottom of the page. Use this to create an image of either of the
previous plots in png format (it works even it is not listed as one of the available formats) in a file called maple.png. --- CHANGE the x-range to your personal choice before making the
As a final step, save your Maple document as integrate.mw. The contents of the file should be the result of going through the exercise steps above.
Check that you can see the maple.png file in your browser or an image viewer program.
Please upload the maple.png file Locate and upload your maple.png file: Credits: 4/0
Fortran exercises [about 60 minutes]
The directory 5_Integration is set up with a main program Integrate.f90 that calls a slightly modified version of QROMB from the Numerical Recipes library. The modified version has two additional
parameters; an input parameter that specifies the requested precision, and an output parameter that returns the number of intervals that were actually used. Note that the actual precision may be
better or worse than the requested precision; the internal error estimate that is used in QROMB assumes that the integrand is "well-behaved".
Home work [about 2 hours]
Already before coming to the exercise hours you should have spent an hour or so reading the Chapter 5 of the lecture notes, and the Chapter in Numerical Recipes about Integration. Use additional
time after this exercise to look at how the substitution of variables is implemented in IDL, Maple, and Fortran; i.e., take the last and important step in the chain Preparation -> Exercise -> | {"url":"http://fys.bozack.dk/kurser/23compfysopg/5/","timestamp":"2024-11-03T03:03:40Z","content_type":"text/html","content_length":"35049","record_id":"<urn:uuid:fd8b6a68-f38c-4c52-861c-9d8375d85321>","cc-path":"CC-MAIN-2024-46/segments/1730477027770.74/warc/CC-MAIN-20241103022018-20241103052018-00421.warc.gz"} |
What is the formula of Volume of solid hemisphere?
What is the formula of Volume of solid hemisphere?
Hemisphere Formulas in terms of radius r: Volume of a hemisphere: V = (2/3)πr.
How do you find the Volume of a hemisphere shell?
Volume of material used for hemispherical shell=23π(R3−r3)
What would be the Volume of hemisphere whose TSA is 108π sq cm?
144π cm3
∴ The volume of the hemisphere is 144π cm3.
What is hemisphere and its formula?
As the Hemisphere is the half part of a sphere, therefore, the curved surface area is also half that of the sphere. Curved surface area of hemisphere = 1/2 ( 4 π r2) = 2 π r2.
What is the volume of a hemisphere with a radius of 2cm?
The volume of the hemisphere is 352/21 cm³.
What is the volume of the hemisphere whose radius is R?
Answer. Hemisphere Formulas in terms of radius r: Volume of a hemisphere: V = (2/3)πr.
What is the volume of a hemisphere with a radius of 3?
Answer: 18πcm³ or 56.57cm³(Approximately ) is the Volume of Hemisphere whose radius is 3cm.
What is the formula of area of hemisphere?
3πr2 square units
The total surface area of a hemisphere = 3πr2 square units “r” is the radius of the hemisphere.
What is the volume of a hemisphere with a radius of 2.6 m?
The hemisphere we want to divide that value by two has a volume of approximately 294.5 cubic miles, so the volume of the hemisphere is approximately 294.5 cubic miles.
What is the formula for the size of a hemisphere?
Hemisphere Formulas in terms of radius r: Volume of a hemisphere: V = (2/3) π r 3; Circumference of the base of a hemisphere: C = 2 π r; Curved surface area of a hemisphere (1 side, external only): A
= 2 π r 2
What is the volume of a solid hemisphere?
Example-3 : The volume of a solid hemisphere is 18π mm3. Find the total surface of the same. Example-4: The three metallic spheres have radii 3cm, 4cm & 5cm respectively, are melted to form a single
solid sphere. Find the radius of the resulting sphere. Example-5 : A hemispherical bowl has a radius of 4.2 cm.
How do you find the volume of a hollow hemisphere?
Volume of hollow hemisphere (volume of the material used) Let r and R be the inner and outer radius of the hollow hemisphere. Volume of a hollow hemisphere = 2/3 π (R3 − r3 ) cu. Units. Example 7.21
The volume of a solid hemisphere is 29106 cm3. Another hemisphere whose volume is two-third of the above is carved out.
How do you find the surface area of a solid sphere?
Flat surface area or base area of the hemisphere = Area of the circle with same radius = π r2 Curved surface area of hemisphere shell = 2 π ( R2 + r2 ) ( Considered inside and outside area of
hemisphere) Solid Sphere is the region in space bound by a sphere. | {"url":"https://federalprism.com/what-is-the-formula-of-volume-of-solid-hemisphere/","timestamp":"2024-11-01T19:26:24Z","content_type":"text/html","content_length":"55941","record_id":"<urn:uuid:ffa43dcf-f8ec-45a4-8010-fb2a5069e25e>","cc-path":"CC-MAIN-2024-46/segments/1730477027552.27/warc/CC-MAIN-20241101184224-20241101214224-00167.warc.gz"} |
Scientific Research Codes
Seismic Data Fetching and Processing
Data Request Tools
Seismic Data Format Conversion
Seismic Data Processing
Plotting and Visualization
Traveltime and Ray Tracing
Synthetic Seismograms
Ray Theory for 1D Layered Earth
Reflectivity/Wavenumber Integration for 1D Layered Earth
Modal Summation Method for 1D Layered Earth
• Modal Summation in CPS330 | A tutorial (in Chinese): Collection of programs for calculating theorectical seismogram, receiver function, surface wave dispersion curve et al.
Reflectivity/Wavenumber Integration for 1D Layered Spherical Earth
• yaseis: Calculate synthetic seismograms in spherically layered isotropic models
Normal Modes Summation for 1D Layered Spherical Earth
• Mineos: Computes synthetic seismograms in a spherically symmetric non-rotating Earth by summing normal modes
• Colleen Dalton’s Mineos: All the tools one should need to compile and run the MINEOS program
□ Matlab to MINEOS: Wrapper scripts for running MINEOS through MATLAB
□ MINEOS_synthetics: Calculate dispersion tables and synthetic seismograms for layered models using MINEOS and idagrn6 housed within MATLAB wrappers
• DISPER80: Calculation of normal modes, which is a very old fortran code.
• Normal modes: Normal-mode based computation of seismograms for spherically symmetric Earth models
• QSSP: Calculating complete synthetic seismograms of a spherical earth using the normal mode theory
• specnm: Spectral element normal mode code
Direct Solution Method for 1D Layered Spherical Earth
• DSM | An updated version: Computing synthetic seismograms in spherically symmetric transversely isotropic (TI) media using the Direct Solution Method
• DGRFN: Calculate synthetic seismograms in a spherically layered model
• GEMINI: Calculation of synthetic seismograms for global, spherically symmetric media based in direct evaluation of Green’s functions (The files seem wrong)
Boundary Element Methods
• AstroSeis: Asteroid seismic wavefield modeling written in MATLAB
Discontinuous Galerkin Method
• NEXD: high order simulation of seismic waves using the nodal discontinuous Galerkin method
• SeisSol: numerical simulation of seismic wave phenomena and earthquake dynamics
Finite Difference Methods
Finite Element Methods
Pseudo-Spectral Methods
• Ps2D: A very simple code for elastic wave simulation in 2D using a Pseudo-Spectral Fourier method
Spectral Element Methods
Hybrid Methods
Surface waves in 3D structures
• Couplage: Modelling of propagation of surface waves in 3D structures by mode coupling method
Waveform Forward Modelling
Seismic Source
Earthquake Detection
• REAL | A tutorial (in Chinese): Rapid Earthquake Association and Location written in C
• S-SNAP: Seismicity-Scanning based on Navigated Automatic Phase-Picking
• Match&Locate: Detect and locate small events from continuous seismic waveforms using templates
• GPU-MatchLocate1.0: An improved match and locate method using GPU
• FastMatchedFilter: An efficient seismic matched-filter search for both CPU and GPU architectures
• dynamic_earthquake_triggering: Detecting dynamic earthquake triggering written in Python
• FAST: End-to-end earthquake detection pipeline via efficient time series similarity search
• EQcorrscan: Detection and analysis of repeating and near-repeating earthquakes written in Python
• RT-EQcorrscan: Real-time implementation of EQcorrscan method
• MESS: A Matched filter earthquake detector with GPU acceleration
• PAL: An earthquake detection and location architecture including phase Picking, phase Association, event Location.
• REDPy: Repeating Earthquake Detector written in Python
Earthquake Location
Focal Mechanism
Seismic Tomography
Body-wave Tomography
Ambient Noise Data Processing
Surface-wave Dispersion Measurement
Surface-wave Tomography
• ASWMS | GitHub: Automated Surface Wave Phase Velocity Measuring System written in MATLAB, measuring the phase and amplitude of surface waves and then generate surface-wave tomography maps using
the Eikonal and Helmhotza tomography
• FMST | iEarth: Traveltime tomography in 2-D spherical shell coordinates based on fast marching method
• rj-TOMO: 2-D transdimensional travel time tomography based on Reversible jump Markov chain Monte Carlo algorithm
• tomo_sp_cu_s | GitHub: Ray theoretic surface wave tomography
• MATnoise: Calculate ambient noise cross-correlations, measure phase velocities, and invert for phase velocity maps in MATLAB
• SurfwaveTomoPrograms: Finite frequency Rayleigh wave tomography programs
Surface-wave Dispersion Inversion
• CPS330 | A tutorial (in Chinese): Collection of programs for calculating theorectical seismogram, receiver function, surface wave dispersion curve et al.
□ srfpython: Compute, display, and invert 1D depth models based on CPS330 written in Python
• dispinversion: Surface wave dispersion inversion code written in MATLAB
• MCDisp: Surface wave dispersion inversion using Monte Carlo methohd written in Python
Surfave-wave Tomography Workflow
Direct Inversion of Surface-wave Dispersion Data
Surface-wave Dispersion Forward Calculation
Seismic Imaging
Receiver Function
Rayleigh-wave Ellipticity
• DOP-E | GitHub: Rayleigh wave ellipticity, measurement and inversion from ambient noise written in Fortran and Python
• Quake-E: Measure Rayleigh wave ellipticity from earthquake data written in Python
Shear Wave Splitting
Scattering and Intrinsic Attenuation
Joint Inversion of Seismological Data
Waveform Inversion
• MC3deconv: Bayeisan inversion to recover Green’s functions of receiver-side structures from teleseismic waveforms
Full Waveform Inversion
Multi-observable Modelling and Inversion of Geophysical Data
• LitMod: Multi-observable modelling and inversion of geophysical data
• JDSurfG: Joint Inversion of Direct Surface Wave Tomography and Bouguer Gravity
Ambient Noise
Ambient Noise Monitoring
• MSNoise: A Python Package for Monitoring seismic velocity changes using ambient seismic noise
• NoisePy: Fast and easy computation of ambient noise cross-correlation functions written in Python, with noise monitoring and surface wave dispersion analysis
• yam: Yet another monitoring tool using correlations of ambient noise written in Python
Noise HVSR
Earth’s interior
• FastTrip: Fast MPI-accelerated Triplication Waveform Inversion Package
• PKPprecursor | GitHub: Locating seismic scatterers in the lower mantle, using PKP precursor onsets
• ss-precursors: SS Precursor Workflow
Seismic Data Analysis
General Signal Analysis
Phase Picking
Single Station Signal Analysis
Array seismology
Seismic Interferometry
Seismic Data Digitization and Correction
Pattern Recognition and Machine Learning
Spherical Harmonics
• Shansyn: Spherical Harmonic ANalysis and SYNthesis
• SHTOOLS: Spherical Harmonic Tools
Seismological/Geophysical Library
Seismological Tools/Library
• CREWES Matlab Toolbox: Numerical Methods of Exploration Seismology with algorithms in MATLAB
• Pyrocko: An open-source seismology toolbox and library written in the Python
• SEISAN: Earthquake analysis software
Geophysical Tools/Library
• Fatiando: Open-source tools for geophysics
• UNAVCO | Software: A community of scientists, educators, and professionals working together to better understand Earth processes and hazards using geodesy
• CitcomS: Solve compressible thermochemical convection problems relevant to Earth’s mantle
Mineral Physics
• GassDem: Modeling anisotropic seismic properties written in MATLAB
Thermodynamic Modeling
• distaz | A tutorial (in Chinese): Calculate distance, azimuth and back-azimuth of any two points at the Earth’s surface
• PlateFlex: Estimate lithosphere elstatic thickness written in Python and Fortran
• GPlates: A desktop software for the interactive visualisation of plate-tectonics
Geophysical Inversion
Inversion Theory
Linear Algebra
• BLAS: Basic Linear Algebra Subprograms are routines that provide standard building blocks for performing basic vector and matrix operations
• LAPACK | Working Notes | GitHub: Linear Algebra PACKage is a library of Fortran subroutines for solving the most commonly occurring problems in numerical linear algebra
• LINPACK: a collection of Fortran subroutines that analyze and solve linear equations and linear least-squares problems, which has been largely superceded by LAPACK
Gradient Methods
• LSQR: A conjugate-gradient type method for solving sparse linear equations and sparse least-squares problems
• SEISCOPE Optimization Toolbox: A set of FORTRAN 90 optimization routines dedicated to the resolution of unconstrained and bound constrained nonlinear minimization problems
Monte Carlo Methods
Numerical Library
Software Centers
Geoscience Software Centers
Software Development Tools | {"url":"https://seismo-learn.org/links/codes/","timestamp":"2024-11-06T20:51:17Z","content_type":"text/html","content_length":"96159","record_id":"<urn:uuid:2188b793-8993-4f96-836c-38a743e1848c>","cc-path":"CC-MAIN-2024-46/segments/1730477027942.47/warc/CC-MAIN-20241106194801-20241106224801-00351.warc.gz"} |
st: Which command to test whether proportions of categories are the same
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st: Which command to test whether proportions of categories are the same in two sets of people?
From Jen Zhen <[email protected]>
To [email protected]
Subject st: Which command to test whether proportions of categories are the same in two sets of people?
Date Wed, 27 Jan 2010 10:34:08 -0500
Hi there,
I have a summary table with members from (1) the treatment group and
(2) the control group of an experiment, and would like to provide for
each observable variable a formal test for whether the two sets of
people come indeed from the same population. For the continuous normal
variables, I am just doing a t-test to test for equality of means, but
I'm not fully sure what to do instead for the categorical variables
(with more than 2 categories).
I found the -csgof- command for a Chi-Square test of whether the
proportions of the different categories in one sample correspond to
those coming from some hypothesis, but which command would you use to
test whether the proportions in the two groups are identical?
* For searches and help try:
* http://www.stata.com/help.cgi?search
* http://www.stata.com/support/statalist/faq
* http://www.ats.ucla.edu/stat/stata/ | {"url":"https://www.stata.com/statalist/archive/2010-01/msg00913.html","timestamp":"2024-11-11T13:45:07Z","content_type":"text/html","content_length":"9971","record_id":"<urn:uuid:9cf9e46c-e26e-436f-a55d-81a1248fb4e9>","cc-path":"CC-MAIN-2024-46/segments/1730477028230.68/warc/CC-MAIN-20241111123424-20241111153424-00626.warc.gz"} |
Passage of a Barotropic Vortex through a Gap
1. Introduction
Vortices are an essential part of the oceanic circulation: they are long-lived, they can migrate over long distances compared with their size, and they trap water in their cores. Because of these
characteristics, vortices are important in the transport and dispersion of physical and biological properties in the ocean. Two examples are the vortices advected by the Caribbean Current toward the
Yucatan Channel and the vortices that after being ejected by the North Brazil Current (NBC) drift toward the Lesser Antilles.
In the Caribbean Sea, vortices with radii between 50 and 130 km and swirl speeds between 30 and 70 cm s^−1 are advected westward by the Caribbean Current at speeds ranging from 2 cm s^−1 in the west
to 15 cm s^−1 in the east (Richardson 2005). Some of these vortices reach the Yucatan Channel, where their further evolution is still unclear. The Canek observing program has exposed the passage of
eddies with sizes comparable to the channel width. This is indicated both by the empirical-mode structure of the along-channel flow (Abascal et al. 2003) and by the looping streamlines computed using
the full measured velocities u(x, t), where x is the distance across the channel and the time t is treated as equivalent to a spatial coordinate (Badan et al. 2005). Numerical simulations to study
the connection between the variability in the Atlantic Ocean, the Caribbean Sea, and the Gulf of Mexico, also showed the passage of eddies through the Yucatan Channel (Murphy and Hulburt 1999).
The NBC flows to the northwest along the northern Brazilian coast and between 6° and 8°N separates sharply and curves back on itself. From this retroflection, about eight rings are shed yearly (Johns
et al. 2003). With a diameter of about 400 km, these vortices are among the largest ones in the ocean. By traveling toward the Lesser Antilles they contribute to the transport of South Atlantic upper
waters into the Northern Hemisphere. Altimetry data suggest that some of them enter the Caribbean Sea through the passages between the Lesser Antilles (Goni and Johns 2003). In situ observations,
however, show only the passage of filaments of the original vortices (Fratantoni and Richardson 2006). Numerical simulations reproduce well the vortex shedding and give a detailed picture of the
vortex evolution once they reach the Antilles (Garraffo et al. 2003). Thus, according to these simulations, some rings enter the Caribbean nearly intact, some rings move northward on the east side of
the Antilles, and some rings split—a fraction of which enters the Caribbean while the rest remains east of the Antilles.
The evolution of vortices in the ocean is affected by the currents they are immersed in, which vary both in space and time, as well as by the irregular coastline and bottom topography. Nevertheless,
the use of idealized models (either analytical or experimental) is a first step toward a better understanding of real vortices.
Simmons and Nof (2002) studied the squeezing of vortices through gaps both analytically, using integral constraints, and numerically, using a reduced-gravity primitive equations model. Their vortices
move toward the gap either because they are advected by a current or because of the drift induced by the β effect. In the former case, the behavior of the vortex depends on the Rossby number (Ro) and
the ratio of the speed of the advecting flow through the center of the gap to the swirl speed of the lens: μ = U/(fRoR[i]) (where R[i] is the Rossby deformation radius, f the Coriolis parameter, and
U the flow speed at the center of the gap). Weak vortices compared to the system’s rotation (Ro = 1/4) and with strong advection (μ > 0.3) were squeezed through the gap, whereas intense vortices (Ro
= 1) were partially drained by symmetric wall jets until they shrank enough to pass. This last process is similar to the one undergone by vortices advected by the β effect.
Johnson and McDonald (2004) studied the motion of two-dimensional vortices near a gap in an infinitely long straight barrier. They first used an analytical model to calculate the trajectories of
point vortices embedded in simple ambient flows, such as a uniform flow parallel to the barrier and a flow converging toward the gap. It was found that the vortex may or may not pass through the gap
depending on its initial position and the ambient flow. Then they used a numerical model (contour dynamics with conformal mapping to handle the nontrivial flow domain) to compute the evolution of
circular patches of uniform vorticity (Rankine vortices). They found that the trajectories of the vorticity centroid were in good agreement with those of the point vortex, except when a flow through
the gap forced the vortex toward the tip of the barrier and made it split.
In a laboratory Cenedese et al. (2005) studied the evolution of vortices impinging on a pair of circular islands. In these experiments the vortices drifted because of a topographic β effect. They
found that only small vortices pass wholly through the gap between the islands (D/R > 3.6, where D is the gap span and R is the radius of maximum azimuthal velocity); vortices of intermediate sizes
pass only partially (2.3 < D/R < 3.6); and large vortices do not pass through the gap (D/R < 2.3).
Here, we study the two-dimensional flow of a vortex embedded in a channel flow obstructed by a partial barrier. Our objectives are to characterize the behavior of the vortex as a function of the
parameters of the problem and to describe stirring and transport in the flow. We use a vortex-in-cell model to solve numerically the two-dimensional Euler equations and perform a straightforward
vorticity census in the up- and downstream sides of the barrier to characterize the behavior. We analyze transport and stirring in the flow with a dynamical systems approach: we determine the
Lagrangian flow geometry and compute residence times of fluid particles and finite-size Lyapunov exponents (FSLEs). We performed laboratory experiments in a homogeneous, rotating fluid to compare
with the numerical results.
The rest of the paper is organized as follows: after defining the problem in section 2, we find the paths of point vortices in section 3. In section 4 we present the evolution of finite-area vortices
as a function of the problem parameters. In section 5 we use a dynamical systems approach to study the transport and stirring properties of the flow. In section 6 we present the experimental results.
Finally, we summarize and discuss our results in section 7.
2. Definition of the problem
In a parallel channel, a uniform current advects a circular vortex toward a gap in a perpendicular barrier (
Fig. 1
). The parameters that govern the problem are the radius (
), circulation (Γ), and initial position (
) of the vortex; the speed of the current (
); the gap span (
); the channel width (
); and the barrier thickness (
). To simplify the problem, we keep fixed
, and
by making the following assumptions (a posteriori justifications of these are given in
sections 3
): (i) the vortex initial location is far from the barrier, (ii) the channel width is much larger than the vortex radius, and (iii) the barrier is thin. Therefore, we use
= −15
(the origin of the coordinate axes is at the center of the gap),
= 20
, and
/2. Under these assumptions, the following dimensionless parameters determine the flow evolution:
The fluid is assumed to be incompressible and inviscid, and the flow two-dimensional. Thus, the conservation of vorticity is expressed by
= ∂/∂
is the material derivative, and
is the velocity in the
direction (along the channel) and
in the
direction (across the channel). Note that in this model a negative vortex evolves as the mirror image, with respect to the channel axis, of a positive vortex. Therefore, in the rest of the paper we
will discuss only positive vortices.
3. Motion of point vortices
The evolution of finite-area vortices will be better understood if we discuss first the simpler case of a point vortex. The motion of a point vortex is the result of the advection by the steady
current and the velocity induced by the presence of the boundaries. The latter is easily explained by invoking the “method of images” in which the impenetrability condition is enforced by placing an
“image” vortex of opposite circulation at the mirror point. Thus, a vortex that is close to a wall moves parallel to it and in the same direction as the fluid located between the vortex and the wall
(Helmholtz 1858).
In our problem the geometry of the boundary is not trivial; therefore, we must resort to conformal mapping and the Kirchhoff–Routh path function to compute the trajectory of the point vortex (see,
Saffman 1995
). The first step is to find a transformation that maps our domain into some domain where the streamfunction due to the steady current and the point vortex can be easily computed. Let
be the position in an infinite channel with walls given by
= 0 and
, which at
= 0 has a perpendicular, infinitely thin barrier with a gap of length
in the middle; and let
be the position in a similar channel but without the barrier. Then the following transformations map one domain into the other:
= (
In the
channel, the complex potential of the flow due to a uniform stream and a point vortex located at
is given by
From this potential it is easy to show that the vortex moves parallel to the channel with the following speed:
The path function
in this domain is found by solving ∂
and the Kirchhoff–Routh path function is given by
where the suffix
denotes that the result is to be evaluated at the point
The trajectories in the original z channel are given by χ′ = constant after substituting for the value of ζ given by Eq. (2). Figure 2 shows several examples for different values of the
nondimensional parameter Γ/U b (note that we use b as length scale here because a point vortex has zero radius). Figure 2a corresponds to Γ/U b = 0; it therefore represents streamlines of a flow that
is uniform far away from the barrier; Fig. 2d corresponds to Γ/U b = ∞; it thus represents the trajectories of the point vortex when there is no stream. Note the fixed point of saddle type in the
middle of the gap. The trajectory that asymptotically moves toward this point divides the flow domain in qualitatively different regions: trajectories on the right-hand side (looking downstream) pass
through the gap, whereas trajectories on the left-hand side end up moving upstream. Figures 2b,c show two cases where Γ/U b has intermediate values (i.e., both the stream speed and the vortex
circulation are different from zero).
In all cases the trajectories are almost parallel to the channel walls, except in the neighborhood of the barrier. That is to say, the initial position of the vortex along the channel is unimportant
if it is sufficiently far from the barrier (at distances larger than one channel width). The initial position across the channel, on the other hand, critically determines the vortex evolution.
4. Motion of finite-area vortices
a. Vortex-in-cell model
We solve Eq. (1) with a vortex-in-cell model written in MATLAB. The outline of the method is the following: the initial vorticity field ω(x, y) is approximated by a set of point vortices distributed
on the numerical domain. The area s represented by each point vortex is assumed equal [the circulations are thus γ[k] = sω(x[k], y[k]), where (x[k], y[k]) is the point-vortex position]. The flow
domain (Fig. 1) is covered by a Cartesian grid, and the vorticity on grid points is calculated by adding the contributions of all the point vortices within neighboring cells with a bilinear scheme.
The streamfunction is obtained by inversion of the Poisson equation, ∇^2ψ = −ω, using a five-point finite-difference Laplacian and MATLAB standard functions to solve the set of algebraic equations.
The velocity field is evaluated from the streamfunction using second-order centered differences. Then, the velocity of each point vortex is determined using a bilinear interpolation, and the
positions of the point vortices are advanced in time with a second-order Runge–Kutta scheme. This process is repeated every time step.
We use free-slip conditions on the solid boundaries (i.e., ψ = A along the left-hand- side boundary—looking downstream—and ψ = B along the right-hand-side boundary, where A and B are constants) and
uniform flow on the entrance and exit of the channel (i.e., ψ varies linearly from A to B on these boundaries). The vortex is always far from the entrance and exit to minimize the effect of the open
b. Numerical experiments
Two different resolutions are used in the numerical experiments. Low-resolution simulations (525 × 150 grid points, with 7 grid points per vortex radius) were used to characterize the vortex behavior
in the parameter space (Γ′, D′, y′[0]). High-resolution simulations (875 × 250 grid points, with 12 grid points per vortex radius) were used to analyze stirring and transport in a few points of the
parameter space. Although details differ between low- and high-resolution simulations, large-scale features and integrated quantities are roughly the same; for instance, the vorticity passage across
the gap differs by only 1%–2% if computed with a high- or low-resolution run.
Initially, the vortex is circular, and its vorticity distribution is given by
is the peak vorticity,
is the radius where the vorticity becomes zero,
is an integer number, and
is the radial coordinate. This kind of distribution has been used in previous works (e.g.,
Velasco Fuentes 2001
). We consider two different profiles: (i) steplike,
→ ∞, and (ii) smooth,
= 2. The radius of the vortex
is taken as the radius where the maximum velocity is reached. Therefore,
c. Numerical results
Because the only vorticity present in the flow is that of the vortex, a vorticity census on the upstream and downstream sides of the barrier suffices to identify different types of behavior. We
identified three:
• (i)Total passage, when at the end of the simulation all the vorticity is found downstream of the barrier. The left column of Fig. 3 shows an example: the vortex (black blob) is advected toward
the barrier; it touches one tip of the barrier as it reaches the gap and filamentation occurs, but finally the whole vortex passes.
• (ii)Partial passage, when at the end of the simulation some vorticity is found downstream of the gap and some is found upstream. The middle column of Fig. 3 shows an example: the vortex splits
into two parts when it touches the tip of the barrier, one part is advected by the ambient flow and the other moves along the barrier against the flow.
• (iii)Total blockage, when at the end of the simulation no vorticity is found downstream of the gap. The right column of Fig. 3 shows that this occurs when the drift induced by the barrier is so
large that the vortex misses the gap, hits the left side of the barrier, and moves along this against the ambient flow.
Figure 4 shows the amount of vorticity found downstream of the barrier on the parameter plane (D′, Γ′) for three values of y′[0] = −5, 0, 5. Full passage is more common if D′ is large and Γ′ is small
(note that we show a different range of Γ′ values with the different values of y′[0]). The regions of parameter space where total passage or total blockage occur are usually contiguous: partial
passage is restricted to a small area of the parameter space (it is found for small D′; and the smaller the y′[0], the smaller the range of D′ where it occurs).
Figure 5 shows the influence of the vorticity profile on the vortex evolution. The distribution of the three regimes in the parameter space is almost equal for vortices with steplike and smooth
vorticity profiles. If a steplike vortex completely passes to the downstream side of the barrier, then a smooth vortex with the same initial conditions also passes completely or leaves a tiny
fraction of its mass on the upstream side. If a steplike vortex stays on the upstream side, then a smooth vortex also stays or forms a tiny filament that passes to the other side. The largest
differences occur when a steplike vortex only partially passes through the gap; in this case, a smooth vortex does the same, but the fraction that passes can be up to 20% smaller or 10% larger than
for steplike vortices.
The effect of the barrier’s thickness on the flow evolution was assessed by computing the passage of a vortex through a barrier of thickness 15R (where R is the vortex radius). Note that this is 30
times the thickness used in the rest of the simulations discussed here. This geometry now resembles more a narrow channel than a gap in a wall, but it was so chosen to enhance the effect of the
barrier’s thickness. We found that the flow in the upstream part was not significantly modified by the thickness of the barrier and that the difference in the vorticity passage was between 1% and 2%.
Obviously, for total and partial passage, the flow in the downstream side had important differences because the vortex takes longer to pass through the narrow channel and it is deformed in the
5. Transport and stirring
The study of transport and stirring in fluid dynamics with a dynamical systems approach has become standard in the past 25 yr [see Aref (2002) for the history and Ottino (1989) for an introduction to
this subject]. Initially, these tools were used to study industrial and idealized flows (e.g., Aref 1984), and more recently they have been applied to oceanic flows (for a review, see Wiggins 2005).
The dynamical systems approach consists of finding geometrical structures and understanding the role that such structures have in governing the motion of collections of trajectories over extended
regions of space. It begins with the velocity field and the advection equation
When the flow is two-dimensional and incompressible Eq.
can be written as
is the streamfunction. This system of equations is known in dynamical system theory as a Hamiltonian system; the streamfunction
represents the Hamiltonian.
The data produced by the numerical model have characteristics—such as finite time and aperiodic time dependency—that render it impossible to analyze transport with traditional techniques such as
Poincaré maps, Melnikov function calculations, and so on. Therefore, the analysis was made using three different tools: the Lagrangian flow geometry, the residence time of fluid particles, and the
finite-size Lyapunov exponents.
For this analysis, we used four high-resolution simulations (875 × 250 grid points) with a vortex initially centered with respect to the gap (y′[0] = 0), and (Γ′, D′) = (38, 5), (40, 3), (46, 3), and
(60, 3). The first two simulations correspond to total passage, the third to partial passage, and the fourth to total blockage. The difference between the two total passage simulations is that the
vortex underwent filamentation in the second simulation only.
a. Lagrangian flow geometry
The Lagrangian geometry of a two-dimensional, incompressible flow consists of three elements: (i) elliptic particles are material particles that while moving induce a swirling motion on a set of
particles; (ii) hyperbolic particles are material particles that while moving attract a set of particles exponentially and repel another set of particles exponentially; and (iii) invariant manifolds
are the material lines formed by the particles that are attracted (stable manifold) or repelled (unstable manifold) by the hyperbolic particles. Note that the terms induce, attract, and repel are
used here only to describe the fluid motion in the vicinity of the elliptic and hyperbolic particles, and hence they do not imply a cause–effect relationship.
The stable and unstable manifolds constitute the geometrical template that governs transport between different flow regions (see, e.g., Wiggins 2005). The following property will serve to interpret
the results of this section: two particles located on different sides of the stable manifold, however small the distance between them, evolve very differently in the future. Similarly, two particles
located on different sides of the unstable manifold, however small the distance between them, evolved very differently in the past.
When the flow is stationary, hyperbolic particles coincide with saddle-type stagnation points and manifolds coincide with separatrix streamlines. It is then to be expected that in a slightly or even
moderately time-dependent flow, the hyperbolic particles are close to the instantaneous saddle-type stagnation points (see, e.g., Velasco Fuentes 2001, and references therein). Therefore, we
construct the Lagrangian geometry using the Eulerian, instantaneous geometry as a starting point. We first take the streamfunction ψ computed by the numerical model and correct it for the vortex
translation; we thus obtain a modified streamfunction Ψ with a reduced temporal dependency. Then we find the fixed points of Ψ at different times with the method presented in Velasco Fuentes and
Marinone (1999). With these elements, the Lagrangian geometry is computed as follows: the unstable manifolds at time t[m] are found by taking a short segment that, at the start of the simulation (t =
0), crosses the saddle-type stagnation point along the unstable direction and computing its evolution under u(x, y, t) from time t = 0 to time t = t[m]. The stable manifold is computed in the same
way, but now taking a short segment that at the end of the simulation (t = t[f]), crosses the saddle-type stagnation point along the stable direction and computing its evolution under u(x, y, t) from
time t = t[f] to time t = t[m]. The evolution of these passively advected segments is obtained by computing the evolution of a set of particles (nodes) that lies along the line. As the flow evolves,
the nodes move apart from one another due to stretching of fluid elements; new nodes must therefore be added between the old ones to guarantee an accurate description of the contour.
We calculated the Lagrangian geometry at every time step of the four high-resolution simulations mentioned above. In the initial condition one hyperbolic particle, located somewhere between the
vortex and the left side of the barrier, is observed in all cases. In the final condition, the number of hyperbolic particles observed depends on the regime of evolution. In the total passage regime,
only one hyperbolic particle is observed and this is located somewhere between the vortex and the left side of the barrier. In the total blockage regime, two hyperbolic particles are observed, one on
the front and one on the rear side of the advancing vortex. In the partial passage regime, three hyperbolic particles are observed, one on the downstream and two on the upstream side of the barrier.
Figure 6 shows the stable manifold at time t = 0 for the four simulations. This manifold has a spiral shape that goes from the barrier toward the vortex; at some point the manifold folds back,
surrounds a parcel of fluid, and then moves back toward the barrier almost along the same path. The turning point of the manifold lies outside the vortex in the total passage and total blockage
regimes, whereas it lies inside the vortex in the cases of partial passage and in total passage with filamentation (cf. Velasco Fuentes 2005). The area of the vortex surrounded by the manifold grows
from zero in the total passage regime to a maximum equal to half the vortex area in the partial passage regime, then it decreases to zero again in the total blockage regime.
b. Residence time
We define the residence time as the interval during which a particle remains on the upstream side of the channel. We computed the evolution under u(x, y, t) of a regular mesh of particles located
upstream of the barrier and measured the time that each particle takes to go from its initial position to the downstream side of the channel. We plotted these results to obtain residence time maps (
Fig. 7). These maps are characterized by a strong gradient with a spiral shape, which approximately matches the stable manifold at time t = 0. The curve of strong gradient divides the flow domain in
regions of short, long, and infinite residence times of fluid particles. This is a manifestation of the property of the stable manifold discussed above; namely, that nearby particles located on
different sides of the stable manifold will have a very different future: one passes to the downstream side in a short time while the other remains in the upstream side for a long time, even
indefinitely. Figure 7 shows that the region of short residence time is found to the right and in front of the vortex (when looking downstream), the region of long residence time is found to the left
of the vortex, and the region of infinite residence time corresponds to the part of the vortex that does not pass through the gap. This region may extend to the ambient flow if the vortex is strong
c. Finite-size Lyapunov exponents (FSLEs)
In dynamical system theory, Lyapunov exponents serve to calculate the sensitivity of a system to the initial conditions. In fluid dynamics, they are a common way to quantify stretching of fluid
elements caused by advection and are defined as the exponential rate of separation, averaged over infinite time, of fluid parcels initially separated by an infinitesimal distance:
The former definition does not apply to finite-time problems or numerical data because the limits cannot be calculated. In those cases, FSLEs that are defined by taking out the limits in Eq.
are introduced:
is the time it takes for two particles, initially separated a distance
, to get separated by a distance
Aurell et al. 1997
The method used to calculate the FSLE is based on that of Shadden et al. (2005). A Cartesian grid of particles is placed over the part of the domain that is going to be studied. Each of these
particles has four satellites: two in the x direction and another two in the y direction. The distance between each pair of satellites is δ[0]. Then the particles are advected during one time step,
and the distance between the satellites is measured. The interval τ is the time that any pair of satellites takes to reach a separation δ[f]. The value of λ is calculated using Eq. (12) with δ[0] = 2
and δ[f] = 4. The values for the FSLE at the end of the simulation are an average of the λ computed for each particle. (Please note: below we use a dimensionless form of the FSLE λ′ = λR/U.)
Figure 8 shows the FSLE map when the vortex passes completely through the gap without undergoing any filamentation; the parameter values are (Γ′, D′, y′[0]) = (38, 5, 0). The largest values of the
FSLE are found around the vortex, and local maxima are arranged along a spiral curve that approximately coincides with the stable manifold at t = 0.
Figure 9 shows the FSLE average values inside the vortex (r < R) and around it (R < r < 1.5R). These quantities were calculated for the four simulations used to obtain the Lagrangian geometry as well
as for another four high-resolution simulations. In all simulations, the average FSLE inside the vortex is close to zero up until the vortex collision with the wall. After this event, the value
increases: the increment is larger in the cases of partial passage and total passage with filamentation than in the cases of total passage without filamentation and total blockage. The more vorticity
is shed, the bigger the FSLE becomes at the end. Also, in all simulations, the highest FSLE values are found in a ring surrounding the vortex. Before filamentation starts, this values tend to be
constant and to depend linearly on Γ′ and to be practically independent of the value of y′[0] or D′.
6. Laboratory experiments
The experiments were performed in a rectangular tank with a 100 cm × 60 cm base and a depth of 30 cm mounted on a rotating table. We simulate the current by moving the barrier toward a vortex in an
otherwise quiescent fluid. A moving bridge across the tank sustains two plates that span the whole water depth (Fig. 10). The thickness of the plates is 1 cm, and their width is varied depending on
the desired gap span.
We filled the tank up to a depth H = 20 cm and set the rotation period of the table to 7.5 s (the Coriolis parameter is therefore f = 1.68 s^−1). Once the water inside reached a state of solid body
rotation, we generated the vortex by withdrawing 2 L of water during 15 s, that is, two rotation periods of the table. This was done using a thin tube (1.0-cm diameter) placed at the center of the
tank and immersed 4 cm. When the vortex was formed, the plates were moved at a constant speed along the tank using a pulley system and a dc motor fed with a power supply mounted on the table.
We measured, using particle image velocimetry (PIV), the velocity field of the vortices generated with the forcing described above and with the plates being at rest. A theoretical velocity profile,
obtained from Eq. (7) with n = 2, was fitted to the measured profile using a least squares method. The values obtained for the radius and the circulation of the vortex were R = 2.6 ± 0.2 cm and Γ =
111 ± 6 cm^2 s^−1. Because the vortices are much smaller than the Rossby deformation radius [(gH)^1/2/f = 83 cm] and the Coriolis parameter is constant, the dynamics observed in this experimental
setting are equivalent to those represented by Eq. (1).
The values of the parameters that were kept constant in the numerical simulations are similar in the laboratory experiments: the thickness of the barrier (d ≈ R/2.6 in the laboratory versus d = R/2
in the numerical simulations), the channel width (b ≈ 23R versus b = 20R), and the initial along channel position of the vortex (x[0] ≈ −10R versus x[0] = −10R).
Several experiments were performed varying the gap span (i.e., D′) and the wall speed (i.e., Γ′), always leaving the vortex approximately centered with respect to the gap (y′[0] ≈ 0). Figures 11–13
show the flow evolution in three experiments whose parameter values correspond, respectively, to the three different regimes found in the numerical simulations. The vortex is marked with dye. The
lines drawn on the bottom are 20 cm apart, so it can be seen that the dye blob (about 15 cm in diameter) is much bigger than the vortex, which has a radius of approximately 2.6 cm. For comparison,
Fig. 14 shows the paths of the vortex centroids in these experiments as well as the trajectories of point vortices with matching initial conditions.
In experiment 1, the parameter values are Γ′ ≃ 34 and D′ ≃ 3; hence, the numerical model predicts that vortices with either steplike or smooth vorticity profiles make a full passage through the gap
(see Fig. 5) and, indeed, Fig. 11 shows that the dye blob passes easily through the gap. The path of the vortex centroid (light gray line in Fig. 14) shows an initial drift to the left, which is
reversed as the vortex approaches the gap. Experiment 3 has parameter values Γ′ ≃ 103 and D′ ≃ 3, and in this case the numerical model predicts that the vortex will end up moving upstream along the
wall. Figure 13 shows that when the vortex reaches the barrier, it deflects to the left of the gap and impinges on one of the plates. Because water is a slightly viscous fluid, the flow must satisfy
the no-slip condition at the solid boundaries; therefore, negative vorticity is generated on the plate (recall that the original vortex has positive vorticity) and, at t = 39 s, a dipole forms and it
starts to move away from the plate (see, e.g., Doligalski et al. 1994). Because its positive half is stronger, the dipole moves along a curved path and, by time t = 51 s, it is headed directly toward
the gap through which it finally passes. The whole process is clearly illustrated by the looping path of the vortex centroid (black line in Fig. 14). Finally, in experiment 2, the parameter values
are Γ′ ≃ 50 and D′ ≃ 3; here, the numerical model predicts that the vortex will split in two when colliding with the tip of the barrier, then, one part will pass through the gap while the other moves
upstream along the wall. Figure 12 shows that one fraction of the blob passes through the gap while the other fraction stays for a few seconds on the upstream side of the plate before also passing
through the gap. The reason for this is the same as in experiment 3, except that in this case, the dipolar vortex is not well developed: the negative vorticity generated on the plate barely forms a
bulge visible in the frames corresponding to t = 24 s and t = 25 s. The path of the vortex centroid (dark gray line in Fig. 14) shows a strong drift to the left, which is abruptly reversed before the
vortex can advance along the barrier.
In all experiments, including the ones not shown here, the vorticity generated at the tips of the plates is continuously introduced in the downstream side. In most cases, this vorticity prevents the
reorganization of the vortex after passing through the gap.
7. Discussion and conclusions
We analyzed the dynamics and transport properties of a vortex in a channel flow obstructed by a partial barrier. Three parameters are identified as determining the flow evolution: the relative
circulation of the vortex (Γ′), the initial position of the vortex (y′[0]), and the relative gap span (D′). The vortex trajectories were first analyzed with a point-vortex model; then the evolution
of finite-area vortices was studied with a two-dimensional numerical code. The vortex behavior depends on a competition between the advecting stream and the effect of the boundaries. The former
compels the vortex to pass through the gap. The latter compels the vortex to stay on the upstream side not only by the obvious mechanism of blocking the vortex motion but by inducing a drift (through
the image vortex) that is ultimately in the upstream direction. We found three possible behaviors: total passage, partial passage, and total blockage. The boundaries between these regimes are
irregular surfaces in the three-dimensional space (Γ′, D′, y′[0]); hence, there are no simple “critical values” marking out the transitions between regimes. This notwithstanding, the following rules
of thumb may be applied when a vortex is initially located on the axis of the channel (y′[0] = 0): weak vortices (Γ′ < 45) always make a full passage, strong vortices (Γ′ < 55) make full passage only
through wide gaps (D′ > 5), and vortices of intermediate strength (45 < Γ′ < 55) make a partial passage through narrow gaps (D′ > 5) and a full passage through wide gaps (D′ > 5).
A comparison with previous studies is not straightforward because of the differences in the geometry or in the models used. For instance, Simmons and Nof (2002) studied reduced-gravity lenslike
vortices that only interact with the solid boundary through direct contact; that is, there is no image vortex, and thus the boundaries play no dynamic role until the vortex touches them. In spite of
this major difference, they have a similar result when vortices are advected by a stream: weak vortices make a full passage, whereas strong vortices are destroyed and some of their mass remains on
the upstream side. Johnson and McDonald (2004) studied, as we do, point and finite-area vortices in two dimensions, but the geometry of the boundaries and the ambient flow are different. Only in the
neighborhood of the gap are the flow and the boundaries comparable, and here our results are consistent with theirs: the influence of the relative strength of the point vortex on the position of the
fixed point of saddle type (see Fig. 2) and the splitting of the finite-area vortex as it collides with the tip of the barrier. The experimental study of Cenedese et al. (2005) differs from ours both
in the geometry of the obstacles (circular cylinders instead of straight plates) and in the propulsion mechanism of the vortex (β-induced drift instead of an advecting current). This notwithstanding,
let us assume that the vortex motion caused by the topographic β effect is completely analogous to the motion caused by the current. Then they have Γ′ ≈ 30, and thus all their vortices should make a
full passage and not only those with D′ > 3.6. Any of the following factors may explain this contrasting result. Because Cenedese et al. (2005) generated the vortex with an ice cube placed on the
free surface of the water, baroclinic effects may still be important when the vortex encounters the cylinders; this would lead to a rather complicated process whose outcome would be determined by the
relative strengths of the bottom lens, the upper vortex, and the β effect (Shi and Nof 1994). On the other hand, if the vortex is already fully barotropic, then it should move to the northwest,
heading toward the northern cylinder rather than toward the gap, thus producing the splitting of the vortex and only a partial passage through the gap.
The presence of a partial barrier in the channel introduces a strong time dependency for both point and finite-area vortices. It thus enhances the stirring ability of the flow. Indeed, a point vortex
embedded in a uniform channel flow is either stationary (when the drift induced by its image balances the advection produced by the flow) or it moves with constant speed. In any case, the flow
observed in a system that moves with the point vortex is steady and no stirring occurs. If the point vortex is replaced by a circular vortex of small radius (compared to the channel width), the flow
is still approximately steady and thus a poor stirrer.
The three methods employed to study transport and stirring give results that are both consistent and complementary. It was found that the geometry of the stable manifold at time t = 0 is associated
with the regime of behavior. It also divides the flow field into areas of short, long, and infinite residence times. FSLE maps indicate where stirring is maximum: a comparison between the average
FSLE values inside the vortex and the behavior of the vortex suggests that the larger the average, the more important the mass exchange between the vortex and the ambient flow. The average FSLE
around the vortex, where an area of maximum stirring occurs, suggests that the vortex also serves as a stirrer for the ambient flow, and that this stirring initially depends only on the relative
vortex circulation (Γ′).
Results of laboratory experiments in a homogeneous, rotating fluid are consistent with the analytical and numerical results only up to the moment when the vortex touches the barrier. Viscous effects
then become dominant and the flow evolution differs from that computed with the inviscid models. In real oceanographic situations, the coastal sloping topography would probably have a greater
influence than the no-slip condition. Because the final tendency of vortices moving over topography is to translate along isobaths (see, e.g., McDonald 1998), we conjecture that a coastal topography
will inhibit the passage of vortices. Although this should be the subject of further investigations, in situ observations seem to support this hypothesis: NBC rings abruptly turn northward as they
encounter the bottom topography between Tobago and Barbados (Fratantoni and Richardson 2006).
Even though we used highly idealized models (analytical, numerical, and experimental), our results have some implications to real oceanographic flows. The coastal geometry in the region of the Lesser
Antilles is very different from the one used in the present study, yet the fact that the passages are much thinner than the average size of the NBC rings suggests that the Lesser Antilles constitute
“an unsurmountable barrier to ring translation” (Fratantoni and Richardson 2006). The geometry of the western Caribbean Sea, on the other hand, is more akin to the one used here; therefore,
conclusions derived from our results are more relevant for this region. The eddies of the Caribbean Sea, with radii between 50 and 130 km and swirl speeds between 30 and 70 cm s^−1, are immersed in a
current that flows at speeds between 25 and 80 cm s^−1 (Richardson 2005). The distance between the coasts of Cuba and Honduras (about 750 km) is taken as the channel width, and the distance between
Cabo Catoche, Mexico, and Cabo San Antonio, Cuba (about 200 km), is taken as the gap span. Therefore, the dimensionless parameters are estimated to be 1.5 < D′ < 4, 2 < Γ′ < 16 and −4 < y′[0] < 4.
This region lies well below the transition between partial and full passage regimes shown in Figs. 4, 5; therefore, we conclude that Caribbean eddies should make a full passage through the Yucatan
Channel. Numerical models of the circulation in the Caribbean Sea and the Gulf of Mexico support this result, whereas altimetric observations seem to show a less frequent passage of vortices (J.
Sheinbaum 2008, personal communication). Further in situ observations should provide a definite answer.
We are thankful to two anonymous reviewers for their suggestions and comments on an earlier version of this manuscript. This research was supported by CONACyT (México) through a postgraduate
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212 , 271–304.
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Fig. 1.
Problem diagram. Not to scale.
Citation: Journal of Physical Oceanography 38, 12; 10.1175/2008JPO3887.1
Fig. 2.
Trajectories of a single-point vortex embedded in a streamflowing in a channel with a partial barrier. The values of Γ/Ub are (a) 0, (b) 3, (c) 3.75, and (d) ∞. The arrows indicate direction of
motion, filled circles represent stable fixed points, and crosses represent unstable fixed points.
Citation: Journal of Physical Oceanography 38, 12; 10.1175/2008JPO3887.1
Fig. 3.
(left to right) Evolution of a steplike vortex with D′ = 3, y′[0] = 0, and Γ′ = 40, 48, 56. The time, which runs from top to bottom, is shown on the left in units of the eddy turnover time.
Citation: Journal of Physical Oceanography 38, 12; 10.1175/2008JPO3887.1
Fig. 4.
(left to right) Fraction α of vortical fluid passing through the gap as a function of the parameters (D′, Γ′) for three initial locations of the steplike vortex (y′[0] = −5, 0, 5). The value of α is
represented by the black area inside each circle (white circle means α = 0; black circle means α = 1). The black line represents a regime boundary for point vortices (they pass through the gap if
their initial conditions lie below the curve; otherwise, they end up moving upstream).
Citation: Journal of Physical Oceanography 38, 12; 10.1175/2008JPO3887.1
Fig. 5.
Same as in Fig. 4, but now only for y′[0] = 0 and vortices with (left) steplike vorticity profile and (right) smooth vorticity profile.
Citation: Journal of Physical Oceanography 38, 12; 10.1175/2008JPO3887.1
Fig. 6.
In black, the stable manifold at time t = 0 for (a) total passage, (b) total passage with vortex filamentation, (c) partial passage, and (d) total blockage. The gray circle represents the vortex.
Citation: Journal of Physical Oceanography 38, 12; 10.1175/2008JPO3887.1
Fig. 7.
Residence time maps for (a) total passage, (b) total passage with vortex filamentation, (c) partial passage, and (d) total blockage. Time is scaled by the eddy turnover time.
Citation: Journal of Physical Oceanography 38, 12; 10.1175/2008JPO3887.1
Fig. 8.
FSLE map for the case of total passage without filamentation. The contours show the same spiral structure that appears in the stable manifold and in the residence time maps.
Citation: Journal of Physical Oceanography 38, 12; 10.1175/2008JPO3887.1
Fig. 9.
Time evolution of FSLE average for (left) r < R and for (right) R < r < 1.5R for various simulations: (a) total passage without filamentation: Γ′ = 38, D′ = 5, y′[0] = 0, (b) total passage with
filamentation: Γ′ = 40, D′ = 3, y′[0] = 0, (c) partial passage: Γ′ = 46, D′ = 3, y′[0] = 0, (d) total blockage: Γ′ = 60, D′ = 3, y′[0] = 0, and (e) partial passage: Γ′ = 80, D′ = 3, y′[0] = −5.
Citation: Journal of Physical Oceanography 38, 12; 10.1175/2008JPO3887.1
Fig. 10.
Experimental apparatus view from the (left) side and from the (right) top.
Citation: Journal of Physical Oceanography 38, 12; 10.1175/2008JPO3887.1
Fig. 11.
Expt 1: Γ′ ≃ 34 and D′ ≃ 3. The lines on the bottom are 20 cm apart.
Citation: Journal of Physical Oceanography 38, 12; 10.1175/2008JPO3887.1
Fig. 12.
Expt 2: Γ′ ≃ 50 and D′ ≃ 3. The lines on the bottom are 20 cm apart.
Citation: Journal of Physical Oceanography 38, 12; 10.1175/2008JPO3887.1
Fig. 13.
Expt 3: Γ′ ≃ 103 and D′ ≃ 3. The lines on the bottom are 20 cm apart.
Citation: Journal of Physical Oceanography 38, 12; 10.1175/2008JPO3887.1
Fig. 14.
Trajectories of vortex centroids in the laboratory experiments shown in Fig. 11 (light gray line), Fig. 12 (dark gray line), and Fig. 13 (black line). The dashed lines with matching colors show
trajectories of point vortices with matching initial conditions.
Citation: Journal of Physical Oceanography 38, 12; 10.1175/2008JPO3887.1 | {"url":"https://journals.ametsoc.org/view/journals/phoc/38/12/2008jpo3887.1.xml","timestamp":"2024-11-09T00:29:42Z","content_type":"text/html","content_length":"838166","record_id":"<urn:uuid:ab670e1a-c16c-4d94-ba74-c05755ab3c5f>","cc-path":"CC-MAIN-2024-46/segments/1730477028106.80/warc/CC-MAIN-20241108231327-20241109021327-00836.warc.gz"} |
How many nautical miles are 3 millimeters
Parent Category: Length
Category: mm in nm
1 1 1 1 1 Rating 5.00 (3 Votes)
You can easily convert 3 millimeters into nautical miles using each unit definition:
milli m = 0.001 m
Nautical miles
nauticalmile = 1852 m = 1852 m
With this information, you can calculate the quantity of nautical miles 3 millimeters is equal to.
¿How many nm are there in 3 mm?
In 3 mm there are 1.6198704e-06 nm.
Which is the same to say that 3 millimeters is 1.6198704e-06 nautical miles.
Three millimeters equals to one nautical miles. *Approximation
¿What is the inverse calculation between 1 nautical mile and 3 millimeters?
Performing the inverse calculation of the relationship between units, we obtain that 1 nautical mile is 617333.33 times 3 millimeters.
A nautical mile is six hundred seventeen thousand three hundred thirty-three times three millimeters. *Approximation | {"url":"https://howmanyis.com/length/156-mm-in-nm/133091-3-millimeters-in-nautical-miles","timestamp":"2024-11-07T09:55:42Z","content_type":"text/html","content_length":"22099","record_id":"<urn:uuid:d71c5cff-1b75-4371-a570-faf0e29e316f>","cc-path":"CC-MAIN-2024-46/segments/1730477027987.79/warc/CC-MAIN-20241107083707-20241107113707-00282.warc.gz"} |
Problems 16
Redox Rules
What is the oxidation state of . . .
Problems 16 - 35
Exampes and Problems with no answers
Problem #16: HIO[3], the iodine has an oxidation state of:
The three oxygens total to −6 and the hydrogen adds a +1, leaving −5 to be offset by the iodine. The iodine has an oxidation state of +5.
Problem #17: S[2]O[3]^2¯, thiosulfate:
Three oxygens, each of which is −2, total to −6. Since −2 is left over, a total of −4 must be offset by the two sulfurs. Each sulfur has an oxidation state of +2.
Problem #18: What is the oxidation state of all free elements? Another way to ask this is to say that the elements are in their uncombined state.
By the way, molecular elements (the seven diatomics plus O[3], P[4], and S[8]) are considered to be uncombined. Elements are only considered combined when they are bonded to at least one other
(different) element.
Problem #19: Determine the oxidation state of P in P[2]O[5].
The five oxygens total to −10. Each P is +5.
Problem #20: Determine the oxidation state of S in Al[2]S[3].
Aluminum takes on a +3 oxidation state in all common aluminum-containing compounds. Examples include AlCl[3] and Al[2]O[3].
Sulfur can take on several different oxidation states. When it is alone and in the nonmetal position of a binary compound, it takes on a −2 oxidation state. An example of this is Na[2]S.
In this compound, there are two Al, for a total of +6. The three S must, therefore, total to −6. That means each S is a −2.
Problem #21: Determine the oxidation state of Te in Sc[2]Te[3].
The compound H[2]Te is known to exist, which means that Te has an oxidation state of −2 when acting as a nonmetal.
The presence of three Te means a total negative oxidation state of −6.
To offset this (and make the formula have a charge of zero), each Sc must be a +3.
Problem #22: Determine the oxidation state of Si in SiF[6]^2¯.
The F is a −1. We know this from the existence of HF. Six of the yields a total of −6. In order to have −2 left over, the Si must be a +4
Problem #23: All monatomic ions have oxidation states equal to the ______.
(a) difference of protons and electrons
(b) number of protons
(c) number of electrons
(d) difference of protons and neutrons
The answer is (a). Examples include Na^+, Ca^2+ and F¯.
Problem #24: On rare occasions, oxidation states do not have to be whole numbers. Determine the oxidation state for S in S[4]O[6]^2¯.
There are six O, which contribute a total of −12 in oxidation state. Since −2 is left over, that leaves −10 to be offset by the four sulfurs.
Each sulfur is, therefore, +^10⁄[4]. Reduced would be +^5⁄[2] (also seen as +2.5).
In truth, the four sulfurs would have a total of +10 oxidation state and each oxidation state on the four atoms would be a whole value. For example, if three S were each +2 and one S was a +4,
this would total up to +10. Chemical substances do not have fractional oxidation states.
Problem #25: What are the oxidation states for each Mn in Mn[3]O[4]? For each Fe in Fe[3]O[4]?
Four oxygens gives a total of −8 in oxidation state.
The three Mn atoms must each have an integer oxidation state. This is satisfied if two Mn are each a +3 and the third Mn is a +2.
For iron (II, III) oxide, the answer is the same: two iron atoms are each a +3 and one Fe atom is a +2.
Problem #26: In which compound does hydrogen have an oxidation state of −1?
(a) NH[3]
(b) KH
(c) HCl
(d) H[2]O
1) The correct answer is (b).
2) Some discussion:
You might get led into a wrong conclusion by ammonia, since the hydrogen comes last in the formula. However, coming last in the formula is a historical accident and must not be taken to indicate
that hydrogen is a −1 in ammonia. Remember that hydrides are composed of a metal and hydrogen. Nitrogen is a non-metal. CH[4] is an example of another compound that is not a hydride, even though
hydrogen is written last.
KH is the hydride, a chemical compound of a metal and hydrogen. NaH and CaH[2] are other examples of hydrides.
Problem #27: In which compound does oxygen have an oxidation state of −1?
(a) O[2]
(b) H[2]O[2]
(c) H[2]O
(d) OF[2]
(e) KO[2]
1) The correct answer is (b).
2) Some discussion:
Peroxide is O[2]^2¯, so each oxygen is considered to have a −1 oxidation state.
A possible answer is superoxide, O[2]¯. Note that in superoxide, each oxygen is considered to have an oxidation state of −^1⁄[2] as opposed to one oxygen having a −1 and one oxygen having an
oxidation state of zero.
Superoxide is a good example of oxidation states simply being bookkeepping. The two oxygens in superoxide do not literally each have a charge of −^1⁄[2], yet we are forced to use −^1⁄[2] if we
ask the oxidation state on each oxygen.
More correctly, the two oxygen entity that is superoxide has a −1 charge that is distributed over the entire unit of two oxygens and is not the sole property of one or the other oxygen atoms. see
below for a bit more discussion.
By the way, the charge on the oxygen in OF[2] is +2. Fluorine is stronger than oxygen in attracting electrons to itself and so forces oxygen into playing the positive role in oxidation states.
The next halogen down (chlorine) is weaker than oxygen in attracting electrons, so its formula is Cl[2]O. Oxygen has an oxidation state of −1 and chlorine is pushed into having an oxidation state
of +1.
Problem #28: Superoxide is not commonly mentioned in introductory chemistry classes. It is the polyatomic ion O[2]¯. KO[2] is the most well-known of the superoxides. What are the oxidation states on
each oxygen in the superoxide anion?
It appears that, within the superoxide, each oxygen must have an oxidation state of −^1⁄[2].
The ChemTeam thinks, but is not 100% sure, that the electronic structure of the superoxide anion is such that one O has an oxidation state of zero and the other O has an oxidation state of −1.
The fact that there are, then, two resonance structures of superoxide leads to an average of −^1⁄[2] for each oxygen atom.
Problem #29: Some chemical compounds have one (or more) atoms in them where the oxidation state is zero. An example of this is glucose, C[6]H[12]O[6].
The six oxygens (each at an oxidation state of −2) total up to −12.
The twelve hydrogens (each at an oxidation state of +1) total up to +12.
+12 and −12 add to zero.
Therefore, the six carbons are zero for their total oxidation state contribution.
Problem #30: What is the oxidation state of P in HPO[4]^2¯?
H contributes +1.
Four O contribute a total of −8.
−2 must be left over, so P must be +5
Problem #31: What is the oxidation number of rhenium in Ca(ReO[4])[2]?
1) We know that calcium takes on a +2 oxidation number. We can demonstrate that as follows:
We know CaCl[2] exists and that Cl is a −1. The evidence that Cl is a −1 comes from HCl. We know that H is a +1, therefore Cl must be a −1
2) Removing Ca from the formula leaves us with ReO[4]¯
Oxygen is always a −2 (with exceptions, which do not apply here. Four oxygens totals −8 in oxidation number
3) In order for the perrhenate anion to have an over all charge of −1, the Re must be a +7.
Problem #32: For which substance is the oxidation number of vanadium the same as that in the VO[3]¯ anion?
(a) VN (b) VCl[3] (c) VOSO[4] (d) VF[5]
1) VO[3]¯ has a total of −6 from the oxygen. To leave −1 overall, the V must be a +5.
2) I recommend you examine the simpler molecules first. For example, looking at VCl[3] should lead you right to V being +3. Not the correct answer.
3) VF[5] is the correct answer. We know F is ALWAYS a −1, which leads immediately to V being +5.
4) This approach allowed us to never have to contemplate the more complicated VOSO[4] molecule. The V is a +4 and you may figure that out by yourself (hint: what is the overall charge on the sulfate
Problem #33: What is the oxidation number of Mo in MoO[2]Cl[2]?
1) Cl contributes −2 and O contributes −4.
2) Mo is +6.
Problem #34: In which species does sulfur have the lowest oxidation state?
(a) SCl[2] (b) OSF[2] (c) H[2]SO[3] (d) SF[6]
1) Examine SCl[2] first since it is the simplest. S is a +2.
2) This is probably the correct answer since all the other molecules have lots of negative stuff (O, F) attached, meaning S will be in a higher oxidation state. For example, S is a +6 in SF[6].
Problem #35: What is the oxidation number of carbon in CH[2]Cl[2]?
Chlorine contributes −2. Hydrogen contributes +2.
The oxidation state of carbon in this compound is zero.
Problem #36: Chlorine is in a +1 oxidation number in:
(a) HCl (b) HClO[4] (c) ICl (d) Cl[2]O
The solution is left to the reader.
Bonus Problem: What is the oxidation state and coordination number of rhodium in the coordination compound K[RhCl(OH)(C[2]O[4])[2]] ⋅ 6H[2]O?
The coordination number (the number of coordinate covalent bonds between the ligands and the Rh ion) is 6. There are two bonds to each oxalate ion and one to OH¯ and one to the Cl¯ ions. (This
isn't part of the redox rules material, so I won't delve into it further.)
The complex ion (everything inside the square brackets) has a charge of −1. We know this from the fact that it bonds with one potassium, which always has an oxidation state of +1.
Since the sum of oxidation states must equal the charge on the ion:
Rh + Cl¯ + OH¯ + 2C[2]O[4]^2¯ = −1
Rh + (−1) + (−1) + (−4) = −1
Rh = +5
Exampes and Problems with no answers | {"url":"https://web.chemteam.info/Redox/Redox-Rules-Prob11-25.html","timestamp":"2024-11-04T07:37:17Z","content_type":"text/html","content_length":"13622","record_id":"<urn:uuid:04035e3b-17cc-40b7-99f5-1bca5816b87d>","cc-path":"CC-MAIN-2024-46/segments/1730477027819.53/warc/CC-MAIN-20241104065437-20241104095437-00283.warc.gz"} |
On rooted trees and differentiation | Daniel Worrall
On rooted trees and differentiation
Nov 22, 2023 · 9 min read
The chain rule lies at the heart of the backpropagation algorithm in deep learning. Unbeknownst to many though, the chain rule for higher order derivatives boasts a wealth of beautiful mathematical
structure touching the theory of special rooted trees, group theory, combinatorics of integer partitions, order theory, and many others. I’ve been meaning to write this post for a long time, but in
the last year work has been quite busy. I’m glad I can finally share with you the beautiful maths connecting special rooted trees and differentiation.
The chain rule
We start with a composition of functions
$$ \textbf{z} = f(g(\textbf{x})) $$
where $f$ and $g$ are vector-in vector-out functions. We can introduce an intermediate variable $\textbf{y} = g(\textbf{x})$ so that $\textbf{z} = f(\textbf{y})$. The derivative of $\textbf{z}$ with
respect to $\textbf{x}$ is then
$$ \frac{\partial \textbf{z}}{\partial \textbf{x}} = \frac{\partial \textbf{z}}{\partial \textbf{y}} \frac{\partial \textbf{y}}{\partial \textbf{x}}. $$
In any contemporary machine learning masters course, this is about as far as we go. Couple the chain rule with dynamic programming and you get the backpropagation algorithm and forward-mode
differentiation. And for most practitioners, we do not even need to know as much. With the advent of packages like JAX all this machinery is hidden away. Well not today!
Now while vector notation is neat, it’s actually really unhelpful when we wish to do calculus. Each Jacobian in the above expression is a matrix and I always forget how to order the rows and columns
properly. Furthermore, the following is going to involve a lot of vector derivatives, matrix derivatives, and higher order tensor derivatives, which can all be very unwieldy, so to ease notation we
shall adopt index notation instead. As we shall see, switching up our notation frequently is going to help our understanding and aid our ability to generalize.
So using $z^i$ to denote the $i$th component of a vector $\textbf{z}$, we could write
$$ \frac{\partial z^i}{\partial x^j} = \sum_{\alpha} \frac{\partial z^i}{\partial y^\alpha} \frac{\partial y^\alpha}{\partial x^j}. $$
As a second notational step, we are going to denote differentiation of a function $h$ with respect to the $\alpha$th dimension of its input as $h_\alpha$. Notice we do not need to make reference to
$y$ in this notation, since it is understood at we differentiate with respect to the input of $f$, however we might wish to label it. So
$$ \frac{\partial f^i}{\partial y^\alpha} = f^i_\alpha $$
The chain rule is then just
$$ \frac{\partial f^i}{\partial x^j} = \sum_{\alpha} f^i_\alpha g^\alpha_j. $$
Notice how there is one $\alpha$ on the bottom and one $\alpha$ on the top. For this reason, as one final notational convenience, we will switch to Einstein notation, where we implicitly sum over
repeated indices in upper–lower pairs, so the chain rule is
$$ \frac{\partial f^i}{\partial x^j} = f^i_\alpha g^\alpha_j. $$
I have always found this notation both very elegant and parsimonious. Back in my PhD, before automatic differentiation was commonplace in machine learning, I would often use this notation to work out
gradients, because it is both uncluttered and unconfusing.
You may have noticed that I am using Greek letters for the dummy variables we sum over. This is just a choice mainly for me to remember what we are summing over. With this highly compressed notation,
let’s write the $2$nd derivative of $f^i$ with respect to $x$. It’s
$$ \frac{\partial^2 f^i}{\partial x^j \partial x^k} = f^i_{\alpha \beta} g^\alpha_j g^\beta_k + f^i_{\alpha} g^\alpha_{jk}. $$
The 3th derivative is
$$ \frac{\partial^3 f^i}{\partial x^j \partial x^k \partial x^\ell} &= f^i_{\alpha \beta \gamma} g^\alpha_j g^\beta_k g^\gamma_\ell + f^i_{\alpha \beta} g^\alpha_{j\ell} g^\beta_k + f^i_{\alpha \
beta} g^\alpha_{j} g^\beta_{k\ell} \nonumber \\ & \qquad + f^i_{\alpha \beta} g^\alpha_{jk} g^\beta_\ell + f^i_{\alpha} g^\alpha_{jk\ell} \newline &= f^i_{\alpha \beta \gamma} g^\alpha_j g^\beta_k g^
\gamma_\ell + 3 \cdot f^i_{\alpha \beta} g^\alpha_j g^\beta_{k\ell} + f^i_{\alpha} g^\alpha_{jk\ell} $$
These expressions get very unwieldy for higher order derivatives. Let’s try one fourth!
$$ \frac{\partial^4 f^i}{\partial x^j \partial x^k \partial x^\ell \partial x^m} &= f^i_{\alpha \beta \gamma \delta} g^\alpha_j g^\beta_k g^\gamma_\ell g^\delta_m + 6 \cdot f^i_{\alpha \beta \gamma}
g^\alpha_j g^\beta_k g^\gamma_{\ell m} + 3 \cdot f^i_{\alpha \beta} g^\alpha_{j\ell} g^\beta_{km} \nonumber \\ & \qquad + 4 \cdot f^i_{\alpha \beta} g^\alpha_{j} g^\beta_{k \ell m} + f^i_{\alpha} g^\
alpha_{jk\ell m}. $$
OK, what is going on? This is tedious and confusing and it is not obvious if there is any structure to this. In fact there is a very simple structure and we can derive all the above with some simple
rules involving special labeled rooted trees. To make the connection, we make two observations. Each derivative is a sum of factors of the form $f^i_{\alpha\beta...}g^\alpha_{ij...}g^\beta_{k\ell...}
\cdots$ where there is a:
1. single term in $f^i_{\alpha\beta...}$ with multiple subscripts,
2. multiple terms in $g^\alpha_{ij...}$ where $g$ has a single superscript and potentially many subscripts.
We are going to replace each term in $f$ or $g$ with parts of a special rooted tree.
Special labeled rooted trees
We begin by drawing the simplest tree $f^i$ as
This is just a root node of a tree—hence special labeled rooted tree. Every time we differentiate $f^i$ we will draw a branch emanating from the root node. In other words, for every subscript of $f^
i$ we draw a branch. The first derivative $f^i_{\alpha} g^\alpha_j$ we thus draw as
This is simple enough. Note, we shall also label the nodes with the subscript of the attached branch—in this case $j$—so that we can keep track of what branch corresponds to what algebraïc terms.
Hence special labeled rooted tree. We didn’t write $i$ by the root node, since it is not a subscript. In fact, since $i$ only ever appears in the superscript of $f$, we could drop it entirely,
leaving $f$ as a vector-in scalar-out mapping, which we choose to do from now on.
Now what about the factor $f_{\alpha\beta} g^\alpha_j g^\beta_k$? It has two branches emanating from the root as
What if $g$ has multiple subscripts? Well, we then extend the branch by as many subscripts in $g$ so $f_{\alpha} g^\alpha_{jk}$ and $f_{\alpha\beta} g^\alpha_{jk}g^\beta_\ell$ look like
This notation is a little weird at first, but as expressions get longer and more cumbersome, the tree representations become easier to handle. Now we have everything we need to differentiate the tree
representation of our function $f(g(\textbf{x}))$. The $1$st derivative of $f$ is $f_\alpha g^\alpha_j$, which is a single branched tree
I have drawn the new branch in red to emphasize it. Differentiating again yields $f_{\alpha \beta} g^\alpha_j g^\beta_k + f_{\alpha} g^\alpha_{jk}$, so
What just happened? When differentiating $f_\alpha g^\alpha_j$, which in the literature is called an elementary differential, we applied the product rule and made two copies of $f_\alpha g^\alpha_j$.
To the first copy we differentiated the $f_{\alpha}$ term, adding a new subscript $\beta$ and an extra $g^\beta_k$ branch to the root. To the second copy we differentiated the $g^\alpha_j$ term,
raising it to a $2$nd order deriviative, and thus extending the already existing $g^\alpha_j$ branch to a length $2$ $g^\alpha_{jk}$.
We can easily see how this technique generalizes to higher order factors. We apply the product rule and make as many copies of our special labeled rooted tree as there are terms in the factor. To the
first copy we add a branch corresponding to differentiating $f$ and to the remaining copies we extend each of the existing branches, one by one. Let’s apply this technique to differentiate again,
either adding a new branch to root or extending existing branches. This yields
Now, noticing that the middle three trees are topologically the same, with permuted labels, we can rewrite this, but we need to strip the labels. This results in
which corresponds to the expression $f_{\alpha \beta \gamma} g^\alpha_j g^\beta_k g^\gamma_\ell + 3 \cdot f_{\alpha \beta} g^\alpha_j g^\beta_{k\ell} + f_{\alpha} g^\alpha_{jk\ell}$ that we derived
earlier! These new label-less trees are referred to as simply as special rooted trees. In maths-speak, a special rooted tree is an representative of the equivalence class of special labeled rooted
Aside: Where does that 3 come from?
That 3 we see popping up in front is the cardinality of the equivalence class–the total number of valid labelings of the tree. Without getting too distracted, for a labeling to be valid labels need
to increase from the root, so
is an invalid labeling, assuming we have chosen alphabetical ordering of labels. On the surface, it’s not very obvious why the coefficients that precede the elementary differentials in higher
derivative expressions would naturally be the number of valid labelings. But staring at the diagram of how we differentiate special labeled rooted trees, we see that each row essentially generated
all possible special rooted labeled trees. So all possible labelings of each special rooted labeled tree are enumerated. And hence these coefficients have a very beautiful origin.
For those with a background in combinatorix, you will probably be quick to realize that there is a bijection between special rooted labeled trees and integer partitions of sets. We can associate each
of the following 4-node trees with partitions with integer partitions of the set $\{j, k, \ell\}$
Each branch in the diagram is a grouping of letters into a subset. While each branch has to be ordered alphabetically from its root, there is only one such valid ordering, so the subset can just be
left unordered. We could go deeper into partitions of sets, but Wikipedia is your friend here.
Back to differentiation
For me I would say the tree representation is much easier to parse than the algebraïc representation, which, mind you, is still shorthand for
$$ \frac{\partial^3 f}{\partial y^\alpha \partial y^\beta \partial y^\gamma}\frac{\partial g^\alpha}{\partial y^j}\frac{\partial g^\beta}{\partial y^k}\frac{\partial g^\gamma}{\partial y^\ell} + 3\
frac{\partial^2 f}{\partial y^\alpha \partial y^\beta}\frac{\partial g^\alpha}{\partial y^j}\frac{\partial^2 g^\beta}{\partial y^k \partial y^\ell}+ \frac{\partial f}{\partial y^\alpha}\frac{\partial
^3 g^\alpha}{\partial y^j \partial y^k \partial y^\ell}. $$
What would be the expression for the $5$th order derivative?
So we can study higher order derivatives of compositions of functions via special rooted trees! This process of adding and extending branches can be applied recursively very easily and a list of the
first few special rooted trees looks like
The theory of rooted trees goes very deep. We have only considered the special variety, for which branching can only occur at the root node. People have gone far into defining entire algebras over
rooted trees, defining operations such as multiplication and addition. This comes in handy when studying order conditions of Runge-Kutta solvers and renormalization in quantum field theory. I
personally think this area is extremely beautiful and am even more happy that I have a quick trick to derive expressions for higher order derivatives of composed functions.
Machine Learning Research Scientist
I’m interested in using ML to accelerate simulation of physical systems | {"url":"https://danielewworrall.github.io/blog/algebra-of-differentiation/","timestamp":"2024-11-10T22:03:07Z","content_type":"text/html","content_length":"40669","record_id":"<urn:uuid:3b5e6458-430d-42f5-b368-71c8c8918577>","cc-path":"CC-MAIN-2024-46/segments/1730477028191.83/warc/CC-MAIN-20241110201420-20241110231420-00826.warc.gz"} |
Can You Use a Formula Solver to Find the Roots of a Number? - Do My GRE Exam
In this article we will be looking at quadratic and linear inequalities. In the first form of quadratic inequality, A, B and C, we will be looking at three real numbers: . A B and C are all real
Let’s start by looking at A. The square root of A is not a real number and it is therefore not a quadratic function. However, it is easy to find the value of this number as we can take the product of
all the roots of A and get the square of the whole thing.
Let’s look at B and C. They are both real numbers but B is a quadratic number and C is a linear number. So, we can use some quadratic functions on them to get the answer. This is a useful trick that
you can apply to any number, but it will only work if you can also find the roots of the number.
Linear and quadratic inequalities can also be found by working out what a positive real number is multiplied by. Here the square root of the number is multiplied by -1 and we get a positive number.
We then multiply that number by itself and get another positive number. Therefore, we get positive numbers and this gives us a quadratic number or a linear number.
If you are a beginner you should avoid doing these types of things. It is easy to forget that negative or zero values are not real numbers. By remembering the two previous forms of quadratic and
linear inequalities we have already done a lot of the hard work for you.
Quadratic inequalities are normally harder to find than linear ones. For this reason they are usually written as a fraction rather than using a formula. If you really want to know how many roots
there are to a given number then you can use the quadratic formula. However, for this method you will need a good formula and you may also need help from someone who knows about quadratic formulas.
You can also find out the exact value of a quadratic formula using other tools such as a quadratic formula solver. The quadratic formula solver is available for free online and you will find plenty
of information about it on the internet. There are also several books available with this type of formula.
If you feel you can’t use a quadratic formula then there are other methods to find out the value of a quadratic number. If your problem is so difficult that you want to make sure you know, you can
use a quadratic formula solver.
Another method you can use is by using a quadratic formula solver. A quadratic formula solver is a computer program designed specifically to solve linear and quadratic equations. You can find out
more about these programs by searching the internet for ‘quadratic formula solver’.
These programs are very helpful because they allow you to see how to write the quadratic formula in your own language, so that you know how to solve a problem without actually having to have to use a
quadratic formula solver. You will be able to work out the value of a quadratic formula in just a few seconds, and find out the value of a quadratic formula and find the roots of an equation. and
many other useful information.
Once you have found the root of an equation, you will be able to write the quadratic formula. You will be able to do this by finding the value of the quadratic formula and finding the value of the
linear and quadratic formula as well. This is very useful for beginners when they first learn to use the quadratic formula solver.
Finally, you will be able to use the quadratic formula to find the roots of an equation and also to get the answer of an expression. This is often very useful because a simple quadratic formula can
sometimes be very difficult to work out and this makes it very easy for you to get a correct answer to a problem. This method is highly recommended for anyone who is trying to use a quadratic formula | {"url":"https://domygreexam.com/can-you-use-a-formula-solver-to-find-the-roots-of-a-number/","timestamp":"2024-11-07T15:41:42Z","content_type":"text/html","content_length":"107306","record_id":"<urn:uuid:ef3c40fb-4a84-4d93-889b-b720a2e19649>","cc-path":"CC-MAIN-2024-46/segments/1730477028000.52/warc/CC-MAIN-20241107150153-20241107180153-00134.warc.gz"} |
Dante's Commedia1564 Edition
1564 Dante’s Commedia: a market gamble.
The 1564 edition is the first by the Venetian typographer Sessa. Upon humanist Francesco Sansovino’s initiative the volume came out as an imposing folio format, with XXVIII+392 leaves and 97 woodcuts
reproducing those commissioned by Marcolini for his 1544 edition. The text is the one reviewed by Bembo for the 1502 Aldine in-8vo edition.
Here was the challenge for Sansovino and Sessa. Competing with both the first pocket and minimalist edition of Dante with a text immediately winning the favor of philologists and the innovative
comment by Vellutello of the 1544 edition. Why venturing against the odds by reprinting Dante after such prestigious predecessors?
The success of the Marcolini edition with Vellutello’s comment, reigniting the audience’s interest for the Commedia’s exegesis, pushed Sansovino and Sessa to courageously conceive a product to enter
a market niche. The return to the medieval/incunabula large format (in-folio) and the insertion of a large system of notes and explanations wanted to offer an elegant edition where the reader could
find all what was written and said about Dante up to then.
Joining the two most appreciated comments, by Landino (first 1481) and Vellutello (first 1544) was not done before, probably for the diverse nature of the two approaches: more allegorical and prone
to digression the first, more incline to facilitating the reading the latter.
The title page highlights the elements on which Sansovino tended to leverage to promote its own edition and to justify the placing on the market of a new book product. First of all, the emphasis on
the name of Dante, and not on the title of the poem, which from the 1545 Ludovico Dolce edition (publisher Giolito de’ Ferrari) had instead been brought back to the center of attention by the
attribution of the adjective “divine”. Worth noting though that the name of the poet stood out in a prominent position on the title pages of the second Aldus edition (1515), of the “Dantino” of
Paganino (1516) and of all the Lyon editions.
The large space devoted to the portrait of Dante, on the same title page, concurs to the centrality of the figure of the poet filling more than half of the page. It is a framed laurel medallion
inside which Dante is represented from the side and with a prominent nose – so much so that the edition was known as «of the big nose». The iconography seems to reflect the physiognomy attributed to
the poet in the famous portrait of Bronzino. The reader seems therefore invited to immediately deal with the figure of the author.
Except from the three full-page woodcuts, preceding each cantica, the smaller engravings are designed according to well recognizable schemes: those of the Inferno are characterized by the circle,
often inserted in a squared frame while the scenes represented are seen from above; in the Purgatorio the prevailing scheme is a truncated cone; in Paradiso the circle represents the astral body,
surrounded by rays of light and flames.
Completely innovative if compared to the previous iconographic tradition, the 97 illustrations are not an artistic representation of scenes inspired by the text, but represent visually Dante’s
journey, as a continuation of the comment and with constant attention to the Comedy’s topography.
The outcome of the typographic gamble was a success for the years to come allowing the Sessa to reprint the edition, with minimal corrections, in 1578 and in 1596. | {"url":"https://www.hermesrarebooks.com/1564-dantes-commedia-a-market-gamble/","timestamp":"2024-11-04T07:02:53Z","content_type":"text/html","content_length":"55869","record_id":"<urn:uuid:0a83d842-70f1-4304-9480-f8765c0c3e4e>","cc-path":"CC-MAIN-2024-46/segments/1730477027819.53/warc/CC-MAIN-20241104065437-20241104095437-00538.warc.gz"} |
Key Features
1. Syllabus checklist
2. Essential theory
3. Student activities
4. Trial tests
5. Model answers
The revised edition of this study guide now has illustrations and content in full colour.
This guide assists students in their preparation for tests and examinations in the Mathematics Applications Unit 1 & 2 ATAR course. The structure is such that students will be able to make use of the
book throughout the year.
This book will challenge and extend students studying Year 11 ATAR mathematics Applications. It has been specifically written to help students revise their work and succeed in their class tests,
half-yearly and yearly exams. It’s packed with concise, student-friendly explanations of every topic, backed up with plenty of step-by-step examples, plus many questions with answers.
The Syllabus Checklist indicates to the students the skills they need to have and the objectives they need to satisfy under each of the major headings of the course.
The Introductory Notes given at the start of each chapter detail all the key ideas associated with each aspect of the course. These notes should be read in conjunction with those given by the
classroom teacher.
The Worked Examples are presented in a very detailed manner and are often accompanied by brief notes and explanations to enhance students understanding of the particular question types.
The Problems to Solve section gives students a wide range of problems and the opportunity to check their understanding of each of the topics. Fully worked solutions are also provided.
The Trial Tests are an additional source of questions and can be used when preparing for classroom tests and examinations. Suggested times are given for the tests and it is important that students
try to work within the stated time constraints. Fully worked solutions are given for these tests and a marking guide is also provided so that students can receive some concrete feedback on their
Tests are provided for both the resource free (no calculator) and the resource rich (calculator allowed) components of the assessment.
About the Author
Greg Hill has been teaching mathematics for over 30 years at various schools throughout the Perth metropolitan area, as well as the country in both government and independent schools.
Greg is currently teaching Maths Applications and Methods at All Saints' College where he has taught mathematics for the past 15 years.
He has taught all levels of mathematics, been a marker for the WACE exams and written several textbooks, including three study guides for Academic Associates covering the ATAR courses. | {"url":"https://database.academicgroup.com.au/Home.htm?cms.rm=BookInfo&BookID=206127","timestamp":"2024-11-10T18:31:20Z","content_type":"text/html","content_length":"14428","record_id":"<urn:uuid:04ba059b-858b-4b96-82a8-ddbf8f145f2d>","cc-path":"CC-MAIN-2024-46/segments/1730477028187.61/warc/CC-MAIN-20241110170046-20241110200046-00509.warc.gz"} |
Science:Math Exam Resources/Courses/MATH100/December 2014/Question 03 (f)
MATH100 December 2014
• Q1 (a) • Q1 (b) • Q1 (c) • Q1 (d) • Q1 (e) • Q1 (f) • Q1 (g) • Q1 (h) • Q1 (i) • Q1 (j) • Q2 (a) • Q2 (b) • Q2 (c) • Q2 (d) • Q2 (e) • Q3 (a) • Q3 (b) • Q3 (c) • Q3 (d) • Q3 (e) • Q3 (f) • Q4 (a) •
Q4 (b) • Q4 (c) • Q5 (a) • Q5 (b) • Q5 (c) • Q6 (a) • Q6 (b) • Q7 (a) • Q7 (b) • Q8 (a) • Q8 (b) • Q8 (c) • Q8 (d) • Q8 (e) • Q8 (f) • Q9 (a) • Q9 (b) • Q10 • Q11 (a) • Q11 (b) •
Question 03 (f)
Compute ${\displaystyle \theta =\arcsin \left(\sin({\frac {31\pi }{11}})\right)}$.
Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is
correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you?
If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it!
Recall the domain and range of ${\displaystyle \arcsin }$.
Checking a solution serves two purposes: helping you if, after having used the hint, you still are stuck on the problem; or if you have solved the problem and would like to check your work.
• If you are stuck on a problem: Read the solution slowly and as soon as you feel you could finish the problem on your own, hide it and work on the problem. Come back later to the solution if you
are stuck or if you want to check your work.
• If you want to check your work: Don't only focus on the answer, problems are mostly marked for the work you do, make sure you understand all the steps that were required to complete the problem
and see if you made mistakes or forgot some aspects. Your goal is to check that your mental process was correct, not only the result.
Found a typo? Is this solution unclear? Let us know here.
Please rate my easiness! It's quick and helps everyone guide their studies.
The function ${\displaystyle \arcsin }$ has domain ${\displaystyle [-1,1]}$ and range ${\displaystyle [-\pi /2,\pi /2]}$, so our answer must lie in this range.
• We know that ${\displaystyle \sin(x)=\sin(x-2\pi )}$; so ${\displaystyle \sin(9\pi /11)=\sin(31\pi /11)}$.
• Also we know that ${\displaystyle \sin(x)=\sin(\pi -x)}$ and so, ${\displaystyle \sin(9\pi /11)=\sin(2\pi /11)}$.
Since ${\displaystyle -\pi /2\leq 2\pi /11\leq \pi /2}$, we conclude that
{\displaystyle {\begin{aligned}\arcsin \left(\sin({\frac {31\pi }{11}})\right)&=\arcsin \left(\sin({\frac {2\pi }{11}})\right)\\&={\frac {2\pi }{11}}\end{aligned}}} | {"url":"https://wiki.ubc.ca/Science:Math_Exam_Resources/Courses/MATH100/December_2014/Question_03_(f)","timestamp":"2024-11-14T02:04:05Z","content_type":"text/html","content_length":"54046","record_id":"<urn:uuid:9d8b691c-2810-4e56-917b-e69c3de0a871>","cc-path":"CC-MAIN-2024-46/segments/1730477028516.72/warc/CC-MAIN-20241113235151-20241114025151-00155.warc.gz"} |
Philosophical Weekend - The A Priori in Science Philosophical Weekend - The A Priori in Science
Ludwig von Mises' theory of the methodological foundations of economics - aprioristic praxeology - is patently false (see below). I have come to this conclusion a long time ago. However, the
shortcoming did not bother me too much, for despite his considerable original achievements, 95% of the good economics in his work stems from other scholars with no such misguided pretension.
Only when I came into closer contact with the amazingly dogmatic Rothbardian von Mises crowd did I return to the issue of von Mises' problematic economic methodology - with a sense of alarm.
Von Mises' praxeology is an attempt at proving how absolute, indubitable, and wholly conclusive knowledge works in the field of economics, and indeed in all areas of human action. What rationalistic
Sure enough, an irresistible attractor to those with a pronounced penchant for dogmatism. Enter Murray Rothbard and his following. Rothbard pretends to have found - thanks to von Mises' praxeological
apriorism - the key to absolute truth in the fields of ethics and political theory. I have discussed this hubristic aspect of Rothbard's work in The Elementary Errors of Anarchism (1) and The
Elementary Errors Anarchism (2).
In More Geometrico, I have alluded to the fundamental problem of aprioristic praxeology.
Below is a brilliant article that spells out more fully the grotestque errors of praxeological apriorism. Have a great philosophical weekend:
Robert Murphy, like Mises, cannot properly distinguish between (1) pure geometry and (2) applied geometry (on which, see Salmon 1967: 38). When Euclidean geometry is considered as a pure mathematical
theory, it can be regarded as analytic a priori knowledge, and asserts nothing necessarily of the external, real world, since it is tautologous and non-informative. (An alternative view derived from
the theory called “conditionalism” or “if-thenism” holds that pure geometry is merely a set of conditional statements from axioms to theorems, derivable by logic, and asserting nothing about the real
world [Musgrave 1977: 109–110], but this is just as devastating to Misesians.)
When Euclidean geometry is applied to the world, it is judged as making synthetic a posteriori statements (Ward 2006: 25), which can only be verified or falsified by experience or empirical evidence.
That means that applied Euclidean geometrical statements can be refuted empirically, and we know that Euclidean geometry – understood as a universally true theory of space – is a false theory (Putnam
1975: 46; Hausman 1994: 386; Musgrave 2006: 329).
The fact that the refutation of Euclidean geometry understood as an empirical theory leaves pure geometry untouched does not help Murphy, because pure geometry per se says nothing necessary about the
universe, and is an elegant but non-informative system.
Albert Einstein was expressing this idea in the following remarks about mathematics in an address called called “Geometry and Experience” on 27 January 1921 at the Prussian Academy of Sciences:
“One reason why mathematics enjoys special esteem ... is that its laws are absolutely certain and indisputable, while those of all other sciences are to some extent debatable and in constant
danger of being overthrown by newly discovered facts. In spite of this, the investigator in another department of science would not need to envy the mathematician if the laws of mathematics
referred to objects of our mere imagination, and not to objects of reality. For it cannot occasion surprise that different persons should arrive at the same logical conclusions when they have
already agreed upon the fundamental laws (axioms), as well as the methods by which other laws are to be deduced therefrom. But there is another reason for the high repute of mathematics, in that
it is mathematics which affords the exact natural sciences a certain measure of security, to which without mathematics they could not attain. At this point an enigma presents itself which in all
ages has agitated inquiring minds. How can it be that mathematics, being after all a product of human thought which is independent of experience, is so admirably appropriate to the objects of
reality? Is human reason, then, without experience, merely by taking thought, able to fathom the properties of real things. In my opinion the answer to this question is, briefly, this:- As far as
the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.”
If we were to pursue this analysis further as applied to economic methodology, it would follow that praxeology – if it is conceived as deduced from analytic a priori axioms – is also an empty,
tautologous, and vacuous theory that says nothing necessary of the real world. And the instant any Austrian asserts that praxeology is making real assertions about the world, it must be judged
synthetic a posteriori, and so is to be verified or falsified by experience or empirical evidence.
What Murphy fails to mention is that the only way to sustain his whole praxeological program is to defend the truth of Kant’s synthetic a priori knowledge, which, as we have seen from the last post,
is a category of knowledge that must be judged as non-existent.
Do make sure to consult the source with its respective video excerpts of Murphy's explanations.
Mises's Non Sequitur on synthetic a priori Knowledge; Tokumaru on Mises's Epistemology; Reply to a "Red Herring on Praxeology"; Mises versus the Vienna Circle; Mises's Flawed Deduction and Praxeology
Recent Comments | {"url":"https://redstateeclectic.typepad.com/redstate_commentary/2013/08/duty-to-hate-.html","timestamp":"2024-11-02T13:43:42Z","content_type":"application/xhtml+xml","content_length":"76115","record_id":"<urn:uuid:a448bbcd-2c00-4d04-9695-154662c7013d>","cc-path":"CC-MAIN-2024-46/segments/1730477027714.37/warc/CC-MAIN-20241102133748-20241102163748-00299.warc.gz"} |
$25 PayPal-WW-Too Cool For School Giveaway Hop-Ends 9/9
This contest is officially over. There were 824 comments-thank you everyone!! The winning number, picked by Random.or was 219
Amber said... 219
I tweeted about the giveaway, I'm @AmberGoo:
Thank you for the giveaway :)
September 2, 2012 12:24 PM
Congratulations Amber!! Now all you have to do is reply to the email I will be sending you in just a few minutes with your PayPal url and I will send you the $25.00.
Welcome to the Too Cool For School Giveaway Hop hosted by
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decided to host a giveaway hop to help everyone win some of those back to school must haves! And I decided to join in! This event will run from September 1st through 9th, which gives you plenty of
time to hop down the linky list below! Each blogger is giving away prizes valued $20 or more, so you don’t want to miss out!
Miki's Hope will be giving $25 Paypal to help offset some of the cost--as long as you have a valid PayPal account-you have a chance to win--World Wide! Please remember to put your email address in
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«Oldest ‹Older 1 – 200 of 800 Newer› Newest» | {"url":"https://www.mikishope.com/2012/09/25-paypal-ww-too-cool-for-school.html","timestamp":"2024-11-12T15:58:06Z","content_type":"application/xhtml+xml","content_length":"309345","record_id":"<urn:uuid:45b5a553-03b5-4ad2-bc68-c0192f59bde1>","cc-path":"CC-MAIN-2024-46/segments/1730477028273.63/warc/CC-MAIN-20241112145015-20241112175015-00103.warc.gz"} |
Very long sampling time using simple model
I want to sample from this model
To do that I have created this pymc model :
with pm.Model() as inference_model_categorical:
w = pm.Dirichlet("w", a=np.ones(max_state))
latent_z = pm.Categorical('z', p=w,shape=N)
alpha = pm.Uniform("alpha", lower=0, upper=0.1)
mu = pt.shared(expected_mean)[latent_z]
obs_distrib = pm.NegativeBinomial('obs',alpha=1/alpha, mu=mu, observed=obs_draw.T)
obs_sample = pm.sample()
However, even when my observation dataset is relatively small (50x100) it takes 3 minutes. Obviously, it does not scale when the dataset increases in size, e.g for a 100x500 dataset it takes more
than 1h30.
I wonder what is the slow bit here? Is it sampling from Negative Binomial (I have also previously designed a mixture of 10 Negative Binomial distributions to solve the same problem and it was equally
Or am I doing something absurd/completely inefficient ?
Thank you for your help
Maybe marginalizing the discrete latent_z will help the sampler. You can try to use MarginalModel to do that automatically.
It also allows you to recover latent_z later with recover_marginals so you don’t lose anything. | {"url":"https://discourse.pymc.io/t/very-long-sampling-time-using-simple-model/16046","timestamp":"2024-11-02T10:37:18Z","content_type":"text/html","content_length":"27973","record_id":"<urn:uuid:2c74002f-cc4e-47e8-913f-bd749b45f16d>","cc-path":"CC-MAIN-2024-46/segments/1730477027710.33/warc/CC-MAIN-20241102102832-20241102132832-00539.warc.gz"} |
Tony Saad
Graduate seminar at the American University of Beirut. January 2005.
My first conference paper, American University of Beirut, May 2005.
Master’s thesis defense at the American University of Beirut. July 2005.
Doctoral defense presentation given at the University of Tennessee Space Institute in November 2009.
Presentation for conference paper AIAA-2010-4287 given at the AIAA JPC conference in June 2010.
Invited talk given at the University of Utah as part of the CRSIM (Combustion and Reaction SIMulation) group meetings.
A summary of quadrature methods for numerical integration. Serves as a great introduction to quadrature methods and could be used as the basis for moment methods.
A summary of using the maximum entropy principle from information theory to reconstruct a PDF (or other distributions) given a finite number of moments. This is quite useful especially when using the
method of moments in population balances or related stochastic transport processes. The document also includes some results from my code for reconstructing some bimodal and trimodal Gaussian
distributions, beta, and log-normal distributions. | {"url":"http://www.tonysaad.net/category/docs/","timestamp":"2024-11-13T05:36:17Z","content_type":"text/html","content_length":"51630","record_id":"<urn:uuid:c0d54ce8-8a37-4964-9e63-cef543b9e67f>","cc-path":"CC-MAIN-2024-46/segments/1730477028326.66/warc/CC-MAIN-20241113040054-20241113070054-00612.warc.gz"} |
Power for split-plot designs is presented two ways. As a split-plot the extra variation from resetting the hard-to-change factors along with fewer resets (groups) causes the power to detect effects
from the hard-to-change factors to plummet.
The signal to noise ratio used to calculate randomized power is computed from the entered standard deviation, the [whole plot] variance ratio and the size of an important effect (Δy).
The entered standard deviation is an estimate of the run to run, subplot, within group variability. The entered standard deviation (s) is squared to compute the run to run variance.
Hard to change factors are only changed from group to group. This causes additional whole plot, group to group variation which is in addition to the run to run variation. This additional variation is
estimated by multiplying the run to run variance by the variance ratio.
The two variances are combined and used to compute the signal to noise ratio for estimating the “If Randomized” power.
Power is meant to be a way to manage expectations for what the analysis will be able to provide. It is calculated by comparing the size of an important effect to an estimate of the standard deviation
that will appear on the ANOVA once the analysis is completed. It is the probability that an important effect can be found significant given the expected standard deviation.
Use as many of the following suggestions as possible to get the estimated power to 80%. There is no requirement for 80% power, but we at Stat-Ease, Inc. feel that it makes for a good design.
Can a higher alpha risk (Type I Error rate) be tolerated?
Increase the significance threshold for power under Edit - Preferences, General - Analysis node. Increasing the alpha raises the acceptable risk of detecting false effects. If you are more willing to
find false effects, you are more likely to find true effects.
If more runs are affordable…
If a full factorial’s power is less than 60%, the best method is to replicate the whole design using Design Tools, Augment Design, Replicate Design.
For larger full-factorial designs having a power around 65%, but too many runs to replicate in full, use the augmentation tools found under Design Tools, Augment Design, Augment. The factorial
optimal is a good choice and will allow adding just a few runs at a time.
If the design is a fractional design, including Min-Run, Irregular, and Optimal, the best way to increase runs is to create a new design. Click yes to Use previous design info, and choose a larger
design from the list.
If no more runs are affordable, look at the design…
Will the changes in the factor levels produce a larger change in the response than the stated delta? If so, use the larger estimate of delta to estimate power. Larger effects are easier to detect.
Can the factor settings be run on a wider interval? A bigger change in the factor settings usually translates to a bigger change in the response.
Can you be satisfied finding only larger effects? If so, increase delta.
If increasing the size of your stated delta is not an option…
Use blocks to isolate known, yet uncontrolled sources of variation. For instance, if the experiment will take several days, build a design with one block per day.
If the noise is coming from your measurement system…
Get a better measurement system – this usually means more cost.
Repeat the measurements you are making and record the average as your response.
If the noise is truly coming from the process and none of the above ways to increase power are suitable, do not run this experiment. Most likely no significant effect will arise, and little will be
learned about the process. | {"url":"https://www.statease.com/docs/latest/screen-tips/intro-and-build/factorial/not-enough-power-split-plot/","timestamp":"2024-11-03T20:17:34Z","content_type":"text/html","content_length":"25061","record_id":"<urn:uuid:c5a292de-8327-4291-a5c4-98a622521892>","cc-path":"CC-MAIN-2024-46/segments/1730477027782.40/warc/CC-MAIN-20241103181023-20241103211023-00303.warc.gz"} |
Calculate Coulomb: Help Solving Homework Problem
• Thread starter Physicsrapper
• Start date
In summary, the conversation discusses a problem involving finding the current delivered by batteries based on the power output of an engine and the weight and vertical distance of a car being
shifted. The equations P = U * I and I = P/U = 12,000 W / 168 V = 71.4 A are used to calculate the current. However, there is confusion about how to calculate the voltage (V) and assistance is
Homework Statement
The engine delivers 12 kW. Per second it can shift the m = 800 kg car over a vertical distance of 1.5 m. Find the current delivered by the batteries.
Homework Equations
P = U * I
I = P/U = 12 000 W / 168 V = 71.4 A
The Attempt at a Solution
My Problem is: I don't really know how to calculate V...
I know that V = J/C and Js = 12 000, but I don't know how to find out the Coulomb.
Can please someone help?
Staff Emeritus
Science Advisor
Homework Helper
Education Advisor
Physicsrapper said:
Homework Statement
The engine delivers 12 kW. Per second it can shift the m = 800 kg car over a vertical distance of 1.5 m. Find the current delivered by the batteries.
Could you please tell us the problem statement exactly as given to you?
Homework Equations
P = U * I
I = P/U = 12 000 W / 168 V = 71.4 A
Where did you get these numbers from?
The Attempt at a Solution
My Problem is: I don't really know how to calculate V...
I know that V = J/C and Js = 12 000, but I don't know how to find out the Coulomb.
Can please someone help?
A volt is a joule per coulomb, but "Js = 12000" doesn't make any sense.
FAQ: Calculate Coulomb: Help Solving Homework Problem
1. How do I calculate Coulomb?
To calculate Coulomb, use the formula F = k(q1*q2)/r^2, where F is the force between two charges, k is the Coulomb's constant (9 x 10^9 N*m^2/C^2), q1 and q2 are the magnitudes of the two charges,
and r is the distance between the two charges.
2. What is the unit of Coulomb?
The unit of Coulomb is Coulomb (C), which is equivalent to ampere-second (A*s) in the SI system of units.
3. How do I convert Coulomb to other units?
To convert Coulomb to other units, use the following conversions: 1 C = 6.24 x 10^18 electrons, 1 C = 1/3.33564 x 10^-10 faradays, and 1 C = 1/2.99792 x 10^9 statcoulombs.
4. What is Coulomb's Law?
Coulomb's Law is the principle that describes the electrostatic interaction between two charged particles. It states that the force between two charges is directly proportional to the product of the
charges and inversely proportional to the square of the distance between them.
5. How is Coulomb's Law different from Newton's Law of Universal Gravitation?
Coulomb's Law describes the electrostatic force between two charged particles, while Newton's Law of Universal Gravitation describes the gravitational force between two massive objects. The two laws
have similar mathematical forms, but the forces they describe are fundamentally different. | {"url":"https://www.physicsforums.com/threads/calculate-coulomb-help-solving-homework-problem.740121/","timestamp":"2024-11-08T05:18:43Z","content_type":"text/html","content_length":"79332","record_id":"<urn:uuid:24423301-2e2d-4bca-bd8e-1ad94445a893>","cc-path":"CC-MAIN-2024-46/segments/1730477028025.14/warc/CC-MAIN-20241108035242-20241108065242-00112.warc.gz"} |
Computational Geometry
Advanced Course, 3+1
Lectures: Tuesday 10:00-12:00, Odd week Thursday 10:00-12:00 Location:Zoom, see below
Lecturers: Raimund Seidel and Sándor Kisfaludi-Bak
First lecture: May 5. 10:15 AM
Tutorials: Even week Thursday 10:00-12:00
Assistant: André Nusser
First tutorial: May 14. 10:15 AM
Credits: 6
Exam: Take-home (can be done virtually)
Prerequisites: Basics of data structures, algorithms, computational complexity, and linear algebra
All students should subscribe to the mailing list at https://lists.mpi-inf.mpg.de/listinfo/compgeo20
Zoom URL: https://zoom.us/j/99444908708
If you still need the password for the lectures and tutorials, please send us an email.
Computational geometry considers problems with geometric input, and its goal is to design efficient algorithms and to study the computational complexity of such problems. A typical input to a
problem is some set of points or segments in the Euclidean plane (or higher dimensional Euclidean space). Examples of problems include computing the convex hull of the point set, finding clusters,
or setting up a data structure to find the nearest point to a given query point. Although not the focus of this course, there is a very rich application domain, including computer graphics,
computer-aided design and manufacturing, machine learning, robotics, geographic information systems, computer vision, integrated circuit design, and many other fields.
The course introduces the most important tools used in the design of computational geomtric algorithms. The larger part of the course will deal with problems that can be solved exacly in near-linear
time, which are practically solvable even on very large inputs. Towards the end we will deal with hard (often NP-hard) problems, and see some tools that help in creating approximation algorithms.
Date Topic Lecturer/Tutor Slides/Assignment
05.05 Introduction - Arrangements, duality, outlook Raimund Seidel pdf
07.05 Convex hulls in the plane Sándor Kisfaludi-Bak pdf
12.05 3-dimensional convex hulls Sándor Kisfaludi-Bak pdf
14.05 Tutorial 1 André Nusser pdf
19.05 Low-dimensional linear programming Raimund Seidel pdf
21.05 Orthogonal range searching Sándor Kisfaludi-Bak pdf
26.05 Line segment intersections, segment trees Raimund Seidel pdf
28.05 Tutorial 2 André Nusser pdf
02.06 Point Location Raimund Seidel pdf
04.06 Voronoi diagrams, Delaunay triangulations Sándor Kisfaludi-Bak pdf
09.06 Quadtrees, compressed quadtrees Raimund Seidel pdf
[S:11.06:S] 16.06, 12:15 Tutorial 3 André Nusser pdf
16.06 Well-separated pair decomposition, spanners Raimund Seidel pdf
18.06 Clustering, k-center, k-median Sándor Kisfaludi-Bak pdf
23.06 Planar separator, shifting for packing and covering Sándor Kisfaludi-Bak pdf
25.06 Tutorial 4 André Nusser pdf
30.06 Range spaces, VC dimension Raimund Seidel pdf
02.07 Coresets Sándor Kisfaludi-Bak pdf
07.07 Hitting set and set cover via local search Sándor Kisfaludi-Bak pdf
09.07 Tutorial 5 André Nusser pdf
14.07 Configuration spaces Raimund Seidel pdf
16.07 Dimension reduction, metric embeddings Sándor Kisfaludi-Bak pdf
• Some of the lectures will have significant overlaps with chapters of the "Dutch book":
Computational Geometry: Algorithms and Applications (3rd edition) by Mark de Berg, Otfried Cheong, Marc van Kreveld, and Mark Overmars.
See here.
• Towards the end of the semester, we will have some overlap with the following book:
Geometric Approximation Algorithms by Sariel Har-Peled.
See here and here. (Note that the published book has much better and much more content than what is available on the author's webpage.) | {"url":"https://www.mpi-inf.mpg.de/de/departments/algorithms-complexity/teaching/summer20/computational-geometry","timestamp":"2024-11-12T02:15:24Z","content_type":"text/html","content_length":"88420","record_id":"<urn:uuid:4c7028a8-c637-4d91-a17c-82ad57ed04ba>","cc-path":"CC-MAIN-2024-46/segments/1730477028242.50/warc/CC-MAIN-20241112014152-20241112044152-00116.warc.gz"} |
11 The number of elements in the set {n∈Z:∣∣n2−10n+19∣∣<6} is... | Filo
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Question Text 11 The number of elements in the set is
Updated On Sep 3, 2023
Topic Complex Number and Binomial Theorem
Subject Mathematics
Class Class 11
Answer Type Video solution: 2
Upvotes 170
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Computer Science Fundamentals Course by Brilliant.org - My Opinion | Course Finder 365
As an avid learner, I recently completed the “Computer Science Fundamentals” course on Brilliant.org. In this review, I’ll walk you through my personal experience, share some handy tips, and present
the pros and cons of the course.
👉 My Impressions About Brilliant.org Learning Experience
Quick Overview: Course Features
Feature Description
Lessons 15 interactive lessons
Main Topics Binary Search, Concurrency, Decision Trees, Interfaces, Parallelism, Programming, etc.
Pre-requisites None. Suitable for beginners with no previous computer science experience
Next Course Recommendations Introduction to Algorithms, Programming with Python
Key Skills Acquired Computational thinking, understanding algorithms, problem-solving
Course Review: Computer Science Fundamentals
In the realm of computer science, mastering the fundamentals is a prerequisite to success. This course proved to be a perfect starting point for me, presenting key computer science concepts in an
accessible and enjoyable manner. The absence of coding requirements was a boon, allowing me to focus solely on core principles.
What set this course apart was the way it encouraged active learning, transforming me from a passive recipient of information into an active participant. The course starts with simple concepts like
“Tools of Computer Science” and gradually builds up to more complex topics like “Thinking with Graphs” and “Graph Search”.
The course provided a balanced mix of theory and practical application. Each lesson was followed by problems that required me to apply the knowledge I had just gained. This interactive approach
helped to solidify my understanding and gave me the confidence to tackle complex problems.
Pros and Cons
Pros Cons
Interactive and engaging lessons Some may prefer coding integrated into the course
No prior computer science experience required
Covers a broad range of fundamental concepts
Encourages problem-solving and critical thinking
1. Active Participation. Engage actively with each lesson and don’t shy away from the problems presented after each module. They reinforce your understanding and improve retention.
2. Regular Practice. Make learning a daily habit. Regular exposure to the material aids comprehension and memory.
3. Patience. Don’t rush through the lessons. Take your time to understand the concepts.
In conclusion, the “Computer Science Fundamentals” course on Brilliant.org offers a comprehensive introduction to computer science, emphasizing critical thinking and problem-solving skills. The pros
of this course far outweigh the minor con. I highly recommend it to anyone wishing to delve into computer science without having any prior knowledge of the field.
Here is the list of other available courses on Brilliant.org at this moment:
• Algebra
• Solving Equations
• Understanding Graphs
• Systems of Equations
• Algebra I
• Algebra II
• Complex Numbers
• Mathematical Thinking
• Everyday Math
• Mathematical Fundamentals
• Number Theory
• Number Bases
• Infinity
• Math History
• Geometry Fundamentals
• Beautiful Geometry
• Geometry I
• Geometry II
• 3D Geometry
• Data Analysis Fundamentals
• Introduction to Probability
• Applied Probability
• Perplexing Probability
• Casino Probability
• Random Variables & Distributions
• Statistics Fundamentals
• Sampling
• Hypothesis Testing
• Logic
• Logic II
• Knowledge and Uncertainty
• Contest Math I
• Contest Math II
• Calculus in a Nutshell
• Pre-Calculus
• Trigonometry
• Calculus Fundamentals
• Integral Calculus
• Multivariable Functions
• Multivariable Calculus
• Introduction to Linear Algebra
• Linear Algebra with Applications
• Vector Calculus
• Differential Equations
• Math for Quantitative Finance
• Group Theory
• Equations in Number Theory
• Logic Puzzles
• Pre-Algebra Puzzles
• Algebra Puzzles
• Advanced Algebra Puzzles
• Geometry Puzzles
• Advanced Geometry Puzzles
• Probability and Statistics Puzzles
• Advanced Number Puzzles
• Math Fundamentals Puzzles
• Discrete Math Puzzles
Computer Science:
• Thinking In Code
• Computer Science Fundamentals
• Introduction to Algorithms
• Algorithms and Data Structures
• Programming with Python
• Next Steps in Python
• Introduction to Neural Networks
• How Technology Works
• Search Engines
• Cryptocurrency
• Quantum Computing
• Artificial Neural Networks
• Reinforcement Learning
• Computer Memory
• Scientific Thinking
• Physics of the Everyday
• The Chemical Reaction
• Classical Mechanics
• Astrophysics
• Gravitational Physics
• Electricity and Magnetism
• Quantum Objects
• Kurzgesagt – Beyond the Nutshell
• Real Engineering
• Quantum Mechanics with Sabine
• Solar Energy
• Computational Biology
• Special Relativity
• Molecules | {"url":"https://coursefinder365.com/posts/computer-science-fundamentals-course-review-brilliant/","timestamp":"2024-11-14T10:16:56Z","content_type":"text/html","content_length":"99707","record_id":"<urn:uuid:e48b973b-e181-4214-81eb-2d41e3a393d5>","cc-path":"CC-MAIN-2024-46/segments/1730477028558.0/warc/CC-MAIN-20241114094851-20241114124851-00594.warc.gz"} |
population standard deviation – Q&A Hub – 365 Data Science
Resolved: population standard deviation
for calculating standard error we need population standard deviation and if we know population standard deviation then why dont we find mean of population directly rather then using confidence
intervals to estimate population mean ?
3 answers ( 2 marked as helpful)
Hi Uzair!
Thanks for reaching out!
Please note that knowing the population standard deviation doesn't mean that we know the population mean. Calculating the population mean directly requires having the entire population data, which is
often too difficult or even impossible to obtain. In most cases, we only have a sample from the population. Therefore, we use the sample mean to estimate the population mean and we calculate a
confidence interval to obtain the uncertainty of this estimation.
Hope this helps.
hey Ivan
appreciate ur detailed response but my point is that if we have population standard deviation then it implies that we have data for population , otherwise how did we calculate population standard
deviation in first place .
Hi Uzair!
You raised a valid point.
However, when we refer to the population standard deviation in estimating the population mean, it doesn't necessarily mean we have the actual population data. The population standard deviation is
often a known value from previous studies or established benchmarks. | {"url":"https://365datascience.com/question/population-standard-deviation/","timestamp":"2024-11-14T03:51:40Z","content_type":"text/html","content_length":"115198","record_id":"<urn:uuid:880c0be6-6450-43aa-a3fe-db3aaa51c52d>","cc-path":"CC-MAIN-2024-46/segments/1730477028526.56/warc/CC-MAIN-20241114031054-20241114061054-00891.warc.gz"} |
AEROELASTICITY & STRUCTURAL DYNAMICS 2024
13:30 Low/high order methods 1
Chair: Daniella Raveh
A modular TSM solver for aeroelastic analysis and optimizations
Cedric Liauzun, Christophe Blondeau
Abstract: Several typical aeroelastic phenomena and instabilities, like flutter, induce periodic oscillations of the structure and of the aerodynamic forces. Numerical methods based on the
harmonic balance technique or the Time Spectral Method (TSM) with a projection on the Fourier space has proven to be very efficient to predict the oscillatory phenomena by resolving the
established regime without solving for the transient one. Such formulations lead however to critical numerical difficulties especially with a fine time sampling. A modular parallel TSM solver
13:30 is developed in order to perform aeroelastic analyses and optimizations of wings. This solver is in charge of performing all the operations regarding the time discretization and the time
30 resolution. An interface with the CFD elsA solver extracts all the needed information related to space discretization. Such architecture allows the adaptation of the TSM solver to any CFD codes
mins (structured/unstructured), and most of all allows assessing and developing easily new resolution algorithms to improve the robustness and the computational efficiency. The structural
deformations are taken into account in the TSM problem by an ALE formulation of the fluid equations. The time resolution of the TSM problem is carried out using an Approximate Newton Krylov
method. Particular attention is paid for the investigation on the methods to solve the linear systems resulting from the ANK approach, especially on their preconditioning. An adjoint
formulation of the TSM approach is also developed in order to perform aeroelastic optimizations with dynamic objective functions. The adjoint solver is actually aimed at replacing the low
fidelity gust load computation based on DLM in an aeroelastic sizing and optimization process. This TSM solver is evaluated for inviscid flows in the cases of a 2D airfoil to which pitching
motions are applied, of a 3D large aspect ratio wing (DLR-F25) subjected to harmonic oscillations which shape is a structural eigen mode one, and subjected to gust loads. A last case concerns
the gust response of a 2D airfoil with plunge and twist degrees of freedom.
Comparison between computational and experimental non-stationary pressure distribution on a pitch-oscilating wing
Bruno Regina, Eduardo Molina, Roberto Silva
Abstract: The objective of this work is to obtain CFD results for the dynamic response of a wing oscillating in pitch in a transonic regime using an open-source tool. The purpose is to verify
14:00 and improve the correspondence with the experimental data as performed in the wind tunnel test for a wing model developed by Embraer. For this, in some analyzes it is proposed to impose a
30 prescribed movement to the wing in the CFD simulations that models the bending observed in the scaled model throughout the tests as a rigid mesh movement in rolling direction. Prescribed motion
mins parameters are extracted directly from the model’s structural deformation measurement data. In addition, simulations of a test case using the Benchmark Supercritical Wing (BSCW) are performed
to investigate the impact of relevant variables in this type of analysis, such as time step and mesh refinement level. The time step was identified as the most influential parameter to
approximate the simulation results to experimentally obtained data. The CFD results for the Embraer wing were able to capture the main behaviors of the magnitude and phase of the non-stationary
pressure coefficient on the wing, mainly for conditions of higher reduced frequencies, with an affordable computational cost.
Aerodynamic analysis of aircraft wings using a coupled PM-BL approach
Lipeng Zhu, Changchuan Xie, Yang Meng
Abstract: The objective of this paper is to develop an aerodynamic model suitable for aeroelastic analysis with low computational cost and sufficient fidelity. The physics-based reduce order
model is based on the unsteady inviscid Panel Method (PM), selected for its low computation time. Viscous effects are modeled with two-dimensional unsteady high-fidelity boundary layer
calculations at various sections along the span and incorporated as an effective shape boundary condition correction inside the PM. The viscous sectional data are calculated with
14:30 two-dimensional differential boundary layer equations to allow viscous effects to be included for a more accurate maximum lift coefficient and spanload evaluations. These viscous corrections
30 are coupled through a modified displacement thickness distribution coupling method for 2D boundary layer sectional data. Predicting the flowfield by solutions based on inviscid-flow theory is
mins usually adequate as long as the viscous effects are negligible. A boundary layer that forms on the surface causes the irrotational flow outside it to be on a surface displaced into the fluid by
a distance equal to the displacement thickness, which represents the deficiency of mass within the boundary layer. Thus, a new boundary for the inviscid flow, taking the boundary-layer effects
into consideration, can be formed by adding to the body surface. The new surface is called the displacement surface and, if its deviation from the original surface is not negligible, the
inviscid flow solutions can be improved by incorporating viscous effects into the inviscid flow equations. For a given wing geometry and freest ream flow conditions, the inviscid velocity
distribution is first obtained with the three-dimensional panel method, and the boundary layer equations are solved along the streamline. The fidelity of the method is verified against 3D RANS
flow solver solutions on a high aspect ratio wing. The overall results show impressive precision of the 3D PM/2D BL approach compared to 3D RANS solutions and in compute times in the order of
minutes on a standard desktop computer. The steady and unsteady analysis results of NACA 0012 airfoil are shown as follows.
Rayleigh-Ritz method with multibody dynamics for highly flexible structures
Leonardo Barros da Luz, Flávio Cardoso-Ribeiro, Pedro Paglione
Abstract: Flexible structures are increasingly prevalent in the commercial aviation industry, and the use of highly flexible structures is a prominent trend for the future. When analyzing those
structures, it is crucial to consider geometric nonlinearities caused by large displacements. This means that the modeling of the structures must incorporate nonlinear structural models, which
15:00 can lead to a reasonable increase in computational costs. To tackle this challenge, a framework has been developed for static and dynamic analyses of highly flexible structures. It is based on
30 a linear structural model, utilizing the Rayleigh-Ritz method, coupled with multibody dynamics. The geometric nonlinearities are modeled through rigid connections between multiple flexible
mins bodies that form the final structure. Two different approaches have been used for the multibody dynamics. The former considers all degrees of freedom of each body and solves only the kinematics
of the constraint to maintain the connections between the bodies, which resulted in an augmented system with Lagrange multipliers that can be used to reconstruct forces and moments of
constraint. The latter utilizes only the independent degrees of freedom whilst reconstructing the dependent ones through the equations that define the constraints between the bodies, directly
solving the constraints. The results obtained show that proposed framework accurately describes the dynamics of highly flexible structures and can be used to simulate structures with various
types of connections, showcasing its versatility for other applications like simulations of morphing structures such as wings with folding wingtips.
end %--> | {"url":"https://conf.ifasd2024.nl/proceedings/show_slot/42.htm","timestamp":"2024-11-09T10:54:48Z","content_type":"text/html","content_length":"13368","record_id":"<urn:uuid:cd8fb2d3-2e9f-4688-abd6-6cd2ef9a8b4e>","cc-path":"CC-MAIN-2024-46/segments/1730477028116.75/warc/CC-MAIN-20241109085148-20241109115148-00566.warc.gz"} |
H. Edwin Romeijn
We consider discounted Markov Decision Processes (MDPs) with countably-infinite state spaces, finite action spaces, and unbounded rewards. Typical examples of such MDPs are inventory management and
queueing control problems in which there is no specific limit on the size of inventory or queue. Existing solution methods obtain a sequence of policies that converges to optimality … Read more
Extreme Point Solutions for Infinite Network Flow Problems
We study capacitated network flow problems with supplies and demands defined on a countably infinite collection of nodes having finite degree. This class of network flow models includes, for example,
all infinite horizon deterministic dynamic programs with finite action sets since these are equivalent to the problem of finding a shortest infinite path in an … Read more | {"url":"https://optimization-online.org/author/romeijn/","timestamp":"2024-11-10T01:33:54Z","content_type":"text/html","content_length":"85647","record_id":"<urn:uuid:a83f7950-d1e6-4e35-96b8-97f6cf0f7104>","cc-path":"CC-MAIN-2024-46/segments/1730477028164.3/warc/CC-MAIN-20241110005602-20241110035602-00393.warc.gz"} |
orksheets for 4th Grade
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Explore printable Number Sense worksheets for 4th Grade
Number Sense worksheets for Grade 4 are an essential tool for teachers looking to enhance their students' mathematical skills and understanding. These worksheets provide a variety of engaging and
challenging activities that cater to the diverse learning needs of Grade 4 students. By incorporating Number Sense worksheets into their lesson plans, teachers can effectively help students develop a
strong foundation in math concepts such as place value, rounding, estimation, and more. Moreover, these worksheets are designed to align with the Common Core State Standards, ensuring that the
content is both relevant and rigorous. With a wide range of topics covered, Number Sense worksheets for Grade 4 are an invaluable resource for teachers striving to create a dynamic and effective math
learning environment.
In addition to Number Sense worksheets for Grade 4, teachers can also utilize Quizizz, an interactive platform that offers a multitude of engaging math activities and assessments. Quizizz allows
educators to create customized quizzes, polls, and even interactive lessons that can be easily integrated into their existing curriculum. This versatile platform not only offers a vast library of
pre-made math quizzes and worksheets but also enables teachers to track student progress and provide instant feedback. By incorporating Quizizz into their teaching strategies, educators can
effectively supplement their Number Sense worksheets for Grade 4 and further support their students' mathematical growth. With its user-friendly interface and diverse range of offerings, Quizizz is
an ideal resource for teachers seeking to enhance their students' learning experience and overall success in math. | {"url":"https://quizizz.com/en-us/number-sense-worksheets-grade-4","timestamp":"2024-11-06T08:44:38Z","content_type":"text/html","content_length":"155135","record_id":"<urn:uuid:38ec429a-ca34-488b-9690-43208874e229>","cc-path":"CC-MAIN-2024-46/segments/1730477027910.12/warc/CC-MAIN-20241106065928-20241106095928-00008.warc.gz"} |
Duplicate Detection Strategies in context of deduplication ratio
30 Aug 2024
Duplicate Detection Strategies: A Review of Deduplication Ratio
Duplicate detection is a crucial step in various applications, including data cleaning, information retrieval, and plagiarism detection. The goal of duplicate detection is to identify and remove
redundant or identical records, thereby improving the quality and efficiency of these applications. In this article, we review various duplicate detection strategies, focusing on their deduplication
ratio, which measures the proportion of duplicates removed from a dataset.
Duplicate detection involves identifying and removing identical or near-identical records from a dataset. This process is essential in various domains, including data cleaning, information retrieval,
plagiarism detection, and more. The deduplication ratio (DR) is a key metric that measures the effectiveness of duplicate detection strategies. It is defined as:
DR = (Number of duplicates removed / Total number of records) * 100
Duplicate Detection Strategies
Several duplicate detection strategies have been proposed in literature, each with its strengths and weaknesses.
1. Hash-Based Approach
The hash-based approach involves computing a hash value for each record and comparing it with the hash values of other records. If two records have the same hash value, they are considered
duplicates. The deduplication ratio (DR) for this approach can be calculated as:
DR = (Number of collisions / Total number of records) * 100
where a collision occurs when two different records produce the same hash value.
2. Jaccard Similarity Coefficient
The Jaccard similarity coefficient measures the similarity between two sets by dividing the size of their intersection by the size of their union. In duplicate detection, this approach involves
computing the Jaccard similarity coefficient for each pair of records and identifying duplicates based on a threshold value.
DR = (Number of pairs with Jaccard similarity >= Threshold / Total number of record pairs) * 100
3. Cosine Similarity
The cosine similarity measures the angle between two vectors in a high-dimensional space. In duplicate detection, this approach involves computing the cosine similarity for each pair of records and
identifying duplicates based on a threshold value.
DR = (Number of pairs with Cosine similarity >= Threshold / Total number of record pairs) * 100
4. Machine Learning-Based Approach
The machine learning-based approach involves training a model to learn the patterns in the data and identify duplicates based on these patterns. This approach can be more effective than traditional
duplicate detection strategies, especially for complex datasets.
DR = (Number of duplicates removed / Total number of records) * 100
Duplicate detection is an essential step in various applications, and the deduplication ratio is a key metric that measures the effectiveness of these strategies. In this article, we reviewed four
duplicate detection strategies: hash-based approach, Jaccard similarity coefficient, cosine similarity, and machine learning-based approach. Each strategy has its strengths and weaknesses, and the
choice of strategy depends on the specific application and dataset.
• [1] Bilenko, M., & Mooney, R. (2003). Vertical clustering of a data stream.
• [2] Jaccard, P. (1908). Nouvelles recherches sur la distribution florale.
• [3] Salton, G., & McGill, M. J. (1986). Introduction to modern information retrieval.
Note: The references provided are fictional and for demonstration purposes only.
Related articles for ‘deduplication ratio ‘ :
• Reading: **Duplicate Detection Strategies in context of deduplication ratio **
Calculators for ‘deduplication ratio ‘ | {"url":"https://blog.truegeometry.com/tutorials/education/f92df98a7b13977f4cc3ee0cc7aad4fa/JSON_TO_ARTCL_Duplicate_Detection_Strategies_in_context_of_deduplication_ratio_.html","timestamp":"2024-11-11T19:22:37Z","content_type":"text/html","content_length":"18650","record_id":"<urn:uuid:acbc460b-0de3-45ca-a509-8978a985cf73>","cc-path":"CC-MAIN-2024-46/segments/1730477028239.20/warc/CC-MAIN-20241111190758-20241111220758-00103.warc.gz"} |
Finite-horizon MDP (Markov Decision Process)
Finite-horizon MDP uses a fixed time horizon for decision-making. In a finite-horizon MDP, the agent makes decisions over a finite number of time steps or stages. The decision process is divided into
discrete time periods, and the agent's goal is often to maximize the cumulative sum of rewards over this finite time horizon.
The formulation of a finite-horizon MDP includes an additional parameter, T, representing the time horizon. The agent takes actions in each time step, and the environment responds with transitions
and rewards. The objective is to find a policy that maximizes the sum of rewards over the specified time horizon.
The formulation of a finite-horizon MDP can be expressed as (S, A, P, R, T), where T is the time horizon. Solving finite-horizon MDPs often involves dynamic programming methods, such as backward
induction or forward dynamic programming, to compute the optimal policy and corresponding value function over the finite time steps. The optimal policy dictates the best action to take at each time
step to maximize the expected cumulative reward by the end of the time horizon.
The expected sum of rewards over time under a certain policy can be given by,
E represents the expectation operator, indicating that the expression is referring to the expected value.
R(S[t], a[t]) represents the immediate reward associated with taking action a[t] in state S[t].
S[t] and a[t]represent the state and action at time step t, respectively.
The sum in Equation 3665a denotes the total sum of rewards over the finite time horizon T. In the MDP, the objective is often to find a policy that maximizes the expected cumulative reward over a
specified time horizon. Then, the corresponding policy is π[t]* (non-stationary policy), which depends on time instead of a stationary policy. | {"url":"https://www.globalsino.com/ICs/page3665.html","timestamp":"2024-11-13T21:49:31Z","content_type":"text/html","content_length":"14680","record_id":"<urn:uuid:721c5e7c-4e3a-4637-84d3-68c2e6eb796a>","cc-path":"CC-MAIN-2024-46/segments/1730477028402.57/warc/CC-MAIN-20241113203454-20241113233454-00163.warc.gz"} |
Homological Algebra Symposium
14:15: Thomas Brüstle (Université de Sherbrooke)
Homological approximations in persistence theory
Multiparameter persistence modules appear in topological data analysis when dealing with noisy data. They are defined over a wild algebra and therefore they do not admit a complete discrete
invariant. One thus tries in persistence theory to “approximate” such a module by a more manageable class of modules. Using that approach we define a class of invariants for persistence modules based
on ideas from homological algebra. This is a report on joint work with Claire Amiot, Benjamin Blanchette and Eric Hanson. No prior knowledge of topological data analysis is required.
15:15 Amit Shah (Aarhus Universitet)
Characterising Jordan-Hölder extriangulated categories via Grothendieck monoids
Abstract: The notions of composition series and length are well-behaved in the context of abelian categories. And, in addition, each abelian category satisfies the so-called Jordan-Hölder property/
theorem. Unfortunately, these ideas are poorly behaved for triangulated categories. However, with the introduction of extriangulated categories, it is interesting to see what sense we can make of
these concepts for extriangulated categories.
I'll present a result that characterises Jordan-Hölder, length extriangulated categories using the Grothendieck monoid of an extriangulated category. This is motivated by the exact category setting
as considered by Enomoto, in which it becomes apparent that Grothendieck monoid is more appropriate to look at than the Grothendieck group. I'll present some examples coming from stratifying systems.
In fact, developing stratifying systems for extriangulated categories was the original motivation of our article. This is joint work with Thomas Brüstle, Souheila Hassoun and Aran Tattar.
16:15 Henrik Holm (Københavns Universitet)
Compact and perfect objects in triangulated categories of quiver representations.
A complex of modules over a ring, A, can be viewed as an A-module valued representation of a certain quiver with relations, Q. The vertices of Q are the integers, there is an arrow q -> q-1 for each
integer q, and the relations are that consecutive arrows compose to zero. Hence the classic derived category of A can be viewed as a triangulated category of representations of Q. It is well-known
that the derived category is compactly generated and that the compact objects are precisely the so-called perfect complexes, i.e. complexes that are isomorphic to a bounded complex of finitely
generated projective A-modules.
While complexes do play a prominent role, other types of quiver representations are important as well. It turns out that if Q is a suitably nice quiver with relations, then there exists a
triangulated category whose objects are the A-module valued representations of Q. This category is called "the Q-shaped derived category" of the ring A.
We will prove that the Q-shaped derived category is always a compactly generated triangulated category. We will also extend the notion of perfect complexes (in the classic derived category) to
perfect objects in the Q-shaped derived category. It turns out that, up to direct summands, perfect and compact objects in the Q-shaped derived category are the same.
The talk is based on a joint paper (arXiv:2208.13282) with Peter Jørgensen from Aarhus University. | {"url":"https://projects.au.dk/homologicalalgebra/seminaraarhus/event/activity/6480?cHash=1ed71bc882b0db4cd40287e5c223d3f9","timestamp":"2024-11-10T05:30:41Z","content_type":"text/html","content_length":"19197","record_id":"<urn:uuid:6cfe9867-1d63-4676-a6b3-ba47c18917c1>","cc-path":"CC-MAIN-2024-46/segments/1730477028166.65/warc/CC-MAIN-20241110040813-20241110070813-00370.warc.gz"} |
2/6/24, 9:56 PM Case – HRM401 Staffing Organizations (2024JAN08FT-1) 1/7 Module 3 – Case EMPLOYEE SELECTION Assignment Overview Signature Assignment:
2/6/24, 9:56 PM Case – HRM401 Staffing Organizations (2024JAN08FT-1)
Module 3 – Case
Assignment Overview
Signature Assignment: Quantitative Reasoning, Introduced
In this assignment, your quantitative reasoning skills will be
assessed. The Quantitative Reasoning rubric will be useful for this
purpose. In this course, HRM401, quantitative reasoning skills will
be assessed at the “introduced” level. In HRM404, they will be
assessed at the “reinforced” level. Finally, in MGT491, your skills
will be assessed at the “emphasized” level. The grading rubric for
information literacy at the undergraduate level has been developed
to measure student success in meeting the HRM401 Case 3
expectations. Rubrics for the other two courses are included in their
respective assignments.
Organizations use a lot of different methods to determine if a job
applicant has the potential to be successful on the job. Selection
tests are used to identify applicants’ skills that cannot be
determined in an interview process. Companies use several
different types of testing methods to rate job applicants “on
aptitude, personality, abilities, honesty and motivation” (Gusdorf,
2008, p. 10). Appropriate tests are standardized, reliable, and valid
in predicting an applicant’s job success.
To fairly compare the performance of multiple job applicants, the
processes used to test them must be identical. This means the test
content and its instructions must be the same for all candidates.
Just as important, though, the skills tested in a selection instrument
2/6/24, 9:56 PM Case – HRM401 Staffing Organizations (2024JAN08FT-1)
should be the same skills used on the job. If a test cannot assess
the ability to perform the job, it has no usefulness in the selection
But, what happens once the new employee is hired, and he does
not fit with the job or company culture? At this point, the HR
Manager must evaluate the entire hiring process to see where the
poor selection of the new employee could have been avoided.
If it happens that a new employee does not work out and leaves the
company, the company’s retention and employee turnover ratios
are impacted with the former lowering and the latter rising.
With an abundance of data available in today’s digital world, it is
possible to predict hiring outcomes and not just track them. This
data usage is only going to become more critical in the years to
come. Three of the important metrics in the recruitment and
selection process are time to fill, time to hire, and selection ratio.
Time to fill refers to the time it takes to find and hire a new
candidate, often measured by the number of days between
publishing a job opening and hiring the candidate. Time to fill is
influenced by supply and demand ratios for specific jobs. It is a
great metric for business planning and offers a realistic view for the
manager to assess the time it will take to attract a replacement for a
departed employee.
In addition, a short time to fill a position usually has a positive effect
on the rest of the team as it means less overtime and instability.
A similar HR metric is time to hire. Time to hire represents the
number of days between the moment a candidate is approached
and the moment the candidate accepts the job. In other words, it
measures the time it takes for someone to move through the hiring
process once they’ve applied. Time to hire provides a solid
indication of how the recruitment team is performing. This metric is
also called ‘Time to Accept.’
2/6/24, 9:56 PM Case – HRM401 Staffing Organizations (2024JAN08FT-1)
The third metric is the selection ratio. When there’s a high number
of candidates, the ratio approaches 0. The selection ratio provides
information such as the value of different assessment tools and can
be used to estimate the utility of a given selection and recruitment
The formula for determining the selection ratio is:
number of hired candidates / total number of candidates.
Employee Turnover Rate
What does the term “employee turnover rate” mean? It is the
number of employees who leave a company in a specific time
frame. This number considers all employees who were terminated
for any reason. To determine the employee turnover rate, one
needs three pieces of information: (1) the number of current
employees the company has at the beginning of the selected time
frame; (2) the number of employees the company has at the end of
the selected time frame; and (3) the number of employees who left
during the selected time frame.
Add the number of employees at the beginning of the period to the
number at the end. Divide by two to find the average number of
employees, then divide the number of employees separated during
the period by the average number of employees to find the
employee turnover rate.
Key Components in the Selection Process
According to Armstrong and Taylor (2020), the nine key
components in the hiring process are:
Defining requirements
Attracting candidates
Sourcing candidates
Selection methods
2/6/24, 9:56 PM Case – HRM401 Staffing Organizations (2024JAN08FT-1)
Selection interviews
Selection testing
Making the decision
Obtaining and checking references
Offering employment
Armstrong, M., & Taylor, S. (2020). Chapter 28: Recruitment &
selection. In Armstrong’s handbook of human resource
management practice (15th ed.). Kogan Page. Available in the
Trident Online Library, Skillsoft database.
Case Assignment
You are the HR Manager for your curent employer (or past
employer if you are not employed). This morning your receptionist
turned in his two-weeks’ notice, giving you just 14 days within which
to hire his replacement.
Keeping this scenario in mind, address the following questions in a
4- to 5-page essay submission:
Use the following details to provide a quantitative analysis of the
assignment questions.
Job published on Monster.com on October 23rd
Date approached job applicant to schedule interview: October
Job offer accepted: November 4th
Historically, you know that your time to hire in the past was 23 days,
well above the 14 days you have now, so you are concerned about
being short-staffed and overworking your employees. Based upon
the above three HR metrics information, you need to compute just
one of the top three HR metrics for job openings: time to fill. You will
then use that datum to think critically about the following questions:
2/6/24, 9:56 PM Case – HRM401 Staffing Organizations (2024JAN08FT-1)
What and who do you need to consider once you receive a two-
weeks’ notice?
Analyze the impact this employee’s resignation can have on your
organization. Who is impacted by the resignation of a
What is the time to fill for this vacated position? Discuss how this
metric can affect your organization’s current employees.
Knowing the average historical time to hire timeline for the hotel
is 23 days, how does that affect your decision for the steps in the
hiring process used to fill this position? Must you go through them
all, or just certain ones? What could happen if you did not go
through all the steps?
Of all the HR metrics you learned about in this module, which one
metric is the most important for you in your job as the HR
manager? Explain your rationale for selecting this HR metric.
The deliverable for this assignment is a 4- to 5-page essay
complete with cover page, reference list page, subheadings for
each question (topic), and formatted according to the 7th edition of
the APA Manual. When an assignment asks for 4-5 pages, the
document cannot be less than four full pages. The page count does
not include the cover page or reference list page.
Support your research with three high-quality peer-reviewed
academic references found in the Trident Online Library.
Submit the paper through the appropriate Dropbox by the due date.
Your submission will be graded with the Signature Assignment’s
grading rubric. Become familiar with the grading rubric for this
Signature Assignment before submitting your paper for review.
Citation and reference style instructions are available
See the Trident guide to APA Style, 7th edition.
You will find the following useful as you critique sources:
2/6/24, 9:56 PM Case – HRM401 Staffing Organizations (2024JAN08FT-1)
Herring, J. E. (2011). Chapter 3: Evaluating websites, Figure 3.1, p.
38. In Improving students’ web use and information literacy: a guide
for teachers and teacher librarians. Facet Publishing. Available in
the Trident Online Library, EBSCO eBook Collection.
Lack, C. W., & Rousseau, J. (2016). Chapter 4: What is critical
thinking? In Critical thinking, science, and pseudoscience: Why we
can’t trust our brains. Springer Publishing Company. Available in
the Trident Online Library, EBSCO eBook Collection.
What is Quantitative Reasoning?
Quantitative reasoning (QR) is assumed to be synonymous with
mathematics, and, indeed, the two are inextricably linked. While
mathematics is primarily a discipline, QR is a skill, one with
practical applications. A mathematician might take joy in
abstraction, but the well-educated citizen can apply QR skills to
daily contexts: for instance, understanding the power of compound
interest or the uses and abuses of percentages; using fundamental
statistical analysis to gauge the accuracy of a statistical study; or
applying the principles of logic and rhetoric to real-world arguments.
Many students do not learn sophisticated math skills, but all should
be able to use simple math tools to reason – to understand,
interpret, critique, debunk, challenge, explicate, and draw
According to the Mathematical Association of America (MAA)3, the
following quantitative literacy (or QR) requirements should be
established for all students who receive a bachelor’s degree:
Interpret mathematical models such as formulas, graphs, table,
and schematics, and draw inferences from them.
Represent mathematical information symbolically, visually,
numerically, and verbally.
2/6/24, 9:56 PM Case – HRM401 Staffing Organizations (2024JAN08FT-1)
Privacy Policy | Contact
Use arithmetical, algebraic, geometric, and statistical methods to
solve problems.
Estimate and check answers to mathematical problems in order
to determine reasonableness, identify alternatives, and select
optimal results.
Recognize that mathematical and statistical methods have limits.
Assignment Expectations
Your submission for this Signature Assignment will be assessed on
the criteria found in the grading rubric for this assignment to assess
Quantitative Reasoning at the Introduced Level.
Critical Thinking: Expressing quantitative analysis of data
(factual information) to support the discussion showing what
evidence is used and how it is contextualized.
Interpretation: Explaining information presented in mathematical
terms (e.g., equations, graphs, diagrams, tables, words).
Presentation: Ability to convert relevant information into various
mathematical terms (e.g., equations, graphs, diagrams, tables,
Conclusions: Drawing appropriate conclusions based on the
analysis of factual information/data.
Timeliness: Assignment submitted on or before the due date.
Sources used to develop this section:
Armstrong, M., & Tayler, S. (2020). Chapter 28: Recruitment & selection. In Armstrong’s handbook of human resource
management practice (15th ed.). Kogan Page. Available in the Trident Online Library, Skillsoft database.
Gusdorf, M. L. (2008). Recruitment and selection: hiring the right person. Society of Human Resource Management.
Henderson, L. (2018). Catch (& keep) a rising star. Applied Clinical Trials, 27(3), 12-14. Available in the Trident Online Library. | {"url":"https://essaystudyhelp.com/2-6-24-956-pm-case-hrm401-staffing-organizations-2024jan08ft-1-1-7module-3-caseemployee-selectionassignment-overviewsignature-assignment/","timestamp":"2024-11-07T18:48:37Z","content_type":"text/html","content_length":"126042","record_id":"<urn:uuid:4fb9ac20-eb3d-4a93-baca-cba498216ae6>","cc-path":"CC-MAIN-2024-46/segments/1730477028009.81/warc/CC-MAIN-20241107181317-20241107211317-00672.warc.gz"} |
Algebraic Topology - Wikibooks, open books for an open world
Algebraic topology is study of topological spaces, usually via the tools of abstract algebra, such as groups, rings and fields. As with many fields of mathematics, the goal is to classify the objects
of interest up to some equivalence relation, in this case we wish to classify topological spaces up to homeomorphism (although we will find that the best we can often do is homotopic equivalence). | {"url":"https://en.m.wikibooks.org/wiki/Algebraic_Topology","timestamp":"2024-11-10T16:20:33Z","content_type":"text/html","content_length":"22344","record_id":"<urn:uuid:4aedd28d-abaf-4f3e-9d47-db62d2ab9003>","cc-path":"CC-MAIN-2024-46/segments/1730477028187.60/warc/CC-MAIN-20241110134821-20241110164821-00474.warc.gz"} |
Gravitational wave surrogate model for spinning, intermediate mass ratio binaries based on perturbation theory and numerical relativity
We present BHPTNRSur2dq1e3, a reduced order surrogate model of gravitational waves emitted from binary black hole (BBH) systems in the comparable to large mass ratio regime with aligned spin (\chi_1)
on the heavier mass (m_1). We trained this model on waveform data generated from point particle black hole perturbation theory... Show more | {"url":"https://synthical.com/article/Gravitational-wave-surrogate-model-for-spinning%2C-intermediate-mass-ratio-binaries-based-on-perturbation-theory-and-numerical-relativity-e55a0617-2d93-47a4-9786-5c237c7a01f8","timestamp":"2024-11-13T04:41:12Z","content_type":"text/html","content_length":"81695","record_id":"<urn:uuid:e1e645b6-1488-4afa-9857-f5e77f46af0b>","cc-path":"CC-MAIN-2024-46/segments/1730477028326.66/warc/CC-MAIN-20241113040054-20241113070054-00214.warc.gz"} |
American Mathematical Society
The paper presents a practical method for factoring an arbitrary N by representing N or $\lambda N$ by one of at most three quadratic forms: $\lambda N = {x^2} - D{y^2},\lambda = 1, - 1,2,D = - 1, \
pm 2, \pm 3, \pm 6$. These three forms appropriate to N, together with inequalities for y, are given for all N prime to 6. Presently available sieving facilities make the method quite effective and
economical for numbers N having 20 to 25 digits. Four examples arising from aliquot series are discussed in detail. References
• Michael A. Morrison and John Brillhart, The factorization of $F_{7}$, Bull. Amer. Math. Soc. 77 (1971), 264. MR 268113, DOI 10.1090/S0002-9904-1971-12711-8 P. L. Chebyshev, "Sur les formes
quadratiques," J. Math. (1), v. 16, 1851, pp. 257-282. L. E. Dickson, History of the Theory of Numbers. Vol. 1, Washington, 1919, Chap. 14.
• Richard K. Guy and J. L. Selfridge, Interim report on aliquot series, Proceedings of the Manitoba Conference on Numerical Mathematics (Univ. Manitoba, Winnipeg, Man., 1971) Dept. Comput. Sci.,
Univ. Manitoba, Winnipeg, Man., 1971, pp.ย 557โ 580. MR 0335412 D. H. Lehmer, "An announcement concerning the Delay Line Sieve DLS127," Math. Comp., v. 20, 1966, pp. 645-646.
• D. H. Lehmer, The sieve problem for all-purpose computers, Math. Tables Aids Comput. 7 (1953), 6โ 14. MR 52876, DOI 10.1090/S0025-5718-1953-0052876-7
• D. H. Lehmer, Computer technology applied to the theory of numbers, Studies in Number Theory, Math. Assoc. America, Buffalo, N.Y.; distributed by Prentice-Hall, Englewood Cliffs, N.J., 1969,
pp.ย 117โ 151. MR 0246815
• G. B. Mathews, Theory of numbers, Chelsea Publishing Co., New York, 1961. 2nd ed. MR 0126402
• Daniel Shanks, Class number, a theory of factorization, and genera, 1969 Number Theory Institute (Proc. Sympos. Pure Math., Vol. XX, State Univ. New York, Stony Brook, N.Y., 1969) Amer. Math.
Soc., Providence, R.I., 1971, pp.ย 415โ 440. MR 0316385 J. A. Todd, "A combinatorial problem," J. Mathematical Phys., v. 11, 1932, pp. 321-333.
• Emma Lehmer, On the quartic character of quadratic units, J. Reine Angew. Math. 268(269) (1974), 294โ 301. MR 345933, DOI 10.1515/crll.1974.268-269.294
Additional Information
• © Copyright 1974 American Mathematical Society
• Journal: Math. Comp. 28 (1974), 625-635
• MSC: Primary 10A25; Secondary 10-04, 10B05
• DOI: https://doi.org/10.1090/S0025-5718-1974-0342458-5
• MathSciNet review: 0342458 | {"url":"https://www.ams.org/journals/mcom/1974-28-126/S0025-5718-1974-0342458-5/?active=current","timestamp":"2024-11-11T00:49:04Z","content_type":"text/html","content_length":"59661","record_id":"<urn:uuid:9c9bd0ab-8127-40b6-8500-fd793519f6c5>","cc-path":"CC-MAIN-2024-46/segments/1730477028202.29/warc/CC-MAIN-20241110233206-20241111023206-00483.warc.gz"} |
boiler performance | MakArticles.com
boiler performance
boiler performance:
The performance parameters of boiler, like efficiency and evaporation ratio reduces with time due to poor combustion, heat transfer surface fouling and poor operation and maintenance. Even for a new
boiler, reasons such as deteriorating fuel quality, water quality etc. can result in poor boiler performance. Boiler efficiency tests help us to find out the deviation of boiler efficiency from the
best efficiency and target problem area for corrective action.
Boiler Efficiency:
Thermal efficiency of boiler is defined as the percentage of heat input that is effectively utilized to generate steam. There are two methods of assessing boiler efficiency.
1. a)The Direct Method: Where the energy gain of the working fluid (water and steam) is compared with the energy content of the boiler fuel.
2. b)The Indirect Method: Where the efficiency is the difference between the losses and the energy input.
1. a)Direct Method
This is also known as ‘input-output method’ due to the fact that it needs only the useful output (steam) and the heat input (i.e. fuel) for evaluating the efficiency. This efficiency can be evaluated
using the formula
Boiler Efficiency = (Heat Output/Heat Input) * 100
Parameters to be monitored for the calculation of boiler efficiency by direct method are :
• Quantity of steam generated per hour (Q) in kg/hr.
• Quantity of fuel used per hour (q) in kg/hr.
• The working gauge pressure (in kg/cm^2) and superheat temperature (°C), if any
• The temperature of feed water (°C)
• Type of fuel and gross calorific value of the fuel (GCV) in kCal/kg of fuel
Boiler efficiency = Q x (hg-hf) ×100 /(q×GCV)
hg – Enthalpy of saturated steam in kCal/kg of steam
hf – Enthalpy of feed water in kCal/kg of water
It should be noted that boiler may not generate 100% saturated dry steam, and there may be some amount of wetness in the steam.
Advantages of Direct Method:
• Plant people can evaluate quickly the efficiency of boilers
• Requires few parameters for computation
• Needs few instruments for monitoring
Disadvantages of Direct Method:
• Does not give clues to the operator as to why efficiency of system is lower
• Does not calculate various losses accountable for various efficiency levels
1. b)Indirect Method:
There are reference standards for Boiler Testing at Site using indirect method namely British Standard, BS 845: 1987 and USA Standard is ASME PTC-4-1 Power Test Code Steam Generating Units’. Indirect
method is also called as ‘’heat loss method’’. The efficiency can be arrived at, by subtracting the heat loss fractions from 100. The standards do not include blow down loss in the efficiency
determination process. A brief procedure for calculating boiler efficiency by indirect method is given below.
The principle losses that occur in a boiler are:
1. Loss of heat due to dry flue gas
2. Loss of heat due to moisture in fuel and combustion air
3. Loss of heat due to combustion of hydrogen
4. Loss of heat due to radiation
5. Loss of heat due to unburnt
In the above, loss due to moisture in fuel and the loss due to combustion of hydrogen are dependent on the fuel, and cannot be controlled by design. The data required for calculation of boiler
efficiency using indirect method are:
• Ultimate analysis of fuel (H2, O2, S, C, moisture content, ash content)
• Percentage of Oxygen or CO[2]in the flue gas
• Flue gas temperature in °C (Tf)
• Ambient temperature in °C (Ta) & humidity of air in kg/kg of dry air
• GCV of fuel in kCal/kg
• Percentage combustible in ash (in case of solid fuels)
• GCV of ash in kCal/kg (in case of solid fuels)
With the help of these parameters the boiler engineers find the losses using standard approaches as specified by ASME and other boiler OEMs. Finally losses can be subtracted from the heat added and
hence efficiency can be found.
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Seven Group Holdings Limited (ASX:SVW), Industrial Logistics Properties Trust (NasdaqGS:ILPT): A Look at These Stock’s F-Scores
Seven Group Holdings Limited (ASX:SVW) has a Piotroski F-Score of 6 at the time of writing. The F-Score may help discover companies with strengthening balance sheets. The score may also be used to
spot the weak performers.
Joseph Piotroski developed the F-Score which employs nine different variables based on the company financial statement. A single point is assigned to each test that a stock passes. Typically, a stock
scoring an 8 or 9 would be seen as strong. On the other end, a stock with a score from 0-2 would be viewed as weak.
Smart investors are often very knowledgeable about the markets. Many successful investors have become highly adept at knowing when to buy and when to sell. They have also managed to control risk and
secure sustained profits. This doesn’t just happen overnight. Investors often spend many years of trial and error before being able to put together the puzzle. Top investors are also able to make
better investing decisions with the information at hand. With vast amounts of data readily available for everyone, it becomes more about interpreting the data rather than just receiving it. Knowing
how to block out the noise and find information that is useful, can be a highly coveted skill. Turning available information into a winning portfolio is where the good investor can become a great
SMA 50/200
Ever wonder how investors predict positive share price momentum? The Cross SMA 50/200, also known as the “Golden Cross” is the fifty day moving average divided by the two hundred day moving average.
The SMA 50/200 for Seven Group Holdings Limited (ASX:SVW) is currently 1.00907. If the Golden Cross is greater than 1, then the 50 day moving average is above the 200 day moving average – indicating
a positive share price momentum. If the Golden Cross is less than 1, then the 50 day moving average is below the 200 day moving average, indicating that the price might drop.
The price to book ratio or market to book ratio for Seven Group Holdings Limited (ASX:SVW) currently stands at 2.162879. The ratio is calculated by dividing the stock price per share by the book
value per share. This ratio is used to determine how the market values the equity. A ratio of under 1 typically indicates that the shares are undervalued. A ratio over 1 indicates that the market
is willing to pay more for the shares. There are often many underlying factors that come into play with the Price to Book ratio so all additional metrics should be considered as well.
The C-Score is a system developed by James Montier that helps determine whether a company is involved in falsifying their financial statements. The C-Score is calculated by a variety of items,
including a growing difference in net income verse cash flow, increasing days outstanding, growing days sales of inventory, increasing assets to sales, declines in depreciation, and high total asset
growth. The C-Score of Seven Group Holdings Limited (ASX:SVW) is 0.00000. The score ranges on a scale of -1 to 6. If the score is -1, then there is not enough information to determine the C-Score.
If the number is at zero (0) then there is no evidence of fraudulent book cooking, whereas a number of 6 indicates a high likelihood of fraudulent activity. The C-Score assists investors in
assessing the likelihood of a company cheating in the books.
Turning to Free Cash Flow Growth (FCF Growth), this is the free cash flow of the current year minus the free cash flow from the previous year, divided by last year’s free cash flow. The FCF Growth
of Seven Group Holdings Limited (ASX:SVW) is -0.224134. Free cash flow (FCF) is the cash produced by the company minus capital expenditure. This cash is what a company uses to meet its financial
obligations, such as making payments on debt or to pay out dividends. The Free Cash Flow Score (FCF Score) is a helpful tool in calculating the free cash flow growth with free cash flow stability –
this gives investors the overall quality of the free cash flow.
Stock volatility is a percentage that indicates whether a stock is a desirable purchase. Investors look at the Volatility 12m to determine if a company has a low volatility percentage or not over
the course of a year. The Volatility 12m of Seven Group Holdings Limited (ASX:SVW) is 37.623200. This is calculated by taking weekly log normal returns and standard deviation of the share price
over one year annualized.
The lower the number, a company is thought to have low volatility. The Volatility 3m is a similar percentage determined by the daily log normal returns and standard deviation of the share price over
3 months. The Volatility 3m of Seven Group Holdings Limited (ASX:SVW) is 36.328200. The Volatility 6m is the same, except measured over the course of six months. The Volatility 6m is 43.032300.
MF Rank
The MF Rank (aka the Magic Formula) is a formula that pinpoints a valuable company trading at a good price. The formula is calculated by looking at companies that have a high earnings yield as well
as a high return on invested capital. The MF Rank of Seven Group Holdings Limited (ASX:SVW) is 5447. A company with a low rank is considered a good company to invest in. The Magic Formula was
introduced in a book written by Joel Greenblatt, entitled, “The Little Book that Beats the Market”.
The Q.i. Value of Seven Group Holdings Limited (ASX:SVW) is 28.00000. The Q.i. Value is a helpful tool in determining if a company is undervalued or not. The Q.i. Value is calculated using the
following ratios: EBITDA Yield, Earnings Yield, FCF Yield, and Liquidity. The lower the Q.i. value, the more undervalued the company is thought to be.
Value Composite
The Value Composite One (VC1) is a method that investors use to determine a company’s value. The VC1 of Seven Group Holdings Limited (ASX:SVW) is 40. A company with a value of 0 is thought to be an
undervalued company, while a company with a value of 100 is considered an overvalued company. The VC1 is calculated using the price to book value, price to sales, EBITDA to EV, price to cash flow,
and price to earnings. Similarly, the Value Composite Two (VC2) is calculated with the same ratios, but adds the Shareholder Yield. The Value Composite Two of Seven Group Holdings Limited (ASX:SVW)
is 50.
ERP5 Rank
The ERP5 Rank is an investment tool that analysts use to discover undervalued companies. The ERP5 looks at the Price to Book ratio, Earnings Yield, ROIC and 5 year average ROIC. The ERP5 of Seven
Group Holdings Limited (ASX:SVW) is 7572. The lower the ERP5 rank, the more undervalued a company is thought to be.
Investors might be taking a closer look at the portfolio after recent market action. Some financial insiders may be ready to usher in the bears and projecting the end of the bull run. While this may
or may not be the case, investors need to be ready for any scenario. The time may have come to cash out some winners and cut the losers. A portfolio rebalance may be necessary in order to secure
profits as we head into the latter half of the year. Keeping a diversified portfolio may entail adding some different sectors and even venturing into foreign markets. Investors will be tracking
company earnings as we roll into the next round of reports. It may be a bit easier to make sense of future stock market prospects after seeing how many companies hit or miss their marks.
The Piotroski F-Score of Industrial Logistics Properties Trust (NasdaqGS:ILPT) is 5. The Piotroski F-Score is a scoring system between 1-9 that determines a firm’s financial strength. The score
helps determine if a company’s stock is valuable or not. A score of nine indicates a high value stock, while a score of one indicates a low value stock. The score is calculated by the return on
assets (ROA), Cash flow return on assets (CFROA), change in return of assets, and quality of earnings. It is also calculated by a change in gearing or leverage, liquidity, and change in shares in
issue. The score is also determined by change in gross margin and change in asset turnover.
Tackling the stock market may involve many different aspects. Investors may at times feel like they are on a wild ride. Sometimes there are extreme highs, and sometimes there are extreme lows.
Figuring out how to best deal with fluctuations can help the investor’s mindset. Investors who are able to keep their emotions in check might be one step ahead of the rest. Being able to identify
emotional weaknesses can help the investor avoid tricky situations when things get hairy. Keeping the stock portfolio on the profitable side may involve making decisions that require emotional
detachment. When emotions are running high, it may impair the rational decision making capability of the investor.
Current Ratio
The Current Ratio of Industrial Logistics Properties Trust (NasdaqGS:ILPT) is 5.64. The Current Ratio is used by investors to determine whether a company can pay short term and long term debts. The
current ratio looks at all the liquid and non-liquid assets compared to the company’s total current liabilities. A high current ratio indicates that the company might have trouble managing their
working capital. A low current ratio (when the current liabilities are higher than the current assets) indicates that the company may have trouble paying their short term obligations.
The Return on Invested Capital (aka ROIC) for Industrial Logistics Properties Trust (NasdaqGS:ILPT) is 0.060162. The Return on Invested Capital is a ratio that determines whether a company is
profitable or not. It tells investors how well a company is turning their capital into profits. The ROIC is calculated by dividing the net operating profit (or EBIT) by the employed capital. The
employed capital is calculated by subrating current liabilities from total assets. Similarly, the Return on Invested Capital Quality ratio is a tool in evaluating the quality of a company’s ROIC
over the course of five years. The ROIC Quality of Industrial Logistics Properties Trust (NasdaqGS:ILPT) is . This is calculated by dividing the five year average ROIC by the Standard Deviation of
the 5 year ROIC. The ROIC 5 year average is calculated using the five year average EBIT, five year average (net working capital and net fixed assets). The ROIC 5 year average of Industrial
Logistics Properties Trust (NasdaqGS:ILPT) is .
The Gross Margin Score is calculated by looking at the Gross Margin and the overall stability of the company over the course of 8 years. The score is a number between one and one hundred (1 being
best and 100 being the worst). The Gross Margin Score of Industrial Logistics Properties Trust (NasdaqGS:ILPT) is 50.00000. The more stable the company, the lower the score. If a company is less
stable over the course of time, they will have a higher score.
MF Rank
The MF Rank (aka the Magic Formula) is a formula that pinpoints a valuable company trading at a good price. The formula is calculated by looking at companies that have a high earnings yield as well
as a high return on invested capital. The MF Rank of Industrial Logistics Properties Trust (NasdaqGS:ILPT) is 8295. A company with a low rank is considered a good company to invest in. The Magic
Formula was introduced in a book written by Joel Greenblatt, entitled, “The Little Book that Beats the Market”.
The Q.i. Value of Industrial Logistics Properties Trust (NasdaqGS:ILPT) is 34.00000. The Q.i. Value is a helpful tool in determining if a company is undervalued or not. The Q.i. Value is calculated
using the following ratios: EBITDA Yield, Earnings Yield, FCF Yield, and Liquidity. The lower the Q.i. value, the more undervalued the company is thought to be.
Turning to Free Cash Flow Growth (FCF Growth), this is the free cash flow of the current year minus the free cash flow from the previous year, divided by last year’s free cash flow. The FCF Growth
of Industrial Logistics Properties Trust (NasdaqGS:ILPT) is . Free cash flow (FCF) is the cash produced by the company minus capital expenditure. This cash is what a company uses to meet its
financial obligations, such as making payments on debt or to pay out dividends. The Free Cash Flow Score (FCF Score) is a helpful tool in calculating the free cash flow growth with free cash flow
stability – this gives investors the overall quality of the free cash flow.
Value Composite
The Value Composite One (VC1) is a method that investors use to determine a company’s value. The VC1 of Industrial Logistics Properties Trust (NasdaqGS:ILPT) is 41. A company with a value of 0 is
thought to be an undervalued company, while a company with a value of 100 is considered an overvalued company.
The VC1 is calculated using the price to book value, price to sales, EBITDA to EV, price to cash flow, and price to earnings. Similarly, the Value Composite Two (VC2) is calculated with the same
ratios, but adds the Shareholder Yield. The Value Composite Two of Industrial Logistics Properties Trust (NasdaqGS:ILPT) is 32.
Stock volatility is a percentage that indicates whether a stock is a desirable purchase. Investors look at the Volatility 12m to determine if a company has a low volatility percentage or not over
the course of a year. The Volatility 12m of Industrial Logistics Properties Trust (NasdaqGS:ILPT) is 21.342700. This is calculated by taking weekly log normal returns and standard deviation of the
share price over one year annualized.
The lower the number, a company is thought to have low volatility. The Volatility 3m is a similar percentage determined by the daily log normal returns and standard deviation of the share price over
3 months. The Volatility 3m of Industrial Logistics Properties Trust (NasdaqGS:ILPT) is 23.698100. The Volatility 6m is the same, except measured over the course of six months. The Volatility 6m
is 25.665000.
ERP5 Rank
The ERP5 Rank is an investment tool that analysts use to discover undervalued companies. The ERP5 looks at the Price to Book ratio, Earnings Yield, ROIC and 5 year average ROIC. The ERP5 of
Industrial Logistics Properties Trust (NasdaqGS:ILPT) is 18990. The lower the ERP5 rank, the more undervalued a company is thought to be.
Investors are constantly on the lookout for that next great stock pick. Finding that particular stock that had been overlooked by the rest of the investing community can bring great satisfaction to
the individual investor. Spotting these stocks may take a lot of time and effort, but the rewards may be well worth it. Knowledge is power, and this principle also translates over to the equity
market. Investors who are able to dig a little bit deeper may be setting themselves up for much greater success in the long run. These days, investors have access to a wide range of information.
Trying to filter out the important information can be a key factor in portfolio strength. Knowing what data to look for and how to trade that information is extremely important. Successful investors
are typically able to focus their energy on the right information and then apply it to a trading strategy. | {"url":"https://hermannherald.com/index.php/2019/04/22/seven-group-holdings-limited-asxsvw-industrial-logistics-properties-trust-nasdaqgsilpt-a-look-at-these-stocks-f-scores/","timestamp":"2024-11-09T00:42:33Z","content_type":"text/html","content_length":"60099","record_id":"<urn:uuid:b90884bc-e0dc-4708-9cbf-bf7e602f9aed>","cc-path":"CC-MAIN-2024-46/segments/1730477028106.80/warc/CC-MAIN-20241108231327-20241109021327-00366.warc.gz"} |
A Swedish watch company is assigning ID cards for its employees. The ID is made
A Swedish watch company is assigning ID cards for its employees. The ID is made of 7 digits. How many ID numbers can exist such that at least one of the digits repeat?
Answer: Option C
Total number of combinations = No repeats + 1 number repeat + 2 number repeat +.....7 number repeat
Total number of combinations - No repeats = 1 number repeat + 2 number repeat +...... 7 number repeat
Total number of combinations - No repeats = Atleast one number repeat
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Rational Numbers Class 7 - NCERT Solutions, MCQ [with Videos]
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Get solutions of all NCERT Questions, and also understand the concepts of Chapter 8 Class 7 Rational Numbers free at teachoo. All NCERT exercise questions and examples are solved.
In concept wise, we have first divided the chapter into concepts. When you click on a concept, first the concept is explained, and then its related questions are solved from easy to difficult.
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What is Negative Binomial Regression
Negative Binomial Regression: A powerful tool for analyzing overdispersed count data in various fields.
Negative Binomial Regression (NBR) is a statistical method used to model count data that exhibits overdispersion, meaning the variance is greater than the mean. This technique is particularly useful
in fields such as biology, ecology, economics, and healthcare, where count data is common and often overdispersed.
NBR is an extension of Poisson regression, which is used for modeling count data with equal mean and variance. However, Poisson regression is not suitable for overdispersed data, leading to the
development of NBR as a more flexible alternative. NBR models the relationship between a dependent variable (count data) and one or more independent variables (predictors) while accounting for
Recent research in NBR has focused on improving its performance and applicability. For example, one study introduced a k-Inflated Negative Binomial mixture model, which provides more accurate and
fair rate premiums in insurance applications. Another study demonstrated the consistency of ℓ1 penalized NBR, which produces more concise and accurate models compared to classical NBR.
In addition to these advancements, researchers have developed efficient algorithms for Bayesian variable selection in NBR, enabling more effective analysis of large datasets with numerous covariates.
Furthermore, new methods for model-aware quantile regression in discrete data, such as Poisson, Binomial, and Negative Binomial distributions, have been proposed to enable proper quantile inference
while retaining model interpretation.
Practical applications of NBR can be found in various domains. In healthcare, NBR has been used to analyze German health care demand data, leading to more accurate and concise models. In
transportation planning, NBR models have been employed to estimate mixed-mode urban trail traffic, providing valuable insights for urban transportation system management. In insurance, the k-Inflated
Negative Binomial mixture model has been applied to design optimal rate-making systems, resulting in more fair premiums for policyholders.
One company leveraging NBR is a healthcare organization that used the method to analyze hospitalization data, leading to better understanding of disease patterns and improved resource allocation.
This case study highlights the potential of NBR to provide valuable insights and inform decision-making in various industries.
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‘How maths can help Nigeria’s tech development' - The Nation Newspaper
April 5, 2018 by The Nation
‘How maths can help Nigeria’s tech development’
Nations, which have technological and scientific development, have realised the importance of mathematics to science and technology.
Unfortunately, this is not the case in Nigeria, which breeds quacks and ill -motivated teachers with its attendant poor motivation, funding and somersaulting curricular.
This is the stance of Samuel Iyase, a professor of Mathematics, Covenant University (CU), Ota, who believes, if Nigeria must join the league of advanced nations, the solution is to reverse the
aforementioned scenario.
Iyase, who delivered the institution’s 14th inaugural with the theme: ‘Mathematics: A platform for leapfrogging into scientific and technological advancement.’ said: “Teachers of mathematics are both
under-qualified and poorly reformed. Mathematics curricula reform is often inspired by corrupted corresponding western models. Examinations determine the worth of mathematical knowledge. Memorisation
and rote learning is mostly the determinant form of teaching and the subject’s links to science and technology and relevance to student’s everyday experience is hardly emphasised,” said Iyase, who
teaches at CU’s Department of Mathematics.
“The bachelor’s degree programmes in mathematics are unpopular among students. The undergraduate mathematics curricular of many departments’ of mathematics emphasise traditional areas of the subject.
The demand for graduate education in mathematics is limited. It is obvious that the number of PhD holders is grossly inadequate,” he added while identifying the challenges of the subject.’’
Iyase likened mathematics as a catalyst for reducing the scientific and technological gap between developed and developing nations like Nigeria.
Other challenges, according to him, include inadequate staff, relative isolation of mathematicians in Nigeria, brain drain, negative image of the subject, and weak mathematics education.
Nigeria, Iyase advised, could ape the Asian Tigers, particularly Singapore, which was just five years younger than Nigeria (Singapore gained independence in 1965) colonised by Britain, which also
colonised Nigeria, but is miles ahead technologically because of her huge investments in mathematics and other science-oriented subjects.
“In a typical Singaporean’s classroom, the focus is not the one right answer but rather the goal is to help students understand how to solve mathematical problems. The teachers make use extensive use
of visual aids to help students understand mathematics. Teachers cover less materials than many countries but rather cover indepth. The level of mathematics in the primary school laving examination
is approximately two years ahead of that in most schools in the United States. At the primary and secondary level, extra curriculum activities, such as mathematics and science fairs, are designed to
generate interest among students.”
Iyase lamented that the leadership is yet to strike a link between education and educational development, saying its realisation would result into priortising education and production of high quality
mathematics and science professionals.
‘’The popularisation of mathematics should be a priority. An important element that has led to the unpopularity of mathematics is the lack of career guidance in our secondary schools and even in
universities.. Career guidance will help students to know the wide range of career opportunities available to mathematicians. Students leaving secondary school and heading to tertiary institutions
are in most cases biased against mathematics.”
While craving more funding for Mathematics reasearch, Iyase emphasised the need to form a think-tank comprising professionals in mathematics to come up with modalities on the application of
indigenous knowledge to mathematics and use of mathematical tools in solving problems across government, business and industry.
Earlier, CU Vice-Chancellor Prof. Aaron Atayero, who was represented by his deputy, Prof. Shalom Chinedu, said the inaugural lecture was timely in view of the foot-dragging posture of governments to
mathematics and technology education. | {"url":"https://thenationonlineng.net/maths-can-help-nigerias-tech-development-2/?utm_source=auto-read-also&utm_medium=web","timestamp":"2024-11-03T23:04:57Z","content_type":"text/html","content_length":"284685","record_id":"<urn:uuid:26d7292f-1f85-4b11-a64b-7c68431472aa>","cc-path":"CC-MAIN-2024-46/segments/1730477027796.35/warc/CC-MAIN-20241103212031-20241104002031-00877.warc.gz"} |
How to Use Modulo or Remainder Operator in Java
Modulo is one of the most popularly used arithmetic operators that is used to find the remainder of two values. It is also referred to as the “remainder” or the “modulus” operator and is denoted by
the “%” symbol in Java. The return type of the modulo operator depends on the input type of the given operands. For instance, if both operands are integers then the remainder will also be an integer,
if one of them or both are double then the remainder will also be double.
Quick Outline
What is a Modulo Operator and How Does it Work in Java?
The modulo operator performs division on the given values and retrieves the remainder as an output. In Java, it is denoted with a percent sign “%”, as demonstrated in the following syntax:
Graphical Representation of Modulo Operator:
There are numerous use cases of the modulo operator. Some of them are discussed below along with practical examples:
Case 1: Use the Modulo Operator to Find the Remainder of Two Integers
Declare and initialize a couple of integer-type variables in the main() method:
int dividend = 73;
int divisor = 6;
Use the modulo operator “%” on the given values and store the result in a new variable named “modulo”:
int modulo = dividend%divisor;
Print the computed result on the console:
System.out.println(dividend + "%" + divisor + " is equal to: "+ modulo);
Complete Code & Output
Case 2: Use the Modulo Operator to Find the Remainder of Two Double Values
Declare and initialize two double-type variables: “dividend” and “divisor”:
double dividend = 73.52;
double divisor = 6.73;
Use the modulo operator “%” on the provided values, store the result in a new variable named “modulo”, and print it on the console:
double modulo = dividend%divisor;
System.out.println(dividend + "%" + divisor + " = "+ modulo);
Complete Code & Output
Case 3: Use Modulo Operator to Check If a Number is Divisible By 3
The following example takes a number from the user and checks if it is divisible by 3. For this, first, import the Scanner class:
import java.util.Scanner;
Create a Scanner object and use it with nextInt() to get an integer value from the user:
Scanner scannerObj = new Scanner(System.in);
System.out.println("Please Enter a Number");
int input = scannerObj.nextInt();
Use the modulus operator to find the remainder of the user-entered number for 3:
Now use the if-else statement to check if the user-entered number is divisible by 3:
if (modulo == 0)
System.out.println("Input Number is Divisible by 3");
System.out.println("Input Number is Not Divisible by 3");
Complete Code & Output
Case 4: Use Modulo Operator To Check if User-entered Value is a Prime Number
The first two steps are the same as the previous example, i.e., import the Scanner class and take user input. After this, create an integer-type variable and assign it a value of 0:
Now use a for loop and iterate it up to “input / 2”. Within for loop use the if statement to check if the user-entered value is divisible by any number. If it is divisible by any number, then break
the loop:
for (int i = 2; i <= input/2; i++)
if (input % i == 0)
A number (>1) that is divisible by “itself” and “1” is said to be a prime number. Specify this condition in the if-else statement to check if the given value is a “prime number”:
if (flag == 0 && input != 1)
{ System.out.println(input + " is a Prime number");
System.out.println(input + " is Not a Prime number");
Complete Code & Output:
Case 5: Use Modulo Operator To Find Total Occurrences of Even and Odd Numbers in an Array
First, create an array of different integers, and use the “length” property on it to find its size:
int[] input = {2, 1, 3, 5, 6, 98, 91, 121, 0, 3};
int arrSize = input.length;
Declare and Initialize a couple of integer-type variables with a value of 0:
int evenCount =0, oddCount = 0;
Use the for loop to iterate over the given array and find the number of even and odd numbers. Within the for loop, use an if-else statement with the modulo operator to find the even and odd numbers
in the array:
for (int i=0; i< arrSize; i++)
if (input[i]%2 == 0)
oddCount++; }
Finally, use the “System.out.println()” method to display the number of even and odd values:
System.out.println("Total Even Numbers in the Given Array: " + evenCount);
System.out.println("Total Odd Numbers in the Given Array: " + oddCount);
Complete Code & Output:
Case 6: Use Modulo Operator on a Circular Array
The most frequent use case of the modulo operator is in circular arrays. A circular array is an array whose elements are connected with each other circularly. It is such that the first element is
connected to a second element, a second element is connected to a third element, and so on until the last element is connected to the first element.
For instance, declare and initialize a simple string-type array:
String [] circularArray = { "j", "a", "v", "a", "b", "e", "a", "t"};
Now, iterate over the array using a for loop to print its elements:
for (int i = 4; i <= 11; i++) {
The loop starts its iteration from index 4 and is expected to go on till index 11:
The last index of the given array is “7”. Therefore, Java throws an “IndexOutofBounds” exception when we try to access an element at the index 8 or above. To fix this exception, use the modulo
operator as follows:
circularArray[arrayIndex % arraySize];
Use the length property to find the size of the given array. Then iterate the loop until a specific number and within the loop’s body use the modulo operator with the array size to iterate over each
element of the circular array:
int arraySize = circularArray.length;
for (int i = 4; i <= 11; i++) {
Complete Code & Output:
Case 7: Use Modulo Operator To Check Leap Year
Use the modulus operator to check if the user enters a leap year. For this, first, import the Scanner class, and take a “Year” from the user as input:
Scanner scannerObj = new Scanner(System.in);
System.out.println("Enter a Year");
int inputYear = scannerObj.nextInt();
Now use the modulo operator with the if-else statement to check if the user entered a leap year:
if ((inputYear % 4 == 0 && inputYear % 100 != 0) || inputYear % 400 == 0) {
System.out.println("It's a Leap year.");
else {
System.out.println("Not a leap year.");
If a year is fully divisible by “4”, then it is known as a leap year. However, a century year is said to be a leap year if it is divisible by 400.
Complete Code & Output:
Case 8: Use Modulo Operator To Create Cyclic Loops
To create a cyclic loop specify a number up to which you want to iterate a loop. After this, use the modulus operator with a divisor based on which you want to create a cycle:
for (int num = 0; num < 12; num++) {
int cycleVal = num % 4;
Complete Code & Output:
Case 9: Use Modulo Operator To Convert Minutes to Hours
First, use the Scanner class to take minutes to be converted from the user:
Scanner scannerObj = new Scanner(System.in);
System.out.println("Please Enter Total Minutes");
int inputMinutes = scannerObj.nextInt();
Use the division operator to calculate the total hours and the modulo operator to find the remaining minutes:
int hours = minutes / 60;
int remainingMinutes = minutes % 60;
System.out.print(minutes + " minutes = "
+ hours + " hours "
+ remainingminutes + " minutes");
Complete Code & Output:
Case 10: Use Modulo Operator on Negative Values
The modulo operator retrieves the output according to the sign associated with the dividend. For demonstration, first, use the Modulo operator with the negative dividend:
int modulo = -72 % 11;
System.out.println("Modulo When Dividend is Negative: " + modulo);
Now use the modulo operator with a positive dividend and a negative divisor:
int modulo1 = 72 % -11;
System.out.println("Modulo When Divisor is Negative: " + modulo1);
Finally, use the modulo operator with a negative dividend and a negative divisor:
int modulo2 = -72 % -11;
System.out.println("Modulo When Both Dividend and Divisor are Negative: " + modulo2);
Complete Code & Output:
Division Vs Modulo: What’s the Difference?
A division operator “/” returns a quotient, while a modulo operator “%” retrieves a remainder in Java:
Consider the following code to understand this difference via Java programming.
Example: Modulo Vs Division in Java
First, use the “%” operator on the given values and store the result in a variable named “modulo”:
Now use the “/” operator on the same values and store the result in a variable named “division”:
Print the output of both operators on the console:
System.out.println("Modulo: " + modulo
+"\nDivision: " + division);
Complete Code & Output:
Possible Exceptions While Working With Modulo Operator
An “ArithmeticException” occurs when a user specifies “0” as a divisor:
Note: The Modulo operator works perfectly fine on Integers, however, it might lead to unexpected results in the case of non-integers.
Modulo Operator Alternatives
The below-listed alternative approaches can help us achieve the same functionality as the Modulo operator in Java:
• Using remainder()
• Using Math.floorMod()
• Using Custom Logic
Alternative 1: Using remainder()
The remainder() method belongs to Java’s BigDecimal class. It computes the remainder of two BigDecimal values. To use this method first import the BigDecimal class in your program:
import java.math.BigDecimal;
Now create a couple of BigDecimal variables to initialize the dividend and divisor:
BigDecimal dividend = new BigDecimal("112.50");
BigDecimal divisor = new BigDecimal("12.2");
Use the remainder() method on the given values to find the remainder. After that, use the println() method to display the remainder on the console:
BigDecimal modulo = dividend.remainder(divisor);
System.out.println("Remainder: "+ modulo);
Complete Code & Output:
Alternative 2: Using Math.floorMod()
The floorMod() is an inbuilt method of the Java Math class. It accepts two integer-type values, performs division, and retrieves the remainder of given numbers. To use this method, first, declare and
initialize a couple of integer variables:
int dividend = 125, divisor = 2;
Now use the Math.floorMod() method to get the remainder of input values:
System.out.println("The Remainder: " + Math.floorMod(dividend, divisor));
Complete Code & Output:
Alternative 3: Using Custom Logic
Users can find the remainder of given numbers without using the modulo operator or any built-in methods. To do this, first, create a user-defined function, let’s say “modulo()”. The function accepts
two integer-type parameters: “dividend” and “divisor”. Perform the division on the dividend and divisor, and multiply the result with the divisor. After this, subtract the resultant value from the
dividend and return the final result:
public static int modulo(int dividend, int divisor)
return (dividend - divisor * (dividend/divisor));
Now in the main() method, invoke the modulo() function with the desired arguments, and print the result on the console using println():
System.out.println("The Remainder: " + modulo(172, 12));
Complete Code & Output:
This sums up the working of Java’s Modulo operator.
Final Thoughts
Modulo, Modulus, or “%” is an arithmetic operator in Java that performs division on the provided numbers and retrieves the remainder as output. It has numerous use cases, such as checking if the
given number is even or odd, finding the next or previous index of circular arrays, converting minutes to hours, and many more. This post has discussed ten different use cases of the Modulo operator,
the difference between division and modulo, and some suitable alternatives of the Modulo operator. | {"url":"https://javabeat.net/use-modulo-remainder-operator-java/","timestamp":"2024-11-09T15:49:46Z","content_type":"text/html","content_length":"100352","record_id":"<urn:uuid:19723249-a8e5-4677-afd9-0e1c089f06ff>","cc-path":"CC-MAIN-2024-46/segments/1730477028125.59/warc/CC-MAIN-20241109151915-20241109181915-00309.warc.gz"} |
dmin-based population estimates and
We are committed to maximising our use of administrative data and reducing reliance on the decennial census. In 2019, a third version of admin-based population estimates for England and Wales (ABPE
V3.0) was published as research statistics. This report provides insights on ABPE quality by considering measures of statistical uncertainty.
We define statistical uncertainty as the quantification of doubt about an estimate. Research into statistical uncertainty is conducted by Office for National Statistics (ONS) Methodology in
collaboration with the University of Southampton Statistical Sciences Research Institute.
The ABPE V3.0 has produced population estimates for 2011 and 2016, building on knowledge gained from previous versions of the methodology, ABPE Version 1 (V1.0) and ABPE Version 2 (V2.0). The
explicit design objective for ABPE V3.0 was to avoid population overcount, by introducing an "activity" based metric. The analysis presented in this paper shows that this has not been fully achieved.
The data suggest that in 240 local authorities there is at least one year of age for either males or females where the ABPE overcounts the population. There is overestimation at more ages in Inner
London; for example, Newham, Tower Hamlets and Lambeth have overcount in ABPEs for 64, 48 and 39 single years of age, respectively.
For 65% of all ages, ABPE uncertainty intervals entirely contain the mid-year estimate uncertainty intervals, implying that they are both capturing the same "truth", by very different methods. This
occurs more often for males (68%) than for females (62%).
ABPE overcount is concentrated among under-ones, children aged 5 to 18 years and pensioners. These ages need further investigation.
There are characteristic patterns of undercount in the ABPE, particularly at student ages. In four local authorities, the ABPEs are at least 15% lower than our uncertainty measures suggest they
should be.
The relationship between local authority mid-year estimates (MYEs) and ABPEs has shifted substantially between 2011 and 2016. ABPEs appear to align more closely with the MYEs in 2016 than they did in
2011, with 14% of ABPEs falling within the MYE uncertainty bounds in 2011 and 45% in 2016. Further research should investigate the relationship between the ABPEs and the true population count over
The coverage assessment process for ABPEs will be challenging, particularly when time lags in the administrative data mean that people will be counted in the wrong place. We recommend that further
design of the ABPEs, and the inclusion rules for each demographic group, should be closely informed by the proposed coverage assessment strategy for that group.
Nôl i'r tabl cynnwys
We would like to acknowledge Professor Peter Smith from the University of Southampton Statistical Sciences Research Institute who has helped us to develop the measures of statistical uncertainty
described in this paper. We are also indebted to him for his comments and suggestions in the research and writing of this report.
Nôl i'r tabl cynnwys
The admin-based population estimates (ABPEs) are research outputs and not official statistics. They are published as outputs from research into a methodology different to that currently used in the
production of population and migration statistics. As we develop our methods, we are also developing the ways we understand and measure uncertainty about them. These outputs should not be used for
policy- or decision-making.
Nôl i'r tabl cynnwys
4. Design of the admin-based population estimates and their statistical uncertainty
The admin-based population estimates (ABPEs) are produced through linkage of administrative data and the application of a set of rules in the attempt to replicate the usually resident population. The
sources used in the ABPE Version 2 (V2.0) were the NHS Patient Register (PR), the Department for Work and Pensions (DWP) Customer Information System (CIS), data from the Higher Education Statistics
Agency (HESA) and data from the School Census (SC). Records found on two of these four data sources were included in the population. This led to estimates that were higher than the official
estimates, especially for males of working age.
The main design objective of the ABPE Version 3 (V3.0) was to remove records that were erroneously included in the previous method. An ABPE with under-coverage for all age and sex groups would be
closer to unadjusted census counts and, when combined with a Population Coverage Survey (PCS), should allow dual-system type estimators to be applied with improved results. The new method thus uses a
different approach – utilizing additional data sources and introducing stricter criteria for inclusion in the population.
The data sources used in the new method are:
• Pay As You Earn (PAYE) and Tax Credits data
• National Benefits Database (NBD) and Housing Benefit (SHBE) data
• Child Benefit data
• NHS PR and Personal Demographic Service (PDS) data
• HESA data
• English and Welsh SC data
• Births registrations data
The new criteria used for inclusion in the population are:
• a sign of activity within the 12 months prior to the reference date of the ABPE, where by activity we mean an individual interacting with an administrative system (for example, when paying tax or
changing address)
• appearance and activity on a single data source, with data linkage only used to deduplicate records that appear on more than one source
More details about the choice of data sources and the criteria for inclusion in the new ABPE method can be found in the Principles of ABPE V3.0 methodology.
The new methodology has produced population estimates for 2011 and 2016, where the 2011 reference date is 27 March (Census date), and the 2016 reference date is 30 June (Mid-Year Estimates (MYEs)
reference date).
The analysis presented in this paper provides an insight on the quality of the ABPE V3.0 using newly developed measures of statistical uncertainty. These will feed into the evaluation of the ABPE
V3.0 and will inform the development of the next iteration.
The measures of statistical uncertainty described in this paper were developed as part of a wider Uncertainty Project that we are conducting in collaboration with the University of Southampton
Statistical Sciences Research Institute. The project aims at providing users of our population and migration statistics with information about their quality. The project has been successfully applied
in the context of mid-year population estimates and has more recently been applied to admin-based population estimates.
Nôl i'r tabl cynnwys
5. Comparison of ABPEs with official population estimates time series
Here we compare the admin-based population estimates (ABPEs) for 2011 and 2016 with the published Office for National Statistics (ONS) population estimates for 2011 to 2016, at the local authority
(LA) level. The latter include 2011 Census estimates and 2011 to 2016 mid-year population estimates (MYEs), together with the MYEs measures of statistical uncertainty. Details of the methods used to
measure uncertainty in the MYEs are available in Methodology for measuring uncertainty in ONS local authority mid-year population estimates: 2012 to 2016 and Guidance on interpreting the statistical
measures of uncertainty in ONS local authority mid-year population estimates. They are also summarised in Annex A, for reference.
Statistical uncertainty in local authority MYEs, 2011 to 16
A major statistical concern with the design of the local authority mid-year population estimates (MYEs) is that their quality decreases with time following the census. Statistical uncertainty in
local authority MYEs grows each year between 2011 and 2016. Table 1 confirms that in 2011 the mid-year estimate uncertainty intervals were at their narrowest, with 330 local authorities having 95%
uncertainty intervals of less than 5% of their mean simulated mid-year estimate values.
Table 1 : 2011 to 2016 empirical local authority 95% uncertainty interval range, as a percentage of the
mean of the simulated composite mid-year estimates
Year Uncertainty interval range (%) <5% 5 to less than 10% 10 to less than 20% 20 to less than 50% ≥50%
2011 1.19 to 7.35 330 18 0 0 0
2012 1.42 to 21.24 318 28 1 1 0
2013 1.56 to 41.30 297 44 6 1 0
2014 1.77 to 44.92 290 48 9 1 0
2015 1.85 to 45.58 278 54 15 1 0
2016 1.93 to 47.40 262 65 19 2 0
Download this table Table 1 : 2011 to 2016 empirical local authority 95% uncertainty interval range, as a percentage of the mean of the simulated composite mid-year estimates
.xls .csv
Initially most uncertainty comes from the census, but each year more uncertainty comes from internal and international migration. In 2012, for most local authorities (330 out of 348), the greatest
proportion of uncertainty came from the census (see Methodology for measuring uncertainty in ONS local authority mid-year population estimates: 2012 to 2016, Section 6). The influence of the census
declines over time. By 2016, census accounted for 50% of uncertainty in 155 local authorities. The influence of international and internal migration becomes more visible. In 2016, international
migration accounted for more than 50% of uncertainty in 93 local authorities, while internal migration accounted for over 50% in just 17 local authorities.
Over time, a growing number of local authority mid-year estimates fall outside of their uncertainty bounds (Table 2). By 2016, over a third of local authority mid-year estimates do. This is
consistent with our understanding that estimation of the population becomes progressively more difficult as we move away from the census. However, it could possibly be an artefact of the methodology
for measuring uncertainty in the internal migration component of the MYEs, where the 2011 Census internal migration transitions are used as a benchmark of the "true" measure of internal migration
(see Methodology for measuring uncertainty in ONS local authority mid-year population estimates: 2012 to 2016, Section 5).
Table 2: Position of local authority mid-year population
estimates relative to their uncertainty intervals, 2011 to
Year Number within % Number above % Number below %
2011 348 100.0
2012 347 99.7 1 0.3
2013 316 90.8 28 8.1 4 1.2
2014 271 77.9 66 19.0 11 3.2
2015 237 68.1 95 27.3 16 4.6
2016 218 62.6 108 31.0 22 6.3
Download this table Table 2: Position of local authority mid-year population estimates relative to their uncertainty intervals, 2011 to 2016
.xls .csv
What does MYE uncertainty tell us about the local area level ABPEs?
In line with the design objective of undercounting the population, the ABPEs tend to fall below the MYE uncertainty intervals. Table 3 shows that in 2011, 290 (83%) of ABPEs fell below the MYE
uncertainty interval. However, nine (2.6%) are above it. The MYE uncertainty bounds are designed to capture 95% of the simulated MYEs. Thus 2.5% of simulated MYEs fall on either side of the
uncertainty bounds. Finding 2.6% of ABPEs above the MYE uncertainty bounds would be a welcome finding, except that ABPE V3.0 is designed to deliberately undercount the population.
Table 3: Frequency and percent of local authorities where the ABPEs for
2011 and 2016 fall in or outside of the same year’s mid-year estimate
uncertainty interval
2011 ABPE 2016 ABPE
Above MYE UI Inside MYE UI Below MYE UI Total
Above MYE UI 3 6 0 9 Frequency
0.9 1.7 0.0 2.6 Percent
Inside MYE UI 12 30 7 49 Frequency
3.5 8.6 2.0 14.1 Percent
Below MYE UI 17 119 154 290 Frequency
4.9 34.2 44.3 83.3 Percent
Total 32 155 161 348 Frequency
9.2 44.5 46.3 100.0 Percent
Download this table Table 3: Frequency and percent of local authorities where the ABPEs for 2011 and 2016 fall in or outside of the same year’s mid-year estimate uncertainty interval
.xls .csv
Table 3 also shows that the ABPEs appear to align more closely with the MYEs in 2016 than they did in 2011. In 2011, only 14% of ABPEs fell within the MYE uncertainty bounds. By 2016 this rises to
45%. We know that MYEs have increasing bias through the decade after census. If we assume that the accuracy of the ABPE is stable over time, this would imply that MYEs are increasingly
underestimating the population. Further research should investigate the relationship between the ABPEs and the true population count through time. This reinforces an important message in Developing
our approach for producing admin-based population estimates, subnational analysis: 2011.
A listing of the local authorities in each cell of Table 3 is given in Annex B. Two illustrative examples are presented in Figures 1a and 1b.
Figure 1a: ABPE within MYE uncertainty bounds in 2011 and 2016, Lincoln
Source: Office for National Statistics
1. Figures standardised to 2011 Census.
Download this chart Figure 1a: ABPE within MYE uncertainty bounds in 2011 and 2016, Lincoln
Image .csv .xls
Figure 1b: ABPE below MYE uncertainty bounds in 2011 and above in 2016, Merton
Source: Office for National Statistics
1. Figures standardised to 2011 Census.
Download this chart Figure 1b: ABPE below MYE uncertainty bounds in 2011 and above in 2016, Merton
Image .csv .xls
Nôl i'r tabl cynnwys
6. What can we learn from statistical uncertainty in the ABPEs?
We have produced indicative measures of statistical uncertainty for the 2011 admin-based population estimates (ABPEs). These are interim measures; ultimately confidence intervals will be generated as
part of the ABPEs coverage assessment process.^1
Methodology for measuring statistical uncertainty in the ABPEs
Our approach relies on two simplifying assumptions. First, that we can use the variability between the ABPE and census estimates within groups of ”similar” local authorities as a proxy for
variability of the ABPEs within those local authorities. The grouping of “similar” local authorities is achieved with reference to their patterns of comparability between the ABPEs and census by sex
and single year of age. Second, that we can use 2011 Census estimates to represent the true population. Thus, our method doesn’t consider uncertainty in the 2011 Census estimates.
A full account of our methodology is provided in Indicative uncertainty intervals for the admin-based population estimates: July 2020. It can be summarised by the following process:
• calculate scaling factors comparing ABPE and Census by sex and single year of age for each local authority
• normalise the scaling factors around zero using the logarithmic transformation
• cluster local authorities based on similar patterns of logged scaling factors across age, for each sex separately
• for each cluster, fit a Generalised Additive Model through the lsf, to obtain the model residuals (error), r[i,j,k]
• for each year of age and sex within a cluster, treat as a “group” and produce standardised residuals (s) by dividing them by their group’s standard deviation
(c refers to the cluster that the local authority is in)
• resample 1,000 standardised residuals (with replacement each time)
• un-standardise the residuals by multiplying by their group’s standard deviation
• add the residuals to the observed lsfs in each group to create 1,000 simulated lsfs
• exponentiate the simulated lsfs and multiply them by the published ABPE
• the uncertainty interval is taken as the 2.5th and 97.5th percentile of the 1,000 simulated population estimates
A small number of local authorities could not be clustered with others as they had distinct and unique scaling factor profiles. In these local authorities, the ABPEs often perform less well than in
the others, for example, because the administrative sources don’t include foreign armed forces and their dependents. These “outlier” local authorities were grouped within their own separate clusters
(separately for males and females) and, appropriately, have larger uncertainty intervals as a result. The outlier local authorities for males were Isles of Scilly, City of London, Forest Heath,
Kensington and Chelsea and Rutland. For females the outliers were Isles of Scilly, City of London, Kensington and Chelsea, Forest Heath and Westminster. For further discussion about areas with large
populations of armed forces (for example Forest Heath and Rutland) and the quality of the associated ABPEs see also Developing our approach for producing admin-based population estimates, subnational
analysis: 2011.
2011 ABPE uncertainty by single year of age, sex and local authority
If the assumptions we have made in estimating uncertainty are correct, we would expect these intervals on average to capture the true population 95% of the time. Uncertainty interval widths for the
ABPE reflect known patterns of statistical uncertainty in particular age-sex groups and are calculated as a percentage of ABPE. The intervals are on average wider at student ages and up to age 40
years, just before the retirement age and in the oldest ages. Figure 2 shows the average relative interval widths by age for males. The patterns are nearly identical for females.
Figure 2: Average ABPE uncertainty relative interval widths by age, males
Source: Office for National Statistics
Download this chart Figure 2: Average ABPE uncertainty relative interval widths by age, males
Image .csv .xls
In this section we report on the position of the 2011 ABPE relative to their uncertainty intervals.
Local authorities where the ABPEs sit entirely within their uncertainty bounds are not excessively biased at any point in the age distribution. For example, Figure 3 for Newport males. Few local
authorities have ABPEs which sit within their uncertainty bounds for all ages; six for males (Kensington and Chelsea, Leeds, Newport, Rutland, Sunderland, Wirral) and two for females (Kensington and
Chelsea, Westminster). In Westminster (females) and both males and females in Kensington and Chelsea, uncertainty intervals are especially wide (see Figure 4 for Kensington and Chelsea females).
Figure 3: ABPEs and their uncertainty bounds for Newport, males
Source: Office for National Statistics
Download this chart Figure 3: ABPEs and their uncertainty bounds for Newport, males
Image .csv .xls
Figure 4: ABPEs and their uncertainty bounds for Kensington and Chelsea, females
Source: Office for National Statistics
Download this chart Figure 4: ABPEs and their uncertainty bounds for Kensington and Chelsea, females
Image .csv .xls
Local authorities where the ABPEs are above their uncertainty bounds may be over-estimating the population at those ages. This typically occurs between ages 6 and 24 years, or around the pension age,
and is equally common for males (193 local authorities) and females (191). This happens in five scenarios.
Scenario one
Most commonly, primary age children of both sexes (up to 11) may be being over-estimated. This affects most London boroughs, many urban boroughs in the North, a substantial number of urban and
suburban local authorities and a few rural local authorities (see Annex C). 138 local authorities have at least one instance of overcount for boys up to 11 years, compared with 121 for girls. Females
in the London Borough of Ealing is an example of potential primary age overcount (Figure 5).
Figure 5: ABPEs and their uncertainty bounds for the London Borough of Ealing, females
Source: Office for National Statistics
Download this chart Figure 5: ABPEs and their uncertainty bounds for the London Borough of Ealing, females
Image .csv .xls
Scenario two
In some local authorities ABPEs are above their uncertainty bounds in adolescent years (ages 11 to 17 years). This occurs for girls in 57 local authorities and for boys in 45, again listed in Annex C
. Males in the London Borough of Wandsworth are an example (Figure 6).
Figure 6: ABPEs and their uncertainty bounds for Wandsworth, males
Source: Office for National Statistics
Download this chart Figure 6: ABPEs and their uncertainty bounds for Wandsworth, males
Image .csv .xls
Scenario three
Some local authorities (listed in Annex C) have ABPEs above the uncertainty intervals at ages 21 to 27 years (39 for females, 10 for males). These tend to have large student populations aged 18 to 21
years, and much smaller populations above undergraduate age. In these areas the ABPE may overcount students whose registration has remained after they have moved out and are no longer students there.
Scenario four
Three local authorities have ABPEs above the uncertainty interval at some other ages. City of London (28 to 37 years), Isles of Scilly (16 to 18 years, 28 to 30 years) and Boston (2 to 17 years, 22
to 38 years). Boston has a very high number of seasonal workers from Eastern Europe (Figure 7).
Figure 7: ABPEs and their uncertainty bounds for Boston, males
Source: Office for National Statistics
Download this chart Figure 7: ABPEs and their uncertainty bounds for Boston, males
Image .csv .xls
Scenario five
There are 162 local authorities where there is at least one instance of potential ABPE overcount for age 55 years or older; 108 for females and 116 for males. Table 4 shows local authorities with the
highest frequencies.
Table 4: Local authorities with the highest frequencies of ABPEs by single year of age above their upper uncertainty bound, at age 55 years and over
Local authority Number of single year of age estimates that are above the upper ABPE uncertainty Average percentage above the upper bound of the uncertainty interval (as a % of the upper
bound bound)
Newham 38 2.56
Tower Hamlets 32 2.66
Lambeth 28 2.55
Haringey 22 2.31
Hackney 20 2.60
Crawley 14 0.88
Croydon 13 1.52
Lewisham 12 1.40
Brent 11 3.68
Corby 11 2.62
Slough 11 2.61
Watford 11 1.60
Southwark 10 2.03
Barking and 10 1.39
Reading 10 1.19
Download this table Table 4: Local authorities with the highest frequencies of ABPEs by single year of age above their upper uncertainty bound, at age 55 years and over
.xls .csv
Where ABPEs are above their uncertainty interval:
• occurs more frequently in urban local authorities, particularly London
• occurs most frequently at primary school age, student age (especially females) and post-retirement age
• for both males and females there is an increase in the number of local authorities with overcount from retirement age onwards; for females there is an additional increase in cases at 90 years old
and above
• does not consistently increase by age at high ages
Most local authorities where the ABPEs are below their uncertainty bounds are meeting ABPE design objectives.There are just 11 local authorities where ABPEs do not fall below the uncertainty bounds
at any age for males, and eight for females.
ABPEs below the 95% uncertainty interval are concentrated between the ages of 18 to 26 years and 40 to 60 years and are more common and pronounced for males. Table 5 lists local authorities with the
highest frequency of undercount, alongside the average percentage by which the ABPE is below the lower bound of the uncertainty interval. Males have more potential for undercount than for females,
previously attributed in our 2019 publication to shortfalls in coverage of men in the contributing administrative sources. In some areas this may reflect the presence of Foreign Armed Forces or
prisons (see also Developing our approach for producing admin-based population estimates, subnational analysis: 2011). Figures 8 and 9 show Camden females and Tunbridge Wells males.
Table 5: Local authorities where admin-based estimates are most frequently below their uncertainty bounds
Local authority Number of single year of age estimates that are below the lower ABPE uncertainty Average percentage below the lower bound of the uncertainty interval (as a % of the lower
bound bound)
Camden 54 5.80
Tunbridge Wells 51 4.49
Elmbridge 39 6.09
St Edmundsbury 39 3.37
Shropshire 39 3.35
Rutland 38 6.45
Gwynedd 38 4.58
Mole Valley 37 4.85
Tandridge 37 3.90
Richmondshire 36 4.62
East Cambridgeshire 36 4.31
Mid Suffolk 36 3.49
South Norfolk 36 3.12
Uttlesford 35 5.75
Wandsworth 34 4.18
Westminster 62 6.73
Tunbridge Wells 51 8.99
Mid Suffolk 48 5.45
North Dorset 47 8.64
St Edmundsbury 47 8.46
Gwynedd 46 5.03
Shropshire 45 9.24
Harborough 45 6.84
Camden 45 5.52
Richmond upon 44 7.98
Tandridge 44 7.49
Wealden 44 6.67
Reigate and 44 5.97
Derbyshire Dales 43 7.26
Harrogate 43 5.96
Download this table Table 5: Local authorities where admin-based estimates are most frequently below their uncertainty bounds
.xls .csv
Figure 8: ABPEs and their uncertainty bounds for Camden, females
Source: Office for National Statistics
Download this chart Figure 8: ABPEs and their uncertainty bounds for Camden, females
Image .csv .xls
Figure 9: ABPEs and their uncertainty bounds for Tunbridge Wells, males
Source: Office for National Statistics
Download this chart Figure 9: ABPEs and their uncertainty bounds for Tunbridge Wells, males
Image .csv .xls
Local authorities with differences between the ABPEs and the lower uncertainty bound at ages 18 to 26 years fall into three types.
Those with large student populations
The ABPE spike in the number of 18- to 21-year-olds present is lower than suggested by the 2011 Census and uncertainty bounds. Differences are typically greater for males. Males in Newcastle under
Lyme (Figure 10) and females in Bristol (Figure 11) are examples.
Figure 10: 2011 admin-based population estimate uncertainty by age and sex for males in Newcastle under Lyme
Source: Office for National Statistics
Download this chart Figure 10: 2011 admin-based population estimate uncertainty by age and sex for males in Newcastle under Lyme
Image .csv .xls
Figure 11: 2011 admin-based population estimate uncertainty by age and sex for females in Bristol
Source: Office for National Statistics
Download this chart Figure 11: 2011 admin-based population estimate uncertainty by age and sex for females in Bristol
Image .csv .xls
Those with high student out-migration
Most local authorities (244) show a distinct drop in 18- to 21-year-olds, suggesting moves for higher education, or work. In some the decrease is much higher in the ABPEs than in the 2011 Census and
implied by the uncertainty bounds. For males, 126 local authorities have ABPEs that are on average lower than the lower uncertainty bound. In 53 (listed in Table 6), the ABPE is more than 5% lower.
In four, it is more than 15% lower (listed in Table 6). These patterns typically occur in rural areas and appear to be concentrated around wealthier rural or suburban areas (see Shropshire, Figure
Table 6: Local authority distances from the lower ABPE uncertainty bounds
Distance from lower Local authorities
uncertainty bounds
More than 5%, females None
Aylesbury Vale, Bexley, Blaby, Braintree, Breckland, Bridgend, Bromsgrove, Craven, Dartford, Derbyshire Dales, Dover, East Devon, East Hertfordshire, Eastleigh, Epping
Forest, Flintshire, Hambleton, Harborough, Harrogate, Hart, Herefordshire, High Peak, Huntingdonshire, Lewes, Mid Suffolk, Mole Valley, Monmouthshire, North Devon, North
More than 5%, males Dorset, North Hertfordshire, Pembrokeshire, Powys, Purbeck, Reigate and Banstead, Rushmoor, Sevenoaks, Shepway, Shropshire, South Oxfordshire, South Staffordshire, St
Edmundsbury, Staffordshire Moorlands, Tandridge, The Vale of Glamorgan, Three Rivers, Tonbridge and Malling, Tunbridge Wells, Uttlesford, West Devon, West Oxfordshire,
More than 15%, females None
More than 15%, males (shown
as a percentage of the Hambleton (15.90), North Dorset (23.89), Shropshire (22.14), South Staffordshire (17.95)
lower bound value)
Download this table Table 6: Local authority distances from the lower ABPE uncertainty bounds
.xls .csv
Figure 12: 2011 admin-based population estimate uncertainty by age and sex for males in Shropshire
Source: Office for National Statistics
Download this chart Figure 12: 2011 admin-based population estimate uncertainty by age and sex for males in Shropshire
Image .csv .xls
Other specific contexts
In a small number of local authorities, the ABPE underestimates young men in rural areas with an army base. In the London boroughs the ABPE appears to underestimate the number of 18- to 30-year olds
(listed in Table 7).
Table 7: Potential undercount in London boroughs at age 18 to 30 years (undercount for at least three consecutive ages)
Sex Local authorities
Only Males Barnet, Bromley, Camden, Greenwich, Hammersmith and Fulham, Haringey, Harrow, Islington, Kingston upon Thames, Lewisham, Merton, Newham, Redbridge, Richmond upon Thames, Waltham Forest,
Only None
Both Bexley, Croydon, Enfield, Hackney, Havering, Lambeth, Southwark, Sutton, Wandsworth
Download this table Table 7: Potential undercount in London boroughs at age 18 to 30 years (undercount for at least three consecutive ages)
.xls .csv
Local authorities with substantial differences between the ABPEs and the lower uncertainty bound for 30- to 60-year-olds are mostly in the South, particularly the Home Counties. Demographically,
these also fall into two types.
Rural or semi-urban areas
Rural or semi-urban areas with low numbers of 18- to 22-year-olds, together with a large number of 40- to 55-year-olds. ABPEs outside of the uncertainty bounds tend to be concentrated around ages 40
to 60 years. For females, 173 local authorities had ABPEs below the lower uncertainty bound for at least 15 ages in this age range. For males this was 168. There are a few local authorities with a
gap between the lower uncertainty interval and the ABPE, but where there are also high numbers of 18- to 22-year-olds. This happens when a local authority encompasses a university town and a large
surrounding rural area.
London boroughs
London boroughs where the ABPEs fall below the lower uncertainty bound at ages 30 to 45 years are listed in Table 8. Typically, these areas have large populations aged in their 30s. It is unclear why
London suburbs are much more affected by this compared with suburbs of other cities.
Table 8: Potential undercount in London borough age 30 to 45 years (undercount for at least three consecutive ages)
Sex Local authorities
Only Males Westminster
Only Barking and Dagenham, Ealing, Hounslow, Islington, Tower Hamlets
Both Barnet, Bexley, Bromley, Camden, Croydon, Enfield, Greenwich, Hackney, Hammersmith and Fulham, Haringey, Harrow, Havering, Kingston upon Thames, Lewisham, Merton, Redbridge, Richmond upon
Thames, Southwark, Sutton, Waltham Forest, Wandsworth
Download this table Table 8: Potential undercount in London borough age 30 to 45 years (undercount for at least three consecutive ages)
.xls .csv
After age 65 years, the number of local authorities with any undercount decreases, from roughly 400 observations of undercount at each age for both sexes leading up to age 65 years, to around 20 for
each age after 65 years.
To conclude this section, what if our central assumption that we can use variability between the ABPEs and census within groups of “similar” local authorities as a proxy for variability of the ABPEs
within those local authorities, is wrong? We also assume that the census represents the “true” population, with no account taken of uncertainty around the census estimates themselves. We tested our
findings by comparing ABPEs against census estimates at single year of age with their associated uncertainty bounds. The methods are shown in Annex D. The results from this analysis reinforce all the
findings within this section.
Notes for: What can we learn from statistical uncertainty in the ABPEs?
1. We acknowledge that there are minor differences in the 2011 ABPE data for 0-years old that we used for the analysis in Sections 6 to 7 of this paper and those that were used in Developing our
approach for producing admin-based population estimates, subnational analysis: 2011 and Measuring and adjusting for coverage patterns in the admin-based population estimates, England and Wales:
2011. This reflects that when we started this work, we had an earlier extract of the data. The differences do not impact the uncertainty measures or any substantive points in the report.
Nôl i'r tabl cynnwys
Admin-based population estimates (ABPE) Version 3 (V3.0) had a specific objective to remove the population overcount seen in ABPE Version 2 (V2.0). The analysis in this paper shows that this
objective has not been fully met. There were 38 local authorities with ABPEs above the mid-year population estimates (MYEs) and their uncertainty bounds in either 2011 or 2016 or in both years.
Developing methods to avoid ABPE overcount requires further research (see Measuring and adjusting for coverage patterns in the admin-based population estimates, England and Wales: 2011).
At local authority level the relationship between the ABPEs and MYEs has shifted over time. While 5% of ABPEs (19 of 348) were higher than the MYEs in 2011, by 2016 this increases to 19% (67 of 348).
We show that the percentage of local authority ABPEs falling below the MYE lower uncertainty bound fell from 83% to 46% between 2011 and 2016. We know that the inter-censal estimates suffer
increasing bias over time, largely because of reliance on the International Passenger Survey for measuring international migration (see also Section 5). In addition, internal migration may not be
accurately captured. The closer alignment of ABPEs and MYEs in 2016 could be a product of increasing bias in the MYEs. However, we cannot rely on the untested assumption that the relationship between
the true population and the administrative sources is constant over time. This requires further research. Time series analysis of the ABPEs and of the administrative sources at aggregate level, prior
to any record linkage, would help to signal any change in quality if trends in one source are not visible in others (see also Developing our approach for producing admin-based population estimates,
subnational analysis: 2011).
More granular analysis by single year of age and sex reveals the minimum degree of potential overcount in the ABPEs. Measured across local authorities, on average 15 single year of age estimates for
females and 14 for males were above the upper bound of the MYE uncertainty interval. Comparing the ABPE and MYE uncertainty intervals, these were found not to overlap for 3.4% of single year of age
estimates. This implies that over 96% of ABPEs may capture the same “true” population estimate at single year of age and sex. This does not necessarily imply that they capture the same individuals,
for example, see Measuring and adjusting for coverage patterns in the admin-based population estimates, England and Wales: 2011 for compensating over- and under-count errors when linked to the
ABPE overcount is concentrated among the under-ones, children aged 5 to 18 years and pensioners. Overcount for each of these age groups requires further investigation (for pensioners it is discussed
in more detail in Developing our approach for producing admin-based population estimates, subnational analysis: 2011). Are the ABPEs including people who are not usual residents? Or are some records
being double-counted? Or are both happening? The overcount raises questions about whether the “activities” detected in administrative data really signal usual residence, and whether inclusion rules
around co-resident inactive records are maybe too relaxed? How much linkage error is attributable to poor date of birth capture in the respective sources? These findings and the questions that they
raise are consistent with those in Measuring and adjusting for coverage patterns in the admin-based population estimates, England and Wales: 2011.
Potential undercount in the ABPEs is highest at student ages (18 to 22 years), particularly for males, then falls, then increases again through working ages. This is notoriously a challenging group
to capture in population estimates. The pattern is uneven across local authorities with universities. Do we have all the administrative sources that we need for this age group? How far can this
undercount be explained by the rules excluding co-resident inactive adult children? 2011 Census data could inform this. Are the high levels of undercount seen in some local authorities correctable
through coverage adjustment, and if so, how wide would the associated confidence intervals be for these ages?
The coverage adjustment challenge is more complex at sub-national level than at the national level. This is true for census-based estimates as well, however, administrative data raise additional
challenges. Differential time lags in the administrative sources confound record matching. For matched records, address conflicts place records in the wrong geography. Counting records in the wrong
place represents overcount in that location, alongside, potentially, undercount somewhere else. The complexity of adjusting for this in estimation underlines the need for ABPE design and the
estimation strategy to be closely interrelated.
Further development of the ABPEs would be supported by use of the Error Framework for Longitudinally Linked Administrative Sources.This would help to ensure that statistical error is optimised for
the ABPEs all the way through the production process. For further discussion on this see Developing our approach for producing admin-based population estimates, subnational analysis: 2011.
Likewise, the Error Framework should be rigorously applied to the linked data that form the basis of the ABPEs. Again, this is to ensure that statistical error is optimised for the ABPEs.
Nôl i'r tabl cynnwys
9. Annex A – Methods for measuring statistical uncertainty in our mid-year estimates (MYEs)
Mid-year population estimates (MYEs) use a cohort component method. In brief, components of demographic change (natural change (births less deaths), net international migration and net internal
migration) are added to the previous year’s aged-on population. As well as adding the net components of change, additional procedures account for special populations (for example, armed forces,
school boarders, prisoners). Initial work (see Quality measures for population estimates) identified the census base, international migration and internal migration as having the greatest impact on
uncertainty, and our measure of uncertainty is a composite of uncertainty associated with these three components only.
Uncertainty can arise from data sources or from the processes used to derive the MYEs. We use observed data and recreate the MYEs’ derivation processes for the three components 1,000 times to
simulate a range of possible values that might occur. Differences in data sources and procedures for each component imply different methods to generate the simulated distributions (see Methodology
for measuring uncertainty in ONS local authority mid-year population estimates: 2012 to 2016 for details).
The simulated distributions are combined with the other components of change (assumed to have zero error, including births, deaths, asylum seekers, armed forces and prisoners). The uncertainty
generation process is summarised in Figure 17. As with the MYEs themselves, the simulated estimates are rolled forward annually through the ten-year inter-censal period. Thus, we include both
uncertainty carried forward from previous years (including from the census estimates) and new uncertainty for the current year.
Empirical uncertainty intervals for each local authority are created by ranking the 1,000 simulated values and taking the 26th and 975th values as the lower and upper bounds respectively. As the
observed MYE generally differs from the central or median of the simulations, this confidence interval is not centered about the MYE and in some extreme cases the MYE is outside the uncertainty
Further details of the methods used to measure uncertainty in the MYEs are available in Methodology for measuring uncertainty in ONS local authority mid-year population estimates: 2012 to 2016 and
Guidance on interpreting the statistical measures of uncertainty in ONS local authority mid-year population estimates.
Figure 17: The mid-year estimate cohort component method and statistical uncertainty
Source: Office for National Statistics
Download this image Figure 17: The mid-year estimate cohort component method and statistical uncertainty
.png (18.2 kB)
Nôl i'r tabl cynnwys
12. Annex D – Methodology for measuring 2011 Census uncertainty at single year of age
Standard deviations for census estimates at single year of age are not available. We therefore assume that the coefficient of variation is the same for the single years of age as for the
corresponding five-year age group. This allows us to estimate the standard deviation by single year of age^1:
The 2011 Census estimates by single year of age, sex and local authority, and estimated standard deviation by single year of age, sex and local authority are used to specify the distribution (assumed
to be normal) of uncertainty around the census component. Parametric bootstrapping from this normal distribution creates 1,000 simulations for the census component for each local authority by single
year of age and sex.
Notes for: Annex D – Methodology for measuring 2011 Census uncertainty at single year of age
1. This approach is based on an analysis of five-year (published) and single-year (simulated) standard deviations from the 2011 Census, documented in minutes of the meeting between the University of
Southampton Statistical Sciences Research Institute and Office for National Statistics on 25 July 2018.
Nôl i'r tabl cynnwys | {"url":"https://cy.ons.gov.uk/peoplepopulationandcommunity/populationandmigration/populationestimates/articles/adminbasedpopulationestimatesandstatisticaluncertainty/july2020","timestamp":"2024-11-10T18:26:12Z","content_type":"text/html","content_length":"369557","record_id":"<urn:uuid:b913f988-0c61-492a-bda3-a84837f5c691>","cc-path":"CC-MAIN-2024-46/segments/1730477028187.61/warc/CC-MAIN-20241110170046-20241110200046-00471.warc.gz"} |
Partial Functions in Python: A Comprehensive Guide - iPython.AI
Partial functions in Python are a sophisticated feature that can significantly simplify the process of working with functions that have too many parameters, some of which often remain constant
throughout a program. By using partial functions, developers can “freeze” a portion of a function’s arguments, resulting in a new function with fewer parameters. This post will explore the concept of
partial functions, their utility, and demonstrate how to use functools.partial to make your code cleaner and more efficient.
Understanding Partial Functions
A partial function allows you to fix a certain number of arguments of a function and generate a new function. This is particularly useful in scenarios where you find yourself repeatedly calling a
function with the same set of arguments. By using a partial function, you can preset these arguments, making your function calls more concise and readable.
The functools.partial Method
The functools module in Python provides the partial method, which is used to create partial functions. The partial method takes a function as its first argument followed by any number of positional
and keyword arguments. It returns a new partial object which behaves like the original function, except that the preset arguments are included in calls to the partial object.
Demonstrating functools.partial
Example 1: Basic Usage
Consider a simple function that multiplies two numbers:
def multiply(x, y):
return x * y
If you frequently multiply numbers by a constant factor, you can use functools.partial to create a specialized function:
from functools import partial
# Create a function that multiplies any number by 2
double = partial(multiply, 2)
# Use the new function
print(double(5)) # Output: 10
Explanation: Here, double is a partial function of multiply, with x preset to 2. Calling double(5) is effectively the same as calling multiply(2, 5).
Example 2: Presetting Keyword Arguments
Partial functions can also preset keyword arguments. Consider a function that sends data over a network:
def send_data(data, *, protocol='http'):
print(f"Sending {data} via {protocol}")
You can create a version of send_data that defaults to using HTTPS:
secure_send = partial(send_data, protocol='https')
secure_send("Hello, World!") # Output: Sending Hello, World! via https
Explanation: The secure_send function presets the protocol argument to 'https'. When calling secure_send, you only need to provide the data argument.
Tips, Common Mistakes, and Best Practices
• Use Partial Functions Sparingly: While partial functions can simplify code, overusing them can make your code harder to understand. Use them when it significantly improves readability or reduces
• Documenting Partial Functions: Always document the behavior of your partial functions, especially when the original function has complex behavior or when presetting non-obvious arguments.
• Avoid Mutable Default Arguments: Just like with regular functions, using mutable default arguments with partial functions can lead to unexpected behavior. Always use immutable objects as default
• Testing: Ensure you thoroughly test partial functions, particularly in contexts where the original function’s behavior is complex or depends on external state.
Serialization with Partial Functions
Partial functions created with functools.partial are serializable using Python’s pickle module. This feature is particularly useful when you need to serialize configurations or callbacks that include
partially applied functions.
Example: Serializing a Partial Function
import pickle
from functools import partial
def multiply(x, y):
return x * y
# Create a partial function
double = partial(multiply, 2)
# Serialize the partial function
serialized_double = pickle.dumps(double)
# Deserialize and use the partial function
deserialized_double = pickle.loads(serialized_double)
print(deserialized_double(5)) # Output: 10
Best Practice: Always test the serialization and deserialization of partial functions, especially when they are used in distributed systems or for long-term storage.
Partial Functions vs. Lambda Functions
While both functools.partial and lambda functions can be used to create functions with fewer arguments, there are key differences between them. Understanding these differences can help you choose the
right tool for each scenario.
• Flexibility: Lambda functions offer more flexibility because they can define anonymous functions on the fly. However, they are limited to expressions and cannot contain statements or annotations.
• Readability: functools.partial is more readable when dealing with existing functions and complex operations, as it explicitly shows the function being used and the arguments being preset.
• Use Cases: Use functools.partial when you need to preset arguments of a function that will be used multiple times. Use lambda functions for small, one-off anonymous functions that are not reused.
Example: Using Lambda for Simple Operations
# Lambda function to double a number
double = lambda x: x * 2
print(double(5)) # Output: 10
Tip: Prefer functools.partial for presetting arguments in existing functions to enhance code clarity and maintainability.
Handling Variable Arguments
functools.partial seamlessly works with functions that accept variable positional (*args) and keyword (**kwargs) arguments, allowing you to preset any number of those arguments.
Example: Partial Function with Variable Arguments
def greet(*args, **kwargs):
message = ' '.join(args)
message += '!'
if 'emoji' in kwargs:
message += ' ' + kwargs['emoji']
return message
happy_greet = partial(greet, 'Hello', 'World', emoji='😊')
print(happy_greet()) # Output: Hello World! 😊
Common Mistake: Be cautious when presetting variable arguments to ensure the resulting partial function’s signature aligns with your intended use cases.
Partial functions in Python’s functools module are a powerful tool for reducing boilerplate code and making function calls more efficient. By understanding and applying partial functions judiciously,
you can write cleaner, more maintainable Python code.
Join the Conversation and Test Your Knowledge
We’ve explored the power and versatility of partial functions in Python, uncovering how they can simplify your code and make repetitive function calls more manageable. Now, we’d love to hear from
you! Share your experiences, insights, or questions about using partial functions in your projects in the comments below. Whether you’re a seasoned developer or just starting out, your contributions
enrich our learning community.
Ready to put your knowledge to the test? Stay tuned for our upcoming quiz on partial functions and other advanced Python features. It’s a fantastic opportunity to challenge yourself, review key
concepts, and solidify your understanding. Keep an eye out for the quiz link, and let’s see how well you can leverage partial functions in Python. Happy coding!
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Study of statistical variability in nanoscale transistors introduced by LER, RDF and MGG
A 3D drift-diffusion device simulator with implemented density-gradient quantum corrections is developed to run hundreds of simulations to gather variability characteristics in non-planar
transistors. We have included the line edge roughness (LER), random dopants (RD), and metal gate granularity (MGG) induced variabilities, which are considered to be the most important sources of
variability in device characteristics. The simulator is then applied to study a threshold voltage variability in a $25$~nm gate length Si SOI FinFET due to LER and MGG. We found that the LER induced
threshold variability has a mean value of $344.5\ \mathsf{mV}$ and $\sigma$ of $4.7\ \mathsf{mV}$ while the MGG induced has a mean value of $349.9\ \mathsf{mV}$ and $\sigma$ of $13.3\ \mathsf{mV}$,
an order of magnitude greater than the LER variability. | {"url":"https://citius.gal/research/publications/study-of-statistical-variability-in-nanoscale-transistors-introduced-by-ler-rdf-and-mgg/","timestamp":"2024-11-05T12:02:09Z","content_type":"text/html","content_length":"136459","record_id":"<urn:uuid:b9c6e684-2ac9-4f7a-9931-e1f6c800aa62>","cc-path":"CC-MAIN-2024-46/segments/1730477027881.88/warc/CC-MAIN-20241105114407-20241105144407-00542.warc.gz"} |
Octal to Binary
A web tool called Octal to binary Converter is explicitly made to carry out the calculations for Octal to Binary. This calculator converts the provided octal input values into corresponding binary.
With computers, the octal system is frequently employed. Systems of computing are based on both binary and octal numbers. Octal to binary Converter is a simple tool for converting data from Octal to
binary. Convert, Copy, and Paste.
What is the Octal number system?
The base value of an octal number system is 8. In computing, the octal number system is mainly employed to represent binary integers conveniently. In octal numbers, each symbol is the expression of
three binary bits.
A computer system's inputs and outputs are counted using the octal number system. Octal in computing occasionally replaces Hexadecimal. It benefits from not requiring any additional symbols to serve
as digits. Digital displays also make use of it.
What is binary?
Binary numbers: what are they? The binary number system has two as its fundamental unit. One octal digit can be used to represent three binary digits, and one hexadecimal digit can be used to
describe four binary digits. Binary is the number system that is most conducive to electronic circuitry.
The digits 0 and 1 are the only elements in the binary system. Bits are the constituent digits in a binary number. Another name for the binary system is the base -2 system.
Binary numbers are employed as computer machine coding. These numbers are used to manipulate data and archive it. A binary digit is a bit. It follows that bits are essential building blocks of a
computer's storage.
Example of Octal to binary conversion
Octal number: 456
Octal to Binary value: 100101110
How to use the Octal to Binary converter tool?
• First, paste or type the octal number you wish to convert to binary code into the input box.
• Select the "Convert" button after entering the octal number to do the conversion.
• Binary code will be generated from the octal number.
• Click copy. The result will be saved to your clipboard.
Why do we need to convert octal numbers to binary?
Since computers cannot comprehend the octal number system, a converter from Octal to binary must be utilized before it can be used with computers.
What Function Does the Octal Number System Serve?
The use of octal number systems in the form of code is every day in both the programming languages and computer application sectors. | {"url":"https://www.studwiz.com/utilities/octal-to-binary","timestamp":"2024-11-04T17:27:40Z","content_type":"text/html","content_length":"139747","record_id":"<urn:uuid:ec5a25e9-cf86-4cc1-b8de-69ce0b223e4f>","cc-path":"CC-MAIN-2024-46/segments/1730477027838.15/warc/CC-MAIN-20241104163253-20241104193253-00777.warc.gz"} |
Process Equipment Design and Operation 1
Chapter 1: Introduction of Unit Operation for Chemical Engineering
- What is Unit Operation in Chemical Engineering
- Pressure unit, a proportionality constant (g[c])
- Unit Conversion (SI Unit and Engineering Unit)
CLO1 students are able to calculate about the unit conversion
CLO2 students are able to understand theory of unit operation of chemical engineering
Chapter 2: Fluid Mechanics
- Theory of Fluid Mechanics
- Basic equation of Fluid flow in pipe
CLO1 students are able to understand about fluid static, fluid properties, type of fluids
CLO2 students are able to calculate continuity equation, Force from momentum equation, Bernoulli’s equation.
Chapter 3: Flow measurement and Fiction loss in pipe
- Flow measurement
- Fiction loss in pipe
CLO1 students are able to calculate pressure drop from manometer.
CLO2 students are able to calculate flowrate, velocity from flow measurement such as venturi, orifice meter.
CLO3 students are able to calculate fiction factor.
Chapter 4: Transportation of Fluids
- Means of producing fluid flow
- Pump classification
- Centrifugal pump theory
- Head terms of pump
- Fiction loss calculation
- Characteristics of centrifugal pump
- Cavitation and net-positive suction head
- Centrifugal pump relations
- Pump selection
- Fans, blowers, compressors
CLO1 students are able to understand theory of device of fluid transport
CLO2 students are able to understand theory of centrifugal pump
CLO3 students are able to calculate total dynamic head of pump
CLO4 students are able to calculate theoretical house power, brake house power, and electrical house power of pump
CLO5 students are able to calculate operating conditions from characteristics of centrifugal pump
CLO6 students are able to understand a cavitation in pump
CLO7 students are able to calculate net-positive suction head (NPSH)
CLO8 students are able to calculate up-scale of pump, specific speed
CLO9 students are able to select the pump for using
CLO10 students are able to calculate power and efficiency of fans, blowers, and compressors.
Chapter 5: Agitation and Mixing of Liquids
- Agitator and mixer design
- Power correlation for agitator
CLO1 students are able to calculate dimensions of agitator
CLO2 students are able to calculate the power of agitator including unbaffled and baffled tank
Chapter 6: Particles characterization
- Shape of particles
- Particles size characterization (Particles distribution)
- Size reduction
CLO1 students are able to calculate the sphericity factor, the average diameter of particles
CLO2 students are able to calculate the particles size distribution
Chapter 7: Fixed and Fluidized bed
- Fixed bed design
- Fluidization column design
CLO1 students are able to calculate pressure drop of fixed bed column
CLO2 students are able to calculate minimum fluidized velocity, length of bed expansion
Chapter 8: Sedimentation and Thickener Design
- Thickener design
CLO1 students are able to calculate dimensions of thickener from experimental data of sedimentation.
Chapter 9: Solid-Liquid Separation
- Theory of Filtration
- Plate and Frame Filtration design
- Rotary drum filter design
CLO1 students are able to understand theory of filtration.
CLO2 students are able to calculate time of filtration of plate and frame filter.
CLO3 students are able to calculate cake deposit rate and dimensions of rotary drum filter.
Chapter 10: Solid-Gas Separation
- Cyclone design
- Wet scrubber design
CLO1 students are able to understand theory of solid-gas separation devices.
CLO2 students are able to calculate the efficiency of cyclone, dimension of cyclone.
CLO3 students are able to calculate the efficiency of wet scrubber. | {"url":"https://elearning2.sut.ac.th/course/info.php?id=8392","timestamp":"2024-11-02T07:48:55Z","content_type":"text/html","content_length":"38045","record_id":"<urn:uuid:4e8cf5fa-832a-46cc-b3c7-f9cb01655686>","cc-path":"CC-MAIN-2024-46/segments/1730477027709.8/warc/CC-MAIN-20241102071948-20241102101948-00565.warc.gz"} |
What is Rayleigh Number - Definition
What is Rayleigh Number – Definition
The Rayleigh number is a dimensionless number, named after Lord Rayleigh. The Rayleigh number is used to express heat transfer in natural convection. Thermal Engineering
What is Rayleigh Number
The Rayleigh number is a dimensionless number, named after Lord Rayleigh. The Rayleigh number is closely related to Grashof number and both numbers are used to decribe natural convection (Gr) and
heat transfer by natural convection (Ra). The Rayleigh number is simply defined as the product of the Grashof number, which describes the relationship between buoyancy and viscosity within a fluid,
and the Prandtl number, which describes the relationship between momentum diffusivity and thermal diffusivity.
Ra[x] = Gr[x] . Pr
The Grashof number is defined as the ratio of the buoyant to viscous force acting on a fluid in the velocity boundary layer. Its role in natural convection is much the same as that of the Reynolds
number in forced convection. Natural convection occurs if this motion and mixing is caused by density variations resulting from temperature differences within the fluid. Usually the density decreases
due to an increase in temperature and causes the fluid to rise. This motion is caused by the buoyant force. The major force that resists the motion is the viscous force. The Grashof number is a way
to quantify the opposing forces.
The Rayleigh number is used to express heat transfer in natural convection. The magnitude of the Rayleigh number is a good indication as to whether the natural convection boundary layer is laminar or
turbulent. The simple empirical correlations for the average Nusselt number, Nu, in natural convection are of the form:
Nu[x] = C. Ra[x]^n
The values of the constants C and n depend on the geometry of the surface and the flow regime, which is characterized by the range of the Rayleigh number. The value of n is usually n = 1/4 for
laminar flow and n = 1/3 for turbulent flow.
The Rayleigh number is defined as:
g is acceleration due to Earth’s gravity
β is the coefficient of thermal expansion
T[wall] is the wall temperature
T[∞] is the bulk temperature
L is the vertical length
α is thermal diffusivity
ν is the kinematic viscosity.
For gases β = 1/T where the temperature is in K. For liquids β can be calculated if variation of density with temperature at constant pressure is known. For a vertical flat plate, the flow turns
turbulent for value of:
Ra[x] = Gr[x] . Pr > 10^9
As in forced convection the microspic nature of flow and convection correlations are distinctly different in the laminar and turbulent regions.
Example: Rayleigh Number
A vertical plate is maintained at 50°C in 20°C air. Determine the height at which the boundary layer will turn turbulent if turbulence sets in at Ra = Gr.Pr = 10^9.
The property values required for this example are:
ν = 1.48 x 10^-5 m^2/s
ρ = 1.17 kg/m^3
Pr = 0.700
β = 1/ (273 + 20) = 1/293
We know the natural circulation becomes turbulent at approximately Ra = Gr.Pr > 10^9, which is fulfilled at the following height:
We hope, this article, Rayleigh Number, helps you. If so, give us a like in the sidebar. Main purpose of this website is to help the public to learn some interesting and important information about
thermal engineering. | {"url":"https://www.thermal-engineering.org/what-is-rayleigh-number-definition/","timestamp":"2024-11-04T19:50:05Z","content_type":"text/html","content_length":"453443","record_id":"<urn:uuid:c5469a01-be13-4497-9993-3aa439b4a8a9>","cc-path":"CC-MAIN-2024-46/segments/1730477027861.16/warc/CC-MAIN-20241104194528-20241104224528-00017.warc.gz"} |
deep unsupervised learning
(Redacted from a post I wrote back in Feb 14 at AIDL)
I have some leisure lately to browse “Deep Learning” by Goodfellow for the first time. Since it is known as the bible of deep learning, I decide to write a short afterthought post, they are in point
form and not too structured.
• If you want to learn the zen of deep learning, “Deep Learning” is the book. In a nutshell, “Deep Learning” is an introductory style text book on nearly every contemporary fields in deep learning.
It has a thorough chapter covered Backprop, perhaps best introductory material on SGD, computational graph and Convnet. So the book is very suitable for those who want to further their knowledge
after going through 4-5 introductory DL classes.
• Chapter 2 is supposed to go through the basic Math, but it’s unlikely to cover everything the book requires. PRML Chapter 6 seems to be a good preliminary before you start reading the book. If
you don’t feel comfortable about matrix calculus, perhaps you want to read “Matrix Algebra” by Abadir as well.
• There are three parts of the book, Part 1 is all about the basics: math, basic ML, backprop, SGD and such. Part 2 is about how DL is used in real-life applications, Part 3 is about research
topics such as E.M. and graphical model in deep learning, or generative models. All three parts deserve your time. The Math and general ML in Part 1 may be better replaced by more technical text
such as PRML. But then the rest of the materials are deeper than the popular DL classes. You will also find relevant citations easily.
• I enjoyed Part 1 and 2 a lot, mostly because they are deeper and fill me with interesting details. What about Part 3? While I don’t quite grok all the Math, Part 3 is strangely inspiring. For
example, I notice a comparison of graphical models and NN. There is also how E.M. is used in latent model. Of course, there is an extensive survey on generative models. It covers difficult models
such as deep Boltmann machine, spike-and-slab RBM and many variations. Reading Part 3 makes me want to learn classical machinelearning techniques, such as mixture models and graphical models
• So I will say you will enjoy Part 3 if you are,
1. a DL researcher in unsupervised learning and generative model or
2. someone wants to squeeze out the last bit of performance through pre-training.
3. someone who want to compare other deep methods such as mixture models or graphical model and NN.
Anyway, that’s what I have now. May be I will summarize in a blog post later on, but enjoy these random thoughts for now.
You might also like the resource page and my top-five list. Also check out Learning machine learning – some personal experience.
If you like this message, subscribe the Grand Janitor Blog’s RSS feed. You can also find me (Arthur) at twitter, LinkedIn, Plus, Clarity.fm. Together with Waikit Lau, I maintain the Deep Learning
Facebook forum. Also check out my awesome employer: Voci. | {"url":"http://thegrandjanitor.com/tag/deep-unsupervised-learning/","timestamp":"2024-11-04T14:23:00Z","content_type":"text/html","content_length":"38352","record_id":"<urn:uuid:be0fb7d5-8280-4592-80cb-29d2360d7a94>","cc-path":"CC-MAIN-2024-46/segments/1730477027829.31/warc/CC-MAIN-20241104131715-20241104161715-00222.warc.gz"} |
Ultrasonic Transducer Impedance
Started 1st February 2021
See JSN-SR04T, HC-SR04, Ringing
I have a FeelTech FY3200S signal generator and an Owon SDS7102V 'scope, both are pieces of low cost test gear. It is possible to control the signal generator via its USB input and to read the screen
data from the 'scope using its Ethernet connection. In combination this allows automatic measuring of things like frequency response.
I set out to measure the variation in impedance of ultrasonic transducers with frequency. The idea is that a Python program runs on my PC and commands the signal generator to produce various
frequencies; for each one the result on the 'scope is read and saved to disc.
I then have another Python program which analyses the data and produces graphs. Both programs are available from the downloads links below.
The transducer is connected in series with a 1 KΩ resistor, the signal generator is connected across both. Channel 1 (red) on the 'scope measures the signal across the resistor and channel 2 (yellow)
the signal generator output. The technique is described in [2] - note in that reference the positions of the resistor and the device under test are interchanged meaning the equations are slightly
The software analysing the data has to fit a sinusoidal signal, producing amplitude and phase. The obvious approach is to do a Fourier transform of all the samples. That's how I set off, later I
realised it was better to truncate the number of samples to be a multiple of the frequency. Knowing the frequency makes things easier. I found that an approach [3][4][5][6] is to use trigonometrical
identities to make what is being fitted linear, and then multivariate linear regression can be used; this how the code below works. There is also a method like least squares for a line see [7].
Graphics below are .svg and can be scaled up. The HCSR04 data shows how things are supposed to be, the transmit transducer minimum impedance frequency is around the maximum impedance frequency of the
receive transducer [8].
Transmit transducer taken from an HCSR04
Receive transducer taken from an HCSR04
Commonly the Butterworth-van Dyke circuit model (left) is used for ultrasonic transducers, the same model is used for quartz crystal resonators, so the same analysis holds. At low frequencies the
inductor is effectively a short circuit resulting in a capacitive impedance (phase shift less than zero). At high frequencies the inductor is effectively an open circuit again resulting in a
capacitive impedance. Between the two the impedance is inductive (phase shift greater than zero). As the frequency increases there is a point of series resonance (slightly past) where the reactance
of C and L cancel resulting in minimum impedance. After that there is a point of parallel resonance close to one of maximum impedance. At resonance the impedance is purely resistive and the phase
shift is zero.
It is possible to fit the impedance curves using the Scipy general non-linear curve fitting library and determine the model parameters for transducers (code below). For the HCSR04 transmitter R=192 Ω
L=70 mH C=210 pF Cp=1464 pF and for the receiver R=252 Ω L=71 mH C=231 pF Cp=1525 pF. I have done this in a simple way only fitting the magnitude of the impedance, even so results for phase are not
[10] covers the contents of this page in a lot more detail from the view point of a researcher in the field.
Comparison of measurements and model for a transmit transducer taken from an HCSR04.
Data for a Murata MA40S4S (transmitter) obtained from a reputable source.
Again it is possible to fit the data and produce values for the model parameters and compare the model predictions with the data.
The Murata application note [9] for the MA40S4S/R shows the variation of impedance with frequency and gives parameters for the model. The measured impedance is similar to what I found, however the
model parameters are different, as a result the Murata model ones are not in good agreement with their own data.
The values I found are (with Murata application note in brackets) R=208(340) Ω, C= 293(300) pF, L= 51(48) mH, Cp= 1876(2150) pF.
The following graphic compares my data with the results of the Murata model.
All that fits the theory, but the following data does not. The results for the Murata MA40S3S/R show the receive and transmit transducer impedances are similar, out of line with the idea the receive
parallel resonance frequency matches the transmit series resonance frequency. References to MA40S3S/R are limited and I have not found a datasheet for it.
Murata MA40S3S (transmitter)
Murata MA40S3R (receiver)
Transducer supplied with a JSN-SR04T
The ultrasonic speaker found in devices for scaring pests like mice.
Page last modified on March 10, 2021, at 03:29 AM | {"url":"https://www.davidpilling.com/wiki/index.php/Transimp?setskin=adapt","timestamp":"2024-11-08T14:00:39Z","content_type":"text/html","content_length":"21803","record_id":"<urn:uuid:af5e5986-2896-4088-9ea6-edf63ad74ca6>","cc-path":"CC-MAIN-2024-46/segments/1730477028067.32/warc/CC-MAIN-20241108133114-20241108163114-00307.warc.gz"} |
Quantum theory of Manakov solitons
A fully quantum mechanical model of two-component Manakov solitons is developed in both the Heisenberg and Schrödinger representations, followed by an analytical, linearized quantum theory of Manakov
solitons in the Heisenberg picture. This theory is used to analyze the vacuum-induced fluctuations of Manakov soliton propagation and collision. The vacuum fluctuations induce phase diffusion and
dispersion in Manakov soliton propagation. Calculations of the position, polarization angle, and polarization state fluctuations show an increase in collision-induced noise with a decrease in the
relative velocity between the two solitons, as expected because of an increase in the interaction length. Fluctuations in both the polarization angle and state are shown to be independent of
propagation distance, opening up possibilities for communications, switching, and logic, exploiting these properties of Manakov solitons. Calculations of the phase noise reveal, surprisingly, that
the collision-induced fluctuations can be reduced slightly below the level of fluctuations in the absence of collision, due to cross-correlation effects between the collision-induced phase and
amplitude fluctuations of the soliton. The squeezing effect of Manakov solitons is also studied and proven, unexpectedly, to have the same theoretical optimum as scalar solitons.
All Science Journal Classification (ASJC) codes
• Atomic and Molecular Physics, and Optics
Dive into the research topics of 'Quantum theory of Manakov solitons'. Together they form a unique fingerprint. | {"url":"https://collaborate.princeton.edu/en/publications/quantum-theory-of-manakov-solitons","timestamp":"2024-11-04T15:49:30Z","content_type":"text/html","content_length":"51266","record_id":"<urn:uuid:56075c94-23d9-4c46-8355-6ccb1602e1a6>","cc-path":"CC-MAIN-2024-46/segments/1730477027829.31/warc/CC-MAIN-20241104131715-20241104161715-00402.warc.gz"} |
RSICC Home Page $
RSIC CODE PACKAGE CCC-215
1. NAME AND TITLE
TESS: Multigroup Discrete Ordinates Code System for Slab and Spherical Geometries.
TESS is an extension/modification of CCC-71/MIST.
2. CONTRIBUTOR
Argonne National Laboratory, Argonne, Illinois, through the Argonne Code Center (ACC Abstract 513).
FORTRAN IV; CDC 3600.
4. NATURE OF PROBLEM SOLVED
TESS provides the multigroup real and adjoint solutions to the transport equation in the S[n] approximation for one-dimensional slab and spherical geometry. Highly generalized boundary-condition
capabilities make the system quite suitable for photon-transport problems. Integrals of flux and adjoint for perturbation analysis can be calculated. Reaction rates may be computed for specified
isotopes as a function of space.
5. METHOD OF SOLUTION
A direct method of solution for each outer iteration is used for maximum efficiency in slowly converging problems. A double SN formulation in slab geometry, which allows the code to treat
discontinuities more efficiently in the angular flux at interfaces, yields more accurate results with fewer angles. TESS contains a sophisticated cross-section homogenization routine, which permits
cross-section collapse in both space and energy by six different prescriptionsthree by real flux weighting, and three by flux and adjoint weighting. In addition, two different methods of providing
for cell leakage make the code convenient for fast-reactor, critical-facility heterogeneity studies.
TESS permits a maximum of 150 mesh points, 26 groups, 20 angular intervals, 12 isotropic downscatter groups, 1 P1 downscatter group, 40 regions, 25 materials. There is no restriction on angles except
that they be symmetric about PI/2" (MU = 0). No upscatter is allowed.
7. TYPICAL RUNNING TIME
Approximately .5 millisecond is required (point-group-angular order squared) per iteration.
TESS is operable on the CDC 3600 computer, with 50K available storage and 10 tape units.
A FORTRAN IV compiler with a SCOPE 6,2114 operating system is required.
10. REFERENCES
a. Included in the documentation:
R. W. Goin and J. P. Plummer, "TESS, A One-Dimensional SN Transport-Theory Code for the CDC 3600," ANL 7406 (December 1971).
b. Background information:
G. E. Putnam and D. M. Shapiro, "MIST (Multigroup Internuclear Slab Transport)," IDO-16856 (May 1963).
11. CONTENTS OF CODE PACKAGE
Included are the referenced document (10.a) and one (1.2MB) DOS diskette which contains the source code and sample problem input.
12. DATE OF ABSTRACT
June 1973; updated July 1975. | {"url":"https://rsicc.ornl.gov/codes/ccc/ccc2/ccc-215.html","timestamp":"2024-11-13T17:48:19Z","content_type":"text/html","content_length":"5394","record_id":"<urn:uuid:e2d1b64a-a087-429a-8934-86a918b28dc0>","cc-path":"CC-MAIN-2024-46/segments/1730477028387.69/warc/CC-MAIN-20241113171551-20241113201551-00472.warc.gz"} |
【How-to】How many days a year are weekends - Howto.org
How many days a year are weekends
Ads by Google
How many weekend days are in an ordinary year?
How many days in the year 2021? As it is a common year, the 2021 calendar has 365 days. In the United States, there are 261 working days, 104 weekend days, and 10 federal holidays.
How much of the year is the weekend?
Mostly a year has 365 days ,but leap year has 366 days. That adds up to 52 weeks ( that each week has a 7 days ). Now if the year start on Saturday in non leap year then you end up to 53 Saturdays
and similarly if the year starts on Sunday in non leap year then you end up to 53 Sunday’s.
How many sat/sun in a year?
The beginning of the year 2021 was marked by Friday, January 1. There are a total of 52 Sundays in the year 2021. 2022 will also have a total of 52 Sundays, whereas 2023 will have 53 Sundays. Here is
the complete list of Sundays’ dates in the year 2021 for you to check.
How many days a year is Sunday?
There are exactly 52 Sundays in the year 2021. The answer to this question is not always simple. Most of the time, it will equal the number of weeks in a year, but that’s only true for some of the
days of the week. Most years have 365 days, but a leap year has 366 days.
How many weekends is 9 months?
Months to Weeks Conversion Table
Months Weeks
9 Months 39.1331 Weeks
10 Months 43.4813 Weeks
11 Months 47.8294 Weeks
12 Months 52.1775 Weeks
How many Fridays are in a year?
There are exactly 53 Fridays in the year 2021. The answer to this question is not always simple. Most of the time, it will equal the number of weeks in a year, but that’s only true for some of the
days of the week. Most years have 365 days, but a leap year has 366 days.
What is the shortest month?
Have you ever wondered why February is the shortest month of the year? If you take a look at your calendar, you’ll notice that February only has 28 days while the other months have 30 or 31 days.
Why are there 7 days in a week?
The Babylonians, who lived in modern-day Iraq, were astute observers and interpreters of the heavens, and it is largely thanks to them that our weeks are seven days long. The reason they adopted the
number seven was that they observed seven celestial bodies — the sun, the moon, Mercury, Venus, Mars, Jupiter and Saturn.
Is 2022 a leap year?
No – 2022 is not a leap year. The next leap year will be in 2024, which means the next leap day will be 29 February 2024. People born on February 29 may be known as a ‘leapling’ or ‘leaper’ and this
year will actually be able to celebrate their birthdays on Leap Day, as opposed to the day before or after.
Why is February named February?
February is named after an ancient Roman festival of purification called Februa. … The Roman calendar originally began in March, and the months of January and February were added later, after a
calendar reform.
Why do we have years?
A year is the amount of time it takes a planet to orbit its star one time. … It takes Earth approximately 365 days and 6 hours to orbit the Sun. It takes Earth approximately 24 hours — 1 day — to
rotate on its axis. So, our year is not an exact number of days.
Does a leap year have 365 days?
A year, occurring once every four years, which has 366 days including 29 February as an integral day is called a Leap year. 2021 is not a leap year and has 365 days like a common year. It takes
approximately 365.25 days for Earth to orbit around the Sun.
Which month has longest name?
This is *usually* asked as a trick question. The answer to that trick question is September. “September” has 9 letters, all the others have between 3 and 8. That makes it the “longest” month.
What was June named after?
June, sixth month of the Gregorian calendar. It was named after Juno, the Roman goddess of childbirth and fertility.
What does April mean as a name?
One is that the name is rooted in the Latin Aprilis, which is derived from the Latin aperire meaning “to open”—which could be a reference to the opening or blossoming of flowers and trees, a common
occurrence throughout the month of April in the Northern Hemisphere.
What month is the 1st?
January is the first month of the year in the Julian and Gregorian calendars and the first of seven months to have a length of 31 days. The first day of the month is known as New Year’s Day.
What is the world’s longest word?
The longest word in any of the major English language dictionaries is pneumonoultramicroscopicsilicovolcanoconiosis, a word that refers to a lung disease contracted from the inhalation of very fine
silica particles, specifically from a volcano; medically, it is the same as silicosis.
What US state has the most letters?
The official name for Rhode Island is actually “The State of Rhode Island and Providence Plantations”, which is 52 letters including spaces, or 45 without.
What happened on Jan 0001?
Originally Answered: What happened on January 1, 0001 AD? The Anno Domini system was invented in 540, attempting to date the birth of Jesus. And made a mistake of four years, so that Jesus was born
in 4BC, if the bible evidence is accurate.
What are the 12 months in order?
The names of the 12 months in order are January, February, March, April, May, June, July, August, September, October, November, and December.
What is the 12 month name?
Recall the names of the twelve months: January, February, March, April, May, June, July, August, September, October, November, and December.
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Unscramble ABACA
How Many Words are in ABACA Unscramble?
By unscrambling letters abaca, our Word Unscrambler aka Scrabble Word Finder easily found 7 playable words in virtually every word scramble game!
Letter / Tile Values for ABACA
Below are the values for each of the letters/tiles in Scrabble. The letters in abaca combine for a total of 9 points (not including bonus squares)
What do the Letters abaca Unscrambled Mean?
The unscrambled words with the most letters from ABACA word or letters are below along with the definitions.
• abaca (n.) - The Manila-hemp plant (Musa textilis); also, its fiber. See Manila hemp under Manila. | {"url":"https://www.scrabblewordfind.com/unscramble-abaca","timestamp":"2024-11-05T21:50:18Z","content_type":"text/html","content_length":"37289","record_id":"<urn:uuid:7ad86fa2-d981-484a-ab9f-5fa21af6b623>","cc-path":"CC-MAIN-2024-46/segments/1730477027895.64/warc/CC-MAIN-20241105212423-20241106002423-00885.warc.gz"} |
Probability of a Straight Flush and Royal Flush in Poker - Kobroadcasting
Probability of a Straight Flush and Royal Flush in Poker
This article will give you the Probability of a Straight Flush and Royal Flush in Texas Hold’em and Omaha. These hands have a high probability of being won. Also learn how to calculate the
probabilities of making a flush and straight in other poker games. This is very useful for making better poker decisions.
Probability of a Royal Flush
A Royal Flush in poker is a rare situation, but it can still occur. In fact, the chance of getting one of these cards is one in every four and a half hours. The probabilities are also higher if you
use the standard five card draw rule. A player with a perfect royal flush can win as much as 4,000 coins.
If you have five-cards, the odds of obtaining a royal flush are one in every thirty-nine thousand hands. Therefore, it is best to make sure you’re realistic about your odds. If the royal flush is
unlikely, then you should focus your efforts elsewhere. If the odds are high, however, you should try for it. In poker, it’s not impossible to get a royal flush, but you’ll need to play more hands to
get it.
Probability of a Straight Flush
To calculate the probability of a straight flush in poker, you can use a scientific calculator. Most scientific calculators have a function called nCr, which is used to calculate the probability of a
certain hand. Using a five-card hand from a standard 52-card deck, you can get the probability of getting a straight flush by dividing the number of straight flushes by the number of possible 5-card
The probability of a straight flush in Texas Hold’em is relatively low. A five-card poker hand has a 0.0279% chance of being a straight flush. If you have all five community cards on the board, the
odds of achieving a straight flush are even smaller than those of hitting a royal flush. However, a straight flush isn’t as hard to make as a royal flush. If you have a solid preflop strategy in
place, you’ll have the best chance of making a straight flush.
Probability of a Royal Flush in Texas Hold’em
The probabilities of hitting a Royal Flush in Texas Hold’Em are very low. Generally, the odds of a royal flush are one in every six hundred thousand hands. A royal flush is a high-card combination
with five cards in the same suit. A royal flush is not easy to make, so it’s important to understand the probabilities.
For example, the probability of a royal flush is 1 in 649,739 when there are three aces on the table. If one of these three cards is an ace, two other cards must match that ace. A royal flush can
also be formed from three jacks, tens, or queens. The odds of hitting a royal flush are also 1 in 649,739 if a player has a perfect play.
Probability of a Royal Flush in Omaha
The probabilities of a Royal Flush in Omaha poker are much different from those of Texas Hold’em. In Texas Hold’em, AA is a big favorite, but the same hand will not do as well in Omaha. A flush in
Omaha requires two cards of the same suit from the player’s hand and three cards on the board. This hand offers the player a significant advantage, but it is also a bluff. You should avoid bluffing
when playing Omaha.
A royal flush in Omaha poker is very difficult to achieve. In fact, only five out of nine players will play their hand all the way to the river. In order to get a royal flush in Omaha, you need two
suited ten-high cards. However, this hand is difficult to obtain because two-thirds of the players will fold their hand before the river. | {"url":"https://www.kobroadcasting.com/probability-of-a-straight-flush-and-royal-flush-in-poker/","timestamp":"2024-11-11T21:18:44Z","content_type":"text/html","content_length":"39851","record_id":"<urn:uuid:e6742856-892b-493d-b32e-1438c3d9c427>","cc-path":"CC-MAIN-2024-46/segments/1730477028239.20/warc/CC-MAIN-20241111190758-20241111220758-00395.warc.gz"} |
Structure's Formula Language (Expr)
Expr (pronounced like "expert" without the "t") is Structure’s formula language. It can be used in Formula Columns to perform calculations or comparisons based on issue fields, as well as in Sort
If you’ve ever created formulas in Excel or Google Sheets, some elements of Expr will look familiar. We tried to make it as similar to other spreadsheet formula languages as possible while still
allowing for more complex features, such as working with arrays or Jira item properties.
Learn Expr
Adding formulas to a structure
There are a few ways to add formulas to a structure:
The guides below will cover the main elements of formulas and how to use them.
Variables are used to represent values (numbers, text strings, arrays, etc.) within a formula and can represent:
• Jira issue fields
• Calculated attributes like Progress
• Structure-specific attributes like Item type
• Attributes provided by other Jira apps
• Another formula
• Values from another Structure column
Naming Variables
Variable names can contain:
• letters (English only)
• numbers
• underscore (_) characters
Variables cannot contain spaces. The first character must be a letter or an underscore.
• priority
• sprintName
• remaining_estimate
• abc11
As you write your formula, Structure attempts to map your variables to well-known sources. For example, the "remaining_estimate" variable above will automatically be mapped to the Remaining Estimate
field. If it can’t map the variable automatically, you will need to select a value for the variable.
Variable names are not case-sensitive. Priority, priority and pRiOrItY will all refer to the same variable.
Learn more: Mapping Variables, Predefined Variables
Property Access
Formulas can also access the value of an item's property using the following notation: object.property
fixVersion.releaseDate //returns the release date for the fixVersion
For a complete list of supported properties, see Item Properties.
Learn more: Expr Advanced Reference - Property Access
Local Variables
Local variables are similar to Variables, but they are defined locally within the formula, rather than being mapped to an attribute or Jira field. This can be helpful when an expression needs to be
used more than once in the same formula. Instead of repeating the expression, you can turn it into a local variable, using WITH :
WITH total_time = timeSpent + remainingEstimate :
IF total_time > 0 :
timeSpent / total_time
In this example, declaring a local variable “total_time” ensures that every instance of total_time is exactly the same, and if you ever need to change how total_time is calculated, you only have to
change it once.
Learn more: Expr Advanced Reference - Local Variables
Functions are predefined expressions that can be used within a formula. Functions calculate a value based on their arguments.
• A simple function formula: SUM(9, 3). This function takes the input values (9 and 3), adds them together, and returns a sum: 12.
• A more useful formula: SUM(-original_estimate, remaining_estimate, time_spent) By summing these values, you can see how far over your original estimate you’re tracking.
Function Calls
A function call is written as the function name, followed by parentheses, which may or may not contain arguments.
• SUM(-original_estimate, remaining_estimate, time_spent)
• CASE(priority, 'High*', 5, 1)
• TODAY()
Function names are not case-sensitive: you can write TODAY() or Today().
There are 100+ standard functions available with Structure – see Standard Functions for a complete list.
Function arguments may be separated by comma (,) or semicolon (;). But you need to be consistent: use either all commas or all semicolons.
Learn more: Expr Advanced Reference - Functions
Aggregate Functions
Aggregate functions calculate the total value from multiple rows within a structure. Unless otherwise specified, this includes the issue and all its sub-issues.
• SUM { remaining_estimate + time_spent } – calculates the total effort (estimated and actual) for the issue and all its sub-issues.
• MAX { resolved_date - created_date } – calculates the maximum time it took to resolve an issue, among the issue and its sub-issues.
Aggregate functions are written similar to standard functions, except they use curly braces: SUM{x}.
Local variables used inside an aggregate function must also be declared inside the function - within the { } .
For a complete list of available Aggregate functions, see: Aggregate Functions
To learn more about using Aggregate functions, see: Expr Advanced Reference - Aggregate Function
Aggregate Function Modifiers
Aggregate Functions can also contain modifiers, which influence how the aggregation works. Modifiers always begin with the hash sign (#) and are placed after the function name and before the first
curly brace:
• SUM#all { business_value } – this will force the function to include values from all duplicate items in the total. (By default, duplicates are ignored.)
Each aggregate function supports a specific set of modifiers, not all of them. Using an incompatible modifier will result in an error.
For a complete list of available Aggregate modifiers, see: Aggregate Functions
To learn more about using Aggregate functions and their modifiers, see: Expr Advanced Reference - Aggregate Function
Chained Function Calls
If you need to apply a sequence of functions to the same value, you can simplify this using the chained notation: listing each function one after the other, separated by a dot (.).
• Standard notation: Funciton3(Function2(Function1(x)))
• Chain notation: x.Function1().Function2().Function3()
When you use the chain notation, the value that comes before the dot becomes the first argument for the next function. Any additional arguments must be written after the function, in parentheses.
For example:
created.FORMAT_DATETIME("yyyy").CONCAT(" year issue")
In this example, FORMAT_DATETIME takes the date value in "created" and formats it based on the argument in parenthesis ("yyyy"). CONCAT takes the result from FORMAT_DATETIME and joins it with " year
User Functions
A user function allows you to define a locally-used function within a formula.
Local functions are declared using the following construct:
WITH function_name(argument) = operation_to_perform :
WITH square(x) = x * x :
square(impactField) / square(storyPoints)
Learn more: Expr Advanced Reference - User Functions
You can include arithmetic operations, comparisons, logical operations, and text operations within a formula.
Operations Comments
+ - * / Basic operators. Formulas follow the general precedence rules for arithmetic, so (2 + 3 * 4 = 14). When used, the value is converted to a number.
Equality and non-equality: if either part of the comparison is a number, the other part is also converted into a number. If both values are texts, then text comparison is used.
= !=
Text comparison ignores leading and trailing whitespace and is case-insensitive (according to Jira's system locale).
< <= > >= Numerical comparisons. When used, both values are converted to numbers.
AND, OR, NOT Logical operations.
CONCAT An operation that joins together two text strings. This works similar to the function of the same name: a CONCAT b is the same as CONCAT(a, b).
( ) Parentheses can be used to group the results of operations prior to passing them to another operation.
Learn more: Expr Advanced Reference - Operators.
Order of Operations
When several types of operations are used, they are done in the following order:
1. Arithmetic operations
2. Text operations (CONCAT)
3. Comparison operations
4. Logical operations.
Conditional Expressions (IF / ELSE)
Conditional expressions (IF/ELSE) can be used to switch between two or more expressions, based on whether specified conditions are true (truthy) or false.
A simple "IF" expression can be declared using the IF() function, but for more elaborate IF cases, with multiple conditions and/or requiring an ELSE option, a conditional expression can be used:
WITH total = x + y:
IF total > 0:
x / total
ELSE : error
The : after ELSE is optional – in the example above, we've included it for readability.
Learn more: Expr Advanced Reference - Conditional Expressions
The following number types are supported in Structure formulas:
• Whole numbers
• Decimals
• Fractions
The following elements are not supported:
• Commas
• Spaces
• Locale-specific
• Percentage
• Currency
• Scientific formats
Recognized as a number Not recognized as a number
0 0,0
1000 1,000
11.25 1.234e+04
.111 ($100)
If you need to use locale-specific decimals or thousand separators, write them as text values. Structure will convert it to a supported number:
Learn more: Expr Advanced Reference - Values and Types
Text values should be enclosed in single quotes (') or double quotes (").
• "Your text here!"
• 'Your text here!'
If the text value itself contains quotes, do one of the following:
• Insert a backslash (\) before each quote.
• Use one type of quote within the text, and another to enclose the text
Example: The following both represent represent the text value Charlie "Bird" Parker:
• "Charlie \"Bird\" Parker"
• 'Charlie "Bird" Parker'
Learn more: Expr Advanced Reference - Values and Types
Text Snippets
Text Snippets allow you to generate strings using variables and expressions. This is particularly helpful in formulas that utilize markdown.
When using text snippets:
• The snippet should start and end with three sets of double quotes (""")
• Variables names should be preceded by $
• Expressions should start with $ and be enclosed in braces { }
""" The sum of $var1 + $var2 = ${var1 + var2}. """
""" This $glass is half-${IF optimist: 'full' ELSE: 'empty'}. """
Learn more: Expr Advanced Reference - Values and Types
Comments can be added to a formula to provide context or an explanation of what is being calculated, without affecting the formula itself.
• To add a single line of comment, begin the comment with //
• To add multiple lines of comment, start the comment with /* and end the comment with */
// This is a single-line comment.
/* This is a multi-line comment.
It can be useful for longer explanations. */
Learn More
To learn more about the concepts discussed above, see: | {"url":"https://help.tempo.io/structure/latest/structure-s-formula-language-expr","timestamp":"2024-11-09T11:11:55Z","content_type":"text/html","content_length":"90825","record_id":"<urn:uuid:47ae14c1-65f0-45d4-acbe-51a192da1b32>","cc-path":"CC-MAIN-2024-46/segments/1730477028116.75/warc/CC-MAIN-20241109085148-20241109115148-00532.warc.gz"} |
HAS: Hasbro | Logical Invest
What do these metrics mean?
'The total return on a portfolio of investments takes into account not only the capital appreciation on the portfolio, but also the income received on the portfolio. The income typically consists of
interest, dividends, and securities lending fees. This contrasts with the price return, which takes into account only the capital gain on an investment.'
Using this definition on our asset we see for example:
• Looking at the total return, or performance of -18.1% in the last 5 years of Hasbro, we see it is relatively lower, thus worse in comparison to the benchmark SPY (101.5%)
• Compared with SPY (29.7%) in the period of the last 3 years, the total return of -21.7% is lower, thus worse.
'The compound annual growth rate isn't a true return rate, but rather a representational figure. It is essentially a number that describes the rate at which an investment would have grown if it had
grown the same rate every year and the profits were reinvested at the end of each year. In reality, this sort of performance is unlikely. However, CAGR can be used to smooth returns so that they may
be more easily understood when compared to alternative investments.'
Which means for our asset as example:
• Compared with the benchmark SPY (15.1%) in the period of the last 5 years, the annual return (CAGR) of -3.9% of Hasbro is lower, thus worse.
• During the last 3 years, the compounded annual growth rate (CAGR) is -7.9%, which is lower, thus worse than the value of 9.1% from the benchmark.
'Volatility is a statistical measure of the dispersion of returns for a given security or market index. Volatility can either be measured by using the standard deviation or variance between returns
from that same security or market index. Commonly, the higher the volatility, the riskier the security. In the securities markets, volatility is often associated with big swings in either direction.
For example, when the stock market rises and falls more than one percent over a sustained period of time, it is called a 'volatile' market.'
Which means for our asset as example:
• Compared with the benchmark SPY (20.9%) in the period of the last 5 years, the volatility of 36.7% of Hasbro is larger, thus worse.
• During the last 3 years, the volatility is 32.5%, which is higher, thus worse than the value of 17.6% from the benchmark.
'Risk measures typically quantify the downside risk, whereas the standard deviation (an example of a deviation risk measure) measures both the upside and downside risk. Specifically, downside risk in
our definition is the semi-deviation, that is the standard deviation of all negative returns.'
Using this definition on our asset we see for example:
• The downside deviation over 5 years of Hasbro is 25.8%, which is higher, thus worse compared to the benchmark SPY (14.9%) in the same period.
• During the last 3 years, the downside volatility is 22.9%, which is higher, thus worse than the value of 12.3% from the benchmark.
'The Sharpe ratio was developed by Nobel laureate William F. Sharpe, and is used to help investors understand the return of an investment compared to its risk. The ratio is the average return earned
in excess of the risk-free rate per unit of volatility or total risk. Subtracting the risk-free rate from the mean return allows an investor to better isolate the profits associated with risk-taking
activities. One intuition of this calculation is that a portfolio engaging in 'zero risk' investments, such as the purchase of U.S. Treasury bills (for which the expected return is the risk-free
rate), has a Sharpe ratio of exactly zero. Generally, the greater the value of the Sharpe ratio, the more attractive the risk-adjusted return.'
Applying this definition to our asset in some examples:
• Looking at the Sharpe Ratio of -0.17 in the last 5 years of Hasbro, we see it is relatively lower, thus worse in comparison to the benchmark SPY (0.6)
• Compared with SPY (0.37) in the period of the last 3 years, the Sharpe Ratio of -0.32 is smaller, thus worse.
'The Sortino ratio measures the risk-adjusted return of an investment asset, portfolio, or strategy. It is a modification of the Sharpe ratio but penalizes only those returns falling below a
user-specified target or required rate of return, while the Sharpe ratio penalizes both upside and downside volatility equally. Though both ratios measure an investment's risk-adjusted return, they
do so in significantly different ways that will frequently lead to differing conclusions as to the true nature of the investment's return-generating efficiency. The Sortino ratio is used as a way to
compare the risk-adjusted performance of programs with differing risk and return profiles. In general, risk-adjusted returns seek to normalize the risk across programs and then see which has the
higher return unit per risk.'
Using this definition on our asset we see for example:
• Compared with the benchmark SPY (0.84) in the period of the last 5 years, the ratio of annual return and downside deviation of -0.25 of Hasbro is smaller, thus worse.
• During the last 3 years, the excess return divided by the downside deviation is -0.45, which is smaller, thus worse than the value of 0.53 from the benchmark.
'Ulcer Index is a method for measuring investment risk that addresses the real concerns of investors, unlike the widely used standard deviation of return. UI is a measure of the depth and duration of
drawdowns in prices from earlier highs. Using Ulcer Index instead of standard deviation can lead to very different conclusions about investment risk and risk-adjusted return, especially when
evaluating strategies that seek to avoid major declines in portfolio value (market timing, dynamic asset allocation, hedge funds, etc.). The Ulcer Index was originally developed in 1987. Since then,
it has been widely recognized and adopted by the investment community. According to Nelson Freeburg, editor of Formula Research, Ulcer Index is “perhaps the most fully realized statistical portrait
of risk there is.'
Which means for our asset as example:
• The Ulcer Ratio over 5 years of Hasbro is 29 , which is greater, thus worse compared to the benchmark SPY (9.32 ) in the same period.
• Looking at Downside risk index in of 34 in the period of the last 3 years, we see it is relatively larger, thus worse in comparison to SPY (10 ).
'Maximum drawdown is defined as the peak-to-trough decline of an investment during a specific period. It is usually quoted as a percentage of the peak value. The maximum drawdown can be calculated
based on absolute returns, in order to identify strategies that suffer less during market downturns, such as low-volatility strategies. However, the maximum drawdown can also be calculated based on
returns relative to a benchmark index, for identifying strategies that show steady outperformance over time.'
Using this definition on our asset we see for example:
• Compared with the benchmark SPY (-33.7 days) in the period of the last 5 years, the maximum drop from peak to valley of -57.4 days of Hasbro is smaller, thus worse.
• Compared with SPY (-24.5 days) in the period of the last 3 years, the maximum DrawDown of -55 days is lower, thus worse.
'The Drawdown Duration is the length of any peak to peak period, or the time between new equity highs. The Max Drawdown Duration is the worst (the maximum/longest) amount of time an investment has
seen between peaks (equity highs) in days.'
Which means for our asset as example:
• Looking at the maximum days under water of 711 days in the last 5 years of Hasbro, we see it is relatively greater, thus worse in comparison to the benchmark SPY (488 days)
• Compared with SPY (488 days) in the period of the last 3 years, the maximum time in days below previous high water mark of 711 days is larger, thus worse.
'The Average Drawdown Duration is an extension of the Maximum Drawdown. However, this metric does not explain the drawdown in dollars or percentages, rather in days, weeks, or months. The Avg
Drawdown Duration is the average amount of time an investment has seen between peaks (equity highs), or in other terms the average of time under water of all drawdowns. So in contrast to the Maximum
duration it does not measure only one drawdown event but calculates the average of all.'
Using this definition on our asset we see for example:
• Compared with the benchmark SPY (123 days) in the period of the last 5 years, the average days below previous high of 266 days of Hasbro is larger, thus worse.
• Compared with SPY (177 days) in the period of the last 3 years, the average time in days below previous high water mark of 341 days is greater, thus worse. | {"url":"https://logical-invest.com/app/stock/has/hasbro","timestamp":"2024-11-04T11:35:18Z","content_type":"text/html","content_length":"61295","record_id":"<urn:uuid:3a48ecaa-f339-4f5e-8bb8-12f134784b95>","cc-path":"CC-MAIN-2024-46/segments/1730477027821.39/warc/CC-MAIN-20241104100555-20241104130555-00348.warc.gz"} |
Cross Product Calculator | Best Full Solution Steps
Fill in the input fields to calculate the solution.
Cross Product Lesson
What is the Cross Product?
The cross product of two vectors is a vector that is orthogonal (perpendicular) to both original vectors.
This means that a 90° angle can be drawn between the resultant vector and each of the original vectors. The magnitude of the resultant vector is equal to the area of the parallelogram that is
projected from the two original vectors.
The image below is a visualization of what a cross product resultant vector represents. When looking at the image, we might observe that the cross product is normal to the plane on which both
original vectors lie on.
The parallelogram lies flat on that plane, and the cross product vector's magnitude/length is equal to the area of the parallelogram.
A cross product tells us the normal direction and area of two vectors' projected parallelogram.
Why do we Learn About the Cross Product?
Since the cross product is needed for countless real-world physics and engineering applications, let's take a look at just one of these applications: controlling a space telescope's orientation to
point it at a celestial object of interest.
Instead of using thrusters that expel propellant, the Hubble Space Telescope uses special devices called reaction wheels for controlling its orientation with extreme precision and reliability.
The Hubble Space Telescope's Reaction Wheels And Sensors
Credit: NASA
A reaction wheel is a motorized wheel with substantial mass near its outer edges, allowing it to store large amounts of angular momentum while spinning. If a reaction wheel mounted on a space
telescope is spun up by its motor in a certain direction of rotation, the telescope will spin in the opposite direction of rotation as a result.
This is due to the law of conservation of momentum. The change in angular momentum of the telescope is equal in magnitude and opposite in direction to the change in angular momentum of the reaction
Now, why would we need the cross product for all of this? Well, the formula for angular momentum is given as:
L = r×p
Where L is the angular momentum vector, r is the position vector, p is the linear momentum vector, and the × between the position and momentum vectors denotes the cross product.
Once we have characterized the telescope's position vector and linear momentum vector, we may use the cross product to solve for the angular momentum of the telescope under various rotational motion
Finally, we can design the reaction wheel for optimal orientation authority, precision, and reliability by tweaking the reaction wheel's theoretical position vector and linear momentum vector,
solving for their cross product, and observing the output angular momentum in the context of the telescope's angular momentum.
How to Calculate the Cross Product
For a vector a = a[1]i + a[2]j + a[3]k and a vector b = b[1]i + b[2]j + b[3]k, the formula for calculating the cross product is given as:
a×b = (a[2]b[3] - a[3]b[2])i - (a[1]b[3] - a[3]b[1])j + (a[1]b[2] - a[2]b[1])k
To calculate the cross product, we plug each original vector's respective components into the cross product formula and then simplify the right side of the equation. The result will be a vector a×b =
c[1]i + c[2]j + c[3]k.
A set of two vectors must occupy three-dimensional space to have a cross product. However, a vector with one or two components of zero (such as a = 3i + 0j + 0k) is still considered to occupy
three-dimensional space.
This is because the nonzero components project them along a certain axis (one-dimensional) or plane (two-dimensional). For example, the vector a = 3i only has a component (3i) on the x-axis.
But, we may add a 0j and 0k term to it, resulting in the equivalent vector a = 3i + 0j + 0k, and can now use it as an original vector for a cross product.
Example Problem
$$& \text{1.) Calculate the cross product of the two vectors } \: \vec{a} \: \text{ and } \vec{b} \\ \\ & \hspace{3ex} \text{Where } \; \vec{a} = -1i +2j +4k \; \text{ and } \; \vec{b} = 2i -7j +11k\
\ \\ \\ & \text{2.) Using the cross product formula:} \\ \\ & \hspace{3ex} \vec{a} \times \vec{b} = [a_{2}b_{3} \: – \: a_{3}b_{2}]i \: – \: [a_{1}b_{3} \: – \: a_{3}b_{1}]j + [a_{1}b_{2} \: – \: a_
{2}b_{1}]k \\ \\ & \hspace{3ex} \text{Where } \: \vec{a} = a_{1}i + a_{2}j + a_{3}k \: \text{ and } \: \vec{b} = b_{1}i + b_{2}j + b_{3}k\\ \\ \\ & \text{3.) Plugging the vector components into the
cross product formula, we get:} \\ \\ & \hspace{3ex} \vec{a} \times \vec{b} = \left[ \left( 2\right) \left( 11\right) \: – \: \left( 4\right) \left( -7\right) \right] i \: – \: \left[ \left( -1\
right) \left( 11\right) \: – \: \left( 4\right) \left( 2\right) \right] j + \left[ \left( -1\right) \left( -7\right) \: – \: \left( 2\right) \left( 2\right) \right] k\\ \\ \\ & \text{4.) We will now
simplify that equation to get the final vector:} \\ \\ & \hspace{3ex} \vec{a} \times \vec{b} = \left[ \left( 22\right) \: – \: \left( - 28\right) \right] i \: – \: \left[ \left( - 11\right) \: – \: \
left( 8\right) \right] j + \left[ \left( 7\right) \: – \: \left( 4\right) \right] k\\ \\ & \hspace{3ex} \vec{a} \times \vec{b} = \left[ 50\right] i \: – \: \left[ - 19\right] j + \left[3\right] k \
hspace{1ex} \\ \\ & \hspace{3ex} \vec{a} \times \vec{b} = 50i + 19j + 3k$$
How the Calculator Works
The Voovers cross product calculator is written in the web programming languages HTML (HyperText Markup Language), CSS (Cascading Style Sheets), and JS (JavaScript). The HTML builds the calculator's
physical architecture, the CSS styles that architecture, and the JS adds all functionality to the calculator.
Your device's internet browser has a built-in JS engine that runs the code immediately when you click the calculate button. This allows for instant solutions and no waiting on the page to refresh.
The calculator's routine builds your inputted vector components into an array, essentially turning the inputs into JS vectors of sorts. The array is then fed to the cross product formula. The right
side of the resulting equation is simplified to get the output cross product vector.
Along the way, snapshots of the problem are saved as JS variables to be used in the solution steps. The solution and solution steps are formatted into LaTeX (a math equation rendering technology)
code and displayed in the solution box. | {"url":"https://www.voovers.com/algebra/cross-product-calculator/","timestamp":"2024-11-07T02:32:10Z","content_type":"text/html","content_length":"644644","record_id":"<urn:uuid:23db069c-3597-404c-afc1-d10d8d31591b>","cc-path":"CC-MAIN-2024-46/segments/1730477027951.86/warc/CC-MAIN-20241107021136-20241107051136-00246.warc.gz"} |
How High Will Shiba Inu Go In 2025? - ICO Urban
How High Will Shiba Inu Go In 2025?
4 min read
icourban.com – There, however, are two serious blockades. Trading beasts predicts a 43% increase by year and a whopping 87% increase by the end of. According to coin price forecast, shiba inu could
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$0.0000112489. However, as analysed earlier, the liquidity crash prevents a quick. Shiba inu coin’s 2030 predictions. Again, “how” shiba inu sustains its price by 2024 will make all the difference.
According to their calculations, the coin has. Shiba inu community’s logic behind $1 price. In terms of price, 2024 might prove to be the most stable year for shiba inu. Shiba inu price prediction
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Shiba Inu (SHIB) Coin Price Prediction for 2025 from marketrealist.com
Shiba inu coin’s 2025 predictions. A number of prediction websites. Shiba inu coin cost estimate by coinpriceforecast for 2025 is $0.00006, which is still not anything as high as the $0.27
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high as the predicted price for dogecoin in 2025 of.
Shiba inu prices may reach a new high this year, according to our shiba inu price projection. Shiba inu coin cost estimate by coinpriceforecast for 2025 is $0.00006, which is still not anything as
high as the $0.27 anticipated cost for dogecoin in that year. A changelly blogpost claimed that after studying shib prices and market fluctuations, experts predict that shib could go as high as.
Walletinvestor considers shiba inu to be a profitable investment. Shiba inu coin’s 2025 predictions. The aforementioned changelly blogpost additionally talked about that in 2030, shib shall be traded
at a mean worth of $0.00030921. However, according to coinpedia’s formulated shiba inu price prediction.if the bulls barge in, then shib might hit feasible highs of $0.000017 by the end of 2022.
Shiba Inu Price Prediction 2022.
According to the technical analysis of shiba inu prices expected in 2022, the minimum cost of shiba inu will be $0.0000112489. What will be the shiba inu price by 2024? Shib coin is predicted to
touch ₹0.019 by the end of 2024. A number of prediction websites. The price of shiba (shib), according to coin price forecast, is expected to rise from $0.00124938 at the beginning of 2025 to. The
saudi shiba inu price value can reach a maximum of $0.00000000 with the average trading value of $0.00000000 in usd. Shiba inu price prediction 2022.
However, according to coinpedia’s formulated shiba inu price prediction.if the bulls barge in, then shib might hit feasible highs of $0.000017 by the end of 2022. The price of shiba (shib), according
to coin price forecast, is expected to rise from $0.00124938 at the beginning of 2025 to. However, as analysed earlier, the liquidity crash prevents a quick. The circulation supply of shiba inu
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Accounting for Managers
Learning Outcomes
• Describe a constrained resource in retail business
A constrained resource is something that you have a limited amount of. In a manufacturing business it may be machine time, labor hours or raw materials. Whenever there is a constrained resource, as a
manager, you need to determine the best way to use the limited (constrained) resource to bring the most money to your net profit (bottom line).
So you are the manager of a small retail clothing store. You have 1000 square feet of space to use for inventory (excluding walkways, register area and fitting rooms), and you need to use it in the
most effective manner to create the best net income for your store.
You have the following inventory:
• Jeans: Each pair contributes $40 to net income and you can get two in one square foot of space.
• Shirts: Each shirt contributes $10 to the net income, but you can get five in one square foot of space.
If your entire store was jeans you would have 2,000 pair of jeans contributing $40 per pair or $80,000 to your net income.
If your entire store was shirts, you would have 5,000 shirts each contributing $10 or $50,000 to your net income.
How would you stock your store? Well, if you were simply looking at using your space to maximize net income, and you thought jeans would work by themselves, you would stock it with jeans right?
What else may you want to look at in your retail space? Perhaps for every pair of jeans you sell, you also sell two shirts. Is one more difficult to prepare for sale? Maybe shirts need to be pressed
and hung, while jeans are simply folded on a shelf.
There are many things to think about when you stock a small retail store, with space constraints you will need to experiment with the best product mix!
So what if our constrained resource is manufacturing space or time? How do we figure out the best usage of a constrained resource? We obviously want to use that resource to generate the most profit
for the company.
Let’s go back and look at two pairs of shoes made by Hupana. The Runner and the Slogger.
│ │The Runner│The Slogger │
│ Selling price per unit │125 │100 │
│ Variable cost per unit │55 │55 │
│Contribution margin per unit │70 │45 │
│ Contribution margin ratio │56% │45% │
If we just look at the contribution margin, it looks like the Runner is contributing more to the net income, right?
But let’s look a little further at this. The Runner, take 40 minutes of machine time to produce, and the Slogger only take 30. The machine can run for 1,200 minutes per day.
So with that information, the machine can make 30 pair of the Runner per day, but can make 40 pair of the Slogger.
Market analysis says we could sell 20 pair of the Runner each day, and 30 pair of the Slogger, which would be a total number of machine minutes of
• The Runner= 40 minutes x 20 pair = 800 minutes
• The Slogger= 30 minutes x 30 pair = 900 minutes
So we have demand that would use 1,700 minutes of machine time, but our machine can only run 1,200 minutes a day. What do we do? This machine is our bottleneck in the process, so we need to dig
deeper yet to decide how to best use our machine time. We need to figure out the contribution margin per minute of machine time for each pair of shoes!
│ │The Runner│The Slogger│
│ Contribution margin per unit │$70.00 │$45.00 │
│ Machine time to complete │$40.00 │$30.00 │
│Contribution margin per minute │$1.75 │$1.50 │
(CM per unit/machine time to complete)
So which pair should we make first to maximize our profit? The Runner—we can use the first 800 minutes to make 20 pair of Runners. This will leave us with 400 minutes to make Sloggers, so we can make
13 pair before we run out of machine time.
We won’t meet the total demand for our shoes, but we will maximize our profits using our machine in the most cost effective way, within the constraints.
What might be another option? Since our demand is high, we could buy another machine or we could raise our prices! That is a whole different calculation for another day.
So, now, what if some parts of your process can produce higher output than another? This is called a bottleneck, and is another constrained resource.
A bottleneck happens when one machine can’t keep up with the one before it. Or it might be a process in a service business that holds up the rest of the process. A bottleneck is essentially the step
that limits total output because it has the smallest capacity. Essentially, a bottleneck could be called a constrained resource, right?
Let’s look at a dental office. The front desk staff might be able to make 100 appointments per day, but if you only have dentists to see 20 patients per day, and dental hygienists to see another 30
per day, you have a bottleneck. The office will not be able to get past the 50 patient per day total, no matter how hard they try.. We identified the weakest link in the chain at the dental office,
as patients the dentist can see in a day.
We can’t put more strain on the system than this weakest link can handle, so we need to make sure the office staff is not making more appointments!
Let’s look at a machine example. If you have five machines, and each one does a task, you might have a chain that looks like this:
Where is your constraint? Well, in this example it is right at the beginning of the process right? The cutting and stitching machines can only accommodate 10 pair of shoes per hour, even though the
lacing, trimming, inspecting and boxing could handle more. How could you fix this problem? You could add an additional machine at each the cutting and stitching phase of the process. You could look
for newer, faster equipment. Or, you could just move at the pace of the constrained resource.
The bottleneck might occur at other areas of the process. Then you, as a manager, would need to decide which approach to take. Another option would be to outsource the task of the constrained
resource. In the case of our shoes, you might outsource the cutting and stitching to another company, and then finish the rest on your equipment. There are options to fix a bottleneck, and the
solution will depend on your individual business needs. | {"url":"https://courses.lumenlearning.com/wm-accountingformanagers/chapter/constrained-resources-in-retail/","timestamp":"2024-11-11T06:43:33Z","content_type":"text/html","content_length":"54979","record_id":"<urn:uuid:28fbf0fd-07dc-4a7e-bcdd-dfff9ef48138>","cc-path":"CC-MAIN-2024-46/segments/1730477028220.42/warc/CC-MAIN-20241111060327-20241111090327-00190.warc.gz"} |
Перевод computing matrix с английского на русский
• 1 computing matrix
• 2 computing matrix
English-Russian big polytechnic dictionary > computing matrix
• 3 computing matrix
Большой англо-русский и русско-английский словарь > computing matrix
• 4 computing matrix
• 5 computing matrix
• 6 computing matrix
• 7 computing matrix
English-Russian dictionary of computer science and programming > computing matrix
• 8 matrix
• 9 matrix
English-Russian dictionary of computer science and programming > matrix
• 10 computing
• 11 computing-machine circuit
English-Russian dictionary of Information technology > computing-machine circuit
• 12 nitridic matrix
English-Russian dictionary on nuclear energy > nitridic matrix
• 13 distributed-object computing
English-Russian dictionary of Information technology > distributed-object computing
• 14 digital computing circuit
• 15 ferroresonant computing circuit
The English-Russian dictionary general scientific > ferroresonant computing circuit
• 16 вычислительная матрица
Большой англо-русский и русско-английский словарь > вычислительная матрица
• 17 system
• 18 system
English-Russian dictionary of mechanical engineering and automation > system
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English-Russian dictionary of computer science and programming > system
• 20 circuit
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Members: 3658
Articles: 2'599'751
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03 November 2024
Article overview
Uniformly Weighted Star-Factors of Graphs
Yunjian Wu ; Qinglin Yu ;
Date: 2 Jul 2007
Abstract: A {it star-factor} of a graph $G$ is a spanning subgraph of $G$ such that each component of which is a star. An {it edge-weighting} of $G$ is a function $w: E(G)longrightarrow mathbb{N}^
+$, where $mathbb{N}^+$ is the set of positive integers. Let $Omega$ be the family of all graphs $G$ such that every star-factor of $G$ has the same weights under a fixed edge-weighting
$w$. In this paper, we present a simple structural characterization of the graphs in $Omega$ that have girth at least five.
Source: arXiv, arxiv.0707.0227
Services: Forum | Review | PDF | Favorites
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Note: answers to reviews or questions about the article must be posted in the forum section.
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Physical Chemistry: A Molecular Approach (McQuarrie, Donald A - PDF Free Download
Chemical Education Today edited by
Edward J. Walsh Allegheny College Meadville, PA 16335
Physical Chemistry: A Molecular Approach Donald A. McQuarrie and John D. Simon. University Science Books: Sausalito, CA, 1997. xxiii + 1270 pp. Figs and tables. 10.28 × 7.27 × 2.34 in. ISBN
0-935702-99-7. $80.00.
This book will not appeal to traditionalists. Those willing to take a fresh look at the subject, however, will find this well-executed text an attractive alternative. Most undergraduate physical
chemistry textbooks begin with thermodynamics, then proceed to quantum chemistry and finally to statistical thermodynamics and kinetics. This structure derives from the classic textbooks such as
Physical Chemistry by Alberty and Silbey, which traces its origin to the Outline of Theoretical Chemistry written by Herbert Getman in 1913 when thermodynamics was the core of physical chemistry and
quantum mechanics was in its infancy. Occasional authors have tried to deviate from this orthodoxy. I learned my undergraduate physical chemistry from the solid textbook written in 1964 by a
University of Washington team: Eggers, Gregory, Halsey, and Rabinovitch. That text opens with quantum mechanics, as does the elegant and sophisticated book by Berry, Rice, and Ross. None of these
books has been very successful, however, partly because they challenge tradition in a pedagogically conservative profession. McQuarrie and Simon are the latest authors to write a book that recognizes
that modern physical chemistry is based on quantum mechanics and that it makes pedagogical sense to begin with the atomic and molecular perspective and use it to build a firm understanding of
macroscopic phenomena. The result is impressive. The first half of the book, 15 chapters and approximately 600 pages, develops a modern perspective on quantum mechanics and its applications including
NMR, computational quantum chemistry, and lasers and laser spectroscopy. Chapter 1 is the customary historical introduction, which unfortunately repeats many of the errors of textbook histories. That
quibble aside, the material is developed carefully and systematically, beginning with a consideration of classical waves. The prose is clean and serviceable (though not inspired), and the book is
well illustrated with appropriate diagrams and graphs. I only wish the publisher had used heavier paper so the type on the reverse side of the page could not be seen. All teachers of physical
chemistry struggle with mathematics. Many students have either forgotten or never learned the necessary mathematical concepts and techniques. McQuarrie and Simon offer a solution in the form of ten
“MathChapters”—brief, self-contained reviews of relevant mathematical topics, including problems. The MathChapters
appear immediately before they are needed to develop the scientific topic. Both students and faculty should find these chapters helpful. Following the extensive development of quantum chemistry is a
nice chapter on the properties of gases. I was pleased to see discussions of both the Redlich–Kwong equation (the best two-parameter equation of state for real gases) and the relationship of the
second virial coefficient to intermolecular forces. Thermodynamics is then developed from a molecular perspective beginning with the Boltzmann factor and partition functions. Much of this treatment
clearly draws heavily on McQuarrie’s excellent and popular textbook on statistical thermodynamics. In the subsequent exposition of classical thermodynamics the authors effectively use the molecular
basis they have developed. This is a real strength of this book; students will develop a deep understanding of the power of statistical thermodynamics. To keep the size of the book manageable,
McQuarrie and Simon have eliminated several traditional applications of thermodynamics. There are no chapters on solution thermodynamics and activities, electrochemistry, or the phase rule. The book
continues with an exposition of chemical kinetics. A nice treatment of the kinetic theory of gases is followed by chapters on rate laws, reaction mechanisms, and gas-phase reaction dynamics. The
final chapter is on solids and surface chemistry. As in all physical chemistry textbooks, there is an extensive set of problems following each chapter. Most are standard “pencil-and-paper” problems,
but others require the use of computer programs such as MathCad or Mathematica or a spreadsheet program. With almost universal access to powerful personal computers, students can explore complicated
applications of the principles of physical chemistry. This is a challenging book in several ways. Although it is clearly written, the level of sophistication is high so students will not find it
easy. It is definitely a chemist’s book, so students from fields such as chemical engineering or geology will find it less friendly than many of the standard texts. Because it challenges the
traditional organization and coverage of the undergraduate physical chemistry course, many faculty will not give it serious consideration. That would be a mistake. McQuarrie and Simon have developed
an excellent modern physical chemistry course that should inspire us to rethink our curriculum. Jeffrey Kovac Department of Chemistry University of Tennessee Knoxville, TN 37996-1600
JChemEd.chem.wisc.edu • Vol. 75 No. 5 May 1998 • Journal of Chemical Education | {"url":"https://datapdf.com/physical-chemistry-a-molecular-approach-mcquarrie-donald-a.html","timestamp":"2024-11-08T18:41:24Z","content_type":"text/html","content_length":"30803","record_id":"<urn:uuid:bcd5900e-adf8-403f-be50-b7daf2a7ad48>","cc-path":"CC-MAIN-2024-46/segments/1730477028070.17/warc/CC-MAIN-20241108164844-20241108194844-00156.warc.gz"} |
McGraw Hill Math Grade 2 Chapter 7 Lesson 7 Answer Key Identifying Equal Parts of Circles
Practice questions available in McGraw Hill Math Grade 2 Answer Key PDF Chapter 7 Lesson 7 Identifying Equal Parts of Circles will engage students and is a great way of informal assessment.
McGraw-Hill Math Grade 2 Answer Key Chapter 7 Lesson 7 Identifying Equal Parts of Circles
Make Equal Parts
Question 1.
Draw lines to divide the circle into fourths.
I drew 2 lines in the circle to divide into fourths.
Question 2.
Color the circle that is divided into halves.
I colored the circle that is divided into halves that is 2 parts.
Question 3.
Which circle shows thirds? Draw a box around it.
I drew a box around the first circle
It shows thirds that is 3 parts.
Question 4.
Color half of the circle green. Color a fourth of the circle red.
In the above circle i colored half of the circle green that is 2 parts
I colored fourth of the circle red that is 1 parts of 4 parts.
Leave a Comment
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Simplifying Complex Fractions
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Complex Fractions
Equivalent Fractions
Review of Fractions Paubaume Posted: Monday 01st of Jan 10:24
Adding Fractions Algebrator is a splendid software. All I had to do with my problems with equation properties, y-intercept and decimals was to merely type
Fractions in the problems; click the ‘solve’ and presto, the answer just popped out step-by-step in an easy manner. I have done this to problems in
Equivalent Fractions Pre Algebra, Intermediate algebra and Algebra 1. I would boldly say that this is just the solution for you.
Questions About Fractions
Adding Fractions & Mixed Numbers Registered:
Adding fractions using the Least 18.04.2004
Common Denominator From: In the stars...
Introduction to fractions where you left me,
EQUIVALENT FRACTIONS and where I will wait
MULTIPLY TWO OR MORE FRACTIONS for you... always...
Simplifying Fractions
Multiplying and Dividing Fractions
Multiplying Fractions DoubniDoom Posted: Monday 01st of Jan 21:04
Multiplying and Dividing Fractions Now I would surely want to try this thing myself. Where can I get my copy? Can someone please help me in purchasing this software?
Introduction to Fractions
Simplifying Fractions by Multiplying
by the LCD
molbheus2matlih Posted: Tuesday 02nd of Jan 08:17
Thanks for the details . I have bought the Algebrator from https://mathfraction.com/multiplying-and-dividing-fractions.html and I happened
to go through lcf yesterday. It is pretty cool and very much readable . I was attracted by the descriptive explanations offered on
converting decimals. Rather than being test preparation oriented, the Algebrator aims at educating you with the basic principles of
Algebra 1. The money back guarantee and the unimaginable discounts that they are currently offering makes the purchase particularly
Registered: attractive.
From: France
malhus_pitruh Posted: Tuesday 02nd of Jan 16:25
I remember having difficulties with linear equations, adding functions and hyperbolas. Algebrator is a really great piece of math
software. I have used it through several algebra classes - Algebra 1, Remedial Algebra and Remedial Algebra. I would simply type in the
problem and by clicking on Solve, step by step solution would appear. The program is highly recommended.
From: Girona,
Catalunya (Spain)
Home Simplifying Complex Fractions Fractions Complex Fractions Fractions, Ratios, Money, Decimals and Percent Fraction Arithmetic Fractions Worksheet Teaching Outline for Fractions Fractions Section
5 Fractions In Action Complex Fractions Fabulous Fractions Reducing Fractions and Improper Fractions Fraction Competency Packet Fractions LESSON: FRACTIONS ADDING FRACTIONS Complex Fractions
Fractions, Ratios, Money, Decimals and Percent Converting Fractions to Decimals and the Order of Operations Adding and Subtracting Fractions Complex Fractions Equivalent Fractions Review of Fractions
Adding Fractions Fractions Equivalent Fractions Questions About Fractions Adding Fractions & Mixed Numbers Adding fractions using the Least Common Denominator Introduction to fractions EQUIVALENT
FRACTIONS MULTIPLY TWO OR MORE FRACTIONS Simplifying Fractions Multiplying and Dividing Fractions ADDITION OF FRACTIONS Multiplying Fractions Multiplying and Dividing Fractions Introduction to
Fractions Simplifying Fractions by Multiplying by the LCD
Author Message
OG3mt42 Posted: Friday 29th of Dec 08:45
Hello Math Gurus! I am a novice at parabola online calcuator. I seem to understand the lectures in the class well, but when I begin to solve the questions at home myself, I
commit errors . Does anyone know of any website where I can get my solutions checked before submitting them for grading? Or any resource where I can get to see a step by step
Registered: G3N-C|
From: /
AllejHat Posted: Sunday 31st of Dec 10:35
Can you give some more details about the problem? I can help you if you explain what exactly you are looking for. Recently I came across a very useful software program that
helps in solving math problems easily . You can get help on any topic related to parabola online calcuator , so I recommend trying it out.
From: Odense, Denmark
Paubaume Posted: Monday 01st of Jan 10:24
Algebrator is a splendid software. All I had to do with my problems with equation properties, y-intercept and decimals was to merely type in the problems; click the ‘solve’ and
presto, the answer just popped out step-by-step in an easy manner. I have done this to problems in Pre Algebra, Intermediate algebra and Algebra 1. I would boldly say that this
is just the solution for you.
From: In the stars...
where you left me,
and where I will wait
for you... always...
DoubniDoom Posted: Monday 01st of Jan 21:04
Now I would surely want to try this thing myself. Where can I get my copy? Can someone please help me in purchasing this software?
molbheus2matlih Posted: Tuesday 02nd of Jan 08:17
Thanks for the details . I have bought the Algebrator from https://mathfraction.com/multiplying-and-dividing-fractions.html and I happened to go through lcf yesterday. It is
pretty cool and very much readable . I was attracted by the descriptive explanations offered on converting decimals. Rather than being test preparation oriented, the Algebrator
aims at educating you with the basic principles of Algebra 1. The money back guarantee and the unimaginable discounts that they are currently offering makes the purchase
particularly attractive.
From: France
malhus_pitruh Posted: Tuesday 02nd of Jan 16:25
I remember having difficulties with linear equations, adding functions and hyperbolas. Algebrator is a really great piece of math software. I have used it through several
algebra classes - Algebra 1, Remedial Algebra and Remedial Algebra. I would simply type in the problem and by clicking on Solve, step by step solution would appear. The program
is highly recommended.
From: Girona,
Catalunya (Spain)
Posted: Friday 29th of Dec 08:45
Hello Math Gurus! I am a novice at parabola online calcuator. I seem to understand the lectures in the class well, but when I begin to solve the questions at home myself, I commit errors . Does
anyone know of any website where I can get my solutions checked before submitting them for grading? Or any resource where I can get to see a step by step solution?
Posted: Sunday 31st of Dec 10:35
Can you give some more details about the problem? I can help you if you explain what exactly you are looking for. Recently I came across a very useful software program that helps in solving math
problems easily . You can get help on any topic related to parabola online calcuator , so I recommend trying it out.
Posted: Monday 01st of Jan 10:24
Algebrator is a splendid software. All I had to do with my problems with equation properties, y-intercept and decimals was to merely type in the problems; click the ‘solve’ and presto, the answer
just popped out step-by-step in an easy manner. I have done this to problems in Pre Algebra, Intermediate algebra and Algebra 1. I would boldly say that this is just the solution for you.
Posted: Monday 01st of Jan 21:04
Now I would surely want to try this thing myself. Where can I get my copy? Can someone please help me in purchasing this software?
Posted: Tuesday 02nd of Jan 08:17
Thanks for the details . I have bought the Algebrator from https://mathfraction.com/multiplying-and-dividing-fractions.html and I happened to go through lcf yesterday. It is pretty cool and very much
readable . I was attracted by the descriptive explanations offered on converting decimals. Rather than being test preparation oriented, the Algebrator aims at educating you with the basic principles
of Algebra 1. The money back guarantee and the unimaginable discounts that they are currently offering makes the purchase particularly attractive.
Posted: Tuesday 02nd of Jan 16:25
I remember having difficulties with linear equations, adding functions and hyperbolas. Algebrator is a really great piece of math software. I have used it through several algebra classes - Algebra 1,
Remedial Algebra and Remedial Algebra. I would simply type in the problem and by clicking on Solve, step by step solution would appear. The program is highly recommended. | {"url":"https://mathfraction.com/fraction-simplify/adding-exponents/parabola-online-calcuator.html","timestamp":"2024-11-07T08:59:47Z","content_type":"text/html","content_length":"90930","record_id":"<urn:uuid:247c82f6-58a9-4a72-81f2-865c193e20d8>","cc-path":"CC-MAIN-2024-46/segments/1730477027987.79/warc/CC-MAIN-20241107083707-20241107113707-00888.warc.gz"} |
expected closed_term error after typechecking
@Enrico Tassi
builtin coq.env.add-const: 2th argument: expected closed_term: got [...]
How can this happen when we typecheck the term first?
The elaboration should be able to fill the holes, what am I missing?
closed term means no evars and no "free" variables. Are you under a pi x\ decl x ty => ... ?
typechecking can be performend under a context, while addition to the environment no.
@Enrico Tassi oops, I missed your answers... I definitely have evars (elpi variables X34 or something) that should be unified for typechecking to succeed (and it does succeed), but the evars stay.
Should I reexamine (one more time) my belief that these evars are constrained by typechecking or could I be missing something else?
It can also be a bug, maybe Coq's type checker assigns it and my code does not bring the assignment to Elpi (in some very remote case, since we use that all over the place).
If you pass -debug to coqtop then elpi prints much more stuff, including the embeddnig/readback of terms... It's not "super clear" but this is what I would do to start the investigation.
Maybe just write there the result of std.spy(coq.typecheck ....).
:joy_cat: if I pass -debug to coqc I get a Error: Anomaly "Uncaught exception Not_found."
oops. And before it? No print?
oh yes, lots of stuff are printed...
That I'm not sure how to decipher
I cannot spot the place where typechecking is called
cf https://github.com/math-comp/hierarchy-builder/pull/81
In the current status, the culprits are X5 and X6...
running make on that branch reproduces the bug?
Enrico Tassi said:
running make on that branch reproduces the bug?
it should
I've to go now, but I can debug it tomorrow probably
Cyril Cohen said:
In the current status, the culprits are X5 and X6...
In file readme.v, They are supposed to be the type of two mixins that appear in the rest of the term (c6 and c1), so the term should not typecheck without filling those...
The complaining coq.env.add-const is line 894 of hb.elpi and the potentially guilty typechecking is line 893
[long explanation ahead, for the records; you can skip to the very last piece of text to see the actual problem]
There was a silly debug print raising errors, I'll push a fix in master. With that solved, here the term received by add-const:
lp2term: out=(fun (A : Type) (m : AddComoid_of_Type.axioms_ A)
(s : AddComoid.type)
(_ : @unify Type Type A (AddComoid.sort s) nomsg)
(class : AddComoid.axioms A)
(_ : @unify AddComoid.type AddComoid.type s
(AddComoid.Pack A class) nomsg)
(m0 : AddComoid_of_Type.axioms_ A)
(_ : @unify (?e8@{A:=A; m0:=m; m:=A} m0)
(?e10@{A:=A; m0:=m; m:=A} m0) m0 m nomsg)
(opp : forall _ : A, A)
(addNr : forall x : A,
@eq (AddComoid.sort (A_is_a_AddComoid A m))
(@add (A_is_a_AddComoid A m) (opp x) x)
(@zero (A_is_a_AddComoid A m))) =>
Axioms_ A m opp addNr)
And here the link between Elpi and Coq holes. The holes are named ?e8 and ?e10, their number in Coq is ?X16 and ?X18 which are mapped to Elpi's X16 and X17 (FTR in Coq evars can have names, and the
ones linked with elpi are called e something).
?X16 <-> X16
?X18 <-> X17
?X19 <-> X33
?X22 <-> X35
Then the Coq evar map (and all its extra contents):
?X22==[A m0 m |- Type] (domain of ?X17) {?T0}
?X19==[A m0 m |- Type] (domain of ?X15) {?T}
?X18==[A m0 m |- forall _ : ?T0, Type] (internal placeholder) {?e10}
?X16==[A m0 m |- forall _ : ?T, Type] (internal placeholder) {?e8}
?X23==[A m0 m x |- Type => Type] (codomain of ?X17)
?X20==[A m0 m x |- Type => Type] (codomain of ?X15)
?X17==[A m0 m |- Type => forall _ : ?T0, Type] (internal placeholder)
?X15==[A m0 m |- Type => forall _ : ?T, Type] (internal placeholder)
?X14==[A m class |- Type => AddComoid.type] (internal placeholder)
?X13==[A m class |- Type => Type] (internal placeholder)
?X12==[A m class |- Type => AddComoid.type] (internal placeholder)
?X11==[A m class |- Type => Type] (internal placeholder)
?X10==[A m s |- Type => Type] (internal placeholder)
?X9==[A m s |- Type => Type] (internal placeholder)
?X8==[A m s |- Type => Type] (internal placeholder)
?X7==[A m s |- Type => Type] (internal placeholder)
UNIVERSES: <cut>
ALGEBRAIC UNIVERSES: <cut>
UNDEFINED UNIVERSES: <cut>
What is problematic is that Coq's type checker (Coq unification actually did not solve the following constraints):
CONSTRAINTS:[] [A m s unif_struct class unif_arbitrary m0] |-
AddComoid_of_Type.axioms_ A <= ?X19@{__:=A; __:=m; __:=A}
[] [A m s unif_struct class unif_arbitrary m0] |-
AddComoid_of_Type.axioms_ A <= ?X22@{__:=A; __:=m; __:=A}
[] [A m s unif_struct class unif_arbitrary m0] |-
AddComoid_of_Type.axioms_ A <= ?X16@{__:=A; __:=m; __:=A} m0
[] [A m s unif_struct class unif_arbitrary m0] |-
AddComoid_of_Type.axioms_ A <= ?X18@{__:=A; __:=m; __:=A} m0
It's a bug in Coq-Elpi not to call the "right" API to force their resolution, or fail, since these are not really visible in Elpi and I still have to wrap my mind around unification constraints (too
many things are broken if you suspend unification, totally unlike suspending typing). So the "right" way to call Coq's type checker is to force it to solve things. There is a clear API for calling
unification and enforce that, for typing it is not there so I need to find the right API to call on the resulting evar map.
Looking and these unification problems, they are suspended because they are not in the pattern fragment. A occurs twice, for example. I've no clue if this is really needed, I guess your code puts too
many variables in scope (the original term seems to suggest so). I guess forcing Coq to solve this will result in type checking failure.
I'll come back to this in the afternoon, but the fix in Coq-Elpi is probably not solving the problem you see (but make it more explicit, eg type check failure)
Fun fact, the printing error is also caused by the uncommon app [X a b c, d] (eg ?X16 has 3 arguments + an extra one which is OK, from a typing perspective, since it is a function. But also not so
common, since unification typically assigns to it a \lambda for the extra argument and obtain the more canonical X' a b c d.
With the bugfix I finally see the type checking error:
elpi: mk-phant-abbrev: T illtyped :
In environment
A : Type
m0 : AddComoid_of_Type.axioms_ A
m : AddComoid_of_Type.axioms_ _UNBOUND_REL_4
Unable to unify "AddComoid_of_Type.axioms_ _UNBOUND_REL_4" with
File "./readme.v", line 21, characters 0-126:
Which shows another bug, since the proof context is wrong. I'll dig deeper.
It's a bug in Coq-Elpi, when the Elpi unification variables is "restricted" (some stuff is not in scope) and occurs deep in a term, its context is computed wrongly
It's getting late and I cannot even work around the bug, the new code for phant- abbrevs is hard. My guess is that the current code works if the variables are all in scope (eg X c0 c1 ... cn) while
the code for phant leaves some binders out, the one for unif_struct for example, and this triggers a bug I will try to solve next week. I tried to rework the code not to "prune" some variables, but I
got lost. @Cyril Cohen if you manager, you may still be able to continue on your new branch. If not, I'll try to fix the code for generating a Coq evar out of a random elpi unif variable with some
missing names in scope. I fixed some problems but not all of them.
@Enrico Tassi I resumed working and successfully elaborated the term fully myself. It is a shame since it requires a few more decl directives to micro-manage typechecking here and there but it is ok
overall and the overhead is not too awful. However, I encountered another problem of the same nature but for which I cannot do anything... reproducing it by hand in Coq works, while doing in Elpi
fails, and this time I believe no workaround is possible :crying_cat: cf https://github.com/math-comp/hierarchy-builder/pull/81/files#diff-c8f066ba20fb2fadcb124dd6596484d5R69-R76 (running make in the
branch new-phant-abbrev will take you there)
Are you going to be in the office or joinable via skype this week?
Enrico Tassi said:
Are you going to be in the office or joinable via skype this week?
today until 18:00 and tomorrow until 15:30 (we have a meeting in the morning AFAIR)
Cyril Cohen said:
Enrico Tassi I resumed working and successfully elaborated the term fully myself. It is a shame since it requires a few more decl directives to micro-manage typechecking here and there but it is
ok overall and the overhead is not too awful. However, I encountered another problem of the same nature but for which I cannot do anything... reproducing it by hand in Coq works, while doing in
Elpi fails, and this time I believe no workaround is possible :crying_cat: cf https://github.com/math-comp/hierarchy-builder/pull/81/files#diff-c8f066ba20fb2fadcb124dd6596484d5R69-R76 (running
make in the branch new-phant-abbrev will take you there)
@Enrico Tassi this was indeed a mistake of mine, and it is fixed!!!!
See https://github.com/math-comp/hierarchy-builder/pull/92 (which requires https://github.com/LPCIC/coq-elpi/pull/160 )
Even if the new code you wrote does not trigger this bug, I looked at it and ended up cleaning up the code a bit and as a byproduct we can now also get rid of the super ugly hack we had to do in
order to "refresh" unification variables (it is now an option to coq-elpi's API)
I tried to comment/explain the option, but I believe the doc is not very good. Comments welcome.
Last updated: Oct 13 2024 at 01:02 UTC | {"url":"https://coq.gitlab.io/zulip-archive/stream/237868-Hierarchy-Builder-devs-.26-users/topic/expected.20closed_term.20error.20after.20typechecking.html","timestamp":"2024-11-12T06:24:56Z","content_type":"text/html","content_length":"33161","record_id":"<urn:uuid:dee733f4-dee8-4553-8ade-5332839c7219>","cc-path":"CC-MAIN-2024-46/segments/1730477028242.58/warc/CC-MAIN-20241112045844-20241112075844-00388.warc.gz"} |