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posted by .
there are 5 whole numbers in a data set. the least number is 14 and the greatest number is 25. the mean and median are both 19.what numbers could be the values in the data set?
i got:
14 19 25.
I do not know how to get the other two missing numbers in the data set? Please advice me.
• math -
well, if you have 5 numbers whose mean is 19, then they must add up to 5*19 = 95
Your sum so far is 58
So, you need two more numbers which add up to 37. Since your median is 19, you need one less than 19 and one greater than 19.
14 17 19 20 25
You can surely find other pairs which also work.
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http://www.mathworks.com/matlabcentral/answers/85304-optimization-where-both-objective-and-non-linear-constraint-are-functions-of-a-function?requestedDomain=www.mathworks.com&nocookie=true | 1,477,455,149,000,000,000 | text/html | crawl-data/CC-MAIN-2016-44/segments/1476988720615.90/warc/CC-MAIN-20161020183840-00359-ip-10-171-6-4.ec2.internal.warc.gz | 569,625,965 | 13,774 | ## Optimization Where Both Objective and Non-Linear Constraint are Functions of a Function
on 22 Aug 2013
### Alan Weiss (view profile)
I am considering an optimization where both the objective and non-linear constraint and functions of a function, such as (excluding some details):
```f = @(w,Y) Y*w;
g = @(w,Y) mean(f(w,Y));
h = @(w,Y) var(f(w,Y));
obj_con = @(w,Y) -g(w,Y);
nonl_con = @(w,Y) deal(h(w,Y)-K,[]);
```
```options = optimset('Algorithm','active-set');
```
```out = fmincon(@(x) obj_con(x,Y),x0,[],[],Aeq,beq,lb,ub,@(x) nonl_con(x,Y),options);
```
I have purposefully made this simpler than what I actually plan to do to get the general point across (in particular, f and h will be more complicated and the optimization may take place with functions other than fmincon).
Using the Matlab profiler, I determined that the function f is called twice at each iteration of the optimization (once for g and once for h).
Is there any way to set up the optimization of the functions so that it is only called once?
One approach I am not interested in is to remove f and make the calculation within g and h. That still does not resolve the issue of having to make such a calculation twice.
## Products
### Alan Weiss (view profile)
on 22 Aug 2013
Objective and Nonlinear Constraints in the Same Function has the information you seek.
Alan Weiss
MATLAB mathematical toolbox documentation
ss4johnny Hall
### ss4johnny Hall (view profile)
on 22 Aug 2013
This looks great. Cheers.
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Thanks for it.
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No voting included on this video?
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Bumped for review.
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Hello from the GMAT Club MBAbot!
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Re: Best MBA Application Tips from GMAT Club Members [#permalink] 23 Jun 2017, 15:30
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• Oct 21st 2008, 08:33 AM
Tim28
Reshaping plane geometry forms;congruent triangles
A rectangle could be reshaped into a parallelogram. Could a triangle be reshaped? I don't think so. What forms could be reshaped without tearing? Maybe this is algebraic topology; reshaping a doughnut into a coffee cup.
I mention congruent triangles because that is the context. I like to think that SSS, ASA, SAS uniquely determine a triangle.
• Oct 22nd 2008, 01:40 AM
HallsofIvy
Quote:
Originally Posted by Tim28
A rectangle could be reshaped into a parallelogram. Could a triangle be reshaped? I don't think so. What forms could be reshaped without tearing? Maybe this is algebraic topology; reshaping a doughnut into a coffee cup.
I mention congruent triangles because that is the context. I like to think that SSS, ASA, SAS uniquely determine a triangle.
What do you mean by "reshaping". From your reference to "topology" you might be allowing any continuous deformation- bending lines,etc.. In that case, any polygon can be reshaped to any other, or to a circle.
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# Epidemiologist: In Brazil, schistosomiasis and malaria are
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Re: Epidemiologist: In Brazil, schistosomiasis and malaria are [#permalink]
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14 Jan 2018, 04:21
Very tough..IMO OA is A
In my case, I was confused between A and E
This is my reasoning
A. Over the past five years, the percentage of infectious disease cases caused by schistosomiasis has remained unchanged, but the percentage of cases caused by malaria has increased substantially.
-> Keep
B. Trends in infectious disease data tend to persist for decades, unless there is a major breakthrough in treatment regimens.
-> 'treatment regimens' : Out of scope
C. Five years ago, many more people died from schistosomiasis than died from malaria.
-> incorrect.
Let's suppose malaria is more fatal than schistomiasis. Then we do not need to think about the percentage.
D. Over the past five years, the percentage of infectious disease cases caused by malaria was not significantly greater than the percentage of cases caused by schistosomiasis.
-> Incorrect. This is just a fact.
E. Over the past five years, the percentage of infectious disease cases caused by diseases other than malaria and schistosomiasis did not increase substantially.
-> Keep
I chose A, because let's suppose there is another disease C.
If the percentage of C is 90%, then E can weaken the passage.
But in A, for example, the percentage of schistosomiasis was always 50%, but the percentage of malaria was changed suddenly
,for example, 5% to 50%(Because schistosomiasis was always 50%), it can strengthen the passage.
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Re: Epidemiologist: In Brazil, schistosomiasis and malaria are [#permalink]
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15 Jan 2018, 03:55
HG0815 wrote:
Very tough..IMO OA is A
In my case, I was confused between A and E
This is my reasoning
A. Over the past five years, the percentage of infectious disease cases caused by schistosomiasis has remained unchanged, but the percentage of cases caused by malaria has increased substantially.
-> Keep
B. Trends in infectious disease data tend to persist for decades, unless there is a major breakthrough in treatment regimens.
-> 'treatment regimens' : Out of scope
C. Five years ago, many more people died from schistosomiasis than died from malaria.
-> incorrect.
Let's suppose malaria is more fatal than schistomiasis. Then we do not need to think about the percentage.
D. Over the past five years, the percentage of infectious disease cases caused by malaria was not significantly greater than the percentage of cases caused by schistosomiasis.
-> Incorrect. This is just a fact.
E. Over the past five years, the percentage of infectious disease cases caused by diseases other than malaria and schistosomiasis did not increase substantially.
-> Keep
I chose A, because let's suppose there is another disease C.
If the percentage of C is 90%, then E can weaken the passage.
But in A, for example, the percentage of schistosomiasis was always 50%, but the percentage of malaria was changed suddenly
,for example, 5% to 50%(Because schistosomiasis was always 50%), it can strengthen the passage.
C cannot be 90% since two most common infectious diseases are malaria and schistosomiasis.
(E) is irrelevant since we are comparing malaria vs schistosomiasis increase. What happened to the number of others is immaterial.
We see that number of schistosomiasis cases has increased substantially. If the percentage of infectious disease cases caused by schistosomiasis has remained same, but the percentage of cases caused by malaria has increased substantially but still in actual number terms, the number of cases of schistosomiasis is the same, it could mean that the initial percentage of schistosomiasis cases was more.
Say if x% cases were of schistosomiasis 5 yrs ago and y% of malaria, assuming that the percentage of cases of schistosomiasis remains constant, when will they account for most of the new disease cases? The number of new cases of schistosomiasis will be x% of the additional number of total cases. They will be majority of the new cases if x > 50%.
Hence (A) works.
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Re: Epidemiologist: In Brazil, schistosomiasis and malaria are [#permalink]
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16 Jan 2018, 01:42
srishti201996 wrote:
mikemcgarry GMATNinja VeritasPrepKarishma
Can you please shed more light on D?
Karishma you gave the following explanation :
D. Over the past five years, the percentage of infectious disease cases caused by malaria was not significantly greater than the percentage of cases caused by schistosomiasis.
This says that % of malaria cases was not much greater (though perhaps a little greater) than % of schistosomiasis cases over the past 5 years. If anything, this weakens our conclusion. It indirectly implies that out of 100 cases 5 yrs ago, malaria cases were slightly more than schistosomiasis cases.
Can you please tell me if my understanding of this is correct?
Say there were 100 cases 5 years ago!
51%-M - 51 cases
49%-S- 49 cases
so S cases were less than M but since now S is the cause of most cases, S would have increased over time.
But we can't say S was greater 5 years ago?
Am i right?
If schistosomiasis has been primarily responsible for the overall increase in infectious disease cases over the past 5 years and we want to conclude that there must have been more cases of schistosomiasis 5 years ago, we need to say that percentage of schistosomiasis cases has either remained same or decreased slightly.
Only then , if today too they are majority in number in the extra cases, they must have been majority in number 5 years back too.
So (A) works.
Let's look at (D).
Over the past five years, the percentage of infectious disease cases caused by malaria was not significantly greater than the percentage of cases caused by schistosomiasis.
(D) says that percentage of malaria cases was not significantly greater than percentage of schistosomiasis cases. We actually want the percentage of schistosomiasis cases to be higher than those of malaria over the past 5 yrs so that majority of extra cases are of schistosomiasis. So option (D) does not work.
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Re: Epidemiologist: In Brazil, schistosomiasis and malaria are [#permalink]
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16 Jan 2018, 17:38
srishti201996 wrote:
mikemcgarry GMATNinja VeritasPrepKarishma
Can you please shed more light on D?
Karishma you gave the following explanation :
D. Over the past five years, the percentage of infectious disease cases caused by malaria was not significantly greater than the percentage of cases caused by schistosomiasis.
This says that % of malaria cases was not much greater (though perhaps a little greater) than % of schistosomiasis cases over the past 5 years. If anything, this weakens our conclusion. It indirectly implies that out of 100 cases 5 yrs ago, malaria cases were slightly more than schistosomiasis cases.
Can you please tell me if my understanding of this is correct?
Say there were 100 cases 5 years ago!
51%-M - 51 cases
49%-S- 49 cases
so S cases were less than M but since now S is the cause of most cases, S would have increased over time.
But we can't say S was greater 5 years ago?
Am i right?
Dear srishti201996,
I'm happy to respond.
My friend, context is everything. The prompt says, "Over the past five years, schistosomiasis has been primarily responsible for the overall increase in infectious disease cases." That's evidence. That means that when we look at the total number of new cases of infectious disease, schistosomiasis accounts for well over 50% of them. If the number new cases of malaria were anything close, anything comparable, to the number of new cases of schistosomiasis, then this statement would be false. To say one thing is primarily responsible is to say that all other things combined are, in aggregate, not as powerful, not as influential, as that one thing. This is absolutely crucial to keep in mind with this argument.
Choice (D) directly contradicts this piece of evidence.
D. Over the past five years, the percentage of infectious disease cases caused by malaria was not significantly greater than the percentage of cases caused by schistosomiasis.
If about the same number of people had one or the other, then it would be patently false to say that only schistosomiasis was "primarily responsible for the overall increase in infectious disease cases."
This directly contradicts the evidence in the prompt. That's not the sign of a good strengthener!
Does this make sense?
Mike
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Re: Epidemiologist: In Brazil, schistosomiasis and malaria are [#permalink]
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19 Oct 2018, 18:48
Premise - Schist has been primarily responsible for the infectious disease.
Conclusion - the number of Schist case may be greater than the number of Mala case.
This is a typical % vs # question.
A is clearly not good enough. Although Schist % could remain unchanged, there is no promise that the change in Mala % won't go beyond the final Schist %. And please note, Schist and Mala are two "common" diseases but not the "only" diseases. So there are other infectious diseases. Let's say that 5 years ago, Schist had 40%, Mala had 35%, and other together had 25%. Option A can easily goes to a situation that after 5 years, Schist still has 40% but Mala has 45%, and the other together has 15%. In this situation, Option A won't strengthen the argument. And to make it strengthen, you will have to make additional (out of scope) assumption that Mala's % won't go beyond Schist's %.
The good answer is B. There is no answer here that is good enough to address the # so purely working on the % is the only way. B tells us that the data trend has been like this for so long, making the case that Schist was the major player 5 years ago very convincing. Imagine, if Schist was the major play and the trend barely changed, then of course we could be so sure that Schist was definitely primarily responsible.
Same logic - Bill Gates was the richest. If the richman ranking has been unchanged for so long. Of course Bill Gates had more money than the others, no doubt.
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Re: Epidemiologist: In Brazil, schistosomiasis and malaria are [#permalink]
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21 Oct 2018, 02:28
thelosthippie wrote:
Epidemiologist: In Brazil, schistosomiasis and malaria are the two most common infectious diseases. Over the past five years, schistosomiasis has been primarily responsible for the overall increase in infectious disease cases. Therefore it is likely that there were more cases of schistosomiasis than malaria five years ago.
Which of the following most strengthens the argument above?
A. Over the past five years, the percentage of infectious disease cases caused by schistosomiasis has remained unchanged, but the percentage of cases caused by malaria has increased substantially.
B. Trends in infectious disease data tend to persist for decades, unless there is a major breakthrough in treatment regimens.
C. Five years ago, many more people died from schistosomiasis than died from malaria.
D. Over the past five years, the percentage of infectious disease cases caused by malaria was not significantly greater than the percentage of cases caused by schistosomiasis.
E. Over the past five years, the percentage of infectious disease cases caused by diseases other than malaria and schistosomiasis did not increase substantially.
Epidemiologist: In Brazil, schistosomiasis and malaria are the two most common infectious diseases. Over the past five years, schistosomiasis has been primarily responsible for the overall increase in infectious disease cases. Therefore it is likely that there were more cases of schistosomiasis than malaria five years ago.
Understand :
1) S and M are most common [ ie. if there are 100 cases of infec diseases , S and M account for more than 50 (S+M>50%)
2)S is the major contributor for the INCREASE for IDs
Conclusion: FIVE YEARS AGO - number of cases of S>M ( note : NUMBER OF CASES)
Prethinking :
let cases with scisht = S
Cases with malaria = M
other cases = O
Therefore : S+M+O =100
New cases =50
S= 30 (assumed as per given info as S is MAJOR contributor for INCREASE)
M= 15( assumed as per given info as S and M both are MOST COMMON so M will still be GREATER than OTHER cases
O=5
Conclusion : before the increase S>M
Do not try to prethink here as there will be 3 cases which you would have to test in order to concur with the conclusion
A. Over the past five years, the percentage of infectious disease cases caused by schistosomiasis has remained unchanged, but the percentage of cases caused by malaria has increased substantially.
: Now as per given ans choice the percentage of cases 5 years ago and over past 5 years is the SAME and percentage of M has inreased (Note: percentage is given and not numbers)
5 years ago : no. of Schiest = S
suppose S account for (x) percent for all cases.--- S= (x)/100 * total cases (100) ........ (1)
over past 5 yrs : total number of sciest cases : S+30
As per A : S+30 = (x)/100 * new total cases (150)........ (2)
Therefore : substitute value of (x)/100 from (1) in (2)
S+30= S/100 *150
Solve for S >> S=60
Therefore , M has to be less than or equal to 40 but cannot be greater than 40..... Therfore the conclusion = S>M
Re: Epidemiologist: In Brazil, schistosomiasis and malaria are &nbs [#permalink] 21 Oct 2018, 02:28
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Sum Of Error Squared
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It's really not important in getting Ward's method to work in SPSS. The mean and standard deviation are calculated as in the previous lesson, but we will expand the statistical terminology in this discussion. THIS IS THE WEBSITE FOR YOU! The number "2" in the equation is not a measured quantity, so it is treated as error-free, or exact. http://comunidadwindows.org/sum-of/sum-squared-error.php
Ben Lambert 19.120 görüntüleme 4:08 Finding the SSE with a Ti 83:84 - Süre: 10:48. The fractional determinate error in Q is 0.028 - 0.0094 = 0.0186, which is 1.86%. Cell 3 combines with cells 8 & 17 (which were already joined at stage 3). It's easiest to first consider determinate errors, which have explicit sign. https://en.wikipedia.org/wiki/Residual_sum_of_squares
Sum Of Squares Error Calculator
However, in most applications, the sampling distribution can not be physically generated (too much work, time, effort, cost), so instead it is derived theoretically. The ordinary least squares estimator for β {\displaystyle \beta } is β ^ = ( X T X ) − 1 X T y . {\displaystyle {\hat {\beta }}=(X^{T}X)^{-1}X^{T}y.} The residual Column B represents the deviation scores, (X-Xbar), which show how much each value differs from the mean. Ward's paper. 2.
Sıradaki Regression I: What is regression? | SSE, SSR, SST | R-squared | Errors (ε vs. For example, a body falling straight downward in the absence of frictional forces is said to obey the law: [3-9] 1 2 s = v t + — a t o Back at the first stage (the zeroth stage being individual cells) this means that the two closest cells in terms of (usually) squared Euclidean distance will be combined. Regression Sum Of Squares The means of each of the variables is the new cluster center.
C1 C2 y Sum of Squares 2.40 41.5304 4.60 2.50 1.60 2.20 0.98 NoteMinitab omits missing values from the calculation of this function. Sum Of Squared Errors Example The underlying mathematics is that of "finite differences," an algebra for dealing with numbers which have relatively small variations imposed upon them. You can also use the sum of squares (SSQ) function in the Calculator to calculate the uncorrected sum of squares for a column or row. https://hlab.stanford.edu/brian/error_sum_of_squares.html Sysmex XN 2000 Sigma-metric analysis of the Sysmex XN 2000 Hematology Analyzer NEW!
It is fundamental to the use and application of parametric statistics because it assures that - if mean values are used - inferences can be made on the basis of a Residual Sum Of Squares Formula But for those not familiar with calculus notation there are always non-calculus strategies to find out how the errors propagate. In Eqs. 3-13 through 3-16 we must change the minus sign to a plus sign: [3-17] f + 2 f = f s t g [3-18] Δg = g f = It is therefore likely for error terms to offset each other, reducing ΔR/R.
Sum Of Squared Errors Example
One drawback is that the error estimates made this way are still overconservative. Kapat Daha fazla bilgi edinin View this message in English YouTube 'u şu dilde görüntülüyorsunuz: Türkçe. Sum Of Squares Error Calculator Let fs and ft represent the fractional errors in t and s. Sum Of Squared Errors Excel Show how the SD is calculated from the variance and SS.
The following worksheet shows the results from using the calculator to calculate the sum of squares of column y. get redirected here This can also be rearranged to be written as seen in J.H. Column C shows the squared deviations which give a SS of 102. This refers to the fact that the values computed from a sample will be somewhat different from one sample to the next. Total Sum Of Squares
John Wiley. Converting the sum of squares into mean squares by dividing by the degrees of freedom lets you compare these ratios and determine whether there is a significant difference due to detergent. If all cases within a cluster are identical the SSE would then be equal to 0. navigate to this website Using this style, our results are: [3-15,16] Δg Δs Δt Δs Δt —— = —— - 2 —— , and Δg = g —— - 2g —— g s t s
It can tell you how good a measuring instrument is needed to achieve a desired accuracy in the results. Sum Of Squared Residuals Calculator the relative error in the square root of Q is one half the relative error in Q. Therefore, the sampling distribution can be calculated when the SD is well established and N is known.
In this way an equation may be algebraically derived which expresses the error in the result in terms of errors in the data.
The fractional error in the denominator is 1.0/106 = 0.0094. UsernamePassword Remember me Forgot login?Register What's New Guizhou Provincial People's Hospital Laboratory INVITRO Sigma Verification of Performance Analytical Bias Exceeds Desirable Quality Goals in 4 of 5 common Immunoassays Analysis of The fractional error may be assumed to be nearly the same for all of these measurements. Sum Of Squared Residuals Formula It can suggest how the effects of error sources may be minimized by appropriate choice of the sizes of variables.
Remember that Column A represents the means of the 12 samples of 100 which were drawn from the large container. Continuing in the example; at stage 2 cells 8 &17 are joined because they are the next closest giving an SSE of 0.458942. Variance. my review here Mathematically it is the square root of SS over N; statisticians take a short cut and call it s over the square root of N.
The mean of the sampling distribution is always the same as the mean of the population from which the samples were drawn. Let SS (A,B,C, A*B) be the sum of squares when A, B, C, and A*B are in the model. She holds BS, MAT and EdD degrees from the University of Louisville, has taken other advanced course work from the School of Medicine and School of Education, and also advanced courses Let's calculate the mean for these twelve "mean of 100" samples, treating them mathematically much the same as the prior example that illustrated the calculation of an individual mean of 100
Using similar notation, if the order is A, B, A*B, C, then the sequential sums of squares for A*B is: SS(A, B, A*B) - SS(A, B) Depending on the data set Then the error in any result R, calculated by any combination of mathematical operations from data values x, y, z, etc. In the operation of division, A/B, the worst case deviation of the result occurs when the errors in the numerator and denominator have opposite sign, either +ΔA and -ΔB or -ΔA For cells described by more than 1 variable this gets a little hairy to figure out, it's a good thing we have computer programs to do this for us.
Unlike the corrected sum of squares, the uncorrected sum of squares includes error. Zady. | 1,629 | 6,758 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4 | 4 | CC-MAIN-2017-47 | longest | en | 0.899213 |
https://inhomestudent2019.com/how-to-determine-increasing-and-decreasing-intervals-on-a-graph-ideas-hack-2022 | 1,653,225,275,000,000,000 | text/html | crawl-data/CC-MAIN-2022-21/segments/1652662545548.56/warc/CC-MAIN-20220522125835-20220522155835-00237.warc.gz | 371,196,686 | 19,638 | # How To Determine Increasing And Decreasing Intervals On A Graph Ideas Hack 2022
How To Determine Increasing And Decreasing Intervals On A Graph Ideas Hack 2022. Using a graph to determine where a function is increasing, decreasing, or constant. Our new production has increased by more than m, so we have increasing returns to scale.
The constant functions are functions that are simultaneously increasing and decreasing (they stay constant). With a graph, or with derivatives. Graph the function (i used the graphing calculator at desmos.com).
Table of Contents
### The First Step Is To Find The First Derivative.
Using a graph to determine where a function is increasing, decreasing, or constant. If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. Example 1 for the following function identify the intervals where the function is increasing and decreasing and the intervals where the function is concave up and concave down.
### Let’s Take A Look At An Example Of That.
It must be a decreasing graph and a function. There are many ways in which we can determine whether a function is increasing or decreasing but w. The function f ( x) = x 2 is a decreasing function in the interval ( − ∞, 0] and increasing in [ 0, + ∞).
### For F(X) = X 4 − 8 X 2 Determine All Intervals Where F Is Increasing Or Decreasing.graphing Rational Functions With Holes.graphs And Models And Graphing Calculator Manual Package (5Th Edition) Edit Edition.identify The Vertex (Peak Point).
This is an easy way to find. If f′(x) > 0, then f is increasing on the interval, and if f′(x) < 0, then f is decreasing on the interval. For a function, y = f (x) to be increasing d y d x ≥ 0 for all such values of interval (a, b) and equality may hold for discrete values.
### Not All Graphs Are Functions, So Just Because A Graph Has A Downward Slope Does Not Mean That It’s A Decreasing Function.
As a result, we have constant returns to scale. H(x) = 3×5−5×3+3 h ( x) = 3 x 5 − 5 x 3 + 3. How to determine increasing and decreasing intervals on a graph.
### We Say That A Function Is Increasing On An Interval If The Function Values Increase As The Input Values Increase Within That Interval.
The constant functions are functions that are simultaneously increasing and decreasing (they stay constant). We say that a function is increasing on an interval if the function values increase as the input values increase within that interval. Again, we increase both k and l by m and. | 585 | 2,529 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.125 | 4 | CC-MAIN-2022-21 | latest | en | 0.805799 |
https://essaygraph.com/essay/the-optimum-windmill-efficiency-essay-20894 | 1,660,264,989,000,000,000 | text/html | crawl-data/CC-MAIN-2022-33/segments/1659882571536.89/warc/CC-MAIN-20220811224716-20220812014716-00067.warc.gz | 255,163,755 | 17,082 | # The Optimum Windmill Efficiency Essay
Published: 2020-02-24 22:01:51
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Windmills convert the wind into either mechanical or electrical energy. If the efficiency of the windmill can be increased, then the need for expensive, polluting, power generators will be reduced. As a result, we would be helping the environment and economy at the same timeThe study that power is directly affected by the angles and/or the number of blades on a windmill and to determine the optimum efficiency for a windmill designThe blade angles: I have predicted that as the angle lowers the obvious reaction to the wind would be more surface areas and thus the more power the wind mill as more wind is striking more of the blades.
The countersuit being that the larger the angles become the less surface areas and thus the windmill produces less power. . Number of blades: According to my own knowledge I predict that the more blades added to the wind mill will produce more power as there is more surface area for the wind to contact. My hypothesis was that the blade angles and also the number of blades would affect the power of a windmill as either variable is increased. This experiment proves my hypothesis correct in saying that more blades and the lower the angle is the more efficient the windmill will be.
As suspected the 4 blades turned out to produce almost double the power (0. 04 W) than the 2 blades did (0. 02 W). This observation has annotations that power is directly proportional to the number of blades but however the results can not only be dependant upon this as too few variations of trials were tested for a rounded, fair result. For the blade angles there was quite a obvious result that the 30i?? produced the highest power (0. 020 W) and quite a substantial difference of 0. 012 W, at (0. 08 W) for the 70i?? angle.
Limitations of the experiment would be that there was not a variation of shape of the blade and change of material. The wind speed and direction was another factor as this was not held constant during the trails. These factors if tweaked slightly could affect the results vastly. The measuring devices used could have been more precise. The wind speed and direction could have been kept constant by fixing the hairdryer in place at a certain angle and distance always from blades for fair results. Varying the blades shapes and material would give a better understanding and a more supporting experiment to prove the hypothesis with.
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This essay has been submitted by a student and contain not unique content | 641 | 3,001 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.90625 | 3 | CC-MAIN-2022-33 | latest | en | 0.952521 |
http://stackoverflow.com/questions/19017419/how-to-make-a-simple-public-key-cryptographic-algorithm?answertab=oldest | 1,405,056,195,000,000,000 | text/html | crawl-data/CC-MAIN-2014-23/segments/1404776425626.86/warc/CC-MAIN-20140707234025-00052-ip-10-180-212-248.ec2.internal.warc.gz | 118,894,644 | 17,699 | # How to make a simple public-key cryptographic algorithm? [closed]
I want to make a simple public-key(asymmetric) encryption. It doesn't have the be secure, I just want to understand the concepts behind them. For instance, I know simple symmetric ciphers can be made with an XOR. I saw in a thread on stackexchange that you need to use trapdoor functions, but I can't find much about them. I want to say, take a group of bytes, and be able to split them someway to get a public/private key. I get the ideas of a shared secret. Say, I generate the random number of 256(not random at all :P), and I split it into 200 and 56. If I do an XOR with 200, I can only decrypt with 200. I want to be able to split numbers random and such to be able to do it asymmetrically.
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## closed as off-topic by GregS, Jonathon Reinhart, madth3, Soner Gönül, RDCSep 26 '13 at 7:35
• This question does not appear to be about programming within the scope defined in the help center.
If this question can be reworded to fit the rules in the help center, please edit the question.
I just want to know how it works, I don't have any uses for encryptions. All of the stuff online explain the outer-shell, but not the generation, etc, of public-key systems. – user2507230 Sep 26 '13 at 0:38
This question appears to be off-topic because it is about crypto theory. – GregS Sep 26 '13 at 0:39
You need to do some reading about crypto. Get a good book. You can't possibly expect to learn the fundamentals of PK crypto on a site dedicated to specific programming problems. – Jonathon Reinhart Sep 26 '13 at 0:41
OK, just simple demo-idea, based on adding/modulto operation.
1. Lets we have modulto value, for our example 256. This is public-known, common value.
2. Lets you generate random secret private key in interval [1-255], for example, pri=133. Keep secret key in the pocket.
3. Generate public key, pub = 256 - pri = 123. This public key (123) you can share to the world. Imagine, 3rd party does not know, how to compute private key from a public. So, they know only public key (123).
4. Someone from public want to send you encrypted ASCII-byte. He get his byte, and adding to it public key by modulto 256 operation:
encrypted = (input_value + pub) % modulto;
For example, I want send you letter "X", ASCII code = 88 in encrypted form. So, I compute:
``````(88 + 123) % 256 = 211;
``````
1. I am sending you value 211 - encrypted byte.
2. You decrypt it by same scheme with your private key:
decrypted = (input_value + pri) % 256 = (211 + 133) % 256 = 88;
Of course, using simple generation pair in this example is weak, because of well-known algorithm for generate private key from a public, and anybody can easy recover private from modulto and public. But, in real cryptography, this algorithms is not known. But, theoretically, can be discovered in future.
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I must add: "The best cyphers are known by all" there's a lot of empirical evidence for this (although some forms change their name to 'obscuration') – Alec Teal Sep 26 '13 at 0:59
The modulto, is it the shared secret, or just the size of the byte it's in reference to? decrypted = (input_value + pri) % 256 = (221 + 123) % 256 = 88; That % 256, if it was the shared secret, then a simple 256 - 123 would result in the private key? – user2507230 Sep 26 '13 at 1:13
I figured it out completely! Thanks man! – user2507230 Sep 26 '13 at 1:33
modulto is shared information. I selected 256, because of adding in the uint8_t automatically doing by modulto 256. So, in the simple implementation, do not needed use this operation. But you can use any another modulto which is more than max_you_byte_value, for example, 150. If pri = 50, then pub = 150-50 = 100. There will work same math: enc = (88 + 100) % 150 = 38; dec = (38 + 50) % 150 = 88. – maxihatop Sep 26 '13 at 1:59
This is an area of pure mathematics, there's a book called "the mathematics of cyphers" it's quite short but a good introduction. I do suggest you stay away from implementing your own though, especially in Java (you want a compiler that targets a real machine for the kind of maths involved, and optimises accordingly). You should ask about this on the math or computer-science stack-exchanges.
I did get a downvote, so I want to clarify. I'm not being heartless but cyphers are firmly in the domain of mathematics, not programming (even if it is discreet maths, or the mathsy side of comp-sci) it requires a good understanding of algebraic structures, some statistics, it's certainly a fascinating area and I encourage you to read. I do mean the above though, don't use anything you make, the people who "invent" these cyphers have forgotten more than you or I know, implement exactly what they say at most. In Java you ought to expect a really poor throughput btw. Optimisations involving register pressure and allocation pay huge dividends in cypher throughput. Java is stack-based for starters.
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The downvote was thoroughly undeserved so I upvoted – James Robinson Sep 26 '13 at 0:49
Java is just-in-time compiled, and certain methods are even implemented as intrinsics inside the JVM. Java is not as slow as you think. – ntoskrnl Sep 26 '13 at 16:39
@ntoskrnl there is no obligation for an implementation to have any sort of JIT, even then the JIT must be fast so it does only the most beneficial optimisations on a small bit of code, consider an actual compiler though, with all the compile time in the world, and link time optimisation and the keyword const, you've really got something. GCC for example puts a lot of work into reducing the penalty of abstraction. Java may be faster than just a VM would be, but it is by no means fast. – Alec Teal Sep 27 '13 at 1:51
A JIT is not required, but there is only one widely used VM, HotSpot, and it has had a JIT since version 1.2, released in 1998. Given adequate runtime, modern versions of HotSpot eventually compile all parts of the program that would benefit from compilation, not just small bits. A JIT also has much more runtime information about the code than a static compiler like GCC, so unnecessary branches, redundant bounds checks, null checks and even synchronization can be elided dynamically. While Java does lack performance is some areas (such as floating point), it is about has fast as C++ in general. – ntoskrnl Sep 27 '13 at 8:54
@ntoskrnl few words, profile guided optimisation. You also can't say "C++ in general" because that can mean SO MANY things. We should avoid the debate really, but it is common knowledge that C(++), Fortran, Go.... so forth, even the vtables are different. There's also memory management and stuff. C++ is not better at floats, it's just that compilers allocate actual machine registers and such. I know a lot about the insides of GCC (and it's Java compiler), fascinating stuff :) – Alec Teal Sep 27 '13 at 15:16 | 1,750 | 6,863 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.78125 | 3 | CC-MAIN-2014-23 | latest | en | 0.928047 |
https://www.physicsforums.com/threads/rc-op-amp-circuit.353749/ | 1,532,086,730,000,000,000 | text/html | crawl-data/CC-MAIN-2018-30/segments/1531676591578.1/warc/CC-MAIN-20180720100114-20180720120114-00534.warc.gz | 955,464,623 | 12,835 | Homework Help: RC Op-Amp Circuit
1. Nov 11, 2009
astonmartin
How would you solve an RC op-amp circuit connected in a non-inverting fashion, such that the second resistor is replaced by a capacitor. This is not the usual differentiator or integrator circuit as far as I can tell?
No specific problem, just generally speaking, how would you approach this
2. Nov 11, 2009
Staff: Mentor
Can you post a sketch of the circuit? I think I can picture what you are asking, but it would be good to be more clear.
In general, you solve all opamp circuits the same way. Assume that there is no voltage between the + and - inputs, by virtue of the high negative feedback gain of the opamp, and assume that there is no input current into the + and - inputs. If there are inductors or capacitors in the circuit, you use the differential or integral relationship between their current and voltage as part of the circuit equations. I usually use KCL equations and solve them.
Then you go back and factor in the non-infinite gain of the opamp, and the non-zero input bias currents, the input offset current and voltage, etc., if applicable to the problem. | 265 | 1,146 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.671875 | 3 | CC-MAIN-2018-30 | latest | en | 0.949739 |
https://en.m.wikipedia.org/wiki/Catenoid | 1,642,540,197,000,000,000 | text/html | crawl-data/CC-MAIN-2022-05/segments/1642320300997.67/warc/CC-MAIN-20220118182855-20220118212855-00386.warc.gz | 302,240,077 | 15,867 | Catenoid
A catenoid is a type of surface, arising by rotating a catenary curve about an axis.[1] It is a minimal surface, meaning that it occupies the least area when bounded by a closed space.[2] It was formally described in 1744 by the mathematician Leonhard Euler.
A catenoid
A catenoid obtained from the rotation of a catenary
Soap film attached to twin circular rings will take the shape of a catenoid.[2] Because they are members of the same associate family of surfaces, a catenoid can be bent into a portion of a helicoid, and vice versa.
Geometry
The catenoid was the first non-trivial minimal surface in 3-dimensional Euclidean space to be discovered apart from the plane. The catenoid is obtained by rotating a catenary about its directrix.[2] It was found and proved to be minimal by Leonhard Euler in 1744.[3][4]
Early work on the subject was published also by Jean Baptiste Meusnier.[5][4]: 11106 There are only two minimal surfaces of revolution (surfaces of revolution which are also minimal surfaces): the plane and the catenoid.[6]
The catenoid may be defined by the following parametric equations:
${\displaystyle x=c\cosh {\frac {v}{c}}\cos u}$
${\displaystyle y=c\cosh {\frac {v}{c}}\sin u}$
${\displaystyle z=v}$
where ${\displaystyle u\in [-\pi ,\pi )}$ and ${\displaystyle v\in \mathbb {R} }$ and ${\displaystyle c}$ is a non-zero real constant.
In cylindrical coordinates:
${\displaystyle \rho =c\cosh {\frac {z}{c}}}$
where ${\displaystyle c}$ is a real constant.
A physical model of a catenoid can be formed by dipping two circular rings into a soap solution and slowly drawing the circles apart.
The catenoid may be also defined approximately by the Stretched grid method as a facet 3D model.
Helicoid transformation
Deformation of a helicoid into a catenoid
Because they are members of the same associate family of surfaces, one can bend a catenoid into a portion of a helicoid without stretching. In other words, one can make a (mostly) continuous and isometric deformation of a catenoid to a portion of the helicoid such that every member of the deformation family is minimal (having a mean curvature of zero). A parametrization of such a deformation is given by the system
${\displaystyle x(u,v)=\cos \theta \,\sinh v\,\sin u+\sin \theta \,\cosh v\,\cos u}$
${\displaystyle y(u,v)=-\cos \theta \,\sinh v\,\cos u+\sin \theta \,\cosh v\,\sin u}$
${\displaystyle z(u,v)=u\cos \theta +v\sin \theta }$
for ${\displaystyle (u,v)\in (-\pi ,\pi ]\times (-\infty ,\infty )}$ , with deformation parameter ${\displaystyle -\pi <\theta \leq \pi }$ ,
where ${\displaystyle \theta =\pi }$ corresponds to a right-handed helicoid, ${\displaystyle \theta =\pm \pi /2}$ corresponds to a catenoid, and ${\displaystyle \theta =0}$ corresponds to a left-handed helicoid.
References
1. ^ Dierkes, Ulrich; Hildebrandt, Stefan; Sauvigny, Friedrich (2010). Minimal Surfaces. Springer Science & Business Media. p. 141. ISBN 9783642116988.
2. ^ a b c Gullberg, Jan (1997). Mathematics: From the Birth of Numbers. W. W. Norton & Company. p. 538. ISBN 9780393040029.
3. ^ Helveticae, Euler, Leonhard (1952) [reprint of 1744 edition]. Carathëodory Constantin (ed.). Methodus inveniendi lineas curvas: maximi minimive proprietate gaudentes sive solutio problematis isoperimetrici latissimo sensu accepti (in Latin). Springer Science & Business Media. ISBN 3-76431-424-9.
4. ^ a b Colding, T. H.; Minicozzi, W. P. (17 July 2006). "Shapes of embedded minimal surfaces". Proceedings of the National Academy of Sciences. 103 (30): 11106–11111. Bibcode:2006PNAS..10311106C. doi:10.1073/pnas.0510379103. PMC 1544050. PMID 16847265.
5. ^ Meusnier, J. B (1881). Mémoire sur la courbure des surfaces [Memory on the curvature of surfaces.] (PDF) (in French). Bruxelles: F. Hayez, Imprimeur De L'Acdemie Royale De Belgique. pp. 477–510. ISBN 9781147341744.
6. ^ "Catenoid". Wolfram MathWorld. Retrieved 15 January 2017. | 1,153 | 3,936 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 16, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.796875 | 4 | CC-MAIN-2022-05 | latest | en | 0.923644 |
https://blender.stackexchange.com/questions/322028/bend-kink-a-long-square-like-a-ribbon | 1,722,654,391,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722640356078.1/warc/CC-MAIN-20240803025153-20240803055153-00202.warc.gz | 104,750,403 | 38,382 | # Bend/kink a long square like a ribbon
I have an request for assistance. It's a bit embarrassing as it might be for you a simple question but I am not a native English speaker so I don't know on what specific terms to search either. The long square itself is in a 45 degree angle (see image 2). I want to know how can I kink it on a certain point and then bend it a certain degree?
I added another picture for the front view, I'm sorry for the confusion.
`
• Do you know (1) edit mode, (2) loop cuts, (3) rotating on local axes ? Commented Jul 24 at 15:10
• Yes but the problem is that the loop cut is in line with long square, the cut needs be horizontal on this 45 degree long square if you will, now it's also 45 degrees. Commented Jul 24 at 15:17
• I hope I'm understanding your issue correctly, but I think using a mirror modifier with a mirror object can get you what you want. Docs Commented Jul 24 at 15:22
• Oh yes Leander I am getting very close to the desired result!! Commented Jul 24 at 15:51
• Jakemoyo thanks for your suggestions! @Leander please formulate your solution in an answer so that I can accept it! And if you like it, a demonstration of how you would smooth the bend. Ty kindly all fellas in here. Commented Jul 24 at 19:56
If you want to add a cut at an arbitrary angle, use the knife cut tool. K
To remove an edge, select the edge and press X > Dissolve Edges / Edge Loops
To modify and edge, you can slide the vertices along existing edges with GG or ShiftV.
To rotate around an edge, ...
1. select the edge and shift-box select (B) the other edges. Then choose active element as the pivot point and Normal as the Transform Orientation. The selection will rotate around the active edge (highlighted in a lighter yellow shade).
2. Rotate around the x-Normal of the edge. RX
To create a smoother transition at the bend, select the edge and bevel it. CtrlB
Adjust the count of divisions with the mouse wheel. | 483 | 1,945 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.9375 | 3 | CC-MAIN-2024-33 | latest | en | 0.89681 |
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You are searching for Buoyancy force of water, Below listing suggest some keywords related this keyword and listing websites with same content
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### Buoyant Force of Water | Science project | Education.com
(5 day ago) A boat floating in water feels two opposing forces: gravity pulling down and something called a buoyant force pushing up. The buoyant force comes from differences in water pressure exerting a force on the boat. The boat floats when the buoyant force is equal and opposite to the boat’s weight.
https://www.education.com/science-fair/article/archimedes-principle-floats-boat/
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### Buoyancy - Wikipedia
(10 day ago) Buoyancy (/ ˈ b ɔɪ ə n s i, ˈ b uː j ə n s i /) or upthrust, is an upward force exerted by a fluid that opposes the weight of an immersed object. In a column of fluid, pressure increases with depth as a result of the weight of the overlying fluid. Thus the pressure at the bottom of a column of fluid is greater than at the top of the column.
https://en.wikipedia.org/wiki/Buoyancy
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### How to Calculate Buoyant Force | Sciencing
(4 day ago) Buoyancy, or buoyant force, is based on Archimedes' Principle. This principle states, "Any object, wholly or partly immersed in a fluid, is buoyed up by a force equal to the weight of the fluid displaced by the object." Archimides' Principle is important in hydro-engineering applications, such as
https://sciencing.com/calculate-buoyant-force-5149859.html
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### How to Calculate Buoyancy: 12 Steps (with Pictures) - wikiHow
(1 year ago) Buoyancy is the force acting opposite the direction of gravity that affects all objects submerged in a fluid. When an object is placed in a fluid, the object's weight pushes down on the fluid (liquid or gas) while an upward buoyancy force pushes upward on the object, acting against gravity.
https://www.wikihow.com/Calculate-Buoyancy
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### Buoyancy Calculator - calculate the buoyant force of an
(7 day ago) Free online Buoyancy calculator with which you can calculate the buoyant force experienced by an object submerged in a liquid substance like sea water, oil, gasoline, etc. The calculator requires that you know the fluid density in imperial or metric units, as well as the volume occupied by the body / object for which the buoyant force is calculated.
https://www.gigacalculator.com/calculators/buoyant-force-calculator.php
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### Pressure
(6 day ago) Buoyancy. Buoyancy arises from the fact that fluid pressure increases with depth and from the fact that the increased pressure is exerted in all directions (Pascal's principle) so that there is an unbalanced upward force on the bottom of a submerged object.
http://hyperphysics.phy-astr.gsu.edu/hbase/pbuoy.html
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### Buoyancy | Encyclopedia.com
(5 day ago) But if the buoyant force is less than the object's weight, the object will sink. Buoyant force is not the same as net force: if the object weighs more than the water it displaces, the force of its weight cancels out and in fact "overrules" that of the buoyant force. At the heart of the issue is density.
https://www.encyclopedia.com/science-and-technology/physics/physics/buoyancy
DA: 20 PA: 48 MOZ Rank: 68 | 997 | 3,849 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.265625 | 3 | CC-MAIN-2020-05 | latest | en | 0.798092 |
pengepanelet.dk | 1,723,750,719,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722641311225.98/warc/CC-MAIN-20240815173031-20240815203031-00433.warc.gz | 355,404,531 | 5,270 | # Log normal
## Log-normal distribution – Wikipedia
In probability theory, a log-normal (or lognormal) distribution is a continuous probability distribution of a random variable whose logarithm is normally …
## Log-normal Distribution – A simple explanation
Log-normal Distribution – A simple explanation | by Maja Pavlovic | Towards Data Science
The log-normal distribution is a right skewed continuous probability distribution, meaning it has a long tail towards the right.
We will briefly look at the definition of the log-normal and then go onto calculate the distribution’s parameters μ and σ from simple data. We will then have a look at how to calculate the mean…
## Log-Normal Distribution: Definition, Uses, and How To Calculate
A log-normal distribution is a statistical distribution of logarithmic values from a related normal distribution. A log-normal distribution can be …
A log-normal distribution is a statistical distribution of logarithmic values from a related normal distribution.
## Log-normal fordelingen – Noter i statistik
Noter i statistik
I forbindelse med biologisk variation ses ofte en anden fordeling (end normalfordelingen), nemlig den såkaldte log-normal-fordeling.
## Log Normal Distribution — from Wolfram MathWorld
. A log normal distribution results if the variable is the product of a large number of independent, identically-distributed variables in the same way that a …
A continuous distribution in which the logarithm of a variable has a normal distribution. It is a general case of Gibrat’s distribution, to which the log normal distribution reduces with S=1 and M=0. A log normal distribution results if the variable is the product of a large number of independent, identically-distributed variables in the same way that a normal distribution results if the variable is the sum of a large number of independent, identically-distributed variables. The probability…
## Log-normal distribution | Properties and proofs – StatLect
Log-normal distribution | Properties and proofs
A random variable is said to have a log-normal distribution if its natural logarithm has a normal distribution. In other words, the exponential of a normal …
The log normal distribution explained, with detailed proofs of important results.
## Log normal distribution | Math, Statistics for data … – YouTube
Log-normal Distribution | Brilliant Math & Science Wiki
The log-normal distribution is the probability distribution of a random variable whose logarithm follows a normal distribution. It models phenomena whose …
The log-normal distribution is the probability distribution of a random variable whose logarithm follows a normal distribution. It models phenomena whose relative growth rate is independent of size, which is true of most natural phenomena including the size of tissue and blood pressure, income distribution, and even the length of chess games. Let …
## Log-normal Distribution | Brilliant Math & Science Wiki
1.3.6.6.9. Lognormal Distribution
The lognormal distribution is used extensively in reliability applications to model failure times. The lognormal and Weibull distributions are probably the most …
## 1.3.6.6.9. Lognormal Distribution
Lognormal Distribution – an overview | ScienceDirect Topics
A log-normal distribution is a continuous distribution of random variable y whose natural logarithm is normally distributed. For example, if random variable y = …
Keywords: log normal | 680 | 3,453 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.90625 | 4 | CC-MAIN-2024-33 | latest | en | 0.755572 |
https://universalzeropoint.com/author/salahealer/ | 1,590,627,044,000,000,000 | text/html | crawl-data/CC-MAIN-2020-24/segments/1590347396300.22/warc/CC-MAIN-20200527235451-20200528025451-00322.warc.gz | 578,216,355 | 46,921 | Author: salahealer
# Sacred Geometry Class 1
Here we are!
I am back to teach Sacred Geometry with people in my new home in Glastonbury.
The classes will take place in Glastonbury in my own place and will be broadcasted online for people who can’t be physically in Glastonbury.
For a lesson, you will be provided a lesson learned papers and a workbook papers.
A lesson lasts two hours.
The first Lesson I prepared is called :
Introduction of a connected universe
Basic Geometry and Numbers
This first lesson will take place on Thursday 21st 2019 from 2 to 4 pm.
The price of these two hours Lesson is £44.
10 spots available in Glastonbury, unlimited online.
In this lesson, you will learn :
• Learn to build Platonic Solids out of paper
• Learn the meaning and the applications of the Tetractys
• Learn to square the circle and the underlying construct of the Cosmos through the Great Pyramid of Giza
• Learn to approach the language of Numbers in this construct
• Learn to connect this construct with Nature (double rainbow)
We will be looking at the five famous Platonic Solids. As a piratical activity, this lesson takes us to experience them through Origami.
The Tetractys has several powerful meanings and was one of the most important cornerstone for the Pythagoreans in the understanding of the universe through number, geometry and letters. We will have a proper look at these different applications in music, arithmetic, ancient culture and how the letters are part of a great universal language strengthening the idea of a connected universe, especially Latin and Hebrew alphabet.
An important geometric construct which involves square and compass called ” Squaring the circle” will also be part of the practical activity. This famous geometric problem well known by the geometers has a simple resolution by approximating the transcendental value of PI.
Finally we will see how this geometric construction relates to the dimensions of Earth and the Moon, and the perception of the double rainbow to the naked eye.
You can directly book here by getting your workbook and learned class papers :
https://sacred-geometry.selz.com/item/5c8a4f1b701f5d07cc9472a6
If you are interested to this class or for further information, please message me directly to salahealer@gmail.com.
# Healing Work
Hi folks!
Here is my new website about my healing work as a multidimensional healer and life coach : http://www.salahealingenergy.com
I will be active on both sites and will keep working on sacred geometry too.
The website universalzeropoint.com is more a website to share my insights and presents my writings about it for a deeper technical points of view. This website will keep you informed about the online classes on my shop Selz : https://sacred-geometry.selz.com/
In addition of the healing work I present on my new website, Soul Alignment Consultation, Soul retrieval, activation with crystals and tarot readings which are tapping into an intuitive and psychic work, the ideal in my life journey is to integrate a practical healing work about numbers and sacred geometry for people to experience. They can reflect about these insights and also benefit from this Light Language about numbers and geometry.
On the menu of the new website, you can see a page of Sacred Geometry linking my official website and my shop Selz for online classes.
Kind Regards
Salah
# The blueprint foundation of Pyramid Energy
#### Pyramid Energy emerges from the base foundation of a Pyramid
Pyramid Energy could be described as the accumulation of standing wave interference inside a pyramid emanating Golden spirals or vortexes. The Fibonacci spiral is an approximation of the Golden Spiral observed in nature.
We begin with 1, then we sum up to 1 resulting in 2. We keep adding to the previous number to get the next number in the Fibonacci sequence ( 1 + 2 = 3, 3 + 2 = 5, etc).
1, 1, 2, 3, 5, 8 and 13 as an example depicted below.
To the monks of early Christianity the geometry of the square symbolized the creation of the structured universe and how the number two, the infinite and finite, can be generated from the one. In ancient Israel King Solomon described the passage from one to two as a reference to ‘Divine Inscrutability’.
Our physical reality is based on the pillar number four, with the four elements of air, earth, fire and water, the four directions and four corners of Earth. The Tetractys, meaning ‘the number four’ is the tetrahedron in three dimensions with four triangular faces. It is the first polygonal solid and the fundamental structure of space-time.
Geometry is the key to understanding the multi-layered universe and a doorway to the study of the divine order of nature. A single point represents ‘Unity’ or ‘the One’ and can also represent the circle or the square.
Square grids are created in the following manner.
1. From the One is born the Essence of Duality, the passage from One to Two, which also symbolizes the Three in One. A square or a circle with a single point in the center is equivalent to ‘Unity’ or ‘the One’ and the pure inseparable essence of all things in Oneness. The Primary Grid 1 x 1 is the simple square.
2. The Secondary Grid 1 x 1 is constructed by drawing diagonals through a single point at the center.
3. The center provides the four coordinates for the division of the sides of the square bringing the Tertiary Grid 1 x 1 or cross, which in ancient times was regarded as a symbol of the Trinity or Three in One.
The three together produce a 2 x 2 Primary Grid. From a 2 x 2 Grid, a 4 x 4 Grid is built through the same steps. This construction was the template for designing Celtic decorative knots in ancient times.
Pyramid Energy can be understood through an expanded fractal of squares revealed in a crop circle at East Field Alton Priors, Wiltshire, United Kingdom on 3rd July 2005. The Alton Priors crop circle is based on a four by four grid of square units clearly visible at its center.
Credit : Lucy Pringle
The Primary Grid 4 x 4 is seen at the center of the Alton Priors crop circle. Four 2 x 2 Grids are placed on each corner of the 4 x 4 Grid. Finally twelve single squares are placed on each corner of the 2 x 2 Grid, bringing a total of 44 squares. The number 44 is a master number insisting on the number 4.
Fractal 44 can be viewed as a 12 x 12 Grid representing the base of a pyramid with four Zero Energy Points through which operate the four creative forces. The universe is ordered through the ether governing the four fundamental forces. Universal motion or spin originates from the ether working through the four forces on any scale from galaxies to atoms.
Binary codes bring important information about the numerical structure of the pyramid. Different sized squares and rectangles appear in the shaded areas. A binary code appears if we consider the yellow rectangle equal to 1 and the green square equal to 0. Binary codes can be read from either left to right or up and down.
0110 = 6 6 suggests the 6 x 6 x 6 Cube.
01110 = 14 = 7 x 2
7 appears as the height of the Great Pyramid in relation to its base.
110011 = 51 = 17 x 3
51 appears in the slope angle of the Great Pyramid and the seven pointed star.
001010100 = 84 = 7 x 12 84 refers to one of the possible resonant frequencies of the Great Pyramid in Hertz.
1110111 = 119 = 7 x 17 119 brings again the number 7 in its divisors.
On each side of the 4 x 4 grid is a 101 doorway. The number 101 represents a ‘zero gateway’ with ones on either side, emanating Zero Point Energy from the zero. The triangular number 101 is linked to the Great Pyramid through the number 5,151.
The Great Pyramid has four faces with a slope angle of 51º51′ and the triangular number 101 counts a total of 5,151 dots.
Fractal 44 is a template unifying the microcosm and macrocosm and a blueprint of the Divine Architecture.
Fractal 44 from a three dimensional view is illustrated on the left.
Fractal 44 consists of 184 cubes in three dimensions with a 4 x 4 x 4 orange cube at its center composed of 64 cubes. Eight blue cubes of 2 x 2 x 2 sit at each corner bringing a total of 128 cubes (64 + 64 = 128).
Finally individual red cubes are placed on the corners of the 2 x 2 x 2 blue cubes adding a further 56 cubes (7 x 8) resulting in a total of 184 cubes (128 + 56 = 184). There are only seven red cubes placed around the blue bloc as the 8th red cube is integrated into the 4 x 4 x 4 orange bloc of 64 cubes.
The number 64 is present at the core of the blueprint. This number appears as an important numerical blueprint on a DNA level. Indeed the genetic code consists of 64 triplets of nucleotides (Adenine A, Guanine G, Cytosine C, Thymine T). These triplets are called codons. With three exceptions, each codon encodes for one of the 20 amino acids used in the synthesis of proteins.
The DNA molecule, the program for all life, is based on the golden section. It measures 34 angstroms long by 21 angstroms wide for each full cycle of its double helix spiral. 34 and 21 are two consecutive numbers of the Fibonacci sequence.
The number 64 is also very present in Chinese philosophy. The I Ching book consists of 64 hexagrams as illustrated below.
There is obviously a link between all these fields. The question is how they are connected each other and how this can be interpreted ?
© Salah-Eddin Gherbi, From the book The Etheric Particle 216
# The depth of a mysterious Pyramid
The music of the heavens was believed to be describable through numbers and geometry with a system of codes originating from the fundamental structure of space-time. The pyramid builders taught that relationships between all things can be expressed through geometry and numbers. Music tuned with these harmonic numbers is a way of expressing resonance within the geometric construct of the universe. The Great Pyramid of Giza is one of the most famous examples of musical architecture since the ratio between Earth and Moon’s radius (11÷3) is a seventh of 528 Hz on a scale from D at 288 Hz. This frequency is supposed to be the frequency of Love, one of the Solfeggio frequencies.
The base of the Great Pyramid is not a perfect square. Each side is slightly concaved. This must be an important factor in its function as an etheric energy device, considering that energy waves are based on hyperbolic geometry.
Top view of the Great Pyramid of Giza
Hyperbolic geometry can be approached through sacred geometry. Below is an example through the geometric construction of the octagon.
The left diagram shows the construction of the octagon in straight lines and the right diagram shows the construction of a curved octagon representing hyperbolic geometry.
The Great Pyramid is linked to Sacred Geometry. A first Vesica Piscis is built and contained in the center of a larger Vesica Piscis. Below is the Vesica Piscis with the outline of the Great Pyramid.
The base leg is 2, the slope side is the Golden Ratio Phi (φ 1.618) and the height is the square root of Phi (√φ). The Great Pyramid has four faces with a golden angle of inclination 51° 51‘ 51“ or 51.84°.
The angle of a seven-pointed star 51.48 degrees is closely related to the slope angle of the Great Pyramid 51.84 degrees through the language of numbers. The Great Pyramid embodies the sacred number 7.
5,151 dots embodies the slope angle in degrees and minutes (51°51’) of the Great Pyramid. This is the total number of the dots in the triangular number 101.
The Tetractys is the triangular number 4 with 4 dots at the base of the triangle. There is a total of 10 dots. The number 10 is said to be the perfect number as it connects the different scales and fields of things in the universe with some fundamental numbers set up in the general map of the cosmos. For example, 864,000 is said to be the diameter of the Sun in miles. Divide this number by 10, it results in the number of seconds in 24 hours which is 86,400 seconds. I explain further in my book how the Mayan Calendar can be built with some of these fundamental numbers, all of digits adding up to 9 and how this relate to the astronomical distances of the Moon and Sun. All is sealed with these numbers speaking as a divine conscious language.
© Salah-Eddin Gherbi, From the book The Etheric Particle 216
# The mysterious Great Pyramid
These fundamental blocs appear in nature in the structure of crystals and the five natural elements; earth, air, fire, water and the quintessence of the heavens (ether). Each of them is associated with a platonic solid. Earth is associated with the cube, air with the octahedron, water with the icosahedron, fire with the tetrahedron and ether with the dodecahedron. The heavenly bodies were encoded in the Great Pyramid of Giza through the number 7. Another key number is 5,040, the Earth’s radius in miles 3,960 added to the Moon’s radius 1,080. The number 5,040 is 7 x 6 x 5 x 4 x 3 x 2 x 1 and carried an important metaphysical meaning to early civilizations.
The fifth element, or ether, is a subtle medium through which the celestial bodies move in harmony. This element encourages the prosperity of life and order in nature. Entropy is the measure of disorder in any process. The Second Law of Thermodynamics stipulates that “the entropy of the universe increases during any spontaneous process”, which contradicts the orderly celestial signature described by the heavenly bodies. As a consequence of the Second Law of Thermodynamics only technologies based on explosion and destruction are explored. When the ether is considered the second law must be dismissed, allowing further explorations into technologies based on implosion and harmony of life.
The beautiful geometric patterns found in nature are a direct expression of the ether or ‘The All’ which orchestrates order in the universe through sound, light, numbers and geometry. In the past physical objects were considered to be connected to their essence in the subtle world. Philosophy, Art and Mathematics were studied with an awareness of the divine transcendental connection of the soul on the earthly plane to the One Quintessence. The Pythagoreans for example considered reality as ‘mathematically describable’. The practice of philosophy aided the transformation of the soul and a connection to a divine order through the science of numbers.
The Great Pyramid has an approximately square base with a perimeter equal to the circumference of a circle with radius equal to its height. The dimensions of the Great Pyramid incorporate measurements from which can be calculated :
• The dimensions of the Earth and Moon.
• The radius ratio between the Earth and Moon.
• The Pythagorean Triangle 3 – 4 – 5.
The pyramid builders appear to have been advanced astronomers.
“Few things in this world are more predictable than the reaction of conventional minds to unconventional ideas.” John Anthony West
Squaring the circle is the challenge of constructing a square with the same area as a given circle by using only a finite number of steps with compass and straight-edge. The resolution approximates the dimensions of the Great Pyramid with a base leg equal to 11 and a height equal to 7. This gives an approximate value of Pi (π) equal to 22÷7 = 3.1428.
Another approach is to take the dimensions of the Great Pyramid in relation to the Golden Ratio Phi (φ) 1.618, divine proportion observed in nature. The square of Phi (√φ) is the height and 2 is the base leg.
Perimeter of the circle : 2 π r = 8
Since 4 divided by √φ is approximately equal to Pi (π), the circumference of a circle of radius r is the height of the pyramid, respecting the equation below.
2 π r = 2 π√φ =
2 (4 ÷√φ) √φ = 2 x 4 = 8
Since the perimeter of the base of the pyramid is 8, the Great Pyramid squares the circle with a value of PI equal to 4 ÷√φ = 3.1446055.
If you are willing to go deeper in this research, there is further discovery about this value in the work presented by the researcher Jain, in his own books and website :
© Salah-Eddin Gherbi, From the book The Etheric Particle 216
# The Tetractys, Ancient Temples and 432
### 432 is a Multdimensional Code
“And philosophers tell us, Kallikles, that communion and friendship and orderliness and temperance and justice bind together heaven and earth and gods and men, and that this universe is therefore called Cosmos or order, not disorder or misrule, my friend.”
The Tetractys is the foundation stone of the Divine Architecture. It held an important mystical meaning to the Pythagoreans who considered it as the base of the structure of the universe in terms of arithmetic, music and geometry. The Tetractys means literally “the number four” and is a triangle composed of 10 points rising upwards, arranged in four rows. The number ten is mathematically known as the fourth “ triangular number” with rows of one, two, three and four points. Each row has an important meaning and brings forward an understanding of the connection between the innermost and the outermost.
The first harmonic number encoded in the Tetractys is 432, a cosmic code which can be read from the base to the top of a step pyramid, such as the ones found in central America. This is another form of pyramid with a flat top (see picture below).
The step pyramids in Central America and Egypt come from the geometry of the Tetractys. A second Tetractys is placed on the top of the first as a fractal forming the second step. The numerical sequence 432 432 … rises from the base upwards.
Step Pyramid of Djoser. Constructed at Saqqara about 4,700 years ago and attributed to Imhotep. The pyramid stood 203 ft tall, with a base of 358 ft x 410 ft and clad in polished white stone.
The Temple of Kukulkan. A 79-ft -high pyramid in southeastern Mexico with nine layers and a square base with sides measuring 181 ft . There are 4 stairways each with 91 steps making a total of 364 steps, the exact number of days in a lunar year. Added to the base platform, the total comes to 365, the number of days in a solar year.
The harmonic number 432 rises from the base upwards. This is a very important number when tuning instruments to resonate with consciousness. 432 is the gematria value for ‘All things’ (παντα) in Greek. From planetary systems to atoms, everything surrounding us is an embodiment of perfect harmony created by numbers, referred to in music as “ Harmonics”.
The Tetractys representing the organization of space from a two dimensional view.
First row : From a single original point everything is created and brought into existence from nothingness. This could be considered as a state of awareness to that which is about to manifest into creation.
Second row : From a single point two further points are generated defining the first dimension. The possibility of going from one point to another brings the idea of motion into consciousness.
Third row : A line drawn between these three dots defines the second dimension. Structure is formed into consciousness with the possibility of quantification and measurement.
Fourth row : A line drawn between these four dots defines the third dimension where geometry takes form. From this triangle all regular polygons can be generated, such as the square, the pentagon, the hexagon etc.
Other fundamental blocs can be built from the original bloc. The first solid appearing is the projection of the tetrahedron shown in light blue. The red hexagon represents the projection of the octahedron with the green cube projected inside.
The icosahedron and dodecahedron are both dual platonic solids. The icosahedron can be placed inside the dodecahedron and vice versa. One has 20 faces with 12 vertices and the other has 12 faces with 20 vertices.
The rhombic dodecahedron has 4,320 degrees and is made from 12 rhombus. The sum of the four angles of a rhombus is always 360 degrees. The rhombic dodecahedron appears in nature in the structure of the honeycomb cells. At the top is a pyramid made from three blue rhombus closing the end of the cell. The opening is a red hexagon prism at the bottom joining to the top with six green trapezes. Each cell is called “half of a rhombic dodecahedron”.
The sum of the angles is 3,240 degrees, again adding up to 9.
3 + 2 + 4 + 0 = 9
The number 9 is an important pillar in the structure of space-time and acts uniquely in the system of numbers. Below is a table listing some musical notes. Notes are based on a D scale from 144 Hz.
“Music is geometry in time.” Arthur Honegger
© Salah-Eddin Gherbi, From the book The Etheric Particle 216
# Kindle ebook The Etheric Particle 216 available
The kindle ebook The Etheric Particle 216 is now available on Amazon in your Kindle store. Enjoy on your iPhone, kindle fire or other devices the universe of numbers and geometry.
# Why are 528 and 432 Frequencies so good for Human Health?
This video below was made to support my colleague Tim Sandars in his project of presenting a new product for the phones using the frequencies 432 and 528 Hz in order to protect our DNA from negative electromagnetic radiation.
How can Sacred Geometry, Fibonacci Sequences and Divine blueprints tell us which frequencies are highly beneficial to the human body in terms of cellular harmonics and DNA Protection? Salah-Eddin Gherbi takes a look at the origin of the mathematical theory of why frequencies 432Hz and 528Hz hold the secret codes for divine connection and human health, specifically DNA protection. You can buy Salah’s incredible book ‘216
The Etheric Particle’ here:
https://www.amazon.com/Etheric-Particle-216-Unifying-Matter/dp/1527207900
Tim Sandars
# The traditional PI (π) a deficient value ?
In the book ‘The Etheric Particle 216’, to “connecting the dots” within the language of numbers and geometry, different values of PI (π) are presented.
One of these values has to be calculated so that the number 666 is presented fully in its expression as an integer. The number 666 is a cornerstone of the fine structure constant α (nearly the inverse ratio 137) in its mathematical expression (formulae) as shown below :
This fundamental constant in Physics measures the strength of the electromagnetic force that controls how charged elementary particles (electrons and photons) interact. Yet the book presents a mathematical significance of its own such as PI (π). Without its mathematical significance with numbers, it’s a tree without water or sun light.
In the formulae presented, there is a physical interpretation for light or photon flux. The number of photons is 10 to the power Omega (ω) (10^ω). This quantity divided by 666² is the average number of photons per square of edge length 666 resulting in 137.036.The number 666 is to do with the light of the sun or divine life force from which the spirit operates through matter within the ether (the fifth element). It is nothing to do with a negative connotation as it could have been said.
The gematria value of Christ Χριστός (Christos) is 1,480. Notice that this number is nearly the surface area of a face of Hypercube 216 10,368 divided by 7. Then one seventh of the area (blue area) encodes the name of Christ (1,481.142). A difference of 1 does not change the meaning behind.
If we consider the value 1,480 as the side of a square, then the diagonal line has nearly a value equal to 2,093. Finally, considering 2,093 as the circumference of a circle, the diameter is 666 with the value of Pi(π) equal to 3.1426869. To determine this value, it is important to know the relationship between the circumference of a circle and its diameter. Knowing the circumference C and its diameter D, the new value of Pi(π) is determined.
The circumference of a circle can be calculated with this equation :
C = π D, D being the diameter of the circle and C the circumference.
Other values of Pi(π) have been presented through the geometric construction squaring the circle. Squaring the circle is the challenge of constructing a square with the same area as a given circle by using only a finite number of steps with compass and straight-edge. The resolution approximates the dimensions of the Great Pyramid with a base leg equal to 11 and a height equal to 7. This gives an approximate value of Pi (π) equal to 22÷7 = 3.142857.
Another approach is to take the dimensions of the Great Pyramid in relation to the Golden Ratio Phi (Φ) 1.618. The square of Phi (√Φ) is the height and 2 is the base leg. If we take these dimensions which are hypothetically the real dimensions of the Great Pyramid, another value of Pi(π) is determined.
The perimeter of the square is 8 and the radius of the circle is the height of the Great Pyramid √Φ equal to 1.272. The resolution of squaring the circle through the Great Pyramid gives the new value of Pi(π) equal to 3.1446055.
This value has been discussed and demonstrated in depth by the researcher Jain in his own books : http://www.jainmathemagics.com/bookofphivol8/.
Another value of Pi (π) was defined in a previous post called “12 a foundation stone in the Divine Governance“. The value 3.14181818 comes from the important connection between the number 12 and the number 9 playing together in the cosmic order. Read the article for further information. It is not in my book “The Etheric Particle 216”. This value is all fresh.
The transcendental number Pi (π) represents a key number bridging matter to spirit and approximately resolves the problem of squaring the circle. Metaphysically speaking, Pi (π) links the two different realms since the square represents energy on the physical level and the circle represents energy on the etheric level. Examining the value of Pi (π) from the perspective of Hypercube 216, a new value of Pi (π) can be calculated.
124,416 (12 faces of Hypercube 216) plus 2,808 (energy release of Hypercube 216) is equal to 127,224 which is a thousand times greater than Xi (ξ) 1.27224 equal to the ratio between the double height and base leg of the Great Pyramid. Xi (ξ) is also equal to the ratio between the diameter D of the circle circling a square of edge length c 72√2, a face of Hypercube 216.
P(circle) = P(square) = π D(circle) = 288√2 (squaring the circle)
D(circle) ÷ c = 2H ÷ B = Xi (ξ) = 1.27224
Pi (π) = P(circle) ÷ D(circle) = P(circle) ÷ (ξ c) = 3.14406086
Gee Mister Spirit, there’s a lot more to mathematics than two times two. Donald Duck 🙂
Squaring the circle of a face of Hypercube 216 leads to a circle of a diameter equal approximately to 129.6. The number 129.6 is an interesting number considering that 1296 is a number of root 9 (1 + 2 + 9 + 6 = 18 and 1 + 8 = 9) and is encoded in many fields. This number is also strongly connected with the number 6 as 6 x 6 x 6 x 6 = 1,296. Multiplied by 2, the result is 2,592, one tenth of the precession of the equinoxes in years. Multiplied by 2 again, the result is 5,184, a numerical code of the Maya Long Count Calendar (12.96 Mayan Baktuns or 5,184 years). Dividing this number by 100, 51.84 is the slope angle of the Great Pyramid in degrees. 1,296 single cubes from Hypercube 216 with a volume of 82,944 in four dimension has a total volume equal to 107,495,424, the volume of Hypercube 216 in four dimension.
The Golden Diamond is the energetic field surrounding everything in the universe. When a double rainbow appears, the human eye sees the first main rainbow at 51.84 degrees from the second one, the slope angle of the Great Pyramid. The double rainbow is an incredible example of divine manifestation in nature through the number 5,184 which is also half of the area of a face of Hypercube 216, and a key number in generating the seven colours of the rainbow.
To conclude, the different values presented show how the traditional PI (π) is deficient within the language of numbers and geometry :
• 3.1446055
• 3.144060869
• 3.142857
• 3.1426968
• 3.1418181
The two first values of PI (π) speak more within the language of numbers. The first three digits of these two are forming the number 144, an important number encoded in Hypercube 216 (the diagonal line of a face). The first one discovered by Jain has a direct relationship with the Golden ratio (Φ 1.618) and the number 4 though. As we know, the number 4 represents the strong foundations, stability, order. It describes our three dimensional reality, the four directions (east, west, north and south), seasons, elements. The number 4 has also a great significance in many cultures.
The number 4 is the numerical blueprint of Fractal 44 a unique template unifying microcosm and macrocosm.
# Pyramid Energy II
Following up the article Pyramid Energy – Part I
Fractal 44 is a fractal of 44 squares. To get more information deciphered, it is interesting to go further in the study of this fractal. Two crop circles combined together present the next geometric step of Fractal 44.
On the left : Crop circle formation, Windmill Hill, Wiltshire, 19th July 1999.
On the right : Crop Circle formation, West Kennet, Wiltshire, 4th August 1999.
Credit : Lucy Pringle
“Geometry is knowledge of the eternally existent.” Pythagoras
The Windmill Hill crop circle represents the feminine aspect or ‘socket’ while the West Kennet crop circle represents the masculine aspect or ‘plug’. The combination of these two crop circles representing the union of masculine and feminine is illustrated below. There are a total of 288 circles representing the ‘socket’. The yellow squares and yellow circles represent the ‘plug’. There are 156 yellow circles (39 x 4) superimposed on the 288 circles. Adding 156 to 288 brings the significant number 444.
The union of Windmill Hill and West Kennet showing a perfect fit.
The harmonic number 444 is 37 times 12. The number 12 has already been seen to hold an important place in the manifested world, also representing the passage from 1 to 2. The number 37 is the twelfth prime number. The numbers 3 and 7 are linked to creation and represent the steps for light to be perceived in many colours by the human eye. Contained within the oneness of white light are the three primary colours and seven colours of the rainbow.
When Fractal 44 is positioned on each of the four corners of the union of these two crop circles an astonishing correlation appears. An area containing 6 x 6 square units highlighted in red is formed encoding the 6 x 6 x 6 cube and a key to the fourth dimension. This Geometric Key brings both a geometric and numerical understanding of how Pyramid Energy works in connection with Fractal 44.
Alton Priors, Windmill Hill and West Kennet crop circles combined.
Fractal 44 repeats itself on each corner of the original bringing a total of 188 single silver squares producing Fractal 188, constituting of five 4 x 4 grids, sixteen 2 x 2 grids and 44 single squares.
In three dimensions there are nine 4 x 4 x 4 hypercubes, sixty-four 2 x 2 x 2 hypercubes and finally four-hundred and forty single cubes bringing a total of 1,528 cubes.
The yellow circles form the masculine aspect of creative force, motion, frequency and voltage as a fractal element in nature.
The purple circles form the feminine aspect of space and capacity ready to receive the masculine creative forces.
The Hebrew word ‘Father’* (אב) has a gematria value of 3. ‘Mother’ (אמ) has a gematria value of 41, adding together to make 44. The gematria value for ‘Child’ (ילד) is also 44. Fractal 44 encodes the Trinity of Father, Mother and Child, well known in Ancient Egypt through the personifications of Osiris, Isis and Horus.
“Behind the wall, the gods play, they play with numbers, of which the universe is made up.” Le Corbusier
Fractal 44 when overlaid on the ground plan of the Temple of Solomon, an interesting geometric correlation appears. The yellow rectangle is the Holy Temple of Solomon. This Temple reflects the structure and motion of the universe. The accumulation point of Zero Energy, a 101 ‘gateway’ is located exactly on the most Holy Place of the Temple which is the sanctuary, shown as a green square inside the yellow rectangle. The sanctuary is a cube of edge length 20 cubits.
The Temple of Solomon from the prophetic vision of Ezekiel is five hundred cubits long and five hundred cubits wide. The Altar is shown as a red square in the centre of the 4 x 4 grid. The position of the Holy Temple is slightly different from the position of the Tabernacle suggested by Villalpando.
The illustration below shows the combination of Fractal 44 and the ground plan of the Temple of Solomon rotated 90 degrees three times. The Holy Temple and the Altar are shown with colours. The inside and outside courtyard, the gates and the 30 chambers along the pavement are shown with red borders.
The Fibonacci spiral is constructed from the green square unit representing the sanctuary. Golden Spirals emerge from Zero Energy Points showing the behaviour of the fifth element, the spiralling ether. The Temple of Solomon is a great reminder of a connected universe, a multiple manifestation of spirals coming from Divine Consciousness. | 7,651 | 33,036 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.703125 | 3 | CC-MAIN-2020-24 | latest | en | 0.918584 |
http://tomasp.net/blog/rss.aspx/?30 | 1,632,750,257,000,000,000 | text/html | crawl-data/CC-MAIN-2021-39/segments/1631780058450.44/warc/CC-MAIN-20210927120736-20210927150736-00461.warc.gz | 63,551,623 | 94,767 | Blog | TomasP.Nethttp://tomasp.net/blogBlog2013, Tomas PetricekBlog The RSS feed has been moved http://tomasp.net/rss.xml 26 Aug 2013 20:54:46 GMT The new feed is available at <a href="http://tomasp.net/rss.xml"> http://tomasp.net/rss.xml </a> Power of mathematics: Reasoning about functional typeshttp://tomasp.net/blog/types-and-math.aspxTue, 14 May 2013 17:54:46 GMTIn this article, I explore the amazing relationship between functional data types and algebraic operations. We will use this relationship to reason about domain model and understand the differences between several possible representations.Tomas Petricek<img src="http://tomasp.net/articles/types-and-maths/distributivity.png" class="rdecor" /> <p>One of the most amazing aspects of mathematics is that it applies to such a wide range of areas. The same mathematical rules can be applied to completely different objects (say, forces in physics or markets in economics) and they work exactly the same way.</p> <p>In this article, we'll look at one such fascinating use of mathematics - we'll use elementary school algebra to reason about functional data types.</p> <p>In functional programming, the best way to start solving a problem is to think about the data types that are needed to represent the data that you will be working with. This gives you a simple starting point and a great tool to communicate and develop your ideas. I call this approach <a href="http://tomasp.net/blog/type-first-development.aspx">Type-First Development and I wrote about it earlier</a>, so I won't repeat that here.</p> <p>The two most elementary types in functional languages are <em>tuples</em> (also called pairs or product types) and <em>discriminated unions</em> (also called algebraic data types, case classes or sum types). It turns out that these two types are closely related to <em>multiplication</em> and <em>addition</em> in algebra...</p> Async in C# and F#: Asynchronous gotchas in C#http://tomasp.net/blog/csharp-async-gotchas.aspxMon, 15 Apr 2013 04:00:03 GMTThis article is inspired by an MVP summit talk about common pitfalls in the C# asynchronous programming model. I look at a number of easy to make mistakes when writing asynchronous code in C# and demonstrate that most of them would not easily happen when using F#.Tomas Petricek<p>Back in February, I attended the annual MVP summit - an <a href="http://www.2013mvpsummit.com/about">event organized by Microsoft for MVPs</a>. I used that opportunity to also visit Boston and New York and do two F# talks and to record a <a href="http://channel9.msdn.com/posts/Tomas-Petricek-How-F-Learned-to-Stop-Worrying-and-Love-the-Data" title="Tomas Petricek (Channel 9): How F# Learned to Stop Worrying and Love the Data">Channel9 lecutre about type providers</a> [<a href="#rf13041502">5</a>]. Despite all the <em>other activities</em> (often involving pubs, other F# people and long sleeping in the mornings), I also managed to come to some talks!</p> <div style="margin-left:auto;margin-right:auto;width:379px;margin-top:10px;margin-bottom:20px;"> <img src="http://tomasp.net/articles/csharp-async-gotchas/async-clinic.png" style="width:379px;" /> </div> <p>One (non-NDA) talk was the <a href="http://blogs.msdn.com/b/pfxteam/archive/2013/02/20/mvp-summit-presentation-on-async.aspx" title="Lucian Wischik, Stephen Toub: Async Clinic">Async Clinic</a> [<a href="#rf13041502">1</a>] talk about the new <code>async</code> and <code>await</code> keywords in C# 5.0. Lucian and Stephen talked about common problems that C# developers face when writing asynchronous programs. In this blog post, I'll look at some of the problems from the F# perspective. The talk was quite lively, and someone recorded the reaction of the F# part of the audience as follows...</p> F# Data: New type provider libraryhttp://tomasp.net/blog/fsharp-data.aspxThu, 28 Mar 2013 03:23:41 GMTF# Data is a new library that gives you all you need to access data in F# 3.0. It implements type providers for WorldBank, Freebase and structured document formats (CSV, JSON and XML) as well as other helpers. This article introduces the library and gives a quick overview of its features.Tomas Petricek<img src="https://raw.github.com/fsharp/FSharp.Data/master/misc/logo.png" class="rdecor" style="width:120px;height:120px;" /> <p>When F# 3.0 type providers were still in beta version, I wrote a couple of type providers as examples for talks. These included the WorldBank type provider (now available <a href="http://www.tryfsharp.org">on Try F#</a>) and also type provider for XML that infered the structure from sample. <br /> For some time, these were hosted as part of <a href="https://github.com/fsharp/fsharpx/">FSharpX</a> and the authors of FSharpX also added a number of great features.</p> <p>When I found some more time earlier this year, I decided to start a new library that would be fully focused on data access in F# and on type providers and I started working on <strong>F# Data</strong>. The library has now reached a stable state and <a href="http://www.navision-blog.de/blog/2013/03/27/fsharpx-1-8-removes-support-for-document-type-provider/">Steffen also announced</a> that the document type providers (JSON, XML and CSV) are not going to be available in FSharpX since the next version.</p> <p>This means that if you're interested in accessing data using F# type providers, you should now go to F# Data. Here are the most important links:</p> <ul> <li><a href="https://github.com/fsharp/FSharp.Data">F# Data source code on GitHub</a></li> <li><a href="http://fsharp.github.com/FSharp.Data/">F# Data documentation & tutorials</a></li> <li><a href="http://nuget.org/packages/FSharp.Data">F# Data on NuGet</a></li> </ul> <p>Before looking at the details, I would like to thank to <a href="https://github.com/ovatsus">Gustavo Guerra</a> who made some amazing contributions to the library! (More contributors are always welcome, so continue reading if you're interested...)</p> Upcoming F# talks and trainings (London, NYC & Boston)http://tomasp.net/blog/events-winter-2013.aspxThu, 07 Feb 2013 23:00:22 GMTAfter a few years, I will be attending the MVP summit again this year. The good news for those interested in F# is that I have two talks scheduled along the way in New York and Boston. Aside from that, we also have dates for a new F# course in London and New Year!Tomas Petricek<img src="http://tomasp.net/articles/events-winter-2013/mvplogo.png" class="rdecor" title="Tomas Petricek" style="margin:10px 35px 15px 35px;width:100px" /> <p>After a few years, I finally managed to find the time to attend the <a href="http://www.2013mvpsummit.com/">MVP Summit</a> this year. The Summit is an annual event where people who are active in Microsoft technical communities come to the Microsoft headquarters to learn about new things (and, of course, tell them how they should be doing their job :-)). The Summit is a great place to meet interesting people (so if you're reading this and will be there, definitely get in touch!) </p> <p>The good news - for those interested in F# - is that I'll be doing two F# talks on the way and we also have a new F# course scheduled for later in the year. <a href="http://tomasp.net/blog/events-winter-2013.aspx">Continue reading to learn more!</a></p>Announcing: Literate programming tools for F#http://tomasp.net/blog/fsharp-literate-programming.aspxTue, 22 Jan 2013 17:35:36 GMTThis article introduces a new F# package that makes it possible to write literate F# programs that combine code with documentation. Given an F# script with a special comments or Markdown document with F# code, you get a nicely formatted HTML that can be used to build documentation or write blogs.Tomas Petricek<img src="http://tomasp.net/articles/fsharp-literate-programming/logo.png" class="rdecor" style="width:120px;height:120px;" /> <p>For some time now, I've been writing my F# blog posts (and other F# articles published elsewhere) by combining F# code snippets and Markdown formatting. In fact, I even wrote a Markdown parser in F# so that I can post-process documents (to generate references etc). You can read about the Markdown parser in an upcoming <a href="http://manning.com/petricek2/">F# Deep Dives</a> book - currently, it is available as a free chapter!</p> <p>During the Christmas break, I finally found enough time to clean-up the code I was using and package it properly into a documented library that is easy to install and use. Here are the most important links:</p> <ul> <li><a href="http://tpetricek.github.com/FSharp.Formatting">F# Formatting home page</a></li> <li><a href="https://github.com/tpetricek/FSharp.Formatting">F# Formatting source code</a> on GitHub</li> <li><a href="https://nuget.org/packages/FSharp.Formatting">F# Formatting package</a> on NuGet</li> </ul> <p>To learn more about the tool and how to use it, <a href="http://tomasp.net/blog/fsharp-literate-programming.aspx">continue reading!</a></p>Processing trees with F# zipper computationhttp://tomasp.net/blog/tree-zipper-query.aspxWed, 19 Dec 2012 14:22:47 GMTOne of the less frequently advertised new features in F# 3.0 is the query syntax. It allows adding custom operations to a computation expression block. This article shows how to define a custom computation for processing trees using zippers. We'll add navigation over a tree as custom operations to get a simple syntax.Tomas Petricek<p>One of the less frequently advertised new features in F# 3.0 is the <em>query syntax</em>. It is an extension that makes it possible to add custom operations in an F# computation expression. The standard <code>query { .. }</code> computation uses this to define operations such as sorting (<code>sortBy</code> and <code>sortByDescending</code>) or operations for taking and skipping elements (<code>take</code>, <code>takeWhile</code>, ...). For example, you can write:</p> <pre class="fssnip"> <span class="l">1: </span><span onmouseout="hideTip(event, 'fstip1', 1)" onmouseover="showTip(event, 'fstip1', 1)" class="i">query</span> { <span class="k">for</span> <span onmouseout="hideTip(event, 'fstip2', 2)" onmouseover="showTip(event, 'fstip2', 2)" class="i">x</span> <span class="k">in</span> <span class="n">1</span> <span class="o">..</span> <span class="n">10</span> <span class="k">do</span> <span class="l">2: </span> <span onmouseout="hideTip(event, 'fstip3', 3)" onmouseover="showTip(event, 'fstip3', 3)" class="k">take</span> <span class="n">3</span> <span class="l">3: </span> <span onmouseout="hideTip(event, 'fstip4', 4)" onmouseover="showTip(event, 'fstip4', 4)" class="k">sortByDescending</span> <span onmouseout="hideTip(event, 'fstip2', 5)" onmouseover="showTip(event, 'fstip2', 5)" class="i">x</span> }</pre> <p>In this article I'll use the same notation for processing trees using the <em>zipper</em> pattern. I'll show how to define a computation that allows you to traverse a tree and perform transformations on (parts) of the tree. For example, we'll be able to say "Go to the left sub-tree, multiply all values by 2. Then go back and to the right sub-tree and divide all values by 2" as follows:</p> <pre class="fssnip"> <span class="l">1: </span><span onmouseout="hideTip(event, 'fsdtip1', 1)" onmouseover="showTip(event, 'fsdtip1', 1)" class="i">tree</span> { <span class="k">for</span> <span onmouseout="hideTip(event, 'fsdtip2', 2)" onmouseover="showTip(event, 'fsdtip2', 2)" class="i">x</span> <span class="k">in</span> <span onmouseout="hideTip(event, 'fsdtip3', 3)" onmouseover="showTip(event, 'fsdtip3', 3)" class="i">sample</span> <span class="k">do</span> <span class="l">2: </span> <span onmouseout="hideTip(event, 'fsdtip4', 4)" onmouseover="showTip(event, 'fsdtip4', 4)" class="k">left</span> <span class="l">3: </span> <span onmouseout="hideTip(event, 'fsdtip5', 5)" onmouseover="showTip(event, 'fsdtip5', 5)" class="k">map</span> (<span onmouseout="hideTip(event, 'fsdtip2', 6)" onmouseover="showTip(event, 'fsdtip2', 6)" class="i">x</span> <span class="o">*</span> <span class="n">2</span>) <span class="l">4: </span> <span onmouseout="hideTip(event, 'fsdtip6', 7)" onmouseover="showTip(event, 'fsdtip6', 7)" class="k">up</span> <span class="l">5: </span> <span onmouseout="hideTip(event, 'fsdtip7', 8)" onmouseover="showTip(event, 'fsdtip7', 8)" class="k">right</span> <span class="l">6: </span> <span onmouseout="hideTip(event, 'fsdtip5', 9)" onmouseover="showTip(event, 'fsdtip5', 9)" class="k">map</span> (<span onmouseout="hideTip(event, 'fsdtip2', 10)" onmouseover="showTip(event, 'fsdtip2', 10)" class="i">x</span> <span class="o">/</span> <span class="n">2</span>) <span class="l">7: </span> <span onmouseout="hideTip(event, 'fsdtip8', 11)" onmouseover="showTip(event, 'fsdtip8', 11)" class="k">top</span> }</pre> <p>This example behaves quite differently to the usual <code>query</code> computation. It mostly relies on custom operations like <code>left</code>, <code>right</code> and <code>up</code> that allow us to navigate through a tree (descend along the left or right sub-tree, go back to the parent node). The only operation that <em>does something</em> is the <code>map</code> operation which transforms the current sub-tree.</p> <p>This was just a brief introduction to what is possible, so let's take a detailed look at how this works...</p> <!-- HTML for Tool Tips --> <div class="tip" id="fstip1">val query : Linq.QueryBuilder<br /><br />Full name: Microsoft.FSharp.Core.ExtraTopLevelOperators.query</div> <div class="tip" id="fstip2">val x : int</div> <div class="tip" id="fstip3">custom operation: take (int)<br /><br />Calls Linq.QueryBuilder.Take </div> <div class="tip" id="fstip4">custom operation: sortByDescending ('Key)<br /><br />Calls Linq.QueryBuilder.SortByDescending </div> <div class="tip" id="fstip5">type Tree<'T> =<br /> | Node of Tree<'T> * Tree<'T><br /> | Leaf of 'T<br /> override ToString : unit -> string<br /><br />Full name: Tree-zipper-query.Tree<_></div> <div class="tip" id="fstip6">union case Tree.Node: Tree<'T> * Tree<'T> -> Tree<'T></div> <div class="tip" id="fstip7">union case Tree.Leaf: 'T -> Tree<'T></div> <div class="tip" id="fstip8">val x : Tree<'T></div> <div class="tip" id="fstip9">override Tree.ToString : unit -> string<br /><br />Full name: Tree-zipper-query.Tree`1.ToString</div> <div class="tip" id="fstip10">match x with<br /> | Node(l, r) -> sprintf "(%O, %O)" l r<br /> | Leaf v -> sprintf "%O" v</div> <div class="tip" id="fstip11">type Path<'T> =<br /> | Top<br /> | Left of Path<'T> * Tree<'T><br /> | Right of Path<'T> * Tree<'T><br /> override ToString : unit -> string<br /><br />Full name: Tree-zipper-query.Path<_></div> <div class="tip" id="fstip12">union case Path.Top: Path<'T></div> <div class="tip" id="fstip13">union case Path.Left: Path<'T> * Tree<'T> -> Path<'T></div> <div class="tip" id="fstip14">union case Path.Right: Path<'T> * Tree<'T> -> Path<'T></div> <div class="tip" id="fstip15">val x : Path<'T></div> <div class="tip" id="fstip16">override Path.ToString : unit -> string<br /><br />Full name: Tree-zipper-query.Path`1.ToString</div> <div class="tip" id="fstip17">match x with<br /> | Top -> "T"<br /> | Left(p, t) -> sprintf "L(%O, %O)" p t<br /> | Right(p, t) -> sprintf "R(%O, %O)" p t</div> <div class="tip" id="fstip18">type TreeZipper<'T> =<br /> | TZ of Tree<'T> * Path<'T><br /> override ToString : unit -> string<br /><br />Full name: Tree-zipper-query.TreeZipper<_></div> <div class="tip" id="fstip19">union case TreeZipper.TZ: Tree<'T> * Path<'T> -> TreeZipper<'T></div> <div class="tip" id="fstip20">val x : TreeZipper<'T></div> <div class="tip" id="fstip21">override TreeZipper.ToString : unit -> string<br /><br />Full name: Tree-zipper-query.TreeZipper`1.ToString</div> <div class="tip" id="fstip22">let (TZ(t, p)) = x in sprintf "%O [%O]" t p</div> <div class="tip" id="fstip23">val left : _arg1:TreeZipper<'a> -> TreeZipper<'a><br /><br />Full name: Tree-zipper-query.left<br /><em><br /><br /> Navigates to the left sub-tree</em></div> <div class="tip" id="fstip24">val failwith : message:string -> 'T<br /><br />Full name: Microsoft.FSharp.Core.Operators.failwith</div> <div class="tip" id="fstip25">val l : Tree<'a></div> <div class="tip" id="fstip26">val r : Tree<'a></div> <div class="tip" id="fstip27">val p : Path<'a></div> <div class="tip" id="fstip28">val right : _arg1:TreeZipper<'a> -> TreeZipper<'a><br /><br />Full name: Tree-zipper-query.right<br /><em><br /><br /> Navigates to the right sub-tree</em></div> <div class="tip" id="fstip29">val current : _arg1:TreeZipper<'a> -> 'a<br /><br />Full name: Tree-zipper-query.current<br /><em><br /><br /> Gets the value at the current position</em></div> <div class="tip" id="fstip30">val x : 'a</div> <div class="tip" id="fstip31">val branches : Tree<int><br /><br />Full name: Tree-zipper-query.branches</div> <div class="tip" id="fstip32">val sample : TreeZipper<int><br /><br />Full name: Tree-zipper-query.sample</div> <div class="tip" id="fstip33">val printfn : format:Printf.TextWriterFormat<'T> -> 'T<br /><br />Full name: Microsoft.FSharp.Core.ExtraTopLevelOperators.printfn</div> <div class="tip" id="fstip34">val up : _arg1:TreeZipper<'a> -> TreeZipper<'a><br /><br />Full name: Tree-zipper-query.up</div> <div class="tip" id="fstip35">val top : _arg1:TreeZipper<'a> -> TreeZipper<'a><br /><br />Full name: Tree-zipper-query.top</div> <div class="tip" id="fstip36">val t : TreeZipper<'a></div> <div class="tip" id="fstip37">val tz : TreeZipper<'a></div> <div class="tip" id="fstip38">Multiple items<br />val unit : v:'a -> TreeZipper<'a><br /><br />Full name: Tree-zipper-query.unit<br /><em><br /><br /> Build tree zipper with singleton tree</em><br /><br />--------------------<br />type unit = Unit<br /><br />Full name: Microsoft.FSharp.Core.unit</div> <div class="tip" id="fstip39">val v : 'a</div> <div class="tip" id="fstip40">val bindSub : f:('a -> TreeZipper<'a>) -> treeZip:TreeZipper<'a> -> TreeZipper<'a><br /><br />Full name: Tree-zipper-query.bindSub<br /><em><br /><br /> Transform leaves in the current sub-tree of 'treeZip'<br /> into other trees using the provided function 'f'</em></div> <div class="tip" id="fstip41">val f : ('a -> TreeZipper<'a>)</div> <div class="tip" id="fstip42">val treeZip : TreeZipper<'a></div> <div class="tip" id="fstip43">val bindT : (Tree<'a> -> Tree<'a>)</div> <div class="tip" id="fstip44">val t : Tree<'a></div> <div class="tip" id="fstip45">val current : Tree<'a></div> <div class="tip" id="fstip46">val path : Path<'a></div> <div class="tip" id="fstip47">Multiple items<br />type TreeZipperBuilder =<br /> new : unit -> TreeZipperBuilder<br /> member Current : tz:TreeZipper<'a> -> 'a<br /> member For : tz:TreeZipper<'T> * f:('T -> TreeZipper<'T>) -> TreeZipper<'T><br /> member Left : tz:TreeZipper<'a> -> TreeZipper<'a><br /> member Right : tz:TreeZipper<'a> -> TreeZipper<'a><br /> member Select : tz:TreeZipper<'a> * f:('a -> 'a) -> TreeZipper<'a><br /> member Top : tz:TreeZipper<'a> -> TreeZipper<'a><br /> member Up : tz:TreeZipper<'a> -> TreeZipper<'a><br /> member Yield : v:'a -> TreeZipper<'a><br /><br />Full name: Tree-zipper-query.TreeZipperBuilder<br /><br />--------------------<br />new : unit -> TreeZipperBuilder</div> <div class="tip" id="fstip48">val x : TreeZipperBuilder</div> <div class="tip" id="fstip49">member TreeZipperBuilder.For : tz:TreeZipper<'T> * f:('T -> TreeZipper<'T>) -> TreeZipper<'T><br /><br />Full name: Tree-zipper-query.TreeZipperBuilder.For<br /><em><br /><br /> Enables the 'for x in xs do ..' syntax</em></div> <div class="tip" id="fstip50">val tz : TreeZipper<'T></div> <div class="tip" id="fstip51">val f : ('T -> TreeZipper<'T>)</div> <div class="tip" id="fstip52">member TreeZipperBuilder.Yield : v:'a -> TreeZipper<'a><br /><br />Full name: Tree-zipper-query.TreeZipperBuilder.Yield<br /><em><br /><br /> Enables the 'yield x' syntax</em></div> <div class="tip" id="fstip53">val tree : TreeZipperBuilder<br /><br />Full name: Tree-zipper-query.tree<br /><em><br /><br /> Global instance of the computation builder</em></div> <div class="tip" id="fstip54">Multiple items<br />type CustomOperationAttribute =<br /> inherit Attribute<br /> new : name:string -> CustomOperationAttribute<br /> member AllowIntoPattern : bool<br /> member IsLikeGroupJoin : bool<br /> member IsLikeJoin : bool<br /> member IsLikeZip : bool<br /> member JoinConditionWord : string<br /> member MaintainsVariableSpace : bool<br /> member MaintainsVariableSpaceUsingBind : bool<br /> member Name : string<br /> ...<br /><br />Full name: Microsoft.FSharp.Core.CustomOperationAttribute<br /><br />--------------------<br />new : name:string -> CustomOperationAttribute</div> <div class="tip" id="fstip55">member TreeZipperBuilder.Left : tz:TreeZipper<'a> -> TreeZipper<'a><br /><br />Full name: Tree-zipper-query.TreeZipperBuilder.Left</div> <div class="tip" id="fstip56">member TreeZipperBuilder.Right : tz:TreeZipper<'a> -> TreeZipper<'a><br /><br />Full name: Tree-zipper-query.TreeZipperBuilder.Right</div> <div class="tip" id="fstip57">member TreeZipperBuilder.Up : tz:TreeZipper<'a> -> TreeZipper<'a><br /><br />Full name: Tree-zipper-query.TreeZipperBuilder.Up</div> <div class="tip" id="fstip58">member TreeZipperBuilder.Top : tz:TreeZipper<'a> -> TreeZipper<'a><br /><br />Full name: Tree-zipper-query.TreeZipperBuilder.Top</div> <div class="tip" id="fstip59">member TreeZipperBuilder.Current : tz:TreeZipper<'a> -> 'a<br /><br />Full name: Tree-zipper-query.TreeZipperBuilder.Current<br /><em><br /><br /> Extracts the current value and returns it</em></div> <div class="tip" id="fstip60">member TreeZipperBuilder.Select : tz:TreeZipper<'a> * f:('a -> 'a) -> TreeZipper<'a><br /><br />Full name: Tree-zipper-query.TreeZipperBuilder.Select<br /><em><br /><br /> Transform the current sub-tree using 'f'</em></div> <div class="tip" id="fstip61">Multiple items<br />type ProjectionParameterAttribute =<br /> inherit Attribute<br /> new : unit -> ProjectionParameterAttribute<br /><br />Full name: Microsoft.FSharp.Core.ProjectionParameterAttribute<br /><br />--------------------<br />new : unit -> ProjectionParameterAttribute</div> <div class="tip" id="fstip62">val f : ('a -> 'a)</div> <div class="tip" id="fstip63">custom operation: right<br /><br />Calls TreeZipperBuilder.Right </div> <div class="tip" id="fstip64">custom operation: left<br /><br />Calls TreeZipperBuilder.Left </div> <div class="tip" id="fstip65">custom operation: current<br /><br />Calls TreeZipperBuilder.Current <br /><em><br /><br /> Extracts the current value and returns it</em></div> <div class="tip" id="fstip66">custom operation: map ('a)<br /><br />Calls TreeZipperBuilder.Select <br /><em><br /><br /> Transform the current sub-tree using 'f'</em></div> <div class="tip" id="fstip67">custom operation: up<br /><br />Calls TreeZipperBuilder.Up </div> <div class="tip" id="fstip68">custom operation: top<br /><br />Calls TreeZipperBuilder.Top </div> <div class="tip" id="fsdtip1">val tree : TreeZipperBuilder<br /><br />Full name: Tree-zipper-query.tree<br /><em><br /><br /> Global instance of the computation builder</em></div> <div class="tip" id="fsdtip2">val x : int</div> <div class="tip" id="fsdtip3">val sample : TreeZipper<int><br /><br />Full name: Tree-zipper-query.sample</div> <div class="tip" id="fsdtip4">custom operation: left<br /><br />Calls TreeZipperBuilder.Left </div> <div class="tip" id="fsdtip5">custom operation: map ('a)<br /><br />Calls TreeZipperBuilder.Select <br /><em><br /><br /> Transform the current sub-tree using 'f'</em></div> <div class="tip" id="fsdtip6">custom operation: up<br /><br />Calls TreeZipperBuilder.Up </div> <div class="tip" id="fsdtip7">custom operation: right<br /><br />Calls TreeZipperBuilder.Right </div> <div class="tip" id="fsdtip8">custom operation: top<br /><br />Calls TreeZipperBuilder.Top </div> Manning: F# Deep Dives deal of the dayhttp://tomasp.net/blog/manning-deep-dives.aspxTue, 18 Dec 2012 17:19:57 GMTThere is an increasing number of commercial F# uses. If you want to learn about the domains where F# is used (including finance, game development, machine learning and other) as well as about common programming techniques in F#, then the upcoming <strong>F# Deep Dives</strong> book is the book for you!Tomas Petricek<img src="http://tomasp.net/articles/manning-deep-dives/cover.jpg" class="rdecor" title="F# Deep Dives" style="margin-bottom:15px" /> <p> The F# language has been around for longer than many people suspect. My <a href="http://tomasp.net/blog/fsquotations.aspx">first, completely outdated, blog post</a> was from May 2006. The Microsoft Research releases, sometime around 2006 were the first stable versions that gained some interest and slowly attracted commercial users. </p> <p>A lot has changed since the early days. F# now includes powerful features like <em>computation expressions</em> and <em>asynchronous workflows</em> and F# 3.0 comes with unique <em>type provider</em> mechanism. </p> <p>There is an increasing number of users from diverse domains: F# is used to model complex domains in <a href="http://techmeshconf.com/dl/techmesh-london-2012/slides/TobiasGedell_EdenAnFWPFFrameworkForBuildingGUITools.pdf">finance</a> and science; asynchronous and concurrent features are used to write server-side components of <a href="http://theburningmonk.com/">social games</a> and <a href="http://www.infoq.com/interviews/trelford-functional">trading systems</a>, but also in <a href="http://techmeshconf.com/dl/techmesh-london-2012/slides/AdamGranicz_DevelopingAndIntegratingWebSharperApplicationsWithFacebook.pdf">web programming</a>; the expressivity of F# is used by machine learning experts to handle dirty data or <a href="http://www.dotnetrocks.com/default.aspx?showNum=293">classify XBox players</a>. Moreover, the <a href="http://fsharp.org">F# Software Foundation</a> has been recently founded to support the collaboration between different commercial users, open-source community and academia. </p> <p>There is an increasing interest in F#, but many of those who approach it ask (excellent) questions such as: <em>"In what problem domains can I benefit from F#?"</em> or <em>"How do I use F# in finance/science/gaming or web programming?"</em> and most importantly <em>"How do I approach different problems in F#?"</em> </p>Learn F# at TechMesh and SkillsMetterhttp://tomasp.net/blog/more-events-autumn-2012.aspxSun, 21 Oct 2012 16:53:04 GMTLooking for an event where you could learn about F#? The second half of autumn will be a busy time with Progressive F# Tutorials happening at the beginning of November and the TechMesh Conference planned for the first week in December!Tomas Petricek<img src="http://tomasp.net/articles/more-events-autumn-2012/tomas-qcon.jpg" class="rdecor" title="Tomas Petricek" style="margin-bottom:15px" /> <p>Autumn is a busy period and I already invited you to a <a href="http://tomasp.net/blog/events-autumn-2012.aspx">couple of interesting events</a>, but there are two more events that you definitely should not miss. In only two weeks, you can come to two-day <a href="http://skillsmatter.com/event/scala/progfsharp-2012">Progressive F# Tutorials</a> packed with tutorials for both F# beginners and experts. At the beginning of December, the <a href="http://techmeshconf.com/">TechMesh Conference</a> comes with three days of talks about alternative (and future) technologies. </p> <p>I'll be speaking at both Progressive F# Tutorials and TechMesh and I'm also doing a tutorial at TechMesh, so if you want to learn about F#, type providers in F# 3.0 and financial computing with F#, here are some talks that you should not miss... </p> Applicative functors: definition and syntaxhttp://tomasp.net/blog/applicative-functors.aspxTue, 21 Aug 2012 14:23:19 GMTIn a recent blog post, Edward Z. Yang talks about applicative functors. He mentions two equivalent definitions - the standard one used in Haskell and an alternative mentioned in the original paper. In this blog post, I describe some reasons why the alternative definition is useful.Tomas Petricek<p>In a recent blog post, <a href="http://blog.ezyang.com/2012/08/applicative-functors/" title="Edward Z. Yang: Applicative functors">Edward Z. Yang talks about applicative functors</a>. He mentions two equivalent definitions of applicative functors - the standard definition used in Haskell libraries (<code>Applicative</code>) and an alternative that has been also presented in the <a href="http://www.soi.city.ac.uk/~ross/papers/Applicative.html" title="C. McBride and R. Paterson: Applicative Programming with Effects">original paper</a>, but is generally less familiar (<code>Monoidal</code>).</p> <p>The standard definition makes a perfect sense with the standard uses in Haskell, however I always preferred the alternative definition. Edward uses the alternative (<code>Monoidal</code>) definition to explain the laws that should hold about applicative functors and to explain <em>commutative</em> applicative functors, but I think it is even more useful.</p> <p>The <code>Monoidal</code> definition fits nicely with a trick that you can use to <a href="http://tomasp.net/blog/idioms-in-linq.aspx" title="T. Petricek: Beyond the Monad fashion (I.): Writing idioms in LINQ">encode applicative functors in C# using LINQ</a> and I also used it as a basis for an F# syntax extension that allows writing code using applicative functors in a similar style as using monads (which is discussed in my draft paper about <a href="http://www.cl.cam.ac.uk/~tp322/papers/notations.html" title="T. Petricek and D. Syme: Syntax Matters: Writing abstract computations in F#">writing abstract computations in F#</a>). And I also think that <em>commutative</em> applicative functors deserve more attention.</p>Why type-first development mattershttp://tomasp.net/blog/type-first-development.aspxThu, 16 Aug 2012 00:21:21 GMTThis article describes type-first development (TFD). A software development methodology that is quite common among functional programmers and uses types as a simple way of communicating ideas about program design.Tomas Petricek<img src="http://tomasp.net/articles/type-first-development/tfd.png" class="rdecor" /> <p>Using functional programming language changes the way you write code in a number of ways. Many of the changes are at a <em>small-scale</em>. For example, you learn how to express computations in a shorter, more declarative way using higher-order functions. However, there are also many changes at a <em>large-scale</em>. The most notable one is that, when designing a program, you start thinking about the (data) types that represent the data your code works with.</p> <p>In this article, I describe this approach. Since the acronym TDD is already taken, I call the approach Type-First Development (TFD), which is probably a better name anyway. The development is not <em>driven</em> by types. It <em>starts</em> with types, but the rest of the implementation can still use test-driven development for the implementation.</p> <p>This article demonstrates the approach using a case study from a real life: My example is a project that I started working on with a friend who needed a system to log journeys with a company car (for expense reports). Using the type-first approach made it easier to understand and discuss the problem.</p> <p>In many ways, TFD is a very simple approach, so this article just gives a name to a practice that is quite common among functional and F# programmers (and we have been <a href="http://functional-programming.net/courses/">teaching it at our F# trainings</a> for the last year)...</p>F# Courses and Talks for Autumn 2012 (I.)http://tomasp.net/blog/events-autumn-2012.aspxWed, 08 Aug 2012 03:47:08 GMTThis article is an invitation to a number of F# events at the end of summer and during autumn. Aside from F# trainings in New York and London, I will be also doing an F# tutorial at CUFP in Copenhagen.Tomas Petricek<img src="http://tomasp.net/articles/events-autumn-2012/tomas.jpg" class="rdecor" title="Tomas Petricek" style="margin-bottom:15px" /> <p>Similarly to the <a href="http://tomasp.net/blog/fsharp-autumn-2011.aspx">last year</a>, I already have a number of F# events planned for the end of the summer and autumn that I'd like to invite you to!</p> <p>The <a href="http://www.infoq.com/news/2012/08/VS2012-Live">Visual Studio 2012 has been completed</a> recently and it comes with F# 3.0. For me, this means two things. Firstly, it is the second Visual Studio version of F#, which means that functional programming is worth taking seriously. Secondly, F# 3.0 comes with <em>type providers</em>, which is a killer feature for working with data. No matter if you're a C# programmer now to functional programming or if you're an F# user in the real-world, I hope you can find some interesting and useful event below! </p> <p>The two main things that I'm going to be involved in are SkilsMatter trainings in London and New York and a few events at the biggest functional conference (ICFP) in Copenhagen...</p> The theory behind covariance and contravariance in C# 4http://tomasp.net/blog/variance-explained.aspxTue, 19 Jun 2012 14:24:52 GMTCovariance and contravariance are two useful features of generics in C# 4.0. Most of the time you don't see them. They just let you write code that you'd expect to work. Actually understanding how they work is more difficult. In this article, I explain that, together with some theory where the two concepts come from.Tomas Petricek<img src="http://tomasp.net/articles/variance-explained/icon.png" title="Category theory is sometimes called 'general abstract nonsense', but it can actually be useful!" class="rdecor" /> <p>In C# 4.0, we can annotate generic type parameters with <code>out</code> and <code>in</code> annotations to specify whether they should behave <em>covariantly</em> or <em>contravariantly</em>. This is mainly useful when using already defined standard interfaces. Covariance means that you can use <code>IEnumerable<string></code> in place where <code>IEnumerable<object></code> is expected. Contravariance allows you to pass <code>IComparable<object></code> as an argument of a method taking <code>IComparable<string></code>.</p> <p>So far, so good. If you already learned about covariance and contravariance in C# 4, then the above two examples are probably familiar. If you're new to the concepts, then the examples should make sense (after a bit of thinking, but I'll say more about them). However, there is still a number of questions. Is there some easy way to explain the two concepts? Why one option makes sense for some types and the other for different types? And why the hell is it called <em>covariance</em> and <em>contravariance</em> anyway?</p> <p>In this blog post, I'll explain some of the mathematics that you can use to think about covariance and contravariance.</p> Reporting events from F# Agentshttp://tomasp.net/blog/agent-event-reporting.aspxSat, 16 Jun 2012 00:23:35 GMTThis article describes different options for reporting events from F# agents. The options include triggering the event directly, using thread pool and in a specified context.Tomas Petricek<p>Over the last year, I wrote quite a lot of articles about agent-based programming in F#. Agents (inspired by Erlang) provide a great abstraction for writing concurrent and scalable systems. They are a great fit for both server-side development (for example, handling a large number of concurrent requests), but also for user interface (for example, keeping state in an application with background tasks and interactive interface).</p> <p>When writing reusable agents, we usually encapsulate agent in an F# object type. The type provides methods for sending messages to the agent. However, sometimes the agent also needs to report some state change that can be handled by another interested agent. This is done using F# events. However, F# events do not specify threading behaviour, so there is a number of options.</p> <p>In this article (inspired by a recent email discussion), I describe three ways of reporting events from an agent. The options differ in what thread is used to report the event. Choosing the right option is important as it affects scalability and simplicity of your agent-based code.</p> F# in Academia: Present at upcoming events!http://tomasp.net/blog/fsharp-academia.aspxMon, 16 Apr 2012 00:19:04 GMTThe F# language combines the best from practice and academia. If you're working on interesting application of F#, have an experience worth sharing or some interesting research or idea, there are two workshops where you can share the idea with wider research and practitioner community, so consider submitting a talk!Tomas Petricek<p>The F# language was born as a combination of the pragmatic and real-world .NET platform and functional programming, which had a long tradition in academia. Many useful ideas or libraries in F# (like <em>asynchronous workflows</em> and <em>first-class events</em>) are inspored by research in functional programming (namely, the work on <em>monads</em>, <em>continuations</em> and <em>functional reactive programming</em>).</p> <p>Exchanging the ideas between the research community and the real-world is one of the areas where F# excels. Indeed, the first applicatiosn of F# inside Microsoft (in the Machine Learning group at Cambridge) were all about this - combining research in machine learning with a language that can be easily used in practice.</p> <p>However, F# and the F# users also made numerous contributions to the programming language research community. Influential ideas that come from F# include <em>active patterns</em> and the F# style of <em>meta-programming</em> for translating F# to JavaScript). I think there is a lot more that the academic community can learn from the F# community, so I'd like to invite you to talk about your ideas at two upcoming academic events!</p> <p>What, why, when, where and how? <a href="http://tomasp.net/blog/fsharp-academia.aspx">Continue reading!</a></p>TryJoinads (VII.) - Implementing joinads for async workflowshttp://tomasp.net/blog/joinads-async-implement.aspxFri, 23 Mar 2012 17:21:51 GMTIn the final article of the TryJoinads series, I discuss how to implement the joinad structure for F# asynchronous workflows. The article also demonstrates the importance of aliasing for <code>match!</code> notation.Tomas Petricek<p>The article <a href="http://tomasp.net/blog/joinads-async-prog.aspx">Asynchronous workflows and joinads</a> gives numerous examples of programming with asynchronous workflows using the <code>match!</code> construct. Briefly, when matching on multiple asynchronous workflows, they are executed in parallel. When pattern matching consists of multiple clauses, the clause that matches on computations that complete first gets executed. These two behaviours are implemented by the <code>Merge</code> and the <code>Choose</code> operation of joinads. Additionally, asynchronous workflows require the <code>Alias</code> operation, which makes it possible to share the result of a started asynchronous workflow in multiple clauses.</p> <p>In this article, we look at the definition of the additional <code>AsyncBuilder</code> operations that enable the <code>match!</code> syntax. We do not look at additional examples of using the syntax, because these can be <a href="http://tomasp.net/blog/joinads-async-prog.aspx">found in a previous article</a>.</p> <p><em><strong>Note:</strong> This blog post is a re-publication of a tutorial from the <a href="http://tryjoinads.org">TryJoinads.org</a> web page. If you read the article there, you can run the examples interactively and experiment with them: <a href="http://tryjoinads.org/index.html?implement/async.html">view the article on TryJoinads</a>.</em></p> TryJoinads (VI.) - Parsing with joinadshttp://tomasp.net/blog/joinads-parsing.aspxWed, 21 Mar 2012 16:27:06 GMTThis article shows how to use joinads (and the <code>match!</code> extension) for writing parsers. Using joinads one can easily express choice and write a parser that recognizes an intersection of languages.Tomas Petricek<p>In functional programming, parser combinators are a powerful way of writing parsers. A parser is a function that, given some input, returns possible parsed values and the rest of the input. Parsers can be written using combinators for composition, for example run two parsers in sequence or perform one parser any number of times.</p> <p>Parsers can also implement the monad structure. In some cases, this makes the parser less efficient, but it is an elegant way of composing parsers and we can also benefit from the syntactic support for monads. In this article, we implement a simple parser combinators for F# and we look what additional expressive power we can get from the <em>joinad</em> structure and <code>match!</code> construct. This article is largely based on a previous article <em>"Fun with Parallel Monad Comprehensions"</em>, which can be found on the <a href="../pubs.html">publications</a> page.</p> <p><em><strong>Note:</strong> This blog post is a re-publication of a tutorial from the <a href="http://tryjoinads.org">TryJoinads.org</a> web page. If you read the article there, you can run the examples interactively and experiment with them: <a href="http://tryjoinads.org/index.html?implement/parsers.html">view the article on TryJoinads</a>.</em></p> Asynchronous client/server in F# (QCon 2012)http://tomasp.net/blog/qcon-async-fsharp.aspxMon, 12 Mar 2012 01:09:02 GMTLast week, I gave a talk on asynchronous programming in F# at QCon London. I used the one hour slot to implement a Social Rectangle Drawing App - an application that showed the importance of asynchronous workflows on both client-side and server-side.Tomas Petricek<img src="http://tomasp.net/articles/qcon-async-fsharp/qcon.png" alt="Qcon" class="rdecor" /> <p>Last week, I gave a talk on asynchronous programming in F# at <a href="http://qconlondon.com/london-2012">London QCon 2012</a>. The talk was a part of <a href="http://qconlondon.com/london-2012/tracks/show_track.jsp?trackOID=560">The Rise of Scala & Functional Programming</a> track organized by Charles Humble. Reactive and asynchronous programming was a topic that was repeated a couple of times during the whole session - Sadek Drobi talked about <a href="http://qconlondon.com/london-2012/presentation/Non%20blocking,%20composable%20reactive%20web%20programming%20with%20Iteratees%20in%20Play2">non-blocking reactive web framework Play2</a> and Damien Katz talked about <a href="http://qconlondon.com/london-2012/presentation/Erlang%20in%20the%20real%20world:%20CouchDB">Erlang and CouchDB</a>.</p> <p>I used the one hour slot to implement "Rectangle Drawing App" - a simple application that shows how to write complete client-server application just using F#. On the server-side, I used asynchronous workflows to write HTTP server with an F# agent. On the client-side, I used asynchronous workflows to express user interface logic and the <a href="http://pitfw.org/">Pit project</a> to run F# code as JavaScript that works everywhere. The app definitely had a huge commercial potential:</p> <div style="text-align:center"> <img src="http://tomasp.net/articles/qcon-async-fsharp/quote.png" alt="Quote" /> </div> TryJoinads (V.) - Implementing the option joinadhttp://tomasp.net/blog/joinads-options.aspxFri, 02 Mar 2012 13:24:21 GMTThe <code>match!</code> research extension for F# can be used to program with a number of monadic computations. In this article, we look how to support it in one of the simplest monads - the maybe monad.Tomas Petricek<p>This article shows how to implement the <em>joinad</em> structure for one of the simplest monads - the <code>option<'T></code> type. This is a slightly oversimplified example. The <code>match!</code> construct can be used to write patterns that specify that a monadic value (in this case <code>option<'T></code>) should contain a certain value, or we can specify that we do not require a value. When working with options, this means the same thing as matching the value against <code>Some</code> and against <code>_</code>, respectively.</p> <p>However, the example demonstrates the operations that need to be implemented and their type signatures. Later articles give more interesting examples including parsers and asynchronous workflows (and you can explore other examples if you look at the <a href="https://github.com/tpetricek/FSharp.Joinads">FSharp.Joiands source code</a> at GitHub).</p> <p><em><strong>Note:</strong> This blog post is a re-publication of a tutorial from the <a href="http://tryjoinads.org">TryJoinads.org</a> web page. If you read the article there, you can run the examples interactively and experiment with them: <a href="http://tryjoinads.org/index.html?implement/options.html">view the article on TryJoinads</a>.</em></p> TryJoinads (IV.) - Concurrency using join calculushttp://tomasp.net/blog/joinads-join-calculus.aspxWed, 22 Feb 2012 17:38:40 GMTThis article shows another application of the <code>match!</code> language extension for F#. This time, we look how to encode join calculus, which is an elegant abstraction for declarative concurrent programming.Tomas Petricek<p>Join calculus provides a declarative way of expressing asynchronous synchronization patterns. It has been use as a basis for programming languages (JoCaml and COmega), but also as a basis for libraries (embedded in C# and Scala). Using joinads, it is possible to embed join calculus in F# with a nice syntax using the <code>match!</code> construct. Formally, join calculus does not form a <em>monad</em>, but it can be viewed as a version of <em>joinad</em> as described in the <a href="../pubs.html">first paper on joinads</a>.</p> <p>The programming model is based on <em>channels</em> and <em>join patterns</em>. A channel can be viewed as a thread-safe mailbox into which we can put values without blocking the caller. In some sense, this is quite similar to <a href="agents.html">F# agents</a>. A join pattern is then a rule saying that a certain combination of values in channels should trigger a specific reaction (and remove values from the channels). The ability to match on multiple channels distinguishes join calculus from F# agents.</p> <p><em><strong>Note:</strong> This blog post is a re-publication of a tutorial from the <a href="http://tryjoinads.org">TryJoinads.org</a> web page. If you read the article there, you can run the examples interactively and experiment with them: <a href="http://tryjoinads.org/index.html?use/joins.html">view the article on TryJoinads</a>.</em></p> TryJoinads (III.): Agent-based programminghttp://tomasp.net/blog/joinads-agents.aspxMon, 20 Feb 2012 12:36:10 GMTAgent-based programming is a great way to write concurrent applications without the usual threading issues. In this article, we look how the "match!" research extension for F# simplifies writing agents. In particular, we can easily implement states that do not handle all incoming messages.Tomas Petricek<p>Another area where the <code>match!</code> syntax can be used is when programming with F# <em>agents</em>, implemented by the <code>MailboxProcessor</code> type. Formally, agents do not form the monad structure in a useful way - when programming with agents, we do not compose a new agents, but instead we write code that (imperatively) receives messages from the agent's mailbox and handles them.</p> <p>This article demonstrates an <code>agent { ... }</code> computation builder that can be used for implementing the body of an agent. Normally, the body of an agent is an <em>asynchronous workflow</em>. The code in the body uses <code>let!</code> to perform asynchronous operations, most importantly to call <code>inbox.Receive</code> to get the next message from the inbox. When the agent intends to handle only certain kinds of messages, it can use <code>inbox.Scan</code>. When using the <code>agent</code> builder, pattern matching on messages can be written using <code>match!</code> and it is possible to write code that ignores certain types of messages simply by writing an incomplete pattern matching.</p> <p><em><strong>Note:</strong> This blog post is a re-publication of a tutorial from the <a href="http://tryjoinads.org">TryJoinads.org</a> web page. If you read the article there, you can run the examples interactively and experiment with them: <a href="http://tryjoinads.org/index.html?use/agents.html">view the article on TryJoinads</a>.</em></p> TryJoinads (II.): Task-based parallelismhttp://tomasp.net/blog/joinad-tasks.aspxFri, 17 Feb 2012 13:10:29 GMTJoinads is a research extension of the F# compiler that makes computation expressions more expressive. In this article, we look how to use the <code>match!</code> notation for working with tasks. The examples include simple parallel map, but also more powerful speculative parallelism.Tomas Petricek<p>The implementation of joinad operations for the <code>Task<'T></code> type is quite similar to the implementation of <code>Async<'T></code>, because the two types have similar properties. They both produce at most one value (or an exception) and they both take some time to complete.</p> <p>Just like for asynchronous workflows, pattern matching on multiple computations using <code>match!</code> gives us a parallel composition (with the two tasks running in parallel) and choice between clauses is non-deterministic, depending on which clause completes first.</p> <p>Unlike asynchronous workflows, the <code>Task<'T></code> type does not require any support for aliasing. A value of type <code>Task<'T></code> represents a <em>running</em> computation that can be accessed from multiple parts of program. In this sense, the type <code>Async<'T></code> is more similar to a function <code>unit -> Task<'T></code> than to the type <code>Task<'T></code> itself.</p> <p>The key difference between tasks and asynchronous workflows is that the latter provides better support for writing non-blocking computations that involve <em>asynchronous</em> long-running operations such as I/O or waiting for a certain event. Tasks are more suitable for high-performance CPU-intensive computations.</p> <p><em><strong>Note:</strong> This blog post is a re-publication of a tutorial from the <a href="http://tryjoinads.org">TryJoinads.org</a> web page. If you read the article there, you can run the examples interactively and experiment with them: <a href="http://tryjoinads.org/index.html?use/tasks.html">view the article on TryJoinads</a>.</em></p> TryJoinads (I.) - Asynchronous programminghttp://tomasp.net/blog/joinads-async-prog.aspxMon, 13 Feb 2012 17:35:44 GMTThis article demonstrates the new expressive power that joinads add to F# asynchronous workflows. The match! syntax can be used for parallel composition, as well as choice, in a wide range of areas.Tomas Petricek<p>Asynchronous workflows provide a way of writing code that does not block a thread when waiting for a completion of long-running operation such as web service call, another I/O operation or waiting for the completion of some background operation. In this article, we look at the new expressive power that <em>joinads</em> add to asynchronous workflows written using the <code>async { ... }</code> block in F#.</p> <p><em><strong>Note:</strong> This blog post is a re-publication of a tutorial from the <a href="http://tryjoinads.org">TryJoinads.org</a> web page. If you read the article there, you can run the examples interactively and experiment with them: <a href="http://tryjoinads.org/index.html?use/async.html">view the article on TryJoinads</a>.</em></p> Introducing TryJoinads.orghttp://tomasp.net/blog/introducing-tryjoinads.aspxMon, 13 Feb 2012 16:21:03 GMTJoinads is a research extension of F# computation expressions that makes them more useful for parallel, concurrent and reactive programming. This article announces a web site TryJoinads.org where you can experiment with the extension using a web-based F# console.Tomas Petricek<div class="rdecor" style="text-align:center"> <a href="http://tomasp.net/articles/introducing-tryjoinads/screen.png" target="_blank"> <img src="http://tomasp.net/articles/introducing-tryjoinads/screen-sm.png" alt="TryJoinads.Org web site" style="border:none" /> </a><br /> <small>(<a href="http://tomasp.net/articles/introducing-tryjoinads/screen.png" target="_blank">Click for a larger version</a>)</small> </div> <p>If you have been following my blog, you've probably already heard of <em>joinads</em>. It is a research extension of F# computation expressions (or monads in Haskell). The extension makes computation expressions more useful in domains like parallel, concurrent and reactive programming. However, it can be used for any type of computation including, for example, parsers. If you're interested in detailed description, you can find it in two academic papers that I blogged about previously: <a href="http://tomasp.net/blog/match-bang-paper.aspx">PADL 2011</a> and <a href="http://tomasp.net/blog/docase-haskell.aspx">Haskell 2011</a>.</p> <p>The extension adds a keyword <code>match!</code> - as the syntax suggests, it is akin to pattern matching using <code>match</code>, but instead of pattern matching on values, you can pattern match on computations like <code>Async<'T></code> (or on other monadic values). Just like other features of computation expressions, the <code>match!</code> syntax is translated to applications of several methods defined by the computation builder.</p> <p>I won't say more about joinads in this post, because you can now easily try joinads yourself...</p>F# courses and talks (Winter 2012 and beyond...)http://tomasp.net/blog/fsharp-talks-courses-2012a.aspxFri, 13 Jan 2012 03:07:13 GMTA couple of months ago, I posted a list of my F# talks and courses for Autumn 2011. Although I tried hard to have fewer speaking engagements during the winter and spring, there are quite a few events thatTomas Petricek<img src="http://tomasp.net/articles/fsharp-talks-courses-2012a/tomas.jpg" class="rdecor" title="I'm not singing at an opera! That's a photo from a normal F# talk..." style="margin-bottom:15px" /> <p>A couple of months ago, I posted a list of my <a href="http://tomasp.net/blog/fsharp-autumn-2011.aspx"> F# talks and courses for Autumn 2011</a>. Although I tried hard to have <em>fewer</em> speaking engagements during the winter and spring, there are quite a few events that I'd like to invite you to. </p> <p>Last year, I spent quite a lot of time talking about asynchronous programming and agents. I think this is still a very important topic and especially agent-based programming in F# is a powerful way to implement concurrency primitives (like blocking queue), as well as complex systems (like <a href="http://www.trayport.com/en/joule/video">trading screens</a> and <a href="http://skillsmatter.com/podcast/scala/functional-londoners-may-meetup">market analysis</a>). I also wrote a series of articles on this topic that <a href="http://msdn.microsoft.com/en-us/library/hh273081.aspx">are available on MSDN</a> and should be a good starting point.</p> <p>Over the next few months, I'll be doing some talks about type providers, which is an upcoming F# 3.0 technology for accessing data. However, I also hope to find some time to look at other directions for F#, especially how it can be used in an online web-based environment, either using Azure or by translating F# to JavaScript using a recently announced <a href="http://pitfw.posterous.com/">open-source project named Pit</a>.</p> <p><a href="http://tomasp.net/blog/fsharp-talks-courses-2012a.aspx">Continue reading</a> to see the list of planned talks, tutorials and courses....</p>Regions and navigation bar for F# in Visual Studiohttp://tomasp.net/blog/regions-navigation.aspxSun, 01 Jan 2012 23:02:47 GMTThe beginning of a new year may be a good time for writing one lightweight blog post - this article shows two hidden features of F# IntelliSense in Visual Studio and also talks about writing plugins using the F# open-source release.Tomas Petricek<p>The beginning of a new year may be a good time for writing one lightweight blog post that I wanted to publish for some time now. During my last internship with the F# team at MSR, I did some work on improving the F# IntelliSense in Visual Studio. This mostly involved the usual features - automatic completion, colouring and tooltips. The F# IntelliSense in Visual Studio 2010 still isn't perfect, but I think it is safe to claim that it is the best IDE experience for a typed functional programming language (aside, you can vote for some F# IDE features <a href="http://visualstudio.uservoice.com/forums/121579-visual-studio/suggestions/2149735-improve-intellisense-support-for-f-">here</a> and <a href="http://visualstudio.uservoice.com/forums/121579-visual-studio/suggestions/2213611-provide-refactoring-support-for-f-code-">here</a>). </p> <div style="text-align:center"> <img src="http://tomasp.net/articles/regions-navbar/vs-small.png" title="F# with regions and navigation bar in Visual Studio" style="margin-bottom:5px;border-style:none" /> </div> F# Math (IV.) - Writing generic numeric codehttp://tomasp.net/blog/fsharp-generic-numeric.aspxSun, 27 Nov 2011 17:19:32 GMTWriting generic numeric code in .NET is difficult, because .NET generics do not support constraints specifying that a type has to support certain numeric operations. In this article, we look how to solve the problem in F#. Using static member constraints, it is possible to write simple generic calculations and using the INumeric interface, we can capture numeric operations for a type and use them when implementing complex types such as a matrix.Tomas Petricek<p>Generic numeric code is some calculation that can be used for working with multiple different numeric types including types such as <code>int</code>, <code>decimal</code> and <code>float</code> or even our own numeric types (such as the type for <a href="http://tomasp.net/blog/fsharp-custom-numeric.aspx">clock arithmetic from the previous article of the series</a>). Generic numeric code differs from ordinary generic F# code such as the <code>'a list</code> type or <code>List.map</code> function, because <em>numeric code</em> uses numeric operators such as <code>+</code> or <code>>=</code> that are defined differently for each numeric type.</p> <p>When writing simple generic code that has some type parameter <code>'T</code>, we don’t know anything about the type parameter and there is no way to restrict it to a numeric type that provides all the operators that we may need to use in our code. This is a limitation of the .NET runtime and F# provides two ways for overcoming it.</p> <ul class="spaces"> <li><strong>Static member constraints</strong> can be used to write generic code where the actual numeric operations are resolved at compile-time (and a generic function is specialized for all required numeric types). This approach makes resulting code very efficient and is generally very easy to use when writing a function such as <code>List.sum</code>.</li> <li><strong>Global numeric associations</strong> (available in F# PowerPack) give us a way to obtain an interface implementing required numeric operations dynamically at runtime. This approach has some runtime overhead, but can be used for complex numeric types (such as <code>Matrix<'T></code>).</li> <li><strong>Combination of both</strong> techniques can be used to implement complex numeric type that is generic over the contained numeric values and has only a minimal runtime overhead.</li> </ul> <p>Static member constraints are a unique feature of F# that is not available in other .NET languages, so if you're interested in writing numeric code for .NET, this may be a good reason for choosing F#. In C# or Visual Basic, you would be limited to the second option (which can be implemented in C#). In dynamic languages (like IronPython), everything is dynamic, so numeric computations can work with any numeric type, but will be significantly less efficient. In the rest of the article, we look at the three options summarized above. </p> <p style="font-style:italic;">This article is a part of a series that covers some F# and F# PowerPack features for numerical computing. Other articles in this series discuss matrices, defining custom numeric types and writing generic code. For links to other parts, see <a href="http://tomasp.net/blog/powerpack-introduction.aspx">F# Math - Overview of F# PowerPack</a>.</p> F# Math (III.) - Defining custom numeric typeshttp://tomasp.net/blog/fsharp-custom-numeric.aspxThu, 24 Nov 2011 19:21:35 GMTIn this article, we look at defining custom numeric types in F#. We'll create a numeric type representing numbers in a clock artihmetic (with base 5) and we'll see how to define custom operators, numeric literals and how to support F# PowerPack matrices.Tomas Petricek<p>In this article, we define an F# numeric type for calculating in the modular arithmetic (also called clock arithmetic) [<a href="#ppcnuml">1</a>]. Modular arithmetic is used for calculations where we want to keep a value within a specified range by counting in cycles. For example, a maximal value on clock is 12 hours. When we add 11 hours and 3 hours, the value overflows and the result is 2 hours. Aside from clocks, this numeric system is also essential in cryptography or, for example, in music.</p> <p>This tutorial shows several techniques that are essential when defining any new numeric type in F#. Most importantly, you’ll learn how to:</p> <ul> <li>Define a numeric type with overloaded operators </li> <li>Define a numeric literal for constructing numbers of our new type</li> <li>Enable calculating with our type in F# lists and matrices</li> <li>Hide implementation details of a numeric type</li> </ul> <p>We define type <code>IntegerZ5</code> that implements modular arithmetic with modulus 5, meaning that valid values are in the range from 0 to 4 and we equip the type with operations such as addition and multiplication. When an operation produces a value that would be outside of the range, we adjust it by adding or subtracting the modulus (in our case 5). Here are some examples of calculations that we’ll be able to write:</p> <pre> 2 + 1 = 3 (mod 5) 4 * 2 = 3 (mod 5) List.sum [ 0; 1; 2; 3 ] = 1 (mod 5) </pre> <p>In the first case, we can perform the operation without any adjustments. In the second case, we multiply 4 by 2 and get 8 as the result, which is out of the required range. To correct it, we calculate the remainder after a division by 5 (written as <code>8 % 5</code> in F#), which gives us 3. Finally, the last example shows that we’d also like to be able to use our type with lists. If we add values 0, 1, 2 and 3, we get 6 which is adjusted to 1.</p> <p style="font-style:italic;">This article is a part of a series that covers some F# and F# PowerPack features for numerical computing. Other articles in this series discuss matrices, defining custom numeric types and writing generic code. For links to other parts, see <a href="http://tomasp.net/blog/powerpack-introduction.aspx">F# Math - Overview of F# PowerPack</a>.</p> F# Math (II.) - Using matrices for graph algorithmshttp://tomasp.net/blog/powerpack-matrix.aspxWed, 09 Nov 2011 01:46:12 GMTThis article introduces the matrix type available in F# PowerPack. It discusses how to create matrices, manipulate matrices using indexing and slices and how to use built-in functions for working with them. As a running example, we use matrix to represent a graph using an adjacency matrix.Tomas Petricek <p>In the <a href="http://tomasp.net/blog/powerpack-numeric.aspx">previous article of this series</a>, we looked at <code>complex</code> and <code>BigRational</code>, which are two numeric types that are available in F# PowerPack. Aside from these two, the PowerPack library also contains a type <code>matrix</code> representing a two-dimensional matrix of floating-point values.</p> <p>In this article, you'll learn how to work with matrices in F#, using some of the functions provided by F# PowerPack. I'll demonstrate the library using an example that represents <em>graphs</em> using a, so called, <em>adjacency matrix</em>. If you're not familiar with this concept, you don't need to worry. It is quite simple and it will be clear once we look at an example. The matrix represents which vertices of a graph are connected with other vertices by an edge. Many of the standard operations on matrices are useful when working with adjacency matrix, so this tutorial will cover the following:</p> <ul> <li>Creating matrices from lists and using functions from the <code>Matrix</code> module</li> <li>Using slices to read or modify a part of matrix</li> <li>Performing standard operations with matrices such as transposition and matrix multiplication</li> <li>Using higher order functions for working with matrices</li> </ul> <p style="font-style:italic;">This article is a part of a series that covers some F# and F# PowerPack features for numerical computing. Other articles in this series discuss matrices, defining custom numeric types and writing generic code. For links to other parts, see <a href="http://tomasp.net/blog/powerpack-introduction.aspx">F# Math - Overview of F# PowerPack</a>.</p> F# Math (I.) - Numeric types in PowerPackhttp://tomasp.net/blog/powerpack-numeric.aspxWed, 02 Nov 2011 02:34:07 GMTThis article discusses two numeric types that are available in F# PowerPack - BigRational represents arbitrary precision rational numbers and complex represents (floating-point) complex numbers. The types can be nicely used from F# as well as from C#.Tomas Petricek<p>In this article, we'll briefly look at two numeric types that are available in F# PowerPack. The type <code>complex</code> represents complex numbers consisting of real and imaginary parts. Both parts are stored as a floating point numbers. The type <code>BigRational</code> represents rational numbers consisting of numerator and denominator of arbitrary sizes. Integers of arbitrary size are represented using <code>BigInteger</code> type that is available in .NET 4.0 (in the <code>System.Numerics.dll</code> assembly). On .NET 2.0, the <code>BigInteger</code> type is also a part of F# PowerPack.</p> <p style="font-style:italic;">This article is a part of a series that covers some F# and F# PowerPack features for numerical computing. Other articles in this series discuss matrices, defining custom numeric types and writing generic code. For links to other parts, see <a href="http://tomasp.net/blog/powerpack-introduction.aspx">F# Math - Overview of F# PowerPack</a>.</p> F# Math - Numerical computing and F# PowerPackhttp://tomasp.net/blog/powerpack-introduction.aspxWed, 02 Nov 2011 02:30:26 GMTThis article is the first article of a series where I'll explain some of the F# features that are useful for numeric computing as well as some functionality from the F# PowerPack library.Tomas Petricek<img src="http://tomasp.net/articles/powerpack-series/z5snip.png" style="float:right;margin:0px 0px 5px 15px" /> <p>This article is the first article of a series where I'll explain some of the F# features that are useful for numeric computing as well as some functionality from the F# PowerPack library. Most of the content was originally written for the <a href="http://msdn.microsoft.com/en-us/library/hh273075.aspx">Numerical Computing in F#</a> chapter on MSDN (that I <a href="http://tomasp.net/blog/real-world-book-msdn.aspx">announced earlier</a>), but then we decided to focus on using F# with third party libraries that provide more efficient implementation and richer set of standard numeric functionality that's needed when implementing machine learning and probabilistic algorithms or performing statistical analysis. If you're interested in these topics, then the last section (below) gives links to the important MSDN articles.</p> <p>However, F# PowerPack still contains some useful functionality. It includes two additional numeric types and an implementation of matrix that integrates nicely with F#. The series also demonstrates how to use features of the F# language (and core libraries) to write numeric code elegantly. In particular, we'll use the following aspects:</p> <ul class="spaces"> <li><strong>Overloaded operators.</strong> Any type can provide overloaded version of standard numeric operators such as +, -, * and / as well as other non-standard operators (such as .*). As a result, libraries can implement their own numeric types which are indistinguishable from built-in types such as int.</li> <li><strong>Numeric literals.</strong> F# math libraries can enable using new numeric literals in the code. For example, you can write a <code>BigRational</code> value representing one third as <code>1N/3N</code>. The <code>N</code> suffix used in the notation is not hardcoded in the F# language and we'll see how to define similar numeric type.</li> <li><strong>Static constraints.</strong> F# supports static member constraints, which can be used for writing functions that work with any numeric type. For example, the <code>List.sum</code> function uses this feature. It can sum elements of any list containing numbers.</li> </ul> <p> These are just a few of the F# language features that are useful when writing numeric code, but there are many others. The usual F# development style using interactive tools, type safety that prevents common errors, units of measure as well the expressivity of F# make it a great tool for writing numeric code. For more information, take a look at the MSDN overview article <a href="http://msdn.microsoft.com/en-us/library/hh304366.aspx">Writing Succinct and Correct Numerical Computations with F#</a>. </p> F# courses and talks (Autumn 2011)http://tomasp.net/blog/fsharp-autumn-2011.aspxFri, 26 Aug 2011 03:04:11 GMTAfter a quiet summer season, it is time to look at the upcoming F# talks and courses. If you want to learn about functional and asynchronous programming, F# and more, you may want to come to our training (organized with SkillsMatter), tutorials or some community events.Tomas Petricek<img src="http://tomasp.net/articles/autumn-2011-talks/tomas.jpg" class="rdecor" title="Tomas speaking at the Functional Programming eXchange 2011" style="margin-bottom:15px" /> <p>The end of the summer holiday season is getting closer. Luckily, I was in Prague last week so I actually noticed there was summer this year!</p> <p>After a few quiet months, the autumn is going to be quite busy. Microsoft's <a href="http://www.buildwindows.com/">//build/</a> conference will reveal the future of software development for Windows, but great things are going on in the F# world too. Don Syme is going to talk about <a href="http://skillsmatter.com/podcast/scala/fsharp3">F# Information Rich Programming</a> at Progressive F# Tutorials in November, which should reveal more about F# 3.0 and type providers!</p> <p>I have quite a few speaking engagements planned already, so if you want to learn about functional programming in .NET (and become a better C# programmer) or about F# and asynchronous programming, here are a few events that you may be interested in...</p> Programming with F# asynchronous sequenceshttp://tomasp.net/blog/async-sequences.aspxThu, 11 Aug 2011 23:30:57 GMTAsynchronous sequences provide a way to represent asynchronous computation that generates multiple values on demand. This article defines asynchronous sequences, combinators for working with them and "asyncSeq" computation builder. Then it implements several examples including a sequential asynchronous Web Crawler.Tomas Petricek<img src="http://tomasp.net/articles/async-sequences/decor.png" class="rdecor" /> <p>In F#, we can represent asynchronous operations that do not block threads and eventually return a value of type <code>'T</code> using asynchronous workflows <code>Async<'T></code>. Asynchronous workflows can be easily constructed using the computation expression syntax <code>async { ... }</code> and there are also a few combinators that express more advanced composition (such as parallel composition or fork-join parallelism).</p> <p>Sometimes, we need to use asynchronous operations that return more than just one value. For example, when downloading data from the internet, we would like to create an <em>asynchronous sequence</em> that returns the data in chunks as they become available.</p> <p>One way to represent asynchronous operations that produce multiple values is to use the <code>IObservable<'T></code> type from .NET. This isn't always the best option though. Observables implement <em>push-based</em> model, which means that chunks of data are generated as quickly as possible (until all chunks are emitted). What if we wanted to take the chunks one-by-one after the previous chunk is processed?</p> <p>In this article, I describe <em>asynchronous sequences</em>. An asynchronous sequence is a simple, yet very powerful concept based on asynchronous workflows. It follows the same core model: results are generated on demand and asynchronously. Unlike asynchronous workflows, asynchronous sequences can be called (on demand) to generate multiple values until the end of the sequence is reached.</p> <p style="font-style:italic">I first discussed asynchronous sequences with Don Syme, Dmitry Lomov and Brian McNamara in an email thread a long time ago. Thanks to Don for enthusiasm about the concept and for the first implementation of some of the combinators!</p> Real-World F# Articles on MSDNhttp://tomasp.net/blog/real-world-book-msdn.aspxWed, 10 Aug 2011 04:38:33 GMTMore than a year ago, I started working on a writing project done with Manning and MSDN team. The idea was to adapt parts of my Real-World Functional Programming book, add some new practical topics and publish the articles on MSDN under the official F# documentation. I'm happy to announce that the articles, covering ASP.NET, F# asynchronous programming and agents, charting and more are now available on MSDN!Tomas Petricek<img src="http://tomasp.net/articles/real-world-book-msdn/msdn.jpg" style="float:right;margin:0px 15px 15px 15px;" /> <p>More than a year ago, Mike Stephens from <a href="http://manning.com">Manning</a> (who was also behind my <a href="http://manning.com/petricek">Real-World Functional Programming</a> book) asked me if I'd be interested in collaborating on a project for MSDN. The idea was to collaborate with Microsoft on creating some additional content for the official <a href="http://msdn.microsoft.com/library/dd233154(VS.100).aspx">F# Documentation</a>.</p> <p>A few days ago, the new content appeared on MSDN, so I finally have an excuse for the recent lack of blogging! Although the content contains a large number of new articles that are not based on my book, you can find it in the MSDN section named after my book, right under <em>Visual F#</em>. If you can't wait to check it out, here are all the links:</p> <ul> <li>The <a href="http://msdn.microsoft.com/en-us/library/hh314518.aspx">Real-World Functional Programming</a> section on MSDN.</li> <li>The <a href="http://code.msdn.microsoft.com/site/search?query=tomas%20petricek&f%5B0%5D.Value=tomas%20petricek&f%5B0%5D.Type=SearchText&ac=8">source code for individual chapters</a> is available on MSDN Code Gallery.</li> <li>I also published <a href="http://functional-programming.net/msdn/">annotated TOC with source code links</a> on my functional programming web site.</li> </ul> <p>While working on the articles, I also wrote about a few topics that we didn't use in the final version. You'll see them on my blog in the next few days, as soon as I edit them into a blog post form. <a href="http://tomasp.net/blog/real-world-book-msdn.aspx">Continue reading</a> for more information about individual chapters.</p>Extending Monads with Pattern Matching (Haskell 2011)http://tomasp.net/blog/docase-haskell.aspxWed, 20 Jul 2011 00:19:37 GMTThe blog post presents a paper that extends Haskell with pattern matching on monadic values. The paper has been accepted for publication at Haskell Symposium 2011 and extends the idea of joinads that I previously created for F#. The paper provides deeper theoretical background and discusses Haskell implementation.Tomas Petricek<p>Some time ago, I wrote a <a href="http://tomasp.net/blog/match-bang-paper.aspx">paper about <em>joinads</em></a> and the <code>match!</code> extension of the F# language. The paper was quite practically oriented and didn't go into much details about the theory behind <em>joinads</em>. Many of the examples from the F# version relied on some imperative features of F#. I believe that this is useful for parctical programming, but I also wanted to show that the same idea can work in the <em>purely functional</em> context.</p> <p>To show that joinads work in the pure setting, I created a Haskell version of the idea. The implementation (available below) is quite simple and consists of a pre-processor for Haskell source files and numerous examples. However, more important part of the recent work of joinads is a more detailed theoretical background.</p> <p>The theory of joinads, together with the language design of Haskell extension that implements it is discussed in a paper <em>Extending Monads with Pattern Matching</em>, which was accepted for publication at the <a href="http://www.haskell.org/haskell-symposium/2011/index.html">Haskell Symposium 2011</a>. Here is the abstract of the paper:</p> <p style="padding-left:60px;padding-right:60px;font-style:italic;"> Sequencing of effectful computations can be neatly captured using monads and elegantly written using <code>do</code> notation. In practice such monads often allow additional ways of composing computations, which have to be written explicitly using combinators. </p><p style="padding-left:60px;padding-right:60px;font-style:italic;"> We identify joinads, an abstract notion of computation that is stronger than monads and captures many such ad-hoc extensions. In particular, joinads are monads with three additional operations: one of type <code>m a -> m b -> m (a, b)</code> captures various forms of <em>parallel composition</em>, one of type <code>m a -> m a -> m a</code> that is inspired by <em>choice</em> and one of type <code>m a -> m (m a)</code> that captures <em>aliasing</em> of computations. Algebraically, the first two operations form a near-semiring with commutative multiplication. </p><p style="padding-left:60px;padding-right:60px;font-style:italic;"> We introduce <code>docase</code> notation that can be viewed as a monadic version of <code>case</code>. Joinad laws make it possible to prove various syntactic equivalences of programs written using <code>docase</code> that are analogous to equivalences about <code>case</code>. Examples of joinads that benefit from the notation include speculative parallelism, waiting for a combination of user interface events, but also encoding of validation rules using the intersection of parsers. </p> <p>Links to the full paper, source code and additional materials are <a href="http://tomasp.net/blog/docase-haskell.aspx#dscl">available below</a>.</p>Fun with parallel monad comprehensions (The Monad.Reader)http://tomasp.net/blog/comprefun.aspxTue, 19 Jul 2011 23:28:29 GMTMonad comprehensions are back in Haskell, more powerful than ever before! The recent implementation adds expressive power by generalizing grouping, ordering and also parallel list comprehensions. This article shows how to use this new expressivity for programming with parsers and writing parallel and concurrent computations.Tomas Petricek<p style="font-style:italic;"> This article is a re-publication of an article that I wrote some time ago for <a href="http://themonadreader.wordpress.com/">The Monad.Reader</a> magazine, which is an online magazine about functional programming and Haskell. You can also read the article in the original PDF format as part of the <a href="http://themonadreader.files.wordpress.com/2011/07/issue18.pdf">Issue 18</a> (together with two other interesting articles). The samples from the article can be found <a href="https://github.com/tpetricek/Haskell.Joinads">on Github</a>. </p> <p>Monad comprehensions have an interesting history. They were the first syntactic extension for programming with monads. They were implemented in Haskell, but later replaced with plain list comprehensions and monadic <code>do</code> notation. Now, monad comprehensions are back in Haskell, more powerful than ever before!</p> <p>Redesigned monad comprehensions generalize the syntax for working with lists. Quite interestingly, they also generalize syntax for zipping, grouping and ordering of lists. This article shows how to use some of the new expressive power when working with well-known monads. You'll learn what "parallel composition" means for parsers, a poor man's concurrency monad and an evaluation order monad.</p> <ul> <li><a href="http://tomasp.net/blog/comprefun.aspx">Continue reading on the web...</a></li> <li><a href="http://themonadreader.files.wordpress.com/2011/07/issue18.pdf">Get The Monad.Reader Issue 18</a> (PDF)</li> </ul>Safer asynchronous workflows for GUI programminghttp://tomasp.net/blog/safe-gui-async.aspxWed, 15 Jun 2011 21:36:40 GMTWhen writing reactive applications using F# asynchronous workflows, it is important to run some operations on the right thread. User interface elements are accessible only on GUI threads and CPU-intensive computations should be done on a background thread. This article describes an extension of F# asynchronous workflows that guarantees correct use of threads using types.Tomas Petricek<img src="http://tomasp.net/articles/safe-gui-async/screen.png" style="float:right; margin:0px 0px 0px 15px;" /> <p>In the <a href="http://tomasp.net/blog/async-non-blocking-gui.aspx">previous article</a>, I discussed how to use F# asynchronous workflows for creating reactive user-interfaces. One of the main concerns was to avoid blocking the GUI thread (to prevent the user-interface from freezing). The workflow shouldn't perform any CPU-intensive computation when running on the GUI thread.</p> <p>The standard F# library provides two ways to run a computation on a background thread from an asynchronous workflow. The <code>StartChild</code> operation starts an operation in the thread pool and returns a workflow that can be called using asynchronous (non-blocking) <code>let!</code> construct. The <code>SwitchToThreadPool</code> operation can be called using <code>do!</code> and resumes the rest of the workflow on a background thread.</p> <p>When using the <code>SwitchToThreadPool</code> operation, we also need to eventually use <code>SwitchToContext</code> to transfer the execution back to the GUI thread (after completing the CPU-intensive calculations). In this article, I describe a variation of F# asynchronous workflows that keeps track of the running thread in the type of the computation. As a result, calling a workflow that should be executed on a GUI thread from a background thread is a compile-time error as opposed to failing at runtime.</p> Writing non-blocking user-interfaces in F#http://tomasp.net/blog/async-non-blocking-gui.aspxFri, 10 Jun 2011 23:36:16 GMTF# asynchronous workflows are mainly used for non-blocking I/O and concurrency, but they provide nice abstraction for writing user interface interactions. This article shows how to avoid blocking the user-interface when performing CPU-intensive processing.Tomas Petricek<img src="http://tomasp.net/articles/async-non-blocking-calls/screen.png" style="float:right; margin:0px 0px 0px 15px;" /> <p>F# asynchronous workflows are best known as a way to write efficient I/O operations or as an underlying mechanism of F# agent-based programming (using the <code>MailboxProcessor</code> type). However, they are also very useful for user-interface programming. I think this is a very interesting and important area, so I already wrote and talked about this topic - it is covered in <a href="http://manning.com/petricek/">Chapter 16 of my book</a> (there is a <a href="http://dotnetslackers.com/articles/net/Programming-user-interfaces-using-f-sharp-workflows.aspx">free excerpt</a>) and I <a href="http://tomasp.net/blog/reactive-talk.aspx">talked about it</a> at F#unctional Londoners meeting.</p> <p>Many applications combine user-interface programming (such as waiting for an event asynchronously) with some CPU-intensive tasks. This article looks at an example of such application and I'll explain how to avoid blocking the user-interface when doing the CPU-intensive task. The article starts with an example that is wrong and blocks the user-interface when doing data processing. Then I'll show you two options for fixing the problem. The three most important functions from the standard F# library that I'll discuss are <code>Async.StartChild</code> and <code>Async.SwitchToThreadPool</code> with <code>Async.SwitchToContext</code>.</p> <p>This is the first article of a mini-series. In the next article, I'll demonstrate a simple wrapper for F# <code>async</code> that makes it more difficult to write <em>wrong</em> programs. The wrapper keeps the desired thread (GUI or background) in the type of the computations and code that would block the user interface will not type-check. But first, let's look at the example...</p> Accessing loosely structured data from F# and C# (GOTO 2011)http://tomasp.net/blog/goto-loosely-structured-data.aspxThu, 26 May 2011 22:51:48 GMTThis article is a summary of a talk about accessing loosely structured data from F# and C# that I gave at GOTO Copenhagen 2011. The article contains examples how to bridge the gap between external data sources and programming language at various scales.Tomas Petricek<img src="http://tomasp.net/articles/fsharp-loosely-typed/goto.png" style="float:right;margin:0px 0px 15px 15px;" /> <p>About two weeks ago, I gave a talk at <a href="http://gotocon.com/cph-2011/">GOTO Conference</a> in Copenhagen at a very interesting .NET session organized by <a href="http://blog.ploeh.dk /">Mark Seemann</a>. In my talk, I focused on the impedance mismatch between the data structures that are used in programming languages (such as classes in C# or records and discriminated unions in F#) and the data structures that we need to access (such as database, XML files and REST services). </p> <p>Clearly, both of the sides have <em>some structure</em> (otherwise, it wouldn't be possible to write any code against them!). Even an XML file that is returned by a REST service has some structure - although the only way to find out about the structure may be to call the service and then look at the result. In this article, I'll briefly summarize the ideas that I presented in the talk. Here are links to the slides as well as the source code from the talk: </p> <ul> <li>You can browse the slides <a href="http://slidesha.re/llTgVk">at SlideShare</a> or you can download them from GitHub in the <a href="https://github.com/tpetricek/Documents/raw/master/Talks%202011/Data%20Access%20(GOTO%20Copenhagen)/data.ppt">PPT format</a>.</li> <li>The source code is in my <a href="https://github.com/tpetricek/Documents/tree/master/Talks%202011/Data%20Access%20(GOTO%20Copenhagen)">GitHub repository</a> and can be downloaded as a single <a href="https://github.com/tpetricek/Documents/raw/master/Talks%202011/Data%20Access%20(GOTO%20Copenhagen)/demos.zip">ZIP file</a>. </li> </ul> Explicit speculative parallelism for Haskell's Par monadhttp://tomasp.net/blog/speculative-par-monad.aspxTue, 17 May 2011 13:59:06 GMTThis article shows how to extend Haskell's Par monad to support cancellation of computations. This makes it possible to implement speculative parallelism using the monad and to build other high-level abstraction such as the unamb operator designed by Conal Elliott.Tomas Petricek<p>Haskell provides quite a few ways for writing parallel programs, but none of them is fully automatic. The programmer has to use some annotations or library to run computations in parallel <em>explicitly</em>. The most recent paper (and library) for writing parallel programs follows the latter approach. You can find more information about the library in a paper by Simon Marlow et al. <a type="external" href="http://research.microsoft.com/en-us/um/people/simonpj/papers/parallel/monad-par.pdf">A monad for deterministic parallelism</a> and it is also available on <a href="http://hackage.haskell.org/package/monad-par" type="external">Hackage</a>. However, I'll explain all the important bits that I'll use in this article.</p> <p>The library provides an explicit way for writing parallel programs using a <code>Par</code> monad. The library contains constructs for spawning computations and sharing state using blocking variables. However, the whole programming model is fully deterministic. I believe that it is sometimes useful to lift the determinacy requirement. Some programs are deterministic, but the fact cannot be (easily) automatically verified. For example, say you have two functions <code>fib1</code> and <code>fib2</code>. They both give the same result, but each of them is more efficient than the other one on certain inputs. To calculate a Fibonacci number, the program could <em>speculatively</em> try to evaluate both functions in parallel and return the result of the one that finishes first.</p> <p>Unfortunately, this cannot be safely implemented using a fully deterministic library. In this article, I'll show some examples where speculative parallelism can be useful and I'll talk about an extension to the <code>Par</code> monad that I implemented (available on <a href="https://github.com/tpetricek/Haskell.ParMonad">GitHub</a>). The extension allows programmers to write <em>speculative computations</em>, provided that they manually verify that their code is deterministic. </p> Variations in F#: Research compiler with Joinads and more!http://tomasp.net/blog/fsharp-variations-joinads.aspxFri, 25 Mar 2011 00:04:08 GMTJoinads are a research extension of the F# language. They simplify conrurrent programming with tasks, reactive programming with events, but can be also used for other types of computations. This article introduces the extension, which is now available, based on the open-source source-drop of F#.Tomas Petricek<p>In this article, I'll write about an experimental extension for F# that I call <em>joinads</em>. If you're following my blog, you may have seen an <a href="http://tomasp.net/blog/match-bang-paper.aspx">academic paper</a> that I wrote about it some time ago. Anyway, the motivation for the extension is that there are many useful programming models for reactive, concurrent and parallel programming that would deserve some syntactic support in the programming language.</p> <p>For example, when programming with <em>futures</em> (the <code>Task<T></code> type), you may want to implement logical "or" operator for tasks that returns <code>true</code> immediately when the first task completes returning <code>true</code>. When programming with <em>events</em> (the <code>IObservable<T></code> type), we'd like to wait for the event that happens first. Finally, when programming using <em>agents</em>, we sometimes need to wait only for certain types of messages. All of these problems can be solved, but require the use of (sometimes fairly complicated) functions. Joinads make it possible to solve them directly using the <code>match!</code> syntax. For example, here is the "or" operator for tasks:</p> <pre class="fssnip"> <span class="l">1: </span><span onmouseout="hideTip(event, 'jofs1', 1)" onmouseover="showTip(event, 'jofs1', 1)" class="i">future</span> { <span class="l">2: </span> <span class="k">match!</span> <span onmouseout="hideTip(event, 'jofs2', 2)" onmouseover="showTip(event, 'jofs2', 2)" class="i">after</span> <span class="n">100</span> <span class="k">true</span>, <span onmouseout="hideTip(event, 'jofs2', 3)" onmouseover="showTip(event, 'jofs2', 3)" class="i">after</span> <span class="n">1000</span> <span class="k">false</span> <span class="k">with</span> <span class="l">3: </span> | <span class="o">!</span><span class="k">true</span>, _ <span class="k">-></span> <span class="k">return</span> <span class="k">true</span> <span class="l">4: </span> | _, <span class="o">!</span><span class="k">true</span> <span class="k">-></span> <span class="k">return</span> <span class="k">true</span> <span class="l">5: </span> | <span class="o">!</span><span onmouseout="hideTip(event, 'jofs3', 4)" onmouseover="showTip(event, 'jofs3', 4)" class="i">a</span>, <span class="o">!</span><span onmouseout="hideTip(event, 'jofs4', 5)" onmouseover="showTip(event, 'jofs4', 5)" class="i">b</span> <span class="k">-></span> <span class="k">return</span> <span onmouseout="hideTip(event, 'jofs3', 6)" onmouseover="showTip(event, 'jofs3', 6)" class="i">a</span> <span class="o">||</span> <span onmouseout="hideTip(event, 'jofs4', 7)" onmouseover="showTip(event, 'jofs4', 7)" class="i">b</span> }</pre> <p>I'll write more about this example (and the implementation) in a later article. This article focuses on the compiler extension itself. I created a first implementation of the idea above during my <a href="http://tomasp.net/blog/internship-match-bang.aspx">internship with Don Syme at MSR Cambridge</a>, but then changed it quite a bit when writing the academic paper mentioned above. However, I never released the source code. </p> <p>Thanks to the <a href="http://blogs.msdn.com/b/dsyme/archive/2010/11/04/announcing-the-f-compiler-library-source-code-drop.aspx">open-source release of F#</a> it is now quite easy to modify the F# compiler and make the modifications available, so I decided I should finally release my F# extensions. I also recently <a href="http://tomasp.net/blog/idioms-in-linq.aspx">blogged</a> <a href="http://tomasp.net/blog/formlets-in-linq.aspx">about</a> encoding <em>idioms</em> (also called <em>applicative functors</em>) in C#. I was wondering how to do that in F# and so I also created a simple extension computations based on this abstraction. The support for <em>idioms</em> is just an experiment, but it could be useful, for example, for programming with formlets. You'll find more about it at the end of the article. </p> <p>You can find the <a href="https://github.com/tpetricek/FSharp.Extensions">source code on my GitHub</a> (there is also a link compiled binaries at the end of the article). The source code is cloned from an F# Mono repository, which means that it should build on Linux and MacOS too. </p> <div class="tip" id="jofs1">val future : FutureBuilder<br /><br />Full name: JoinadsDemo.future<br /></div> <div class="tip" id="jofs2">val after : int -> 'a -> Task<'a><br /><br />Full name: JoinadsDemo.after<br /></div> <div class="tip" id="jofs3">val a : bool<br /><br /> type: bool<br /> implements: IComparable<br /> implements: IConvertible<br /> implements: IComparable<bool><br /> implements: IEquatable<bool><br /> inherits: ValueType<br /></div> <div class="tip" id="jofs4">val b : bool<br /><br /> type: bool<br /> implements: IComparable<br /> implements: IConvertible<br /> implements: IComparable<bool><br /> implements: IEquatable<bool><br /> inherits: ValueType<br /></div> Beyond the Monad fashion (II.): Creating web forms with LINQhttp://tomasp.net/blog/formlets-in-linq.aspxMon, 14 Mar 2011 17:14:49 GMTFormlets are elegant functional abstraction for describing web forms encapsulating both rendering and functionality. In this article, we look how to write formlets in C#. Although formlets are not monads, we can still use elegant LINQ syntax. Interestingly, using the join clause...Tomas Petricek<img src="http://tomasp.net/articles/formlets-in-linq/screen.png" style="margin:15px;float:right;" /> <p>The LINQ query syntax can be used for various things. Aside from writing queries, you can also use it to encode any <em>monads</em>. This has become a fashionable topic, so you can learn more about it at many .NET conferences (for example <a href="http://gotocon.com/cph-2011/tracks/show_track.jsp?trackOID=434">GOTO 2011</a>). There are also many blog posts on this topic and I explained it in details in Chapter 12 of <a href="http://manning.com/petricek">my book</a>, which is available as a <a href="http://manning.com/petricek/SampleChapter12.pdf">free sample chapter</a> (PDF).</p> <p>However, you can also use LINQ syntax for writing different types of computations. In a <a href="http://tomasp.net/blog/idioms-in-linq.aspx">previous blog post</a>, I introduced <em>idioms</em> (also called <em>applicative functors</em>) and I demonstrated how to use the <code>join</code> syntax in LINQ to write computations based on idioms. We looked at a slightly boring, but simple example - zipping of lists - and we also implemented matrix transposition.</p> <p>In this blog post, we look at a more exciting example. I explain <em>formlets</em>, which is an <em>idiom</em> for building web forms. Formlets give us an elegant functional way to create reusable components that encapsulate both visual aspect (HTML) and behavior (processing of requests). You can think of them as functional ASP.NET controls. Formlets come from the <a href="http://groups.inf.ed.ac.uk/links/formlets/">Links project</a> and they are now used in commercial products like <a href="http://www.websharper.com/tutorials/GettingStartedWithFormlets.aspx">WebSharper</a>. In this article, you'll see that we can (mis)use LINQ to get a nicer syntax for writing code using formlets. My C# implementation of formlets is based on a nice <a href="http://bugsquash.blogspot.com/2011/01/simple-implementation-of-formlets-in-f.html">F# formlets by Mauricio Scheffer</a>.</p> Beyond the Monad fashion (I.): Writing idioms in LINQhttp://tomasp.net/blog/idioms-in-linq.aspxThu, 10 Mar 2011 13:26:00 GMTEveryone tells you that LINQ is a <em>monad</em>, but LINQ can be used to enocde other types of computations too. This article demonstrates that you can use LINQ to program using <em>idioms</em>, which are in some ways more useful than monads.Tomas Petricek<p>Thanks to LINQ and Erik Meier, monads have become a fashionable topic in the C# developer community. Indeed, no serious developer conference on .NET can get away without having a talk on monads. The attractive thing about LINQ and monads is that the <code>SelectMany</code> operator roughly corresponds to the <em>bind</em> function that defines a monad. In practice, LINQ is used for working with collections of data (<code>IEnumerable<T></code>), but you can also define <em>bind</em> (i.e. <code>SelectMany</code>) for some other data types and use the LINQ syntax for working with other types. You won't be really using the full LINQ syntax. You'll probably use just nested <code>from</code> clauses (for <em>binding</em>) and <code>select</code> at the end to return the result.</p> <p>However, monads are not the only notion of computation that we can work with. More interestingly, they are also not the only notion of computation that you can encode using LINQ! In this article, I'll briefly introduce <em>idioms</em> (also called <em>applicative functors</em>), which is another useful abstract type of computations. Idioms can be used for a few things that cannot be done using monads.</p> <p>A provocative summary of this article is: <span style="font-variant:small-caps">"Everyone who tells you that LINQ is a monad is wrong!"</span></p> <p>The truth is that LINQ syntax can be used for encoding <em>queries</em> (obviously), <em>monads</em> (as you were told), but also for <em>idioms</em> as you'll learn today (and quite possibly for other types of computations). In this article, we look at a basic example, but I'll describe a more complex real-world scenario in the next blog post.</p> MonoDevelop & Teaching F# & QCon tutorialhttp://tomasp.net/blog/mono-teaching-qcon-talks.aspxWed, 09 Mar 2011 16:01:39 GMTIt appears that I have been doing a lot more talking than writing in the last two months. This blog post provides links to materials from my recent F# talks, including MonoDevelop presentation, talk about Teaching F# and recent QCon tutorial with Phil Trelford.Tomas Petricek<div style="float:right;text-align:center;font-size:small;margin:10px;"> <img src="http://tomasp.net/articles/mono-teaching-qcon-talks/app.png" style="margin-bottom:5px" /><br /> Point of sale application from QCon tutorial </div> <p>It appears that I have been doing a lot more talking than writing in the last two months. I'm hoping to change this direction and I have two articles almost ready, so stay tuned! I was also posting all my interesting F# snippets to <a href="http://fssnip.net/authors/Tomas+Petricek">fssnip.net</a>, which has grown quite a bit since I announced it in the last blog post. Thanks to everybody who submitted their snippets already and I'm looking forward to more! By the way, you can now run snippets using <a href="http://tryfs.net/">tryfs.net</a> by clicking at "Load in TryF#" button.</p> <p>In the meantime, the queue with talk materials that I wanted to post on my blog has grown to 3. I talked about F# in MonoDevelop in the <a href="http://weblog.savanne.be/376-fosdem-2011-mono-room-slides">Mono room at FOSDEM</a> in February, then I did an online talk for the <a href="http://www.communityforfsharp.net/">Community for F# </a>. Finally, this week, I did a tutorial on F# with <a href="http://www.trelford.com/blog/">Phil Trelford</a> at QCon in London (to fill in for Michael Stal due to unexpected health reasons).</p> <p>Before I move on to writing about my recent experiments with LINQ, you can find materials from all of the recent talks below... </p>Announcing F# snippets web sitehttp://tomasp.net/blog/fssnip-website.aspxSun, 12 Dec 2010 02:19:34 GMTWhen writing F# code, I often write some nice code snippet or helper function that I'd like to share with the F# community. Unfortunately, there was no good website for easy sharing of F# snippets - until today.Tomas Petricek<a href="http://fssnip.net"> <img src="http://tomasp.net/articles/fssnip-website/web.png" class="rdecor" style="border:0px" /> </a> <p>When writing F# programs, I often write some nice code snippet or some useful helper function that I'd like to share with the F# community. Unfortunately, my blog posts are usually longer and more elaborate, so I never get to blogging about it. Now that I have a twitter (<a href="http://twitter.com/tomaspetricek">follow me if you don't already</a>) I thought I could just post the snippet somewhere, but there was no good web site for posting F# snippets - until now! </p> <ul> <li>If you can't wait any further, then go directly to the new F# snippets web site at <a href="http://fssnip.net">fssnip.net</a>. </li> </ul> <p>The web site uses my earlier project <a href="http://tomasp.net/blog/fswebsnippets-intro.aspx">F# Web Snippets</a> to format F# source code. It highlights colors and adds JavaScript tooltips using services provided by the F# compiler, which means that you'll get almost the same experience as when reading code in Visual Studio. I also wanted to make the page a repository of browsable snippets, so you can use it in two ways...</p>F# in Education & Concurrency with Agentshttp://tomasp.net/blog/education-and-agents-talks.aspxTue, 30 Nov 2010 19:18:13 GMTThis article contains materials for two talks that I had in November. First, I presented the F# plugin for MonoDevelop at the F# in Education workshop in Boston (using 3D functional library) and then I talked about agent-based concurrency (with Twitter and image processing examples) in London.Tomas Petricek<img src="http://tomasp.net/articles/education-and-agents-talk/castle.jpg" class="rdecor" /> <p>November was quite a busy month for me. First, I traveled to Cambridge (the "new one" in Massachusetts :-)) to present my work on the F# plugin for MonoDevelop at the F# in Education workshop. Shortly after getting back to London, I started working on a presentation about Concurrent Programming with Agents at the F#unctional Londoners meeting. </p> <p>Now that both of the events are over, I'd like to write a short summary and also finally publish my slides and demos. In addition, both of the events were recorded (thanks to External Research group at MSR and SkillsMatter), so if you missed them, you can watch the recording...</p> <p>Both of the events were really great and I had a chance to meet quite a few interesting people. One of the things that make F# great is the community around it. I think that one unique aspect of the F# community is its diversity. The same language is appealing to high school teachers, academics and researchers as well as software developers and technical directors from the industry. This combination is really valuable for both sides. It helps to transfer ideas from research to practice it gives researchers clear picture of problems in the industry that deserve their attention.</p> Concurrent programming with F# agents in Londonhttp://tomasp.net/blog/fun-londoners-agents.aspxTue, 23 Nov 2010 04:40:01 GMTJust a quick reminder for everybody living near London interested in F# - I'll be giving a talk about concurrent programming using F# agents on Wednesday. We'll look at the <code>MailboxProcessor</code> type and at some common patterns for working with it.Tomas Petricek<p>If you live anywhere near London and are interested in F#, then you probably already follow the <a href="http://www.meetup.com/FSharpLondon/" type="external">F#unctional Londoners</a> group started by Carolyn Miller and <a href="http://www.trelford.com/blog/" type="external">Phil Trelford</a>. I gave a talk at the user group in June about <a href="http://tomasp.net/blog/reactive-talk.aspx">Reactive programming in F#</a> (if you missed that, you can view <a href="http://skillsmatter.com/podcast/open-source-dot-net/tomas-petricek-reactive-programming-in-fsharp">the recording</a>). I really enjoyed talking to an audience where most of the people already played with F#, so when I met with Phil recently, I couldn't resist offering another presentation.</p> <p>My next talk will be about <strong>Concurrent programming with Agents</strong> using the <code>MailboxProcessor</code> type. A part of the talk will be inspired by my recent blog series <a href="http://tomasp.net/blog/tag/38.aspx">about parallel programming</a>, but I just finished another pretty cool example, so you should come even if you read my blog! This time, we'll have two talks, so you can also look forward to Phil Trelford's <strong>Behaviour Driven Development with TickSpec</strong> (you just cannot miss his debugging demo!).</p> <img src="http://tomasp.net/img/londoners.png" style="float:right; margin:10px" /> <h2>When, what & where?</h2> <ul> <li><strong>See also: <a href="http://www.meetup.com/FSharpLondon/calendar/15327706/" type="external">Concurrency with Agents and BDD with TickSpec</a></strong> at F#unctional Londoners</li> <li><strong>Date & time:</strong> 24 November (Wednesday), 7:00 PM</li> <li><strong>Location:</strong> The Skills Matter eXchange, 116-120 Goswell Road, London</li> </ul> <p>Last time, I brought a copy of my <a href="http://www.manning.com/petricek" type="external">Real-World Functional Programming</a> as a giveaway and I think I still have a few copies lying around...</p> <h2>Talk teaser: F# agents</h2> <p>F# agents (the <code>MailboxProcessor</code> type) are an implementation of message passing concurrency. This is a very attractive alternative to shared memory or even standard task-based or data-parallel concurrency models. It makes it easy to write reactive applications that receive inputs from various sources in parallel (e.g. user interface, network, background tasks etc.) Agents communicate by sending (immutable) messages to each other, which makes the application easy to understand. If you design the application correctly (and structure it using enough agents) it can be also very scalable. Among other things, I'll show the following examples:</p> <ul> <li><strong>Agent-based chat</strong> - A simple example to introduce agents will be a chat room that uses agent to store the state of a chat. You'll see that an asynchronous and concurrent application can be written quite easily with F#. You'll also see how to expose this service using a few lines of beautiful F# code inspired by <code>Node.js</code>.</li> <li><strong>Reusable agents, buffering and blocking</strong> - We'll also look at a few agents that are not directly bound to any application and you can use them to implement common communication patterns. If you have a few agents like this, you can easily put together a sophisticated application just by composing existing agents.</li> </ul> Asynchronous C# and F# (III.): How does it work?http://tomasp.net/blog/async-compilation-internals.aspxSun, 21 Nov 2010 03:15:38 GMTIn this article, we look at the internals of asynchronous programming models in F# and a future version of C#. We compare the compilation in C# (based on state machines) and the compilation in F# (based on combinators) and we look at advantages and disadvantages of both of the approaches.Tomas Petricek<p>Some time ago, I started writing a series about the differences between the asynchronous model in F# (in Visual Studio 2010) and the asynchronous language extensions for C# proposed at PDC 2010. In the <a href="http://tomasp.net/blog/csharp-fsharp-async-intro.aspx">first article</a>, I showed how both of the language features look and I highlighted a couple of differences. In the <a href="http://tomasp.net/blog/async-csharp-differences.aspx">second article</a>, I discussed the support for cancellation (available only in F#) and how the two models differ <em>semantically</em> (i.e. what are differences in the behaviour). However, I didn't talk about more techincal differences and, in particular, how is the asynchronous code compiled. We'll look at this topic today...</p> <p>Although the C# asynchronous programming model is very similar to F# asynchronous workflows, the compilation looks quite different. The C# compiler uses a similar technique as when compiling iterators and creates a state machine, while the F# compiler uses an approach based on higher order functions (combinators) that's shared with (most) other computation expressions.</p> <p>I won't discuss the syntax of F# asynchronous workflows or the C# asynchronous extensions in this article, so if you're new to one of these, here are links to other articles in this series: </p> <ul> <li><a href="http://tomasp.net/blog/csharp-fsharp-async-intro.aspx">Asynchronous C# and F# (I.): Simultaneous introduction</a></li> <li><a href="http://tomasp.net/blog/async-csharp-differences.aspx">Asynchronous C# and F# (II.): How do they differ?</a></li> <li><strong>Asynchronous C# and F# (III.): How does it work?</strong></li> <li>Asynchronous C# and F# (IV.): Calling F# libraries from C# <em>(not yet available)</em></li> </ul> <p>Let's start by looking at the mechanism used in the C# compiler. If you already know how iterators work in C# 2.0, then you'll find it quite easy to understand. If you're not familiar with iterators, then don't worry - I'll make the explanation self-contained.</p> F# community on GitHub & MonoDevelop updatehttp://tomasp.net/blog/monodevelop-update.aspxFri, 19 Nov 2010 14:01:37 GMTIf you're interested in the open-source release of F# or the F# plugin for MonoDevelop, you can now find them on GitHub. I started F# community organization that will manage the two projects. You can also join our mailing-list to receive all updates related to open-source community.Tomas Petricek<img src="http://tomasp.net/articles/monodevelop-update/github.png" class="rdecor" /> <p>When I talked with Miguel de Icaza and Michael Hutchinson at the <a href="http://research.microsoft.com/en-us/events/fsharpined/">F# in Education workshop</a> some time ago, someone mentioned that it would be nice to have a clone of the official F# code drop that could accept patches from the community. I also talked with Michael about <a href="http://github.com">GitHub</a> and I think I finally understood why everybody uses it today. I said to myself that I'll need to take a look at it when I'll have a bit of time... After coming back from the workshop, I was quite busy getting the F# plugin for MonoDevelop out, but after I wrote about it, I finally found some time to look at <a href="http://github.com">GitHub</a>.</p> <p>I really like the way Mono team uses GitHub. They have a single "mono" organization that is owned by several people from the Mono community and all important projects that are parts of Mono have their repository as part of the "mono" organization. Thanks to GitHub, everyone can easily clone the repository, do some changes and submit a "pull request" to the main repository.</p> <p>I thought that the F# community could follow the same model, so I started the <a href="https://github.com/fsharp">F# community organization</a> on GitHub...</p> F# in MonoDevelop and cross-platform web sites & screencastshttp://tomasp.net/blog/fsharp-in-monodevelop.aspxTue, 16 Nov 2010 02:35:20 GMTThe first version of the F# language binding for MonoDevelop is now available. Using the F# compiler service, it provides autocompletion, information tool tips and background type-checking. For more information and installation instructions, watch two screencasts showing F# on LinuxTomas Petricek<p>About a week ago, I attended the F# in Education workshop in Boston. It was a great event with many interesting people around. I believe that the workshop was very exciting for everyone who is interested in F#, but uses Mac or Linux. The F# team recently made some effort to improve the F# support on Mono (meaning mainly Mac and Linux). The recent <a href="http://blogs.msdn.com/b/dsyme/archive/2010/11/10/november-2010-f-2-0-free-tools-update.aspx" type="external">November 2010 CTP update</a> contains several bugfixes that make it possible to use F# on Mono 2.8. Another great thing that happened at the workshop is the <a href="http://blogs.msdn.com/b/dsyme/archive/2010/11/04/announcing-the-f-compiler-library-source-code-drop.aspx" type="external">open source release of F#</a> (see also <a href="http://tirania.org/blog/archive/2010/Nov-11.html" type="external">blog post</a> by Miguel with a post-check-in photo). At the workshop, I also announced my contribution to the cross-platform F# story, a project that I've been working on recently - <strong>the F# language binding for MonoDevelop.</strong> </p> <div class="rdecor" style="text-align:center;"> <a target="_blank" href="http://tomasp.net/articles/fsharp-in-monodevelop/screen.png"><img src="http://tomasp.net/articles/fsharp-in-monodevelop/screen-sm.png" style="border:0px;margin-bottom:5px" /></a><br /> <a target="_blank" href="http://tomasp.net/articles/fsharp-in-monodevelop/screen.png"><small>Click here for a larger screenshot</small></a> </div> <p>I promised to make it available as soon as possible after the workshop. As usually, things take longer, than one would like, but I'm finally ready to announce the initial (beta) version of the plugin. The screenshot on the right shows some of the features of the F# language binding. As you can see, there is an F# Interactive tool window, syntax highlighting as well as IntelliSense auto-completion.</p> <p>If you're interested in trying it out, here are links to the repository (you can use it to install the language binding from the MonoDevelop Add-ins manager) and source code. The F# plugin needs to be able to locate F# installation and it also requires more F# assemblies to be installed in the GAC, so you may as well want to read the instructions before trying it :-).</p> <ul class="spaces"> <li><a href="http://functional-variations.net/monodevelop/" type="external">Project homepage</a> at the Functional Variations web site has more information about the project as well as detailed installation instructions.</li> <li>I also created a web page that contains information about <a href="http://functional-variations.net/crossplatform/" type="external">installing F# on Mac and Linux</a> which explains how to install F#, such that the MonoDevelop plugin can find it.</li> <li>The source code is available in the <a href="http://fsxplat.codeplex.com/" type="external">F# cross-platform packages and samples</a> project at CodePlex (under the Apache 2.0 license). You can find it in the <code>monodevelop</code> subdirectory.</li> <li>Online repositiory with a MonoDevelop package is available at: <a href="http://functional-variations.net/addin">http://functional-variations.net/addin</a>.<br /> <em>(If you're a hacker, the easiest way to get it working is to add <code>FSharp.Compiler*</code> to GAC and set <code>FSHARP_COMPILER_BIN</code> environment variable to F# installation location)</em></li> </ul> <p>If you want to see some interesting uses of the F# MonoDevelop plugin, you can also watch <a href="http://research.microsoft.com/en-us/events/fsharpined/videos.aspx" type="external">my talk at the F# in Education event</a>. In one demo, I used F# on Mac to play with a simple, composable functional 3D library. In another example I demonstrated how to asynchronously process stock prices on Linux. The last demo, showing my <code>match!</code> extension didn't work all that well, because I had too many virtual machines running, but I'll blog about <code>match!</code> again sooner or later!</p> <p>In addition to the F# plugin for MonoDevelop itself, I'd also like to mention two web sites that I've been working on and some interesting cross-platform F# screencasts...</p> Asynchronous C# and F# (II.): How do they differ?http://tomasp.net/blog/async-csharp-differences.aspxMon, 01 Nov 2010 16:36:00 GMTThe asynchronous programming support in C# announced at PDC 2010 is largely inspired by F# asynchronous workflows. In this article we look at some of the differences between the two including cancellation support in F# and the distinction between "hot task" model of C# and "task generator" model of F#.Tomas Petricek<p>Anders Hejlsberg announced the support for asynchronous programming in the next version of C# announced at PDC 2010. The extension looks very similar to F# asynchronous workflows (which are already available in Visual Studio 2010). Despite the large similarity, there are a couple of differences between the two programming models. I already mentioned some of them briefly in <a href="http://tomasp.net/blog/csharp-fsharp-async-intro.aspx">the first article of this series</a>. In this article, we'll look at some of the technical differences between the two models.</p> <p>The most notable non-technical difference is that F# asynchronous workflows are already available in a supported version of Visual Studio and can be used on a large number of .NET runtimes (including, for example, Windows Phone and Silverlight). However, there are surprisingly many technical differences as well. In this article, I'll talk about the support for cancellation, which is available in F# and is not (currently) available in the C# preview. We'll also look at the difference between model where tasks are created as running and the delayed model.</p> <p>This article is the second part of a short series about the asynchronous programming support in C# and F#. The previous article shows a simple example in both of the languages and the next articles explain how does the feature work (and how you can customize its behavior) as well as how to call F# libraries from C#:</p> <ul> <li><a href="http://tomasp.net/blog/csharp-fsharp-async-intro.aspx">Asynchronous C# and F# (I.): Simultaneous introduction</a></li> <li><strong>Asynchronous C# and F# (II.): How do they differ?</strong></li> <li><a href="http://tomasp.net/blog/async-compilation-internals.aspx">Asynchronous C# and F# (III.): How does it work?</a></li> <li>Asynchronous C# and F# (IV.): Calling F# libraries from C# <em>(not yet available)</em></li> </ul> <p>Let's start by looking at, perhaps, the most important technical difference - the built-in support for cancellation available in F# asynchronous workflows.</p> Asynchronous C# and F# (I.): Simultaneous introductionhttp://tomasp.net/blog/csharp-fsharp-async-intro.aspxFri, 29 Oct 2010 04:34:51 GMTOne of the exciting new technologies announced at PDC 2010 is a preview of asynchronous programming support for C#. In this article, I briefly introduce the new features and I demonstrate how they relate to F# asynchronous workflows already available in Visual Studio 2010. We'll also look at some differences between the two.Tomas Petricek<img src="http://tomasp.net/articles/csharp-fsharp-async-intro/pdc2010.png" style="float:right;margin:5px;margin-left:20px;" /> <p>One of the exciting new technologies that was announced at <a href="http://www.microsoftpdc.com/">PDC 2010</a> is the support for <em>asynchronous programming</em> in C#. So what exactly is <em>asynchronous programming</em>? Many applications today need to connect to some service or external data source including, for example, Web Services and REST APIs. This calls may take a long time to run, but we want to run them without blocking the application.</p> <p>Currently, you can run the operation on a background thread or using a <code>Task</code>, but coordinating multiple such operations is difficult. What if you for example need to wait until any (or all) of downloads complete and run some more code then? This is not only difficult, but it also scales badly, because blocking .NET threads is a bad practice (Threads are expensive and when they're just waiting for other operation to complete, we're wasting valuable resources). This problem has been the main motivation for including <em>asynchronous workflows</em> in F# about 3 years ago. In F#, this also enabled various interesting programming styles - for example <a href="http://dotnetslackers.com/articles/net/Programming-user-interfaces-using-f-sharp-workflows.aspx" type="external">creating GUI using asynchronous workflows</a> (also discussed in Chapter 16 of <a href="http://manning.com/petricek">my book</a> and in in <a href="http://tomasp.net/blog/reactive-talk.aspx">my recent talk</a>). The C# asynchronous programming support and the <code>await</code> keyword is largely inspired by F# <em>asynchronous workflows</em> (I was quite surprised that F# wasn't more visibly mentioned in the PDC talk). </p> <p>In this article series, I'll demonstrate both F# and C# asynchronous programming model, I'll look at features that are missing in one or the other as well as a few subtle differences (that may be unexpected) and finally, I'll write about writing (asynchronous) F# libraries that are easy to use from C#. The plan for the series is following:</p> <ul> <li><strong>Asynchronous C# and F# (I.): Simultaneous introduction</strong></li> <li><a href="http://tomasp.net/blog/async-csharp-differences.aspx">Asynchronous C# and F# (II.): How do they differ?</a></li> <li><a href="http://tomasp.net/blog/async-compilation-internals.aspx">Asynchronous C# and F# (III.): How does it work?</a></li> <li>Asynchronous C# and F# (IV.): Calling F# libraries from C# <em>(not yet available)</em></li> </ul> <p>Let's start with a brief overview of asynchronous programming features in C# and F#...</p> F# Parallel Extras (III.): Financial dashboard with cancellationhttp://tomasp.net/blog/parallel-extra-adash-cancellation.aspxWed, 27 Oct 2010 11:13:08 GMTIn this article, we revisit an F# implementation of a financial dashboard example from Parallel Programming with .NET. The article explains and demonstrates how to use the built-in support for cancellation in F# asynchronous workflows.Tomas Petricek<p>In this article we'll look at several improvements that can be done to the Financial dashboard example (originally from the <a href="http://parallelpatterns.codeplex.com/" type="external">Parallel Programming with Microsoft .NET</a> book). When I was translating samples in the book from C# to F#, the sample struck me, because it looks like a perfect fit for F# asynchronous workflows (instead of the <code>Task<T></code> type used in the C# version). I already talked about an <a href="http://tomasp.net/blog/fsharp-parallel-adash.aspx">alternative implementation</a> based on asynchronous workflows. However that version was still following some of the programming patterns, from the original C# version, which are not idiomatic in F#. In this article, I'll talk about a few other improvements that we can make to the sample...</p> <p>In the original version of the sample (in both C# and F#), we explicitly checked whether a cancellation token has been cancelled in every single operation. This was needed in C#, because tasks do not support cancellation automatically. However, F# asynchronous workflows make cancellation easier. They automatically check if the computation should be cancelled at the beginning and the end of every asynchronous call. Our first change will be to use this feature. Also, the original version propagates a <code>null</code> value when the computation is cancelling. In F# we don't need that and we'll only change the type of the overall result to <code>option<T></code>, so that we can notify the user interface (but we don't need to propagate cancellation explicitly). Finally, the original version contained sequential implementation, but didn't provide any way of actually running it, so we'll do a bit of refactoring to make that sample actually useable.</p> F# Parallel Extras (II.): Agent-based blocking queuehttp://tomasp.net/blog/parallel-extra-blockingagent.aspxWed, 27 Oct 2010 11:12:08 GMTIn this article, we'll look at type that implements an (asynchronous) blocking queue using F# agents. This can be used, for example, when implementing the pipeline pattern as demonstrated in the <a href="http://tomasp.net/blog/parallel-extra-image-pipeline.html">previous article</a>.Tomas Petricek<p>In the <a href="http://tomasp.net/blog/parallel-extra-image-pipeline.aspx">previous article</a>, we briefly introduced the <code>BlockingQueueAgent<T></code> type and we used it to implement the pipeline pattern (from Chapter 7 of <a href="http://parallelpatterns.codeplex.com/" type="external">Parallel Programming with Microsoft .NET</a>) using asynchronous workflows. The type was used to represent intermediate buffers with a limited size. In this article we'll take a look at the implementation of the type. The type implements a very useful pattern in agent-based parallel programming, so you can use it in your work, but it could be also interesting as a demonstration of the F# <code>Agent<T></code> type (an recommended alias for the <code>MailboxProcessor<T></code> type).</p> <p>The <code>BlockingQueueAgent<T></code> type is similar to <code>BlockingCollection<T></code> from .NET 4.0. It has methods for adding and removing elements that block when the operation cannot be done (e.g. adding when the queue is full or removing when the queue is empty). The most important difference is that it can be used <em>asynchronously</em>. This means that when we call its operations form F# asynchronous workflow (using <code>let!</code> and <code>do!</code>), the operation will block the calling workflow, but it will not block any physical thread. We start by looking at the overall structure of the agent and then look at the body of the agent which implements its behavior (using a state machine)...</p> F# Parallel Extras (I.): Image pipeline using agentshttp://tomasp.net/blog/parallel-extra-image-pipeline.aspxWed, 27 Oct 2010 11:11:08 GMTIn this article, we look at an F# implementation of an image processing pipeline demo from the Parallel Programming with Microsoft .NET. We'll use message-passing and asynchronous workflows, which leads to a more elegant and similarly efficient code.Tomas Petricek<p>In a <a href="http://tomasp.net/blog/fsharp-parallel-samples.aspx">recent blog post series</a>, I wrote about parallel programming samples that accompany the <a href="http://parallelpatterns.codeplex.com/" type="external">Parallel Programming with Microsoft .NET</a> book by patterns & practices group at Microsoft. The F# translation of the samples that I wrote about mostly followed the style used in the book, so it used patterns that are typical for C#. However, some of the samples can be written in F# in a more interesting way...</p> <p>In this article, we'll take a look at agent-based implementation of the Image pipeline example (from chapter 7). A <em>pipeline</em> is a useful pattern if you need to process large number of inputs in parallel and the processing consists of multiple phases or steps. In the original implementation, the pipeline was implemented using <code>BlockingCollection<T></code> and <code>Task<T></code> types from .NET 4.0.</p> <p>In this article, I'll show a version that uses F# agents and asynchronous workflows. We'll use a <code>BlockingQueueAgent<T></code> type, which is <a href="http://tomasp.net/blog/parallel-extra-blockingagent.aspx">discussed in another article</a>. It represents a queue with limited capacity that asynchronously blocks the process that is adding values if there is no space in the buffer and blocks the process that reads values when there are no values. This type can be elegantly used to implement the pipeline pattern. In this article, we'll demonstrate it by writing a four-phase pipeline that processes images. As you'll see, the agent-based version of the code is very much easier to write and has similar performance as the original version.</p> Reactive, parallel and concurrent programming in F# (PADL 2011)http://tomasp.net/blog/match-bang-paper.aspxMon, 25 Oct 2010 00:00:37 GMTAn academic paper that presents an extension for F# computation expressions, which can be used for encoding a wide range of reactive, parallel and concurrent programming models in a simple way in F#.Tomas Petricek<p>Don Syme blogged about <a href="http://blogs.msdn.com/b/dsyme/archive/2010/10/21/the-f-asynchronous-programming-model-padl-2010-pre-publication-draft.aspx" type="extenal"> a paper on the F# Asynchrounous Programming Model</a> that I helped to write. Without any doubt, the asynchronous programming features of F# are one of the reason for its success and also influence other teams in Microsoft. However, I'm very glad that there is now also an academic paper that makes this idea accessible to the academic community. I believe that the ideas could evolve in interesting ways when used in other programming languages and also, it is now easier to create research projects that build on top of the F# model.</p> <p>Don already mentioned that we have another paper accepted at PADL. The paper describes work that started during my internship at Microsoft Research in 2009. It presents a simple language extension for <em>computation expressions</em> that makes them even more useful in some reactive, concurrent and parallel programming models. Note that this is only a research project and there are currently no plans to support the extension in the F# language (although, if there will, eventually, be an open-source F# release, then you'll hear about the extension again...)</p> <p>Here is the abstract of the paper (accepted at <a href="http://www.dcc.fc.up.pt/PADL-2011/">PADL 2011</a>) and a PDF download link:</p> <h3 style="padding-left:60px;padding-right:60px;">Joinads: A retargetable control-flow construct for reactive, parallel and concurrent programming</h3> <p style="padding-left:60px;padding-right:60px;font-style:italic;"> Modern challenges led to a design of a wide range of programming models for reactive, parallel and concurrent programming, but these are often difficult to encode in general purpose languages. We present an abstract type of computations called joinads together with a syntactic language extension that aims to make it easier to use joinads in modern functional languages. </p> <p style="padding-left:60px;padding-right:60px;font-style:italic;"> Our extension generalizes pattern matching to work on abstract computations. It keeps a familiar syntax and semantics of pattern matching making it easy to reason about code, even in a non-standard programming model. We demonstrate our extension using three important programming models – a reactive model based on events; a concurrent model based on join calculus and a parallel model using futures. All three models are implemented as libraries that benefit from our syntactic extension. This makes them easier to use and also opens space for exploring new useful programming models.</p> <ul> <li>Download the <a href="http://tomasp.net/academic/joinads/joinads.pdf">full text</a> (PDF, pre-publication draft)</li> </ul> <p>The paper can still be revised before the final publication, so any comments and suggestions for improvement are largely welcome. You can contact me either via comments (below) or using email at <a href="mailto:tomas@tomasp.net">tomas@tomasp.net</a>. I would be also quite interested to hear from anybody who would like to implement similar feature in other programming languages (for example Haskell or Scala).</p> Formatting F# source code for the Webhttp://tomasp.net/blog/fswebsnippets-intro.aspxMon, 18 Oct 2010 01:42:38 GMTReading F# source code in Visual Studio is much easier than in plain text, because the background type checker provides useful information about types, functions and members via tool tips. This article introduces a tool that makes it possible to bring the same user experience to your F# code snippets published on the Web.Tomas Petricek<img src="http://tomasp.net/fswebsnippets/logo-sm.png" style="float:right;margin:10px 5px 10px 10px" /> <p>Languages with type-inference make it possible to write shorter code, because a smart compiler infers the types automatically. Even though we don't write the types, they are still there and are used to check whether our code doesn't contain (certain type of) bugs. However, types are not only useful for safety, but also when understanding code. When you see a function together with its type (especially higher-order functions) you can understand code much more easily than when you just see its name. When writing F# code, you can see all the types thanks to great integration for Visual Studio. However, what if you post a code sample to a web site or a blog? Many F# code snippets (including some on this blog) are just difficult to read without types. </p> <p>A few weeks ago, I was talking with James Margetson (from the F# team) about the possible uses of some functionality provided by the F# compiler and he suggested that we could use them to solve the problem I described in the introduction. Wouldn't it be nice if you could place a mouse cursor over an identifier in an F# blog post and see the same type information as the one that would appear in Visual Studio? </p> <p>Here is an example of what I'm talking about: </p> <pre class="fssnip"> <span class="l">1: </span><span class="c">///</span><span class="c"> </span><span class="c">Asynchronously</span><span class="c"> </span><span class="c">download</span><span class="c"> </span><span class="c">the</span><span class="c"> </span><span class="c">content</span><span class="c"> </span><span class="c">of</span><span class="c"> </span><span class="c">a</span><span class="c"> </span><span class="c">web</span><span class="c"> </span><span class="c">page</span> <span class="l">2: </span><span class="k">let</span> <span onmouseout="hideTip(event, 'ftp8', 43)" onmouseover="showTip(event, 'ftp8', 43)" class="i">downloadUrl</span> <span onmouseout="hideTip(event, 'ftp9', 44)" onmouseover="showTip(event, 'ftp9', 44)" class="i">url</span> <span class="o">=</span> <span onmouseout="hideTip(event, 'ftp33', 45)" onmouseover="showTip(event, 'ftp33', 45)" class="omitted">(...)</span> <span class="l">3: </span> <span class="l">4: </span><span class="c">///</span><span class="c"> </span><span class="c">Download</span><span class="c"> </span><span class="c">specified</span><span class="c"> </span><span class="c">pages</span><span class="c"> </span><span class="c">and</span><span class="c"> </span><span class="c">add</span><span class="c"> </span><span class="c">their</span><span class="c"> </span><span class="c">lengths</span> <span class="l">5: </span><span class="k">let</span> <span onmouseout="hideTip(event, 'ftp22', 46)" onmouseover="showTip(event, 'ftp22', 46)" class="i">getTotalLength</span> <span onmouseout="hideTip(event, 'ftp23', 47)" onmouseover="showTip(event, 'ftp23', 47)" class="i">urls</span> <span class="o">=</span> <span onmouseout="hideTip(event, 'ftp10', 48)" onmouseover="showTip(event, 'ftp10', 48)" class="i">async</span> { <span class="l">6: </span> <span class="k">let!</span> <span onmouseout="hideTip(event, 'ftp24', 49)" onmouseover="showTip(event, 'ftp24', 49)" class="i">texts</span> <span class="o">=</span> <span class="l">7: </span> <span onmouseout="hideTip(event, 'ftp23', 50)" onmouseover="showTip(event, 'ftp23', 50)" class="i">urls</span> <span class="o">|></span> <span onmouseout="hideTip(event, 'ftp25', 51)" onmouseover="showTip(event, 'ftp25', 51)" class="i">List</span><span class="o">.</span><span onmouseout="hideTip(event, 'ftp26', 52)" onmouseover="showTip(event, 'ftp26', 52)" class="i">map</span> <span onmouseout="hideTip(event, 'ftp8', 53)" onmouseover="showTip(event, 'ftp8', 53)" class="i">downloadUrl</span> <span class="l">8: </span> <span class="o">|></span> <span onmouseout="hideTip(event, 'ftp27', 54)" onmouseover="showTip(event, 'ftp27', 54)" class="i">Async</span><span class="o">.</span><span onmouseout="hideTip(event, 'ftp28', 55)" onmouseover="showTip(event, 'ftp28', 55)" class="i">Parallel</span> <span class="l">9: </span> <span class="k">return</span> <span onmouseout="hideTip(event, 'ftp24', 32)" onmouseover="showTip(event, 'ftp24', 32)" class="i">texts</span> <span class="o">|></span> <span onmouseout="hideTip(event, 'ftp29', 56)" onmouseover="showTip(event, 'ftp29', 56)" class="i">Seq</span><span class="o">.</span><span onmouseout="hideTip(event, 'ftp30', 57)" onmouseover="showTip(event, 'ftp30', 57)" class="i">sumBy</span> <span onmouseout="hideTip(event, 'ftp31', 58)" onmouseover="showTip(event, 'ftp31', 58)" class="i">String</span><span class="o">.</span><span onmouseout="hideTip(event, 'ftp32', 59)" onmouseover="showTip(event, 'ftp32', 59)" class="i">length</span> }<a target="_blank" class="fssniplink" href="http://tomasp.net/fswebsnippets">F# Web Snippets</a> </pre> <p>If you cannot wait and want to create F# source code snippets like this yourself, then go straight to <a href="http://tomasp.net/fswebsnippets">F# Web Snippets</a> (please use the web based version carefully - processing is pretty demanding!). If you first want to know how it works and how to use it, as well as where to get the source code, then continue reading...</p> <!-- HTML code for ToolTips --> <div class="tip" id="ftp1">namespace System<br /></div> <div class="tip" id="ftp2">namespace System.IO<br /></div> <div class="tip" id="ftp3">namespace System.Net<br /></div> <div class="tip" id="ftp4">namespace Microsoft<br /></div> <div class="tip" id="ftp5">namespace Microsoft.FSharp<br /></div> <div class="tip" id="ftp6">namespace Microsoft.FSharp.Control<br /></div> <div class="tip" id="ftp7">module WebExtensions<br /><br />from Microsoft.FSharp.Control<br /></div> <div class="tip" id="ftp8">val downloadUrl : string -> Async<string><br /><br />Full name: Untitled.downloadUrl <br /><br /><em>Asynchronously download the content of a web page</em><br /></div> <div class="tip" id="ftp9">val url : string<br /><br /> type: string<br /> implements: IComparable<br /> implements: ICloneable<br /> implements: IConvertible<br /> implements: IComparable<string><br /> implements: seq<char><br /> implements: Collections.IEnumerable<br /> implements: IEquatable<string><br /></div> <div class="tip" id="ftp10">val async : AsyncBuilder<br /><br />Full name: Microsoft.FSharp.Core.ExtraTopLevelOperators.async<br /></div> <div class="tip" id="ftp11">val req : WebRequest<br /><br /> type: WebRequest<br /> implements: Runtime.Serialization.ISerializable<br /> inherits: MarshalByRefObject<br /></div> <div class="tip" id="ftp12">type HttpWebRequest =<br /> class<br /> inherit System.Net.WebRequest<br /> member Abort : unit -> unit<br /> member Accept : string with get, set<br /> member AddRange : int -> unit<br /> member AddRange : int * int -> unit<br /> member AddRange : string * int -> unit<br /> member AddRange : string * int * int -> unit<br /> member Address : System.Uri<br /> member AllowAutoRedirect : bool with get, set<br /> member AllowWriteStreamBuffering : bool with get, set<br /> member AutomaticDecompression : System.Net.DecompressionMethods with get, set<br /> member BeginGetRequestStream : System.AsyncCallback * obj -> System.IAsyncResult<br /> member BeginGetResponse : System.AsyncCallback * obj -> System.IAsyncResult<br /> member ClientCertificates : System.Security.Cryptography.X509Certificates.X509CertificateCollection with get, set<br /> member Connection : string with get, set<br /> member ConnectionGroupName : string with get, set<br /> member ContentLength : int64 with get, set<br /> member ContentType : string with get, set<br /> member ContinueDelegate : System.Net.HttpContinueDelegate with get, set<br /> member CookieContainer : System.Net.CookieContainer with get, set<br /> member Credentials : System.Net.ICredentials with get, set<br /> member EndGetRequestStream : System.IAsyncResult -> System.IO.Stream<br /> member EndGetRequestStream : System.IAsyncResult * System.Net.TransportContext -> System.IO.Stream<br /> member EndGetResponse : System.IAsyncResult -> System.Net.WebResponse<br /> member Expect : string with get, set<br /> member GetRequestStream : unit -> System.IO.Stream<br /> member GetRequestStream : System.Net.TransportContext -> System.IO.Stream<br /> member GetResponse : unit -> System.Net.WebResponse<br /> member HaveResponse : bool<br /> member Headers : System.Net.WebHeaderCollection with get, set<br /> member IfModifiedSince : System.DateTime with get, set<br /> member KeepAlive : bool with get, set<br /> member MaximumAutomaticRedirections : int with get, set<br /> member MaximumResponseHeadersLength : int with get, set<br /> member MediaType : string with get, set<br /> member Method : string with get, set<br /> member Pipelined : bool with get, set<br /> member PreAuthenticate : bool with get, set<br /> member ProtocolVersion : System.Version with get, set<br /> member Proxy : System.Net.IWebProxy with get, set<br /> member ReadWriteTimeout : int with get, set<br /> member Referer : string with get, set<br /> member RequestUri : System.Uri<br /> member SendChunked : bool with get, set<br /> member ServicePoint : System.Net.ServicePoint<br /> member Timeout : int with get, set<br /> member TransferEncoding : string with get, set<br /> member UnsafeAuthenticatedConnectionSharing : bool with get, set<br /> member UseDefaultCredentials : bool with get, set<br /> member UserAgent : string with get, set<br /> static member DefaultCachePolicy : System.Net.Cache.RequestCachePolicy with get, set<br /> static member DefaultMaximumErrorResponseLength : int with get, set<br /> static member DefaultMaximumResponseHeadersLength : int with get, set<br /> end<br /><br />Full name: System.Net.HttpWebRequest<br /><br /> type: HttpWebRequest<br /> implements: Runtime.Serialization.ISerializable<br /> inherits: WebRequest<br /> inherits: MarshalByRefObject<br /></div> <div class="tip" id="ftp13">Multiple overloads <br />WebRequest.Create(requestUri: Uri) : WebRequest <br />WebRequest.Create(requestUriString: string) : WebRequest<br /></div> <div class="tip" id="ftp14">type Uri =<br /> class<br /> new : string -> System.Uri<br /> new : string * bool -> System.Uri<br /> new : string * System.UriKind -> System.Uri<br /> new : System.Uri * string -> System.Uri<br /> new : System.Uri * string * bool -> System.Uri<br /> new : System.Uri * System.Uri -> System.Uri<br /> member AbsolutePath : string<br /> member AbsoluteUri : string<br /> member Authority : string<br /> member DnsSafeHost : string<br /> member Equals : obj -> bool<br /> member Fragment : string<br /> member GetComponents : System.UriComponents * System.UriFormat -> string<br /> member GetHashCode : unit -> int<br /> member GetLeftPart : System.UriPartial -> string<br /> member Host : string<br /> member HostNameType : System.UriHostNameType<br /> member IsAbsoluteUri : bool<br /> member IsBaseOf : System.Uri -> bool<br /> member IsDefaultPort : bool<br /> member IsFile : bool<br /> member IsLoopback : bool<br /> member IsUnc : bool<br /> member IsWellFormedOriginalString : unit -> bool<br /> member LocalPath : string<br /> member MakeRelative : System.Uri -> string<br /> member MakeRelativeUri : System.Uri -> System.Uri<br /> member OriginalString : string<br /> member PathAndQuery : string<br /> member Port : int<br /> member Query : string<br /> member Scheme : string<br /> member Segments : string []<br /> member ToString : unit -> string<br /> member UserEscaped : bool<br /> member UserInfo : string<br /> static val UriSchemeFile : string<br /> static val UriSchemeFtp : string<br /> static val UriSchemeGopher : string<br /> static val UriSchemeHttp : string<br /> static val UriSchemeHttps : string<br /> static val UriSchemeMailto : string<br /> static val UriSchemeNews : string<br /> static val UriSchemeNntp : string<br /> static val UriSchemeNetTcp : string<br /> static val UriSchemeNetPipe : string<br /> static val SchemeDelimiter : string<br /> static member CheckHostName : string -> System.UriHostNameType<br /> static member CheckSchemeName : string -> bool<br /> static member Compare : System.Uri * System.Uri * System.UriComponents * System.UriFormat * System.StringComparison -> int<br /> static member EscapeDataString : string -> string<br /> static member EscapeUriString : string -> string<br /> static member FromHex : char -> int<br /> static member HexEscape : char -> string<br /> static member HexUnescape : string * int -> char<br /> static member IsHexDigit : char -> bool<br /> static member IsHexEncoding : string * int -> bool<br /> static member IsWellFormedUriString : string * System.UriKind -> bool<br /> static member TryCreate : string * System.UriKind * System.Uri -> bool<br /> static member TryCreate : System.Uri * string * System.Uri -> bool<br /> static member TryCreate : System.Uri * System.Uri * System.Uri -> bool<br /> static member UnescapeDataString : string -> string<br /> end<br /><br />Full name: System.Uri<br /><br /> type: Uri<br /> implements: Runtime.Serialization.ISerializable<br /></div> <div class="tip" id="ftp15">val resp : WebResponse<br /><br /> type: WebResponse<br /> implements: Runtime.Serialization.ISerializable<br /> implements: IDisposable<br /> inherits: MarshalByRefObject<br /></div> <div class="tip" id="ftp16">member WebRequest.AsyncGetResponse : unit -> Async<WebResponse><br /></div> <div class="tip" id="ftp17">val stream : Stream<br /><br /> type: Stream<br /> implements: IDisposable<br /> inherits: MarshalByRefObject<br /></div> <div class="tip" id="ftp18">WebResponse.GetResponseStream() : Stream<br /></div> <div class="tip" id="ftp19">val reader : StreamReader<br /><br /> type: StreamReader<br /> implements: IDisposable<br /> inherits: TextReader<br /> inherits: MarshalByRefObject<br /></div> <div class="tip" id="ftp20">type StreamReader =<br /> class<br /> inherit System.IO.TextReader<br /> new : System.IO.Stream -> System.IO.StreamReader<br /> new : System.IO.Stream * bool -> System.IO.StreamReader<br /> new : System.IO.Stream * System.Text.Encoding -> System.IO.StreamReader<br /> new : System.IO.Stream * System.Text.Encoding * bool -> System.IO.StreamReader<br /> new : System.IO.Stream * System.Text.Encoding * bool * int -> System.IO.StreamReader<br /> new : string -> System.IO.StreamReader<br /> new : string * bool -> System.IO.StreamReader<br /> new : string * System.Text.Encoding -> System.IO.StreamReader<br /> new : string * System.Text.Encoding * bool -> System.IO.StreamReader<br /> new : string * System.Text.Encoding * bool * int -> System.IO.StreamReader<br /> member BaseStream : System.IO.Stream<br /> member Close : unit -> unit<br /> member CurrentEncoding : System.Text.Encoding<br /> member DiscardBufferedData : unit -> unit<br /> member EndOfStream : bool<br /> member Peek : unit -> int<br /> member Read : unit -> int<br /> member Read : char [] * int * int -> int<br /> member ReadLine : unit -> string<br /> member ReadToEnd : unit -> string<br /> static val Null : System.IO.StreamReader<br /> end<br /><br />Full name: System.IO.StreamReader<br /><br /> type: StreamReader<br /> implements: IDisposable<br /> inherits: TextReader<br /> inherits: MarshalByRefObject<br /></div> <div class="tip" id="ftp21">member StreamReader.AsyncReadToEnd : unit -> Async<string><br /></div> <div class="tip" id="ftp22">val getTotalLength : string list -> Async<int><br /><br />Full name: Untitled.getTotalLength <br /><br /><em>Download specified pages and add their lengths</em><br /></div> <div class="tip" id="ftp23">val urls : string list<br /><br /> type: string list<br /> implements: Collections.IStructuralEquatable<br /> implements: IComparable<List<string>><br /> implements: IComparable<br /> implements: Collections.IStructuralComparable<br /> implements: Collections.Generic.IEnumerable<string><br /> implements: Collections.IEnumerable<br /></div> <div class="tip" id="ftp24">val texts : string []<br /><br /> type: string []<br /> implements: ICloneable<br /> implements: Collections.IList<br /> implements: Collections.ICollection<br /> implements: Collections.Generic.IList<string><br /> implements: Collections.Generic.ICollection<string><br /> implements: seq<string><br /> implements: Collections.IEnumerable<br /> inherits: Array<br /></div> <div class="tip" id="ftp25">Multiple items <br />module List<br /><br />from Microsoft.FSharp.Collections <br /><br />--------------------<br /> <br />type List<'T> =<br /> | ( [] )<br /> | ( :: ) of 'T * 'T list<br /> with<br /> interface Collections.IEnumerable<br /> interface Collections.Generic.IEnumerable<'T><br /> member Head : 'T<br /> member IsEmpty : bool<br /> member Item : index:int -> 'T with get<br /> member Length : int<br /> member Tail : 'T list<br /> static member Cons : head:'T * tail:'T list -> 'T list<br /> static member Empty : 'T list<br /> end<br /><br />Full name: Microsoft.FSharp.Collections.List<_><br /><br /> type: List<'T><br /> implements: Collections.IStructuralEquatable<br /> implements: IComparable<List<'T>><br /> implements: IComparable<br /> implements: Collections.IStructuralComparable<br /> implements: Collections.Generic.IEnumerable<'T><br /> implements: Collections.IEnumerable<br /></div> <div class="tip" id="ftp26">val map : ('T -> 'U) -> 'T list -> 'U list<br /><br />Full name: Microsoft.FSharp.Collections.List.map<br /></div> <div class="tip" id="ftp27">Multiple items <br />type Async<'T><br /><br />Full name: Microsoft.FSharp.Control.Async<_> <br /><br />--------------------<br /> <br />type Async<br />with<br /> static member AsBeginEnd : computation:('Arg -> Async<'T>) -> ('Arg * AsyncCallback * obj -> IAsyncResult) * (IAsyncResult -> 'T) * (IAsyncResult -> unit)<br /> static member AwaitEvent : event:IEvent<'Del,'T> * ?cancelAction:(unit -> unit) -> Async<'T> (requires delegate and 'Del :> Delegate)<br /> static member AwaitIAsyncResult : iar:IAsyncResult * ?millisecondsTimeout:int -> Async<bool><br /> static member AwaitWaitHandle : waitHandle:Threading.WaitHandle * ?millisecondsTimeout:int -> Async<bool><br /> static member CancelDefaultToken : unit -> unit<br /> static member Catch : computation:Async<'T> -> Async<Choice<'T,exn>><br /> static member FromBeginEnd : beginAction:(AsyncCallback * obj -> IAsyncResult) * endAction:(IAsyncResult -> 'T) * ?cancelAction:(unit -> unit) -> Async<'T><br /> static member FromBeginEnd : arg:'Arg1 * beginAction:('Arg1 * AsyncCallback * obj -> IAsyncResult) * endAction:(IAsyncResult -> 'T) * ?cancelAction:(unit -> unit) -> Async<'T><br /> static member FromBeginEnd : arg1:'Arg1 * arg2:'Arg2 * beginAction:('Arg1 * 'Arg2 * AsyncCallback * obj -> IAsyncResult) * endAction:(IAsyncResult -> 'T) * ?cancelAction:(unit -> unit) -> Async<'T><br /> static member FromBeginEnd : arg1:'Arg1 * arg2:'Arg2 * arg3:'Arg3 * beginAction:('Arg1 * 'Arg2 * 'Arg3 * AsyncCallback * obj -> IAsyncResult) * endAction:(IAsyncResult -> 'T) * ?cancelAction:(unit -> unit) -> Async<'T><br /> static member FromContinuations : callback:(('T -> unit) * (exn -> unit) * (OperationCanceledException -> unit) -> unit) -> Async<'T><br /> static member Ignore : computation:Async<'T> -> Async<unit><br /> static member OnCancel : interruption:(unit -> unit) -> Async<IDisposable><br /> static member Parallel : computations:seq<Async<'T>> -> Async<'T []><br /> static member RunSynchronously : computation:Async<'T> * ?timeout:int * ?cancellationToken:Threading.CancellationToken -> 'T<br /> static member Sleep : millisecondsDueTime:int -> Async<unit><br /> static member Start : computation:Async<unit> * ?cancellationToken:Threading.CancellationToken -> unit<br /> static member StartChild : computation:Async<'T> * ?millisecondsTimeout:int -> Async<Async<'T>><br /> static member StartImmediate : computation:Async<unit> * ?cancellationToken:Threading.CancellationToken -> unit<br /> static member StartWithContinuations : computation:Async<'T> * continuation:('T -> unit) * exceptionContinuation:(exn -> unit) * cancellationContinuation:(OperationCanceledException -> unit) * ?cancellationToken:Threading.CancellationToken -> unit<br /> static member SwitchToContext : syncContext:Threading.SynchronizationContext -> Async<unit><br /> static member SwitchToNewThread : unit -> Async<unit><br /> static member SwitchToThreadPool : unit -> Async<unit><br /> static member TryCancelled : computation:Async<'T> * compensation:(OperationCanceledException -> unit) -> Async<'T><br /> static member CancellationToken : Async<Threading.CancellationToken><br /> static member DefaultCancellationToken : Threading.CancellationToken<br />end<br /><br />Full name: Microsoft.FSharp.Control.Async<br /></div> <div class="tip" id="ftp28">static member Async.Parallel : computations:seq<Async<'T>> -> Async<'T []><br /></div> <div class="tip" id="ftp29">module Seq<br /><br />from Microsoft.FSharp.Collections<br /></div> <div class="tip" id="ftp30">val sumBy : ('T -> 'U) -> seq<'T> -> 'U (requires member ( + ) and member get_Zero)<br /><br />Full name: Microsoft.FSharp.Collections.Seq.sumBy<br /></div> <div class="tip" id="ftp31">type String =<br /> class<br /> new : char -> string<br /> new : char * int * int -> string<br /> new : System.SByte -> string<br /> new : System.SByte * int * int -> string<br /> new : System.SByte * int * int * System.Text.Encoding -> string<br /> new : char [] * int * int -> string<br /> new : char [] -> string<br /> new : char * int -> string<br /> member Chars : int -> char<br /> member Clone : unit -> obj<br /> member CompareTo : obj -> int<br /> member CompareTo : string -> int<br /> member Contains : string -> bool<br /> member CopyTo : int * char [] * int * int -> unit<br /> member EndsWith : string -> bool<br /> member EndsWith : string * System.StringComparison -> bool<br /> member EndsWith : string * bool * System.Globalization.CultureInfo -> bool<br /> member Equals : obj -> bool<br /> member Equals : string -> bool<br /> member Equals : string * System.StringComparison -> bool<br /> member GetEnumerator : unit -> System.CharEnumerator<br /> member GetHashCode : unit -> int<br /> member GetTypeCode : unit -> System.TypeCode<br /> member IndexOf : char -> int<br /> member IndexOf : string -> int<br /> member IndexOf : char * int -> int<br /> member IndexOf : string * int -> int<br /> member IndexOf : string * System.StringComparison -> int<br /> member IndexOf : char * int * int -> int<br /> member IndexOf : string * int * int -> int<br /> member IndexOf : string * int * System.StringComparison -> int<br /> member IndexOf : string * int * int * System.StringComparison -> int<br /> member IndexOfAny : char [] -> int<br /> member IndexOfAny : char [] * int -> int<br /> member IndexOfAny : char [] * int * int -> int<br /> member Insert : int * string -> string<br /> member IsNormalized : unit -> bool<br /> member IsNormalized : System.Text.NormalizationForm -> bool<br /> member LastIndexOf : char -> int<br /> member LastIndexOf : string -> int<br /> member LastIndexOf : char * int -> int<br /> member LastIndexOf : string * int -> int<br /> member LastIndexOf : string * System.StringComparison -> int<br /> member LastIndexOf : char * int * int -> int<br /> member LastIndexOf : string * int * int -> int<br /> member LastIndexOf : string * int * System.StringComparison -> int<br /> member LastIndexOf : string * int * int * System.StringComparison -> int<br /> member LastIndexOfAny : char [] -> int<br /> member LastIndexOfAny : char [] * int -> int<br /> member LastIndexOfAny : char [] * int * int -> int<br /> member Length : int<br /> member Normalize : unit -> string<br /> member Normalize : System.Text.NormalizationForm -> string<br /> member PadLeft : int -> string<br /> member PadLeft : int * char -> string<br /> member PadRight : int -> string<br /> member PadRight : int * char -> string<br /> member Remove : int -> string<br /> member Remove : int * int -> string<br /> member Replace : char * char -> string<br /> member Replace : string * string -> string<br /> member Split : char [] -> string []<br /> member Split : char [] * int -> string []<br /> member Split : char [] * System.StringSplitOptions -> string []<br /> member Split : string [] * System.StringSplitOptions -> string []<br /> member Split : char [] * int * System.StringSplitOptions -> string []<br /> member Split : string [] * int * System.StringSplitOptions -> string []<br /> member StartsWith : string -> bool<br /> member StartsWith : string * System.StringComparison -> bool<br /> member StartsWith : string * bool * System.Globalization.CultureInfo -> bool<br /> member Substring : int -> string<br /> member Substring : int * int -> string<br /> member ToCharArray : unit -> char []<br /> member ToCharArray : int * int -> char []<br /> member ToLower : unit -> string<br /> member ToLower : System.Globalization.CultureInfo -> string<br /> member ToLowerInvariant : unit -> string<br /> member ToString : unit -> string<br /> member ToString : System.IFormatProvider -> string<br /> member ToUpper : unit -> string<br /> member ToUpper : System.Globalization.CultureInfo -> string<br /> member ToUpperInvariant : unit -> string<br /> member Trim : unit -> string<br /> member Trim : char [] -> string<br /> member TrimEnd : char [] -> string<br /> member TrimStart : char [] -> string<br /> static val Empty : string<br /> static member Compare : string * string -> int<br /> static member Compare : string * string * bool -> int<br /> static member Compare : string * string * System.StringComparison -> int<br /> static member Compare : string * string * System.Globalization.CultureInfo * System.Globalization.CompareOptions -> int<br /> static member Compare : string * string * bool * System.Globalization.CultureInfo -> int<br /> static member Compare : string * int * string * int * int -> int<br /> static member Compare : string * int * string * int * int * bool -> int<br /> static member Compare : string * int * string * int * int * System.StringComparison -> int<br /> static member Compare : string * int * string * int * int * System.Globalization.CultureInfo * System.Globalization.CompareOptions -> int<br /> static member Compare : string * int * string * int * int * bool * System.Globalization.CultureInfo -> int<br /> static member CompareOrdinal : string * string -> int<br /> static member CompareOrdinal : string * int * string * int * int -> int<br /> static member Concat : obj -> string<br /> static member Concat : obj [] -> string<br /> static member Concat : string [] -> string<br /> static member Concat : obj * obj -> string<br /> static member Concat : string * string -> string<br /> static member Concat : obj * obj * obj -> string<br /> static member Concat : string * string * string -> string<br /> static member Concat : obj * obj * obj * obj -> string<br /> static member Concat : string * string * string * string -> string<br /> static member Copy : string -> string<br /> static member Equals : string * string -> bool<br /> static member Equals : string * string * System.StringComparison -> bool<br /> static member Format : string * obj -> string<br /> static member Format : string * obj [] -> string<br /> static member Format : string * obj * obj -> string<br /> static member Format : System.IFormatProvider * string * obj [] -> string<br /> static member Format : string * obj * obj * obj -> string<br /> static member Intern : string -> string<br /> static member IsInterned : string -> string<br /> static member IsNullOrEmpty : string -> bool<br /> static member Join : string * string [] -> string<br /> static member Join : string * string [] * int * int -> string<br /> end<br /><br />Full name: System.String<br /><br /> type: String<br /> implements: IComparable<br /> implements: ICloneable<br /> implements: IConvertible<br /> implements: IComparable<string><br /> implements: seq<char><br /> implements: Collections.IEnumerable<br /> implements: IEquatable<string><br /></div> <div class="tip" id="ftp32">val length : string -> int<br /><br />Full name: Microsoft.FSharp.Core.String.length<br /></div> <div class="tip" id="ftp33">async { <br /> let req = HttpWebRequest.Create(Uri(url)) <br /> let! resp = req.AsyncGetResponse()<br /> let stream = resp.GetResponseStream()<br /> let reader = new StreamReader(stream)<br /> return! reader.AsyncReadToEnd() }<br /></div> Parallel Programming in F# (IV.): Financial dashboard examplehttp://tomasp.net/blog/fsharp-parallel-adash.aspxMon, 06 Sep 2010 10:30:00 GMTIn this article, we'll take a look at the Adatum Financial Dashboard sample from Parallel Programming with Microsoft .NET and we'll compare implementations using tasks and asynchronous workflows.Tomas Petricek<p>In the fourth part of the Parallel Programming in F# series, we'll take a look at the Adatum Financial Dashboard sample. The sample is a part of <a href="http://parallelpatterns.codeplex.com/" type="external">Parallel Programming with Microsoft .NET</a>, which is a guide that introduces common parallel programming patterns on .NET 4.0. The C# version of the sample is in details discussed in the guide, but the F# translation contains several additional interesting aspects that I'll introduce in this article.</p> <p>The sample simulates a financial modelling application that performs processing of market data in several steps that can be partly executed in parallel. In this article we'll compare two implementations. The first one (similar to the C# version) uses the <code>Task<'T></code> type from .NET 4.0 and chains steps using the <code>ContinueWith</code> method. The second version is F# specific and it implements step as a sequential computation wrapped in asynchronous workflows. Partial results are reported to the user interface using events.</p> Parallel Programming in F# (III.): Aggregating datahttp://tomasp.net/blog/fsharp-parallel-aggregate.aspxMon, 06 Sep 2010 10:20:00 GMTIn this article, we'll take a look at F# samples from Chapter 4 of Parallel Programming with Microsoft .NET. We'll discuss several options for implementing the Map/Reduce pattern.Tomas Petricek<p>In this part of the Parallel Programming in F# series, we'll explore examples of parallel aggregation from Chapter 4 of <a href="http://parallelpatterns.codeplex.com/" type="external">Parallel Programming with Microsoft .NET</a>, which is a guide that introduces common parallel programming patterns on .NET 4.0. The C# version of the sample is in details discussed in the guide. In this article, we'll look at the F# translation and in particular at several functions from the <code>PSeq</code> module. Some of the functionality is currently available only in the "PSeq.fs" distributed with the samples, but will eventually appear in F# PowerPack as well. </p> <p>Aggregation of data in parallel is an interesting problem. As we've seen in the previous article, PLINQ and tasks make it easy to parallelize independent blocks of code that don't share any state. Unfortunatelly, not all programs are like that. In particular, we often need to aggregate all elements of a sequence - when writing sequential code in F#, you would use the <code>Seq.fold</code> function. In this article, we'll look at functions that implement fold parallel.</p> Parallel Programming in F# (II.): Using PLINQ and Taskshttp://tomasp.net/blog/fsharp-parallel-plinq.aspxMon, 06 Sep 2010 10:10:00 GMTIn this article, we'll look at several F# samples from Chapters 2 and 3 of Parallel Programming with Microsoft .NET. We'll look at using Task Parallel Library (TPL) and Parallel LINQ from F#, including the <code>PSeq</code> module from F# PowerPack.Tomas Petricek<p>In this part of the Parallel Programming in F# series, we'll look at some basic examples of parallel programming in F# that are available in <a href="http://parallelpatterns.codeplex.com/" type="external">Parallel Programming with Microsoft .NET</a>. This is a guide that introduces common parallel programming patterns on .NET 4.0. The guide discusses the samples in C#, but it also contains an F# translation of the source code. Since the languages are different, the F# version deserves a brief explanation.</p> <p>In this article, we'll discuss some of the F# examples and we'll look at a couple of aspects that are specific for F#. In particular, we'll look at working with Parallel LINQ (both directly and using <code>PSeq</code> module from F# PowerPack) and working with tasks. We'll also look at an interesting example (using closures) where C# version doesn't behave as expected, but a literal translation in F# corrects the problem.</p> Parallel Programming in F# (I.): Introducing the sampleshttp://tomasp.net/blog/fsharp-parallel-samples.aspxMon, 06 Sep 2010 10:00:00 GMTIn this article series, I'll introduce the F# version of samples for the Parallel Programming with Microsoft .NET book written by the patterns & practices group at Microsoft.Tomas Petricek<img src="http://tomasp.net/articles/fsharp-parallel-samples/book.png" style="float:right;margin:20px;" /> <p><a href="http://parallelpatterns.codeplex.com/" type="external">Parallel Programming with Microsoft .NET</a> is a guide written by the patterns & practices group at Microsoft. It introduces .NET programmers to patterns for including parallelism in their applications (using support for parallel programming in .NET 4.0). It introduces techniques such as parallel loops, parallel tasks, data aggregation and so on. The book includes numerous samples in C# and Visual Basic that can be easily copied and adapted to match your needs.</p> <p>As part of a contracting work for the F# team, I developed an F# version of the samples, which is now available on the <a href="http://parallelpatterns.codeplex.com/" type="external">book web site</a>. You can get it by downloading <a href="http://parallelpatterns.codeplex.com/releases/view/50473">F# code samples</a> (ZIP) from the 1.0 release, or you can download the <a href="http://parallelpatterns.codeplex.com/SourceControl/list/changesets" type="external">latest version of the source code</a> directly. The F# version of the code is mostly a direct translation of the C# versions, but there are a few interesting places that are worth discussing. In particular, some of the samples use the <code>PSeq</code> module from F# PowerPack and I also added a version of one example that uses F# asynchronous workflows.</p> <p>In this article series, I'll look at several interesting examples from the F# version of the source code. We'll look how to use PLINQ and Tasks (which are available in .NET 4.0) from F# (Part II.) including some advanced topics such as the Map-Reduce algorithm (Part III.). We'll also look at a larger example built using tasks and an alternative implementation using asynchronous workflows (Part IV.) Here are links to the individual articles:</p> <ul> <li><strong>Parallel Programming in F# (I.): Introducing the samples</strong></li> <li><a href="http://tomasp.net/blog/fsharp-parallel-plinq.aspx">Parallel Programming in F# (II.): Using PLINQ and Tasks</a></li> <li><a href="http://tomasp.net/blog/fsharp-parallel-aggregate.aspx">Parallel Programming in F# (III.): Aggregating data</a></li> <li><a href="http://tomasp.net/blog/fsharp-parallel-adash.aspx">Parallel Programming in F# (IV.): Financial dashboard example</a></li> </ul> The Duality of Object and Event referenceshttp://tomasp.net/blog/event-object-duality.aspxMon, 19 Jul 2010 16:58:05 GMTThis article describes an interesting example of mathematical duality in programming languages - the duality between references between objects and references between events. The idea is useful for understading what events are garbage and can be garbage collected.Tomas Petricek<p>Mathematical duality [<a href="http://tomasp.net/blog/event-object-duality.aspx
#duallinks">2</a>] is a very useful and elegant concept that gives us a nice way of speaking about objects or structures that behave in some way exactly conversely. There is no clear definition of what <em>duality</em> is. However, the idea is that when we have two structures that behave conversely and we know that something is true about the first one, then we get the opposite statement about the other structure "for free" (if you know how to translate from one structure to the other).</p> <p>In this article, I'll talk about an interesting example of duality that (to my best knowledge) wasn't described by anyone before. The two dual structures are <strong>references between objects</strong> in a normal program and <strong>references between events</strong> in a reactive application. The statement that is going to become obvious thanks to the duality principle is describing which of the objects (or events) are garbage and can be safely collected by garbage collector.</p> <p>This topic is in much more details discussed in a paper [<a href="http://tomasp.net/blog/event-object-duality.aspx
#duallinks">4</a>] I wrote with <a href="http://research.microsoft.com/en-us/people/dsyme/">Don Syme</a> and that I presented at the ISMM Workshop (see also <a href="http://tomasp.net/blog/pldi-2010-trip.aspx">my trip report from PLDI</a>). In this article, I'll try to give an accessible description of the most interesting idea from the paper...</p> Dynamic in F#: Reading data from SQL databasehttp://tomasp.net/blog/dynamic-sql.aspxFri, 09 Jul 2010 02:03:00 GMTIn this article we look at working with SQL databases in F# using ADO.NET. We'll see how to use dynamic invoke operator to make the usual ADO.NET code remarkably elegant and simple...Tomas Petricek<p>When reading data from a SQL database in F#, you have a couple of options. You can use F# implementation of LINQ, which allows you to write queries directly in the F# language or you can use standard ADO.NET classes such as <code>SqlCommand</code>. The second option is often good enough - when you just need to call a simple query, you probably don't want to setup the whole LINQ infrastructure (generate classes, reference F# PowerPack, etc.) Unfortunately, ADO.NET classes are a bit ugly to use. When calling an SQL stored procedure, you need to specify the name of the procedure as a string, you need to add parameters one-by-one by creating instances of <code>SqlParameter</code>, you need to dynamically cast results from the <code>obj</code> type and so on...</p> <p>In this article, we'll look how to use the <em>dynamic operator</em> to make the experience of using ADO.NET from F# dramatically better. Dynamic operator (there are actually two of them) are a simple way of supporting dynamic invoke in F#. We can use it to write code that looks almost like an ordinary method call or property access, but is resolved dynamically at runtime (using the name of the method or property). The following example shows what we'll be able to write at the end of this article:</p> <pre lang="fsharp"> // Call 'GetProducts' procedure with 'CategoryID' set to 1 use conn = new DynamicSqlConnection(connectionString) use cmd = conn?GetProducts cmd?CategoryID <- 1 conn.Open() // Read all products and print their names use reader = cmd.ExecuteReader() while reader.Read() do printfn "Product: %s" reader?ProductName </pre> <p>If you ever tried to call a SQL stored procedure directly using the <code>SqlCommand</code>, then you can surely appreciate the elegance of this code snippet. Let's now take a look at a larger example and some of the neat tricks that make this possible...</p> PLDI 2010 Trip Reporthttp://tomasp.net/blog/pldi-2010-trip.aspxMon, 05 Jul 2010 23:23:02 GMTIn June, I attended PLDI 2010, which is one of the big "programming language" conferences. I presented a paper based on some work that I did during my internship at MSR at one of the workshops and I also attended many interesting talks...Tomas Petricek<p>In June, I attended my first "big" academic conference <a href="http://cs.stanford.edu/pldi10" type="external">Programming Languages Design and Implementation (PLDI 2010)</a> in Toronto. I attended the conference, because I presented a paper that I wrote with Don Syme as a result of my internship at Microsoft Research, but I'll write more about that shortly (and thanks to MSR for partly supporting my attendance at the conference!)</p> <p>As far as I understand it, the focus of the conference is more on <em>implementation</em>. Many people believe that the current programming languages are good enough and we need to make sure that they run well (e.g. compilers optimize code to run better on multi-core) and that we need better tools for working with them (e.g. automatic verification of the code we write), so these areas were the main focus of the conference. However, there were some very interesting talks on the <em>design</em> of programming languages, which is an area that I personally find more interesting... </p> Recording and samples from my Reactive F# talkhttp://tomasp.net/blog/reactive-talk.aspxSun, 27 Jun 2010 14:49:28 GMTAlmost a week ago, I <a href="http://tomasp.net/blog/fun-londoners-reactive.aspx">posted an invitation</a> to my F# talk at the F#unctional Londoners user group. The talk has been recorded, so you can view it online now and you can also get all the Silverlight demos...Tomas Petricek<p>Almost a week ago, I <a href="http://tomasp.net/blog/fun-londoners-reactive.aspx">posted an invitation</a> to my F# talk at the F#unctional Londoners user group. The theme of my talk was <em>reactive programming</em>, which was also a topic of my <a href="http://tomasp.net/academic/reactive-thesis.aspx">Master's thesis</a> (defended earlier in June), so I really enjoyed talking about it. In the talk, I discussed the two approaches that you can use for developing reactive applications in F# (using examples in Silverlight): </p> <a href="http://skillsmatter.com/podcast/open-source-dot-net/tomas-petricek-reactive-programming-in-fsharp"> <img src="http://tomasp.net/articles/reactive-talk-london/pic.jpg" style="margin:10px; float:right; border-style:none;" /> </a> <ul> <li><strong>Declarative</strong> (or <em>data-flow</em> oriented) allows you to describe "what" should be done with data that your component receives from various events (such as mouse position etc.) This can be written using F# event combinators such as <code>Event.map</code> and <code>Event.scan</code>.</li> <li><strong>Imperative</strong> (or <em>control-flow</em> oriented) - in this style, we describe various states of the component (e.g. semaphore with green, orange and red) and describe transitions between the states. This can be written using F# <em>asynchronous workflows</em> and the <code>AwaitObservable</code> primitive (which you can get as part of the source code).</li> </ul> <p>Thanks to the folks from <a href="http://skillsmatter.com">SkillsMatter</a> who provided place for the meetup and helped with the organization, the talk was also recorded and is already available online! Below, you can also get all the nice Silverlight demos that I used during the talk...</p> <p>Thanks again to Carolyn Miller and <a href="http://www.trelford.com/blog/" type="external">Phil Trelford</a> for organizing the talk and also to <a href="http://blogs.msdn.com/b/dsyme">Don Syme</a> for taking me to the airport in the early morning (at 4 AM...) after the talk.</p> <h2>Links & Resources</h2> <ul> <li><a href="http://skillsmatter.com/podcast/open-source-dot-net/tomas-petricek-reactive-programming-in-fsharp" type="external">Reactive Programming in F#</a> (recording) - Skills Matter</li> <li>Slides from the talk (<a href="http://tomasp.net/articles/reactive-talk-london/reactive_fsharp.pdf" type="external">PDF</a>, <a href="http://tomasp.net/articles/reactive-talk-london/reactive_fsharp.pptx" type="external">PPTX</a> formats)</li> <li><a href="http://tomasp.net/articles/reactive-talk-london/reactive_fsharp.zip" type="external">Reactive F# demos in Silverlight</a> (includes <code>AwaitObservable</code> implementation)</li> </ul>Reactive Programming with F# in Londonhttp://tomasp.net/blog/fun-londoners-reactive.aspxTue, 15 Jun 2010 02:54:39 GMTI'll be visiting London on June 23 and I'll be talking at the F#unctional Londoners user group. The theme of the talk is Reactive Programming with F# and you can expect many interesting F# features including asynchronous workflows and event combinators.Tomas Petricek<p>If you’re a registered member of the <a href="http://www.meetup.com/FSharpLondon/" type="external">F#unctional Londoners</a> user group, then you maybe already know that I'll be visiting London on <strong>June 23</strong> and I’ll be talking about <strong>Reactive programming with F#</strong>. If you're not a registered member and occasionally visit London, then you should definitely register. The user group is organized by Carolyn Miller and <a href="http://www.trelford.com/blog/" type="external">Phil Trelford</a> (whom I met some time ago at Microsoft Research in Cambridge). Among others, previous speakers include <a href="http://strangelights.com/blog/" type="external">Robert Pickering</a> (who also presented some samples based on my <a href="http://tomasp.net/blog/accelerator-intro.aspx">F# and Accelerator</a> series). Finally, another reason for joining the group is that it has a great name (as well as a logo)!</p> <img src="http://tomasp.net/img/londoners.png" style="float:right; margin:10px" /> <h2>When, what & where?</h2> <ul> <li><strong><a href="http://www.meetup.com/FSharpLondon/calendar/13501027/" type="external">Tomas Petricek on Reactive Programming with F#</a></strong></li> <li><strong>Date & time:</strong> 23 June (Wednesday), 6:30 PM</li> <li><strong>Location:</strong> The Skills Matter eXchange, 116-120 Goswell Road, London</li> </ul> <p>By the way, I'll also have a free copy of my <a href="http://www.manning.com/petricek" type="external">Real-World Functional Programming</a> book to give away during the talk!</p> <h2>Reactive Programming with F#</h2> <p>I'm sure you're already convinced to come. Nevertheless, you may still want to know what I'm going to talk about. There are many areas where F# offers clear benefits such as parallel & concurrent programming. I believe that <strong>reactive programming</strong> is another great area for F#. In reactive programming, we face quite different problems than in other programming styles. We (as the authors of the application) can no longer specify what the application should do. Instead, the application needs to be able to handle many possible combinations of events. This aspect of programming is sometimes called <em>inversion of control</em>.</p> <p>Reactive programming is important for programming user interfaces, especially today when user interfaces are becoming more interactive and more "fancy". To demonstrate this, I'm working on some nice <strong>Silverlight</strong> demos for the talk! However, it is also needed to handle other kinds of events such as completion of background task or message from other application. We'll look at the two essential techniques that F# provides for reactive programming:</p> <ul> <li><strong>Declarative event combinators</strong> - one way of writing reactive applications is to specify the whole event processing declaratively by saying "what" should be done with occurrences of events. This is particularly useful when we need to encode simpler logic with a clear <em>data-flow</em>.</li> <li><strong>Imperative using workflows</strong> - for more complicated interactions, we can use <em>asynchronous workflows</em>. This makes the code more explicit, but we get full control over the <em>control-flow</em> of the application. Even though this approach is more "imperative" it can be used for writing nicely composable functional code as well.</li> </ul> <p>I'm looking forward to seeing you at the talk next week!</p>ASP.NET and F# (I.) - Creating MVC web applications in F#http://tomasp.net/blog/fsharp-mvc-web.aspxSun, 09 May 2010 20:43:52 GMTThis article shows how to use F# for developing ASP.NET web applications using the MVC framework. It also shows how to access data using LINQ in F# and how to simplify web programming using F# meta-programming, modules and records.Tomas Petricek<p>Some time ago, I wrote a couple of examples of <a href="http://tomasp.net/blog/aspnet-in-fsharp.aspx"> developing web applications in F# using ASP.NET</a>. Since then, the F# language and runtime has changed a little bit and there are also new technologies available in ASP.NET, so I thought I'd write a more up-to-date article on this topic. In this article, I'll present a simple "demo" F# web application that you can use as a starting point when creating your own projects (you'll also find a convenient Visual Studio 2010 template below). The article shows the following interesting things:</p> <ul> <li><strong>ASP.NET MVC</strong> - We're going to use ASP.NET MVC Framework to create the web application. As the article name suggests, most of the actual program code including models and controllers will be implemented in F#.</li> <li><strong>F# LINQ to SQL</strong> - The application uses a sample Northwind database and we'll write queries for selecting data from the database using LINQ support that's available in the <a href="http://fsharppowerpack.codeplex.com/" type="external">F# PowerPack</a>.</li> <li><strong>F# features</strong> - The application also uses some nice F# features that are quite useful for developing web applications. We'll use modules and records to implement the model and we'll also use advanced meta-programming features for constructing LINQ queries.</li> </ul> <p>If you want to use F# for creating an MVC application, you have a few options. It should be possible to create the web application solely as an F# project. However, we'll use a more convenient approach. We'll create a standard C# MVC project and move all the actual implementation to an F# library. We'll look at the application structure shortly. The following screenshot shows a page that lists products in the Northwind database:</p> <div style="text-align:center;"> <img src="http://tomasp.net/articles/fsharp-mvc-web/web.png" /> </div> Programming user interfaces using F# workflowshttp://tomasp.net/blog/excerpt-gui-workflows.aspxThu, 18 Feb 2010 00:25:51 GMTF# asynchronous workflows can be used to solve a wide range of programming problems. In this article we'll look how to use asynchronous workflows for elegantly expressing the control flow of interaction with the user. We'll also look at clear functional way for encoding drag and drop-like algorithm.Tomas Petricek<p>Numerous Manning partners already published several exceprts from my <a href="http://www.manning.com/petricek/" target="external">Real-World Functional Programming</a> book. You can find a list on the <a href="http://functional-programming.net/" type="external">book's web page</a>. However, the last excerpt published <a href="http://dotnetslackers.com/articles/net/Programming-user-interfaces-using-f-sharp-workflows.aspx" type="external">at DotNetSlackers</a> is particularly interesting. It discusses how to use F# asynchronous workflows to write GUI applications. This is a very powerful programming pattern that is very difficult to do in any other .NET language. We first discussed it with Don Syme during my internship at Microsoft Research and I found it very elegant, so I made some space for it in the book. In fact, the entire Chapter 16 discusses various reactive programming techniques that can be used in F#.</p> <img src="http://tomasp.net/articles/excerpt-gui-workflows/app.png" style="margin:15px;float:right;" /> <p style="padding-left:40px;padding-right:40px;font-style:italic;">When designing applications that don't react to external events, you have lots of control flow constructs available, such as if-then-else expressions, for loops and while loops in imperative languages, or recursion and higher-order functions in functional languages. Constructs like this make it easy to describe what the application does. The control flow is clearly visible in the source code, so drawing a flowchart to describe it is straightforward.</p> <p style="padding-left:40px;padding-right:40px;font-style:italic;">Understanding reactive applications is much more difficult. A typical C# application or GUI control that needs to react to multiple events usually involves mutable state. When an event occurs, it updates the state and may run more code in response to the event, depending on the current state. This architecture makes it quite difficult to understand the potential states of the application and the transitions between them. Using asynchronous workflows, we can write the code in a way that makes the control flow of the application visible even for reactive applications.</p> <p style="text-indent:0px">You can read the complete article here: <a href="http://dotnetslackers.com/articles/net/Programming-user-interfaces-using-f-sharp-workflows.aspx">Programming user interfaces using F# workflows </a> [<a href="http://dotnetslackers.com/articles/net/Programming-user-interfaces-using-f-sharp-workflows.aspx" target="_blank">^</a>]. It is also worth adding that Manning offers <strong>30% discount</strong> to DotNetSlackers readers (see the article for details!)</p>Using custom grouping operators in LINQhttp://tomasp.net/blog/custom-linq-grouping.aspxSun, 07 Feb 2010 20:13:32 GMTIn LINQ, we can group data using the "group by" clause. However, there are other potentially useful implementations of grouping. For example, we may want to group only adjacent elements or group ascending or descending parts of the data. This article shows how to use custom behavior when grouping data using "group by" in LINQ query.Tomas Petricek<p>You can use LINQ to write queries that perform grouping of data using <code>group by</code> or ordering of data using <code>orderby</code> clause. LINQ provides the default (and the most common) implementation of both of the operations, but sometimes you may need a slightly different behavior when grouping or ordering data (this article is motivated by a <a href="http://stackoverflow.com/questions/2194761/can-i-use-linq-to-retrieve-only-on-change-values" type="external">question on StackOverflow</a> which needs to do exactly that for grouping).</p> <p>Let's look at a simple example, which shows when we may need a different behavior when grouping data. For example, we may have the following list of stock trades containing a name of a stock and the price of the trade (stored for example as a list of <code>TradeInfo</code> classes with properties <code>Name</code> and <code>Price</code>):</p> <pre lang="csharp"> { { Name = "MSFT", Price = 80.00 }, { Name = "MSFT", Price = 70.00 }, { Name = "GOOG", Price = 100.00 }, { Name = "GOOG", Price = 200.00 }, { Name = "GOOG", Price = 300.00 }, { Name = "MSFT", Price = 30.00 }, { Name = "MSFT", Price = 20.00 } }</pre> <p>Now, we may want to group adjacent trades into a single summary record which will contain the name of the stock (which is same for all trades in each group), the number of trades in the group and an average price in the group. The desired results are:</p> <pre lang="csharp"> { { Name = "MSFT", Count = 2, AvgPrice = 75.00 }, { Name = "GOOG", Count = 3, AvgPrice = 200.00 }, { Name = "MSFT", Count = 2, AvgPrice = 25.00 } }</pre> <p>The operation that we want to do is very similar to <code>group by</code> in LINQ, but it doesn't do quite the same thing! If we used <code>group by</code>, we would get only two groups as the result. However, as I wrote earlier, we want to group only <em>adjacent trades</em>. You could write your own extension method to do this, but then you need to leave the elegant LINQ query syntax. In this article, I'll show you how to get the desired results using a simple LINQ query with a <code>group by</code> clause...</p>Deal of the day: Real-World Functional Programminghttp://tomasp.net/blog/book-deal.aspxSun, 24 Jan 2010 17:00:41 GMTSome time ago, I received my copies of <strong>Real-World Functional Programming</strong>. I started working on it back in May 2008 and as many people who had more experience with writing books told me, it took longer than I was expecting!Tomas Petricek<p>Some time ago, I received my copies of <strong>Real-World Functional Programming</strong>. I started working on it back in May 2008 and as many people who had more experience with writing books told me, it took longer than I was expecting! Anyway, I have to say, it was worth it, holding the actual printed book with my name on the cover is just fantastic!</p> <br /> <a href="http://manning.com/petricek"><img src="http://tomasp.net/articles/book-deal/book.jpg" style="border:0px; float:right;margin:10px;" /></a> <p>The goal of the book is to present functional programming concepts and ideas in a readable form. I wanted to create a book that will teach you how to <em>think functionally</em> without using the usual <em>shock therapy</em> that people usually feel when seeing functional programming for the first time. There are already a couple of reviews that suggest I was quite successful:</p> <ul> <li><em>Functional Programming for the Real World, by Tomas Petricek and Jon Skeet, has been a very helpful book for moving to F# from C#, as the authors do a fantastic job of helping to explain the differences between OOP and FP. </em><br /> <a href="http://www.amazon.com/Functional-Programming-Real-World-Examples/dp/1933988924" type="external">James Black at Amazon.com</a> </li> <li><em>This book isn’t just a simple introduction to programming in F#; it’s an introductory text on functional programming covering the many reasons why it is time for this programming paradigm to finally be accepted by mainstream programmers. And it also contains much more... </em><br /> <a href="http://www.simple-talk.com/community/blogs/clivet/archive/2010/01/03/85227.aspx" type="external">CliveT, Software Engineer at Red Gate Software</a> </li> <li>... and there are many other great comments about the book at <a href="http://www.manning.com/petricek">Manning book page</a>.</li> </ul> <h2>Deal of the day (January 24)</h2> <p>Finally, here is one great news if you're interested in getting the book! <strong>Real-World Functional Programming</strong> is Manning's Deal of the Day this Sunday, January 24. On this day, the print book is available for \$20 from the <a href="http://www.manning.com/petricek">Manning website</a>, with code <code>dotd0124</code>.</p> Accelerator and F# (IV.): Composing computations with quotationshttp://tomasp.net/blog/accelerator-quotations.aspxTue, 12 Jan 2010 03:20:36 GMTIn this article series we're talking about the Accelerator project, which can be used from F# to write code that runs in parallel on GPU or multi-core CPU. In this article, we'll look at building complex data-parallel programs with F# quotations, we'll implement blur filter and we'll also discuss architecture and performance.Tomas Petricek<p>In this article series, we're talking about the Accelerator project and I'm presenting an F# library that I implemented, which allows you to use Accelerator [<a href="http://tomasp.net/blog/accelerator-quotations.aspx#accelfsh4links">references</a>] in a more sophisticated way. We've seen two examples of using Accelerator directly (see also <a href="http://tomasp.net/blog/accelerator-intro.aspx">introduction</a> and <a href="http://tomasp.net/blog/accelerator-life-game.aspx">Game of Life</a>). In the <a href="http://tomasp.net/blog/accelerator-dataparallel.aspx">previous article</a> I introduced my F# library for working with Accelerator. We've seen F# functions from the <code>DataParallel</code> module, we implemented an algorithm that rotates an image using these functions and finally, we've seen that we can take this ordinary F# code and run it using Accelerator. This is all possible thanks to F# quotations, which we can use to get an AST (a source code) of an F# function we wrote (if the function is marked in some special way).</p> <img src="http://tomasp.net/articles/accelerator-quotations/blur.png" alt="Blurred photo of Prague" style="float:right; margin:10px" /> <p>In this part of the series, we're going to look at working with quotations explicitly. We'll use meta-programming techniques to work with Accelerator. Meta-programming means writing programs that manipulate with other programs or pieces of code. This is exactly what we're going to do in this article. We'll write an F# function (running on CPU) that builds a program, which we'll then run using Accelerator.</p> <p>This is quite interesting approach, which isn't possible when we call Accelerator methods as standard F# functions or .NET methods. The benefit is that we'll clearly see which parts of program run on CPU and what parts execute on GPU or using X64 multi-core target. We could also perform more complicated optimizations with the code (because this wouldn't affect the readability). Just for your reference, here is the list of articles in this series in case you missed some of them:</p> <ul> <li><a href="http://tomasp.net/blog/accelerator-intro.aspx">Accelerator and F# (I.): Introduction and calculating PI</a></li> <li><a href="http://tomasp.net/blog/accelerator-life-game.aspx">Accelerator and F# (II.): The Game of Life on GPU</a></li> <li><a href="http://tomasp.net/blog/accelerator-dataparallel.aspx">Accelerator and F# (III.): Data-parallel programs using F# quotations</a></li> <li><strong>Accelerator and F# (IV.): Composing computations with quotations</strong></li> </ul> <p>However, enough with theory and let's take a look at some code samples! This time, we'll implement blurring of an image (also called convolution). Another example how to write this in F# using Accelerator is Satnam Singh's blog post [<a href="#accelfsh4links">4</a>]. Our example will be different, because we'll write the code as standard F# program and then have it translated to Accelerator automatically using quotations. We'll also talk about the architecture of the library that we're using and look at some performance results.</p> Accelerator and F# (III.): Data-parallel programs using F# quotationshttp://tomasp.net/blog/accelerator-dataparallel.aspxMon, 04 Jan 2010 12:50:13 GMTWe already discussed how to write programs that run on GPU using MSR Accelerator. In this article, we'll write an image rotation using data-parallel F# functions and then use a library that translates it to Accelerator automatically.Tomas Petricek<p>If you've been following this article series, you already know that Accelerator is a MSR library [<a href="http://tomasp.net/blog/accelerator-dataparallel.aspx#accelfsh3links">1</a>, <a href="#accelfsh3links">2</a>] that allows you to run code in parallel on either multi-core CPU or using shaders on GPU (see <a href="http://tomasp.net/blog/accelerator-intro.aspx">introduction</a>). We also discussed a direct way to use Accelerator from F# (by calling Accelerator methods directly) and <a href="http://tomasp.net/blog/accelerator-life-game.aspx">implemented Conway's Game of Life</a>. In this article, we'll look at more sophisticated way of using Accelerator from F#. We'll introduce F# quotations and look at translating 'normal' F# code to use Accelerator.</p> <img src="http://tomasp.net/articles/accelerator-dataparallel/rotated.png" alt="Rotated Prague photo" style="float:right; margin:10px" /> <p>In general, F# quotations allow us to treat F# code as data structure and manipulate with it. This is very similar to C# expression trees, but the F# implementation is more powerful. We can also mark a standard method or a function with a special attribute that tells the compiler to store quotation of the body. Then we can access the quotation and traverse it or modify it. In this article we'll use a function that takes an F# quotation (containing a limited set of functions) and executes it using MSR Accelerator. Implementing this functionality is a bit complicated, so we won't discuss the implementation now. We'll leave this for some future article of this series. In future, we'll also look at other interesting possibilities that we have when writing code using quotations. Here is a list of articles in this series and of the articles that I'm planning to add:</p> <ul> <li><a href="http://tomasp.net/blog/accelerator-intro.aspx">Accelerator and F# (I.): Introduction and calculating PI</a></li> <li><a href="http://tomasp.net/blog/accelerator-life-game.aspx">Accelerator and F# (II.): The Game of Life on GPU</a></li> <li><strong>Accelerator and F# (III.): Data-parallel programs using F# quotations</strong></li> <li><a href="http://tomasp.net/blog/accelerator-quotations.aspx">Accelerator and F# (IV.): Composing computations with quotations</a></li></ul> Accelerator and F# (II.): The Game of Life on GPUhttp://tomasp.net/blog/accelerator-life-game.aspxMon, 28 Dec 2009 21:16:03 GMTThis article shows how to use Accelerator from F#, which I <a href="accelerator-intro.aspx">already discussed</a>, to implement a massively parallel version of the famous Conway's Game of Life.Tomas Petricek<p>In the <a href="accelerator-intro.aspx">previous article</a>, I introduced the Microsoft Research Accelerator library. It allows us to write computations with arrays in C# and execute them in parallel on multi-core CPU or more interestingly, using GPU shaders. In the previous artcile, we've seen how Accelerator works and how it can be accessed from F#. In this article, we'll look at one more interesting F# demo - we'll implement the famous Conway's Game of Life [<a href="accelerator-life-game.aspx#accelfsh2links">1</a>] using Accelerator. We'll use a v2 version of Accelerator which has been announced just recently and is available from Microsoft Connect [<a href="accelerator-life-game.aspx#accelfsh2links">2</a>].</p> <div style="text-align:center;"> <object width="425" height="344"><param name="movie" value="http://www.youtube.com/v/wiZnTfx2re8&hl=en&fs=1"></param><param name="allowFullScreen" value="true"></param><param name="allowscriptaccess" value="always"></param><embed src="http://www.youtube.com/v/wiZnTfx2re8&hl=en&fs=1" type="application/x-shockwave-flash" allowscriptaccess="always" allowfullscreen="true" width="425" height="344"></embed></object> </div> <p>This article is the second one from a series about using Accelerator from F#. Today, we'll use Accelerator types directly from F# - this is the simplest possible approach and is very similar to the way you'd work with Accelerator in C#. However, we can use some nice F# features such as custom operators to make the code more readable. In the next article, we'll discuss a different approach - we'll look how to execute more "standard" F# code (that doesn't reference Accelerator explicitly) with Accelerator using F# quotations. The list of articles may change, but here is a list of articles that I'm currently planning to write:</p> <ul> <li><a href="http://tomasp.net/blog/accelerator-intro.aspx">Accelerator and F# (I.): Introduction and calculating PI</a></li> <li><strong>Accelerator and F# (II.): The Game of Life on GPU</strong></li> <li><a href="http://tomasp.net/blog/accelerator-dataparallel.aspx">Accelerator and F# (III.): Data-parallel programs using F# quotations</a></li> <li><a href="http://tomasp.net/blog/accelerator-quotations.aspx">Accelerator and F# (IV.): Composing computations with quotations</a></li> </ul> Accelerator and F# (I.): Introduction and calculating PIhttp://tomasp.net/blog/accelerator-intro.aspxMon, 21 Dec 2009 03:21:03 GMTThis article shows how to write F# programs that run in parallel as shader programs on GPU or on multi-core CPU using Microsoft Research Accelerator project.Tomas Petricek<img src="http://tomasp.net/articles/accelerator-intro/montecarlo.png" alt="Calculating Pi using Monte-Carlo" style="float:left; margin:10px" /> <p>I already wrote about two projects that I worked on during an internship at MSR back in 2007 (<a href="http://tomasp.net/blog/aspnet-in-fsharp.aspx" type="external">ASP.NET support in F#</a> and <a href="http://tomasp.net/blog/fswebtools-intro.aspx" type="external">F# WebTools</a>). Even though this was more than 2 years ago (and I did one more internship at MSR in the meantime), I still have one more project that I never published on the web. The folks from the F# team reminded me of this project recently, so I thought I could finally publish it. The project used Microsoft Research Accelerator [<a href="#accelfsh1links">1</a>, <a href="#accelfsh1links">2</a>], which is a C# library for developing array-based computations and executing them on a GPU. More recently, the Accelerator team at MSR published Accelerator v2 [<a href="#accelfsh1links">3</a>], which was a good motivation to update my original project...</p> <p>In this article, we'll look at the simplest way of using Accelerator from F#. Accelerator provides a managed interface that can be naturally used from both C# and F#. We can use a mix of method calls and overloaded operators to describe a computation. In F#, we'll also define our additional custom operators to make the code a bit nicer. After we introduce Accelerator using a simple C# demo, we'll look how to calculate an approximate value of the PI number using a Monte-Carlo method.</p> <p>This article is the first one from a series about using Accelerator from F#. The list of articles may change, but here is a list of articles that I'm currently planning to write:</p> <ul> <li><strong>Accelerator and F# (I.): Introduction and calculating PI</strong></li> <li><a href="http://tomasp.net/blog/accelerator-life-game.aspx">Accelerator and F# (II.): The Game of Life on GPU</a></li> <li><a href="http://tomasp.net/blog/accelerator-dataparallel.aspx">Accelerator and F# (III.): Data-parallel programs using F# quotations</a></li> <li><a href="http://tomasp.net/blog/accelerator-quotations.aspx">Accelerator and F# (IV.): Composing computations with quotations</a></li> </ul> Real-World Functional Programming: Completed and printed!http://tomasp.net/blog/book-completed.aspxSat, 19 Dec 2009 21:54:28 GMTIf you're following my blog, you probably noticed that I was working on a book about functional programming using F# and C#. The great news is that the book is finally completed and will be available on December 24!Tomas Petricek<p>If you're following my blog or if you're interested in F# or functional programming in .NET, you probably noticed that I was working on a book <a href="http://manning.com/petricek">Real-World Functional Programming</a>. At some point, we called it <em>Functional Programming for the Real-World</em>, but then we changed the title back to a better sounding version <em>Real-World Functional Programming</em> (subtitle <em>With examples in F# and C#</em>). The book is also reason for a lower number of blog posts over the last year. Over the last month or so, we were doing the final edits, reviewing the final PDF version (I fixed quite a lot minor issues, synchronized book with the Beta 2 F# release and so on). Anyway, before a few days, I received the following email (as an author, I receive the same emails as those who ordered the book through the <a href="http://www.manning.com/about/meap.html">Manning Early Access Program</a>, so that I can see what we're sending to our dear readers):</p> <table><tr><td> <img style="margin:10px" src="/articles/book-completed/cover.png" /> </td><td> <p style="font-style:italic; margin:10px 30px 10px 10px; text-indent:0px;"> Dear Tomas Petricek, <br /> We are pleased to announce that <strong>Real-World Functional Programming</strong> is now complete! As a MEAP subscriber you can download your copy of the finished ebook right now! (...) This ebook is the final version, identical to the softbound edition, which is currently being printed and will be available on <strong>December 24</strong>. If you chose the printed book option when you originally subscribed, we'll ship it to you automatically—no action required from you. </p> </td></tr></table> <h2>Finally finished!</h2> <p>Yes, that's right. The book is finally completed and as far as I know, it has been printed last week! If you already ordered the book, you won't receive it before Christmas, but it should come shortly after. I can't wait to see the book actually <em>printed</em>. The transition from the Word drafts I initially wrote to a final PDF version was already felt fantastic and I thought <em>"It looks like a real book!"</em> Among other things, there are now graphical arrows with comments inside listings, which looks really great and makes code listings much easier to read. Now I can look forward to seeing the <em>actual book</em>. Maybe I'm too conservative, but I have to say that I'm really glad that I wrote the book before everything is going to be published just electronically!</p> <p>Here is a couple of links that you may found interesting if you want to look inside the book...</p>Functional Programming: Available Chapter Excerpts & Discounthttp://tomasp.net/blog/functional-excerpts-and-discount.aspxSun, 26 Jul 2009 03:41:14 GMTThe work on my book Functional Programming for the Real World is slowly getting to the end. If you want to look inside, you can read some of the chapter excerpts that were published on the internet.Tomas Petricek<p>The work on my book <a href="http://www.functional-programming.net" target="external">Functional Programming for the Real World</a> is slowly getting to the end. I'm currently creating index for the last couple of chapters and doing final updates based on the feedback from reviews and also from the <a href="http://www.manning-sandbox.com/forum.jspa?forumID=460&start=0" type="external">forum at manning.com</a> (this means that if you have some suggestions, it's the best time to post them - I haven't yet replied to all of them, but I'll certainly do that before the manuscript will go to the production).</p> F# Webcast (IV.) - Developing standard .NET librarieshttp://tomasp.net/blog/fsharp-webcast-objects.aspxMon, 15 Jun 2009 20:09:04 GMTThis webcast demonstrates how to wrap an existing F# code into an object oriented library that can be nicely used from C# and how to use it when developing ASP.NET web application. The demo uses script for processing RSS feeds from the previous webcast.Tomas Petricek<p>In the previous parts of this webcast series we've developed an F# script that downloads RSS feeds asynchronously and in parallel and searches them for the specified keywords. We followed the usual F# development style, so after introducing <a href="fsharp-webcast-functional.aspx">the basic functional concepts</a>, we wrote the code in <a href="fsharp-webcast-dotnet.aspx">the simples possible style</a> and demonstrated how to use <code>System.Xml</code> and <code>System.Net</code> namespaces. Then we <a href="fsharp-webcast-async.aspx">refactored the existing code</a>, to run asynchronously and process the results potentially in parallel, which was very easy thanks to F# <em>asynchronous workflows</em>.</p> <p>In this part of the series, we'll make the next evolutionary step of our sample application. We'll turn the code that originally used F# tuples and lists into code that uses standard .NET objects and we'll also see how to declare a class in F#. This simple modification will turn the script into an F# library that is almost indistinguishable from a library developed in C#. We'll also look how you can use the library from C# web application to show the interop between C# and F# in practice. We'll start with the code from the <a href="fsharp-webcast-async.aspx">previous part</a>, so if you missed that, you may want to check it out or download the source code.</p> F# Webcast (III.) - Using Asynchronous Workflowshttp://tomasp.net/blog/fsharp-webcast-async.aspxFri, 05 Jun 2009 03:39:39 GMTIn the previous part you've seen how to write a simple function for downloading RSS feeds and processing them. In this part, we look how to improve the function to download data asynchronously and process them potentially in parallel.Tomas Petricek<p>In this webcast, we'll look at improving the code for downloading and processing RSS feeds that I presented in <a href="fsharp-webcast-dotnet.aspx">the second part</a> (if you didn't see earlier parts, <a href="fsharp-webcast-dotnet.aspx">the first one</a> was an introduction to basic functional ideas). The previous part demonstrated how to use .NET libraries and we implemented a simple <code>downloadUrl</code> function for obtaining content of from the web and we've also seen how to load the data into an XML document object and how to filter items. In this part, we'll modify the code to run asynchronously and potentially in parallel. To use some of the functionality, you'll need to get <code>FSharp.PowerPack.dll</code>, which is available with the VS 2008 installation or as a separated download for VS 2010 [<a href="#fswc_asy">4</a>]. </p> <p>Now that we have the first version of the code, we can start <em>refactoring</em> it. I'm using the term in a slightly vague meaning - we're of course going to change the behavior of the code. We'll wrap it into F# <em>asynchronous workflow</em> to run without blocking threads and we'll also run multiple downloads in parallel. However, this can still be viewed as refactoring in some sense, because we're not changing the <em>core</em> behavior of the code. As you can see from the webcast, these kinds of refactorings are also very nicely supported by F# syntax...</p> F# Webcast (II.) - Using .NET librarieshttp://tomasp.net/blog/fsharp-webcast-dotnet.aspxMon, 01 Jun 2009 14:57:53 GMTThis is the second part of the webcast series that introduces the F# language. It shows how to use .NET libraries from F# to download RSS feed and how to work with the obtained data using tuples, sequence expressions and other F# features.Tomas Petricek<p>About a week ago I posted <a href="fsharp-webcast-functional.aspx">the first part</a> of my F# webcast series. It focused on explainining the basic ideas behind functional programming such as immutability, recursion and passing functions as arguments to other functions (or methods in C#). In the first part, we've seen some C# code to demonstrate the ideas and also a bit of F#, mainly to show the basic language features. </p> <p>The second part is going to be exclusively about F#. It'll demonstrate how we can start writing a demo application that grabs data from RSS feeds and processes them. You'll learn how to access .NET libraries from F# (in particular, we'll use <code>System.Net</code> and <code>System.Xml</code>). We'll develop the code iteratively, which means that we'll start by simply enumerating the RSS elements using <code>for</code> loop and printing the results and then we'll refactor the code to use <em>tuples</em> and <em>sequence expressions</em> to turn it into processing code that generates a sequence of feed items. Finally we'll also demonstrate how to use some of the functions from the previous part such as <code>List.filter</code> in practice.</p>F# Webcast (I.) - Introducing functional conceptshttp://tomasp.net/blog/fsharp-webcast-functional.aspxMon, 25 May 2009 13:39:54 GMTNow that Visual Studio 2010 beta 1 is out, it may be a good time finally try the new F# language. To make the exploration easier, I created a web cast series that demonstrates interesting aspects of F#. In this part, we'll look at basic functional concepts and working with data.Tomas Petricek<p>Now that <a href="http://www.microsoft.com/visualstudio/en-us/products/2010/default.mspx" type="external">Visual Studio 2010 Beta 1</a> is out, it is finally a good time to take a look at one of the (in my opinion) most interesting new features in the new release - <a href="http://blogs.msdn.com/dsyme/archive/2009/05/20/visual-studio-2010-beta1-with-f-is-now-available-plus-matching-f-ctp-update-for-vs2008.aspx" type="external">the F# language</a>. F# existed for quite a long time now as Microsoft Research project, but is now becoming a real Microsoft product. Interestingly, F# is still available as a <a href="http://www.microsoft.com/downloads/details.aspx?displaylang=en&FamilyID=7bb32f32-9fac-4f34-ad56-b0bda130cf00" type="external">plugin for Visual Studio 2008</a>, so if you want to try it you don't have to install the whole new beta of 2010.</p> <p>There are already many resources for learning F# including my <a href="http://tomasp.net/blog/functional-overview.aspx">functional programming overview</a>, which is a Manning Greenpaper for the book <a href="http://www.functional-programming.net" type="external">Functional Programming for the Real World</a> that I'm writing with Jon Skeet and my <a href="http://tomasp.net/blog/fsharp-i-introduction.aspx">four-part F# introduction</a>. There are also some useful links on the official <a href="http://www.fsharp.net">F# web site</a> including some talk recordings. However, I haven't yet seen any good F# webcast focusing mainly on showing F# source code, starting from simple functional concepts to the real-world features like asynchronous workflows and object-oriented programming in F#, so I decided to create one.</p> <p style="text-indent:0px;"><strong>So, here it is...</strong></p> Internship project: Reactive pattern matchinghttp://tomasp.net/blog/internship-match-bang.aspxSun, 17 May 2009 23:00:28 GMTI already mentioned that I was doing my second internship with Don Syme at MSR Cambridge. This time, I was in Cambridge for 6 months from October until April, so it has been more than a month since I left, but as you can guess I didn't have time to write anything about the internship until now...Tomas Petricek<a href="http://cid-6ddff5260c96e30a.skydrive.live.com/albums.aspx"> <img src="http://tomasp.net/articles/internship-match-bang/image.jpg" alt="Cambridge, 2009" class="ldecor" style="border:0px;float:left; margin:20px" /> </a> <p>I already <a href="http://tomasp.net/blog/book-source-available.aspx">mentioned</a> that I was doing my second internship with <a href="http://blogs.msdn.com/dsyme/" type="external">Don Syme</a> at Microsoft Research in Cambridge. This time, I was in Cambridge for 6 months from October until April, so it has been more than a month since I left, but as you can guess I didn't have time to write anything about the internship until now... There isn't much to say though, because the internship was simply fantastic. Cambridge is a beautiful place (here are some <a href="http://cid-6ddff5260c96e30a.skydrive.live.com/browse.aspx/2008%20Autumn%20-%20Cambridge" type="external">autumn</a> and <a href="http://cid-6ddff5260c96e30a.skydrive.live.com/browse.aspx/2009%20Winter%20-%20Cambridge" type="external">winter</a> photos), the Microsoft Research lab in Cambridge is full of smart people, so it is a perferct working environment (except that you realize that you're not as clever as you think :-)). Also, it is just a few meters away from the <a href="http://www.cl.cam.ac.uk" type="external">Computer Laboratory</a> of the Cambridge University, so there are always many interesting talks and seminars. So, big thanks to Don Syme, James Margetson and everyone else who I had a chance to work with during the internship.</p> <p>One of the reasons why I didn't have much time to write about the internship earlier is that I was invited to the <a href="http://www.langnetsymposium.com/" type="external">Lang.NET Symposium</a> shortly after the end of the internship. I had a chance to talk about my project there as well and there is even a video recording from the talk (the link is below), so you can watch it to find out more about my recent F# work.</p> Imperative computation in F# (II.) - Writing break and continuehttp://tomasp.net/blog/imperative-ii-break.aspxSat, 25 Apr 2009 16:31:15 GMTIn the previous article of this series, we've implemented a computation expression that allows us to write imperative 'return' in F#. In this article, we'll add support for 'break' and 'continue'.Tomas Petricek<p>As I already wrote in the <a href="http://tomasp.net/blog/imperative-i-return.aspx">first part of this series</a>, the F# language doesn't support some of the language constructs known from imperative languages such as C#. In particular, we cannot use imperative <code>return</code> statement that returns the result of a function from any place in the function code. In functional languages, every construct is an expression, so to get the overall result of the function, the F# language evaluates the expression and the value of the expression is used as the result. In the previous article, we've seen that we can simulate this construct in the F# language using F# computation expressions and I showed how to implement computation named <code>imperative</code> that allows us to write for example the <code>exists</code> function for working with sequences like this:</p> <pre lang="fsharp"> let exists f inp = imperative { for v in inp do if f(v) then return true return false } </pre> <p>In this article, we're going to look at two more imperative constructs and we're going to talk about <code>break</code> and <code>continue</code>. We'll see that we can quite easily extend the computation builder from the previous article to allow writing code that is syntactically very close to what you would write in C#. As I already mentioned, there are of course some performance overheads when using computation expressions, but I find it very interesting how nice imperative syntax we can get in functional F#:</p> <pre lang="fsharp"> imperative { for x in 1 .. 10 do if (x % 3 = 0) then do! continue printfn "number = %d" x } </pre> <p>The only difference between this code and the code we'd probably write if F# supported <code>continue</code> as a keyword is that we need to wrap the code inside the <code>imperative</code> computation and that we need to add the <code>do!</code> primitive before the <code>continue</code> value. Now that we've seen an example of using the <code>continue</code> value inside the imperative computations, let's look how we can extend the computation builder from the previous article to add this feature...</p> Imperative computation in F# (I.) - Returning results from a functionhttp://tomasp.net/blog/imperative-i-return.aspxThu, 19 Mar 2009 02:05:03 GMTEven though F# supports some imperative constructs such as for and while loops, it doesn't support some of the advanced constructs like imperative return and break. In this series, we'll look how we can implement these constructs ourselves using F# computation expressions.Tomas Petricek<p>One of the limitations of F# is that it doesn't very well support some of the advanced imperative language constructs such as <code>break</code>, <code>continue</code> or imperative style of returning value from a function, meaning that you can't write something like <code>return false</code> in the middle of the function. This has good reasons. F# doesn't in principle have the notion of <em>currently executing statement</em> and instead treat every code you write as an expression. Clearly, when there is no <em>current statement</em>, we cannot jump to other statements. If you're looking for more information about these basic principles, you can take a look at my book <a href="http://www.functional-programming.net" target="external">Real World Functional Programming</a>, which covers this distinction in details in chapter 2, but we'll look at a brief example that will clarify this idea shortly.</p> <p>Often, there is really no need to use <code>break</code> or other imperative constructs in F#, because you can write the same thing more elegantly using one of the provided higher order function such as <code>Seq.exists</code> or <code>Seq.tryfind</code>. However, there are still some cases where the imperative programming style makes it easier to express our original intention. Also, implementing your own higher order functions (akin to <code>Seq.exists</code>) would sometimes be much easier if we could just use imperative return.</p> <p>So, what can be done about this?</p>Real World Functional Programming: Second review finished!http://tomasp.net/blog/functional-2nd-review.aspxMon, 02 Mar 2009 00:40:50 GMTI've been working on the <a href="http://www.functional-programming.net" target="external">Real World Functional programming in .NET</a> book for quite some time now. In fact, I had the first discussions with Michael Stephens from Manning in March last year and I started thinking about the book at that time...Tomas Petricek<p>I've been working on the <a href="http://www.functional-programming.net" target="external">Real World Functional Programming in .NET</a> book for quite some time now. In fact, I had the first discussions with Michael Stephens from Manning in March last year and I started thinking about the book at that time, so it has been occupying my mind for almost a year now! Until recently, I was feeling that we're not getting much closer to the end of this project, because writing a book is just <em>a lot</em> of work. However, I think I can finally see that we're getting closer to actually finishing the book. At Manning, we've recently finished the second review, which means that I've just got another set of very useful comments - a big thanks to all the reviewers! I'm also getting close to finishing the first draft of the whole manuscript (depending on the reviews, the content may still change a bit, but I expect to write at most one new chapter from now). Hopefully, the drafts will soon make it to the MEAP release of the book.</p> Source code for Real World Functional Programming available!http://tomasp.net/blog/book-source-available.aspxThu, 12 Feb 2009 02:10:59 GMTJust a short update regarding the book I'm working on. First of all, the source code for the first 11 chapters is now available! Secondly, I did some changes to the TOC and you can now find the commented TOC on the book web site.Tomas Petricek<a href="http://cid-8c3f26b4befe2dfa.skydrive.live.com/self.aspx/2009%20-%20Winter%20-%20Cambridge/P1060023.jpg" target="_blank"><img src="http://tomasp.net/articles/book-source-available/cambridge.jpg" class="ldecor" /></a> <p>As you can see, there has been quite a bit of silence on this blog for a while. There are two reasons for that - the first is that I'm still working on the book <a type="external" href="http://www.manning.com/petricek">Real World Functional Programming</a>, so all my writing activities are fully dedicated to the book. The second reason is that I'm having a great time doing an internship in the <a href="http://research.microsoft.com/en-us/groups/ppt">Programming Principles and Tools</a> group at Microsoft Research in Cambridge with the F# team and namely the F# language designer <a href="http://blogs.msdn.com/dsyme/" type="external">Don Syme</a>. The photo on the left side is the entrance gate to the Trinity College of the Cambridge University taken during the few days when there was a snow. I recently started using Live Gallery, so you can find more photos from Cambridge in my <a href="http://cid-8c3f26b4befe2dfa.skydrive.live.com/browse.aspx/2009%20-%20Winter%20-%20Cambridge" type="external">online gallery</a>. Anyway, I just wanted to post a quick update with some information (and downloads!) related to the book... </p> Functional Programming in .NET using C# and F# (Manning Greenpaper)http://tomasp.net/blog/functional-overview.aspxThu, 11 Dec 2008 01:48:07 GMTThis article is partially an excerpt from my <a href="http://www.manning.com/petricek">book</a>. It introduces the benefits of functional pogramming, and explains the essential aspects of the functional style using F# and C# 3.0. Finally, it also shows how functional style influences the application architecture.Tomas Petricek<p> Functional programming languages have been around for a while and were always astonishing for their ability to express the ideas in a succinct, declarative way allowing the developer to focus on the essence of problem rather than on technical details of the solution. Recently, functional paradigm is gaining new prominence as an efficient way to handle development of multi-processor, parallel and asynchronous applications.</p> <p> Functional ideas are arising in C# as well as in other main-stream languages and functional languages are becoming an alternative for real-world projects. Also, Microsoft recently introduced a new language called F#, which has a strong background in traditional functional languages, but as a .NET language also benefits from the rich .NET and Visual Studio ecosystem.</p> <div class="rdecor"> <img src="http://www.tomasp.net/img/cover_main.gif" alt="Book cover" /><br /><small>Available via MEAP | 500 pages<br />Softbound print: March 2009 (est.)</small></div> <p> This article is partially an excerpt from my book <strong><a href="http://www.manning.com/petricek">Real-world Functional Programming in .NET</a></strong> [<a href="#fpgpref">1</a>]. Thanks to my editors at <a href="http://www.manning.com" type="external">Manning</a> I have the permission to publish it on my blog. We’ll look at several aspects of functional programming and how the same concepts, which are essential for the functional paradigm, look in the F# and in C# 3.0 with LINQ. We will shortly look at the basic programming language features like lambda functions and type inference that are now available in both F# and C#. Functional programming isn’t only about language features, but also about using different programming style, so we’ll look at some high level concepts as well. These include using immutable data structures for developing code that can be executed in parallel and writing code in a more declarative style.</p> <p> Thanks to the combination of C# 3.0 and F#, this article shows the ideas in a way that should be familiar to you in C#, but also shows a further step that you can take with a primarilly functional language F#. If you're a .NET developer and you want to understand what functional programming is and how it can help you to become better and more productive then continue reading. If you'll find this article interesting, then don't forget to check out the <a href="http://www.manning.com/petricek">book</a>, which explains everything in larger detail and discusses many other interesting ideas.</p> Reactive Programming (IV.) - Developing a game in Reactive LINQhttp://tomasp.net/blog/reactive-iv-reactivegame.aspxMon, 24 Nov 2008 03:00:00 GMTIn this article, we'll implement a simple iteractve game using the <strong>Reactive LINQ</strong> project. The article shows that this way of handling events gives us amog other things a great degree of composability.Tomas Petricek<p>In this part of the article series about <strong>Reactive LINQ</strong>we're going to implement a slightly more complicated application using the library that I introduced in the previous three articles. We're going to use basic event stream queries from the <a href="reactive-ii-csevents.aspx">second article</a> as well as advanced operators introduced in the <a href="reactive-iii-linqoperators.aspx">third part</a>. This time, I'll also show the F# version of all the examples, so we're going to build on the ideas from the <a href="reactive-i-fsevents.aspx">first part</a>.</p> <p>I originally wanted to write the demo only in Visual Basic, because I think that it is really amazig to show an idea that came from functional programming in a language that no one (maybe until recently) connects with functional programming. Then I realized that I really want to show the F# version too, because F# was an inspiration for the whole <strong>Reactive LINQ</strong> idea and it is interesting alone as well. But finally, I thought that don't showing the C# version may look offensive to many readers (especially since I'm still C# MVP...). So, I ended up writing the game in all three languages, but the code is surprisingly similar in all of them!</p> Reactive Programming (III.) - Useful Reactive LINQ Operatorshttp://tomasp.net/blog/reactive-iii-linqoperators.aspxFri, 21 Nov 2008 19:59:02 GMTIn the previous article, I introduced <strong>Reactive LINQ</strong>. Today, we're going to look at other operators that canbe used for working with events. We'll see aggregation is useful and how to dynamically change (switch) behavior.Tomas Petricek<p>In the <a href="reactive-ii-csevents.aspx">previous article</a>, I introduced <strong>Reactive LINQ</strong>. I explained the different point of view that we can use when working with .NET events. The idea is that .NET events can be viewed as streams of values. The value is information about the event (such as position of a mouse click or a mouse movement). These streams can be processed using LINQ queries - we can for example filter all values that are not interesting for us using <code>where</code> LINQ clause. For example if we want to handle clicks only in some specified area.</p> <p>In the previous article, I talked about basic LINQ query operators such as <code>select</code> and <code>where</code> and some useful methods that <strong>Reactive LINQ</strong> provides (for example for merging event streams). Today, we'll take a look at two more advanced kinds of operations that we can use for working with event streams. In particular, we'll talk about aggregation operators (that you certainly know from LINQ) and about switching. Switching is a concept from functional reactive programming and it allows us to change dynamically how the application behaves. However, I'll explain this in a more detail soon.</p> <p>In this article, I'm going to use mostly C# (and some Visual Basic). The functionality that I'm describing in this part isn't part of the standard F# <code>Event</code> module that I discussed in <a href="reactive-i-fsevents.aspx">the first part</a>. I implemented most of them in F# too, but I'm not going to write the samples in both of the versions in this part. If you've seen the first two articles, you'll be definitely able to use the F# versions as well, because they follow exactly the same ideas as the C#/LINQ versions. I'm going to talk about a larger demo application in the last section and I'll show an F# version as well, so you'll see some F# examples in the next part. This part serves more as a reference of the available operators, so you may read only some parts of it, then jump to the last one (to see an exciting example!) and then come back here.</p> Reactive programming (II.) - Introducing Reactive LINQhttp://tomasp.net/blog/reactive-ii-csevents.aspxWed, 19 Nov 2008 19:57:15 GMTIn the second part of the series about reactive programming, I introduction the <strong>Reactive LINQ</strong> project, which allows writing event processing code in C# using LINQ queries.Tomas Petricek<p>In this article I'm going to introduce my project <strong>Reactive LINQ</strong>. This is largely inspired by the ideas that come from functional reactive programming in the Haskell language and from functionality that's available for working in events in F#. I introduced these ideas in my previous article in this mini-series, so if you're interested in learning more about these interesting technologies, you should definitely read the previous article about <a href="reactive-i-fsevents.aspx">First class events in F#</a>.</p> <p>In this article, we're going to look how to apply the same ideas to the C# language and how to use LINQ queries for processing events. This article is <a href="http://tomasp.net/blog/dynamic-linq-queries.aspx">just</a> <a href="http://tomasp.net/blog/csharp-async.aspx">another</a> my article that shows how to implement some idea from functional programmin in C#. I believe this will once again show that the new features in the C# 3.0 aren't just about querying databases, but are more widely useful even in situations that are not directly related to data-processing. </p> Reactive programming (I.) - First class events in F#http://tomasp.net/blog/reactive-i-fsevents.aspxSun, 16 Nov 2008 17:14:04 GMTThe LINQ project and changes in C# 3.0 are interesting because they allow implementing many ideas from functional languages in C#. In this article I'll explain "first-class events" in F# and later I'll implemet similar concept using LINQ.Tomas Petricek<p>I believe that the LINQ project and changes in C# 3.0 and VB 9 are interesting because they allow rewriting of many ideas from functional programming. An ability to express queries easily is one of these ideas, but it is definitely not the only one. There are many other interesting ideas. The C# 3.0 language isn't primary a functional language, so it isn't easy to discover the idea if you use only C#, but it is possible to implement it if you know the idea already.</p> <p>I already wrote a few interesting C# examples that were inspired by some functional idea. I'm a big fan of the F# language, so it is not a surprise that I started with an F# version of the problem and then looked at the way to do the same thing in C#. In particular, this is how my article about building dynamic queries in C# came to the existence - the F# version used <a href="http://tomasp.net/blog/dynamic-flinq.aspx">FLINQ and Quotations</a> and then I demonstrated how to do the same in <a href="http://tomasp.net/blog/dynamic-linq-queries.aspx">C# using expression trees</a>. Another example is my article about asynchronous programming in C# <a href="http://tomasp.net/blog/csharp-async.aspx">using iterators</a>, which shows how to implement something like F# <a href="http://blogs.msdn.com/dsyme/archive/2007/10/11/introducing-f-asynchronous-workflows.aspx">asynchronous workflows using iterators</a> in C# 2.0.</p> <h3>Functional Reactive Programming</h3> <p>Today, I'm going to look at another very interesting idea from functional programming. It is called <em>Functional Reactive Programming</em> and it comes from the Haskell community. You can find a list of related <a href="http://www.haskell.org/frp/" type="external">Haskell projects here</a>. However, similar things (though they are not purely functional and simplified) are available in the F# language as well. Don Syme introduced them in his blog post called <a href="http://blogs.msdn.com/dsyme/archive/2006/03/24/559582.aspx">F# First Class Events: Simplicity and Compositionality in Imperative Reactive Programming</a>. In this article, I'm going to briefly introduce the implementation available in F# and I'll extend it a little bit to allow some more interesting things. In the second article from this series, I'll show how to implement the same thing in C# 3.0 (and in VB 9 too!)</p> Calculating with infinite sequences on MSDNhttp://tomasp.net/blog/sequences-on-msdn.aspxThu, 13 Nov 2008 02:36:30 GMTAbout a year ago, I wrote an article about infinite sequences on MSDN. I remembered about it this week, because these topics will be discussed in the book I'm working on as well...Tomas Petricek<p>About a year ago, I wrote <a href="http://tomasp.net/blog/lazy-computation-on-msdn.aspx">an article</a> about using lazy computations in C# 3.0. It was published by the C# Community PM <a href="http://blogs.msdn.com/charlie/" type="external">Charlie Calvert</a> at the C# Developer Center. The article was a first of two articles where I wanted to demonstrate that C# 3.0 can be used for implementing useful constructs known from functional languages. I realized that I never posted the link to the second article to my blog, so you can find the annotation and link below.</p> <p>However, I remembered about these two articles because I was just working on chapters 11 and 12 of the <a href="http://tomasp.net/blog/functional-net-update.aspx">Real-world Functional Programming in .NET</a> book that I’m writing. Lazy values, which were the topic of my first article, are discussed in the second part of chapter 11 and IEnumerable and F# sequences are the topic for the first part of chapter 12. Because I already wrote two articles on this topic, I had to think really hard to find better (and still simple enough) examples where these concepts are useful in practice. I also finally have enough space to show how these two concepts relate and talk about some interesting background – for example in Haskell, lazy sequences are in fact just ordinary lists that are lazy thanks to the Haskell nature. </p> <p>A year ago, I definitely wouldn’t believe that today, I’ll be writing about the same topics, but this time as part of a book that has partly the same goal as these two articles – to show that functional programming ideas are really useful in the real-world and can enrich your programming toolbox (no matter whether you’re using C# or F# language). Anyway, here is the link to the second article – as usual when I look at something that I worked on a long time ago, I think I should rewrite it to make it better :-), but it still gives you an idea what is the book that I’m working on about...</p>Functional Programming in .NET book - An updatehttp://tomasp.net/blog/functional-net-update.aspxMon, 20 Oct 2008 22:10:04 GMTRecently, I announced on my blog that I’m working on a book for Manning called Real-world Functional Programming in .NET. It is more than a month since I wrote about it, so here is a brief update...Tomas Petricek<p>Recently, I announced on my blog that I’m working on a book for <a href="http://www.manning.com" type="external">Manning</a> called <em>Real world Functional Programming in .NET</em>. The goal of the book is to explain the most interesting and useful ideas of functional programming to a real world C# developer. I'm writing this book, because I believe that functional programming is becoming increasingly important. Here is a couple of reasons why you should have this book on your bookshelf:</p> <ul> <li><strong>Ideas behind C# 3.0 and LINQ</strong> - these main-stream technologies are inspired by functional programming and the new C# 3.0 features give us definitely much more than just a new way to query databases. The book explains the ideas behind these features and shows how to use them more efficiently.</li> <li><strong>Learning the F# language</strong> - <a href="http://blogs.msdn.com/somasegar/archive/2007/10/17/f-a-functional-programming-language.aspx" type="external">F# is becoming a first-class citizen</a> in the Visual Studio family of languages, which alone would be a good reason for learning it! Even if you're not going to use it for your next large .NET project, you'll find it useful for quick prototyping of ideas and testing how .NET libraries work thanks to the great interactive tools. </li> <li><strong>Real world examples</strong> - the book includes a large set of real-world examples that show how to develop real applications in a functional way - both in F# and C#. Among other things, the examples show how to utilize multi-core CPUs, how to better obtain and process data and how to implement animations and GUI applications in a functional way.</li> </ul> <p>The book is available via the MEAP (Manning Early Access Program) and if you want to get a better idea what is the book about, you can read the <a href="http://www.manning.com/petricek/" type="external">first chapter for free</a>. Anyway, it is more than a month since I <a href="http://tomasp.net/blog/functional-programming-book.aspx">posted the announcement</a>, so I decided to write a brief update....</p>Announcing: Real-world Functional Programming in .NEThttp://tomasp.net/blog/functional-programming-book.aspxTue, 02 Sep 2008 20:03:15 GMTIf you’ve been reading my blog or seen some my articles, you know that I’m a big fan of the F# language and functional programming style. Today, I'm very pleased to announce that I'm writing a book on this topic!Tomas Petricek<p>If you’ve been reading my blog or seen some my articles, you know that I’m a big fan of the F# language and functional programming style. I’m also often trying to present a bit different view of C# and LINQ – for me it is interesting mainly because it brings many functional features to a main-stream language and allows using of many of the functional patterns in a real-world. Elegant way for working with data, which is the most commonly used feature of C# 3.0, is just one example of this functional approach. Talking about real-world applications of functional programming, there is also fantastic news about F#. It was announced last year that F# will become fully supported Visual Studio language and the first CTP version of F# was released this week!</p> <p>I always thought that the topics mentioned in the previous paragraph are really interesting and that functional programming will continue to become more and more important. That’s why I’m really excited by the news that I’d like to announce today – I’m writing a book about functional programming in F# and C#....</p>Dynamic Lookup in F#http://tomasp.net/blog/fsharp-dynamic-lookup.aspxWed, 04 Jun 2008 01:50:08 GMTDynamic languages allow you to represent a member using a symbol or a string and to use this symbol to work with the member. In this article I'll show how to do same thing in statically-typed way in F#.Tomas Petricek<p>Many people view <em>dynamic</em> and <em>statically-typed</em> languages as two distinct groups (and this is often a reason for never-ending discussions). In this article, I'll try to show one interesting example, which demonstrates that these two groups are not in fact that distinct and that you can implement a common <em>dynamic</em> language feature in F#, which is undoubtedly <em>statically-typed</em>. The feature that I'm talking about is dynamic invoke using a symbolic representation of the member (this is something that can be done using <em>symbols</em> in Ruby, but I'll shortly explain what exactly I mean).</p> <p>I intentionally wrote <em>statically-typed</em> and <em>dynamic</em> instead of <em>dynamically-typed</em>. In my understanding <em>dynamic</em> is a broader term while <em>dynamically-typed</em> and <em>statically-typed</em> are of course two distinct groups. On the other side <em>dynamic</em> refers to language features that are usually available in <em>dynamically-typed</em> languages, just because it is easy to support them in a nice way. This doesn't mean that having a <em>dynamic</em> feature in a <em>statically-typed</em> language would be impossible - it is just more difficult to implement it in a way that would be similarly elegant. </p> Thesis: Client-side Scripting using Meta-programminghttp://tomasp.net/blog/webtools-thesis.aspxMon, 17 Mar 2008 10:07:04 GMTContains a link to my Bachelor Thesis about F# WebTools, which I partially worked on during my visit in Microsoft Research and which I successfully defended last year.Tomas Petricek<p>I realized that I haven’t yet posted a link to my Bachelor Thesis, which I partially worked on during my visit in Microsoft Research and which I successfully defended last year. The thesis is about a client/server web framework for F# called F# WebTools, which I already <a href="http://tomasp.net/blog/fswebtools-intro.aspx" type="external">mentioned here</a> and its abstract is following:</p> <p style="padding-left:40px;padding-right:40px;font-style:italic;">“Ajax” programming is becoming a de-facto standard for certain types of web applications, but unfortunately developing this kind of application is a difficult task. Developers have to deal with problems like a language impedance mismatch, limited execution runtime in web browser on the client-side and no integration between client and server-side parts that are developed as a two independent applications, but typically form a single and homogenous application. In this work we present the first project that deals with all three mentioned problems but which still integrates with existing web technologies such as ASP.NET on the server and JavaScript on the client. We use the F# language for writing both client and server-side part of the web application, which makes it possible to develop client-side code in a type-safe programming language using a subset of the F# library, and we provide a way to write both server-side and client-side code as a part of single homogeneous type defining the web page logic. The code is executed heterogeneously, part as JavaScript on the client, and part as native code on the server. Finally we use monadic syntax for the separation of client and server-side code, tracking this separation through the F# type system.</p> <p style="text-indent:0px">The full text is available here: <a href="/articles/webtools-thesis/fswebtools.pdf">Client side scripting using meta-programming</a> (PDF, 1.31MB) </p>New Version of Phalanger with Silverlight and VS 2008 Supporthttp://tomasp.net/blog/phalanger-vs2008.aspxTue, 11 Mar 2008 01:14:21 GMTThis article introduces new version of the Phalanger project, which incudes support for Silverlight 1.1 (alpha) and Visual Studio 2008 Integration package.Tomas Petricek<p>At the <a href="http://langnetsymposium.com/talks.asp" type="external">Lang.NET Symposium</a> I presented several new features in Phalanger. I already posted the presentation and samples on the blog (<a href="http://tomasp.net/blog/phalanger-at-langnet.aspx" type="external">here</a>) and the talk is also available as a video on the Lang.NET web site (<a href="http://langnetsymposium.com/talks.asp" type="external">here</a> - actually, due to the huge demand the site is down now, but I hope it gets back soon!) Anyway, the most interesting thing is that I've used Phalanger Integration for <strong>Visual Studio 2008</strong> during the talk, which wasn't available in any Phalanger release until now.</p> <p>I have to mention one more thing before talking more about the new release - Phalanger Integration for VS 2008 works with Visual Studio Shell, which means that you can get <strong>Visual Studio 2008 with Phalanger Support for free!</strong> Yes, that's right. Microsoft offers so called Visual Studio 2008 Shell, which is an "empty" IDE with no integrated languages and you can install Phalanger Integration into this version, which means that you can get very good Phalanger IDE (for Windows) for no cost at all!</p> <p>If you can't wait to install this new version, you can skip the overview article and <a href="/blog/phalanger-vs2008.aspx#phpm08down">go directly to the installation links</a>.</p> F# Support for ASP.NET and Notes on Sampleshttp://tomasp.net/blog/aspnet-in-fsharp.aspxSat, 08 Mar 2008 23:07:29 GMTIn this article I look at the F# suppot for ASP.NET and at some interesting aspects of the samples that are available in the F# distribution.Tomas Petricek<p>As I mentioned earlier, I spent three months as an intern in Microsoft Research in Cambridge last year and I was working with Don Syme and James Margetson from the F# team. Most of the time I was working on the F# Web Toolkit, which I introduced on the blog some time ago [<a href="#myfsstuff">1</a>], but I also worked on a few additions that are now part of the F# release. Probably the most useful addition is a new implementation of the CodeDOM provider for the F# language which makes it possible to use ASP.NET smoothly from F# (but it can be used in some other scenarios as well) together with two ASP.NET sample applications that you can explore and use as a basis for your web sites. This was actually a part of the distribution for a few months now (I of course wanted to write this article much earlier...), so you may have already noticed, but anyway, I'd still like to write down a short description of these ASP.NET samples and also a few tips for those who're interested in writing web applications in F#. </p> Phalanger at Lang.NET Symposium http://tomasp.net/blog/phalanger-at-langnet.aspxSat, 02 Feb 2008 11:51:38 GMTLast week I attended the Lang.NET Symposium and I also did a short presentation about Phalanger. The slides and demos from the talk are attached.Tomas Petricek<p>Last week I attended the <a href="http://www.langnetsymposium.com/" type="external">Lang.NET Symposium</a> and I also did a short presentation about Phalanger (below you can find the demos and slides from my talk). By the way – during the trip from Prague to Seattle I missed a connecting flight from Paris, so I had one day to visit Paris and since I was traveling on Saturday I actually quite enjoyed it :-), so that’s where the picture comes from.</p> <p>Overall it was really a fantastic event with many great talks from many interesting people. I hope that there will be recordings as a last year, so I won’t comment every topic that I found interesting (that would be really a long post). But just quickly – people from Microsoft often talked about DLR (dynamic language runtime) related topics, which was interesting as we’re planning to look at DLR in Phalanger. Luckily, <a href="http://netevil.org/" type="external">Wez Furlong</a> from the PHP community was there too, so we discussed how we could work on “PHP on DLR” project together (see also our <a href="http://news.php.net/php.on.dlr" type="external">mailing list</a>).</p> <a target="_blank" href="/articles/phalanger-at-langnet/photo.jpg"><img style="float:right;margin:10px;border:0px" alt="Trip to Seattle" src="/articles/phalanger-at-langnet/photo_sm.jpg" /></a> <p>There were also two talks about F# (from <a type="external" href="http://blogs.msdn.com/lukeh">Luke Hoban</a> and <a href="http://www.devhawk.net/" type="external">Harry Pierson</a>), and it was a lot of fun to hang out with them. Finally, Erik Meijer presented the <a href="http://labs.live.com/volta" type="external">Volta</a> project, which I was particularly interested in as it shares many goals and ideas with my F# Web Tools.</p> <p>Non-Microsoft talks covered wider range of topics including Mono and Moonlight project (by <a href="http://tirania.org/blog" type="external">Miguel de Icaza</a>) and I actually had a chance to talk with Miguel about Phalanger and we even tried running the Helicopter sample on Moonlight – there were some issues, but it seems quite promising, so I hope to have the sample running on Moonlight on Linux quite soon! Miguel mentioned that the installation of Moonlight is currently a bit painful (due to some issues with media codecs), but it should be fixed in next few weeks, so I hope to be able to try it on my machine too!</p>Writing Silverlight applications in PHPhttp://tomasp.net/blog/php-in-silverlight.aspxFri, 07 Dec 2007 17:16:14 GMTIn this article we will look how Phalanger can be used for developing Silverlight applications in the PHP language. We look at basic concepts like XAML as well as at a more complicated game.Tomas Petricek<p>In my <a href="http://tomasp.net/blog/phalanger-future-notes.aspx">last post</a> about Phalanger I mentioned that our important goal is to support the Silverlight (2.0) platform. Shortly Silverlight is a cross-browser platform that can be used for developing client-side components that run in the web browser and contain rich media, graphics and can interactively communicate with the user. The language that can be used for writing Silverlight code can be in general any .NET language, so our goal is to allow using PHP by making Phalanger compatible with Silverlight.</p> <img src="/articles/php-in-silverlight/car_intro_sm.png" alt="Simple Silverlight App in PHP" style="margin:10px; float:left;" /> <p>First steps were already made and it is becoming possible to write some very interesting things in Silverlight using PHP, there is of course still a lot of work to do and we're discussing the future development with PHP development team (you can join the mailing list <a href="http://news.php.net/php.on.dlr" type="external">PHP on DLR</a> for more info). In this article we will first show a very basic Silverlight example that uses PHP and later I will shortly comment more complicated example - a game (quite addicting, so be careful :-)!) where you have to fly with helicopter and avoid the walls. The source code for helicopter game is also attached, so feel free to modify it or create similar games!</p> <p>If you can't wait to try the demos before looking at the sources, here are the links:</p> <ul> <li><a href="http://tomasp.net/articles/php-in-silverlight/simplegui.html" type="external">Simple car demo</a> - Click on the car and it will move!</li> <li><a href="http://tomasp.net/articles/php-in-silverlight/game.html" type="external">Helicopter game demo</a> - Click left button to fly up!</li> </ul>A few notes about Phalanger futurehttp://tomasp.net/blog/phalanger-future-notes.aspxSun, 02 Dec 2007 23:50:53 GMTThis post discusses Phalanger future and relations to the DLR and Silverlight as well as our intention to closely communicate wth the PHP community.Tomas Petricek<p>First, I'd like to aplogoize for the lack of new about the Phalanger project recently. I spent some time working as an intern with the F# team in MSR Cambridge and I also had final bachelor exam this autumn. Anyway, this doesn't mean that there isn't anything new and interesting regarding the Phalanger project comming soon - actually (as I believe) the opposite is true! The topics that I'm going to further discuss in this article is our upcomming support for Silverlight platform, the relation between Phalanger and DLR and also our desire to make Phalanger more open to the community, so stay tuned!</p> Infinite Cheese Fractal using WPF 3D and F#http://tomasp.net/blog/infinite-cheese.aspxSat, 24 Nov 2007 23:22:04 GMTThis article describes a 3D version of famous Sierpinski carpet fractal implemented in the F# language using WPF 3D libraries from .NET 3.0.Tomas Petricek<p>I always liked fractals, because they look like objects from another world, but on the other side if you look at some things in our world you can see many similarities with fractals (but not quite as ideal with the infinite level of precision). One of my favorite fractals is 3D version of Sierpinski carpet [<a href="#wpffractref">1</a>], which itself is based on very famous Cantor set. Quite long time ago I thought that it would be nice to implement animation of flying through this fractal, but I was never good in 3D graphics and it looked like a lot of work, so I never get to doing it. Luckily, now with F#, which makes it very easy to write the code to generate the fractal and with WPF 3D, which can be easily used to animate the fractal, I finally had everything I needed to do it, so here it is! </p> <div style="text-align:center;"> <object width="425" height="344"><param name="movie" value="http://www.youtube.com/v/8wV7UgLeKdM&hl=en&fs=1"></param><param name="allowFullScreen" value="true"></param><param name="allowscriptaccess" value="always"></param><embed src="http://www.youtube.com/v/8wV7UgLeKdM&hl=en&fs=1" type="application/x-shockwave-flash" allowscriptaccess="always" allowfullscreen="true" width="425" height="344"></embed></object> </div> Asynchronous Programming in C# using Iteratorshttp://tomasp.net/blog/csharp-async.aspxThu, 15 Nov 2007 03:08:35 GMTIn this article we will look how to write programs that perform asynchronous operations like manipulation with network in C# using iterators without the typical inversion of control caused by the use of delegates.Tomas Petricek<p>In this article we will look how to write programs that perform asynchronous operations without the typical inversion of control. To briefly introduce what I mean by 'asynchronous' and 'inversion of control' - asynchronous refers to programs that perform some long running operations that don't necessary block a calling thread, for example accessing the network, calling web services or performing any other I/O operation in general. The inversion of control refers to the code structure that you have to use when writing a code that explicitly passes a C# delegate as a callback to the asynchronous method (typically called <code>Begin<em>Something</em></code> in .NET). The asynchronous method calls the delegate when the operation completes, which reverses the way you write the code - instead of encoding the control flow using typical language constructs (e.g. <code>while</code> loop) you have to use global variables and write your own control mechanism.</p> <p>The funny thing about this article is that it could have been written at least 3 years ago when a beta version of Visual Studio 2005 and C# 2.0 became first available, but it is using iterators in a slightly bizarre way, so it is not easy to realize that this is possible. Actually, I will use some C# 3.0 methods in the article as well, but only extension methods and mainly just to keep the code nicer. As with my earlier article about building LINQ queries at runtime, I realized that it can be done in C# when I was playing with the F# solution (called F# Asynchronous Workflows), where this approach is very natural, so I will shortly mention the F# implementation as well.</p> F# Overview (IV.) - Language Oriented Programminghttp://tomasp.net/blog/fsharp-iv-lang.aspxSat, 03 Nov 2007 00:00:04 GMTIn the fourth article of the F# overview series, I will shortly describe how I understad the language oriented paradigm and how the F# language can be used for developing libraries using this paradigm.Tomas Petricek<p>In the fourth article of the F# overview series, I will shortly describe how I understad the language oriented paradigm and how the F# language can be used for developing libraries using this paradigm. We will look how discriminated unions relate to this paradigm and at three specific features that support this paradigm, namely <em>active patterns</em>, <em>computation expressions</em> and <em>quotations</em>.</p> <p>Defining precisely what the term <em>language oriented programming</em> means in context of the F# language would be difficult, so I will instead explain a few examples that will demonstrate how I understand it. In general, the goal of language oriented programming is to develop a <em>language</em> that would be suitable for some (more specific) class of tasks and use this language for solving these tasks. Of course, developing a real programming language is extremely complex problem, so there are several ways for making it easier. As the most elementary example, you can look at XML files (with certain schema) as language that are processed by your program and solve some specific problem (for example configuring the application). As a side note, I should mention that I'm not particularly happy with the term ‘language’ in this context, because the term can be used for describing a wide range of techniques from very trivial constructs to a complex object-oriented class libraries, but I have not seen any better term for the class of techniques that I’m going to talk about.</p>F# Overview (III.) - Imperative and Object-Oriented Programminghttp://tomasp.net/blog/fsharp-iii-oop.aspxSat, 03 Nov 2007 00:00:03 GMTIn the third part of the F# overview, we will look at the F# features that are essential for a smooth interoperability with other .NET languages and form a second part of the F# core language - that is object oriented and imperative programming.Tomas Petricek<p>In the third part of the F# Overview article series, we will look at language features that are mostly well known, because they are present in most of the currently used programming languages. Indeed, I'm talking about imperative programming, which is a common way for storing and manipulating application data and about object oriented programming which is used for structuring complex programs.</p> <p>In general, F# tries to make using them together with the functional constructs described in the <a href="fsharp-ii-functional.aspx">previous part</a> [<a href="fsharp-ii-functional.aspx" target="_blank">^</a>] as natural as possible, which yields several very powerful language constructs.</p>F# Overview (II.) - Functional Programminghttp://tomasp.net/blog/fsharp-ii-functional.aspxSat, 03 Nov 2007 00:00:02 GMTIn the second part of the F# overview we will look at functional programming, which is probably the most important paradigm used with the F# language, because F# is built on the same grounds as many functional languages.Tomas Petricek<p>In the second part of the F# overview we will look at functional programming, which is probably the most important paradigm used with the F# language, because F# is built on the same grounds as many functional languages. We will first examine the standard F# data types, which are useful to allow the functional programming style and we will also look at a few functional tricks.</p> <p>As already mentioned in the <a href="fsharp-i-introduction.aspx">Introduction</a> for this article series, F# is a typed functional language, by which I mean that types of all values are determined during the compile-time. However, thanks to the use of a type inference, the types are explicitly specified in the code very rarely as we will see in the following examples. Basic data types (aside from a standard set of primitive numeric and textual types that are present in any .NET language) available in F# are tuple, discriminated union, record, array, list, function and object. In the following quick overview, we will use the F# interactive, which is a tool that compiles and executes the entered text on the fly.</p> F# Overview (I.) - Introductionhttp://tomasp.net/blog/fsharp-i-introduction.aspxSat, 03 Nov 2007 00:00:01 GMTFirst article of the F# Overview series introduces the F# language and gives a quick overview of the programming paradigms that will be discussed in the upcoming articles.Tomas Petricek<p>In my bachelor thesis I included a short introduction that covered all of the important aspects of the F# programming language and I thought that it may be useful to extend it a little bit to cover also a topics that were not important for my thesis and post it as an article, so there is one and relatively short article that introduces all the interesting F# features. The article got however a bit longer than I expected, so I decided to split it into a three parts that would introduce three different <em>paradigms</em> that are supported by F#. Of course, this series won't teach you everything about F#, but it tries to cover the main F# design goals and (hopefully) presents all the features that make F# interesting and worth learning. In this first part I will shortly introduce F# and the supported paradigms that will be discussed in the upcoming articles.</p> Lazy Computation in C# on MSDNhttp://tomasp.net/blog/lazy-computation-on-msdn.aspxSat, 06 Oct 2007 01:29:59 GMTI think that one of the interesting things about C# 3.0 is that it gives you the ability to use many techniques known from functional languages...Tomas Petricek<p>I think that one of the interesting things about C# 3.0 is that it gives you the ability to use many techniques known from functional languages (like Haskell or F#). Most of the articles about C# 3.0 and LINQ focus on the queries and LINQ to SQL, but I believe that using these functional techniques deserve some attention as well. This is why I'm very happy that my article about one of these techniques - representing lazy computations - is now available at the C# Developer Center. I would like to thank to <a href="http://blogs.msdn.com/charlie/default.aspx">Charlie Calvert</a> [<a href="http://blogs.msdn.com/charlie/default.aspx" target="_blank">^</a>], who is the Community Program Manager for C# and who edited and published my article there. Here is the annotation:</p> <p style="padding-left:40px;padding-right:40px;font-style:italic;">Most of the programming languages used in practice (including for example C#, VB.NET, C++, Python or Java) employ so called eager evaluation, which means that the program evaluates all expression and statements in the order in which they are written, so all the preceding statements and expressions are evaluated before executing the next piece of code. This, for example, means that all arguments to a method call are evaluated before calling the method. Sometimes it may be useful to delay an execution of some code until the result is actually needed, either because the result may not be needed at all (but we can’t tell that before executing some computation) or because we don’t want to block the program for a long time by executing all computations in advance and instead we want to execute the computations later, when we will actually need the result. </p> <p style="padding-left:40px;margin-bottom:20px;padding-right:40px;font-style:italic;">In this article we will look how these lazy computations can be written in C# (using some of the new language features from version 3.0). We will first implement a Lazy class to represent this kind of computation, then look at a few simple examples to demonstrate how the class can be used, and finally we will examine one slightly more complicated, but practically useful application. </p> <p style="text-indent:0px">You can read the complete article here: <a href="http://msdn2.microsoft.com/en-us/vcsharp/bb870976.aspx">Lazy Computation in C# </a> [<a href="http://msdn2.microsoft.com/en-us/vcsharp/bb870976.aspx" target="_blank">^</a>]</p>F# Quotations Samples on CodePlexhttp://tomasp.net/blog/fsharp-quotation-samples.aspxThu, 20 Sep 2007 04:33:49 GMTThis article describes a few samples available in the F# Samples project at CodePlex that demonstrate how to work with the F# quotations using active patterns.Tomas Petricek<p>Some time ago, Granville Barnett (see his <a href="http://gbarnett.org/">homepage and old blog</a> [<a href="http://gbarnett.org/" target="_blank">^</a>] or a <a href="http://weblogs.asp.net/gbarnett/">new blog</a> [<a href="http://weblogs.asp.net/gbarnett/" target="_blank">^</a>]) had a great idea and started a CodePlex project called <a href="http://www.codeplex.com/fsharpsamples">F# Samples</a> [<a href="http://www.codeplex.com/fsharpsamples" target="_blank">^</a>] to host various samples written in F# to demonstrate the most important concepts of both functional programming and F#. I quite like this idea, so I asked Granville if I could join and add some samples that I wrote and today I finally found a time to update what I wanted to upload to the latest version of F# and put it online.</p> Building LINQ Queries at Runtime in F#http://tomasp.net/blog/dynamic-flinq.aspxSat, 18 Aug 2007 02:38:11 GMTIn this article I will introduce FLinq, the F# support for language integrated query and show how we can construct a database queries dynamically in a type-safe way in F#.Tomas Petricek<p>In an article about building LINQ queries at runtime in C# 3.0, I described how you can build a LINQ query dynamically, for example by combining a set of conditions using the 'or' operator in the where clause. I mentioned that the way I implemented it is largely influenced by the F# language, which provides very natural way for manipulations with code like this. In this article I will first shortly introduce FLINQ sample, which is an F# library implementing LINQ support and than I will implement the same examples I presented in the earlier article in F#.</p> Building LINQ Queries at Runtime in C#http://tomasp.net/blog/dynamic-linq-queries.aspxMon, 30 Jul 2007 02:10:17 GMTCommon criticism of LINQ is that it doesn't support a scenario where queries are build dynamically at the runtime. In this article I show that this can be acutally done very well for most of the common scenarios.Tomas Petricek<p>Since the first beta versions of LINQ we could hear comments that it is perfect for queries known at compile-time, however it is not possible to use it for building queries dynamically at runtime. In this article I show that this can be actually done very well for most of the common cases. The solution offered by Microsoft (mentioned in [<a href="#dynqlinks">1</a>]) is to build query from a string, however this has many limitations and it in fact goes completely against what LINQ tries to achieve, which is writing queries in a type-safe way with full compile-time checking. In this article I will first show a few support functions to make the life a bit easier and then we will use them for building two sample applications that allows user to build a query dynamically. The solution is largely motivated by my previous use of F#, where working with “expressions” is possible at more advanced level, however I’ll write about F# later and now let’s get back to C# 3.0...</p>F# Web Tools: "Ajax" applications made simplehttp://tomasp.net/blog/fswebtools-intro.aspxFri, 13 Jul 2007 04:32:29 GMTThis article introduces the F# Web Toolkit, which is an "Ajax" web framework that solves three major problems that many people have to face when developing modern web applications.Tomas Petricek<p>Traditional "Ajax" application consists of the server-side code and the client-side part written in JavaScript (the more dynamicity you want, the larger JS files you have to write), which exchanges some data with the server-side code using XmlHttpRequest, typically in JSON format. I think this approach has 3 main problems, which we tried to solve in F# Web Toolkit. There are a few projects that try to solve some of them already - the most interesting projects are Volta from Microsoft [<a href="#fswtintrolinks">1</a>], Links language [<a href="#fswtintrolinks">3</a>] from the University of Edinburgh and Google Web Toolkit [<a href="#fswtintrolinks">2</a>], but none of the projects solve all three problems at once. </p> <ol> <li>Limited client-side environment</li> <li>Discontinuity between server and client side</li> <li>Components in web frameworks are only server-side</li> </ol> <p>The aim of the F# Web Toolkit is to solve all these three problems...</p>Using PHP objects from C# in a type-safe wayhttp://tomasp.net/blog/ducktyping-in-phalaner.aspxMon, 30 Apr 2007 01:26:24 GMTIn this article we present new features in the Phalanger beta 4 which make it possible to use objects from any PHP script in C# using type-safe way.Tomas Petricek<p>When you want to call PHP scripts from mainstream .NET languages, like C# you can follow two different ways. First you can use the pure mode as I demonstrated in one of the earlier articles on PHP application called Texy!. This approach can be used only for some specific applications, because pure mode has several restrictions - the two most important restrictions are that no global code or inclusions are allowed (you have to specify all source files during the compilation), but thanks to this restrictions Phalanger is able to produce classes that are compatible with .NET and can be called from C#. Second option is to create object dynamically by its name and perform all method invocations by name too. This approach can be used with any PHP scripts, but it isn't very convenient. In this article we present new features in the Phalanger beta 4 which extend the second approach and make it possible to use objects from any PHP script in C# using type-safe way.</p> Phalanger 2.0 Beta 4 available!http://tomasp.net/blog/phalanger-beta4.aspxSun, 22 Apr 2007 16:24:09 GMTThis week we finished new release of the Phalanger project, what PHP applications are supported and what new features are available in this release?Tomas Petricek<p>This week we finished new release of Phalanger (the PHP compiler for .NET platform). The goal in this release was to fix many minor bugs preventing us from running some of the famous and most often deployed open-source PHP applications, so with the new release you'll be able to run for example <strong>MediaWiki</strong>, the wiki application that evolved from system used on Wikipedia or probably the best-known PHP blogging and publishing system <strong>WordPress</strong>. Other applications that we tested can be found at Phalanger website in <a href="http://php-compiler.net/doku.php?id=apps">the list of tested PHP applications</a> [<a href="http://php-compiler.net/doku.php?id=apps" target="_blank">^</a>]. Compatibility is very important for us, so if you have troubles running any open-source PHP application, let us know and we'll include it in our list!</p> <p>Another thing that we focused on is interoperability between PHP scripts compiled using Phalanger and other .NET languages. Using .NET objects from Phalanger is very intuitive and has almost no limitations, however the other way is a bit difficult because of the dynamic nature of PHP language. If your PHP application can be compiled in the Phalanger <strong>pure</strong> mode, than the PHP objects can be exported and made available to C# and other languages. The methods of objects exported using this method take <code>object</code> (the base class for every .NET object) as a parameter, because PHP checks types at runtime, so this may be a bit confusing for the users. In the Beta 4 we tried to target these two issues - first, the fact that you have to use pure mode and second, the fact that exported objects can't contain any information about accepted types. This is a topic for entire article, so I'll write about it soon... Stay tuned :-)!</p> <p>Here are the links for Phalanger 2.0 Beta 4 release:</p> <ul> <li><a href="http://www.codeplex.com/Phalanger/Release/ProjectReleases.aspx?ReleaseId=3375"> Phalanger 2.0 Beta 4 release page</a> [<a href="http://www.codeplex.com/Phalanger/Release/ProjectReleases.aspx?ReleaseId=3375" target="_blank">^</a>] - CodePlex</li> <li><a href="http://www.codeplex.com/PhalangerMySQL/Release/ProjectReleases.aspx?ReleaseId=3502"> Phalanger MySQL extension Beta 4</a> [<a href="http://www.codeplex.com/PhalangerMySQL/Release/ProjectReleases.aspx?ReleaseId=3502" target="_blank">^</a>] - CodePlex</li> </ul> Keep your multi-core CPU busy with F#http://tomasp.net/blog/fsparallelops.aspxSat, 24 Mar 2007 23:13:48 GMTCode which makes it possible to write applications that take advantage of multi-core CPUs by parallelizing F# filter and map functions.Tomas Petricek<p>The growth of computer CPU speed is slowly being replaced by the growth of number of CPUs (or cores) in the computer at least for the close future. This causes a revolution in the way software is written, because traditional and most widely used way of writing concurrent applications using threads is difficult and brings several serious issues. Some predictions say that within a few years, almost every computer will have about 16 cores, so there is a huge need for programming paradigms or idioms that help developers write concurrent software easily (see also <a href="http://www.gotw.ca/publications/concurrency-ddj.htm">The Free Lunch Is Over</a> [<a href="http://www.gotw.ca/publications/concurrency-ddj.htm" target="_blank">^</a>] written by Herb Sutter).</p> <p>Functional programming languages (especially pure functional languages) are interesting from this point of view, because the program doesn't have side-effects which makes it very easy to parallelize it (programs in pure functional languages can't have any side-effects by design, in other functional languages like F# the side-effects can be eliminated by following functional programming style). </p> <p>This article describes the code that makes it possible to parallelize some common F# constructs like the <code>List.map</code> and <code>List.filter</code>...</p>CLinq - LINQ support for the C++/CLI languagehttp://tomasp.net/blog/clinq-project.aspxFri, 02 Mar 2007 17:11:05 GMTCLinq project is a library that makes it possible to use LINQ technologies from the C++/CLI language.Tomas Petricek<p>I started working on this project, because I attended C++ class at our university and I had to do some application in C++. Because I hate doing useless projects I wanted to work on something interesting and so I started thinking whether it would be possible to enable LINQ support in C++/CLI...</p> <p>C++/CLI is a very flexible language and the following example proves that enabling LINQ support in C++/CLI isn't impossible. The following database query returns name of contact and company for all customers living in London:</p> <pre lang="c++"> // create connection to database NorthwindData db(".. connection string .."); // declare database query Expr<Customers^> cvar = Var<Customers^>("c"); CQuery<String^>^ q = db.QCustomers ->Where(clq::fun(cvar, cvar.City == "London")) ->Select(clq::fun(cvar, cvar.ContactName + Expr<String^>(", ") + cvar.CompanyName)); // execute query and output results for each(String^ s in q->Query) Console::WriteLine(s); </pre> <p>If you are interested in more information about CLinq project you can...</p> <ul> <li><a href="/articles/clinq-project.aspx">.. continue and read the entire article</a></li> <li><a href="http://www.codeplex.com/linqextensions">Visit the CodePlex project homepage</a> [<a href="http://www.codeplex.com/linqextensions" target="_blank">^</a>]</li> </ul>Overload resolution in Phalangerhttp://tomasp.net/blog/phalanger-overload-resolution.aspxThu, 15 Feb 2007 21:46:45 GMTPHP doesn't support method overloading, so Phalanger has to solve an interesting problem when calling overloaded .NET method from PHP.Tomas Petricek<p>PHP language itself doesn't method support overloading (having two methods with same name, but different number or types of parameters). This brings an interesting problem to Phalanger, because most of .NET languages support this and if we want to be able to call any .NET object from PHP we need to add support (at least) for calling of overloaded methods. The latest Phalanger release contains overload resolution described in the <em>Integrating PHP with CLR</em> document [<a href="#phpoverloadlnk">1</a>].</p> <p>For example, when calling the <code>Console::WriteLine</code> method (which has a lot of overloads), Phalanger dynamically generates a piece of code that we call dynamic stub, which is responsible for choosing the most appropriate overload depending on the actual parameter types. This stub is generated only once for every method, which makes this implementation very efficient. The difficult part of overload resolution is, how can the stub determine what is the best overload? PHP language has a lot of implicit conversions, so when you pass the string <code>"10.2 Little Piggies"</code> to a method it can be implicitly converted to float (<code>10.2</code>) (For more details see [<a href="#phpoverloadlnk">2</a>]). Another example of implicit conversion is that any boolean value can be converted to string (empty string or string <code>"0"</code> are converted to <code>false</code>, every other string is converted to <code>true</code>).</p> <p>In this article I'll describe how does the dynamic stub look like in current version of Phalanger, what problems can it cause and how are we going to fix it in the future version!</p>Quotations Visualizer for F# 1.1.13.8http://tomasp.net/blog/quotvis-1.1.13.8.aspxWed, 14 Feb 2007 23:35:03 GMTLittle update to my F# quotations visualizer tool to make it compatible with the latest version of F# (1.1.13.8).Tomas Petricek<p>Quotation Visualizer is my tool that shows visual representation of F# quotations. Stephen noticed (Thanks!) that Quotation Visualizer doesn't compile with the latest version of F# (1.1.13.8), so here is the updated version:</p> <ul> <li><a href="http://tomasp.net/articles/quotvis-update/quotvis_bin.zip">Download executable</a> (51kB)</li> <li><a href="http://tomasp.net/articles/quotvis-update/quotvis_src.zip">Download sources</a> (77kB)</li> </ul> <p class="noindent">If you want to know more about this tool, here are links to previous articles about it:</p> <ul> <li><a href="http://tomasp.net/blog/quotvis.aspx">F# quotations visualizer</a></li> <li><a href="http://tomasp.net/blog/quotvis-reloaded.aspx">F# quotations visualizer - reloaded!</a></li> </ul> <h2>What was wrong?</h2> <p>This tool is written using F# light syntax, which means that you don't have to write all the semicolons and F# compiler uses whitespace to determine end of the blocks (and some other constructs). This compiler option is relatively new so it is still evolving. First issue that I had is with class declaration - the following code is not valid with the latest F# version:</p> <pre lang="fsharp"> type MyForm = class inherit Form as base // ... end </pre> <p>I used it because it looks more familiar to C# developers :-). Instead of it you have to write the following:</p> <pre lang="fsharp"> type MyForm = class inherit Form as base // ... end </pre> <p>The second issue was with the pipeline operator which is useful when working with lists (or other sequences). The correct syntax for using pipeline operator (for expressions that are longer than one line) is following:</p> <pre lang="fsharp"> let filteredList = oldArray |> Array.to_list |> List.map ( fun m -> /* ... */ ) |> List.filter ( fun m -> /* ... */ ) </pre> Compiling Texy! with Phalangerhttp://tomasp.net/blog/aspnettexy.aspxMon, 12 Feb 2007 00:45:45 GMTThis article describes how to compile Texy! with Phalanger and how to use the produced assembly in ASP.NET application written in C#.Tomas Petricek<p>Texy! [<a href="#texyphallinks">1</a>] is a convertor from text format (similar to formats used in some wiki applications) to valid XHTML code written in PHP. The syntax is described at Texy! web page [<a href="#texyphallinks">2</a>]. Unfortunately, it is only in Czech language, but the syntax is very straightforward, so you can understand it without learning Czech :-).</p><p> In this article, we'll examine how to compile Texy! using Phalanger in pure mode. In this mode it is possible to use objects from PHP like any other .NET objects, so we can later used the compiled assembly for example in the following C# code:</p> <pre> <span class="c">// Create instance of Texy! parser</span> Texy t = <span class="k">new</span> Texy(); <span class="c">// Call the 'process' method and cast result to string</span> <span class="k">string</span> parsed = (<span class="k">string</span>)t.process(txtTexy.Text); <span class="c">// Display parsed text using literal</span> ltrOutput.Text = parsed; </pre>Can't return anonymous type from method? Really?http://tomasp.net/blog/cannot-return-anonymous-type-from-method.aspxTue, 23 Jan 2007 23:54:31 GMTThis article describes anonymous types - one of the new C# 3.0 features and shows interesting trick that can be used when returning anonymous type from method.Tomas Petricek<p>One of the new features introduced in C# 3.0 which will be available in Visual Studio "Orcas" (currently in CTP version) is anonymous type. Anonymous type is something very similar to tuple type from Cω [<a href="#returnanonymous">1</a>] (which is based on tuple types known from many functional programming languages including F#). Anonymous types are extremely useful in LINQ queries, because it allows you to construct type with several properties without declaring the type (with all the properties). Example of query with anonymous type looks like this:</p> <pre lang="csharp"> var q = from c in db.Customers where c.Country = "Czech Republic" select new { FullName=c.Name+" "+c.Surname, Address=c.Address }; </pre> <p>Ok, it's probabbly not the best example, but it demonstrates the point - you want to return some information from query and you don't need to declare type that contains <code>FullName</code> and <code>Address</code> properties before, because you need it only for this single query (and you want to return only these two fields, so you don't transfer additional data that you don't need from database).</p><p>Now let's get to the second point... </p> Phalanger has a new website!http://tomasp.net/blog/new-phalanger-website.aspxSun, 14 Jan 2007 00:49:42 GMTArticle about Phalanger project with links to some interesting articles about Phalanger and describtion of the new web site.Tomas Petricek<p>As you may know, I became new project lead for the <a href="http://php-compiler.net/">Phalanger project</a> [<a href="http://php-compiler.net/" target="_blank">^</a>]. Phalanger was started as a project at Charles University (where I'm studying) by Tomas Matousek, Ladislav Prosek and 4 other guys, the first version was very successful and they started wokring on the second version which introduces PHP in the family of first-class .NET languages (which makes it fully interoperable with the rest of .NET world). After releasing the second version, Tomas and Ladislav moved to Microsoft and convinced me to continue in the Phalanger development. Most of the work on the 2.0 version was already done, so we're currently working on implementing the rest of the PHP/CLR language extensions, making Phalanger more compatible with existing PHP apps and so on. For more information about the history of Phalanger visit the <a href="http://www.php-compiler.net/doku.php?id=core%3ahistory">project history page</a> [<a href="http://www.php-compiler.net/doku.php?id=core%3ahistory" target="_blank">^</a>].</p> <p>I think that Phalanger is in the phase when it can be very interesting for both PHP and .NET communities, but it never got greater publicity and there are not very much examples and articles to demonstrate the interesting Phalanger features. To improve this we started working on the new Phalanger website where users could share their experiences, tips etc. We used PHP wiki called <a href="http://wiki.splitbrain.org/wiki:dokuwiki">DokuWiki</a> [<a href="http://wiki.splitbrain.org/wiki:dokuwiki" target="_blank">^</a>] (running, of course on Phalanger) and you can find the new website here:</p> <ul> <li><a href="http://www.php-compiler.net">Phalanger - Homepage</a> [<a href="http://www.php-compiler.net" target="_blank">^</a>] (the new project homepage)</li> <li><a href="http://www.php-compiler.net/doku.php?id=user-wiki">Phalanger - User wiki</a> [<a href="http://www.php-compiler.net/doku.php?id=user-wiki" target="_blank">^</a>] (you can edit pages in user wiki after logging in)</li> </ul> <p>I also wrote two articles about Phalanger (and I'm working on more :-)) to explain the most important and interesting Phalanger features and concepts. You can find the articles at our web:</p> <ul> <li> <a href="http://www.php-compiler.net/doku.php?id=core%3aphalanger_for_.net_developers">Phalanger for .NET developers</a> [<a href="http://www.php-compiler.net/doku.php?id=core%3aphalanger_for_.net_developers" target="_blank">^</a>] - focused on .NET interoperability and features interesting for C# developers </li> <li> <a href="http://www.php-compiler.net/doku.php?id=core%3aphalanger_for_mono_users">Phalanger for Mono users</a> [<a href="http://www.php-compiler.net/doku.php?id=core%3aphalanger_for_mono_users" target="_blank">^</a>] - Phalanger 2.0 supports Mono, so here is an introduction for Mono users</li> </ul> <p>I'll also continue blogging about Phalanger, so you can expect more information about Phalanger, problems that we're currently solving as well as some other tips, tricks in this blog. If you're interested only in Phalanger you can use <a href="http://tomasp.net/blog/rss.aspx?30">this RSS feed</a> to monitor new articles in this blog (it shows only articles with the Phalanger tag).</p>F# presentation at Czech .NET Group meetinghttp://tomasp.net/blog/fsharp-presentation.aspxTue, 14 Nov 2006 00:52:59 GMTContains links to slides and demos from my presentation focused on F# and functional programming, which I did at the Czech .NET User Group meeting.Tomas Petricek<p>On 2nd of November I did a presentation on F# and functional programming at the Czech .NET User Group meeting. Because I spent quite a lot of time with puting the presentation together I wanted to make it available to wider audience, so I translated the slides and examples to English (anyway, translating the content took me only a few minutes :-)). In case that some of the readers prefer Czech version, I attached the original documents too.</p><p>In the presentation I tried to introduce some basic concepts of functional programming (immutable values, lazy evaluation) to the audience with no experience with functional programming, as well as present some of the most interesting features of F# (like strict type system based on type inference, .NET interoperability and metaprogramming). The whole contents of the presentation is following:</p><ul><li><strong>Functional programming in F#</strong> - Introduction to the F# type system</li><li><strong>Some useful functional idioms</strong> - How to do Foldl/Map/Filter functions and Lazy evaluation in C#</li><li><strong>Interactive scripting</strong> - What is important for scripting, mathematical simulation</li><li><strong>Interoperability between F# and other .NET languages</strong> - How to use .NET libraries from F# and F# libraries from ohter .NET languages</li><li><strong>F# as a language for ASP.NET</strong> - How to use F# as a language for ASP.NET development</li><li><strong>Meta-programming in F#</strong> - Meta-programming features in F# and the FLINQ project</li></ul><h2>Downloads</h2><ul><li>Presentation - <a href="http://www.tomasp.net/articles/fsharp-presentation/fsharp-intro.ppt">Czech</a> (889 kB), <a href="http://www.tomasp.net/articles/fsharp-presentation/fsharp-intro-en.ppt">English</a> (894 kB)</li><li>Demos - <a href="http://www.tomasp.net/articles/fsharp-presentation/demos.zip">Czech</a> (500 kB), <a href="http://www.tomasp.net/articles/fsharp-presentation/demos-en.zip">English</a> (501 kB)</li></ul>Concepts behind the C# 3.0 languagehttp://tomasp.net/blog/csharp3-concepts.aspxSun, 15 Oct 2006 15:19:03 GMTIn this article I'll describe concepts that influenced the design of the C# 3.0. Most of these concepts are known from other programming languages like Haskell, LISP or languages developed at Microsoft Research.Tomas Petricek<p>One of the lectures that I attended last year was <a href="http://www.mff.cuni.cz/toISO-8859-2.en/vnitro/is/sis/predmety/kod.php?kod=PRG003">Programming Methodology and Philosophy of Programming Languages</a>. The lecture was mostly about history of programming languages and how several features evolved, disappeared and than after many years appeared again in another programming language.</p><p>As I final work I decided to write an article that describes ideas that influenced the design of the C# 3.0 language. Some of these features are known from functional languages (for example from LISP or Haskell), some other were developed at Microsoft Research and appeared in the F# language or Cω. I also wanted to show in what ways are these features limited in the C# 3.0. I think that thanks to these limitation, the C# 3.0 is still a simple (or at least not difficult) to understand which is very important for mainstream language, but I find it interesting to know what is possible in other (less limited) languages.</p><ul><li>You can also <a href="http://tomasp.net/articles/csharp3-concepts/csharp3-concepts.pdf">download the article in PDF</a> (404kB)</li><li>The article is also available at <a href="http://www.codeproject.com/useritems/csharp3-concepts.asp">CodeProject.com</a></li></ul>F# metaprogramming and classeshttp://tomasp.net/blog/fsclassmeta.aspxSat, 14 Oct 2006 01:36:10 GMTThis article presents prototype that makes it possible to use F# metaprogramming to analyse and translate classes written in special way. Tomas Petricek<p>F# quotations allows you to easily write programs that manipulate with data representation of program source code. If you're not familiar with quotations I recommend reading my previous article [<a href="#fsclassmeta-links">1</a>] that contains short introduction to this topic first. Quotations can be used for example for translating subset of the F# language to another code representation or another language.</p><p>To get the quotation data of the expression you can either use <code><@ .. @></code> operator or <code>resolveTopDef</code> function. In the first case the code written between the "<code><@</code>" and "<code>@></code>" is converted to data during the compilation. The <code>resolveTopDef</code> function allows you to get quotation data of top-level definition (function) from compiled library at runtime (you have to use <code>--quotation-data</code> command line switch while compiling the library). I mentioned that quotations can be used to represent only subset of the F# language. Currently, one of the quotation limitations is that it's not possible to enclose the whole class in the quotation operators. It is also not possible to get the representation of the whole class at runtime nor the representation of class members (for example methods). </p><p>In this article I'll present a simple method that makes it possible to use F# quotations for working with classes as well, however this is rather a prototype that can be used for experimenting and discovering areas where working with classes might be useful, not a fully working solution.</p>F# quotations visualizer - reloaded!http://tomasp.net/blog/quotvis-reloaded.aspxSun, 01 Oct 2006 21:39:06 GMTNew and improved version of quotation visualizer. Supports more language constructs and makes it possible to open quotations from compiled F# assembly.Tomas Petricek<div style="float:right;margin-left:10px;"><a href="http://www.tomasp.net/articles/quotvis-reloaded/screen.png" target="_blank"><img style="margin:10px;border-style:none;" src="http://tomasp.net/articles/quotvis-reloaded/screen-sm-sm.jpg" alt="Quotation Visualizer" /></a></div><p>Some time ago, I wrote an article about useful utility called <a href="http://www.tomasp.net/blog/quotvis.aspx">F# quotations visualizer</a>. This utility can be used to show visual representation of F# quotations, that can represent (subset of) source code written in F#. There are two ways that you can use to get F# quotations - first is using operators <code><@@ ... @@></code> (this returns quotation of the code written inside the operator), second method is to get quotation of top level definition from compiled F# assembly (you have to explicitly enable this using command line switch <code>--enable-quotation-data</code> while compiling assembly). </p><p>Because I added several new features to the original Quotations visualizer, I decided to publish the latest version - here is the list of main improvements:</p><ul><li>Rewritten using active patterns (new F# language feature)</li><li>It is possible to extract quotations from compiled F# assembly (if it contains quotation data)</li><li>Added support for several missing language constructs</li></ul>F# CodeDOM Provider on the CodePlexhttp://tomasp.net/blog/codeplex-fsharp-codedom.aspxWed, 23 Aug 2006 00:13:46 GMTCodeDOM generator for the F# language posted to the new Microsoft community site called CodePlex!Tomas Petricek<p>You probably already saw my post regarding CodeDOM generator for the F# language and how to use it with ASP.NET. To make it more accessible for everyone, I created project at the new Microsoft community site called <a href="http://www.codeplex.com">CodePlex</a> [<a href="http://www.codeplex.com" target="_blank">^</a>].</p><ul><li>To learn more about the project, visit <a href="http://www.codeplex.com/Wiki/View.aspx?ProjectName=fscodedom">Project Home Page</a></li><li>If you want to send some comments, go to <a href="http://www.codeplex.com/Project/ListForums.aspx?ProjectName=fscodedom">Discussion Board</a></li><li>You can also download latest source code - <a href="http://www.codeplex.com/SourceControl/ListDownloadableCommits.aspx?ProjectName=fscodedom">Latest Check-Ins</a></li><li>And finally, the latest releases can be found at the <a href="http://www.codeplex.com/Release/ProjectReleases.aspx?ProjectName=fscodedom">Releases Page</a></li></ul><p> BTW: CodePlex looks like a really good site. It is based on Visual Studio Team System (which means that developers of the project can do most of the work directly from Visual Studio). It provides management of "Work Items" (TODO list), source control and many other useful things! For example if you have any feature requests or bug requests, send them to the discussion and I can easilly create work item from the message in the discussions. </p><p> If you are interested in this project and you want to help with developing of some parts, or if you are working on a project that is related to CodeDOM and F#, please let me know. Any help or feedback is kindly welcome! </p>ASP.NET web applications in F#http://tomasp.net/blog/aspnet-fsharp-intro.aspxSun, 13 Aug 2006 21:06:33 GMTThis article shows how ASP.NET can be extended to support F# language using CodeDOM provider.Tomas Petricek<p>CodeDOM (Code Document Object Model) is set of objects (located in <code>System.CodeDom</code> namespace) that can be used for representing logical structure of .NET source code. These classes are used for generating Web service references (using <code>wsdl.exe</code> tool), for generating typed datasets and in many other situations. The most interesting use of CodeDOM classes is in ASP.NET where ASP.NET generates code from <code>aspx</code>/<code>ascx</code> files and compiles this code into web site assemblies (together with the code written in code behind files).</p><p>This means, that you can use any language for developing ASP.NET web sites, as long as you implement CodeDOM provider that generates source code from CodeDOM structure and can compile these source files (this can be simply done by executing command line compiler). I was recently working on CodeProvider for the F# language, and finally it supports everything what is needed by ASP.NET (however it is complete and it doesn't work for example with <code>wsdl.exe</code>). Using this CodeDOM provider you can write ENTIRE web site in F# (including in-line code enclosed in <% ... source code ... %>). I also created project template for F# web site that can be imported to Visual Studio 2005, so you can easilly try writing web pages in F#...</p>LINQ extensions - Simplified keyword searchhttp://tomasp.net/blog/linq-expand-update.aspxFri, 28 Jul 2006 03:57:38 GMTArticle describes LINQ extension that adds support for returning rows that contain any or all of specified keywords in string column.Tomas Petricek<p>Recently, I came across interesting question at LINQ Forums (Dynamic conditions: How to achieve multiple "OR" conditions with LINQ? [<a href="#updlq">1</a>]). The question is whether LINQ (and especially LINQ to SQL) provides any simple way to return only records that contain one or more of specified keywords in the name. The question looks simple, but it is simple only if you know the number of keywords that you want to look for. In this case you can write following LINQ query:</p><pre><span class="c">// Products that contain "kwd1" or "kwd2" in the name </span><br /><span class="k">var</span> q = <span class="k">from</span> p <span class="k">in</span> db.Products <span class="k">where</span> p.ProductName.Contains("kwd1") || p.ProductName.Contains("kwd2") <span class="k">select</span> p; </pre><p>The problem with previous code is that you can't use it if the list of keywords is dynamically entered by user (and so its length may vary). Of course, if you want to run query on in-memory data, you can get very nice results by writing extension method called <code>ContainsAny</code> that performs test for keyword array, but if you want to be able to translate query to SQL, the situation is a bit complicated.</p>F# quotations visualizerhttp://tomasp.net/blog/quotvis.aspxWed, 21 Jun 2006 02:20:03 GMTApplication that displays graphical representation of given F# quotation (using Windows Forms TreeView control)Tomas Petricek<p>I already <a href="http://tomasp.net/blog/fsquotations.aspx">explained</a> what F# quotations are and I explained how you can do some simple manipulations with it. In this article I'd like to present an application that I wrote and that can be helpful when working with quotations. It displays clear graphical representation of given F# quotation (using Windows Forms TreeView control). </p><div style="text-align:center;"><a href="http://tomasp.net/articles/quotvis/qv_apps.gif" target="_blank"><img style="margin:10px;border-style:none;" src="http://tomasp.net/articles/quotvis/qv_apps_sm.gif" alt="Quotation Visualizer" /></a></div>Calling functions in LINQ querieshttp://tomasp.net/blog/linq-expand.aspxSat, 10 Jun 2006 14:26:52 GMTThis article describes method that allows you to reuse parts of LINQ queries across data access layer.Tomas Petricek<p>The <a href="http://msdn.microsoft.com/data/ref/linq/">LINQ Project</a> [<a href="http://msdn.microsoft.com/data/ref/linq/" target="_blank">^</a>] is an extension to .NET Framework and most important .NET languages (C# and VB.Net) that extends these languages with query operators and some language features that make it possible to integrate queries in the languages. Thanks to LINQ you can write queries that read data from database (or any other data source). For example, imagine that you want to write set of queries for eshop and you need to perform a price calculation in more queries. The problem with LINQ queries is that you can't simply call a function written in C# that calculates price. The following example is NOT WORKING for this reason:</p><pre><span class="c">// function used in filter</span><br /><span class="k">static</span> <span class="k">decimal</span> CalcPrice(Nwind.Product p) { <span class="k">return</span> p.UnitPrice * 1.19m; }</pre><pre><span class="c">// query that uses MyFunc</span><br /><span class="k">var</span> q = <span class="k">from</span> p <span class="k">in</span> db.Products <span class="k">where</span> CalcPrice(p) > 30m <span class="k">select</span> p </pre><p>I think that this is a big limitation, because when you want to keep some more complex logic in the data access layer you should be able to reuse parts of queries that are similar across more queries. The good thing is that with latest release, LINQ became extensible so it is possible to write a extensions that allow this scenario...</p><ul><li>You can also <a href="http://tomasp.net/articles/linq-expand/linq-expand.pdf">download the article in PDF</a> (80kB)</li></ul>Slides and demos from F# presentationhttp://tomasp.net/blog/fsharp-slides-and-demos.aspxFri, 09 Jun 2006 21:14:39 GMTI did a F# presentation at .NET seminar at our university, so here are the slides and demos...Tomas Petricek<p>This semester I attended Advanced .NET Seminar that was led by <a href="http://tmd.havit.cz/">Tomas Matousek</a> [<a href="http://tmd.havit.cz/" target="_blank">^</a>] who is one of the authors of <a href="http://www.php-compiler.net">Phalanger project</a> [<a href="http://www.php-compiler.net" target="_blank">^</a>] (Which is an amazing project by the way. It takes PHP source code and compiles it without any modification to .NET). Seminar was mostly focused on Rotor and .NET internals, so if you want to learn more about these topics you can look at <a href="http://tmd.havit.cz/Teaching/CLR.htm">Advanced .NET programming</a> [<a href="http://tmd.havit.cz/Teaching/CLR.htm" target="_blank">^</a>] slides (by Tomas Matousek).</p><p>I did one presentation at this seminar too. It was about the F# language developed at Microsoft Research. It was just a quick overview of F# features, because F# is very rich topic, so it coveres only the language (functional vs. imperative behavior), F# type system, compilation of F# constructs to .NET and interoperability with .NET (for example how to create windows forms application in F#). At the end, I also mentioned F# meta-programming that allows you to look at F# code as data.</p><ul><li><a href="http://tomasp.net/academic/files/fsharp.pdf">The F# language</a> (67kB) - presentation slides in PDF</li><li><a href="http://tomasp.net/academic/files/fsharp-samples.zip">F# Samples</a> (54kB) - zipped VS 2005 solution with samples</li></ul>F# - Simple quotations transformationhttp://tomasp.net/blog/fsquotations.aspxSun, 28 May 2006 15:58:20 GMT This article describes very simple code that I wrote while learning how to work with the F# quotations library. Tomas Petricek<p>This article describes very simple code that I wrote while learning how to work with the F# quotations library. Using the F# quotations you can get tree representation of the quoted expression. This allows you to write code that takes code written in F# as data and performs some code analysis or compiles/translates that code to different language. This is very similar to the new C# 3.0 expression trees where you can get expression tree from lambda expression and translate this tree for example to SQL (using DLINQ). However expression trees in C# 3.0 are very limited when compared with F# quotations, so that's one of the many reasons why F# is interesting language.</p>Aho-Corasick string matching in C#http://tomasp.net/blog/ahocorasick.aspxSun, 04 Dec 2005 00:18:30 GMTC# implementation of very efficient Aho-Corasick keyword matching algorithm with multiple keywords support.Tomas Petricek<p>I implemented this algorithm because I worked on one project where we needed to filter bad language in comments submited by users (You wouldn't believe what anonymous users sometimes write). First I tried simple solution using <code>String.IndexOf</code> and using <code>Regex</code>, but none of these solutions was very suitable for this problem, so I decided to implement Aho-Corasick algorithm which is probabbly the best algorithm for this purpose.</p><p>Article (published here an on CodeProject.com) describes implementation of this algorithm for pattern matching. In simple words this algorithm can be used for searching text for specified keywords. This implementation is usefull when you have a set of keywords and you want to find all occurences in text or check if any of the keywords is present in the text. You should use this algorithm especially if you have large number of keywords that don't change often, because in this case it is much more efficient than other algorithms that can be simply implemented using .NET class library.</p><p>Aho-Corasick search algorithm is very efficient if you want to find large number of keywords in the text, but if you want to search only for a few keywords it is better to use simple method using <code>String.IndexOf</code>. </p> | 78,139 | 311,852 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.328125 | 3 | CC-MAIN-2021-39 | latest | en | 0.855297 |
https://www.primidi.com/captives/plot | 1,601,130,748,000,000,000 | text/html | crawl-data/CC-MAIN-2020-40/segments/1600400244231.61/warc/CC-MAIN-20200926134026-20200926164026-00792.warc.gz | 981,301,861 | 4,174 | # Captives - Plot
Plot
A young dentist (Ormond) working in a British prison starts to become attracted to a violent inmate (Roth) after the break-up of her marriage, and embarks upon an illicit affair with him.
### Other articles related to "plot, plots":
Babington Plot - Mary's Imprisonment
1567, she became the focus of numerous plots and intrigues to restore England to the Catholic fold ... behalf anyone plotted against the queen, even if the claimant were ignorant of the plot, would be excluded from the line and executed ... execution of anyone who would benefit from the death of the Queen if a plot against her was discovered ...
Q-Q Plot - Interpretation
... The points plotted in a Q–Q plot are always non-decreasing when viewed from left to right ... being compared are identical, the Q–Q plot follows the 45° line y = x ... linearly transforming the values in one of the distributions, then the Q–Q plot follows some line, but not necessarily the line y = x ...
Zoltan, Hound Of Dracula (film) - Plot
... Zoltan opens another coffin shaken loose from the crypt, this one holding the body of an innkeeper, Nalder, who once owned the crypt ... Zoltan removes the stake from the innkeeper's chest, reanimating the innkeeper ...
Les Misérables - Plot - Volume II – Cosette
... Valjean arrives at Montfermeil on Christmas Eve ... He finds Cosette fetching water in the woods alone and walks with her to the inn ...
Bresenham's Line Algorithm - Derivation - Algorithm
... plot(x0,y0, x1,y1) dx=x1-x0 dy=y1-y0 D = 2*dy - dx plot(x0,y0) y=y0 for x from x0+1 to x1 if D > 0 y = y+1 plot(x,y) D = D + (2*dy-2*dx) else plot(x,y) D = D + (2*dy) Running this ...
### Famous quotes containing the word plot:
The westward march has stopped, upon the final plains of the Pacific; and now the plot thickens ... with the change, the pause, the settlement, our people draw into closer groups, stand face to face, to know each other and be known.
Woodrow Wilson (1856–1924)
“The plot thickens,” he said, as I entered.
Sir Arthur Conan Doyle (1859–1930)
After I discovered the real life of mothers bore little resemblance to the plot outlined in most of the books and articles I’d read, I started relying on the expert advice of other mothers—especially those with sons a few years older than mine. This great body of knowledge is essentially an oral history, because anyone engaged in motherhood on a daily basis has no time to write an advice book about it.
Mary Kay Blakely (20th century) | 621 | 2,493 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.390625 | 3 | CC-MAIN-2020-40 | latest | en | 0.920572 |
https://www.physicsforums.com/threads/limit-one-sided.198458/ | 1,531,738,597,000,000,000 | text/html | crawl-data/CC-MAIN-2018-30/segments/1531676589251.7/warc/CC-MAIN-20180716095945-20180716115945-00446.warc.gz | 957,151,629 | 14,172 | # Homework Help: Limit (one-sided)
1. Nov 15, 2007
### gop
1. The problem statement, all variables and given/known data
$$lim_{x\rightarrow1-}\frac{\arccos x}{\sqrt{1-x}}=?$$
Hint: substitute x=cos(t)
2. Relevant equations
3. The attempt at a solution
I, as usual, tried to factor the terms and multiplied with the binomial theorems (to get rid of the square root in the denominator). However, this doesn't lead to any two terms that would cancel out.
I also tried to use the squeeze theorem but ended up with a range from zero to infinity (So I had no two functions that have the same limit).
The solution is $$\sqrt{2}$$ according to my CAS.
Last edited: Nov 15, 2007
2. Nov 15, 2007
### Kreizhn
The problem is that this is an indeterminate limit in it's current form. Thus we must apply L'Hopitals rule. You'll find that the derivative of the top is
$$\displaystyle - \frac{1}{\sqrt{1-x^2}}$$
and the bottom is
$$\displaystyle - \frac{1}{2\sqrt{1-x}}$$
When you put it all together, collect under a single root, and make all necessary cancellations, you're left with the limit of a continuous function, namely
$$\displaystyle \lim _{x \to 1} \frac{2}{\sqrt{x+1}}$$
Last edited: Nov 15, 2007
3. Nov 16, 2007
### gop
Hi
First of all, thx for your answer. My first guess was also to go with L'Hopitals rule; however, we haven't done differentiation/integration yet and so I doubt that we are allowed to use it.
However, I'm not really sure how do do it then else especially when considering the hint about substituting x with cos(t).
thx
4. Nov 16, 2007
### Sourabh N
you don't need L'hopital's rule. when you put x = cos t you denom will be like
$$\sqrt{1 - cos t}$$ = $$\sqrt{2 sin^{2}(t/2)}$$
= $$\sqrt{2}$$ sin t/2 , and num is t; now you can put the limit.
5. Nov 16, 2007
### gop
well I use, as mentioned in the previous post, the identities of sine and cosine and I also changed the limit from x->1 to t->0, to get
$$lim_{t\rightarrow{0-}}\frac{\sqrt{2}\cdot t}{2\cdot\sin t/2}$$
However, the problem still exists. When I plug in t=0 I get still 0/0.a
6. Nov 16, 2007
### Sourabh N
Actually, the val for this particular limit : t / sin t is found to be 1 and is used as an identity(I mean whenever this form comes, we can directly put the limit value for it as 1).
7. Nov 16, 2007
### gop
thx for your effort now I got it
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook | 736 | 2,447 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.875 | 4 | CC-MAIN-2018-30 | latest | en | 0.931358 |
https://cloud.tencent.com/developer/article/1423141 | 1,571,782,875,000,000,000 | text/html | crawl-data/CC-MAIN-2019-43/segments/1570987824701.89/warc/CC-MAIN-20191022205851-20191022233351-00396.warc.gz | 414,244,883 | 14,802 | 一起刷题吧 | 100+Python编程题带你快速上手（附答案）
100+编程练习帮大家轻松学习Python，春节也要抓紧学习哟~
Level 1：初级。刚入门 Python 或者正在学一些基础课程的同学们。通常包含 1 到 2 个类或函数的问题都可以解决，甚至答案都可能在一些教材中就能找到。
Level 2：中级。已经系统学习过 Python，并且已经有一定的编程背景的同学们，可以解决包含 3 个及以上类或函数的问题，不过这些答案就在教材找不到了。
Level 3：高级：可以用 Python 中非常丰富的各种库、标准包或更高级的技术，结合数据结构和算法，来解决复杂的问题。
```Question 1
Level 1
Question:
Write a program which will find all such numbers which are divisible by 7 but are not a multiple of 5,
between 2000 and 3200 (both included).
The numbers obtained should be printed in a comma-separated sequence on a single line.
Hints:
Consider use range(#begin, #end) method```
```Question 2
Level 1
Question:
Write a program which can compute the factorial of a given numbers.
The results should be printed in a comma-separated sequence on a single line.
Suppose the following input is supplied to the program:
8
Then, the output should be:
40320
Hints:
In case of input data being supplied to the question, it should be assumed to be a console input.```
```Question 3
Level 1
Question:
With a given integral number n, write a program to generate a dictionary that contains (i, i*i) such that is an integral number between 1 and n (both included). and then the program should print the dictionary.
Suppose the following input is supplied to the program:
8
Then, the output should be:
{1: 1, 2: 4, 3: 9, 4: 16, 5: 25, 6: 36, 7: 49, 8: 64}
Hints:
In case of input data being supplied to the question, it should be assumed to be a console input.
Consider use dict()```
```Question 4
Level 1
Question:
Write a program which accepts a sequence of comma-separated numbers from console and generate a list and a tuple which contains every number.
Suppose the following input is supplied to the program:
34,67,55,33,12,98
Then, the output should be:
['34', '67', '55', '33', '12', '98']
('34', '67', '55', '33', '12', '98')
Hints:
In case of input data being supplied to the question, it should be assumed to be a console input.
tuple() method can convert list to tuple```
```Question 5
Level 1
Question:
Define a class which has at least two methods:
getString: to get a string from console input
printString: to print the string in upper case.
Also please include simple test function to test the class methods.
Hints:*Solution 1*
l=[]
for i in range(2000, 3201):
if (i%7==0) and (i%5!=0):
l.append(str(i))
print ','.join(l)
___________________________________
*Solution 2*
def fact(x):
if x == 0:
return 1
return x * fact(x - 1)
x=int(raw_input())
print fact(x)
___________________________________
*Solution 3*
n=int(raw_input())
d=dict()
for i in range(1,n+1):
d[i]=i*i
print d
___________________________________
*Solution 4*
values=raw_input()
l=values.split(",")
t=tuple(l)
print l
print t
___________________________________
*Solution 5*
class InputOutString(object):
def __init__(self):
self.s = ""
def getString(self):
self.s = raw_input()
def printString(self):
print self.s.upper()
strObj = InputOutString()
strObj.getString()
strObj.printString()Use __init__ method to construct some parameters```
0 条评论 | 912 | 3,056 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.609375 | 3 | CC-MAIN-2019-43 | latest | en | 0.742811 |
https://supportforums.cisco.com/t5/email-security/plotting-senderbase-information-on-a-world-map/td-p/912424 | 1,519,590,833,000,000,000 | text/html | crawl-data/CC-MAIN-2018-09/segments/1518891816912.94/warc/CC-MAIN-20180225190023-20180225210023-00074.warc.gz | 786,563,685 | 34,037 | cancel
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ESA: 11.0.0-274 WSA: 10.5.1-296 SMA: 11.0.0-128 Email Plug-in (Reporting): 1.0.1-048 Email Plug-in (Encryption): 1.0.0-036
Community Member
## Plotting Senderbase Information on a World Map
Greetings,
I have whipped up a quick script some of you may find useful.
ip2mapplot.py is a Python script for resolving a number of IP addresses to latitude / longitude coordinates and plotting them on a world map
Below is an image generated from one days worth of Senderbase drops on our Ironport MGAs:
[img:f531ef1b7c]http://insecure.io/images/a/a6/Map_sbrs_small.jpg[/img:f531ef1b7c]
Source code is available here: http://research.mince.ac.nz/ip2mapplot.py
Further instructions here: http://insecure.io/index.php/Code/ip2mapplot
Cheers,
si
5 REPLIES
Community Member
## Re: Plotting Senderbase Information on a World Map
Awesome, thanks for sharing the script and instructions !
Just one thing to mention. Your link to matplotlib documentation is going to Basemap page. To make matplotlib to work the matplotlib-toolkits "basemap"is required.
Community Member
## Re: Plotting Senderbase Information on a World Map
Interesting to see that the SPAM pattern is very similar.
Here are my stats from yesterday (Sunday)
[+] Found 289282 unique IP addresses
[+] Determining unique latitude / longitude points
[+] Plotting 15950 discrete points on map
[-] Plotting 15613 points for x < 100
[-] Plotting 259 points for 100 < x < 500
[-] Plotting 64 points for 500 < x < 2500
'[-] Plotting 14 points for x > 2500
Community Member
## Re: Plotting Senderbase Information on a World Map
Here's what our map looks like with one week's worth of data on hosts with a SBRS of -10 to -4.
[img:c91b0e4b2a]http://web.acd.ccac.edu/~bpoyner/ironport/ironport-map-small.jpg[/img:c91b0e4b2a]
[+] Found 691344 unique IP addresses
[+] Determining unique latitude / longitude points
[+] Plotting 15037 discrete points on map
[-] Plotting 14098 points for x < 100
[-] Plotting 772 points for 100 < x < 500
[-] Plotting 131 points for 500 < x <2500> 2500
I don't know if anybody else ran into this issue, but as-is the script provided by si doesn't work with python 2.3. You'll get the following error message:
[+] Determining unique latitude / longitude points
Traceback (most recent call last):
File "./ip2mapplot.py", line 41, in ?
latlon = count.partition(',')
AttributeError: 'str' object has no attribute 'partition'
You have to change partition to split, and change the latlon array reference accordingly.
Community Member
## Re: Plotting Senderbase Information on a World Map
Good point regarding python2.3 bpoyner, I only tested on v2.4
Community Member
## Re: Plotting Senderbase Information on a World Map
I used this script few years ago but now I have lost the code and I can't find it from the links bellow either.
Does anyone know where to get this code ? This was very nice script to see where the spam is really coming from
278
Views
0 | 809 | 3,005 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.546875 | 3 | CC-MAIN-2018-09 | latest | en | 0.718372 |
https://web2.0calc.com/questions/henry-made-6-identical-necklaces-each-having-beads | 1,657,213,699,000,000,000 | text/html | crawl-data/CC-MAIN-2022-27/segments/1656104495692.77/warc/CC-MAIN-20220707154329-20220707184329-00200.warc.gz | 662,750,114 | 5,512 | +0
# Henry made 6 identical necklaces, each having beads and a pendant. The total cost of the beads and pendants for all 6 necklaces was
0
152
1
Henry made 6 identical necklaces, each having beads and a pendant. The total cost of the beads and pendants for all 6 necklaces was \$31.80. If the beads cost a total of \$14.40, how much did each pendant cost?
Dec 1, 2021
edited by Guest Dec 1, 2021
#1
0
Let the cost of each pendant is x then the cost of
6 pendant is 6x.
Given each necklaces has a pendant
Hence, the cost of pendant for all 6 necklaces is 6x
Given, the cost of total beads is \$14.40
Hence, the total cost of the beads and pendants of
all 6 necklaces is 6x + \$14.40.
Given, the total cost of the beads and pendants of all
6 necklaces is \$31.80
Hence 6x + \$14.40 = \$31.80
=> 6x = \$17.40
=> x = \$2.90
Hence, the cost of each pendant is \$2.90
Dec 2, 2021 | 295 | 895 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.34375 | 4 | CC-MAIN-2022-27 | latest | en | 0.89638 |
https://sports.answers.com/Q/Why_do_you_say_love_love_serivce_when_beginning_a_game_in_tennis | 1,716,938,747,000,000,000 | text/html | crawl-data/CC-MAIN-2024-22/segments/1715971059160.88/warc/CC-MAIN-20240528220007-20240529010007-00484.warc.gz | 455,824,032 | 48,253 | 0
# Why do you say love love serivce when beginning a game in tennis?
Updated: 12/19/2022
Wiki User
15y ago
you say love love, because that officially means 0-0, the score is 0, 0
Wiki User
15y ago
Earn +20 pts
Q: Why do you say love love serivce when beginning a game in tennis?
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Still have questions?
Related questions
### What word symbolizes zero in tennis?
Love, in tennis or table tennis zero or nothing means love
Tennis.
### In what game does love have no value?
TENNIS, Love means ZERO in Tennis, this was on a homework for math...thought id help you out...
### In which spot beginning with 't' is a score of zero called love?
The sport is tennis.
### What is love 15?
It is the score in a tennis game after the person that served has lost the first rally. Love is the same as zero in tennis terminology.
### Which sport do they say forty love?
You would hear those words in tennis. They are for keeping score in a game. The game points go from love (0) to 15, 30, 40 and then game. If it is 40 all, it is deuce. To win a deuce, you must win by 2 points. It goes from deuce to the advantage of the player who won that point, and then game.
You mean tennis?
### What are the points in Tennis?
It is 0 (Love) - 30 - 40 - Game Point.
### In tennis zero score is?
The term "Love' is used in the game of tennis to refer to 0 or zero score. For example, if I were serving and had lost 2 consecutive points the score would be 0-30 or love-30. Also, at the beginnings of each set 0-0 score for both players, it can be called "love-love"
### Why is tennis points love thirty forty?
The tennis points go like this: Love (0 points) 15 (1 point) 30 (2 points) 40 (3 points) Game (4 points) That is just how tennis is played.
### The term 'love' is used in which two game?
love is used in the games of badminton and lawn tennis. it means ZERO or NO POINT | 505 | 1,884 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.03125 | 3 | CC-MAIN-2024-22 | latest | en | 0.946109 |
https://cracku.in/21-in-2005-out-of-the-total-number-of-applications-re-x-ibps-po-2017 | 1,721,010,632,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763514655.27/warc/CC-MAIN-20240715010519-20240715040519-00207.warc.gz | 151,928,210 | 23,041 | Instructions
Refer to the bar graph and answer the given questions.
Question 21
# In 2005, out of the total number of applications received for subjects A and B together, only 30% were accepted. What was the total number of applications accepted for subjects A and B together in 2005 ?
Solution
The total number of applications received for subjects A =280
The total number of applications received for subjects B = 130
The total number of applications received for subjects A and B in 2005 = 280 + 130 = 410
30 % of the total number of applications received for subjects A and B in 2005 = 0.3 $$\times$$ 410
=123
Option B is the correct answer. | 157 | 650 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.15625 | 4 | CC-MAIN-2024-30 | latest | en | 0.962725 |
https://www.physicsforums.com/threads/combustion-analysis-empirical-and-molecular-formula.956891/ | 1,721,466,985,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763515079.90/warc/CC-MAIN-20240720083242-20240720113242-00068.warc.gz | 797,836,124 | 18,447 | # Combustion Analysis- Empirical and molecular formula
• Chemistry
• Dustyneo
In summary, the conversation was about finding the empirical and molecular formula for menthol, a substance found in mentholated cough drops. Through combustion, the masses of CO2 and H2O produced from a 0.1005 g sample of menthol were given. The correct approach was to find the mass of C, H, and O in the sample, and use their ratios to determine the empirical formula. The molecular formula was then found by using the molar mass of menthol. The resulting formula was C10H20O, with a molar mass of approximately 156 g/mol.
Dustyneo
## Homework Statement
Menthol, the substance we can smell
in mentholated cough drops, is composed of C, H, and O. A
0.1005-g sample of menthol is combusted, producing 0.2829 g
of CO2 and 0.1159 g of H2O. What is the empirical formula
for menthol? If menthol has a molar mass of 156 g/mol, what is its molecular formula?.
The empirical and molecular formulas are C 10H20O
2. Homework Equations
Whole-number multiple = molecular weight /empirical formula weight
## The Attempt at a Solution
Cant arrive at the same answer. I started off using the masses of the combustion products, in the case of carbon
(0,2829 g CO2 ) (mol CO2 /44,0 g CO2) (mol C/mol CO2) =
0,00643 mol C
As for H and O, I got 0,129 mol and 0,00643 mol respectively. Then comparing the relative number of moles of each element
C: 0,00643/0,00643=1 H: 0,129/0,00643=20 O:0,00643/0,00643 = 1 lead me obtaining CH20O as the empirical formula. What am I doing wrong?
Please show us how you got the 0.129 mol for H.
And 0.00643 mol for O.
Made a calculation mistake for H, the corrected value is 0,0129
(0,1159 g H2O) (mol H2O/ 18,0 g H2O) (2 mol H/ mol H2O)= 0,0129 mol H
For O, I also noticed that the actual number is closer to 0,00644:
(0,1159 g H2O) (mol H2O/ 18,0 g H2O) ( mol O/ mol H2O) = 0,00644 mol O
How do you know that all the O in the H2O, and none of that in the CO2, comes from the O in the compound rather than the oxygen in the air? You need to take the equation
aCxHyOz + bO2 → cCO2 + dH2O
and balance it.
Chestermiller
To add to what mjc123 wrote, finding mass of oxygen in the compound is quite easy once you know mass of carbon and hydrogen (and actually doesn't require stoichiometry).
mjc123 said:
How do you know that all the O in the H2O, and none of that in the CO2, comes from the O in the compound rather than the oxygen in the air? You need to take the equation
aCxHyOz + bO2 → cCO2 + dH2O
and balance it.
Ok. In order to fill the values for a, c and d, I did these calculations,
Finding the amount of menthol molecules,
(0,1005 g C10H20O ) (mol C10H20O /156,09 G C10H20O) (6,02 X 1023 C10H20O molecules / mol C10H20O ) = 3,88 x 1020 menthol molecules
CO2 molecules
(0,2829 g CO2) (mol CO2/44,0 g CO2 ) (6,02 X 1023 molecules CO2 /mol CO2) = 3,87 X 1021 CO2 molecules
H2O molecules
(0,1159 g H2O) (mol H2O /18,0 g)(6,02 x 1023 water molecules/mol H2O) = 3,88 x 1021 water molecules
Simplifying these number of molecules into the equation (number of water and CO2 molecules is 10 times the amount of menthol molecules) I get
C10H20O + bO2 → 10 CO2 + 10 H2O . Am I on the right track?
Last edited:
That's cheating, because you are using the formula of menthol in your calculation.
Go back to what Borek said. You have 0.2829g CO2. What mass of C does this contain? It can only have come from the menthol, so this is the mass of C in 0.1005g menthol.
You have 0.1159g water. How much H does this contain? It can only have come from the menthol, so this is the mass of H in 0.1005g menthol.
Now you have the mass of C and H, what is the mass of O in 0.1005g menthol?
Having the mass fractions, convert them into mole fractions, and work out the simplest whole-number ratio.
mjc123 said:
What mass of C does this contain? It can only have come from the menthol
How much H does this contain? It can only have come from the menthol
can only have come from the menthol
I think I grasped where the mistake was . So I proceeded to only get the mass amount for C and H.
(0,2829 g CO2)(mol CO2/44,0 g CO2)(mol C/mol CO2 )(12,0 g C/mol C) = 0,0772 g C
(0,1159 g H2O)(mol H2O/18,0 g H2O) (2 mol H/mol H2O)( 1 g H/mol H) = 0,0129 g H
Then substracting the addition of these masses from the menthol to get the amount of O:
(0,1005 g) - (0,0772 + 0,0129) = 0,0104 g O
Obtaining moles and comparing relative numbers
(0,0772 g C)(mol C/ 12,0 g C) = 0,00643 mol C
(0,0129 g H)(mol H/ g H)= 0,0129 mol H
(0,0104 g O)(mol O/16,0 g O)= 0,0006504 mol H
C: 0,00643/0,0006504≈ 10 H: 0,0129/0,0006504≈20 O: 0,0006504/0,0006504=1 giving C10H20O as the empirical formula, with a formula weight of aprox. 156 amu. Then using the relevant equation
156 amu/156 amu=1 indicates C10H20O also being the molecular formula. Thanks for the help.
Borek
## 1. What is combustion analysis?
Combustion analysis is a method used to determine the empirical and molecular formula of a compound by burning a sample of the compound in the presence of excess oxygen and measuring the amount of carbon dioxide and water produced.
## 2. How does combustion analysis work?
In combustion analysis, a sample of the compound is heated in a combustion chamber with a known amount of excess oxygen. The compound reacts with the oxygen to form carbon dioxide and water, which are then collected and measured. These measurements are used to calculate the empirical and molecular formula of the compound.
## 3. What is the difference between empirical and molecular formula?
The empirical formula is the simplest ratio of the elements present in a compound, while the molecular formula is the actual number of atoms of each element in a molecule of the compound.
## 4. Why is combustion analysis important?
Combustion analysis is important because it allows scientists to determine the chemical formula of a compound, which is essential for understanding its properties and behavior. It is also a crucial step in the process of synthesizing and identifying new compounds.
## 5. Are there any limitations to combustion analysis?
Yes, there are some limitations to combustion analysis. For example, it can only be used for compounds that contain carbon and hydrogen. It also assumes that all of the carbon in the compound is converted to carbon dioxide during the combustion process, which may not always be the case. Additionally, combustion analysis does not provide information about the arrangement of atoms in a molecule, only the ratio of elements.
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2K | 2,077 | 7,096 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.59375 | 4 | CC-MAIN-2024-30 | latest | en | 0.87204 |
https://www.airmilescalculator.com/distance/mba-to-ebb/ | 1,723,480,720,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722641045630.75/warc/CC-MAIN-20240812155418-20240812185418-00884.warc.gz | 487,198,489 | 48,710 | # How far is Entebbe from Mombasa?
The distance between Mombasa (Moi International Airport) and Entebbe (Entebbe International Airport) is 568 miles / 914 kilometers / 494 nautical miles.
The driving distance from Mombasa (MBA) to Entebbe (EBB) is 729 miles / 1174 kilometers, and travel time by car is about 16 hours 4 minutes.
568
Miles
914
Kilometers
494
Nautical miles
1 h 34 min
109 kg
## Distance from Mombasa to Entebbe
There are several ways to calculate the distance from Mombasa to Entebbe. Here are two standard methods:
Vincenty's formula (applied above)
• 568.092 miles
• 914.256 kilometers
• 493.659 nautical miles
Vincenty's formula calculates the distance between latitude/longitude points on the earth's surface using an ellipsoidal model of the planet.
Haversine formula
• 568.385 miles
• 914.727 kilometers
• 493.913 nautical miles
The haversine formula calculates the distance between latitude/longitude points assuming a spherical earth (great-circle distance – the shortest distance between two points).
## How long does it take to fly from Mombasa to Entebbe?
The estimated flight time from Moi International Airport to Entebbe International Airport is 1 hour and 34 minutes.
## Flight carbon footprint between Moi International Airport (MBA) and Entebbe International Airport (EBB)
On average, flying from Mombasa to Entebbe generates about 109 kg of CO2 per passenger, and 109 kilograms equals 239 pounds (lbs). The figures are estimates and include only the CO2 generated by burning jet fuel.
## Map of flight path and driving directions from Mombasa to Entebbe
See the map of the shortest flight path between Moi International Airport (MBA) and Entebbe International Airport (EBB).
## Airport information
Origin Moi International Airport
City: Mombasa
Country: Kenya
IATA Code: MBA
ICAO Code: HKMO
Coordinates: 4°2′5″S, 39°35′39″E
Destination Entebbe International Airport
City: Entebbe
Country: Uganda
IATA Code: EBB
ICAO Code: HUEN
Coordinates: 0°2′32″N, 32°26′36″E | 531 | 2,011 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.890625 | 3 | CC-MAIN-2024-33 | latest | en | 0.822307 |
https://forum.math.toronto.edu/index.php?PHPSESSID=0hqmjkcjsq14fjjtiagrlt5lf0&topic=2109.0;prev_next=prev | 1,718,462,856,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198861594.22/warc/CC-MAIN-20240615124455-20240615154455-00279.warc.gz | 234,950,616 | 5,549 | ### Author Topic: TUT5103 Quiz4 (Read 3726 times)
#### Shang Wu
• Newbie
• Posts: 3
• Karma: 0
##### TUT5103 Quiz4
« on: October 18, 2019, 02:21:01 PM »
Find the solution of the given initial value problem.
\begin{align*}
y''+y&=0, \\
y(\pi /3)&=2, \\
y'(\pi /3)&=-4
\end{align*}
Solution:
First we solve the characteristic equation:
\begin{align*}
r^2+1&=0\\
r&=\pm i
\end{align*}
so here $\lambda = 0, \mu = 1$, the general solution for the homogeneous equation is
\begin{align*}
y_1=c_1\cos(t)+c_2\sin(t)
\end{align*}
We can check the Wronskian is $1\neq 0$.
Differentiate y, we get
\begin{align*}
y'=-c_1\sin(t)+c_2\cos(t)
\end{align*}
Now substitute the initial values:
\begin{align*}
y(\pi /3)&=2 \\
c_1\cos(\pi /3) +c_2\sin(\pi/3) &=2\\
\frac{1}{2}c_1+\frac{\sqrt{3}}{2}c_2 &=2\\
y'(\pi /3) &=-4\\
-c_1\sin(\pi/3)+c_2\cos(\pi/3)&=-4\\
-\frac{\sqrt{3}}{2}c_1+\frac{1}{2}c_2 &=-4
\end{align*}
Solve for $c_1, c_2$, we get
\begin{align*}
c_1 = 1+2\sqrt{3}, c_2 = \sqrt{3}-2
\end{align*}
Then the solution of the initial value problem is
\begin{align*}
y = (1+2\sqrt{3})\cos(t) + (\sqrt{3}-2)\sin(t)
\end{align*} | 503 | 1,118 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.5 | 4 | CC-MAIN-2024-26 | latest | en | 0.377634 |
https://web2.0calc.com/questions/number-theory_43441 | 1,643,262,987,000,000,000 | text/html | crawl-data/CC-MAIN-2022-05/segments/1642320305141.20/warc/CC-MAIN-20220127042833-20220127072833-00243.warc.gz | 648,160,220 | 5,262 | +0
# Number Theory
0
116
1
Let f(x)=12x+7 and g(x) = 2x+5 whenever x is a positive integer. Define h(x) to be the greatest common divisor of f(x) and g(x). What is the sum of all possible values of h(x)?
Jul 9, 2021 | 79 | 219 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.90625 | 3 | CC-MAIN-2022-05 | latest | en | 0.560585 |
https://mtacademy.co.uk/specification/19/66/a-level-maths-ocr-b-mei-h640-numerical-methods | 1,656,443,480,000,000,000 | text/html | crawl-data/CC-MAIN-2022-27/segments/1656103573995.30/warc/CC-MAIN-20220628173131-20220628203131-00459.warc.gz | 460,362,365 | 7,465 | ## OCR B (MEI) H640
### Are you studying this syllabus?
#10.1
Be able to locate the roots of $$f(x) = 0$$ by considering changes of sign of $$f(x)$$ in an interval of $$x$$ in which $$f(x)$$ is sufficiently well-behaved.
Finding an interval in which a root lies. This is often used as a preliminary step to find a starting value for the methods in 10.3 and 10.4.
#10.2
Be aware of circumstances under which change of sign methods may fail.
e.g. when the curve of $$y = f(x)$$ touches the x-axis.
e.g. when the curve of $$y = f(x)$$ has a vertical asymptote.
e.g. there may be several roots in the interval.
#10.3
Be able to carry out a fixed point iteration after rearranging an equation into the form x = g(x) and be able to draw associated staircase and cobweb diagrams.
e.g. write $$x^3 - x - 4 = 0$$ as
$$x = \sqrt[3]{x+4}$$ and use the iteration
$$x_{n+1} = \sqrt[3]{x_n+4}$$ with an appropriate starting value.
Includes use of $$\boxed{ANS}$$ key on calculator.
Notation: iteration, iterate
#10.4
Be able to use the Newton-Raphson method to find a root of an equation and represent the process on a graph.
#10.5
Understand that not all iterations converge to a particular root of an equation.
Know how Newton-Raphson and fixed point iteration can fail and be able to show this graphically.
#10.6
Be able to find an approximate value of a definite integral using the trapezium rule, and decide whether it is an over- or an under-estimate.
In an interval where the curve is either concave upwards or concave downwards.
Notation: Number of strips
#10.7
Use the sum of a series of rectangles to find an upper and/or lower bound on the area under a curve.
#10.8
Use numerical methods to solve problems in context. | 472 | 1,739 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.859375 | 4 | CC-MAIN-2022-27 | latest | en | 0.881617 |
https://icexp.com/reader/the-awesome-bowling-robot-is-surely-fake-heres-how-to-tell/ | 1,566,633,975,000,000,000 | text/html | crawl-data/CC-MAIN-2019-35/segments/1566027319915.98/warc/CC-MAIN-20190824063359-20190824085359-00538.warc.gz | 493,541,314 | 12,891 | # The Awesome Bowling Robot Is Surely Fake. Here's How to Tell
It really doesn't matter if it's real or fake (but it's surely fake—even Snopes says so). This spinning robot arm that bowls just looks awesome. Even better, it's a great chance to talk about some physics. In fact, I would recommend reading this Twitter thread with physics teachers talking about the video. It's great.
But like I said, it's fake. So, why is it fake? Here are some things we can look at.
### Motion of the Ball in the Air
The ball goes from the robot arm all the way to the bowling pins without hitting the ground. After the ball leaves the arm, there is only the gravitational force pulling downward (assume the air resistance force is negligible). That's exactly the same as projectile motion in your introductory physics course. The key to this kind of motion is that the horizontal and vertical motion of the ball can be treated independently. Since there isn't a horizontal force on the bowling ball (after it leaves the throwing arm) it would travel with a constant horizontal velocity. In the vertical direction, the ball starts with zero vertical velocity and then accelerates downward at 9.8 meters per second per second (due to the gravitational force).
But that makes analysis a little simpler. If the ball is launched horizontally (that's at least how it appears), I can get the launch speed by measuring the time it takes to travel to the bowling pins. Oh, it's fast—that's why I'm going to use my favorite (and free) video analysis tool: Tracker Video Analysis.
From the video, the ball takes 0.767 seconds to travel the length of a bowling lane, a distance of 18.29 meters (60 feet). This gives a horizontal velocity of:
This launch velocity of 23.85 m/s (53 mph) is the launch speed of the ball only for the case in which it is shot out with no vertical velocity component. If we consider the vertical direction, the ball will drop for the same amount of time that it takes to travel down the lane. Since I know that time and the vertical acceleration, I can calculate this vertical drop.
Note that this assumes the starting y-position is zero meters and the starting y-velocity is zero m/s (oh, and g = 9.8 m/s2). This gives a vertical drop of 2.88 meters (9.4 feet). So yeah—that ball couldn't be launched horizontally with that speed and make it all the way to the pins without hitting the ground. You would either have to launch it with a faster speed or launch it at a non-zero angle. I will leave both of those calculations to you for homework.
### Motion of the Spinning Arm
I already have an estimate for the launch speed of the ball from the time it takes to get down the lane. But how does this compare to the rotation rate of the robot arm? Let's just measure it. Again, using video analysis I can look at the time it takes to rotate. In this case I marked the time when the ball is at the bottom of the rotation cycle. Then I can plot the angular position (in radians) as a function of time. Here's what I get.
You can see that the rotation rate does indeed increase as time goes on and the robot arm gets up to throwing speed. By looking at the slope of this line near the end, I can get a final rotation rate. This puts the angular velocity at 93.65 radians per second.
OK, but there is a connection between the angular velocity and the launch velocity. If the ball is moving around in a circle with a radius r with an angular velocity ω, then the following must be true.
If the bowling ball has a diameter of 21 cm, then the circular radius of motion from the robot arm would be 40.5 cm (from video analysis). That would put the ball's launch velocity at 42 m/s (94 mph)—which is quite a bit faster than the measured velocity based on the time to move down the lane.
Working backward from the previous launch velocity, I can find another value for the rotation speed. If the ball is launched with a speed of 23.85 m/s, then the robot arm would have an angular velocity of 53 radians per second.
### Forces to Hold the Ball
So, I now have two rotation rates for the robot arm. One value is based on the measured launch speed and the other value is based on the measured angular position of the arm. But either way, if there is a ball moving in a circle, there needs to be a force acting on it. That force is from those robot gripper finger things (I guess those are robot fingers).
Any object that moves in a circle has an acceleration. This is because acceleration is defined as a the time rate of change of velocity—and velocity is a vector. So just changing the direction of motion is indeed an acceleration. The value of this acceleration depends on both the rotation rate and the radius of the circle. This acceleration has the following magnitude.
How do you get an object to accelerate? You apply a force. In this case there must be a force pushing the ball toward the center of the circle to get it to accelerate. That force would have to be the product of the acceleration and the mass.
# fma
I can calculate the acceleration (based on both estimates for angular velocity) and I can approximate the ball mass at 4.5 kilograms (for a 10-pound ball). That would put the required robot force at either 1,138 newtons or 3,552 newtons (256 or 799 pounds). Even at the lower estimated force, this is fairly high. Oh sure, a robot could hold on to a ball with superhuman forces—but in this case it is just using frictional forces.
How about another homework question? Suppose the coefficient of static friction between the ball and the "fingers" is 0.8. What compressive force would need to be applied to hold on to the ball?
### Even MORE Questions
If you want to play with this video some more, here are some other things for you to consider:
• What about the timing of the release? Pick one of the angular velocities along with the correct angle of release so that the ball hits the pins without first hitting the floor. What if the ball is released 0.01 seconds too late or too early? How much would this delay change the trajectory of the ball?
• Speaking of release: Notice that in the video, the ball appears to be released at the top of the circular motion at a point where the ball should be traveling away from the bowling pins. Yes, that's crazy.
• Estimate the kinetic energy of the ball and the time it takes to get the ball up to maximum rotation speed. What power (in watts) does this require?
• Use the approximate ball speed and mass. Estimate how much energy should go to the pins during impact. If these pins were then shot straight up (they aren't), how high would they go?
• Is it reasonable to ignore air resistance for this situation?
• Estimate the force required to hold the robot down to the floor during this shot.
### Fake Shake
One more thing. One way to make a fake video is to use a real video and then add special effects. It's probably much easier to add special effects to a video that was recorded with a camera on a tripod. However, it might not seem as genuine to use a tripod as it would to have someone just holding a camera. But handheld cameras shake a little bit. So a fake video could add some fake camera shake after the special effects were added.
I think that's what happened here. If you plot the motion of the background for the BowlBot video, you get this.
But what if you repeat something like this with a real hand-held camera? You should get something like this:
In my experience, real camera shakes are much more random-looking and not so smooth. Actually, a camera shake is very similar to a random walk. OK, there is the possibility that there is real camera shake on the bowling video and then someone used software to smooth it out. But still, that shake doesn't look normal.
Even if that BowlBot is fake—it probably won't be too long before someone builds a real one.
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• 📩 Get even more of our inside scoops with our weekly Backchannel newsletter | 1,838 | 8,395 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.75 | 4 | CC-MAIN-2019-35 | longest | en | 0.940156 |
https://anova-learning.com/brockview/pie-chart-worksheets-for-grade-6-pdf.php | 1,679,866,228,000,000,000 | text/html | crawl-data/CC-MAIN-2023-14/segments/1679296946535.82/warc/CC-MAIN-20230326204136-20230326234136-00324.warc.gz | 119,170,983 | 11,054 | # Pie Chart Worksheets For Grade 6 Pdf
Summer Camp Activites Super Teacher Worksheets. The pie graph worksheets contain unique circle graphs on data interpretation, data conversion into fraction or percent, draw a pie diagram and more., Grade 15 Math Worksheets For 6th Graders, 5th Grade Math Worksheets And .. Circle Graphs in Black and White (A) 6th Grade Math Word Problems Worksheet : Kelpies 6th Grade Math Word Problems Worksheet - Math Worksheets7th Grade Math Word Problems Pie Graph Worksheets.
### Pie Chart Worksheets Ks2 Pdf – odmartlifestyle.com
Worksheet Creating Pie Charts #1. Pie Charts 1. Globesun is a travel company. Last year’s income from holidays to France, Spain, Italy and the USA are shown in the pie chart opposite. Income from these holidays totalled £12 000 000. (a) How much income did they get from holidays to France? (b) How much did they get from holidays to Spain? 2. Glendale High School has a roll, Grade 15 Math Worksheets For 6th Graders, 5th Grade Math Worksheets And .. Circle Graphs in Black and White (A) 6th Grade Math Word Problems Worksheet : Kelpies 6th Grade Math Word Problems Worksheet - Math Worksheets7th Grade Math Word Problems Pie Graph Worksheets.
We also have a bunch of pie charts worksheets with either with numbers or percentage as representations. These math pie graph exercises come with grade 6 ratio and percent calculations. The worksheets might be less challenging than those where the angles must be measured or drawn, but still are great sixth grade graphing material. All grade 6 09/05/2016В В· An explanation of how to make and use circle graphs. How to use a protractor to divide the circle, make line segments and angles. Wedges and sectors explained. #7.2.
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On this worksheet students must create a pie chart based on tabular data. Includes a partially complete calculation table as a prompt. Show Answers Creating Pie Charts #2 . Home > Printable Resources > Math Worksheets > Statistics & Probability > Creating Pie Charts #2; Hide Adverts----- Note: The Information above this point will not be sent to your printer -----The table below shows the What is a pie chart and how can they be used to present information? This lesson plan uses a video lesson to outline key facts about pie charts. An...
Solutions for the assessment Pie charts - reading and drawing 1) 12 2) 90. Title: Print Layout - Mathster Created Date: 20140105095133Z Suitable PDF printable data and graphs worksheets for children in the following grades : kindergarten, 1st grade, 2nd grade, 3rd grade, 4th grade, 5th grade, 6th grade and 7th grade. Worksheets cover the following graphs and data topics: sets and Venn diagrams, bar graphs, linear graphs, plotting graphs, reading data on graphs, interpreting
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### Grade 6 Math Chart tarleton.edu
Drawing pie charts worksheet Teaching Resources. We also have a bunch of pie charts worksheets with either with numbers or percentage as representations. These math pie graph exercises come with grade 6 ratio and percent calculations. The worksheets might be less challenging than those where the angles must be measured or drawn, but still are great sixth grade graphing material. All grade 6, printable grade 6 math worksheet Our math worksheets are made for math students in ESL or native speaking math classrooms and tutoring purposes. We use them in our own math classes and are convinced that our pdf worksheets could also be used in an online math education or ….
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### Reading Pie Charts Worksheet and Quiz & Worksheet Bar
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Interpreting Pie Charts Worksheet Tes Name : Score : Printable Math Worksheets @ www.mathworksheets4kids.com Jerry Walter Andrew Jason 120 30 90 10 Daniel 50 10 % Walter 50 % 50 3 10 The pie graph shows the information on the number of farm animals owned by some farm
## Math Worksheets on Graphs Data and Sets For Kids From
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### Grade 6 Math Chart tarleton.edu
Data Handling worksheet, Pie Chart worksheet, Math Reading Science Tests for Grades , Practice Sample Test, Free Online Worksheets On this worksheet students must create a pie chart based on tabular data. Includes a partially complete calculation table as a prompt. Show Answers Creating Pie Charts #2 . Home > Printable Resources > Math Worksheets > Statistics & Probability > Creating Pie Charts #2; Hide Adverts----- Note: The Information above this point will not be sent to your printer -----The table below shows the
The best source for free pie graph worksheets. Easier to grade, more in-depth and best of all... 100% FREE! Kindergarten, 1st Grade, 2nd Grade, 3rd Grade, 4th Grade, 5th Grade and more! Pie Chart. Displaying all worksheets related to - Pie Chart. Worksheets are Mathematics linear 1ma0 pie charts, Bar charts histograms line graphs pie charts, Gcse exam questions on pie charts grade d their, Pie charts, Pie graph, Summer camp activites, The pie graph shows the information on the number of farm, Rock restaurant surveyed a sample of customers on their.
On this worksheet students must create a pie chart based on tabular data. Includes a partially complete calculation table as a prompt. Show Answers Creating Pie Charts #2 . Home > Printable Resources > Math Worksheets > Statistics & Probability > Creating Pie Charts #2; Hide Adverts----- Note: The Information above this point will not be sent to your printer -----The table below shows the About This Quiz & Worksheet. This quiz/worksheet combo can be used to gauge your knowledge of bar graphs and pie charts. You'll be tested on reading bar graphs and pie charts and answering related
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15/11/2012В В· http://www.homecampus.com.sg : Learn how to read, make and interpret pie charts. Find notes at http://my.homecampus.com.sg/Learn/Primary-Grade-6/Data-Analysi... Grade 6 Pie Graphing Worksheets For Printable Download. Favorite Animal at the Zoo. Students create and interpret pie graphs based on animals.
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Grade 6 Pie Graphing Worksheets For Printable Download. Favorite Animal at the Zoo. Students create and interpret pie graphs based on animals. 6 The table shows some information about the favourite sport of some students. (a) A student is selected at random. i) Find the probability their favourite sport is netball. ii) Find the probability their favourite sport is not netball. (b) Draw an accurate pie chart to show this information. (Total for question 6 is 6 marks) Colour Frequency Angle
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About This Quiz & Worksheet. This quiz/worksheet combo can be used to gauge your knowledge of bar graphs and pie charts. You'll be tested on reading bar graphs and pie charts and answering related Solutions for the assessment Pie charts - reading and drawing 1) 12 2) 90. Title: Print Layout - Mathster Created Date: 20140105095133Z
Grade 6 Pie Graphing Worksheets For Printable Download. Favorite Animal at the Zoo. Students create and interpret pie graphs based on animals. printable grade 6 math worksheet Our math worksheets are made for math students in ESL or native speaking math classrooms and tutoring purposes. We use them in our own math classes and are convinced that our pdf worksheets could also be used in an online math education or …
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About This Quiz & Worksheet. This quiz/worksheet combo can be used to gauge your knowledge of bar graphs and pie charts. You'll be tested on reading bar graphs and pie charts and answering related A Resource for Free-standing Mathematics Qualifications Pie Charts The Nuffield Foundation 1 Photo-copiable A pie chart shows how something is divided into parts - it is a good way of showing the proportion (or fraction) of the data that is in each category. Work through this example:
Solutions for the assessment Pie charts - reading and drawing 1) 12 2) 90. Title: Print Layout - Mathster Created Date: 20140105095133Z Interpreting Pie Charts Worksheet Tes
Pie Chart. Showing top 8 worksheets in the category - Pie Chart. Some of the worksheets displayed are Mathematics linear 1ma0 pie charts, Bar charts histograms line graphs pie charts, Gcse exam questions on pie charts grade d their, Pie charts, Pie graph, Summer camp activites, The pie graph shows the information on the number of farm, Rock restaurant surveyed a sample of customers on their. Solutions for the assessment Pie charts - reading and drawing 1) 12 2) 90. Title: Print Layout - Mathster Created Date: 20140105095133Z
### Pie Graph Worksheets Free CommonCoreSheets
Pie Chart Worksheets Teacher Worksheets. What is a pie chart and how can they be used to present information? This lesson plan uses a video lesson to outline key facts about pie charts. An..., Bar Graph Worksheets. Read, create, and interpret bar graphs with these worksheets. Box Plots (Box-and-Whisker Plots) Create box plots on a number line using the values for Q1, median, Q3, minimum, and maximum. (Approx grade levels: 6, 7, 8) Line Graph Worksheets. Read and create line graphs with these worksheets. Line Plot (Dot Plot) Worksheets.
Grade 6 Math Chart tarleton.edu. Pie Chart. Displaying all worksheets related to - Pie Chart. Worksheets are Mathematics linear 1ma0 pie charts, Bar charts histograms line graphs pie charts, Gcse exam questions on pie charts grade d their, Pie charts, Pie graph, Summer camp activites, The pie graph shows the information on the number of farm, Rock restaurant surveyed a sample of customers on their., The best source for free pie graph worksheets. Easier to grade, more in-depth and best of all... 100% FREE! Kindergarten, 1st Grade, 2nd Grade, 3rd Grade, 4th Grade, 5th Grade and more!.
### Pie Chart Worksheets Lesson Worksheets
A Resource for Free-standing Mathematics Qualifications. On this worksheet students must create a pie chart based on tabular data. Includes a partially complete calculation table as a prompt. Show Answers Creating Pie Charts #2 . Home > Printable Resources > Math Worksheets > Statistics & Probability > Creating Pie Charts #2; Hide Adverts----- Note: The Information above this point will not be sent to your printer -----The table below shows the https://en.wikipedia.org/wiki/Pie_chart On this worksheet students must create a pie chart based on tabular data. Includes a partially complete calculation table as a prompt. Show Answers Creating Pie Charts #2 . Home > Printable Resources > Math Worksheets > Statistics & Probability > Creating Pie Charts #2; Hide Adverts----- Note: The Information above this point will not be sent to your printer -----The table below shows the.
Grade 6 Pie Graphing Worksheets For Printable Download. Favorite Animal at the Zoo. Students create and interpret pie graphs based on animals. We also have a bunch of pie charts worksheets with either with numbers or percentage as representations. These math pie graph exercises come with grade 6 ratio and percent calculations. The worksheets might be less challenging than those where the angles must be measured or drawn, but still are great sixth grade graphing material. All grade 6
9+ Reading Pie Charts Worksheetinterpreting pie charts worksheet, interpreting pie charts worksheet ks3, interpreting pie charts worksheet pdf, interpreting pie 6 The table shows some information about the favourite sport of some students. (a) A student is selected at random. i) Find the probability their favourite sport is netball. ii) Find the probability their favourite sport is not netball. (b) Draw an accurate pie chart to show this information. (Total for question 6 is 6 marks) Colour Frequency Angle
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PIE CHART WORKSHEETS - GRADES 4, 5 AND 6. Subject. Math, Graphing, Other (Math) Grade Levels. 4 th, 5 th, 6 th, Homeschool. Resource Type. Worksheets. Product Rating. 4.0 (4 Ratings) File Type. PDF (1 MB 12 pages) Product Description. Using British Football Clubs and Hogwarts as well as other examples, learn all about Pie Charts. How to draw an accurate pie chart:-• Find the total of the interpreting pie charts worksheet pdf, interpreting pie charts worksheet tes, interpreting pie charts worksheet ks3, reading pie charts worksheet ks3, reading pie
Name : Score : Printable Math Worksheets @ www.mathworksheets4kids.com Jerry Walter Andrew Jason 120 30 90 10 Daniel 50 10 % Walter 50 % 50 3 10 The pie graph shows the information on the number of farm animals owned by some farm Lesson Plan 3: Pie Graphs PIE GRAPHS Faculty Name: Leslie Patten School: Cypress Park Elementary Grade Level: 5th grade 1 Teaching objective(s) The students will gather, organize, and display data in an appropriate pie (circle) graph. 2 Instructional Activities Tell the students, “Today we will be learning how to gather, organize, and display data using pie graphs.” Ask, “Can anyone tell
Step 3: Distribute the Scholastic News: Read a Pie Chart Worksheet printable. Discuss that a chart represents a whole — in this case, the world's oil supplies. Encourage students to talk about which countries have the largest slice of the pie. Discuss why the … 9+ Reading Pie Charts Worksheetinterpreting pie charts worksheet, interpreting pie charts worksheet ks3, interpreting pie charts worksheet pdf, interpreting pie
Solutions for the assessment Pie charts - reading and drawing 1) 12 2) 90. Title: Print Layout - Mathster Created Date: 20140105095133Z Grade 15 Math Worksheets For 6th Graders, 5th Grade Math Worksheets And .. Circle Graphs in Black and White (A) 6th Grade Math Word Problems Worksheet : Kelpies 6th Grade Math Word Problems Worksheet - Math Worksheets7th Grade Math Word Problems Pie Graph Worksheets
Pie Chart worksheet, Math Reading Science Tests for Grades , Practice Sample Test, Free Online Worksheets Step 3: Distribute the Scholastic News: Read a Pie Chart Worksheet printable. Discuss that a chart represents a whole — in this case, the world's oil supplies. Encourage students to talk about which countries have the largest slice of the pie. Discuss why the …
reading pie charts worksheet grade 6, interpreting pie charts worksheet, interpreting pie charts worksheet tes, reading pie charts worksheet, reading pie charts 6 The table shows some information about the favourite sport of some students. (a) A student is selected at random. i) Find the probability their favourite sport is netball. ii) Find the probability their favourite sport is not netball. (b) Draw an accurate pie chart to show this information. (Total for question 6 is 6 marks) Colour Frequency Angle
The pie graph worksheets contain unique circle graphs on data interpretation, data conversion into fraction or percent, draw a pie diagram and more. that the learners study Data Handling from Grade 4 onwards. In the case where learners in Grades 5, 6 or 7 have not had any prior experience of data handling at school, the teacher should choose appropriate activities from those recommended for the previous grades. GRADE 4 Car Colours
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This page has several pie graph worksheets. The "Basic Pie Graphs" require students to have a basic understanding of fractions. The "Advanced Pie Graphs" require students to understand percentages./p> Basic Pie Graphs. Summer Camp Pie Graph FREE . Use the information in the summer camp pie graph to answer the questions. Requires knowledge of fractions. (Approx. grade levels 2-4) 4th through Pie Chart worksheet, Math Reading Science Tests for Grades , Practice Sample Test, Free Online Worksheets
Pie Chart Reading. Showing top 8 worksheets in the category - Pie Chart Reading. Some of the worksheets displayed are Pie charts, The pie graph shows the information on the number of farm, Rock restaurant surveyed a sample of customers on their, Pie graph, Favorite sports graph, Mathematics linear 1ma0 pie charts, Graphs and charts, Grade 4 fractions work. Interpreting Pie Charts Worksheet Tes
that the learners study Data Handling from Grade 4 onwards. In the case where learners in Grades 5, 6 or 7 have not had any prior experience of data handling at school, the teacher should choose appropriate activities from those recommended for the previous grades. GRADE 4 Car Colours This page has several pie graph worksheets. The "Basic Pie Graphs" require students to have a basic understanding of fractions. The "Advanced Pie Graphs" require students to understand percentages./p> Basic Pie Graphs. Summer Camp Pie Graph FREE . Use the information in the summer camp pie graph to answer the questions. Requires knowledge of fractions. (Approx. grade levels 2-4) 4th through
Step 3: Distribute the Scholastic News: Read a Pie Chart Worksheet printable. Discuss that a chart represents a whole — in this case, the world's oil supplies. Encourage students to talk about which countries have the largest slice of the pie. Discuss why the … Circle Graph Worksheets 6th Grade Kcvah Best Of Grade 6 Pie And Circle Graph Worksheets With Sixth Grade Math.So, if you want to get this wonderful image about Circle Graph Worksheets 6th Grade Kcvah Best Of Grade 6 Pie And Circle Graph Worksheets With Sixth Grade Math, just click save button to save this images to your computer.
ANSWER KEY 1 2 1 4 canoeing camp fires horseback riding Super Teacher Worksheets - www.superteacherworksheets.com Summer Camp Activites horseback riding crafts camp fire canoeing A group of kids spent a week at Big Tree Summer Camp. 09/05/2016В В· An explanation of how to make and use circle graphs. How to use a protractor to divide the circle, make line segments and angles. Wedges and sectors explained. #7.2.
Pie Charts 1. Globesun is a travel company. Last year’s income from holidays to France, Spain, Italy and the USA are shown in the pie chart opposite. Income from these holidays totalled £12 000 000. (a) How much income did they get from holidays to France? (b) How much did they get from holidays to Spain? 2. Glendale High School has a roll The best source for free pie graph worksheets. Easier to grade, more in-depth and best of all... 100% FREE! Kindergarten, 1st Grade, 2nd Grade, 3rd Grade, 4th Grade, 5th Grade and more! | 7,115 | 31,721 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.15625 | 3 | CC-MAIN-2023-14 | latest | en | 0.855172 |
https://www.media4math.com/2.NBT.B.6 | 1,679,766,417,000,000,000 | text/html | crawl-data/CC-MAIN-2023-14/segments/1679296945368.6/warc/CC-MAIN-20230325161021-20230325191021-00003.warc.gz | 999,190,536 | 13,004 | ## CCSS.MATH.CONTENT.2.NBT.B.6: Add up to four two-digit numbers using strategies based on place value and properties of operations.
There are 110 resources.
Title Description Thumbnail Image Curriculum Topic
## Math Clip Art--Geometry Concepts--Geometry Tools--Number Line Set 1
Math Clip Art--Geometry Concepts--Geometry Tools--Number Line Set 1
This is part of a collection of math clip art images about selected topics in Geometry. Also look at our Geometry Basics math clip art collection.
Exploring Coordinate Systems, Coordinate Systems
## Math Clip Art--Geometry Concepts--Geometry Tools--Number Line Set 2
Math Clip Art--Geometry Concepts--Geometry Tools--Number Line Set 2
This is part of a collection of math clip art images about selected topics in Geometry. Also look at our Geometry Basics math clip art collection.
Exploring Coordinate Systems, Coordinate Systems
## Worksheet: Adding Place Value (1000s), Worksheet 1
Worksheet: Adding Place Value (1000s), Worksheet 1
This is part of a collection of math worksheets on the topic of adding within 1000 using place value.
Place Value
## Worksheet: Adding Place Value (1000s), Worksheet 4
Worksheet: Adding Place Value (1000s), Worksheet 4
This is part of a collection of math worksheets on the topic of adding within 1000 using place value.
Place Value
## Worksheet: Adding Place Value (1000s), Worksheet 5
Worksheet: Adding Place Value (1000s), Worksheet 5
This is part of a collection of math worksheets on the topic of adding within 1000 using place value.
Place Value
## Worksheet: Adding Two-Digit Numbers, Worksheet 1
Worksheet: Adding Two-Digit Numbers, Worksheet 1
This is part of a collection of math worksheets on the topic of adding two-digit numbers.
## Worksheet: Adding Two-Digit Numbers, Worksheet 2
Worksheet: Adding Two-Digit Numbers, Worksheet 2
This is part of a collection of math worksheets on the topic of adding two-digit numbers.
## Worksheet: Adding Two-Digit Numbers, Worksheet 3
Worksheet: Adding Two-Digit Numbers, Worksheet 3
This is part of a collection of math worksheets on the topic of adding two-digit numbers.
## Worksheet: Adding Two-Digit Numbers, Worksheet 4
Worksheet: Adding Two-Digit Numbers, Worksheet 4
This is part of a collection of math worksheets on the topic of adding two-digit numbers.
## Worksheet: Adding Two-Digit Numbers, Worksheet 5
Worksheet: Adding Two-Digit Numbers, Worksheet 5
This is part of a collection of math worksheets on the topic of adding two-digit numbers.
## Worksheet: Adding Two-Digit Numbers--Mixed Set 1
Worksheet: Adding Two-Digit Numbers--Mixed Set 1
This is part of a collection of math worksheets on the topic of adding two-digit numbers.
## Worksheet: Adding Two-Digit Numbers--Mixed Set 10
Worksheet: Adding Two-Digit Numbers--Mixed Set 10
This is part of a collection of math worksheets on the topic of adding two-digit numbers.
## Worksheet: Adding Two-Digit Numbers--Mixed Set 11
Worksheet: Adding Two-Digit Numbers--Mixed Set 11
This is part of a collection of math worksheets on the topic of adding two-digit numbers.
## Worksheet: Adding Two-Digit Numbers--Mixed Set 12
Worksheet: Adding Two-Digit Numbers--Mixed Set 12
This is part of a collection of math worksheets on the topic of adding two-digit numbers.
## Worksheet: Adding Two-Digit Numbers--Mixed Set 13
Worksheet: Adding Two-Digit Numbers--Mixed Set 13
This is part of a collection of math worksheets on the topic of adding two-digit numbers.
## Worksheet: Adding Two-Digit Numbers--Mixed Set 14
Worksheet: Adding Two-Digit Numbers--Mixed Set 14
This is part of a collection of math worksheets on the topic of adding two-digit numbers.
## Worksheet: Adding Two-Digit Numbers--Mixed Set 15
Worksheet: Adding Two-Digit Numbers--Mixed Set 15
This is part of a collection of math worksheets on the topic of adding two-digit numbers.
## Worksheet: Adding Two-Digit Numbers--Mixed Set 16
Worksheet: Adding Two-Digit Numbers--Mixed Set 16
This is part of a collection of math worksheets on the topic of adding two-digit numbers.
## Worksheet: Adding Two-Digit Numbers--Mixed Set 17
Worksheet: Adding Two-Digit Numbers--Mixed Set 17
This is part of a collection of math worksheets on the topic of adding two-digit numbers.
## Worksheet: Adding Two-Digit Numbers--Mixed Set 18
Worksheet: Adding Two-Digit Numbers--Mixed Set 18
This is part of a collection of math worksheets on the topic of adding two-digit numbers.
## Worksheet: Adding Two-Digit Numbers--Mixed Set 19
Worksheet: Adding Two-Digit Numbers--Mixed Set 19
This is part of a collection of math worksheets on the topic of adding two-digit numbers.
## Worksheet: Adding Two-Digit Numbers--Mixed Set 2
Worksheet: Adding Two-Digit Numbers--Mixed Set 2
This is part of a collection of math worksheets on the topic of adding two-digit numbers.
## Worksheet: Adding Two-Digit Numbers--Mixed Set 20
Worksheet: Adding Two-Digit Numbers--Mixed Set 20
This is part of a collection of math worksheets on the topic of adding two-digit numbers.
## Worksheet: Adding Two-Digit Numbers--Mixed Set 3
Worksheet: Adding Two-Digit Numbers--Mixed Set 3
This is part of a collection of math worksheets on the topic of adding two-digit numbers. | 1,191 | 5,264 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.390625 | 3 | CC-MAIN-2023-14 | latest | en | 0.661149 |
http://www.learnalberta.ca/content/memg/Division02/Estimation/index.html | 1,508,225,859,000,000,000 | text/html | crawl-data/CC-MAIN-2017-43/segments/1508187820930.11/warc/CC-MAIN-20171017072323-20171017092323-00554.warc.gz | 493,945,094 | 1,867 | Estimation
Definition
Estimation is the approximation of a number, calculation, quantity, or measurement.
Approximation of a Number
The process used to approximate a number is called rounding.
Approximation of a Calculation
A process used to simplify a calculation by rounding the numbers involved in a calculation.
If an approximate answer to the sum 470 + 310 is required, one could round each of the numbers to the nearest hundred to estimate the sum. 470 could be rounded to 500, and 310 could be rounded to 300. The resulting estimate of the sum would be 800, where the actual sum would be 780.
As the rounding becomes greater, the approximation or estimate becomes less precise.
Approximation of a Quantity
An educated guess as to the number of elements in a group.
Estimate how many candies are on the necklace below, then count the candies to see how close your estimate was.
Approximation of a Measurement
A visual approximation the length, area, volume or other measurable attribute of an object. | 210 | 1,018 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.3125 | 3 | CC-MAIN-2017-43 | latest | en | 0.912971 |
http://openstudy.com/updates/50bcbbdfe4b0017ef6257272 | 1,444,238,821,000,000,000 | text/html | crawl-data/CC-MAIN-2015-40/segments/1443737875203.46/warc/CC-MAIN-20151001221755-00222-ip-10-137-6-227.ec2.internal.warc.gz | 230,750,887 | 10,689 | ## x1xofxaxkndx 2 years ago ***edited*** how do i do this??? 2x + 2 = 10
1. rizwan_uet
put constants on one side and see what you get
2. x1xofxaxkndx
constants ??
3. x1xofxaxkndx
do u guys know?
4. amistre64
"what" + 2 = 10?
5. x1xofxaxkndx
8
6. amistre64
then 2x has to equal 8 2 times "what" = 8 ?
7. x1xofxaxkndx
4
8. amistre64
good, then x has to be 4
9. x1xofxaxkndx
i get it lol thanks
10. J.A.P.A.N
simple 2x+2=10 so you look at the 2 you are going to subtract it from itself so +2-2=0 then -2-10=8 so bring it down 2x+8 then divide so the answer is 4
11. amistre64
if you wanna go the algebra route: 2x + 2 = 10 ; subtract 2 from each side -2 -2 ----------- 2x = 8 ; divide off the 2 /2 /2 ----------- x = 4 | 305 | 737 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.859375 | 4 | CC-MAIN-2015-40 | longest | en | 0.68715 |
https://www.physicsforums.com/threads/resultant-of-3-vectors-along-the-sides-of-an-equilateral-triangle.822278/ | 1,726,879,593,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725701425385.95/warc/CC-MAIN-20240920222945-20240921012945-00225.warc.gz | 856,620,338 | 18,906 | # Resultant of 3 vectors along the sides of an equilateral triangle
• cr7einstein
In summary, the problem involves finding the resultant of three parallel forces with magnitudes of 10N, 20N, and 30N acting on a point in the directions of the sides of an equilateral triangle. The answer cannot be zero as the triangle only represents the direction of the forces, not their magnitudes. The correct method involves drawing the forces as a chain and calculating the resultant using the x and y components.
cr7einstein
## Homework Statement
Hi all,
It is a homework problem, but I really don't quite understand the question. It reads-
"3 forces of magnitudes 10N, 20N, and 30N acting on a point are parallel to the sides of an equilateral triangle, taken in order. Find their resultant"
## The Attempt at a Solution
What I think is, as the resultant of 3 vectors forming a closed figure is 0, the answer should be 0.But the answer is given as $$10 \sqrt{3}$$. How?
Draw a picture
Compute x and y components of each vector
Add x components to get x component of sum
Add y components to get y component of sum
If needed, put resultant back into magnitude angle form with Pythagoras and atan
Thanks.
The problem is I don't know how to draw the diagram, and why should the resultant not be zero? It does form a closed figure, doesn't it?
Also, aren't there 3 vectors? SO, am I supposed to take one of them along the X axis?
The resultant would only be zero if all three forces had the same magnitude.
Draw F1 along the x axis.
Draw F2 with a 120 deg angle wrt the +x axis.
Draw F3 with a 210 deg angle wrt the +x axis.
+1 to that.
Note the question says the vectors are parallel to the sides of an equilateral triangle not that they are arranged in a triangle.
cr7einstein said:
What I think is, as the resultant of 3 vectors forming a closed figure is 0
You are confusing two concepts. If you take the forces acting at a point and draw them as a chain in which:
• The head end of one touches the tail of the next
• Each line is parallel to the force it represents
• The length of each line is proportional to the magnitude of the force
then the line from the tail of the first in the chain to the head of the last in the chain represents the resultant. In particular, if it forms a closed polygon then the resultant is zero.
But the equilateral triangle here does not represent the force magnitudes. It is only telling you the directions of the forces. If you try to draw a triangle in which all the angles are 60 degrees but you make the lines different lengths then it won't close.
## 1. What is the formula for calculating the resultant of 3 vectors along the sides of an equilateral triangle?
The formula for calculating the resultant of 3 vectors along the sides of an equilateral triangle is R = A + B + C, where R is the resultant vector and A, B, and C are the individual vectors along the sides of the triangle.
## 2. How do you determine the direction of the resultant vector?
The direction of the resultant vector can be determined by using the law of cosines and trigonometry. The angle between the resultant vector and the first vector can be calculated using the formula cosθ = (A² + R² - B²) / (2AR), where θ is the angle and A and B are the magnitudes of the first and second vectors, respectively. The direction of the resultant vector will be in the same direction as the first vector.
## 3. Can the resultant of 3 vectors along the sides of an equilateral triangle be negative?
No, the resultant of 3 vectors along the sides of an equilateral triangle cannot be negative. Vectors are represented by both magnitude and direction, and the resultant vector will always have a positive magnitude and direction in the same direction as the first vector.
## 4. How does the angle between the vectors affect the magnitude of the resultant vector?
The angle between the vectors can affect the magnitude of the resultant vector. If the vectors are in the same direction, the magnitude of the resultant vector will be equal to the sum of the magnitudes of the individual vectors. However, if the vectors are not in the same direction, the magnitude of the resultant vector will be less than the sum of the individual vectors.
## 5. Can the resultant of 3 vectors along the sides of an equilateral triangle be greater than the sum of the individual vectors?
Yes, the resultant of 3 vectors along the sides of an equilateral triangle can be greater than the sum of the individual vectors. This can occur when the vectors are not in the same direction and the angle between them is less than 60 degrees. In this case, the magnitude of the resultant vector will be greater than the sum of the individual vectors.
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2K | 1,160 | 4,936 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.15625 | 4 | CC-MAIN-2024-38 | latest | en | 0.955207 |
https://compphys.go.ro/how-to-solve-a-quantum-many-body-problem/ | 1,638,035,514,000,000,000 | text/html | crawl-data/CC-MAIN-2021-49/segments/1637964358208.31/warc/CC-MAIN-20211127163427-20211127193427-00453.warc.gz | 256,597,101 | 27,355 | # How to solve a quantum many body problem
### Introduction
Quite a bit of time passed since my last post on this blog. I had a visit to the sunny Spain, I switched to a double-surface hang glider and I had to take a little care of my firm. Despite those things, I did a little bit of work for the blog, but it took me a little longer than I anticipated. This is a first post of ‘theory’ before presenting the code I implemented. If you want to take a look before having the description available, here it is: a Hartree-Fock program1. I posted the project on GitHub a couple of weeks ago, but I just didn’t have the patience to start writing about it.
This post will be more general, not addressing the project much, but I hope I’ll refer it in more than one post, so here it is. It’s just an opportunity to collect together some links for those that need more info than the one that will be exposed in the next post, than a detailed description.
### The Problem
The problem appears to be simple, you have a bunch of particles, you want to see what happens to them. They might be some protons and neutrons in a nucleus, or a nucleus and the electrons in an atom, or more than one nucleus and more electrons forming a molecule. Or even larger systems, forming nanostructures or even crystals. The problem turns out to be very complex because they are interacting. A problem with more than two particles interacting – even with relativity dropped – cannot be solved exactly, you’ll have to resort to simplifications in order to obtain approximate solutions. The first simplification is to drop out relativity. With the Schrödinger equation, one can take relativity into account, but I’ll simply ignore it for now. The Hamiltonian for such a system is:
$\hat{H}=\hat{K} + \hat{V}$
where K is the kinetic energy term and V is the potential energy term. The potential energy can be a sum of internal potential energy and external potential energy, because of an external field. The external field might be time dependent, which would complicate things a bit. From now on, unless explicitly stated, I’ll consider the external potential to be zero. This is the second simplification. Now, let’s switch to the equation that deals with such a system.
### Schrödinger equation
With no more words, here it is:
$i\hbar\frac{\partial\Psi}{\partial t}\Psi=\hat{H}\Psi$
where:
$\hat{H}=\frac{\hat{p}^2}{2m}+\hat{V}$
I deliberately did not detail yet the dependency of $\Psi$ or the operators, because their form depends on the particular representation. You often meet them in the position representation, but they can be also given in the momentum representation (or other representation!). In position representation, $\Psi$ is a function of time and all particles positions it describes. More about representations, maybe later.
Don’t forget about the simplifications we use, if you want to consider an external magnetic field, too, for example, check out the Schrödinger–Pauli equation.
You may ‘justify’ the equation by taking a plane wave and hit it with time and position partial derivatives, trying to form the operators and arrange them in such a way to get the wave equation. You’ll also need to consider the de Broglie hypothesis, $p=\hbar k$ together with Planck-Einstein relation, $E=\hbar \omega$. This should not be considered a derivation! For another nice justification, you may check out the Feynman lectures2.
The equation is a linear equation. This means that if you have two solutions for the equation, any linear combination of them is also a solution. So it’s not only a plane wave that is a solution for the equation, but you may also compose wave packets out of them that are also solutions.
If the Hamiltonian does not depend explicitly on time, one can use separation of variables to find stationary solutions of the equation. One obtains the time independent Schrödinger equation:
$\hat{H}\Psi = E \Psi$
Don’t forget that the wave function still evolves in time, the time evolution operator being $e^{-\frac{i\hat{H}t}{\hbar}}$ that for an energy eigenstate becomes $e^{-\frac{iEt}{\hbar}}$. Don’t forget that a superposition of such states is also a solution to time dependent equation, too.
Since we got rid of external potentials (and that includes those that vary in time) wanting to simplify the problem as much as possible, we’re from now on considering the time independent equation, the time dependency being trivial. We’re going to use another simplification, to get rid of all sorts of constants that complicate the formulae, that is, we’re using the atomic units.
The Hamiltonian for our bunch of particles being nuclei and electrons in a molecule is:
$\hat{H} = \sum\limits_{i=1}^{N} \hat{p}_i^2/2 + \sum\limits_{i=1}^{M} \hat{P}_i^2/(2 M_i) + \frac{1}{2} \sum\limits_{i,j=1;i\neq j}^{N}\frac{1}{|\vec{r}_i-\vec{r}_j|} - \sum\limits_{i=1}^{N}\sum\limits_{j=1}^{M}\frac{Z_j}{|\vec{r}_i-\vec{R}_j|} + \frac{1}{2} \sum\limits_{i,j=1;i\neq j}^{M}\frac{Z_i Z_j}{|\vec{R}_i-\vec{R}_j|}$
N is the number of electrons, M the number of nuclei, Z is the atomic number. The first two terms are the kinetic energy terms for electrons and nuclei, respectively, the next ones being in order: the electron-electron repulsion potential energy, the electron-nucleus attraction energy term and the nucleus-nucleus repulsion energy term. The interaction is nothing more than the plain old Coulomb interaction.
It looks complicated and it’s even way more difficult to solve than the looks might suggest. For a single nucleus and one electron only it can be solved analytically but even that is not exactly easy. Having a bunch of electrons and nuclei creates a problem that is analytically intractable. Even if you try to solve it as it is using some naive numerical approach, it’s not easy solvable even for four particles. Can we simplify it even more?
### Born–Oppenheimer approximation
Yes we can, but this will only approximate the solution to the complete equation. The approximation turns out to be very good in many cases, so here it is. It is based on the observation that the electrons are very light compared with nuclei. Even compared with a single proton, the electron is more than 1800 times lighter. As a consequence, the nuclei ‘move’ much slower than the electrons, the electronic cloud adjusting to the nuclei configuration almost instantly. This allows separation of the motion of nuclei from the Schrödinger equation, you may treat them separately even using a classical approach. With the Born–Oppenheimer approximation the Hamiltonian we’ll have to solve first becomes:
$\hat{H} = \sum\limits_{i=1}^{N} \hat{p}_i^2/2 + \frac{1}{2} \sum\limits_{i,j=1;i\neq j}^{N}\frac{1}{|\vec{r}_i-\vec{r}_j|} - \sum\limits_{i=1}^{N}\sum\limits_{j=1}^{M}\frac{Z_j}{|\vec{r}_i-\vec{R}_j|}$
that is, we eliminated the nuclei kinetic energy term and the nucleus-nucleus repulsion energy term, which remain to be handled separately. We have now only the electrons kinetic energy term, the electron-electron interaction term and the electron-nucleus interaction term.
### Representations, notations, formalism and so on…
Obviously I cannot enter into details here, I cannot write an entire quantum physics book in a blog post. There are plenty of books, there are plenty of resources on internet, too. I already pointed the Feynman lectures vol III2, I will point out another resource, chosen arbitrarily: Quantum Mechanics, by Richard Fitzpatrick3.
There are (or will be, hopefully) posts on this blog that might require you to be familiar with the Dirac notation, with various representations, the different ‘pictures’ (Schrödinger picture, Heisenberg picture, interaction picture), second quantization, Hilbert space, Fock space and so on… Unfortunately you’ll either have to be familiar with those – in which case there is a low probability that you need to read this post 🙂 – or be willing to look yourself into them, I cannot explain them all here. I’m trying to keep things simple and give links to more details but this is not always possible.
When I started writing this post I wanted to give some details in this paragraph about the relationship between matrix mechanics and the wave formulation and also about some things linked above and maybe more, but I realized that it would be way too much to write than I’m willing and have patience to do, so I’ll let it as it is. Maybe some other time… but I must warn you that you’ll see a lot of matrices in the quantum mechanics related programs (and not only there, the matrix representation is very useful).
### Exact diagonalization
This is another way one could try to attack the problem. Unfortunately it’s not very useful for complex systems, because of the exponential increase of the vector space. That does not mean it’s not useful, a quick google search might reveal a lot of hits. This is just the first hit I got: Exact Diagonalization, being a part of a Quantum Simulation course4. I thought that at least the method should be mentioned here.
### Variational principle
Ok, so we reached the important part, the variational principle. It’s used not only in the Hartree-Fock method about which I already have the program on GitHub1, but in many other cases, for example in Variational Quantum Monte Carlo or Density Functional Theory. I intend to make some programs that use the two mentioned methods for this blog, by the way.
This principle is so important for this post that the image on top contains an important formula. It’s the energy functional, with the wave vector assumed normalized. I think that the Wikipedia page is quite a good start, but anyway, I’ll detail a part here, too. Let’s start with the right hand side of the energy functional:
$\langle\Psi|\hat{H}|\Psi\rangle = \sum\limits_{i, j} \langle\Psi|\Psi_i\rangle\langle\Psi_i|\hat{H}|\Psi_j\rangle\langle\Psi_j|\Psi\rangle$
There is nothing fancy going on, just the unit operator being inserted twice. It’s the superposition principle in action, if you have a particular basis for your vector space, you may decompose/write your vector using its projections on the vectors that form the basis:
$|\Psi\rangle = \sum\limits_i c_i|\Psi_i\rangle$
with the component along a particular basis vector being not surprisingly, the projection onto that vector (that is, the scalar product between them):
$c_i = \langle\Psi_i|\Psi\rangle$
So, the Hamiltonian acting on an eigenvector gives the eigenvalue (by the way, we use the energy eigenvectors as basis):
$\langle\Psi|\hat{H}|\Psi\rangle = \sum\limits_{i, j} \langle\Psi|\Psi_i\rangle E_j \langle\Psi_i|\Psi_j\rangle\langle\Psi_j|\Psi\rangle$
But the eigenvectors are orthogonal, so:
$\langle\Psi|\hat{H}|\Psi\rangle = \sum\limits_i \langle\Psi|\Psi_i\rangle E_i \langle\Psi_i|\Psi\rangle = \sum\limits_i E_i |\langle\Psi_i|\Psi\rangle |^2 = \sum\limits_i E_i | c_i |^2$
Obviously, using the smallest energy from the spectrum, that is, the ground state energy, we find:
$\langle\Psi|\hat{H}|\Psi\rangle = \sum\limits_i E_i |c_i|^2 \geq \sum\limits_i E_0 |c_i|^2$
The ground state energy is just a constant, it can be taken out of the sum and using the fact that the wave vector is normalized, one gets:
$\langle\Psi|\hat{H}|\Psi\rangle \geq E_0$
Ok, but what does it mean? It means that no matter what wave function we try, we’ll get an energy that is bigger than the ground state energy (or equal, if we manage to pick up the ground state – or a ground state, if there are more of them).
If we try one at random, we get one expectation value. By some method we pick another wave function and calculate the expectation value for it. If it’s smaller, we drop the first guess and keep the new one. We can repeat the trials until hopefully we are close enough to the ground state. How we pick the state and how we modify it depends on the particular method and I’ll detail it for the specific program.
I should also mention here that you could derive the time independent Schrödinger equation by using variational calculus and imposing that a stationary state has the energy variation vanishing in the first order if the wave vector suffers a small variation $\delta \Psi$ from the stationary state.
### Perturbation theory
I want to mention perturbation theory here, because I might use it in a future project for this blog. Not only that, but related with the following subject, Hartree-Fock, it can be used for a Post Hartree-Fock improvement, see Møller–Plesset perturbation theory.
Since we assumed that the Hamiltonian we have to deal with is not explicitly time dependent, I’ll let aside for now the time-dependent perturbation theory. If ever needed for this blog, I’ll detail it there.
The time independent perturbation theory is detailed well on the linked Wikipedia page, I want to emphasis here just the main ideas. In the case you have a Hamiltonian that you cannot solve, but you can write it as a sum of a Hamiltonian that can be solved (either exactly or by some approximation method) and a small term, then you can use the perturbation theory to get an approximate solution for the whole Hamiltonian. You need to expand both the eigenstates and eigenvalues of the full Hamiltonian in Taylor series at the unperturbed eigenstate/eigenvalue and substitute them into the time independent Schrödinger equation. Expanding and identifying the terms that have the same power allows you to get the correction terms. Obviously one has to stop at a certain order, when the approximate solution is close enough to the real one.
### Conclusion
We ended up with a Hamiltonian which is still quite complex and very hard to solve even for simple systems. If we could simplify somehow the interaction terms we could try to solve it, but as it is it’s still very difficult. There are various ways of doing that, but that’s a subject for other posts.
So that’s it for now. The next post will be about Hartree-Fock theory. Then another one will follow that will present the program1
1. A Hartree-Fock program The project on GitHub.
2. Feynman lectures Vol III, Chapter 16, The Dependence of Amplitudes on Position.
3. Quantum Mechanics by Richard Fitzpatrick.
4. Quantum Simulation course at Institute for Theoretical Physics – Weimer Group, Lecturer: Dr. Hendrik Weimer.
5. Introduction to Electronic Structure Calculations: The variational principle by Ivo Filot.
This site uses Akismet to reduce spam. Learn how your comment data is processed. | 3,433 | 14,491 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 40, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.96875 | 3 | CC-MAIN-2021-49 | longest | en | 0.948995 |
https://www.enotes.com/homework-help/set-50-data-values-has-mean-18-and-variance-4-368268 | 1,632,526,967,000,000,000 | text/html | crawl-data/CC-MAIN-2021-39/segments/1631780057584.91/warc/CC-MAIN-20210924231621-20210925021621-00600.warc.gz | 781,890,735 | 18,174 | a set of 50 data values has a mean of 18 & variance of 4 find the probability of a data value <20 find the standard score z for data value = 20 please explain and show work
Expert Answers
We are given a set with n=50, `bar(x)=18` , and `sigma=4` .
Find the probability that a data value is less than 20:
Convert 20 to a `z` score:
`z=(20-18)/4=0.5`
Then `P(x<20)=P(z<0.50)=.6915` or 69.15% will be less than 20
****************************************************
Since you were given n, I wonder if your actual...
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We are given a set with n=50, `bar(x)=18` , and `sigma=4` .
Find the probability that a data value is less than 20:
Convert 20 to a `z` score:
`z=(20-18)/4=0.5`
Then `P(x<20)=P(z<0.50)=.6915` or 69.15% will be less than 20
****************************************************
Since you were given n, I wonder if your actual question is about a sample mean, not an actual data value. If that is the case, the question is what is the probability of obtaining a sample mean less than 20 if the sample size is 50:
Convert 20 to a z-score; note that since this is from a sample we use `z=(x-mu)/(sigma/sqrt(n))` :
`z=(20-18)/(4/sqrt(50))=3.54`
Then `P(x<20)=P(z<3.54)` From a standard normal table we find `P(z<.54)=.9998` (Most tables stop at z=3.5 -- this value is from a graphing calculator.)
Approved by eNotes Editorial Team | 439 | 1,496 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.96875 | 4 | CC-MAIN-2021-39 | latest | en | 0.830247 |
https://www.speedsolving.com/threads/weekly-competition-2010-06.18988/ | 1,560,832,571,000,000,000 | text/html | crawl-data/CC-MAIN-2019-26/segments/1560627998607.18/warc/CC-MAIN-20190618043259-20190618065259-00505.warc.gz | 916,897,588 | 33,550 | # Weekly competition 2010-06
#### AvGalen
All current (new) scramblers from the WCA are used.
• For all 3x3x3 events (including FMC) Cube Explorer was used to generate a random position and provide an inverse scramble (generator) for that position.
• For all cubes > 3x3x3 (mediumcubes) a "w" means "Wide" so you turn not just the slice, but also the outer layer.
• For all cubes > 5x5x5 (bigcubes) normally a subscript number indicates the amount of layers to turn like a wide turn. U32 would mean to turn the the U layer and the 2 layers beneath it (3 in total) a half turn. However, this forum doesn't support subscript, so I transform the default notation to "3U2" notation which also means "turn the 3 uppermost layers a half turn".
• For Megaminx R and D are "double layer moves of the entire megaminx. The U moves are normal U moves, not "double layer" or cube rotations
• For Square1 the new notation is not entirely clear about when to perform a slice/half-turn. I adjusted the scrambles so that no slice-turns are to be performed at the beginning or the end (unless the scramble begins or ends with (0,0))
• Clock hasn't changed, but just so you know: UddU u=-1,d=5 would mean Up-Left-pin is Up, Up-Right-pin is Down, Down-Left-pin is Down, Down-Right-pin is Up and that you need to turn a corner that has its pin up rotated counterclockwise by 1 hour and that you need to turn a corner that has its pin down rotated clockwise by 5 hours
• Pyraminx small letters are for the tips
Just to make sure everyone understands: We follow the official WCA rules for all events. Here are some things that people often don't know:
• For multiple blind you can choose how many cubes you are going to do (let me know if 15 scrambles is not enough). If you choose 5 cubes you have to use the first 5 scrambles.
• For one-handed you can use both hands during inspection
• For with feet you can only use feet during inspection
• For 3x3x3 Fewest Moves there is a 1 hour time limit.
• For relay you have 15 seconds of inspection in total, you can use any order to solve the cubes and the rest of the relay-rules should be obvious
For every event you participate in you will be rewarded points. You will also be rewarded points according to your ranking. Because this is quite a complicated system you can read about it in this thread. The results of the competition will be available as soon as possible after the competition closes at the end of the thread.
If you think other events should be added to this competition you can influence that in the 2008: Other events for Weekly competition thread
This competition starts now and ends wednesday/thursday nightchange (officialy), but I will only close a competition after the new one is on-line. If a competition doesn't start at wednesday/thursday nightchange you still get the full 7 days to participate.
2x2x2
1. U2 R' F2 U' R2 U R F2 U'
2. R2 U2 F R U2 R U R2 F'
3. U F2 R2 U' F U2 R U'
4. R U2 R2 F' U' R' F R U2
5. R2 F R' F' U F2 U2
3x3x3
1. D2 L' B2 L2 U2 R' U2 F2 L' R U' B F D B2 D' B U2 R F' D'
2. L2 U2 F2 U2 R2 F L2 F' U2 B' F' L2 R' U F R F L D F2 L
3. U B2 U L2 F2 U F2 L U' L R D U' L' F' L U2 L U'
4. R2 B2 R2 D' B2 F2 R2 D' L2 R2 F' D U' B' U R2 U2 R' D' U R'
5. R2 B L2 F U2 R2 F2 R2 B2 R2 U' F' D2 R' F' D B U F2 D2 F'
4x4x4
1. Uw2 Rw2 Fw2 L2 R Fw' R' Fw2 R2 D' Fw U' L' Uw2 R2 B2 F2 Uw R U2 Rw' F L B' Fw' Uw' L' R' B F D' F D Fw F' R' F D' Fw' U
2. Fw2 Uw' L2 B' D' Uw2 L Uw2 B D Fw L2 B2 Uw' Fw2 Uw2 U2 Rw2 R2 F' L' U Rw' D Fw' Rw' R2 B' U' Fw' U L' Uw Fw' R Fw' F L R' F2
3. Fw' Uw2 Rw2 U2 Fw' L' Uw U' F2 L2 Rw Fw2 D Uw U Rw' D R2 D Rw F' D' U Fw' D' Uw2 Fw' R2 F2 U Rw R Uw2 L' Fw R' B Fw Rw Uw2
4. L F2 L' B2 Fw' D Fw2 L U2 Rw2 D Fw L' D' U Rw2 U Fw2 L' Rw' B2 Rw' B Fw F2 L' B Fw2 F L' R' F2 Rw Uw2 U F Rw' R' F' R
5. Uw2 Rw2 Uw2 B' Fw2 F L' Rw' R2 D Uw' U2 Fw L F' D Uw2 L' D' Uw Rw' R2 D B' Rw' Fw D2 U B2 Fw2 F' Rw Fw D2 U2 B2 Fw' R' D Uw
5x5x5
1. L2 Fw2 Lw R F' L2 U' L' Rw' Uw U Bw' L2 Rw' Bw Rw R' D2 Rw2 Uw' B2 F2 L B Fw' F' Dw' Fw' Rw D Lw' R' D' L2 Dw Bw2 Rw' F' L2 B2 D2 Rw B' Fw2 Uw' F' D' Dw L2 Dw2 Uw2 L2 D Lw' Dw2 Uw2 Fw2 Lw Uw' L'
2. R2 Dw Lw D L' Rw2 U' Fw' D Uw' R' Dw U B Fw F' Dw' Rw2 R F' U' Lw2 D B' Fw' L' D2 Fw' D' B' Lw2 Dw Bw2 Fw F2 D2 B' R2 Dw' Uw Bw' L' D' Dw' Uw' U' R' B2 L Uw2 F2 R Fw' F' Dw2 Uw' Lw2 Bw U2 R2
3. D Dw U2 Bw' Dw' Fw' Dw2 B2 D U2 F2 U2 R2 D U L2 Rw Uw Bw F L2 Rw2 R Uw2 Fw Dw2 Fw' U2 Lw F2 Uw2 Lw2 Rw R F' Lw2 U' Fw2 F2 D Bw' Fw Rw' R' Fw Lw B' F' L2 U2 B Fw' F' L2 Rw' Dw L2 F R' Uw
4. R' F' Lw' B' Fw' D2 Fw2 L' Bw2 Rw Fw Lw' F2 Rw2 D' Bw F R Dw Rw Bw' D Fw' U' R F Lw' Rw R D Dw2 B' Lw2 D2 L Uw' Rw2 F L' Bw L' R2 Bw2 U L' Uw2 R' D2 U2 Rw2 D2 Rw F' Uw Rw2 B2 D' Dw2 U2 L
5. Bw' Lw2 D2 Uw2 Lw U Bw D' L2 B' U Bw2 R2 B2 Lw' R' U' Bw Dw B2 L2 B Fw' Uw2 U2 Rw' R U2 Fw L2 Rw Dw' Uw2 Rw2 R D' Dw' Uw B Fw2 Dw' L' F' L2 U2 Lw2 R2 Fw' D Uw' Rw' R2 Fw2 Dw2 L R' D' B' Lw Rw
6x6x6
1. L' 3R' 2U' 2L' 2R' R' B' 2D 2L2 U' 2F 3U' 2U L2 D2 3U 2U' 2L' 3U' 3F2 3U' B2 3R2 2R B 2B2 L2 2L 3R2 2D' L 3R2 2R' B 2U2 U2 2R2 F2 D 2D' 3U 2L' R2 D2 F' 2D' 2F2 F2 L 2D2 2L B' 2B 3F 2D' 2R 2U F 3U2 2F2 2L2 2U' U' F2 L F 2U' 3F2 3R' 2R 2D' F2 2D' 3U2 2U 2L2 B 2L' 3R 2F2
2. B' 3R' R2 U 2B' 3U2 L 2L 3R 2R R' 2U L2 2D2 3U U' 2L' 2R2 R 2U2 2L' D' 2R 3F' F 3U2 L 2B L' 3R2 2B2 2L2 2U L2 3R' 2R2 2B 2F R 3F2 2D R 3F' 2R' B2 D' F' U' 2L2 2D' L2 2L' 2R2 2B 2F2 2U 2L2 3U2 B 2B 3F' 2F' 2L' D' L' 2L 3R D 2U2 3R2 3F' 2F 2R 2B 2L2 D' 2R R 2U R2
3. 3R 2U 3F' 2U' 2L' 2U R D2 2D 2U2 2R2 U2 2B' R2 2U' B 2F' D' 3U' 3R' 3U' 2F' 3R' 3U' 3F F 2L2 3R R' D 3F D2 U' B 2U2 3R2 D' 2D' 3F2 2R2 R 2F 3R D2 R 3F' 2D 2L 2R' F 3U' U2 2B 2D2 2L2 F' L2 2L2 B' L2 3R2 2R2 B2 2U' U' 3F2 F2 D2 U L2 3R2 R 3U2 B2 2L 2R' B2 2L' 3R2 2D'
4. 2B2 F2 2D 2F 2L' 3R B 2B2 2F2 2D' B F' L2 3R2 D 2B' L2 2U L2 D R2 3F2 L2 3R 3U' U' B 2B' 3U' 2R R U' 2L R2 D' 3R' D2 R' 3F2 D' 2L' 2U 2F2 2L2 D' 3U U 2L2 F' D2 2D R2 3U 2U' 2L2 R2 2U B2 3U' 2U2 3F' 2F' 2R2 D2 U B' 2R 2B2 2R2 3F' 2D' 3U' U2 F' 3U2 2L2 3R' F' 3U' B2
5. 2R R D 2L R2 D2 2D2 2U 3R 2U' 2R2 3F 2F' L 3F' 2U L2 3U2 U 2L' U' B L2 3R2 2B2 R' F' 2D 3R' 2F 3R D' B' 3R 2F 2D2 2U 2L D' 3U' L' R 2U 2B' 2U' F' U 3F F 3R 2F2 3U2 U2 2B L2 2U' 2B' D 3F L2 3U2 2U' 3R2 3F U L2 U 2L2 F' R2 2B2 3F' 2R' D 2R' B' 2B2 F2 3R U
7x7x7
1. 2B' 3L' D2 2B2 3L D2 2D2 U' 3B2 3L2 2B' 2F 3D2 3U2 3L' 3F2 2D 2L2 3U' U' 2B 2U2 B' 2B2 2F2 F2 3L2 3R 3U2 3B2 2U2 B 3F' 2D2 2L2 2U' 2B 3U' 2L 2F 2R 3U' 2F D' 2L' R' 3F 2R2 U' F 3R' 3U' 3L 2R' R2 B2 L' R2 F2 L' 2L' 2R 3U' 3R2 3D F' 2U 3R' 2U' 2B F2 L2 R2 2B2 2D' 3F' 3L' B2 2D2 3D2 3R2 2F2 D2 U2 L 2L2 2R 3U' U' 2L' 3U' 2U 2R 3F2 2L' 3L' 2D 3D 3F' U
2. D' 2B 3B 3D 2L2 B' 3R 3D' 3U2 U' R' 3F 2D R2 3U2 2U2 U 2B2 2F L' 3L 2U2 F' 2R' R' F' D' 2D' 3B' 2F' 3U2 2U L B 3U B2 3L2 3R 2R R2 D 2U2 L2 3L 3R2 2R' 2B' L2 R2 2U U' 3L 3F D' 3U2 U2 3F2 2F' 2L2 R2 3U 2L' 2R2 3U 2R 3F2 L2 3L2 3B 3U' L2 3D2 F' 3U' R2 D2 U 2B2 F' D 3B' 2F' 2L2 3L2 3F L 2L 3F2 3U' 3L 3R' R 2U 3B' 2L' 3U2 2U U2 3R' 2B'
3. R' 2U 3R2 F 3D' L2 3R2 2R' R2 2U2 3R' 3F 3D2 R 3D 2B' 2L2 2F F 2U' U 2L' 3L' D 2U L' 3R F' L' 2L2 3B' D2 F' R2 B 3R2 U 2R2 B U' 3F F' 3D2 2R' 2F2 3U' 2B' 2D2 R' D2 B 2F 2R R2 B 2L' 3B 2L2 3L 2R2 B2 3F' 3R' 2R2 R B 3D2 3U' 2B' 3U' B 2D' 3L2 D' 3U' B 3F 3L2 2D 3D B2 F 3U' 2U2 L2 3L2 2R 2D' 2L' R' 3D2 F2 U' B2 2B2 2D' R' 2D' U' 2B
4. 3R' 3D2 R2 2F F' D2 R 3D 3U2 L' 3F 2D2 3L' R B 3F' 3U 2L2 3L2 2R2 3U L' 3L' R2 2B 3D R' D2 2F2 D 2D' 2U 2L' 3L 3D' F 2U' 3F 2F2 2L' 2D' 2U 3R F 3U 2L F' 2U' 3B 2D U' 3L 3R' 2B 2L2 3L2 F' 3U' 2R2 2F 2R2 R' B2 U2 2R2 2B2 3U2 U2 2F 3R2 2U B 2B2 3B2 2U L2 2D2 B 3U' 2R2 2B 3L2 3U' U2 2F2 L 2L2 3L R 2B' U 2F 2L' 3R2 3D 2R 3B 2F' U' B
5. U' 2L F' 2R2 D 2F2 D2 L2 2R 2D R' 3D' B' L' 3F2 D2 U L2 2R 3F' D' 3U 2F2 2D' 2R R' 3D2 3L' B2 3R' 3F' F' 2U' 3R F R2 U 3F' 3D' 2F' 3R2 3U U' B' 3B 3F2 2F2 D2 B2 2B2 D 3D' B 3B F2 R' U' 2F2 F L2 3D2 3U' 2L' 3F 3L2 B2 3R' R2 D 3D' U' 2L D 2R2 2B2 U' 3L 3B 2D 3F2 2L2 3L 3U 2U2 R2 3D' R B F' 3L 2D2 3D2 2R2 3F 3R2 2F2 3D 2L2 3B2 3F2
2x2x2 Blindfolded
1. U R2 U F' R2 U R U
2. R' U2 F2 R' F U' R2 F2 R' U2
3. U2 R2 F' U' R U2 F2
3x3x3 Blindfolded
1. R2 D' B2 R2 F2 L2 R2 D' U2 R F D2 U' R2 F' L U2 F2 R B' D2
2. L U2 F2 R' B2 L2 D2 L U2 R D' B' L2 D' F' L' D L2 R2 U F'
3. U' R2 D2 R2 D2 U' F2 D L2 D L F' R' D' U' F L2 D2 B'
4x4x4 Blindfolded
1. L R Uw' B2 F D' Uw R' Fw2 R B L2 D F2 R D2 Rw Uw2 Rw Fw F2 Uw2 U L2 Rw' R U' B2 Fw2 R' D2 F' Rw2 R B' F' D Uw' Fw2 F
2. D2 Rw' B2 Fw2 U2 Rw' U2 B2 U B' D2 B' Uw B2 F2 D' F2 L R' Uw L2 F Uw' R' F D2 Uw U' R F' L R B Uw' Fw2 F' L2 R2 U B
3. U B F D2 Uw2 B2 Fw' Uw U' R' B2 Uw Rw2 Fw Rw2 Uw' Rw' D2 Rw' F L' U2 Fw2 D' Fw' Uw2 F' Rw' R2 F' U Rw2 R2 D R2 U' R U2 L2 Rw
5x5x5 Blindfolded
1. Lw' B Rw2 Fw2 D2 Dw U2 L' U2 Rw' Uw' F' D2 Lw Rw' Bw' Fw R' Bw Fw D2 Rw B2 U' Rw' R' Bw2 F2 L R2 Bw2 L' Dw2 Lw2 Fw2 R2 Bw Dw U' B F U' Bw2 U' Fw D' Fw L' D Dw' L' Bw Fw2 F D2 L2 D F R2 Fw'
2. B D Bw2 L' Rw F L' B' U' Lw2 Rw2 R2 Bw U B2 Uw L2 Bw2 Fw2 U2 Fw' Uw' Rw' Dw2 B2 L' Fw Uw U R Bw' L' Lw' Bw2 Fw2 F Rw Fw' Dw2 B Lw2 Bw' Rw Uw' Bw2 L2 Lw2 Rw2 R' D L F' Dw B' F' L2 Uw' Rw R' D
3. Fw' Dw' Bw U2 Bw' D Dw Uw' Bw2 Rw D2 Dw' B2 Rw' B' Bw R' Bw Lw' U B' Dw' Uw2 Lw2 B' Dw Bw2 F Dw B Uw B2 Bw2 Fw' F Lw2 Rw2 Fw' Dw2 Uw B Bw2 Fw' Dw U2 Bw2 L' Lw' Rw' D Fw Dw2 Bw Uw L' Dw2 Lw2 U B2 Fw
3x3x3 Multiple Blindfolded
1. L2 D' U2 B2 U B2 L2 D L2 B2 F2 L D U2 B F2 U F R' B F2
2. B' U2 F2 U2 R2 B' R2 D2 B' L2 F L2 D F' R' U' L' D' U2 L2 D2
3. U2 B2 L2 U2 F2 U' F2 U2 L2 D B' D R' D2 L2 B R U' F' L' U
4. B2 U2 F2 U2 R D2 U2 B2 L U2 R D' L F U F D2 F D L' U
5. R2 U L2 D' R2 F2 U' L2 U2 F2 U' F' L2 R' B2 D L' B2 R2 B U'
6. F2 U2 F2 L F2 R' U2 L D2 L2 U2 B2 F R' F L' R D2 U B' U
7. D2 B2 D2 L B2 F2 L' F2 R F2 R B' D' L' R2 F' U' F' U' B' R'
8. F2 U2 F2 D2 R D2 L2 B2 D2 R F2 L D2 B D2 L D B U2 F' L2
9. R U2 F2 R' F2 R' F2 L B2 R F R' U' B R B F2 L' U' R' F2
10. L' D2 F2 R' F2 R2 B2 R' F2 D' L F D L' B2 R' F L B F'
11. L2 U2 B2 D' B2 U' F2 R2 U2 B L U' L2 R2 F D2 U B' L D'
12. F2 L U2 R U2 L D2 U2 L R' U R D U R2 F' L2 D R2 D R'
13. U' L2 F2 U F2 L2 D L2 D R2 F2 U2 L' F L2 U' R' F2 U2 L2 U2
14. U' L2 F2 D U F2 L2 U L2 R2 F2 R2 F' D R2 F L2 B' R' F L2
15. U' L2 D L2 U L2 U' L2 F2 U B' U' L R' D U2 B' F2 U' L F
3x3x3 One Handed
1. R F2 D2 R' B2 U2 B2 R' B2 L B L D B' U' R F R2 U2 L F2
2. L' U2 R' B2 U2 L2 D2 R D2 F2 R B2 D' L' U' R B R' D'
3. R2 U F2 L2 D' R2 B2 F2 U' F2 D2 L U L' B' L' D F D U' B'
4. F2 D2 L2 B L2 F U2 R2 F2 D' R2 F' R F2 U' F L' F2 U' R2 U2
5. F2 R2 U' B2 D' F2 U2 F2 U B2 R2 D' U2 L B D2 F2 L' R B' R'
3x3x3 With Feet
1. B2 F2 D2 F2 D' B2 D L2 B2 F2 L' U L2 F2 R' F D' R B' L
2. R2 D2 L2 R' B2 D2 B2 D2 L U2 B2 R2 U B2 F2 R' U B2 F R B
3. D2 B2 F2 D' F2 D2 R2 F2 D' F2 U' F2 R' B' R' U F L U2 F2 L'
4. L2 D2 F' L2 U2 B R2 U2 B' U2 F' R F U' R2 F2 L' D B2 U' R'
5. L2 B D2 F' L2 F' D2 U2 B' U2 R2 F' R' D' R' B2 F2 L' D' R D
3x3x3 Match the scramble
1. R2 U2 R F2 R B2 L2 U2 R B F' R2 D' L B' F2 L2 D R' U2
2. R2 F2 U' L2 D' B2 U2 B2 L2 D L F D B' R D F2 L2 R' D' F2
3. L F2 D2 U2 L D2 F2 R F2 R' D' F L2 F2 U2 R2 D2 R F D U
4. D2 U' B2 L2 R2 D' R2 U2 R2 B D2 R U B' D L R' F2 R F
5. U2 R2 B2 D2 R' D2 B2 R' B2 L2 D2 U' L D' L' B F2 L' F U2
3x3x3 Fewest Moves
1. L2 D L2 U L2 B2 R2 U L2 U B2 U B' D R U L B' F' U2
2x2x2 + 3x3x3 + 4x4x4 Relay
2. R2 F2 R U' R U' F' R
3. F2 R2 D' R2 B2 F2 U L2 F R' B' F D' B2 R F L R' F' R
4. D' L2 D' Uw2 B2 Fw2 D' L D' Uw' Fw2 U' L Uw2 Rw2 D2 L' Fw Rw' U2 Fw2 U2 Fw2 Uw F U' L' U Fw2 Rw D' B Fw D' B' R Uw2 R' Fw2 F
2x2x2 + 3x3x3 + 4x4x4 + 5x5x5 Relay
2. U' F' R' U2 F2 R' U' R2 U
3. L2 B' L2 F' R2 F2 U2 R2 B R2 D2 L B2 R2 D F' R' U' F2 U' B2
4. L Rw U' Rw' B2 U Fw F' L2 R2 D B2 Fw2 U2 Fw Rw R' D' Uw' Fw F L2 Rw2 R B' Uw' F D' Uw F' L2 Fw Rw D' U2 Rw' R' D U' Rw
5. L D2 Bw2 Dw' L B Fw' F2 Lw' Dw Uw B Rw B' L2 Rw Dw2 Rw Fw2 L2 Uw' Fw2 R' D' Dw2 L B2 Bw Lw2 Uw L' Bw' D' B Dw2 Lw Rw' U R2 Bw' Dw' Bw Fw2 L' F' L Lw' Rw D' Dw' L Dw' Fw' D2 Dw' Lw D2 Dw U2 Fw2
Magic (Just do 5 solves)
1.
2.
3.
4.
5.
Master Magic (Just do 5 solves)
1.
2.
3.
4.
5.
Clock
1. UUdd u=-2,d=1 / dUdU u=4,d=-2 / ddUU u=5,d=-5 / UdUd u=5,d=-1 / dUUU u=-1 / UdUU u=1 / UUUd u=-2 / UUdU u=0 / UUUU u=-3 / dddd d=-3 / UUUU
2. UUdd u=-1,d=0 / dUdU u=-5,d=-3 / ddUU u=0,d=-2 / UdUd u=-2,d=-3 / dUUU u=-5 / UdUU u=4 / UUUd u=6 / UUdU u=3 / UUUU u=3 / dddd d=5 / UUUU
3. UUdd u=-4,d=1 / dUdU u=3,d=-3 / ddUU u=-2,d=0 / UdUd u=0,d=2 / dUUU u=0 / UdUU u=2 / UUUd u=-1 / UUdU u=4 / UUUU u=4 / dddd d=5 / UUUd
4. UUdd u=0,d=-3 / dUdU u=0,d=6 / ddUU u=6,d=5 / UdUd u=-2,d=-2 / dUUU u=-2 / UdUU u=-2 / UUUd u=-5 / UUdU u=-4 / UUUU u=4 / dddd d=6 / UdUd
5. UUdd u=5,d=-1 / dUdU u=3,d=5 / ddUU u=-4,d=-1 / UdUd u=-3,d=2 / dUUU u=1 / UdUU u=0 / UUUd u=-1 / UUdU u=1 / UUUU u=0 / dddd d=2 / UUUd
MegaMinx
1. R++ D++ R-- D-- R-- D++ R++ D-- R-- D++ U
R-- D++ R-- D-- R++ D-- R-- D++ R++ D-- U'
R-- D-- R++ D++ R-- D-- R-- D++ R-- D++ U
R++ D++ R-- D++ R-- D-- R-- D-- R++ D-- U'
R-- D-- R++ D++ R-- D-- R-- D-- R-- D-- U'
R-- D-- R-- D++ R++ D-- R++ D++ R++ D-- U'
R++ D++ R-- D-- R-- D++ R-- D++ R-- D-- U'
2. R++ D++ R-- D-- R-- D-- R-- D++ R++ D++ U
R-- D++ R++ D++ R-- D++ R++ D-- R++ D-- U'
R++ D-- R++ D-- R-- D-- R-- D++ R++ D++ U
R-- D++ R++ D++ R++ D++ R++ D-- R++ D++ U
R-- D++ R++ D-- R-- D-- R++ D-- R-- D++ U
R-- D++ R++ D++ R++ D++ R++ D-- R-- D++ U
R-- D-- R-- D-- R++ D-- R-- D-- R++ D-- U'
3. R++ D++ R++ D++ R++ D-- R-- D-- R++ D++ U
R-- D-- R++ D++ R-- D++ R-- D-- R++ D-- U'
R++ D-- R-- D++ R++ D-- R-- D-- R-- D++ U
R++ D-- R-- D++ R-- D-- R-- D-- R++ D++ U
R++ D++ R++ D-- R-- D-- R-- D++ R-- D++ U
R++ D-- R-- D-- R-- D-- R-- D-- R-- D-- U'
R-- D++ R-- D-- R-- D++ R-- D++ R++ D-- U'
4. R-- D++ R++ D-- R-- D++ R-- D-- R++ D++ U
R++ D-- R-- D++ R++ D-- R-- D++ R++ D-- U'
R++ D++ R-- D++ R++ D-- R++ D++ R-- D-- U'
R-- D-- R++ D++ R-- D-- R-- D-- R++ D-- U'
R++ D++ R++ D++ R++ D++ R++ D++ R-- D++ U
R++ D-- R++ D-- R++ D++ R-- D++ R-- D-- U'
R++ D-- R++ D-- R++ D++ R++ D-- R++ D++ U
5. R++ D++ R++ D-- R-- D++ R++ D++ R-- D-- U'
R++ D-- R-- D++ R-- D++ R-- D++ R++ D++ U
R-- D++ R-- D++ R-- D-- R++ D++ R-- D++ U
R-- D-- R++ D-- R++ D-- R++ D-- R++ D-- U'
R++ D-- R-- D++ R++ D++ R-- D-- R++ D-- U'
R++ D++ R-- D++ R++ D-- R-- D-- R++ D++ U
R++ D++ R++ D-- R-- D++ R++ D++ R++ D++ U
PyraMinx
1. L R' U R L' U R' L R L' U R' L' u l b'
2. R' U R' L U' R' L' U L B L B' L U R L B' r' b
3. R' L' U' L' R U L' R' U L' U L U' R' L' u b
4. R' U R L' U L R U' B U' B' R' U B' u r' l b
5. R' U L U' R' L' R' U' L' U L R L' B' u b
Square-1
1. (-3,2) (0,3) (3,0) (4,0) (6,3) (0,5) (6,0) (-4,3) (-2,4) (-4,0) (-5,4) (2,3) (2,0) (4,0) (0,1) (0,4) (6,5)
2. (6,5) (0,-5) (-3,0) (0,3) (3,3) (-5,0) (5,0) (0,3) (6,4) (-3,4) (-4,5) (0,1) (0,3) (0,3) (-2,1) (0,4) (-4,0) (0,0)
3. (0,-4) (3,-2) (-3,0) (6,5) (0,2) (-2,4) (6,3) (0,3) (0,3) (0,2) (-2,0) (2,2) (6,0) (5,4) (-4,4) (0,3) (5,0)
4. (0,6) (0,6) (3,0) (-1,4) (6,4) (6,1) (0,5) (2,3) (-2,1) (6,5) (6,0) (6,5) (-2,1) (0,5) (0,5) (-2,0) (0,0)
5. (0,5) (0,-3) (-3,1) (0,3) (0,2) (6,0) (6,0) (-5,1) (5,0) (-2,1) (0,2) (0,2) (-3,4) (-2,2) (0,4) (6,2) (0,2) (0,0)
#### onionhoney
##### Member
2x2
(2.54) 3.29 (4.69) 2.82 3.08 = 3.06
use speedstacks timer this time~
2 of them is solved using CLL(i have learned about 15 algs or so)
3x3
(13.82) 10.93 12.50 10.79 (10.70)= 11.41
this result is pretty good. :lol My TypeF is even better.
3x3 OH
25.25 25.91 24.36 (26.32)(22.71)=25.17
4x4
2:04.64 2:12.42 2:02.51 DNS DNS=DNF
i don't like big cubes~
2x2BLD
46.47 DNF DNF=46.47
maybe i should learn a new method
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#### aronpm
##### Member
2x2x2: 11.80, (15.84), 10.53, (9.03), 12.55 = 11.63
3x3x3: 21.09, 23.21, (19.83), 23.33, (26.44) = 22.54
4x4x4: 2:11.61, (1:54.19), (2:23.65), 2:12.84, 2:06.46 = 2:10.30
Comment: Fail 3x3x3 average. Sub-20 avg next week plz.
3x3x3 Blindfolded: DNF(2:31.46), DNF, DNF(2:20.19) = DNF
Comment: Crap.
3x3x3 Multiple Blindfolded: 2/4 = 0 in 27:11.36
Comment: Tried to play it safe but I messed up anyway. Fourth cube was off by a 3-cycle and third cube was off by parity. I even thought I messed up a J perm on the second cube, but I must have fixed it. Measly 18 minute memo, I haven't practiced in a while. (did sub-20 4 cubes after this... >.>)
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#### Faz
##### Former Clock NR Holder
2x2: 2.28, 6.75, 3.59, 2.19, 3.47 = 3.11
Pyraminx: 10.22, 4.26, 4.26, 6.84, 6.81 = 5.97
Sq-1: 25.03, 22.88, 23.64, 26.68, 23.65 = 24.10
Ugh too much parity.
3x3: 9.38, 9.38, 10.66, 9.51, 9.35 = 9.43
4th one had a pop :s
OH: 16.42, 24.58, 33.27, 21.20, 18.97 = 21.58
Lol dropped cube twice.
4x4: 58.11, 46.82, 52.62, 41.83, 44.18 = 47.87
Lmao.
5x5: 1:25.28, 1:30.70, 1:25.06, 1:25.77, 1:25.96 = 1:25.67
Lol I suck.
2x2BLD: 16.66+, 14.93+, 10.65+ = 10.65
234: 1:10.12
4x4 was like... 1 min :s
2345: 2:37.77
lolfail.
Megaminx: 1:28.42, 1:14.96, 1:22.41, DNF(1:49.16), 1:19.57 = 1:23.47
My megaminx is crap.
6x6: 3:02.83, 3:08.66, 3:05.27, 2:48.78, 2:50.09 = 2:59.40
My 6x6 is crap
3x3BLD: 3:18.33, DNF(2:25.31), DNF(2:32.55) = 3:18.33
Ugh I suck so much.
7x7: 4:49.44, 4:31.79, 5:01.10, 4:41.06, 4:42.88 = 4:44.46
Good.
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#### Yes We Can!
##### Member
2x2: 3.99, (7.90), (3.83), 5.01, 4.64 = 4.55
2x2BLD: 34.36, DNF, DNF = 34.36
3x3BLD: DNF, 2:41.64, 2:07.66 = 2:07.66
3x3: 12.27, (12.11), (20.45), 12.31, 13.12 = 12.56
3x3OH: 29.49, (25.92), (30.82), 29.73, 29.10 = 29.44
4x4BLD: 26:32.69, DNF, 17:57.93 = 17:57.93
New PB and first sub-20!!!
MultiBLD: 3/4 in 31:41
Ugh, messed up the first cube. I think I failed an algorithm in an unconcentrated second. Hyprul: You win :/
5x5: (1:48.65), (2:56.52), 2:10.81, 2:01.69, 1:55.40 = 2:02.61
Uuuuh, a new PB average framed by two awesome sub-2 singles
Pyra: (14.22), 12.94, (7.68), 13.87, 12.32 = 13.04
4x4: 1:02.30, 1:15.37, 1:07.57, (59.22), (1:35.14) = 1:08.41
3x3FMC: 42 moves
scramble: L2 D L2 U L2 B2 R2 U L2 U B2 U B' D R U L B' F' U2
Solution:
F' U' F (1x2x2)
B' R D' F2 R' (2x2x2)
L2 D' L (2nd pair)
z2 B' R B (double x-cross)
F R' F' R (3rd pair)
U2 L U L' U L' B L B' (4th pair)
y R U2 R' U' R U' R' (OLL)
L2 B2 L' F' L B2 L' F L' U2 (PLL)
The cancellations are in bold.
Magic: (DNF), 1.71, 3.09, (1.52), 2.15 = 2.32
2x2-4x4 Relay: 1:26.06
2x2-5x5 Relay: 3:16.74
Wow! PB by 30 seconds! Amazing for me! Splits were: 4 - 13 - 1:03 - 1:56 Sub-2 5x5!
Megaminx: 1:57.27, (2:04.13), 1:57.30, 1:57.28, (1:45.58) = 1:57.28
Wow, the SD is just wow. 0.01 standard deviation for Megaminx
Match the scramble: (DNF), 2:43.96, 3:05.72, 4:51.36, (1:57.95) = 3:33.68
First time really doing this.
7x7: (6:43.31), 6:59.97, (8:36.69), 7:11.88, 7:02.80 = 7:04.88
Really good! These were my first 2 sub-7s!
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#### Inf3rn0
##### Member
2x2: 12.81, 11.62, 8.43, 13.18, 9.70 = 11.38
I should work on this.
More to come and hopefully i'll get round to clock this week.
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#### Jin
##### Member
3x3 - 18.09, 15.56, 17.88, 16.23, 16.06 =16.72
2x2- 7.17, 8.51, 7.25, 7.12, 7.34 =7.25
#### mande
##### Member
Megaminx: (4:10.66), 3:25.52, 3:51.31, 3:25.39, (2:55.47) = 3:34:07
Comment: Good warm up for comp on Saturday-Sunday. First sub 3 single
3x3: 19.07, (15.69), (23.00), 16.73, 17.92 = 17.91
Comment: Very good.
2x2: (7.51), 6.68, 5.07, 6.11, (4.62) = 5.95
Comment: Awesome.
3x3 OH: 41.37, 36.38, (28.22), (49.82), 37.20 = 38.31
Comment: Very good single, OK average.
3x3 BLD: 1:49.92, DNF, 2:33.59 = 1:49.92
Comment: Brilliant. Why didn't I get such times in comp?
3x3 FMC: 42 moves
Comment: Will post solution after some time, I'm quite busy now.
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#### SimonWestlund
##### Member
2x2: 2.10, 3.51, 3.77, 3.65, 2.13 = 3.10
3x3: 11.61, 11.69, 12.29, 8.45, 11.72 = 11.67 - 0.05 SD
4x4: 56.36, 53.21, 55.48, 53.35, 53.64 = 54.16 - O, OP, O, O, OP
5x5: 1:42.13, 1:49.40, 1:47.41, 1:32.00, 1:36.85 = 1:42.13
6x6: 3:21.42, 3:12.41, 3:19.53, 3:04.21, 3:35.54 = 3:17.79
7x7: 5:03.59, 5:51.39, 5:24.32, 5:12.23, 5:06.42 = 5:14.32
2x2 BLD: 32.13, 34.50, 23.59 = 23.59
3x3 BLD: DNF, 2:27.97, 1:55.71 = 1:55.71
4x4 BLD: DNF, 14:56, DNS = 14:56 - Awesome!
3x3 Multi: 3/4 21:31 - 3 cycle edges off on the last cube.
3x3 MTS: 1:06.25, 1:07.25, 1:21.54, 1:01.53, 1:06.32 = 1:06.61
3x3 OH: 24.47, 23.98, 20.55, 22.70, 21.13 = 22.60
2-4 relay: 1:04.01 - 45, 14, 4
2-5 relay: 3:12.95 - grr..
Magic: 1.56, 1.43, 1.75, 1.96, 1.35 = 1.58
Master Magic: 5.16, 5.71, 4.44, 4.03, 3.67 = 5.01 - PB single.
Clock: 10.21, 9.43, 9.68, 10.91, 9.79 = 9.90
Megaminx: 1:03.03, 56.63, 59.28, 1:03.74, 1:00.31 = 1:00.87
Pyraminx: 5.99, 7.20, 4.84, 5.05, 5.32 = 5.45
Square-1: 19.37, 19.32, 29.91, 19.26, 25.01 = 21.23
3x3 FMC: 39
Scramble: L2 D L2 U L2 B2 R2 U L2 U B2 U B' D R U L B' F' U2
Solution: R' F2 R U' F' U' F2 z2 y F R' F' R' U2 R' F R U' R U' R' U' R U R' U2 F U2 F' U2 L' U L R U2 R' U' R U' R' U (39)
Explanation
2x2x2: R' F2 R U' F' U' F2 (7)
2x2x3: z2 y F R' F' R' (11)
F2L#3: U2 R' F R U' R U' R' U' R U R' (23)
F2L#4 + LL: U2 F U2 F' U2 L' U L R U2 R' U' R U' R' U (39)
A solution I found in about 10 minutes. Didn't have a lot of time to try more.
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#### Hyprul 9-ty2
##### Member
2x2 : (3.16), 4.22, 5.19, 4.83, (5.29) = 4.74
Really nice average
3x3 : 13.43, 13.20, 14.14, (15.06), (11.58) = 13.59
Woah, amazing speed-boost :O
3x3 BLD : 1:47.04, DNF(2:44.46), 2:16.20 = 1:47.04
Scramble 1 was really easy And scramble 2 sucked =.=
2x2 BLD : 46.09, 39.69+, 29.40 = 29.40
Yay Full success.
3x3 OH : (25.22), 26.04, (29.58), 29.13, 27.86 = 27.68
Square-1 : 40.28, (32.53), 46.73, 44.98, (48.75) = 44.00
Is it me or are all the scrambles really easy >_> Maybe its my really ineffective cube forming
Megaminx : 2:27.51, 2:23.07, (2:11.37), 2:23.07, (2:29.63) = 2:24.55
Magic : (1.89), 1.52, 1.63, (1.28), 1.37 = 1.51
4x4 : 1:00.83, (1:07.59), 59.10, 57.90, (54.60) = 59.28
That last single <3
2-3-4 Relay : 1:25.51
No parity
3x3 FMC : 39 moves
Scramble : L2 D L2 U L2 B2 R2 U L2 U B2 U B' D R U L B' F' U2
Solution : U2 B R F U L R2 U' B2 F' U' F U' D' R U R' D R' U' R U2 B' U B2 U2 B' U R' U' R
L F2 R' F' R F' L' U
X-cross : U2 B R F U L R2 U' B2 - 9
F2L 2 : F' U' F U' D' R U R' D - 9(18)
F2L 3 : R' U' R U2 B' U B - 7(25)
F2L 4 : B U2 B' U R' U' R - 7(32)
OLL : L F2 R' F' R F' L' U - 8(40)
Turning the bolded moves into 1 B2 cuts one move; 40-1 = 39
Lol me so sucky at FMC
3x3 Multi BLD : 3/3 in 10:54.51
Yessss
4x4 BLD : 15:12.96, 15:30.48, DNS = 15:12.96
2 amazing solves!
3x3 MTS : (1:50.35), 1:35.36, 1:49.52, 1:44.62, (1:32.63) = 1:43.17
Last edited:
#### 04mucklowd
##### Member
2x2: 5.28, 6.90, 6.85, 6.58, 6.73 = 6.72
3x3: 19.15, 18.77, 21.63, 20.21, 24.01 = 20.33
5x5: 2:17.63, 2:16.23, 2:32.61, 2:17.63, 2:31.45 = 2:22.24
Megaminx: 2:02.96, 2:10.18, 2:02.49, 2:10.87, 2:23.81 = 2:08.00
my bro come in on the last solve
3x3 FM = 62
Last edited:
#### trying-to-speedcube...
##### Member
2x2: 3.06, 4.76, 3.83, 4.86, 4.30 = 4.30
3x3: 14.42, 17.76, 15.11, 13.08, 13.85 = 14.46
4x4: 55.51, 48.41, 47.59, 44.55, 55.57 = 50.50
5x5: 1:32.56, 1:31.03, 1:28.13, 1:32.25, 1:31.18 = 1:31.49
6x6: 3:18.83, 3:13.29, 3:12.71, 3:26.02, 2:59.94 = 3:14.94
7x7: 4:58.47, 4:37.03, 5:10.25, 4:55.71, 5:04.47 = 4:59.55
3x3BLD: 1:38.50, DNS, DNS = 1:38.50
4x4BLD: 9:54.04, DNS, DNS = 9:54.04
5x5BLD: DNF, DNS, DNS = DNF
MultiBLD: 5/5 29:19!
3x3OH: 29.87, 27.46, 28.30, 27.54, 28.11 = 27.98
3x3MTS: 50.52, 52.63, 49.87, 54.92, 53.65 = 52.27
3x3FMC: 46 moves
Magic: 1.28, 1.27, 1.31, 2.83, 1.25 = 1.29
Master Magic: 3.06, 3.61, 3.05, 3.68, 2.87 = 3.24
2-3-4 relay: 1:26.58
2-3-4-5 relay: 3:10.95
Clock: 11.11, 8.69, 9.56, 7.40, 10.02 = 9.30
Pyraminx: 6.88, 8.30, 6.80, 7.25, 4.61 = 6.98
Megaminx: 1:32.01, 1:31.39, 1:27.44, 1:25.23, 1:26.27 = 1:28.37
Square-1: 18.71, 16.93, 18.90, 14.02, 21.52 = 18.18
FMC solution:
U2 L U F' U2 F' L' F U F2 D' F' D' F D' F' D2 F L' D2 L D L' D L F L D L' D' F' B' D B D2 R D R' D2 L' D L D' L' D' L2
Lol.
Last edited:
#### Muesli
2x2x2
(5.45), 7.13, 6.36, 5.68, (7.33),= 6.39
Meh. Not too bad, not too good.
3x3x3
20.58, 22.03, 20.70, (23.24), (20.44) = 21.10
Meh. That's alright I guess.
Pyraminx
(19.88), 16.87, (12.46), 18.88, 12.76 = 16.71
Meh. Need practise.
Last edited:
#### Laura O
##### Member
3x3: 32.08, (29.57), 37.27, (39.43), 30.11 = 33.15
4x4: 3:02.90, 2:39.66, (3:27.36), 2:45.59, (2:24.23) = 2:49.38
Pyraminx: 13.50, (10.60), (14.72), 11.97, 14.28 = 13.15
Clock: (10.56), (9.44), 9.91, 9.47, 9.93 = 9.77
Last edited:
2x2x2:
1: 00:16.55
2: 00:15.97
3: 00:16.62
4: 00:15.79
5: 00:12.06
Avg. 5: 00:15.40
3x3x3:
1: 00:35.49
2: 00:39.79
3: 00:29.30
4: 00:36.42
5: 00:35.85
Avg. 5: 00:35.37
4x4x4:
1: 03:18.14
2: 03:03.88
3: 03:27.77
4: 03:34.00
5: 03:47.96
Avg. 5: 3:26.64
2-3-4 relay:
04:49.57
3x3x3 OH:
1: 01:42.50
2: 01:34.52
3: 01:23.16
4: 01:38.95
5: 01:39.85
Avg. 5: 01:35.79
Last edited:
#### MistArts
##### Member
2x2x2: (2.54), (5.16), 3.25, 4.36, 3.54 = 3.72
3x3x3: 20.22, 19.80, (18.00), (20.84), 19.05 = 19.69
Last edited:
#### Edmund
##### Member
3
15.81
(21.68), 17.79, 14.84, 14.79, (14.73)
erry solve was better than the next. these were my first 5 solves the day so it's no wonder the first 2 solves were so bad.
#### Edam
2x2 (6.77), 8.28, 7.84, 9.61, (15.61) = 8.58
3x3 (18.52), 17.21, (15.88), 17.80, 17.02 = 17.34
4x4 1:32.75, 1:31.44, (1:34.58), 1:16.11, (1:08.56)= 1:26.77
5 solves, 9 parity fixes.. annoying. also 3 bad times for me.. but one good
5x5 2:37.94, 2:35.84, 2:31.78, (2:31.33), (3:03.18) = 2:35.19
not sure what happened on the 5th solve to make it so slow
6x6 (5:34.27), 6:00.97, 5:47.31, 6:56.61 , (7:29.63) = 6:14.96
lolpop
3x3oh: (1:13.67), 1:12.84, 57.79, (55.74), 56.91 = 1:02.52
234: 1:53.65
1.34 seconds james, close
2345: 4:24.75
magic 1.21, 1.13, 1.44, (1.03), (DNF) = 1.26
it would seem i suck at magic today
Last edited:
#### Evan Liu
##### Member
2x2: (8.66) 6.70 7.81 (6.58) 7.83
3x3: (23.78) (19.64) 22.06 20.47 21.69 => 21.41
4x4: (2:07.34) (1:27.80) 1:35.81 1:49.52 1:42.30 => 1:42.54
Comment: Fail. I average 1:20s...
5x5: (3:41.35) 3:19.44 (3:07.11) 3:39.74 3:18.27 => 3:25.82
3x3 OH: 39.64 40.69 (48.42) 47.22 (37.78) => 42.52
2x2x2 + 3x3x3 + 4x4x4 Relay: 2:01.08
2x2x2 + 3x3x3 + 4x4x4 +5x5x5 Relay: 5:52.15
Magic: 1.47 (2.04) (1.32) 1.83 1.73 => 1.68
Last edited: | 15,367 | 26,079 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.671875 | 3 | CC-MAIN-2019-26 | latest | en | 0.936817 |
https://www.physicsforums.com/threads/fluids-rate-of-flow-homework-help.597529/ | 1,607,006,737,000,000,000 | text/html | crawl-data/CC-MAIN-2020-50/segments/1606141727782.88/warc/CC-MAIN-20201203124807-20201203154807-00020.warc.gz | 693,189,880 | 16,732 | # Fluids rate of flow homework help
## Homework Statement
Two cylindrical pipes both carry an ideal fluid (zero viscosity) in laminar flow. Pipe A has radius Ra = 2 and flow velocity Va = 8cm/s. Pipe B has radius Rb = 4cm and flow velocity Vb = 4cm/s.
A) Calculate the cross section of pipe A and pipe B.
B) Calculate the rate of flow in liters/second (1l = 1000cm cubic)
## Homework Equations
maybe v1a1 = v2a2 ?
## The Attempt at a Solution
v1a1 = v2a2
= (8cm/s)(2cm) = (4cm/s)(4cm) = 1 ?
It`s wrong.
Last edited:
Related Introductory Physics Homework Help News on Phys.org
okay. Now tell me what is a1, a2?
tms
## Homework Equations
maybe v1a1 = v2a2 ?
Just what do $a_1$ and $a_2$ represent?
Also, are these pipes connected end to end, or are they in parallel?
you mean...
Last edited:
tms
What has pressure got to do with it?
Go back to your first equation: what is $a_1$? This is not a trick question.
I have to calculate cross section of pipe A and B.
My book says cross-sectional area is VA.
I am confused with these formulas because I have the following:
Flow rate = VA
Flow rate = V/T
So, flow rate = cross sectional area = VA?
Last edited:
R = 2 = area 1 = 4
R = 4 = area 2 = 16
?
Last edited:
I think I know it...
Last edited:
would that be correct?
I just need this to finish my homework.
I think I know it:
I think I am supposed to use pi. So, could it be: 3.14 x 4^2 = 50.24 for cross section pipe B?
Last edited:
I know the answer! I got the answer! I got the answer!! Just a question: how should I leave the flow rate considering the answer for B = 0.20096, should I say the answer is 0.20 or 0.200 l/s ?
tms
I have to calculate cross section of pipe A and B.
My book says cross-sectional area is VA.
Assuming $V$ is volume and $A$ is area, something is wrong, either the book or your reading of it. The units are odd, too: $\mathrm{L}^5$. If $V$ and $A$ mean something else, then I don't know.
I am confused with these formulas because I have the following:
Flow rate = VA
Flow rate = V/T
What is $T$?
So, flow rate = cross sectional area = VA?
Think units. What units must flow rate have?
tms
I know the answer! I got the answer! I got the answer!! Just a question: how should I leave the flow rate considering the answer for B = 0.20096, should I say the answer is 0.20 or 0.200 l/s ?
Since the problem, as you gave it, uses only one significant figure, then your answer should have no more than one significant figure. | 710 | 2,482 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.125 | 4 | CC-MAIN-2020-50 | latest | en | 0.943388 |
http://themathmompuzzles.blogspot.com/2010/01/new-york-devil.html | 1,511,469,398,000,000,000 | text/html | crawl-data/CC-MAIN-2017-47/segments/1510934806939.98/warc/CC-MAIN-20171123195711-20171123215711-00506.warc.gz | 290,858,326 | 17,218 | ## Wednesday, January 20, 2010
### New York Devil
A man from New Jersey was complaining that he doesn't have enough money. A devil descended from the sky and offered a deal to this man:
"Feel all this cash you have in your wallet? I can double it every time you cross George Washington bridge from NY to NJ. However, when you cross the bridge in the other direction you have to pay the \$8 toll."
The man quickly agreed, but was left without any cash after just four trips.
Enter your answer on our Family Puzzle Marathon page. Solve three and get a prize!
W said...
If we work backwards:
On the last trip, he must have had \$8 coming back. Before that, when crossing, he must have had \$4 which was doubled to \$8.
Coming back the third time, he must have had \$12 since \$12 - \$8 = \$4 he had before going over the 4th time from NY to NJ.
So in going over the 3rd time from NY to NJ, he must have had \$6 (that doubled to the \$12).
Coming back from the 2nd time, he must have had \$6 + \$8 = \$14.
And then, crossing over the 2nd time from NY to NJ, that means he must have had \$14 / 2 = \$7.
Coming back the 1st time, \$7 + \$8 = \$15
And then crossing over the 1st time = \$15 / 2 = \$7.50.
Let's just double check to see if that makes sense.
1) 7.5 * 2 = 15 ; 15 - 8 = 7
2) 7 * 2 = 14 ; 14 - 8 = 6
3) 6 * 2 = 12 ; 12 - 8 = 4
4) 4 * 2 = 8 ; 8 - 8 = 0!
So he must have started out with \$7.50 He should really have started with an amount > \$8.
Maria said...
Or he should have done some math before jumping into a deal with the devil.
Bravo W!
New puzzle tomorrow.
Kim said...
Congratulations on the great article, Maria! http://www.boston.com/news/local/articles/2010/01/21/needhams_math_mom_inspires_children_parents_to_love_numbers/?page=full
Maria said...
Thank you, Kim. And thanks to everyone in the Family Puzzle Marathon community. You are the ones that make it all fun and cool.
Kim was referring to the article about TheMathMom in today's West edition of the Boston Globe.
Anonymous said...
Robin figured this one out. It has to be \$15.00, because the man starts in NJ.
Trip #1: \$15.00-8=\$7.00, double it for the way back, and you get \$14.
Trip #2: \$14-8=\$6.00, double it for the way back, and you get \$12.
Trip #3: \$12-8=\$4.00, double it for the way back, and you get \$8.
Trip #4: \$8-\$8 =\$0, double it for the way back, and you get \$0
Maria said...
Very impressive, Robin!
I was re-telling this puzzle to my kids yesterday, and you know how kids always ask the right questions. My son asked: "Where the man was starting hos journey from, NJ, right?" and I felt that there is a hole in the solution...
Robin must have has this child-like scientific curiosity. Welcome to the marathon! You get your first puzzle-point. | 781 | 2,774 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.1875 | 4 | CC-MAIN-2017-47 | longest | en | 0.971207 |
https://bettersolutions.com/excel/functions/pricemat-function.htm | 1,723,643,469,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722641113960.89/warc/CC-MAIN-20240814123926-20240814153926-00503.warc.gz | 91,344,086 | 4,609 | # PRICEMAT
PRICEMAT(settlement, maturity, issue, rate, yield [,basis])
Returns the price of a security that pays interest at maturity.
settlement The settlement date of the security. maturity The maturity date of the security. issue The issue date of the security. rate The interest rate of the security. yield The annual yield of the security. basis (Optional) The type of day counting to use:0 = 30/360 (default)1 = Actual/Actual2 = Actual/3603 = Actual/3654 = 30E/360
REMARKS
* If "settlement" is not an integer, it is truncated.* If "settlement" is not a valid date, then #NUM! is returned.* If "settlement" >= "maturity", then #NUM! is returned.* If "maturity" is not an integer, it is truncated.* If "maturity" is not a valid date, then #NUM! is returned.* If "issue" is not an integer, it is truncated.* If "issue" is not a valid date, then #NUM! is returned.* If "rate" < 0, then #NUM! is returned.* If "yield" < 0, then #NUM! is returned.* If "basis" is left blank, then 0 is used.* If "basis" is not an integer, it is truncated.* If "basis" < 0, then #NUM! is returned.* If "basis" > 4, then #NUM! is returned.* You can use the PRICE function to return the price of a security that pays interest at regular intervals.* You can use the PRICEDISC function to return the price of a discounted security (no interest payments).* For the Microsoft documentation refer to support.microsoft.com* For the Google documentation refer to support.google.com
A 1 =PRICEMAT("2/15/1999", "4/13/1999", "11/11/1998", 0.061, 0.061, 0) = #VALUE! | 434 | 1,544 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.515625 | 3 | CC-MAIN-2024-33 | latest | en | 0.822872 |
https://alexaanswers.amazon.com/question/5HtwSxq1JiMLsD9dQzbzIe | 1,642,538,802,000,000,000 | text/html | crawl-data/CC-MAIN-2022-05/segments/1642320300997.67/warc/CC-MAIN-20220118182855-20220118212855-00495.warc.gz | 152,375,730 | 41,347 | Food
How much dry parsley equals a half a cup of fresh parsley?
Just use a third the amount your recipe calls for if you're swapping dried herbs for fresh. So if your recipe calls for 1 tablespoon of fresh parsley, use 1 teaspoon of dried parsley, because 1 tablespoon equals 3 teaspoons
{{ relativeTimeResolver(1573241602013) }}
LIVE
534 | 81 | 342 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.546875 | 3 | CC-MAIN-2022-05 | latest | en | 0.825351 |
https://www.jiskha.com/display.cgi?id=1170110559 | 1,519,275,663,000,000,000 | text/html | crawl-data/CC-MAIN-2018-09/segments/1518891814002.69/warc/CC-MAIN-20180222041853-20180222061853-00697.warc.gz | 893,057,091 | 4,146 | # math,correction
posted by .
the problem is:
4x+y>=4
so after solving for the equation line formula y=mx+b
I got :
y>= -4x+4
the points to plot was:
(-1,8),(0,4),(1,0),(2,-4)
and the line will be solid and the shading for solution would be on top going in that-------> direction.
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Physics Past Year Paper Compartment Anskey (Delhi Set -1) - 2014, Class 12, CBSE Class 12 Notes | EduRev
Created by: Ambition Institute
Class 12 : Physics Past Year Paper Compartment Anskey (Delhi Set -1) - 2014, Class 12, CBSE Class 12 Notes | EduRev
``` Page 1
Compartment Page No. 1 20
th
July, 2014 final
MARKING SCHEME
SET 55/1/1 (Compartment)
Q.No. Expected Answer/Value Points Marks Total
Marks
1. i. The two point charges( and ) should be of opposite nature.
ii. Magnitude of charge must be greater than that of charge
½
½ 1
2. Random motion of free electrons gets directed towards the point at a higher
potential.
Alternatively:
Random motion becomes a (partially) directed motion.
1
1
3. Diamagnetic material
= 1 +
½
½ 1
4. Due to the heating effect of eddy currents set up in the metallic piece. 1 1
5.
Effective power
(Alternatively: Effective power radiated decreases with an increase in
wavelength.)
1
1
6.
Alternatively: Also accept if the student gives only the following diagram:
1
1
7. Two monochromatic sources, which produce light waves, having a constant phase
difference, are known as coherent sources.
1 1
8. When a constant current flows through a wire, the Potential difference, between
any two points on the wire of uniform cross section, is directly proportional to the
length of the wire between these points.
Alternatively:
V or = constant
1
1
9
Charge on inner surface : - Q
Charge on outer surface : + Q
Electric field at point
E =
½
½
1
2
Charges on the inner and outer surfaces ½ + ½
Expression for electric field 1
Page 2
Compartment Page No. 1 20
th
July, 2014 final
MARKING SCHEME
SET 55/1/1 (Compartment)
Q.No. Expected Answer/Value Points Marks Total
Marks
1. i. The two point charges( and ) should be of opposite nature.
ii. Magnitude of charge must be greater than that of charge
½
½ 1
2. Random motion of free electrons gets directed towards the point at a higher
potential.
Alternatively:
Random motion becomes a (partially) directed motion.
1
1
3. Diamagnetic material
= 1 +
½
½ 1
4. Due to the heating effect of eddy currents set up in the metallic piece. 1 1
5.
Effective power
(Alternatively: Effective power radiated decreases with an increase in
wavelength.)
1
1
6.
Alternatively: Also accept if the student gives only the following diagram:
1
1
7. Two monochromatic sources, which produce light waves, having a constant phase
difference, are known as coherent sources.
1 1
8. When a constant current flows through a wire, the Potential difference, between
any two points on the wire of uniform cross section, is directly proportional to the
length of the wire between these points.
Alternatively:
V or = constant
1
1
9
Charge on inner surface : - Q
Charge on outer surface : + Q
Electric field at point
E =
½
½
1
2
Charges on the inner and outer surfaces ½ + ½
Expression for electric field 1
Compartment Page No. 2 20
th
July, 2014 final
10.
Alternatively:
Applying Ampere circuital law for the rectangular loop abcd
=
Bh = (nh)
B =
½
½
½
½ 2
11.
=
As = 0
? =
? = =
?
wavelength ( )of emitted electrons,
½
½
½
Drawing of magnetic field lines ½
Obtaining the expression for magnetic field 1 ½
Finding the relation 1 ½
Drawing the graph ½
Page 3
Compartment Page No. 1 20
th
July, 2014 final
MARKING SCHEME
SET 55/1/1 (Compartment)
Q.No. Expected Answer/Value Points Marks Total
Marks
1. i. The two point charges( and ) should be of opposite nature.
ii. Magnitude of charge must be greater than that of charge
½
½ 1
2. Random motion of free electrons gets directed towards the point at a higher
potential.
Alternatively:
Random motion becomes a (partially) directed motion.
1
1
3. Diamagnetic material
= 1 +
½
½ 1
4. Due to the heating effect of eddy currents set up in the metallic piece. 1 1
5.
Effective power
(Alternatively: Effective power radiated decreases with an increase in
wavelength.)
1
1
6.
Alternatively: Also accept if the student gives only the following diagram:
1
1
7. Two monochromatic sources, which produce light waves, having a constant phase
difference, are known as coherent sources.
1 1
8. When a constant current flows through a wire, the Potential difference, between
any two points on the wire of uniform cross section, is directly proportional to the
length of the wire between these points.
Alternatively:
V or = constant
1
1
9
Charge on inner surface : - Q
Charge on outer surface : + Q
Electric field at point
E =
½
½
1
2
Charges on the inner and outer surfaces ½ + ½
Expression for electric field 1
Compartment Page No. 2 20
th
July, 2014 final
10.
Alternatively:
Applying Ampere circuital law for the rectangular loop abcd
=
Bh = (nh)
B =
½
½
½
½ 2
11.
=
As = 0
? =
? = =
?
wavelength ( )of emitted electrons,
½
½
½
Drawing of magnetic field lines ½
Obtaining the expression for magnetic field 1 ½
Finding the relation 1 ½
Drawing the graph ½
Compartment Page No. 3 20
th
July, 2014 final
½
2
12.
(Any two of the following)
i. No chromatic aberration.
ii. Less spherical aberration.
iii. Large magnifying power.
iv. Large resolving power
v. [Note : or any other two advantages.]
1
½ + ½
2
13.
Input Output
A A' B B' Y
0 1 0 1 0
0 1 1 0 0
1 0 0 1 0
1 0 1 0 1
Identification : AND Gate
½
1
½ 2
Schematic diagram of reflecting telescope 1
Drawing the logic circuit of the combination ½
Truth table 1
Identification ½
Page 4
Compartment Page No. 1 20
th
July, 2014 final
MARKING SCHEME
SET 55/1/1 (Compartment)
Q.No. Expected Answer/Value Points Marks Total
Marks
1. i. The two point charges( and ) should be of opposite nature.
ii. Magnitude of charge must be greater than that of charge
½
½ 1
2. Random motion of free electrons gets directed towards the point at a higher
potential.
Alternatively:
Random motion becomes a (partially) directed motion.
1
1
3. Diamagnetic material
= 1 +
½
½ 1
4. Due to the heating effect of eddy currents set up in the metallic piece. 1 1
5.
Effective power
(Alternatively: Effective power radiated decreases with an increase in
wavelength.)
1
1
6.
Alternatively: Also accept if the student gives only the following diagram:
1
1
7. Two monochromatic sources, which produce light waves, having a constant phase
difference, are known as coherent sources.
1 1
8. When a constant current flows through a wire, the Potential difference, between
any two points on the wire of uniform cross section, is directly proportional to the
length of the wire between these points.
Alternatively:
V or = constant
1
1
9
Charge on inner surface : - Q
Charge on outer surface : + Q
Electric field at point
E =
½
½
1
2
Charges on the inner and outer surfaces ½ + ½
Expression for electric field 1
Compartment Page No. 2 20
th
July, 2014 final
10.
Alternatively:
Applying Ampere circuital law for the rectangular loop abcd
=
Bh = (nh)
B =
½
½
½
½ 2
11.
=
As = 0
? =
? = =
?
wavelength ( )of emitted electrons,
½
½
½
Drawing of magnetic field lines ½
Obtaining the expression for magnetic field 1 ½
Finding the relation 1 ½
Drawing the graph ½
Compartment Page No. 3 20
th
July, 2014 final
½
2
12.
(Any two of the following)
i. No chromatic aberration.
ii. Less spherical aberration.
iii. Large magnifying power.
iv. Large resolving power
v. [Note : or any other two advantages.]
1
½ + ½
2
13.
Input Output
A A' B B' Y
0 1 0 1 0
0 1 1 0 0
1 0 0 1 0
1 0 1 0 1
Identification : AND Gate
½
1
½ 2
Schematic diagram of reflecting telescope 1
Drawing the logic circuit of the combination ½
Truth table 1
Identification ½
Compartment Page No. 4 20
th
July, 2014 final
14.
Equivalent magnetic moment of the coil
=IA
=I b
( = unit vector to the plane of the coil)
Torque =
= I b
= 0
(as are parallel or antiparallel, to each other)
[Note: Also give credit, when student obtains the relation
, and substitutes and writes
½
½
½
½
2
15.
(i) Conductor (ii) Semiconductor
=
In conductors, average relaxation time decreases with increase in temperature,
resulting in an increase in resistivity.
In semiconductors, the increase in number density (with increase in temperature)
is more than the decrease in relaxation time; the net result is, therefore, a decrease
in resistivity.
½ + ½
½
½ 2
16.
i. emf induced
e =
= 0.1 x 10 x 10
-2
x 20 V
= 0.2 volt
ii. Current in the loop
i =
= A = 0.1 A
½
½
½
½ 2
Obtaining the expression for the torque 2
Drawing the two plots ½ + ½
Explanation of Behaviour ½ + ½
Calculation of
i. emf induced in the arm PQ 1
ii. Current induced in the loop 1
Page 5
Compartment Page No. 1 20
th
July, 2014 final
MARKING SCHEME
SET 55/1/1 (Compartment)
Q.No. Expected Answer/Value Points Marks Total
Marks
1. i. The two point charges( and ) should be of opposite nature.
ii. Magnitude of charge must be greater than that of charge
½
½ 1
2. Random motion of free electrons gets directed towards the point at a higher
potential.
Alternatively:
Random motion becomes a (partially) directed motion.
1
1
3. Diamagnetic material
= 1 +
½
½ 1
4. Due to the heating effect of eddy currents set up in the metallic piece. 1 1
5.
Effective power
(Alternatively: Effective power radiated decreases with an increase in
wavelength.)
1
1
6.
Alternatively: Also accept if the student gives only the following diagram:
1
1
7. Two monochromatic sources, which produce light waves, having a constant phase
difference, are known as coherent sources.
1 1
8. When a constant current flows through a wire, the Potential difference, between
any two points on the wire of uniform cross section, is directly proportional to the
length of the wire between these points.
Alternatively:
V or = constant
1
1
9
Charge on inner surface : - Q
Charge on outer surface : + Q
Electric field at point
E =
½
½
1
2
Charges on the inner and outer surfaces ½ + ½
Expression for electric field 1
Compartment Page No. 2 20
th
July, 2014 final
10.
Alternatively:
Applying Ampere circuital law for the rectangular loop abcd
=
Bh = (nh)
B =
½
½
½
½ 2
11.
=
As = 0
? =
? = =
?
wavelength ( )of emitted electrons,
½
½
½
Drawing of magnetic field lines ½
Obtaining the expression for magnetic field 1 ½
Finding the relation 1 ½
Drawing the graph ½
Compartment Page No. 3 20
th
July, 2014 final
½
2
12.
(Any two of the following)
i. No chromatic aberration.
ii. Less spherical aberration.
iii. Large magnifying power.
iv. Large resolving power
v. [Note : or any other two advantages.]
1
½ + ½
2
13.
Input Output
A A' B B' Y
0 1 0 1 0
0 1 1 0 0
1 0 0 1 0
1 0 1 0 1
Identification : AND Gate
½
1
½ 2
Schematic diagram of reflecting telescope 1
Drawing the logic circuit of the combination ½
Truth table 1
Identification ½
Compartment Page No. 4 20
th
July, 2014 final
14.
Equivalent magnetic moment of the coil
=IA
=I b
( = unit vector to the plane of the coil)
Torque =
= I b
= 0
(as are parallel or antiparallel, to each other)
[Note: Also give credit, when student obtains the relation
, and substitutes and writes
½
½
½
½
2
15.
(i) Conductor (ii) Semiconductor
=
In conductors, average relaxation time decreases with increase in temperature,
resulting in an increase in resistivity.
In semiconductors, the increase in number density (with increase in temperature)
is more than the decrease in relaxation time; the net result is, therefore, a decrease
in resistivity.
½ + ½
½
½ 2
16.
i. emf induced
e =
= 0.1 x 10 x 10
-2
x 20 V
= 0.2 volt
ii. Current in the loop
i =
= A = 0.1 A
½
½
½
½ 2
Obtaining the expression for the torque 2
Drawing the two plots ½ + ½
Explanation of Behaviour ½ + ½
Calculation of
i. emf induced in the arm PQ 1
ii. Current induced in the loop 1
Compartment Page No. 5 20
th
July, 2014 final
17.
(i) Intensity of incident radiation I = nhv,
where n is number of photons incident per unit time per unit area.
For same intensity of two monochromatic radiations of frequency
and
=
As >
?
Therefore the number of electrons emitted for monochromatic radiation of
frequency , will be more than that for radiation of frequency
[Alternatively: Also accept if the student says that, for same intensity of incident
radiation, the number of emitted electrons is same for each of the two frequencies
(ii) hv =
For given (work function of metal)
increases with
Maximum Kinetic energy of emitted photoelectrons will be more for
monochromatic light of frequency as > )
½
½
½
½ 2
18.
Work done in bringing the charge from infinity to position
Hence, total work done in assembling the two charges
OR
Work done in moving a unit positive charge along distance
=
= V – (V +
= -
E= -
(i) Electric field is in the direction in which the potential decreases steepest.
(ii) Magnitude of Electric field is given by the change in the magnitude of
potential per unit displacement, normal to the equipotential surface at the
point.
½
½ +½
½
½
½
½
½
2
2
Explanation of parts (i) and (ii) 1+1
Obtaining the expression for total work done 2
Derivation of relation between Electric field and potential gradient 1
Two important conclusions ½ + ½
```
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; | 3,927 | 13,113 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.53125 | 4 | CC-MAIN-2020-40 | latest | en | 0.888934 |
http://www.math-only-math.com/cardinal-number-of-a-set.html | 1,503,236,258,000,000,000 | text/html | crawl-data/CC-MAIN-2017-34/segments/1502886106754.4/warc/CC-MAIN-20170820131332-20170820151332-00626.warc.gz | 605,584,218 | 9,123 | # Cardinal Number of a Set
What is the cardinal number of a set?
The number of distinct elements in a finite set is called its cardinal number. It is denoted as n(A) and read as ‘the number of elements of the set’.
For example:
(i) Set A = {2, 4, 5, 9, 15} has 5 elements.
Therefore, the cardinal number of set A = 5. So, it is denoted as n(A) = 5.
(ii) Set B = {w, x, y, z} has 4 elements.
Therefore, the cardinal number of set B = 4. So, it is denoted as n(B) = 4.
(iii) Set C = {Florida, New York, California} has 3 elements.
Therefore, the cardinal number of set C = 3. So, it is denoted as n(C) = 3.
(iv) Set D = {3, 3, 5, 6, 7, 7, 9} has 5 element.
Therefore, the cardinal number of set D = 5. So, it is denoted as n(D) = 5.
(v) Set E = { } has no element.
Therefore, the cardinal number of set D = 0. So, it is denoted as n(D) = 0.
Note:
(i) Cardinal number of an infinite set is not defined.
(ii) Cardinal number of empty set is 0 because it has no element.
Solved examples on Cardinal number of a set:
1. Write the cardinal number of each of the following sets:
(i) X = {letters in the word MALAYALAM}
(ii) Y = {5, 6, 6, 7, 11, 6, 13, 11, 8}
(iii) Z = {natural numbers between 20 and 50, which are divisible by 7}
Solution:
(i) Given, X = {letters in the word MALAYALAM}
Then, X = {M, A, L, Y}
Therefore, cardinal number of set X = 4, i.e., n(X) = 4
(ii) Given, Y = {5, 6, 6, 7, 11, 6, 13, 11, 8}
Then, Y = {5, 6, 7, 11, 13, 8}
Therefore, cardinal number of set Y = 6, i.e., n(Y) = 6
(iii) Given, Z = {natural numbers between 20 and 50, which are divisible by 7}
Then, Z = {21, 28, 35, 42, 49}
Therefore, cardinal number of set Z = 5, i.e., n(Z) = 5
2. Find the cardinal number of a set from each of the following:
(i) P = {x | x ∈ N and x$$^{2}$$ < 30}
(ii) Q = {x | x is a factor of 20}
Solution:
(i) Given, P = {x | x ∈ N and x$$^{2}$$ < 30}
Then, P = {1, 2, 3, 4, 5}
Therefore, cardinal number of set P = 5, i.e., n(P) = 5
(ii) Given, Q = {x | x is a factor of 20}
Then, Q = {1, 2, 4, 5, 10, 20}
Therefore, cardinal number of set Q = 6, i.e., n(Q) = 6
Set Theory
Sets
Objects Form a Set
Elements of a Set
Properties of Sets
Representation of a Set
Different Notations in Sets
Standard Sets of Numbers
Types of Sets
Pairs of Sets
Subset
Subsets of a Given Set
Operations on Sets
Union of Sets
Intersection of Sets
Difference of two Sets
Complement of a Set
Cardinal number of a set
Cardinal Properties of Sets
Venn Diagrams | 871 | 2,498 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.875 | 5 | CC-MAIN-2017-34 | longest | en | 0.935378 |
http://orange.biolab.si/trac/changeset/539f49e3586dbe0b5713f9bd7bde76369808fbc0/orange | 1,394,397,111,000,000,000 | text/html | crawl-data/CC-MAIN-2014-10/segments/1394010305626/warc/CC-MAIN-20140305090505-00025-ip-10-183-142-35.ec2.internal.warc.gz | 132,875,058 | 14,606 | # Changeset 10362:539f49e3586d in orange
Ignore:
Timestamp:
02/24/12 13:12:28 (2 years ago)
Branch:
default
rebase_source:
b107b292c78ab9b716058336d460ba28782be01a
Message:
Small (but numerous) code style improvements in the first third of scoring.py
File:
1 edited
Unmodified
Added
Removed
• ## Orange/evaluation/scoring.py
r10343 import math, functools import math import functools from operator import add import numpy def log2(x): """Calculate logarithm in base 2.""" return math.log(x)/math.log(2) return math.log(x) / math.log(2) def check_non_zero(x): """Throw Value Error when x = 0.0.""" if x==0.0: raise ValueError, "Cannot compute the score: no examples or sum of weights is 0.0." """Throw Value Error when x = 0.""" if x == 0.: raise ValueError, "Cannot compute the score: no examples or sum of weights is 0." def gettotweight(res): """Sum all the weights""" totweight = reduce(lambda x, y: x+y.weight, res.results, 0) if totweight==0.0: raise ValueError, "Cannot compute the score: sum of weights is 0.0." totweight = reduce(lambda x, y: x + y.weight, res.results, 0) if totweight == 0.: raise ValueError, "Cannot compute the score: sum of weights is 0." return totweight weights=res.weights, baseClass=res.baseClass, classifiers=[res.classifiers[i]] if res.classifiers else [], test_type = res.test_type, labels = res.labels) test_type=res.test_type, labels=res.labels) r.results = [] for te in res.results: def class_probabilities_from_res(res, **argkw): """Calculate class probabilities""" probs = [0.0] * len(res.class_values) probs = [0.] * len(res.class_values) if argkw.get("unweighted", 0) or not res.weights: for tex in res.results: probs[int(tex.actual_class)] += 1.0 probs[int(tex.actual_class)] += 1. totweight = gettotsize(res) else: totweight = 0.0 totweight = 0. for tex in res.results: probs[tex.actual_class] += tex.weight if iteration_is_outer: if not stats: raise ValueError, "Cannot compute the score: no examples or sum of weights is 0.0." raise ValueError, "Cannot compute the score: no examples or sum of weights is 0." number_of_learners = len(stats[0]) stats = filter(lambda (x, fN): fN>0.0, zip(stats,fold_n)) stats = [ [x[lrn]/fN for x, fN in stats] for lrn in range(number_of_learners)] stats = filter(lambda (x, fN): fN > 0, zip(stats, fold_n)) stats = [[x[lrn] / fN for x, fN in stats] for lrn in range(number_of_learners)] else: stats = [ [x/Fn for x, Fn in filter(lambda (x, Fn): Fn > 0.0, zip(lrnD, fold_n))] for lrnD in stats] stats = [[x / Fn for x, Fn in filter(lambda (x, Fn): Fn > 0, zip(lrnD, fold_n))] for lrnD in stats] if not stats: raise ValueError, "Cannot compute the score: no classifiers" if not stats[0]: raise ValueError, "Cannot compute the score: no examples or sum of weights is 0.0." raise ValueError, "Cannot compute the score: no examples or sum of weights is 0." if report_se: def ME(res, **argkw): MEs = [0.0]*res.number_of_learners MEs = [0.] * res.number_of_learners if argkw.get("unweighted", 0) or not res.weights: else: for tex in res.results: MEs = map(lambda res, cls, ac = float(tex.actual_class), tw = tex.weight: res + tw*abs(float(cls) - ac), MEs, tex.classes) MEs = map(lambda res, cls, ac=float(tex.actual_class), tw=tex.weight: res + tw * abs(float(cls) - ac), MEs, tex.classes) totweight = gettotweight(res) return [x/totweight for x in MEs] return [x / totweight for x in MEs] MAE = ME @deprecated_keywords({"predictedPositive": "predicted_positive", "isPositive": "is_positive"}) def addTFPosNeg(self, predicted_positive, is_positive, weight = 1.0): def addTFPosNeg(self, predicted_positive, is_positive, weight=1.0): """ Update confusion matrix with result of a single classification def check_argkw(dct, lst): """check_argkw(dct, lst) -> returns true if any items have non-zero value in dct""" return reduce(lambda x,y: x or y, [dct.get(k, 0) for k in lst]) return reduce(lambda x, y: x or y, [dct.get(k, 0) for k in lst]) def regression_error(res, **argkw): if argkw.get("SE", 0) and res.number_of_iterations > 1: # computes the scores for each iteration, then averages scores = [[0.0] * res.number_of_iterations for _ in range(res.number_of_learners)] norm=None scores = [[0.] * res.number_of_iterations for _ in range(res.number_of_learners)] norm = None if argkw.get("norm-abs", 0) or argkw.get("norm-sqr", 0): norm = [0.0] * res.number_of_iterations nIter = [0]*res.number_of_iterations # counts examples in each iteration a = [0]*res.number_of_iterations # average class in each iteration norm = [0.] * res.number_of_iterations # counts examples in each iteration nIter = [0] * res.number_of_iterations # average class in each iteration a = [0] * res.number_of_iterations for tex in res.results: nIter[tex.iteration_number] += 1 a[tex.iteration_number] += float(tex.actual_class) a = [a[i]/nIter[i] for i in range(res.number_of_iterations)] a = [a[i] / nIter[i] for i in range(res.number_of_iterations)] if argkw.get("unweighted", 0) or not res.weights: else: scores[i][tex.iteration_number] += (float(cls) - ai)**2 else: # unweighted<>0 else: # unweighted != 0 raise NotImplementedError, "weighted error scores with SE not implemented yet" if argkw.get("norm-abs") or argkw.get("norm-sqr"): scores = [[x/n for x, n in zip(y, norm)] for y in scores] else: scores = [[x/ni for x, ni in zip(y, nIter)] for y in scores] scores = [[x / n for x, n in zip(y, norm)] for y in scores] else: scores = [[x / ni for x, ni in zip(y, nIter)] for y in scores] if argkw.get("R2"): else: # single iteration (testing on a single test set) scores = [0.0] * res.number_of_learners norm = 0.0 scores = [0.] * res.number_of_learners norm = 0. if argkw.get("unweighted", 0) or not res.weights: for tex in res.results: if argkw.get("abs", 0): scores = map(lambda res, cls, ac = float(tex.actual_class): scores = map(lambda res, cls, ac=float(tex.actual_class): res + abs(float(cls) - ac), scores, tex.classes) else: scores = map(lambda res, cls, ac = float(tex.actual_class): scores = map(lambda res, cls, ac=float(tex.actual_class): res + (float(cls) - ac)**2, scores, tex.classes) else: # UNFINISHED MSEs = [0.]*res.number_of_learners MSEs = [0.] * res.number_of_learners for tex in res.results: MSEs = map(lambda res, cls, ac = float(tex.actual_class), tw = tex.weight: MSEs = map(lambda res, cls, ac=float(tex.actual_class), tw=tex.weight: res + tw * (float(cls) - ac)**2, MSEs, tex.classes) totweight = gettotweight(res) if argkw.get("norm-abs", 0) or argkw.get("norm-sqr", 0): scores = [s/norm for s in scores] scores = [s / norm for s in scores] else: # normalize by number of instances (or sum of weights) scores = [s/totweight for s in scores] scores = [s / totweight for s in scores] if argkw.get("R2"): scores = [1.0 - s for s in scores] scores = [1. - s for s in scores] if argkw.get("sqrt", 0): """MSE(res) -> mean-squared error""" if argkw.get("SE", 0) and res.number_of_iterations > 1: MSEs = [[0.0] * res.number_of_iterations for _ in range(res.number_of_learners)] nIter = [0]*res.number_of_iterations MSEs = [[0.] * res.number_of_iterations for _ in range(res.number_of_learners)] nIter = [0] * res.number_of_iterations if argkw.get("unweighted", 0) or not res.weights: for tex in res.results: else: raise ValueError, "weighted RMSE with SE not implemented yet" MSEs = [[x/ni for x, ni in zip(y, nIter)] for y in MSEs] MSEs = [[x / ni for x, ni in zip(y, nIter)] for y in MSEs] if argkw.get("sqrt", 0): MSEs = [[math.sqrt(x) for x in y] for y in MSEs] else: MSEs = [0.0]*res.number_of_learners MSEs = [0.] * res.number_of_learners if argkw.get("unweighted", 0) or not res.weights: for tex in res.results: MSEs = map(lambda res, cls, ac = float(tex.actual_class): MSEs = map(lambda res, cls, ac=float(tex.actual_class): res + (float(cls) - ac)**2, MSEs, tex.classes) totweight = gettotsize(res) else: for tex in res.results: MSEs = map(lambda res, cls, ac = float(tex.actual_class), tw = tex.weight: res + tw * (float(cls) - ac)**2, MSEs, tex.classes) MSEs = map(lambda res, cls, ac=float(tex.actual_class), tw=tex.weight: res + tw * (float(cls) - ac)**2, MSEs, tex.classes) totweight = gettotweight(res) if argkw.get("sqrt", 0): MSEs = [math.sqrt(x) for x in MSEs] return [x/totweight for x in MSEs] return [x / totweight for x in MSEs] def RMSE_old(res, **argkw): input_type = self.get_input_type(test_results) if input_type == self.CONFUSION_MATRIX: self[:] = [self.from_confusion_matrix(test_results)] self[:] = [self.from_confusion_matrix(test_results)] elif input_type == self.CONFUSION_MATRIX_LIST: self[:] = self.from_confusion_matrix_list(test_results) self[:] = self.from_classification_results(test_results) elif input_type == self.CROSS_VALIDATION: self[:] = self.from_crossvalidation_results(test_results) self[:] = self.from_crossvalidation_results(test_results) def from_confusion_matrix(self, cm): correct_predictions = 0. if isinstance(cm, ConfusionMatrix): all_predictions += cm.TP+cm.FN+cm.FP+cm.TN correct_predictions += cm.TP+cm.TN all_predictions += cm.TP + cm.FN + cm.FP + cm.TN correct_predictions += cm.TP + cm.TN else: for r, row in enumerate(cm): check_non_zero(all_predictions) ca = correct_predictions/all_predictions ca = correct_predictions / all_predictions if self.report_se: return ca, ca*(1-ca)/math.sqrt(all_predictions) return ca, ca * (1 - ca) / math.sqrt(all_predictions) else: return ca def from_classification_results(self, test_results): CAs = [0.0]*test_results.number_of_learners CAs = [0.] * test_results.number_of_learners totweight = 0. for tex in test_results.results: w = 1. if self.ignore_weights else tex.weight CAs = map(lambda res, cls: res+(cls==tex.actual_class and w), CAs, tex.classes) CAs = map(lambda res, cls: res + (cls == tex.actual_class and w), CAs, tex.classes) totweight += w check_non_zero(totweight) ca = [x/totweight for x in CAs] ca = [x / totweight for x in CAs] if self.report_se: return [(x, x*(1-x)/math.sqrt(totweight)) for x in ca] return [(x, x * (1 - x) / math.sqrt(totweight)) for x in ca] else: return ca def from_crossvalidation_results(self, test_results): CAsByFold = [[0.0]*test_results.number_of_iterations for _ in range(test_results.number_of_learners)] foldN = [0.0]*test_results.number_of_iterations CAsByFold = [[0.] * test_results.number_of_iterations for _ in range(test_results.number_of_learners)] foldN = [0.] * test_results.number_of_iterations for tex in test_results.results: w = 1. if self.ignore_weights else tex.weight for lrn in range(test_results.number_of_learners): CAsByFold[lrn][tex.iteration_number] += (tex.classes[lrn]==tex.actual_class) and w CAsByFold[lrn][tex.iteration_number] += (tex.classes[lrn] == tex.actual_class) and w foldN[tex.iteration_number] += w @deprecated_keywords({"reportSE": "report_se", "unweighted": "ignore_weights"}) def AP(res, report_se = False, ignore_weights=False, **argkw): def AP(res, report_se=False, ignore_weights=False, **argkw): """ Computes the average probability assigned to the correct class. """ if res.number_of_iterations == 1: APs=[0.0]*res.number_of_learners APs=[0.] * res.number_of_learners if ignore_weights or not res.weights: for tex in res.results: APs = map(lambda res, probs: res + probs[tex.actual_class], APs, tex.probabilities) APs = map(lambda res, probs: res + probs[tex.actual_class], APs, tex.probabilities) totweight = gettotsize(res) else: totweight = 0. for tex in res.results: APs = map(lambda res, probs: res + probs[tex.actual_class]*tex.weight, APs, tex.probabilities) APs = map(lambda res, probs: res + probs[tex.actual_class] * tex.weight, APs, tex.probabilities) totweight += tex.weight check_non_zero(totweight) return [AP/totweight for AP in APs] APsByFold = [[0.0]*res.number_of_learners for _ in range(res.number_of_iterations)] foldN = [0.0] * res.number_of_iterations return [AP / totweight for AP in APs] APsByFold = [[0.] * res.number_of_learners for _ in range(res.number_of_iterations)] foldN = [0.] * res.number_of_iterations if ignore_weights or not res.weights: for tex in res.results: APsByFold[tex.iteration_number] = map(lambda res, probs: res + probs[tex.actual_class], APsByFold[tex.iteration_number], tex.probabilities) APsByFold[tex.iteration_number] = map(lambda res, probs: res + probs[tex.actual_class], APsByFold[tex.iteration_number], tex.probabilities) foldN[tex.iteration_number] += 1 else: for tex in res.results: APsByFold[tex.iteration_number] = map(lambda res, probs: res + probs[tex.actual_class] * tex.weight, APsByFold[tex.iteration_number], tex.probabilities) APsByFold[tex.iteration_number] = map(lambda res, probs: res + probs[tex.actual_class] * tex.weight, APsByFold[tex.iteration_number], tex.probabilities) foldN[tex.iteration_number] += tex.weight @deprecated_keywords({"reportSE": "report_se", "unweighted": "ignore_weights"}) def Brier_score(res, report_se = False, ignore_weights=False, **argkw): def Brier_score(res, report_se=False, ignore_weights=False, **argkw): """ Computes the Brier's score, defined as the average (over test examples) of sumx(t(x)-p(x))2, where x is a class, t(x) is 1 for the correct class if res.number_of_iterations == 1: MSEs=[0.0]*res.number_of_learners MSEs=[0.] * res.number_of_learners if ignore_weights or not res.weights: totweight = 0.0 totweight = 0. for tex in res.results: MSEs = map(lambda res, probs: res + reduce(lambda s, pi: s+pi**2, probs, 0) - 2*probs[tex.actual_class], MSEs, tex.probabilities) MSEs = map(lambda res, probs: res + reduce( lambda s, pi: s + pi**2, probs, 0) - 2 * probs[tex.actual_class], MSEs, tex.probabilities) totweight += tex.weight else: for tex in res.results: MSEs = map(lambda res, probs: res + tex.weight*reduce(lambda s, pi: s+pi**2, probs, 0) - 2*probs[tex.actual_class], MSEs, tex.probabilities) MSEs = map(lambda res, probs: res + tex.weight * reduce( lambda s, pi: s + pi**2, probs, 0) - 2 * probs[tex.actual_class], MSEs, tex.probabilities) totweight = gettotweight(res) check_non_zero(totweight) if report_se: return [(max(x/totweight+1.0, 0), 0) for x in MSEs] ## change this, not zero!!! else: return [max(x/totweight+1.0, 0) for x in MSEs] BSs = [[0.0]*res.number_of_learners for _ in range(res.number_of_iterations)] ## change this, not zero!!! return [(max(x / totweight + 1., 0), 0) for x in MSEs] else: return [max(x / totweight + 1., 0) for x in MSEs] BSs = [[0.] * res.number_of_learners for _ in range(res.number_of_iterations)] foldN = [0.] * res.number_of_iterations if ignore_weights or not res.weights: for tex in res.results: BSs[tex.iteration_number] = map(lambda rr, probs: rr + reduce(lambda s, pi: s+pi**2, probs, 0) - 2*probs[tex.actual_class], BSs[tex.iteration_number], tex.probabilities) BSs[tex.iteration_number] = map(lambda rr, probs: rr + reduce( lambda s, pi: s + pi**2, probs, 0) - 2 * probs[tex.actual_class], BSs[tex.iteration_number], tex.probabilities) foldN[tex.iteration_number] += 1 else: for tex in res.results: BSs[tex.iteration_number] = map(lambda res, probs: res + tex.weight*reduce(lambda s, pi: s+pi**2, probs, 0) - 2*probs[tex.actual_class], BSs[tex.iteration_number], tex.probabilities) res + tex.weight * reduce(lambda s, pi: s + pi**2, probs, 0) - 2 * probs[tex. actual_class], BSs[tex.iteration_number], tex.probabilities) foldN[tex.iteration_number] += tex.weight stats = statistics_by_folds(BSs, foldN, report_se, True) if report_se: return [(x+1.0, y) for x, y in stats] return [(x + 1., y) for x, y in stats] else: return [x+1.0 for x in stats] return [x + 1. for x in stats] def BSS(res, **argkw): return [1-x/2 for x in apply(Brier_score, (res, ), argkw)] return [1 - x / 2 for x in apply(Brier_score, (res, ), argkw)] def IS_ex(Pc, P): """Pc aposterior probability, P aprior""" if Pc>=P: return -log2(P)+log2(Pc) if Pc >= P: return -log2(P) + log2(Pc) else: return -(-log2(1-P)+log2(1-Pc)) return -(-log2(1 - P) + log2(1 - Pc)) @deprecated_keywords({"reportSE": "report_se"}) def IS(res, apriori=None, report_se = False, **argkw): def IS(res, apriori=None, report_se=False, **argkw): """ Computes the information score as defined by `Kononenko and Bratko (1991) \ apriori = class_probabilities_from_res(res) if res.number_of_iterations==1: ISs = [0.0]*res.number_of_learners if res.number_of_iterations == 1: ISs = [0.] * res.number_of_learners if argkw.get("unweighted", 0) or not res.weights: for tex in res.results: for i in range(len(tex.probabilities)): cls = tex.actual_class ISs[i] += IS_ex(tex.probabilities[i][cls], apriori[cls]) * tex.weight ISs[i] += (IS_ex(tex.probabilities[i][cls], apriori[cls]) * tex.weight) totweight = gettotweight(res) if report_se: return [(IS/totweight,0) for IS in ISs] else: return [IS/totweight for IS in ISs] return [(IS / totweight, 0) for IS in ISs] else: return [IS / totweight for IS in ISs] ISs = [[0.0]*res.number_of_iterations for _ in range(res.number_of_learners)] ISs = [[0.] * res.number_of_iterations for _ in range(res.number_of_learners)] foldN = [0.] * res.number_of_iterations for i in range(len(tex.probabilities)): cls = tex.actual_class ISs[i][tex.iteration_number] += IS_ex(tex.probabilities[i][cls], apriori[cls]) ISs[i][tex.iteration_number] += IS_ex(tex.probabilities[i][cls], apriori[cls]) foldN[tex.iteration_number] += 1 else: for i in range(len(tex.probabilities)): cls = tex.actual_class ISs[i][tex.iteration_number] += IS_ex(tex.probabilities[i][cls], apriori[cls]) * tex.weight ISs[i][tex.iteration_number] += IS_ex(tex.probabilities[i][cls], apriori[cls]) * tex.weight foldN[tex.iteration_number] += tex.weight k = len(res.results[0].classes) if k<2: if k < 2: raise TypeError, "nothing to compare (less than two classifiers given)" if k==2: if k == 2: return apply(Wilcoxon, (res, statistics), argkw) else: tfpns = [ConfusionMatrix() for _ in range(test_results.number_of_learners)] if class_index<0: if class_index < 0: numberOfClasses = len(test_results.class_values) if class_index < -1 or numberOfClasses > 2: cm = [[[0.0] * numberOfClasses for _ in range(numberOfClasses)] for _ in range(test_results.number_of_learners)] cm = [[[0.] * numberOfClasses for _ in range(numberOfClasses)] for _ in range(test_results.number_of_learners)] if ignore_weights or not test_results.weights: for tex in test_results.results: return cm elif test_results.baseClass>=0: elif test_results.baseClass >= 0: class_index = test_results.baseClass else: isPositive=(lr.actual_class==class_index) for i in range(test_results.number_of_learners): tfpns[i].addTFPosNeg(lr.probabilities[i][class_index]>cutoff, isPositive) tfpns[i].addTFPosNeg(lr.probabilities[i][class_index] > cutoff, isPositive) else: for lr in test_results.results: isPositive=(lr.actual_class==class_index) isPositive=(lr.actual_class == class_index) for i in range(test_results.number_of_learners): tfpns[i].addTFPosNeg(lr.probabilities[i][class_index]>cutoff, isPositive, lr.weight) tfpns[i].addTFPosNeg(lr.probabilities[i][class_index] > cutoff, isPositive, lr.weight) else: if ignore_weights or not test_results.weights: for lr in test_results.results: isPositive=(lr.actual_class==class_index) isPositive = (lr.actual_class == class_index) for i in range(test_results.number_of_learners): tfpns[i].addTFPosNeg(lr.classes[i]==class_index, isPositive) tfpns[i].addTFPosNeg(lr.classes[i] == class_index, isPositive) else: for lr in test_results.results: isPositive=(lr.actual_class==class_index) isPositive = (lr.actual_class == class_index) for i in range(test_results.number_of_learners): tfpns[i].addTFPosNeg(lr.classes[i]==class_index, isPositive, lr.weight) tfpns[i].addTFPosNeg(lr.classes[i] == class_index, isPositive, lr.weight) return tfpns colPriors = [sum(r[i] for r in confusion_matrix) for i in range(dim)] total = sum(rowPriors) rowPriors = [r/total for r in rowPriors] colPriors = [r/total for r in colPriors] rowPriors = [r / total for r in rowPriors] colPriors = [r / total for r in colPriors] ss = 0 for ri, row in enumerate(confusion_matrix): if not e: return -1, -1, -1 ss += (o-e)**2 / e df = (dim-1)**2 ss += (o - e)**2 / e df = (dim - 1)**2 return ss, df, statc.chisqprob(ss, df) return -1 return confusion_matrix.TP/tot return confusion_matrix.TP / tot warnings.warn("Can't compute specificity: one or both classes have no instances") return -1 return confusion_matrix.TN/tot return confusion_matrix.TN / tot return [PPV(cm) for cm in confusion_matrix] else: tot = confusion_matrix.TP+confusion_matrix.FP tot = confusion_matrix.TP + confusion_matrix.FP if tot < 1e-6: import warnings return [NPV(cm) for cm in confusion_matrix] else: tot = confusion_matrix.FN+confusion_matrix.TN tot = confusion_matrix.FN + confusion_matrix.TN if tot < 1e-6: import warnings warnings.warn("Can't compute NPV: one or both classes have no instances") return -1 return confusion_matrix.TN/tot return confusion_matrix.TN / tot @deprecated_keywords({"confm": "confusion_matrix"}) try: r = (((truePositive * trueNegative) - (falsePositive * falseNegative))/ math.sqrt( (truePositive + falsePositive) * ( truePositive + falseNegative ) * ( trueNegative + falsePositive ) * ( trueNegative + falseNegative ) ) ) r = (((truePositive * trueNegative) - (falsePositive * falseNegative)) / math.sqrt((truePositive + falsePositive) * (truePositive + falseNegative) * (trueNegative + falsePositive) * (trueNegative + falseNegative))) except ZeroDivisionError: # Zero difision occurs when there is either no true positives if b_is_list_of_matrices: try: return [scotts_pi(cm, b_is_list_of_matrices=False) for cm in confusion_matrix] return [scotts_pi(cm, b_is_list_of_matrices=False) for cm in confusion_matrix] except TypeError: # Nevermind the parameter, maybe this is a "conventional" binary
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# Does the GMAT discriminate non-english speakers?
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Manager
Joined: 14 Mar 2011
Posts: 192
Re: Does the GMAT discriminate non-english speakers? [#permalink]
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11 Jul 2011, 17:01
1
I do not think GMAT discriminates with non-English speakers. Gmat basically tests our analytical and communication skills and having proper verbal ability is one of the things which can certainly make a person better business person. TOP MBA programs require a test which gives verbal and analytical ability of a person. Both verbal and quant section of GMAT tests your logical ability and your ability to infer something from a limited amount of data. GMAT being a test of america naturally comes in english language, when international test takers are taking Gmat, they essentially want to take admission in the universities in which learning medium is english, so it is imperative that they know standard english.
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Joined: 23 Apr 2012
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Location: Jamaica
Concentration: Marketing, Statistics
GMAT Date: 09-26-2012
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Re: Does the GMAT discriminate non-english speakers? [#permalink]
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28 May 2012, 11:47
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Hello everyone, I'm a recent addition to the GMAT Club and a newbie in every way! I have been going through the numerous posts, reading the various advice tips offered, as well as gaining insight into this test. So I came across this post and I wanted to share a photo that I believe pictorially represents the views being put forth.
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Joined: 23 May 2011
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Re: Does the GMAT discriminate non-english speakers? [#permalink]
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31 May 2012, 11:12
Quote:
By the way-2, here is another question: why verbal score outweights the quantative score in overall GMAT score?
I mean GMAT scaled score of Q40 V45 is higher than CMAT scaled score of Q45 V40. Why?!
Hello! I am a Manhattan GMAT instructor and I can answer this.
The GMAT was not *designed* to have verbal count more than quant (at least at the high ranges) -- this phenomenon is simply the result of the fact that, globally, more GMAT test takers get very high quant scores than very high verbal scores.
Simply put, if you get a 45Q, you are in a club with quite a lot of people! If you get a 45V, you are in a much more exclusive club! Some of that is for exactly the reasons detailed in this forum -- native English speakers, or those who got a very good education in English, tend to score better in verbal.
That said, some of my very best verbal students are non-native speakers (at the end of the Manhattan GMAT Foundations of GMAT Verbal book, I include a letter from one of my former students who is Indian and who got a 780), and some of my native-speaking students are very confused that they are doing so poorly in verbal. (As I always tell them, if you think what you hear on TV is proper written English, you will get a B- performance, at best.)
Sometimes, having to learn rules explicitly is superior to feeling like you've just known something all your life. For instance, many native speakers have never thought about the simple little fact that regular verbs in English have an "s" when singular and no "s" when plural. This, of course, is exactly the OPPOSITE of what someone learning English for the first time would expect!
I'll just add one more thing -- some commenters think the GMAT shouldn't require science reading! Of course, a huge number of MBAs go into tech-related fields! And, of course, most businesses you might end up working for are, er ... *about* something other than business.
Good luck! I really respect the students who've come through my classroom and have put in a huge amount of effort to master the nuances of the English language, and to be able to comprehend graduate-level reading on any topic.
Sincerely,
Jennifer
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Joined: 14 Dec 2011
Posts: 173
Schools: LBS '14 (A)
GMAT 1: 730 Q50 V39
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Re: Does the GMAT discriminate non-english speakers? [#permalink]
### Show Tags
31 May 2012, 13:11
JenDziura wrote:
Quote:
By the way-2, here is another question: why verbal score outweights the quantative score in overall GMAT score?
I mean GMAT scaled score of Q40 V45 is higher than CMAT scaled score of Q45 V40. Why?!
Hello! I am a Manhattan GMAT instructor and I can answer this.
The GMAT was not *designed* to have verbal count more than quant (at least at the high ranges) -- this phenomenon is simply the result of the fact that, globally, more GMAT test takers get very high quant scores than very high verbal scores.
Simply put, if you get a 45Q, you are in a club with quite a lot of people! If you get a 45V, you are in a much more exclusive club! Some of that is for exactly the reasons detailed in this forum -- native English speakers, or those who got a very good education in English, tend to score better in verbal.
That said, some of my very best verbal students are non-native speakers (at the end of the Manhattan GMAT Foundations of GMAT Verbal book, I include a letter from one of my former students who is Indian and who got a 780), and some of my native-speaking students are very confused that they are doing so poorly in verbal. (As I always tell them, if you think what you hear on TV is proper written English, you will get a B- performance, at best.)
Sometimes, having to learn rules explicitly is superior to feeling like you've just known something all your life. For instance, many native speakers have never thought about the simple little fact that regular verbs in English have an "s" when singular and no "s" when plural. This, of course, is exactly the OPPOSITE of what someone learning English for the first time would expect!
I'll just add one more thing -- some commenters think the GMAT shouldn't require science reading! Of course, a huge number of MBAs go into tech-related fields! And, of course, most businesses you might end up working for are, er ... *about* something other than business.
Good luck! I really respect the students who've come through my classroom and have put in a huge amount of effort to master the nuances of the English language, and to be able to comprehend graduate-level reading on any topic.
Sincerely,
Jennifer
What about the skewed tilt in the favor of "idioms"? How do you take that into account?
Though Indians may look non-native, most of them taking GMAT have been studying English since childhood; it's a British legacy. India has many different languages, and as such, English is the lingua franca of the country.
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Re: Does the GMAT discriminate non-english speakers? [#permalink]
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31 May 2012, 19:14
Quote:
What about the skewed tilt in the favor of "idioms"? How do you take that into account?
Though Indians may look non-native, most of them taking GMAT have been studying English since childhood; it's a British legacy. India has many different languages, and as such, English is the lingua franca of the country.
Hi there,
Idioms are being de-emphasized by GMAC in favor of more questions that hinge on meaning, which I think makes sense. (Not that my opinion is very important! If the GMAT wanted us all to learn to hop on one foot while patting our heads, I would teach people to do that.)
I have been to India, albeit briefly. I could write all day about the idiomatic differences between US and Indian English! Of course, many expressions in Indian English are closer to the original British (for some reason, Americans think that "thrice" is a very snooty word, whereas in India and the UK, it's just a normal word, like "twice.") Stores in India have "timings" instead of "hours"; one "gives" an exam rather than "takes" one. A Citibank ATM in Bangalore informed me, "Your transaction is getting done," which just sounds funny to an American (in the US, it would probably say, "Your transaction is being processed.") Of course, it makes perfect sense to "prepone" a meeting. (Maybe now you can tell a little something about the kind of person who becomes a GMAT instructor!)
In short, there are all kinds of nuances that are interesting, but I find that these sorts of things simply do not come up on the GMAT.
Idioms that DO come up include, for instance, "capable OF" and "ability TO" (you cannot be capable to do something, or have the ability of doing something). I think anyone who learns English in the UK, Australia, India, the US, or elsewhere would/should know that.
Separately from one's GMAT studies, it is worth considering whether there is value in learning to write more like an (educated) American if one intends to work in the US. That, I cannot answer.
But I think the GMAT is moving in the right direction by including more problems about meaning. We have numerous posts about this topic on the Manhattan GMAT blog -- I'm new so I can't seem to post links, but google "Meaning is Mean! A GMATPrep Sentence Correction Problem" for a nice example.
Sincerely,
Jennifer
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Re: Does the GMAT discriminate non-english speakers? [#permalink]
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31 May 2012, 20:46
Disclaimer/Caveat: I am a non-native speaker of the language AND run a training company that focuses on GMAT Verbal.
Interesting thread that got picked up by the GMATClub Newsletter. My \$0.02 on this.
1) GMAT does not test vocabulary. Someone mentioned GRE - check that to get an idea how tough it can get! Even if you don't understand a few words that's okay - you can always put it in context and figure out what it means.
2) In SC I feel non-native speakers sometimes have an advantage because when you speak in your native language you really don't think noun-verb-gerund-yada yada! Heck it is almost impossible - you just intuitively know what is right and what is not. So as a non-native speaker you can actually look at it and says well this is a modifier, this modifies this noun etc. I mean SC can actually be like math in some cases. A bunch of rules you need to follow.
3) Actually on a higher score, SC doesn't really test you so much on strict rules of grammar but more on how you are able to apply yourself to a context. It is about logic and figuring out what the sentence means. If you apply logic then the rules of grammar will make sense. But if you apply just the rules of grammar then it will not be logical.
4) CR has little to do with English skills actually and is a direct application of logic. Infact in my classes the teaching usually veers around day to day analogies we are all comfortable dealing with. Once you start looking at it from that perspective CR is really interesting AND easy to solve.
5) RC is about processing power - your ability to digest a dense passage and answer questions that are inferential. To be frank this is a function of your brain power. If you are a native speaker perhaps you expend less power and if you are non-native you perhaps spend more mental currency. Apart from that I really don't see how this is different from say data interpretation, which I think non-natives are good at.
Coming back to the original post I think Indians (and to some extent, based on what I know, even Chinese, and Russians) are good at math because of 2 reasons (a) a culture that places more emphasis on learning the rules than questioning the status quo (b) focus on math because softer-skills, and and liberal arts were never considered important. So when you look at an SC question you were not able to answer instead of internalizing the problem (i.e. this is stuff I need to figure out) we tend to externalize the problem (i.e. maybe there is a rule of grammar that I did not know). I think it is this attitude which stops us from scoring high on the test more than anything else.
I am sorry if I ended up stereotyping but these are my thoughts on the matter,
Arun
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Re: Does the GMAT discriminate non-english speakers? [#permalink]
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01 Jun 2012, 10:39
My two cents worth of thought:
I am not a native English speaker. I have quite high abilities to deal with number properties questions involving for example divisibility properties. But I cannot distinguish between very fine nuances in sentence correction, and I am not an expert in English grammar for sure. So, am I a good candidate to be acccepted to an MBA school? (I am now even wondering whether my last sentence is correct English...) It seems that none of the above is relevant. The demand is really high, and candidates are not able to influence the selection criteria. So, really it won't harm to improve your thinking abilities by doing some basic math and improving your English, is just a bonus. It seems that I am a fatalist...if you cannot get into the desired business school, it means you are not supposed to be there... think of an alternative. It means, you must do something else.
Some might say this is not fair, others might say this is called life! The best thing is to take it easy!
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Re: Does the GMAT discriminate non-english speakers? [#permalink]
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02 Jun 2012, 08:02
This Thread is very interesting. Alot of great viewpoints have been expressed thus far. As a native speaker I do emphasize with non native speakers taking the GMAT. The material in the verbal section must be tough to get through for anyone let alone someone who speaks english as a second or third language. However, what about the advantage it seems non english speakers possess on the quant section? US Citizens who were born and raised here spent k to 12 education learning english, and most of us dont even understand nor use the language correctly. Also other countries tend to prepare applicants much better in terms of quant. It is a long known fact that in the US are students are struggling in math and sciences. ( I can't think of a single math teacher I had in k-12 that actually had a bachelors in mathematics) I mention all of this because both sides are forced to play catch up when studying for the GMAT. Upon looking at what the GMAT covers I have had to purchase Bob Miller's Algebra and Geometry books to assist my studying in the quant section.I live right outside of Detroit,MI. 50% of the population in Detroit is functionally illiterate. That means it is extremely likely anyone who would take the GMAT from this area would be at a great disadvantage in terms of verbal as well and these are people who grew up speaking only english. Based on any applicant or tester's life experiences, they will come to the exam with certain advantages and disadvantages. From these previous experiences during the time of GMAT prep we spot our weaknesses and we strive to make them our strengths.
*Random Notes * Standardized tests aren't perfect by any means Testing African American Students by Asa Hilliard is an amazing book detailing the biased that can/is involved in standardized testing practices, read it in college, must read for anyone interested in diving deeper into this topic.
Also here is the source i used for mentioning 50% of Detroit is functionally illiterate.
http://www.huffingtonpost.com/2011/05/07/detroit-illiteracy-nearly-half-education_n_858307.html
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Re: Does the GMAT discriminate non-english speakers? [#permalink]
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02 Jun 2012, 22:32
JenDziura wrote:
Hi there,
................................
Sincerely,
Jennifer
Jennifer,
I agree with most of what you said.
It was a trap I had set for you, and you went straight for it. We do agree that just knowing English is not enough; a person need to know American English. This becomes more of an issue when someone is stuck between two choices that hinge on nuances that are not so clear to a non-native. Even in Quant section there are many questions that depend upon verbal tricks.
I don't agree that GMAT is unfair to non-natives, but rather believe that native American English speakers have an advantage in the test. Historically, GMAT was designed for American Schools that wanted a standardized tests for admissions. Now, all over the world, schools are relying on GMAT. This fact alone speaks for the beauty of the tests.
GMAT is phasing out idioms, and that may level the playing field in some respect, but there is a long road ahead.
Regards,
someone somewhere in middle of little nothings
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Does the GMAT discriminate non-english speakers? [#permalink]
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27 Jul 2014, 11:06
Does anyone know whether the situation has changed in the past few years? I understand and write English pretty well, and it is a rare case that I don't know a word or can't guess its meaning with high enough accuracy. However, I find that I spend a lot more time reading the passages than I would if they were in my native language. This is true in both the verbal and the quant part of the test. I wonder if the GMAT Prep verbal questions and passages are representative of what I'll encounter in the real test about two weeks from now...
By the way, how common is the word "reciprocal" in standard English? I stumbled across it in the quant part of today's practise test, and had no idea what it meant. I had to make an educated guess that wasn't so educated after all; I thought that it meant the first degree of the number (as in, the number to the power of one). Turned out it means the inverse of a number. The question itself was extremely simple, probably 500-600 level, so I felt kinda bad about my failure to infer the meaning of reciprocal.
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Does the GMAT discriminate non-english speakers? [#permalink]
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07 Jan 2015, 04:15
2
Disclaimer : Following is a hypothetical statement. I collected some information and correlated them to reach at following hypothesis. Therefore, do not rely 100% on it. I believe, following hypothesis has potential to offer us missing piece of GMAT puzzle.
Few Facts:
Post MBA salaries and quality of life in countries such as India are quite low, and in addition, good colleges that take GMAT scores are few. Under this scenario most of the educated "Indian IT male" prefer to do MBA from countries such as USA. Further, it is quite apparent that Indians are good at quants and most of them are smart enough to command concepts of SC in few month, concepts published in official verbal material.
Hypothesis:
Considering above mentioned facts and my experiences with GMAT, I have reached on this conclusion that GMAC is trying to curb population explosion from India by making verbal section tough. To make verbal section tough GMAC has created a separate question set for Indians -- in past many Indian test takers from India reported that questions appearing in exam were very different from questions published by GMAC so far. Also, I have observed that as your attempts increases, questions appearing in exam get more streamlined with questions published in official guide -- means after your second attempt you will start seeing familiar official pattern of SC questions in test. Therefore, If you want to score best in this test in your first or second attempt then you should take this test from USA, Singapore or Australia, markets where local demand and supply for MBA degree is in balance. In these countries test takers mostly claim that MGMAT SC guide is more than sufficient to score best in SC (OR VERBAL), whereas in India test takers are going crazy in search of question types appearing in exam. Further, in OG15 GMAC has not released "new variety" of questions, a variety that usually occur in verbal section of Indian test takers, because such variety does not exist for other nationals. Hence, bottom line for Indians is do not spend years in preparing for GMAT simply give more attempts in a year.
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Re: Does the GMAT discriminate non-english speakers? [#permalink]
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11 Dec 2016, 22:52
Hi all. Fascinating thread. I'm also non-native speaker, and English is also my third language (first two - Kazakh and Russian). I agree that in some cases GMAT really discriminates non-native speakers, specially, in terms of RC. While SC is looking not too complicated even for non-native speaker (just learn the rules and follow the instructions). CR, in my opinion, is not about English, but more about logic. There is no doubt that Verbal part is going to be much more challenging for non-native speakers rather than for native speakers. So, my opinion is - yes, it discriminates, but still it's possible for non-native speaker crack verbal. Anyway, it doesn't matter, because this debates won't solve none of our problems. Then the decision should be just to study hard.
Right now I'm trying to crack RC, and it's really challenging for me. I have just 50%-70% of success, and I think that it's pretty bad... but anyway, I'll try.
I don't agree with statement that:
Quote:
I'll just add one more thing -- some commenters think the GMAT shouldn't require science reading! Of course, a huge number of MBAs go into tech-related fields! And, of course, most businesses you might end up working for are, er ... *about* something other than business.
Because, yes, being consultant (I mean after MBA) I can face problems outside of management, business and economics vocabulary scope, but I'm trying to pass GMAT with aim to enroll to MBA program to learn things not in astronomy and biology areas, but in business area. And I will expand my biology and astronomy vocabulary later. I'm pretty sure that if I don't know some animal, chemistry, astronomy, history or insect vocabulary right now, it won't correlate at all with my potential success in MBA and business areas.
But for non-native speakers in terms of whole application process isn't it an advantage that we know more than one language?
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Re: Does the GMAT discriminate non-english speakers? [#permalink]
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23 May 2017, 03:43
2
PTK wrote:
nonameee wrote:
frank1 wrote:
If it really works as language test, why are international students required to take TOEFL in addition to taking GMAT.
That's something I could never understand. Language wise the GMAT is a much more difficult test than the TOEFL. Yet, international students have to take the TOEFL as well and pay additional money for one more test.
I may agree with you, since GMAT tests language ability as well. However, TOEFL has listening and speaking sections, these sections GMAT does not have.
RC in gmat is much harder than in TOEFL.
Some universities even for Ms degree do not require GMAT, only TOEFL, and TOEFL score requirements may start from 61 points.
I think most of internationl students would agree to exlude from GMAT the verbal part.
Nevertheless, I agree with WALKER, that english proficiency is very important for MBA degree. (just imagine you are an associte in IB or management consulting company and there are ridiculous ERRORS in your presentation, funny isn't it?
Without doubts, english proficiency would increase significantly, while studying/staying two years on campus in english language environment, but still the pre-MBA strong level of English is required.
sorry but I do not agree with WALKER. Im working in quantitative portfolio management and I want to enrol for a Master in FINANCE (not biology, not archaeology) at a Business School. So where is the point of reading paragraphs about fishes, flowers, and all this wired stuff. Not understanding these particular paragraphs doesn't necessarily mean that Im struggling with english. I got 8 in IELTS, I read dozens of high quality finance books in english at ease, economist, financial times and so on and so forth. But when its comes to gmat and its about cosmic space and in order to answer the questions it is essential to understand particular words its sometimes just impossible for me to get the answer right. Till today I don't see the point of native speakers taking the verbal part (I'm sorry guys but its ridiculous easy) You can bash me for that but just try to do such a paragraph in german and then we can come back to this discussion. Gmat discriminates non-natives. Period! Where is the point doing TOELFS or IELTS ???? anyway it doesn't help so as non-native you just have to go hard or home.....
saying that, good luck with the german version.....
Sieben der folgenden Aussagen entsprechen dem Inhalt des Artikels „Biologischer Zündstoff“.
Ordnen Sie die Aussagen den jeweiligen Textabschnitten (11–16) zu. Eine Aussage ist bereits als Beispiel markiert und zugeordnet. Zwei Aussagen passen nicht. Markieren Sie Ihre Lösungen auf dem Antwortbogen.
Beispiel
0 Energiegewinnung aus Pflanzen führt, so die Annahme,
zu einer ausgeglichenen Kohlendioxid-Bilanz.
Aussagen
a Das Verfahren zur Gewinnung von BTL-Kraftstoff ist derzeit noch
zu kostspielig.
Die moderne Zivilisation auf einen nachhaltigen Weg zu bringen, gleicht mehr und mehr dem Versuch, ei- nen Deich zu halten, gegen den die Flut drückt. Hat man gerade noch mit bloßen Händen den einen Riss gestopft, tun sich daneben schon die nächsten auf. Der jüngste Fall: Pflanzen als Energiequelle der Zu- kunft. Vor zwei Jahren noch gepriesen, vergeht nun kaum ein Monat, in dem nicht Umwelt- und Entwick- lungsorganisationen vor dramatischen Konsequenzen für Klima, Umwelt und Ernährungssicherheit warnen.
Beispiel
Die Idee klang bestechend: Anstatt fossile Energieträger wie Kohle und Erdöl zu verbrennen und damit zusätzliches Kohlendioxid in die Atmosphäre zu blasen, könnte man Energie und Kraftstoffe aus Pflanzen gewinnen. Die Lösung wäre klimaneutral, weil dabei nur das CO2 freigesetzt wird, das die Pflanzen für ihr Wachstum zuvor der Atmosphäre entnommen haben. Anders als das endliche Erdöl wachsen Pflanzen nach. Und aus Bauern könnten „Energiewirte“ werden, die eine neue Einkommensquelle erschließen. Eine Win-win-Situation – für Umwelt, Verkehr, Wirtschaft und Arbeit.
Der erste Imageschaden kam mit der soge- nannten „Tortilla-Krise“. Weil die USA für ihre ehrgeizigen Bioethanol-Pläne mehr Mais benötigten, als sie selbst pro- duzieren konnten, wurde in Mexiko dazugekauft – wo- raufhin dort die Preise anzogen und Tortillas aus Maismehl, die Grundlage der mexikanischen Küche, in kurzer Zeit immer teurer wurden. Aus Biokraftstoffen wurden „Agro- Kraftstoffe“, landwirtschaftliche Erzeugnisse, die eigentlich auf den Teller gehören, aber im Tank landen.
Dazu kamen Berichte, in Malaysia oder Bra- silien – das schon seit Jahrzehnten im großen Stil Bioetha- nol aus Zuckerrohr herstellt – weiche der ohnehin schon bedrohte Regenwald neuen Monokulturen aus Energie- pflanzen. Einmalige Lebensräume der Erde, die eine schier unvorstellbare Vielfalt von Arten beherbergten, würden im Namen von Ökologie und Klimaschutz vernichtet. „Bio- kraftstoffe sind ein Angriff auf die Biodiversität“, wetterte die Umweltkoryphäe Ernst Ulrich von Weizsäcker.
Für einen weiteren Kratzer im Lack sorgte jetzt die Wissenschaft. Der niederländische Chemie-Nobel- preisträger Paul Crutzen hatte mit Kollegen die Emissionen von Lachgas (N2O) untersucht, die durch den Einsatz von Kunstdünger auf Biospritfeldern entstehen. Lachgas ist fast
300-mal treibhauswirksamer als CO2. Ergebnis: Die Treib- hauswirksamkeit von Biodiesel aus Raps sei 70 Prozent größer als die von fossilem Diesel, bei Mais seien es 50 Prozent. Nur Zuckerrohr schneide besser ab. Die Studie ist zwar um- stritten; Kritiker werfen Crutzen vor, von veralteten Dünge- methoden und Rapssorten ausgegangen zu sein. Doch nun befand auch eine OECD-Studie, die USA, Kanada und die EU könnten ihre verkehrsbedingten Treibhausgasemissionen bis 2015 mittels Biosprit nur um 0,8 Prozent senken.
Einen Ausweg könnte das Verfahren „Biomass to Liquid“ (BTL) bieten. Bei diesem Verfahren gelingt es, Bio- masse in Gas zu verwandeln und dessen Moleküle dann in die des gewünschten Kraftstoffs. So entsteht etwa syntheti- scher Diesel, der dieselben Eigenschaften wie Diesel aus Erdöl hat. Weil anders als bei Biodiesel oder Pflanzenöl keine Nahrungspflanzen benötigt werden, spricht man von „Bio- kraftstoffen der zweiten Generation“. BTL verwertet vor allem Holz, Stroh und andere Biomasse. Das verwendete Holz kommt zum Teil als sogenanntes Restholz aus dem Wald oder wird von schnell wachsenden Bäumen wie beispielsweise Pappeln gewonnen. Bei diesem BTL-Kraftstoff fallen laut einer Schweizer Studie 40 bis 60 Prozent weniger Treibhaus- gase an als bei fossilem Diesel; wird Waldrestholz verwendet, ist die Bilanz noch günstiger.
Gerade für die Luftfahrt wäre der BTL-Kraft- stoff eine Alternative, da herkömmliche Biokraftstoffe in Flughöhen mit Temperaturen um minus 50 Grad zähflüssig werden. Das BTL-Verfahren ermöglichte aber synthetisches Kerosin mit den gleichen Eigenschaften wie das bisherige herzustellen. Um damit den weltweiten Flugverkehr im heu- tigen Umfang aufrechtzuerhalten, wäre allerdings eine Fläche für den Holzanbau von 120 Millionen Hektar nötig, dreimal größer als Deutschland. Deshalb setzen Flugzeughersteller wie Boeing auf Kerosin aus Algen, die neuerdings als Klima- retter und unerschöpfliche Energiequelle gepriesen werden.
Eine Patentlösung für Bioenergie aus Pflanzen gibt es nicht. Was in Europa ökologisch machbar ist, kann sich anderswo als fatal erweisen. Wenn etwa in Afrika Ener- giepflanzen für den Export in großen Monokulturen angebaut werden sollen, verknappt dies weiter das Trinkwasser auf ei- nem ohnehin trockenen Kontinent. Sogar eine genügsame und nicht essbare Pflanze wie die Jatropha, die seit Kurzem als Energiepflanze für südliche Breiten Schlagzeilen macht, wird zum Problem, wenn internationale Konzerne sie plötz- lich im großen Stil auf fruchtbarem Ackerland anbauen wollen. Richtig genutzt könnte Jatropha aber als regionaler Energielieferant die Abhängigkeit von Ölimporten lindern. Außerdem verbessert sie in ausgelaugten Böden nach einigen Jahren den Wasserhaushalt.
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Re: Does the GMAT discriminate non-english speakers? [#permalink]
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23 May 2017, 07:27
daviddaviddavid completely agree with you. I was also wondering how passages about birds and fishes will help me in business
Re: Does the GMAT discriminate non-english speakers? &nbs [#permalink] 23 May 2017, 07:27
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Given, * is a binary operation on R defined by a*b=a+b-ab
Let . Then
Thus, So, * is a binary operation on R.
Now,
Commutativity : , we have,
So, * is commutative on R
Associativity : , we have,
So, * is associative on R
Identity Element : Let e be the identity element in R, then
So, 0 is the identity element in R.
Inverse of an Element : Let a be an arbitrary element of R and b be the inverse of a. Then,
This inverse exist only if . So, every element of R is invertible except -1.
.
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https://www.reddit.com/user/According_Pop7428 | 1,642,667,202,000,000,000 | text/html | crawl-data/CC-MAIN-2022-05/segments/1642320301730.31/warc/CC-MAIN-20220120065949-20220120095949-00170.warc.gz | 983,887,522 | 16,603 | ×
[–][S] 0 points1 point (0 children)
Thank you MathMagic,
Indeed, when texte1 is defined by :
``````texte1=Text(LaTeX("Hello"), A + (0, -10 c), false, true, 0, -1)
``````
then there is no more bug and the file opens correctly by double-click.
I had done some experiments that led me not far from this conclusion but I had not made the link with the LaTeX display mode! ;)
[–][S] 0 points1 point (0 children)
That's great !
Thanks a lot !
[–][S] 0 points1 point (0 children)
Thank you very much Mathmagic for your perfectly working solution!
I find it extremely unfortunate that there is (as far as I know) no documentation on how scripts are handled by GeoGebra internally: I wasted more than a day trying to figure out why the two commands ZoomIn/CenterView didn't work together.
By any chance, do you have a list of commands that can't work together in the same script?
también podemos conseguir ambos efectos en un solo comando zoomin() pero explicarlo y crearlo no es fácil
If you have the time and inclination, I'd be particularly interested to know your alternative solution to my problem (a simple file without explanation will be enough).
[–][S] 0 points1 point (0 children)
Thanks but that dooesn't solve the problem if A is not a free point.
[–][S] 0 points1 point (0 children)
It seems to me that this is not entirely true.
If myfunction is defined and then, if you write "xmyfunction" in the input box, GeoGebra considers it as "x myfunction(x)".
Test file : https://www.geogebra.org/m/awkqbpke
[–][S] 0 points1 point (0 children)
Yes, I can see your point... although it may seem strange to want to target a segment with an input box. ;)
I just want students to be able to enter a function into the input box and then I would like to compare that function to another previously defined function (say f). But, obviously, this is problematic if the student enters "f" instead of something like "2x+1".
But there is more to it than that. I have just noticed that if, after validating "SetValue(g,-5x)", GeoGebra is asked to recompute all objects (ctrl+R), the function g reverts to the definition of f as if the SetValue had had no effect.
[–][S] 0 points1 point (0 children)
Thanks MathMagic,
I came to the same conclusion as you. But I still think that this behaviour of GGB is not really "normal" as it is the first time that I see such a recalculation of all the objects in the figure. Besides, if you write f(x)=2x and then redefine as f(x)=3x, there is no problem.
Things should be "logical" or happen according to precise (or at least clearly stated) rules.
It gets really complicated to try to produce complex files when you have to deal with so much unexpected behaviour (see my previous post : https://www.reddit.com/r/geogebra/comments/pb8rmc/on_update_bug/)
[–][S] 0 points1 point (0 children)
[–][S] 1 point2 points (0 children)
Thank you MathMagic for your solution.
Your workaround is effective for the submitted example. Unfortunately my real project is much more complex and it appears quite tricky to know exactly when the On Update event is triggered or not. It is unfortunate that the GeoGebra documentation is not more precise on the subject. I have the impression that using listeners via Javascript (whith registerObjectUpdateListener) is much more reliable. On the other hand, it forces to write more code... | 845 | 3,386 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.53125 | 3 | CC-MAIN-2022-05 | latest | en | 0.91212 |
https://ch.mathworks.com/matlabcentral/cody/problems/44342-spot-the-first-occurrence-of-5/solutions/1297354 | 1,603,825,755,000,000,000 | text/html | crawl-data/CC-MAIN-2020-45/segments/1603107894426.63/warc/CC-MAIN-20201027170516-20201027200516-00673.warc.gz | 262,326,238 | 17,331 | Cody
# Problem 44342. Spot the First Occurrence of 5
Solution 1297354
Submitted on 18 Oct 2017 by LY Cao
This solution is locked. To view this solution, you need to provide a solution of the same size or smaller.
### Test Suite
Test Status Code Input and Output
1 Pass
assessFunctionAbsence({'regexp','regexpi','regexprep','str2num'},'FileName','locOf5.m')
2 Pass
x = 2:2:20; y_correct = 0; assert(isequal(locOf5(x),y_correct))
3 Pass
x = rot90(1:10); y_correct = 6; assert(isequal(locOf5(x),y_correct))
4 Pass
x = [1 2 5 5 9 1 5 6 5]; y_correct = [2 0 1]; assert(isequal(locOf5(x),y_correct))
5 Pass
x = magic(5); y_correct = [0 2 0 0 0]; assert(isequal(locOf5(x),y_correct))
6 Pass
x = [1 2 3 4 5; 5 4 3 2 1 2 3 5 2 1 1 5 2 6 8 3 5 2 2 5]; y_correct = [2 4 3 0 1]; assert(isequal(locOf5(x),y_correct)) % %% % x = randi([-10,10],20,1e6); % x(x==5) = 0; % p = sort(randi([0 size(x,1)],5,size(x,2))); % y_correct = p(1,:); % p(2:end,~y_correct) = 0; % [~,col,v] = find(p); % x((col-1)*size(x,1)+v) = 5; % assert(isequal(locOf5(x),y_correct))
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Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting! | 463 | 1,190 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.09375 | 3 | CC-MAIN-2020-45 | latest | en | 0.448222 |
http://physics.qandaexchange.com/?qa=470/rotation-in-truck | 1,568,987,708,000,000,000 | text/html | crawl-data/CC-MAIN-2019-39/segments/1568514574039.24/warc/CC-MAIN-20190920134548-20190920160548-00496.warc.gz | 133,994,537 | 7,946 | # rotation of wheels and axle in accelerating truck
72 views
In the below question
In that while writting the equation of $a_0$ and torque , why they haven't consider the pseudo force.
And what does the 'a' signifies ?
edited Dec 29, 2018
$a_0$ just represent the acceleration due to frictional force
while the given 9m/$s^2$ represent the acceleration of C.O.M and pseudoforce will be for that.
Pseudo forces are applied only when a non-inertial frame of reference is being used. In this case the frame of reference is the ground, which is inertial. $a=9m/s$ is the acceleration of the truck relative to the ground. $a_0$ is the acceleration of the CM of the discs relative to the ground.
It is possible to solve this problem using a non-inertial frame which moves with the lorry. Then a pseudo-force of $-ma$ must be applied to the CM of each disk. The value found for the friction force in this frame will be the same as that in the ground frame.
In the inertial frame the only unbalanced force acting on the disk is friction $f$ with the floor of the truck. There is no pseudo-force. $f$ opposes relative motion, so it is in the forward direction, the same as $a$.
The force $f$ applied at the rim is equivalent to a force $f$ applied to the CM of the disk together with a torque $fR$ about the CM.
Applying Newton's 2nd Law to the CM of the disk, $f=Ma_0$ , where $M$ is the mass of the disk. Likewise, the torque $fR$ on the disk is equal to $J\alpha$ where $J=\frac12MR^2$ is moment of inertia and $\alpha$ is angular acceleration. Eliminating $f$ we get $R\alpha=2a_0$.
The torque rotates the disk backwards relative to the truck. There is no slipping between the disk and the truck so the acceleration of the CM of the disk relative to the truck is $-R\alpha$.
Relative to the ground the acceleration of the CM of the disk is $a_0=a-R\alpha$ therefore $$a_0=\frac13 a$$ $$R\alpha=\frac23 a$$ $$f=\frac13 Ma$$
answered Dec 9, 2016 by (28,806 points)
edited Dec 31, 2018 | 533 | 1,989 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.1875 | 4 | CC-MAIN-2019-39 | latest | en | 0.906046 |
https://www.mathlearnit.com/what-is-51-195-as-a-decimal | 1,675,539,702,000,000,000 | text/html | crawl-data/CC-MAIN-2023-06/segments/1674764500151.93/warc/CC-MAIN-20230204173912-20230204203912-00085.warc.gz | 885,104,284 | 6,792 | # What is 51/195 as a decimal?
## Solution and how to convert 51 / 195 into a decimal
51 / 195 = 0.262
51/195 converted into 0.262 begins with understanding long division and which variation brings more clarity to a situation. Both represent numbers between integers, in some cases defining portions of whole numbers In certain scenarios, fractions would make more sense. Ex: baking, meal prep, time discussion, etc. While decimals bring clarity to others including test grades, sale prices, and contract numbers. If we need to convert a fraction quickly, let's find out how and when we should.
## 51/195 is 51 divided by 195
Converting fractions to decimals is as simple as long division. 51 is being divided by 195. For some, this could be mental math. For others, we should set the equation. The two parts of fractions are numerators and denominators. The numerator is the top number and the denominator is the bottom. And the line between is our division property. We use this as our equation: numerator(51) / denominator (195) to determine how many whole numbers we have. Then we will continue this process until the number is fully represented as a decimal. This is our equation:
### Numerator: 51
• Numerators are the parts to the equation, represented above the fraction bar or vinculum. Any value greater than fifty will be more difficult to covert to a decimal. 51 is an odd number so it might be harder to convert without a calculator. Large two-digit conversions are tough. Especially without a calculator. Now let's explore the denominator of the fraction.
### Denominator: 195
• Denominators differ from numerators because they represent the total number of parts which can be found below the vinculum. Larger values over fifty like 195 makes conversion to decimals tougher. But 195 is an odd number. Having an odd denominator like 195 could sometimes be more difficult. Ultimately, don't be afraid of double-digit denominators. Now it's time to learn how to convert 51/195 to a decimal.
## Converting 51/195 to 0.262
### Step 1: Set your long division bracket: denominator / numerator
$$\require{enclose} 195 \enclose{longdiv}{ 51 }$$
We will be using the left-to-right method of calculation. This method allows us to solve for pieces of the equation rather than trying to do it all at once.
### Step 2: Extend your division problem
$$\require{enclose} 00. \\ 195 \enclose{longdiv}{ 51.0 }$$
Because 195 into 51 will equal less than one, we can’t divide less than a whole number. Place a decimal point in your answer and add a zero. Now 195 will be able to divide into 510.
### Step 3: Solve for how many whole groups you can divide 195 into 510
$$\require{enclose} 00.2 \\ 195 \enclose{longdiv}{ 51.0 }$$
Since we've extended our equation we can now divide our numbers, 195 into 510 (remember, we inserted a decimal point into our equation so we we're not accidentally increasing our solution) Multiple this number by our furthest left number, 195, (remember, left-to-right long division) to get our first number to our conversion.
### Step 4: Subtract the remainder
$$\require{enclose} 00.2 \\ 195 \enclose{longdiv}{ 51.0 } \\ \underline{ 390 \phantom{00} } \\ 120 \phantom{0}$$
If you don't have a remainder, congrats! You've solved the problem and converted 51/195 into 0.262 If you still have a remainder, continue to the next step.
### Step 5: Repeat step 4 until you have no remainder or reach a decimal point you feel comfortable stopping. Then round to the nearest digit.
Remember, sometimes you won't get a remainder of zero and that's okay. Round to the nearest digit and complete the conversion. There you have it! Converting 51/195 fraction into a decimal is long division just as you learned in school.
### Why should you convert between fractions, decimals, and percentages?
Converting between fractions and decimals depend on the life situation you need to represent numbers. They each bring clarity to numbers and values of every day life. This is also true for percentages. It’s common for students to hate learning about decimals and fractions because it is tedious. But 51/195 and 0.262 bring clarity and value to numbers in every day life. Here are examples of when we should use each.
### When you should convert 51/195 into a decimal
Pay & Salary - Anything to do with finance or salary will leverage decimal format. If you look at your pay check, you will see your labor is worth $20.26 per hour and not$20 and 51/195.
### When to convert 0.262 to 51/195 as a fraction
Cooking: When scrolling through pintress to find the perfect chocolate cookie recipe. The chef will not tell you to use .86 cups of chocolate chips. That brings confusion to the standard cooking measurement. It’s much clearer to say 42/50 cups of chocolate chips. And to take it even further, no one would use 42/50 cups. You’d see a more common fraction like ¾ or ?, usually in split by quarters or halves.
### Practice Decimal Conversion with your Classroom
• If 51/195 = 0.262 what would it be as a percentage?
• What is 1 + 51/195 in decimal form?
• What is 1 - 51/195 in decimal form?
• If we switched the numerator and denominator, what would be our new fraction?
• What is 0.262 + 1/2? | 1,255 | 5,232 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.75 | 5 | CC-MAIN-2023-06 | latest | en | 0.90061 |
https://www.aqua-calc.com/convert/surface-density/grain-per-square-nanometer | 1,534,768,456,000,000,000 | text/html | crawl-data/CC-MAIN-2018-34/segments/1534221216453.52/warc/CC-MAIN-20180820121228-20180820141228-00215.warc.gz | 823,857,024 | 10,908 | Select a surface density conversion table with which to
Convert grain per (square nanometer) to other surface density measurement units
Select units whose names contain any of the following checked keywords, where ∗ is a wildcard for partial matches:
Convert grain per (square nanometer) to:CorrelationFormula
1 gr/nm² = 6.479891 × 10+15 centner/ha6.479891 × 10+15 × gr/nm² = centner/ha
1 gr/nm² = 15.4323584 gr/ha15.4323584 × gr/nm² = gr/ha
1 gr/nm² = 0.009999999998 gr/Ų0.009999999998 × gr/nm² = gr/Ų
1 gr/nm² = 1.0 × 10+14 gr/cm²1.0 × 10+14 × gr/nm² = gr/cm²
1 gr/nm² = 9.29030400001 × 10+16 gr/ft²9.29030400001 × 10+16 × gr/nm² = gr/ft²
1 gr/nm² = 6.4516 × 10+14 gr/inch²6.4516 × 10+14 × gr/nm² = gr/inch²
1 gr/nm² = 1.0 × 10+18 gr/m²1.0 × 10+18 × gr/nm² = gr/m²
1 gr/nm² = 1 000 000 gr/µm²1 000 000 × gr/nm² = gr/µm²
1 gr/nm² = 1 000 000 gr/µm²1 000 000 × gr/nm² = gr/µm²
1 gr/nm² = 1 000 000 000 000 gr/mm²1 000 000 000 000 × gr/nm² = gr/mm²
1 gr/nm² = 9.999999998 × 10-7 gr/pm²9.999999998 × 10-7 × gr/nm² = gr/pm²
1 gr/nm² = 8.3612736 × 10+17 gr/yd²8.3612736 × 10+17 × gr/nm² = gr/yd²
1 gr/nm² = 0.0006479891 g/Ų0.0006479891 × gr/nm² = g/Ų
1 gr/nm² = 6 479 891 000 000 g/cm²6 479 891 000 000 × gr/nm² = g/cm²
1 gr/nm² = 6.02001572769 × 10+15 g/ft²6.02001572769 × 10+15 × gr/nm² = g/ft²
1 gr/nm² = 41 805 664 775 600 g/in²41 805 664 775 600 × gr/nm² = g/in²
1 gr/nm² = 6.479891 × 10+16 g/m²6.479891 × 10+16 × gr/nm² = g/m²
1 gr/nm² = 64 798.91 g/µm²64 798.91 × gr/nm² = g/µm²
1 gr/nm² = 64 798.91 g/µm²64 798.91 × gr/nm² = g/µm²
1 gr/nm² = 64 798 910 000 g/mm²64 798 910 000 × gr/nm² = g/mm²
1 gr/nm² = 0.06479891 g/nm²0.06479891 × gr/nm² = g/nm²
1 gr/nm² = 6.479891 × 10-8 g/pm²6.479891 × 10-8 × gr/nm² = g/pm²
1 gr/nm² = 5.41801415492 × 10+16 g/yd²5.41801415492 × 10+16 × gr/nm² = g/yd²
1 gr/nm² = 6.479891 × 10+17 kg/ha6.479891 × 10+17 × gr/nm² = kg/ha
1 gr/nm² = 6.479891 × 10-7 kg/Ų6.479891 × 10-7 × gr/nm² = kg/Ų
1 gr/nm² = 6 479 891 000 kg/cm²6 479 891 000 × gr/nm² = kg/cm²
1 gr/nm² = 6 020 015 727 690 kg/ft²6 020 015 727 690 × gr/nm² = kg/ft²
1 gr/nm² = 41 805 664 776 kg/in²41 805 664 776 × gr/nm² = kg/in²
1 gr/nm² = 64 798 910 000 000 kg/m²64 798 910 000 000 × gr/nm² = kg/m²
1 gr/nm² = 64.79891 kg/µm²64.79891 × gr/nm² = kg/µm²
1 gr/nm² = 64.79891 kg/µm²64.79891 × gr/nm² = kg/µm²
1 gr/nm² = 64 798 910 kg/mm²64 798 910 × gr/nm² = kg/mm²
1 gr/nm² = 6.479891 × 10-5 kg/nm²6.479891 × 10-5 × gr/nm² = kg/nm²
1 gr/nm² = 6.479891 × 10-11 kg/pm²6.479891 × 10-11 × gr/nm² = kg/pm²
1 gr/nm² = 54 180 141 549 200 kg/yd²54 180 141 549 200 × gr/nm² = kg/yd²
1 gr/nm² = 6.37755102034 × 10-10 long tn/Ų6.37755102034 × 10-10 × gr/nm² = long tn/Ų
1 gr/nm² = 6 377 551.02 long tn/cm²6 377 551.02 × gr/nm² = long tn/cm²
1 gr/nm² = 5 924 938 775 long tn/ft²5 924 938 775 × gr/nm² = long tn/ft²
1 gr/nm² = 41 145 408.1 long tn/in²41 145 408.1 × gr/nm² = long tn/in²
1 gr/nm² = 63 775 510 203 long tn/m²63 775 510 203 × gr/nm² = long tn/m²
1 gr/nm² = 0.0637755102 long tn/µm²0.0637755102 × gr/nm² = long tn/µm²
1 gr/nm² = 0.0637755102 long tn/µm²0.0637755102 × gr/nm² = long tn/µm²
1 gr/nm² = 63 775.5102 long tn/mm²63 775.5102 × gr/nm² = long tn/mm²
1 gr/nm² = 6.37755102 × 10-8 long tn/nm²6.37755102 × 10-8 × gr/nm² = long tn/nm²
1 gr/nm² = 6.37755102034 × 10-14 long tn/pm²6.37755102034 × 10-14 × gr/nm² = long tn/pm²
1 gr/nm² = 53 324 449 004 long tn/yd²53 324 449 004 × gr/nm² = long tn/yd²
1 gr/nm² = 64.79891 µg/ha64.79891 × gr/nm² = µg/ha
1 gr/nm² = 647.9891 µg/Ų647.9891 × gr/nm² = µg/Ų
1 gr/nm² = 6.479891 × 10+18 µg/cm²6.479891 × 10+18 × gr/nm² = µg/cm²
1 gr/nm² = 6.02001572769 × 10+21 µg/ft²6.02001572769 × 10+21 × gr/nm² = µg/ft²
1 gr/nm² = 4.18056647756 × 10+19 µg/inch²4.18056647756 × 10+19 × gr/nm² = µg/inch²
1 gr/nm² = 6.479891 × 10+22 µg/m²6.479891 × 10+22 × gr/nm² = µg/m²
1 gr/nm² = 64 798 910 000 µg/µm²64 798 910 000 × gr/nm² = µg/µm²
1 gr/nm² = 64 798 910 000 µg/µm²64 798 910 000 × gr/nm² = µg/µm²
1 gr/nm² = 6.479891 × 10+16 µg/mm²6.479891 × 10+16 × gr/nm² = µg/mm²
1 gr/nm² = 64 798.91 µg/nm²64 798.91 × gr/nm² = µg/nm²
1 gr/nm² = 0.06479891 µg/pm²0.06479891 × gr/nm² = µg/pm²
1 gr/nm² = 5.41801415492 × 10+22 µg/yd²5.41801415492 × 10+22 × gr/nm² = µg/yd²
1 gr/nm² = 0.6479891 mg/Ų0.6479891 × gr/nm² = mg/Ų
1 gr/nm² = 6.479891 × 10+15 mg/cm²6.479891 × 10+15 × gr/nm² = mg/cm²
1 gr/nm² = 6.02001572769 × 10+18 mg/ft²6.02001572769 × 10+18 × gr/nm² = mg/ft²
1 gr/nm² = 4.18056647756 × 10+16 mg/in²4.18056647756 × 10+16 × gr/nm² = mg/in²
1 gr/nm² = 6.479891 × 10+19 mg/m²6.479891 × 10+19 × gr/nm² = mg/m²
1 gr/nm² = 64 798 910 mg/µm²64 798 910 × gr/nm² = mg/µm²
1 gr/nm² = 64 798 910 mg/µm²64 798 910 × gr/nm² = mg/µm²
1 gr/nm² = 64 798 910 000 000 mg/mm²64 798 910 000 000 × gr/nm² = mg/mm²
1 gr/nm² = 64.79891 mg/nm²64.79891 × gr/nm² = mg/nm²
1 gr/nm² = 6.479891 × 10-5 mg/pm²6.479891 × 10-5 × gr/nm² = mg/pm²
1 gr/nm² = 5.41801415492 × 10+19 mg/yd²5.41801415492 × 10+19 × gr/nm² = mg/yd²
1 gr/nm² = 2.285714288 × 10-5 oz/Ų2.285714288 × 10-5 × gr/nm² = oz/Ų
1 gr/nm² = 228 571 428 250 oz/cm²228 571 428 250 × gr/nm² = oz/cm²
1 gr/nm² = 2.12349805198 × 10+14 oz/ft²2.12349805198 × 10+14 × gr/nm² = oz/ft²
1 gr/nm² = 1 474 651 429 130 oz/in²1 474 651 429 130 × gr/nm² = oz/in²
1 gr/nm² = 2.2857142825 × 10+15 oz/m²2.2857142825 × 10+15 × gr/nm² = oz/m²
1 gr/nm² = 2 285.71429 oz/µm²2 285.71429 × gr/nm² = oz/µm²
1 gr/nm² = 2 285.71429 oz/µm²2 285.71429 × gr/nm² = oz/µm²
1 gr/nm² = 2 285 714 283 oz/mm²2 285 714 283 × gr/nm² = oz/mm²
1 gr/nm² = 0.002285714288 oz/nm²0.002285714288 × gr/nm² = oz/nm²
1 gr/nm² = 2.285714288 × 10-9 oz/pm²2.285714288 × 10-9 × gr/nm² = oz/pm²
1 gr/nm² = 1.91114824679 × 10+15 oz/yd²1.91114824679 × 10+15 × gr/nm² = oz/yd²
1 gr/nm² = 0.6430149333 dwt/ha0.6430149333 × gr/nm² = dwt/ha
1 gr/nm² = 0.0004166666666 dwt/Ų0.0004166666666 × gr/nm² = dwt/Ų
1 gr/nm² = 4 166 666 666 670 dwt/cm²4 166 666 666 670 × gr/nm² = dwt/cm²
1 gr/nm² = 3.87096 × 10+15 dwt/ft²3.87096 × 10+15 × gr/nm² = dwt/ft²
1 gr/nm² = 26 881 666 666 700 dwt/inch²26 881 666 666 700 × gr/nm² = dwt/inch²
1 gr/nm² = 4.16666666667 × 10+16 dwt/m²4.16666666667 × 10+16 × gr/nm² = dwt/m²
1 gr/nm² = 41 666.6667 dwt/µm²41 666.6667 × gr/nm² = dwt/µm²
1 gr/nm² = 41 666.6667 dwt/µm²41 666.6667 × gr/nm² = dwt/µm²
1 gr/nm² = 41 666 666 667 dwt/mm²41 666 666 667 × gr/nm² = dwt/mm²
1 gr/nm² = 0.04166666667 dwt/nm²0.04166666667 × gr/nm² = dwt/nm²
1 gr/nm² = 4.166666666 × 10-8 dwt/pm²4.166666666 × 10-8 × gr/nm² = dwt/pm²
1 gr/nm² = 3.483864 × 10+16 dwt/yd²3.483864 × 10+16 × gr/nm² = dwt/yd²
1 gr/nm² = 1.428571429 × 10-6 lb/Ų1.428571429 × 10-6 × gr/nm² = lb/Ų
1 gr/nm² = 14 285 714 274 lb/cm²14 285 714 274 × gr/nm² = lb/cm²
1 gr/nm² = 13 271 862 816 800 lb/ft²13 271 862 816 800 × gr/nm² = lb/ft²
1 gr/nm² = 92 165 714 240 lb/in²92 165 714 240 × gr/nm² = lb/in²
1 gr/nm² = 1.42857142737 × 10+14 lb/m²1.42857142737 × 10+14 × gr/nm² = lb/m²
1 gr/nm² = 142.857143 lb/µm²142.857143 × gr/nm² = lb/µm²
1 gr/nm² = 142.857143 lb/µm²142.857143 × gr/nm² = lb/µm²
1 gr/nm² = 142 857 143 lb/mm²142 857 143 × gr/nm² = lb/mm²
1 gr/nm² = 0.0001428571429 lb/nm²0.0001428571429 × gr/nm² = lb/nm²
1 gr/nm² = 1.42857142867 × 10-10 lb/pm²1.42857142867 × 10-10 × gr/nm² = lb/pm²
1 gr/nm² = 1.19446765351 × 10+14 lb/yd²1.19446765351 × 10+14 × gr/nm² = lb/yd²
1 gr/nm² = 7.14285713687 × 10-10 short tn/Ų7.14285713687 × 10-10 × gr/nm² = short tn/Ų
1 gr/nm² = 7 142 857.14 short tn/cm²7 142 857.14 × gr/nm² = short tn/cm²
1 gr/nm² = 6 635 931 441 short tn/ft²6 635 931 441 × gr/nm² = short tn/ft²
1 gr/nm² = 46 082 857.1 short tn/in²46 082 857.1 × gr/nm² = short tn/in²
1 gr/nm² = 71 428 571 369 short tn/m²71 428 571 369 × gr/nm² = short tn/m²
1 gr/nm² = 0.07142857137 short tn/µm²0.07142857137 × gr/nm² = short tn/µm²
1 gr/nm² = 0.07142857137 short tn/µm²0.07142857137 × gr/nm² = short tn/µm²
1 gr/nm² = 71 428.5714 short tn/mm²71 428.5714 × gr/nm² = short tn/mm²
1 gr/nm² = 7.142857137 × 10-8 short tn/nm²7.142857137 × 10-8 × gr/nm² = short tn/nm²
1 gr/nm² = 7.14285713687 × 10-14 short tn/pm²7.14285713687 × 10-14 × gr/nm² = short tn/pm²
1 gr/nm² = 59 723 382 838 short tn/yd²59 723 382 838 × gr/nm² = short tn/yd²
1 gr/nm² = 0.004628493572 st/ha0.004628493572 × gr/nm² = st/ha
1 gr/nm² = 1.020408163 × 10-7 st/Ų1.020408163 × 10-7 × gr/nm² = st/Ų
1 gr/nm² = 1 020 408 162 st/cm²1 020 408 162 × gr/nm² = st/cm²
1 gr/nm² = 947 990 201 200 st/ft²947 990 201 200 × gr/nm² = st/ft²
1 gr/nm² = 6 583 265 303 st/inch²6 583 265 303 × gr/nm² = st/inch²
1 gr/nm² = 10 204 081 624 100 st/m²10 204 081 624 100 × gr/nm² = st/m²
1 gr/nm² = 10.2040816 st/µm²10.2040816 × gr/nm² = st/µm²
1 gr/nm² = 10.2040816 st/µm²10.2040816 × gr/nm² = st/µm²
1 gr/nm² = 10 204 081.6 st/mm²10 204 081.6 × gr/nm² = st/mm²
1 gr/nm² = 1.020408163 × 10-5 st/nm²1.020408163 × 10-5 × gr/nm² = st/nm²
1 gr/nm² = 1.02040816334 × 10-11 st/pm²1.02040816334 × 10-11 × gr/nm² = st/pm²
1 gr/nm² = 8 531 911 810 800 st/yd²8 531 911 810 800 × gr/nm² = st/yd²
1 gr/nm² = 6.479891 × 10-10 t/Ų6.479891 × 10-10 × gr/nm² = t/Ų
1 gr/nm² = 6 479 891 t/cm²6 479 891 × gr/nm² = t/cm²
1 gr/nm² = 6 020 015 728 t/ft²6 020 015 728 × gr/nm² = t/ft²
1 gr/nm² = 41 805 664.8 t/in²41 805 664.8 × gr/nm² = t/in²
1 gr/nm² = 64 798 910 000 t/m²64 798 910 000 × gr/nm² = t/m²
1 gr/nm² = 0.06479891 t/µm²0.06479891 × gr/nm² = t/µm²
1 gr/nm² = 0.06479891 t/µm²0.06479891 × gr/nm² = t/µm²
1 gr/nm² = 64 798.91 t/mm²64 798.91 × gr/nm² = t/mm²
1 gr/nm² = 6.479891 × 10-8 t/nm²6.479891 × 10-8 × gr/nm² = t/nm²
1 gr/nm² = 6.479891 × 10-14 t/pm²6.479891 × 10-14 × gr/nm² = t/pm²
1 gr/nm² = 54 180 141 549 t/yd²54 180 141 549 × gr/nm² = t/yd²
1 gr/nm² = 0.03215074667 oz t/ha0.03215074667 × gr/nm² = oz t/ha
1 gr/nm² = 2.083333333 × 10-5 oz t/Ų2.083333333 × 10-5 × gr/nm² = oz t/Ų
1 gr/nm² = 208 333 333 333 oz t/cm²208 333 333 333 × gr/nm² = oz t/cm²
1 gr/nm² = 1.93548 × 10+14 oz t/ft²1.93548 × 10+14 × gr/nm² = oz t/ft²
1 gr/nm² = 1 344 083 333 330 oz t/inch²1 344 083 333 330 × gr/nm² = oz t/inch²
1 gr/nm² = 2.08333333333 × 10+15 oz t/m²2.08333333333 × 10+15 × gr/nm² = oz t/m²
1 gr/nm² = 2 083.33333 oz t/µm²2 083.33333 × gr/nm² = oz t/µm²
1 gr/nm² = 2 083.33333 oz t/µm²2 083.33333 × gr/nm² = oz t/µm²
1 gr/nm² = 2 083 333 333 oz t/mm²2 083 333 333 × gr/nm² = oz t/mm²
1 gr/nm² = 0.002083333333 oz t/nm²0.002083333333 × gr/nm² = oz t/nm²
1 gr/nm² = 2.083333333 × 10-9 oz t/pm²2.083333333 × 10-9 × gr/nm² = oz t/pm²
1 gr/nm² = 1.741932 × 10+15 oz t/yd²1.741932 × 10+15 × gr/nm² = oz t/yd²
1 gr/nm² = 0.002679228889 troy/ha0.002679228889 × gr/nm² = troy/ha
1 gr/nm² = 1.736111111 × 10-6 troy/Ų1.736111111 × 10-6 × gr/nm² = troy/Ų
1 gr/nm² = 17 361 111 111 troy/cm²17 361 111 111 × gr/nm² = troy/cm²
1 gr/nm² = 16 129 000 000 000 troy/ft²16 129 000 000 000 × gr/nm² = troy/ft²
1 gr/nm² = 112 006 944 444 troy/inch²112 006 944 444 × gr/nm² = troy/inch²
1 gr/nm² = 1.73611111111 × 10+14 troy/m²1.73611111111 × 10+14 × gr/nm² = troy/m²
1 gr/nm² = 173.611111 troy/µm²173.611111 × gr/nm² = troy/µm²
1 gr/nm² = 173.611111 troy/µm²173.611111 × gr/nm² = troy/µm²
1 gr/nm² = 173 611 111 troy/mm²173 611 111 × gr/nm² = troy/mm²
1 gr/nm² = 0.0001736111111 troy/nm²0.0001736111111 × gr/nm² = troy/nm²
1 gr/nm² = 1.73611111076 × 10-10 troy/pm²1.73611111076 × 10-10 × gr/nm² = troy/pm²
1 gr/nm² = 1.45161 × 10+14 troy/yd²1.45161 × 10+14 × gr/nm² = troy/yd²
What is grain per square nanometer (gr/nm²)? - Back to surface density conversions
Foods, Nutrients and Calories
MCCORMICK, GRILL MATES, SEASONING, MONTREAL CHICKEN, UPC: 052100325170 weigh(s) 142.02 gram per (metric cup) or 4.74 ounce per (US cup) [ weight to volume | volume to weight | price | density ]
Fatty acids, total polyunsaturated food sources
Gravels, Substances and Oils
CaribSea, Freshwater, African Cichlid Mix, Sahara Sand density is equal to 1473.7 kg/m³ or 92 lb/ft³ with specific gravity of 1.4737 relative to pure water. Calculate how much of this gravel is required to attain a specific depth in a cylindricalquarter cylindrical or in a rectangular shaped aquarium or pond [ weight to volume | volume to weight | price ]
Californium (Cf) weigh(s) 5.1 gram per (cubic centimeter) or 2.948 ounce per (cubic inch) [ weight to volume | volume to weight | price | density ]
Volume to weightweight to volume and cost conversions for Diesel fuel with temperature in the range of 10°C (50°F) to 140°C (284°F)
Weights and Measurements
Gram per foot (g/ft) is a non-metric measurement unit of linear or linear mass density.[...]
Energy or fuel economy of an electric vehicle is used to estimate mileage and electricity cost associated with and usage of the vehicle.[...] | 6,630 | 12,589 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.78125 | 3 | CC-MAIN-2018-34 | longest | en | 0.174477 |
http://www.studymode.com/essays/Smu-i-Sem-Stat-Assignments-Set-492840.html | 1,529,543,315,000,000,000 | text/html | crawl-data/CC-MAIN-2018-26/segments/1529267863980.55/warc/CC-MAIN-20180621001211-20180621021211-00400.warc.gz | 494,143,892 | 25,759 | # Smu I Sem Stat Assignments Set 2
Pages: 9 (2088 words) Published: November 25, 2010
MBA SEMESTER 1
MB0040 – STATISTICS FOR MANAGEMENT- 4 Credits
(Book ID: B1129)
Assignment Set- 1 (60 Marks)
Note: Each question carries 10 Marks. Answer all the questions
1. What do you mean by Statistical Survey? Differentiate between “Questionnaire” and “Schedule”.
ANS: Definition of statistical survey:
A Statistical survey is a scientific process of collection and analysis of numerical data. Statistical surveys are used to collect numerical information about units in a population. Surveys involve asking questions to individuals. Surveys of human populations are common in government, health, social science and marketing sectors.
Stages of Statistical Survey: Statistical surveys are categorized into two stages – planning and execution. The two broad stages of Statistical survey AS FOLLOWS:
[pic]
Planning a Statistical Survey: The relevance and accuracy of data obtained in a survey depends upon the care exercised in planning. A properly planned investigation can lead to best results with least cost and time. Steps involved in the planning stage are as follows:
Step 1: Nature of the problem to be investigated should be clearly defined in an unambiguous manner. Step 2: Objectives of the investigation should be stated at the outset. Objectives could be to: • Obtain certain estimates
• Establish a theory
• Verify an existing statement
• Find relationship between characteristics Step 3: The scope of the investigation has to be made clear. The scope of investigation refers to the area to be covered, identification of units to be studied, nature of characteristics to be observed, accuracy of measurements, analytical methods, time, cost and other resources required. Step 4: Whether to use data collected from primary or secondary source should be determined in advance. Step 5: the organization of investigation is the final step in the process. It encompasses the determination of the number of investigators required, their training, supervision work needed, funds required.
Execution of Statistical survey: Control methods should be adopted at every stage of carrying out the investigation to check the accuracy, coverage, methods of measurements, analysis and interpretation. The collected data should be edited, classified, tabulated and presented in diagrams and graphs. The data should be carefully and systematically analysed and interpreted.
Differentiate between “Questionnaire” and “Schedule”:
Questionnaires contain simple questions and are filled by respondents. Schedules also contain questions but responses are recorded directly by the investigator.
2. The table shows the data of Expenditure of a family on food, clothing, education, rent and other items. Depict the data shown in the table using Pie chart.
|Items |Expenditure |
|Food |4300 |
|Clothing |1200 |
|Education |700 |
|Rent |2000 |
|Others |600 |
ANS:
[pic]
Fig: Pie-chart showing expenditure of a family on various items
3. Average weight of 100 screws in box A is 10.4 gms. It is mixed with 150 screws of box B. Average weight of mixed screws is 10.9 gms. Find the average weight of screws of box B.
ANS: GIVEN THAT:
• n1=100,
• n2 = 150,
• X1 = 10.4 Gms,
• [pic]= 10.9 Gms,
• X2 =?
WE KNOW THAT:
[pic]
10.9 = (100*10.4) + (150 X2) / 100+150 10.9 = 1040 + 150 X2 / 250
10.9*250 = 1040 + 150 X2
2725 = 1040 + 150 X2
150 = 2725-1040
X2 =1685 / 150
X2 = 11.23 Gms
Therefore, the average weight... | 821 | 3,498 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.484375 | 3 | CC-MAIN-2018-26 | latest | en | 0.899819 |
http://www.tutorsglobe.com/homework-help/macroeconomics/equilibrium-in-the-flexible-price-model-74348.aspx | 1,550,577,194,000,000,000 | text/html | crawl-data/CC-MAIN-2019-09/segments/1550247489933.47/warc/CC-MAIN-20190219101953-20190219123953-00101.warc.gz | 432,123,869 | 8,826 | #### Equilibrium in the Flexible-Price Model
Equilibrium in the Flexible-Price Model:
Equilibrium and the Real Interest Rate:
In the flexible-price full-employment classical supposition GDP and national income Y equal potential output Y*:
Y = Y*
However the determinants of the components of real GDP are various. We saw that the exchange rate is a function of (a) the real interest rate difference between home and abroad and (b) foreign exchange traders' opinions:
ε = εo - εr x (r - rf)
We saw the determinants of consumption expenditure:
C = Co + Cy x (1-t) x y
Of investment expenditure:
I = Io - Ir x r
And of net exports:
NX = (Xyf x yf) + (Xs x εo) - (Xs x εr x r) + (Xs x εr x rf) - (IMy x Y)
Fourth as well as last we left the determination of government purchases to the political scientists:
G = G
These four components add up to aggregate demand or conceptually at least, total expenditure, written E when we want to emphasize that, it isn’t quite the same as real GDP Y. Nevertheless the circular flow principle guarantees that in equilibrium aggregate demand will add up to real GDP Y:
C + I + G + NX = E = Y
However, the determinants of each of the components of total spending E seem to have nothing at all to do with the production function that determines the level of real GDP Y. How does aggregate demand add up to potential output? Can we be sure that all the output businesses think they can sell when they hire more workers is in fact sold? The answer is that in the flexible-price full employment classical model of this section, the real interest rate r plays the key balancing role in making sure that the economy reaches and stays at equilibrium.
To understand what makes aggregate demand equal to potential output, we need to look at the market in which the interest rate functions as the price: the market for loanable funds. When you lend money the interest rate is the price you charge and the price the borrower pays. Thus we need to look at the flow of loanable funds through the financial markets, the places where household savings and other inflows into financial markets are balanced by outflows to firms seeking capital to expand their productive capacity. The equilibrium we are looking for is one in which supply equals demand in the financial markets. According to the circular flow principle if financial markets are in equilibrium then the sum of all the components of spending is equal to real GDP.
If supply equals demand in the flow-of-funds through financial markets then aggregate supply (real GDP, Y, equal to potential output Y*) is equal to aggregate demand (the sum of all the components of total spending: C+I+G+NX). To see this, begin by assuming that real GDP is equal to potential output Y* and that the circular flow principle holds: real GDP is equal to aggregate demand:
Y* = Y = C + I + G + NX
Then rewrite this expression by moving everything except for investment spending I over to the left-hand side.
Y* - C - G - NX = I
Now comprise taxes T in the left-hand side:
(Y* - C - T) + (T - G) - NX = I
Note that the right-hand side is merely investment the net flow of purchasing power out of the financial markets as firms increase money to build factories and structures and boost their productive capacity. The left-hand side is equivalent to total savings: the flow of buying power into financial markets as the government, households and foreigners seek to save by committing their money to buy precious financial assets here at home. Therefore we see that whenever the circular flow principle holds the supply and demand in the flow of money through financial markets balances as well.
The (Y*-C-T) inside the initial set of parentheses are households' savings. For the reason that national income is equal to potential output, Y* is merely total household income. Subtract taxes, Take income, subtract consumption spending and what is left is household savings: the flow of buying power from households into the financial markets.
The (T-G) inside the subsequent set of parentheses are just government savings: the government's budget excess (or the government’s budget deficit, government dissaving, if G happens to be larger than T). They are the flow of money from the government into the financial markets.
Minus Net Exports Equals the Capital Inflow
:
The final term--minus net exports -NX--is the net flow of purchasing power that foreigners channel into domestic financial markets. If net exports are less than zero foreigners have some dollars left over. They then have to do a little with these extra dollars. Foreigners find dollars valuable in only two ways. First, they are of use for buying our exports (however if net exports are less than zero there aren’t enough exports to soak up all the dollars they earn). Second, dollars are helpful for besides buying stocks, buildings, property here--land, bonds. Therefore this last term is the net flow of purchasing power into domestic financial markets by foreigners wishing to park a few of their savings here. (moreover when net exports are positive, this term is the net amount of domestic savings diverted into overseas financial markets).
What happens if the flow-of-funds doesn’t balance--if at the current long-term real interest rate r the flow of savings into the financial markets surpasses the demand by corporations and others for purchasing power to finance investments? If the left-hand side is exceeding the right, a few financial institutions-- mutual funds, banks, venture capitalists, insurance companies, whatever--will discover purchasing power piling up as more money flows into their accounts than they can find good securities as well as other investment vehicles to commit it to. They will try to underbid their contenders for the privilege of lending money or buying equity in some particular set of investment projects. How do they underbid? They underbid by saying that they would admit a lower interest rate than the market interest rate r. Therefore if the flow of savings exceeds investment the interest rate r falls. As the interest rate r fell the number as well as value of investment projects firms and entrepreneurs found it worthwhile to undertake rises.
Excess Supply of Savings in the Flow-of-Funds Market:
Legend: When the interest rate is such that there is an surplus supply of savings:
Some savers are about to propose to accept a lower interest rate and the interest rate is about to drop.
The process will discontinue when the interest rate r adjusts to bring about equilibrium in the loan able funds market. The flow of investments into the financial markets will then be just equal to the flow of purchasing power out of financial markets, as well as into the hands of firms and entrepreneurs using it to finance investment.
Solving the Model:
At what stage of the real interest rate will the flow-of-funds through financial markets in equilibrium?
First let’s look at the determinants of the provider of private savings:
Y* - C - T = (1 - t - (1-t) Cy) Y* - Co
Second let’s seem at the determinants of public savings:
T - G = tY* - G bar
Third let’s seem at the determinants of international savings:
- NX = IMyY + Xεεrr - XyfYf - Xεεo - Xεεrrf
These three added mutually make up the flow-of-funds supply of savings. The flow-of-funds demand for savings is merely the investment function:
I = Io - Irr
Equilibrium is, obviously where the supply of savings is equal to investment demand. To get an unambiguous expression for the interest rate, start by writing out the determinants of all the pieces of savings:
Grouping all the terms that depend on Y* on the left of the left-hand side all the terms that depend on international factors on the right of the left-hand side, all the terms that are constant in the middle of the left –hand side, and move all the terms with the real interest rate r over to the right-hand side:
Moreover divide by -(Ir + Xεεr) to determine the equilibrium real interest rate r:
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2015 ©TutorsGlobe All rights reserved. TutorsGlobe Rated 4.8/5 based on 34139 reviews. | 1,961 | 9,342 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.84375 | 3 | CC-MAIN-2019-09 | latest | en | 0.941506 |
https://www.physicsforums.com/threads/help-with-fluid-mechanics.750222/ | 1,607,083,705,000,000,000 | text/html | crawl-data/CC-MAIN-2020-50/segments/1606141735600.89/warc/CC-MAIN-20201204101314-20201204131314-00226.warc.gz | 796,243,435 | 14,878 | # Help with fluid mechanics?
Help with fluid mechanics!?
Suppose a cylindrical barrel falls off a ship and sinks to the bottom of the sea at a depth of 1.61 km. Assume that the seawater is incompressible, so that its density at the bottom of the sea is the same at the surface :1020 kg/m^3
If the pressure inside the barrel is 1.00 atm (it was sealed at sea level) and the total surface area of the barrel is 3.50 m^2 , find the NET INWARD FORCE acting on the surface of the barrel when it reaches the bottom of the ocean.
For my attempt, I used the formula Ptot = P surface + ρ density of water x g x h.
The total pressure I got was 116 atm, then I plugged this pressure into P = F/A and got a force of 4. 67 x 10^6 N...
I am not sure what I am supposed to be doing first actually, any guidance would be helpful!
Related Introductory Physics Homework Help News on Phys.org
UltrafastPED
Gold Member
So it is the surface area of the barrel, times the net pressure (116 - 1)=115 atm, pointing inwards.
Net force = pressure x area.
Your hydrostatic pressure formula looks correct: http://hyperphysics.phy-astr.gsu.edu/hbase/pflu.html
... so double-check your calculations, and you are all done. | 304 | 1,199 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.296875 | 3 | CC-MAIN-2020-50 | latest | en | 0.895651 |
https://threesixty360.wordpress.com/tag/anniversary/ | 1,566,559,216,000,000,000 | text/html | crawl-data/CC-MAIN-2019-35/segments/1566027318375.80/warc/CC-MAIN-20190823104239-20190823130239-00001.warc.gz | 669,677,760 | 16,207 | ## Posts Tagged ‘anniversary’
### One year down…
October 31, 2008
Since all the cool kids are doing it, allow me to post a “me too!” brief retrospective here to celebrate our first year.
Actually, “me too!” is pretty much how I got here to begin with. I knew that two faculty at Nazareth College were starting a math blog, and after hearing about what they envisioned, I asked to be allowed in on the fun, even if I teach at the rival college up the road. And fun it has been! I haven’t had this much fun thinking, reading, and writing about vaguely-math-related-stuff since I was killing time in grad school on sci.math and other nether realms of USENET, in the pre-web days of the net. Thank you Batman and Ξ for sharing this space!
We (or at least I) don’t plan out topics in advance; most posts are either driven by stuff we see in the news, cool things that happen in class, or flashes of inspiration in the car driving home from work. And there’s no telling what will hit a chord… who knew that Godzilla would become a recurring character on a math blog? or that Basketball Man and George Orwell Man would keep searching for those images?
Here’s to another year of friends near and far, food, horrid puns, and of course Godzilla, sharing both serious and whimsical slices of mathematics. Cheers!
### Happy Anniversary!
October 31, 2008
One year ago today, Batman set up this site and wrote our very first post. It was seen by approximately 3 people. At that point I had a different username, but then I saw Batman and TwoPi’s names and I got jealous and picked the Greek symbol Xi (Ξ) because in grad school someone had told me once about a class where the prof was using Ξ for some variable, and it occurred in a fraction. The top was just Ξ, but the bottom was Ξ with a bar on top. The fraction ended up looking like this:
I thought that was about the coolest fraction I’d ever seen, and I would have been Xi-over-Xi-bar if I could have, but Xi was the closest I could come.
In thinking about the posts I’ve written, my artistic abilities are rather limited (as any of my students will tell you) so I’m disproportionately proud whenever I manage to create pictures for the posts. And it’s been a surprise (not any more, but at first) how often Godzilla makes guest appearances. He’s like Charo on the Love Boat: once he jumped into the blogging world (with a photo of himself eating Buffalo-Chicken Dip) he hasn’t looked back.
Happy Anniversary 360! And since the Anniversary falls on such an auspicious day, I’ll share one of my favorite sophomore-level math jokes:
Q: Why do mathematicians think that Halloween and Christmas fall on the same day?
A: Because 31 Oct = 25 Dec.*
* Think 31 Base 8 and 25 Base 10 | 644 | 2,740 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.609375 | 3 | CC-MAIN-2019-35 | latest | en | 0.96949 |
https://stats.stackexchange.com/questions/264016/why-lasso-or-elasticnet-perform-better-than-ridge-when-the-features-are-correlat | 1,653,262,431,000,000,000 | text/html | crawl-data/CC-MAIN-2022-21/segments/1652662550298.31/warc/CC-MAIN-20220522220714-20220523010714-00360.warc.gz | 627,678,279 | 69,884 | # Why Lasso or ElasticNet perform better than Ridge when the features are correlated
I have a set of 150 features, and many of them are highly correlated with each other. My goal is to predict the value of a discrete variable, whose range is 1-8. My sample size is 550, and I am using 10-fold cross-validation.
AFAIK, among the regularization methods (Lasso, ElasticNet, and Ridge), Ridge is more rigorous to correlation among the features. That is why I expected that with Ridge, I should obtain a more accurate prediction. However, my results show that the mean absolute error of Lasso or Elastic is around 0.61 whereas this score is 0.97 for the ridge regression. I wonder what would be an explanation for this. Is this because I have many features, and Lasso performs better because it makes a sort of feature selection, getting rid of the redundant features?
Suppose you have two highly correlated predictor variables $$x,z$$, and suppose both are centered and scaled (to mean zero, variance one). Then the ridge penalty on the parameter vector is $$\beta_1^2 + \beta_2^2$$ while the lasso penalty term is $$\mid \beta_1 \mid + \mid \beta_2 \mid$$. Now, since the model is supposed highly colinear, so that $$x$$ and $$z$$ more or less can substitute each other in predicting $$Y$$, so many linear combination of $$x, z$$ where we simply substitute in part $$x$$ for $$z$$, will work very similarly as predictors, for example $$0.2 x + 0.8 z, 0.3 x + 0.7 z$$ or $$0.5 x + 0.5 z$$ will be about equally good as predictors. Now look at these three examples, the lasso penalty in all three cases are equal, it is 1, while the ridge penalty differ, it is respectively 0.68, 0.58, 0.5, so the ridge penalty will prefer equal weighting of colinear variables while lasso penalty will not be able to choose. This is one reason ridge (or more generally, elastic net, which is a linear combination of lasso and ridge penalties) will work better with colinear predictors: When the data give little reason to choose between different linear combinations of colinear predictors, lasso will just "wander" while ridge tends to choose equal weighting. That last might be a better guess for use with future data! And, if that is so with present data, could show up in cross validation as better results with ridge.
We can view this in a Bayesian way: Ridge and lasso implies different prior information, and the prior information implied by ridge tend to be more reasonable in such situations. (This explanation here I learned , more or less, from the book: "Statistical Learning with Sparsity The Lasso and Generalizations" by Trevor Hastie, Robert Tibshirani and Martin Wainwright, but at this moment I was not able to find a direct quote).
But the OP seems to have a different problem:
However, my results show that the mean absolute error of Lasso or Elastic is around 0.61 whereas this score is 0.97 for the ridge regression
Now, lasso is also effectively doing variable selection, it can set some coefficients exactly to zero. Ridge cannot do that (except with probability zero.) So it might be that with the OP data, among the colinear variables, some are effective and others don't act at all (and the degree of colinearity sufficiently low that this can be detected.) See When should I use lasso vs ridge? where this is discussed. A detailed analysis would need more information than is given in the question.
• Good point about the possibility of ridge working better on future data. The distinction between error on cross-validation in the present data and usefulness on new data is too often missed. For some estimate of the latter, the OP could repeat the entire LASSO, elastic-net and ridge model-building processes on multiple bootstrap samples of the data, and then examine errors when applied to the full data set. That at least tests the model-building process.
– EdM
Feb 26, 2017 at 18:15
• It is not obvious to me why it would be advantageous to chose equal weights for collinear data? Can someone elaborate on that point? Sep 11, 2019 at 14:49
• @RamonMartinez I think the idea is that it may be better to keep all the features with an equal weight than to pick a random subset (what lasso will do). Since the subset is random, there's no guarantee that it's the right subset out of sample. Averaging all the features is still not as good as knowing the the true subset, but may be closer than an unlucky random subset. That said if the features are all really colinear I'd expect them to stay colinear OOS in which case most random subsets are probably fine if you only care about prediction. Feb 10, 2020 at 21:23
• Perhaps I did not read it carefully enough, but are you not explaining why ridge should beat lasso while the OP experiences the opposite and is asking for an explanation? Apr 11, 2020 at 16:43
• @Richard Hardy: You are right, I have to amend this answer. But my answer says---When the data give little reason to choose between different linear combinations of colinear predictors, lasso will just "wander" while .... In this case there apparently is some to choose ... Apr 11, 2020 at 16:55
most important difference between lasso and ridge is that lasso naturally makes a selection, expecially where covariates are very correlated. it's impossible to be really sure without seeing the fitted coefficients, but it's easy to think that among those correlated features, many were simply useless. | 1,250 | 5,429 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 11, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.03125 | 3 | CC-MAIN-2022-21 | longest | en | 0.941752 |
http://www.aspmessageboard.com/showthread.php?123192-Stuck-in-a-Cartesian-logic-blob | 1,477,558,489,000,000,000 | text/html | crawl-data/CC-MAIN-2016-44/segments/1476988721174.97/warc/CC-MAIN-20161020183841-00417-ip-10-171-6-4.ec2.internal.warc.gz | 314,612,462 | 14,066 | Stuck in a Cartesian logic blob
# Thread: Stuck in a Cartesian logic blob
1. Senior Member
Join Date
Dec 1969
Posts
194
## Stuck in a Cartesian logic blob
I have 150 records with 6 fields containing a number 1-5,<BR><BR>I'm trying to select any record where field 1 exceeds the number 2, field 2 exceeds the number 2, field three exceeds 4, etc.<BR><BR>What I'm getting is the 276 records in the name table times the 150 records in the skill table.<BR><BR>This is my statement.<BR><BR>strSKILLS = "SELECT Fname, Lname, SID, Skill1, "<BR> strSKILLS = strSKILLS & "skill2, skill3, slill4, skill5, skill6 "<BR> strSKILLS = strSKILLS & "FROM names, skills "<BR> strSKILLS = strSKILLS & "WHERE names.ID = skills.SID "<BR> strSKILLS = strSKILLS & "AND skill1 > 2 "<BR> strSKILLS = strSKILLS & "OR skill2 > 2 "<BR> strSKILLS = strSKILLS & "OR skill3 > 2 "<BR> strSKILLS = strSKILLS & "OR skill4 > 2 "<BR> strSKILLS = strSKILLS & "OR skill5 > 2 "<BR> strSKILLS = strSKILLS & "OR skill6 > 2 "<BR> strSKILLS = strSKILLS & "ORDER BY skill1 ASC"<BR><BR>Kind of wordy, Any help would be appreciated.<BR><BR>
2. Senior Member
Join Date
Dec 1969
Posts
2,930
## AND or OR???
maybe, parentheses? AND (skill1 > 2 or skill2 > 2 or skill3 > 2 etc...)<BR><BR>or do all AND's like AND skill1 > 2 AND skill2 > 2 AND ... AND skill6 > 2... i don't know your logic, so this is the only help i can offer...
3. Senior Member
Join Date
Dec 1969
Posts
2,930
## Tip
Whenever you have a logic problem, just go through in your head... <BR><BR>"I want to select all the records where one of these skill levels is greater than 2"<BR><BR>=<BR><BR>AND (skill1 > 2 OR skill2 > 2 OR skill3 > 2 etc...)<BR><BR>...<BR><BR>"I want to select all records where all the skill levels are greater than 2"<BR><BR>=<BR><BR>AND skill1 > 2 AND skill2 > 2 AND skill3 > 2 AND ... etc...<BR><BR>hope that helps you now and in the future.
4. Senior Member
Join Date
Dec 1969
Posts
194
## RE: Tip
I knew what I wanted.(the first example)<BR><BR>The ( ) is what did it. Thanks!
5. Senior Member
Join Date
Dec 1969
Posts
2,930
## oh...
sorry... also, you're selecting From names and skills...<BR>so add this <BR><BR>strSKILLS = "SELECT Names.Fname, Names.Lname, Names.SID, Names.Skill1, "<BR>strSKILLS = strSKILLS & "Names.skill2, Names.skill3, Names.slill4, Names.skill5, Names.skill6 "<BR><BR>that might help... sorry i didn't see that before.<BR>
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• | 873 | 2,675 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.65625 | 3 | CC-MAIN-2016-44 | latest | en | 0.795025 |
http://www.cfd-online.com/Forums/cd-adapco/54266-help-steady-flow-implicit-multiple-frames.html | 1,440,869,070,000,000,000 | text/html | crawl-data/CC-MAIN-2015-35/segments/1440644064517.22/warc/CC-MAIN-20150827025424-00260-ip-10-171-96-226.ec2.internal.warc.gz | 360,511,129 | 16,237 | help:steady flow with implicit multiple frames
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December 20, 2004, 08:44 help:steady flow with implicit multiple frames #1 RickLee Guest Posts: n/a hi all, I come from Taiwan. My English is not very good. So... my model: a axial fan in the middle of very long channel. how to make the channel's wall is stationary and the fan is rotation? I use the method of tutorial 7.4. But the result is inner(omega=300) velocity is very large and outer(omega=0) is suddenly become zero.It is not continuous in the interface. Even I use Boundary couple, it's the same. How to define the model in steady flow with implicit MRF or single rotating frame? help .
December 21, 2004, 05:15 Re: help:steady flow with implicit multiple frames #2 sunlight Guest Posts: n/a hello i use MRF for radial ventilator and also get huge values for velocity at some regions but get OK values for pressure. at many parts the velocity is ok though. have you decreased the residual ( i used 0.001 and 0.0005 and 1000 iterations) for speed in radial case: c (absolute) = u (rotation) + w (relative) the u component is due to rotation and this is zero after blade ends therefore at the interface the c is not continuous. am i wrong? greetings
December 21, 2004, 20:46 Re: help:steady flow with implicit multiple frames #3 RickLee Guest Posts: n/a hi sunlight: Thank for your Response.But I still think my result is wrong.Because my blade is have a little distance with inner channel,but the velocity in ineer channel is very big and in outer channel "suddenly" become zero. All of the region in outer channel is zeor,too. I guess the interface in inner and outer region is not couple even I use the boundary couple in it's interface.In fact,the momentum in inner region is not translation to outer region.
December 22, 2004, 03:51 Re: help:steady flow with implicit multiple frames #4 Brian Guest Posts: n/a Before looking at the results, you remembered to do a "REFRAME STATIC", right? Otherwise you're looking at computational values, and you will see discontinuities.
December 22, 2004, 21:40 Re: help:steady flow with implicit multiple frames #5 RickLee Guest Posts: n/a Thanks for Brian: Can you tell me how to define the static "REFRAME STATIC"? My fan is steady state model.Can it define the "REFRAME STATIC"?
December 23, 2004, 03:11 Re: help:steady flow with implicit multiple frames #6 Brian Guest Posts: n/a It's a command - REFR. See HELP REFR for details, but basically it adds the rotation speed to the velocities in the regions that are rotating. This is a post-processing function, it has no effect on your solution. The static reference frame is from a viewpoint that is not moving, so you will see high rotation speeds in the rotating areas in this frame. The computational frame (default, REFR COMP) will show very little rotation, as the viewpoint is rotating with the rotating part, but stationary for the non-rotating parts. I hope that makes sense - it may be easier to try it and think about what you're seeing in each case. I am sure you will get it.
December 23, 2004, 05:54 Re: help:steady flow with implicit multiple frames #7 Ricklee Guest Posts: n/a Thank for Brian.I already slove my problem.My result is considered resonable now.Thank for your help.
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All times are GMT -4. The time now is 13:24. | 984 | 3,939 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.734375 | 3 | CC-MAIN-2015-35 | longest | en | 0.916849 |
https://webapps.stackexchange.com/questions/115244/formatting-the-results-of-divide-as-a-fraction-without-being-simplified-google | 1,701,914,332,000,000,000 | text/html | crawl-data/CC-MAIN-2023-50/segments/1700679100626.1/warc/CC-MAIN-20231206230347-20231207020347-00893.warc.gz | 680,976,778 | 40,950 | # Formatting the results of =divide as a fraction without being simplified (google sheets)
I'm dividing the value in one cell by a value in another cell. I want the final result to be in fraction form and not reduce to the smallest equivalent fraction.
I've figured out how to get the result of the `=divide` to format in fraction form `(# ???/???)`.
However, I cannot find a way to keep Google Sheets from simplifying it.
For example:
`=DIVIDE(O4,M10)` in my sheet should show `20/80` - but it converts to `1/4`.
I want to see `20/80`. The denominator will change, so I can't do this `# ??/80`.
It also cannot be formatted as text, because this fraction needs to be used in future math operations.
Tips?
• yes. the fractions are equivalent, but the 20/80 is really a ratio of (points earned/total points possible). The spreadsheet later converts that fraction to a percentage. But it would be nice to see the 20/80--mathematically they are the same, but in terms of a ratio, it communicates something different. Mar 8, 2018 at 21:50
Try this instead of `DIVIDE`,
``````=QUERY(O4/M10,"select Col1 format Col1 '# ?/"&M10&"'")
• By dynamically formatting Denominator to always be M10 through `QUERY`,We preserve the underlying number as well as the format(as opposed to `TEXT` ,Where we cannot change the underlying real value.) | 331 | 1,332 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.703125 | 3 | CC-MAIN-2023-50 | longest | en | 0.910001 |
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# Programming Challenge
restonpiston
Hi, I was looking at youtube videos haphazardly and stumble upon this one:
Here they explain a cool way to decompose numbers but they don't know the method to do that.
The decomposition rules are as follows:
You can only use one type of number from 1 to 9
You can only use operations of sum, subtraction, multiplication, division, exponentiation and concatenation
You must look for the shortest expression
Using this rules you can decompose 814 in:
22*(2+2+2)^2+22
I thought about it for a bit and realize that it would be an interesting challenge for many people.
So here is my idea, post your solution of the problem if you have one and we will discuss it against the others.
I dont have the solution myself, so it would be challenge for me. Also, use your favourite language,
but if you don't mind, make it in python so we all have a common syntaxis.
Have fun!
jestoy0514
Hi restonpiston, have you solve the problem yourself. If so can you please share it with us. It is quite interesting.
restonpiston
Unfortunately, my junior year of CS is keeping me pretty busy, but I will give it a try whenever I have enough time
restonpiston
I have a proof of concept of it. It doesn't work yet, but you can see the basics behind it.
Code: import re; import math; import itertools as it def count(operandos): d=["+","-","*","/","^","."]; solucion=operandos[-1] operandos=operandos[:-1]#https://stackoverflow.com/questions/509211/explain-slice-notation for op in it.permutations(operandos): #print(op) for o in comb_general(d,len(operandos)-2): a="" if op[0]==1 and op[1]==3 and op[2]==5 and op[3]==7: pass; if o[0]=="+" and o[1]=="^" and o[2]=="+" and o[3]==".": pass; if op[0]==1 and op[1]==3 and op[2]==5 and op[3]==7 and op[4]==8 and o[0]=="+" and o[1]=="^" and o[2]=="+" and o[3]==".": print("Help") # for i in range(len(o)): # a=a+str(op[i])+str(o[i]) # a=a+str(op[len(op)-1]) conto=0; contop=0; salida=True; while (conto=len(cadena): return aux; # a=cadena[i] # if a=="(": # for j in range(i+1,len(cadena)): # if cadena[j]==")": # aux=recurs(cadena[i+1:j]) # s1="" # s2="" # if i-1>0: # s1=cadena[:i-1] # if j+10: s1=cadena[:i] if j+1 | 729 | 2,683 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.609375 | 4 | CC-MAIN-2018-05 | latest | en | 0.871798 |
https://www.storyboardthat.com/storyboards/aeddd19f/arkin-9b-physics-ar-integration | 1,638,384,346,000,000,000 | text/html | crawl-data/CC-MAIN-2021-49/segments/1637964360881.12/warc/CC-MAIN-20211201173718-20211201203718-00173.warc.gz | 1,031,054,944 | 24,589 | Arkin 9b physics ar integration
This storyboard was created with StoryboardThat.com
Storyboard Text
• "but why?"
• "no time! tell you later! score a goal!"
• "Shary, kick the ball!"
• "Yes!"
• "yeah, yeah, I know."
• "hey, you said you would explain-"
• "Well, basically, it's just inertia. The ball doesn't have much inertia, so a small kick (or small force) can get it moving. The harder you kick, the more speed you give it. So something moving will never stop moving (or rolling) until an object or friction,"
• "In this case, the net, stops it. And what is at rest stays at rest. But if nothing stops it, it will stay at the same velocity.
• "you GOT IT!"
• "so I had to kick the ball to get it going." | 191 | 710 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.578125 | 3 | CC-MAIN-2021-49 | latest | en | 0.96778 |
https://www.assignmentessays.com/a-three-year-old-machine-has-a-cost-of-31000-an-estimated-residual-value/ | 1,540,227,907,000,000,000 | text/html | crawl-data/CC-MAIN-2018-43/segments/1539583515352.63/warc/CC-MAIN-20181022155502-20181022181002-00420.warc.gz | 861,584,364 | 12,269 | # A three-year-old machine has a cost of \$31,000, an estimated residual value
| October 3, 2018
A three-year-old machine has a cost of \$31,000, an estimated
residual value of \$1,000, and an estimated useful life of five years. The
company uses straight-line depreciation.
Calculate the net book
Net book
value
\$
A three-year-old machine has a cost of \$45,000, an estimated
residual value of \$5,000, and an estimated useful life of four years. The
company uses double-declining-balance depreciation.
Calculate the net book
value at the end of each year.(Round your answers to the nearest dollar amount. Do not round
response.)
First year
Second year
Third year
Net book
value
\$
\$
\$
A three-year-old machine has a cost of \$21,000, has an estimated
residual value of \$1,000 and an estimated useful life of 40,000 machine
hours. The company uses units-of-production depreciation and ran the
machine 3,200 hours in year 1; 7,050 hours in year 2; and 7,500 hours in year
3.
Calculate the net book
value at the end of the third year.(Do not round your intermediate calculations.
Net book
value
\$
Purity Ice Cream Company bought a new ice cream maker at the
beginning of the year at a cost of \$12,000. The estimated useful life was
four years, and the residual value was \$960. Assume that the estimated
productive life of the machine was 9,200 hours. Actual annual usage was 3,680
hours in year 1; 2,760 hours in year 2; 1,840 hours in year 3; and 920 hours
in year 4.
Required:
1.
Complete a separate
a.
Straight-line.
Year
Depreciation
Expense
Accumulated
Depreciation
Net
Book Value
At acquisition
\$
1
\$
\$
2
3
4
b.
Units-of-production (use
four decimal places for the per unit output factor).
Year
Depreciation
Expense
Accumulated
Depreciation
Net
Book Value
At acquisition
\$
1
\$
\$
2
3
4
c.
Double-declining-balance.
Year
Depreciation
Expense
Accumulated
Depreciation
Net
Book Value
At acquisition
\$
1
\$
\$
2
3
4
three intangible assets at the end of 2011 (end of the accounting year):
a.
A copyright purchased on January 1, 2011, for a cash cost of
\$12,300. The copyright is expected to have a 10-year useful life to Cheshire.
b.
Goodwill of \$65,000 from the purchase of the Hartford Company on
July 1, 2010.
c.
A patent purchased on January 1, 2010, for \$39,200. The inventor
had registered the patent with the U.S. Patent Office on January 1, 2006.
Required:
1.
Compute the
Acquisition cost
\$
Goodwill
Patent
2.
Compute the amortization of each intangible at December 31,
2011. The company does not use contra-accounts. (Assume the company uses
straight-line method)(Leave no cells blank – be certain to enter “0” wherever
Amortization
\$
Goodwill
Patent
3.
Show how these assets and any related expenses should be
reported on the balance sheet and income statement for 2011. (Assume there
Income
statement for 2011:
Operating
expenses:
\$
Balance
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Positive SSL | 860 | 3,135 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.578125 | 4 | CC-MAIN-2018-43 | latest | en | 0.894223 |
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SLOPE STABILITY ANALYSIS. Boiana Mato UDK: DOI: Summary: Both.
3.4 Janbu and Morgenstern-Price methods of stability analysis . .. that fact that the mechanical analysis of slope stability provides us with knowledge of what.
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http://teach4ever.net/algebra-i/q2-syllabus-a/ | 1,670,079,367,000,000,000 | text/html | crawl-data/CC-MAIN-2022-49/segments/1669446710933.89/warc/CC-MAIN-20221203143925-20221203173925-00119.warc.gz | 45,011,233 | 16,775 | # Q2 Syllabus (A)
Basic skills Warm-up. Should be able to put the controls at 9 and -9 and do 20 Random problems in 60 seconds WITHOUT A CALCULATOR: CLICK HERE. Do not change settings. Click GO. Work for 60 seconds then show score.
REVIEW WEEK:
In order to succeed in this class, you need to be able to do all of these things to 100% – not necessarily on the first try but given enough chances you must be able to do all these things or it is unlikely you will be successful going on. In college, these are known as prerequisites.
For the video links, they may or may not work from school. Most of the worksheets have additional help at the top and the bottom of the page.
Monday Oct 29
Distribution 2.7
Tuesday Oct 30
http://teach4ever.net/SignInWorksheets/Alg2RvwLikeTermsSignin.html
http://teach4ever.net/SignInWorksheets/Alg2Rvw2LikeTermsSignin.html
Wednesday Oct 31
http://teach4ever.net/SignInWorksheets/Alg3_3a_EquationsSignin.htm
http://www.teach4ever.net/SignInWorksheets/Alg3_3b_EquationsSignin.htm
Thursday Nov 1
http://teach4ever.net/SignInWorksheets/Alg3_4ExpressionsSignIn.html
http://teach4ever.net/SignInWorksheets/Alg7_2aEGraphingEquationsSignIn.html
Friday Nov 2
http://teach4ever.net/SignInWorksheets/Alg7_5aSlopeInterceptSignIn.htm
http://teach4ever.net/SignInWorksheets/Alg7_5bSlopeInterceptSignIn.html
Monday Nov. 5
Section 8.1 Systems of Equations.
p. 360 5-25. Make sure you follow the examples given in class.
Tuesday Nov. 6
Solving by Substitution.
Wed Nov. 7
Section 8.1 Systems of Equations.
p. 360 5-25. Make sure you follow the examples given in class.
Thur Nov. 8
Solving by Substitution (Second time – should have done twice). If you have already done once and can show me two more WITH WORK – you can opt to help other people in class instead of doing it a second time.
Friday Nov. 9
Brief interview of the THIRD way to find the simultaneous solution: ADDITION (sometimes called elimination or even subtraction).
QUIZ!, must show work.
Homework: Practice more from this week if needed. Plan to re-take quiz on Tuesday if needed. Find a you-tube video that explains this if needed!!
Monday Nov. 12
HOLIDAY
MONDAY AFTERNOON IS THE LAST DAY TO MAKE UP ANYTHING FROM BEFORE OCTOBER 15.
Tuesday Nov. 13
MUST SHOW WORK AND submit answers.
MUST COMPLETE AT LEAST 5 in class to get full credit and finish a total of 10.
Wednesday Nov. 14
Start on word problems. ALL of these require an equation (probably two but some of you are cleverer than I). For each one state:
1) What your variables are: For instance d=cost per day and t=total cost
2) What your equations are: For instance 25 + 2c=t and 30+1.5c=t
3) Use substitution or the addition method to solve. Since these are real world problems, you are LIKELY to end of with a decimal from time to time.
Thursday Nov. 15
More on word problems
Friday Nov 16
Continue on Word Problems and Addition Method.
Quiz over addition method and word problems.
Last 20 minutes. Pick any 4 problems (of differing types) here . Copy them down on the paper provided. Show your work. Show the check. ONE OF THEM must be done by the addition method to get full credit. FOLLOW DIRECTIONS PROVIDED.
Monday Nov. 19
Practice Test over graphing with particular emphasis on Systems of equations.
Tuesday Nov. 20
TEST.
Bonus Question to work on after test
•BONUS QUESTION:
•You have a gigantic jar of pennies and nickels. You weigh them and find their TOTAL weight to be 4570 grams. The change counter at the store says adds up to \$30.94. If nickels weigh 5 grams and pennies weigh 2.5 grams, how many of each do you have? ON A SEPARATE SHEET OF PAPER Write down the question and using any method you like find the answer.
Wednesday Nov. 21
Very shortened day. GGN Review for Extra Credit.
Extra Credit over break (can count up to two homework assignments IF DONE WELL). On a separate sheet of paper create a 10 question MULTIPLE CHOICE test related to ALL of the material we’ve covered so far (Chapters 1,2,3,7,8) – use the book, internet work (look at last quarter syllabus as well!), and warm-ups as a source of ideas. Each problem should have at least four possible answers. There should be a key of correct answers at the end of the test. At least ONE question should have an x-y graph (hand-drawn is fine).
Example:
What is a solution to y=x+1?
a) (1,1) b) (2,3) c) (4,-4) d) (2,1)
Today for extra credit GGN
Monday Nov. 26
CRITICAL THAT YOU UNDERSTAND THE BASICS OF THESE NEXT TWO ASSIGNMENTS!!
It’s also important that you know the symbol and the meaning of the Less Than, Greater Than, Less Than or Equal to, and Greater Than or Equal To signs.
Inequalities and their graphs.
HW/CW: p.173 1-40. For each problem, write the question and provide the answer according to the directions. As always, check your odds as you go.
Tuesday Nov. 27
HW/CW p.178 1-40. For each problem, write the question and provide the answer according to the directions. As always, check your odds as you go.
Wednesday Nov. 28
Multiplication Property of Inequalities.
This is where it differs from what we have done before as multiplying(dividing) both sides by a NEGATIVE, flips the inequality sign.
Do this internet worksheet.
Thursday Nov. 29
Do this worksheet on expressions of inequalities and this one similar to yesterday’s (only a little harder).
Quiz like this on Monday!!
Friday Nov. 30
Repeat Yesterday’s worksheets. Should have done both twice. Do more than twice if you think you need more practice OR would like better scores.
Check here to see what you should have done so far this quarter.
If done early, practice for quiz below. Be sure you know how to graph the answers (see Monday the 26th’s work in book for examples of how to graph)
Monday Dec. 3
Quiz like work from last week.
Introduction to chapter 9.
HW: P. 408 1-30
Tuesday Dec. 4
•Human number line
–If YOU work in the question and the people on both sides of you work, point at both of them.
–If YOU work and only one person next to you works, point towards them and hold a solid fist in front of you.
–If YOU don’t work but one person next to you works, point towards them and make a zero in front of you.
–Classwork?: p. 408 31-50. Check your odds.
Wednesday Dec. 5
Do this as review and then do this. Be sure to look at examples at bottom.
Thursday Dec. 6
More absolute value practice
This worksheet from yesterday a second time. (Some of you haven’t done it the first time).
Friday Dec. 7
Review InEqualities by doing this one ONE MORE TIME (should be third – make sure you’ve don three times by Monday!!!) Re-quiz on Monday. Higher score, I’ll count it twice. Lower score, stuck with it for try #2, keep score for first try.
Remember: On a number line you have x>#. You circle the # (shade it if >=) and then test numbers on either side to see if they work. Testing the point to the left and the right of the point you picked is the best way to know which side to shade. I
Want to practice over the weekend and won’t have access to the internet – ask for a paper practice copy!
Monday Dec. 10
TODAY AND TOMORROW AFTER SCHOOL ARE THE LAST DAYS TO RE-TAKE ANY QUIZZES as well as complete any internet work FROM Oct 29-Dec 9. For all your classes you should be forming a plan as to how to best finish up the semester – waiting until the last minute is not a plan.
HW/CW: and/or’s graphing worksheet.
re-Quiz over inequalities. MUST copy problem, show work, and graph.
Tuesday Dec. 11
Introduction to section 9-4. Absolute values in Inequalities.
HW (due Thursday). p. 415 1-36
Practice Quiz over disjunctions (ors) and conjunctions(ands).
1-6 should be done as “and” pairs and 7-12 should be done as “or” pairs. Make sure you understand the “empty set” and “all real numbers” exceptions. For the practice quiz. Do 1 and 2 then show me the conjunction graph to ensure you are doing it right. Then do 7 and 8 as a disjunction. Show me again. Finish. Attempt to get this done BEFORE the end of class so I can check your graphs.
Wednesday Dec. 12
Most of you are not ready for the quiz yet.
1) Check Homework Worksheet using the key in the U: drive. If your graph is incorrect, mark it as incorrect. If you did not do the graph, DO THE GRAPH. Turn in when done.
2) Finish work from yesterday
3) Start Homework that is due tomorrow. p. 415 1-36. Most of these absolute value problems require you to turn them into an “and” or an “or”. If you didn’t take notes yesterday on when and how to do this, then read pages 413-415.
Thursday Dec. 13
Go over absolute value homework.
Logic Puzzles. (related to the and/or) – Worksheet. Don’t lose. You will need for tomorrow.
Quiz over disjunctions (ors) and conjunctions(ands).
1-6 should be done as “and” pairs and 7-12 should be done as “or” pairs.
Friday Dec. 14
More Logic Puzzles – Using the back of the worksheet from yesterday (or on a separate sheet of paper), look at several of the puzzles on the link below. You should do this in groups of 2 to 4. For each puzzle you look at, write down what time you start, what time you figured it out (or gave up and looked at the answer), a brief description of the problem, and a brief description of an answer someone came up with. NO ONE IS AUTOMATICALLY GOOD AT MATH OR PUZZLES – we get better because we stick with them, try different things, and practice. The ability to sit and think about a problem that does not initially make sense is the sign of a mature, independent thinker.
http://www.puzzle.dse.nl/logical/index_us.html
TURN IN THE WORK ABOVE TO THE GUEST TEACHER.
Extra Credit over break (can count up to two homework assignments IF DONE WELL). On a separate sheet of paper create a 10 question MULTIPLE CHOICE test related to ALL of the material we’ve covered so far (Chapters 1,2,3,4,7,8,9) – use the book, internet work (look at last quarter syllabus as well!), and warm-ups as a source of ideas. Each problem should have at least four possible answers. There should be a key of correct answers at the end of the test. At least ONE question should be related to each chapter. Beside each question, write which chapter it came from. Since there are 7 chapters and 10 questions, the last three questions may come from any chapter but you still must say where they came from. MAKE SURE YOU READ THESE DIRECTIONS TWICE. Gave a similar assignment over the Thanksgiving break and many people did not get as many points as they could have simply because they did not read the directions.
Wed. Jan. 2 (13)
Graphing on x-y plane review. In class worksheet to be turned in. If absent, do page 419 4-23, 2 equations per graph. SPECIAL INSTRUCTIONS: Change all inequalities into equal signs.
Thur. Jan 3 (12)
Graphing inequalities on x-y plane. 9.4
Big idea: On a number line you have x>#. You circle the # (shade it if >=) and then test numbers on either side to see if they work. When doing this on the x-y plane, the only real difference is the line creates a boundary line and you shade everything on one side of the plane or the other – testing a point to see which side is correct. If its a > or < (compared to >= or <=) the line is dashed instead of solid because the line itself will not satisfy the inequality.
Homework (Graph paper provided). p. 419. Starting with #3, every 3rd problem. 3,6,9… up to 39. CHECK YOUR ODDS.
Friday Jan 4(11)
Identifying Graphed Inequalities by their picture and determining the expressions. Misc review on graphing on x-y plane.
IN CLASS WORKSHEET
Mon. Jan 7(10)
Graphing SYSTEMS of inequalities.
Like Friday except TWO sets on the same graph. The solution is the one that works for both.
DUE AT END OF CLASS: p. 423 1-6. For each inequality in the system you MUST
1) Write the inequality and then rewrite the inequality as an equation (your boundary line)
2) Graph the line by either a) finding three sets of points OR b) re-writing as slope-intercept form.
3) Make the boundary line dotted or shaded depending on the original inequality
4) Choose a test point and plug it into the original inequality. State as True or False.
5) Shade the correct half-plane based on the results of your test point
Do the same for the second inequality in the system following the same steps.
EXTRA CREDIT. #22,23
Homework. p. 427 Chapter Review. 11-38. Pick and choose at least 20 and check your answers as you go. All answers in the back of the book. Be sure to write the question and show your work. Hand-drawn graphs are fine.
Tue. Jan. 8 (9)
Multiple choice quiz on systems of equations.
Pre-Quiz on Chapter 5 Exponents and Polynomials. Write down your answers (right or wrong) as you go.
Cheat Sheet assigned – due on day of practice exam (Tuesday)- this is an assignment but can also be used during the exam. Failure to do it shows that either you are a genius who already have 101% or that you totally don’t care what you get for a grade. If you lose it, it’ll cost you a quarter to get a new one!
Wed. Jan 9 (8)
5-1 and 5-2 – Rules for exponents p. 207 9-66 (every 3rd problem. 9,12,15,18.. – check odds) – Due at end of class. Write down each problem (Ask about this – if we are running short on time I MAY not require this for the class problems).
HW: p. 212 9-66 (every 3rd problem. 9,12,15,18.. – check odds) Write down each problem.
Thur. Jan 10 (7)
5-3 Multiplying and dividing, Review of like terms.
HW p. 215 9-66 (every 3rd problem. 9,12,15,18.. – check odds) Write down each problem.
NOTEBOOKS DUE TOMORROW. You need to go through and number your warm-ups. Each one should already have a date on it. Your first one for this quarter is likely dated 10/22. Simply Write a 1 by YOUR FIRST ONE, a 2 by YOUR SECOND ONE, and so on. If you have 22 warm-ups it should be number 1,2,3…22. If you have 30 warm-ups, it should be numbered 1,2,3…30. Beside the very last one (THURSDAY) Write TOTAL: and the number of warm-ups. 34 or more warm-ups is 100%. They are worth 3 points each. Every one over 34 is worth 1 point of extra credit. Have your notebook numbered and ready to go at the start of class tomorrow. If it is not ready at the start of class it is late (10 points off for late and 5 points off for following directions). If it is not ready by the start of class Monday, 50% off. ALSO – MAKE SURE YOUR NAME IS ON the first page and the last page!!
Fri. Jan 11 (6)
5-4 Scientific Notation
HW/Classwork p. 219 1-39 Odds. Check back of the book as you go. Write down each problem. [Did this myself – took me ten minutes including checking the back of the book – only needed my calculator for one problem where I was too lazy to do the division long hand]
Additional suggested homework for Sunday night. Do 2 or 3 problems from each of the 4 sections in Chapter 5 in order to review for quiz. (Put some of this on cheat sheet?)
Notebooks due.
Practice Quiz on Chapter 5
This week
Mon. Jan 14(5) – Last week of the semester. If you’ve been planning ahead, this week should be a breeze. If your affairs are not in order, woe is you.
More practice on Scientific Notation. Do evens from book in class.
Quiz over Chapter 5
EXTRA CREDIT (IN CLASS ONLY): Something from my Geometry class: A different way of looking at Surface Area and Volume – try THIS. Basic idea: COUNT the cubes for volume. Count the squares ON THE SURFACE for surface area. You have to “count” the ones you cannot see as well.
Homework – Finish Cheat Sheet. Due tomorrow!! Make sure you have your book at home!!
Tue. Jan 15(4)
Practice Exam – Cheat Sheets due!
Wed. Jan 16(3)
GGN to review for tomorrows’s exam.
Bring a book or something to do silently to do after the test (although most of you will need the entire time).
Remember to bring your cheat sheet.
Homework: Go through notes, warm-ups, book, internet, looking for at least 3 more things to add to your cheat sheet.
Thur. Jan 17(2)
Semester Final – Cheat sheet may be used (for those of you who forgot on Tuesday I will give half credit for those who bring them COMPLETED)
If You finish early, did you try the extra credit from Monday? Find something SILENT to do. Everyone deserves a chance to finish their test with quiet.
Fri. Jan 18(1) – Last day of the semester!
Did you do extra credit from Monday? Are you MISSING any tests or quizzes?
Give Mr. T feedback (Grade him!)
Monday January 21 is MLK day – No School
Tuesday is a teacher workday – No School
Wednesday – You may or may not have a new teacher on Wednesday. I have told the district I can work Wed and Thur if your new teacher has not completed their paperwork. (A new permanent teacher is coming – we will have picked them last week) | 4,401 | 16,786 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.265625 | 3 | CC-MAIN-2022-49 | latest | en | 0.773472 |
https://forums.creativecow.net/thread/227/37088 | 1,545,028,504,000,000,000 | text/html | crawl-data/CC-MAIN-2018-51/segments/1544376828318.79/warc/CC-MAIN-20181217042727-20181217064727-00639.warc.gz | 590,028,775 | 5,719 | ADOBE AFTER EFFECTS: Forum Expressions Tutorials Creative Cloud
# How get a random position with fixed numbers
FAQ • VIEW ALL
How get a random position with fixed numbers on Oct 12, 2017 at 10:55:37 pm
I heave a fixed positions for X - simple [1, 4, 6, 9, 45, etc] and fixed posotions for Y [3, 8, 56, 32, etc]
What expressions i need to use to set my object in random X position of [1, 4, 6, 9, 45, etc] and Y of [3, 8, 56, 32, etc] in every frame ?
Re: How get a random position with fixed numberson Oct 13, 2017 at 7:35:54 am
I don't know how you save your variables. I will asume that you declare them inside your expression. This first expression if for using same position of x and y(third x matches third y)
```xArray = [100,300,500,700]; yArray = [200,400,600,800]; randomPosition = Math.round(random()*(xArray.length-1)); x = xArray[randomPosition]; y = yArray[randomPosition]; [x,y]```
This code is for using random x and random y.
```xArray = [100,300,500,700]; yArray = [200,400,600,800]; xrandomPosition = Math.round(random()*(xArray.length-1)); yrandomPosition = Math.round(random()*(xArray.length-1)); Math.floor(random()*xArray.length); x = xArray[xrandomPosition]; y = yArray[yrandomPosition]; [x,y]```
Feel free to ask if you need any further explanation.
Andrei | 394 | 1,295 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.90625 | 3 | CC-MAIN-2018-51 | latest | en | 0.66929 |
http://www.theconcreteproducer.com/castinplace-concrete/how-precisely-should-labs-round-off-compressive-strength-results-.aspx | 1,464,372,573,000,000,000 | text/html | crawl-data/CC-MAIN-2016-22/segments/1464049276964.77/warc/CC-MAIN-20160524002116-00128-ip-10-185-217-139.ec2.internal.warc.gz | 836,368,994 | 12,178 | Question: We had some cores drilled in a pavement section where there was some question about compressive strength. We got the compressive strength report back from the lab, and the strength was rounded to the nearest 1 psi. Is this correct?
Answer:Compressive strength is nothing more than a ratio between applied load and the surface area. For cores or cast-in-place cylinders, the surface area is calculated with the following equation: Area = Pi * D / 4, where D is the diameter of the core or cylinder.
When the diameter of the cylinder is measured to the nearest 0.01 inch, the final compressive strength should be recorded to the nearest 10 psi for both cast-in-place cylinders and cores, according to ASTM C 39 Section 8.1 and ASTM C 42 Section 6.8.2. However, should the diameter of a core have a precision of only 0.1 inch, the final compressive strength should be rounded to the nearest 50 psi. There is no provision for reporting to the nearest 50 psi for cast-in-place cylinders, only for drilled cores. In no case should the compressive strength ever be rounded to the nearest 1 psi.
It's also important to note that in calculating the ratio between applied load and area, you also have to use a strength correction factor, determined by the ratio between the length of the cylinder and the diameter. You can find this ratio in ASTM C 39 Sec. 8.2 and ASTM C 42 Sec. 6.7.2. The precision and accuracy of the diameter measurement determines the final precision of the compressive strength. | 335 | 1,504 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.90625 | 3 | CC-MAIN-2016-22 | latest | en | 0.949736 |
https://craftofcoding.wordpress.com/2021/02/08/why-python-is-horrible-for-recursion/ | 1,620,250,459,000,000,000 | text/html | crawl-data/CC-MAIN-2021-21/segments/1620243988696.23/warc/CC-MAIN-20210505203909-20210505233909-00034.warc.gz | 207,073,038 | 21,721 | # Why Python is horrible for recursion
If you are going to choose one language to write recursive algorithms in, then avoid Python. Why? It is just too restrictive. There are a number of reasons for this. Firstly Python is intrinsically lethargic, i.e. it will take a long time to run algorithms. Next, the Python interpreter doesn’t perform any sort of recursion optimization. Due to this, the recursion limit is often quite low. On most systems it is set at 1000. This means when a recursive function has to recurse many times, an error will be generated by the system.
RecursionError: maximum recursion depth exceeded in comparison
This is done to avoid a stack overflow, and so that infinite recursions are avoided. Nice. But not very useful. We can of course override this using the function setrecursionlimit(), which takes one parameter, the value of the new recursion limit. But honestly, it is likely best to use another language altogether.
import sys
sys.setrecursionlimit(10**6)
To illustrate the inability of Python to cope with recursion, we will implement a recursive Slowsort algorithm in Python, and C. This algorithm was chosen, not because of its great abilities, but rather because of the fact that it is inefficient, and will spur the use of recursive resources. Below is the algorithm written in Python.
def slowsort(A, i, j):
if i >= j:
return
m = int((i+j) / 2)
slowsort(A, i, m)
slowsort(A, m+1, j)
if A[j] < A[m]:
A[j], A[m] = A[m], A[j]
slowsort(A, i, j-1)
The code is then run with the following code, which reads from a file, and sorts the numbers:
with open('num25.txt') as file:
lines = [int(i) for i in file]
a = 0
b = len(lines)-1
slowsort(lines,a,b)
To sort a mere 25 numbers with this algorithm takes 655 seconds in Python. The same algorithm written in C it takes 0 seconds (probably nanoseconds). In many respects if you are programming in Python, there is very little likelihood you will really need recursion anyway.
This site uses Akismet to reduce spam. Learn how your comment data is processed. | 494 | 2,046 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.890625 | 3 | CC-MAIN-2021-21 | latest | en | 0.892427 |
https://www.physicsforums.com/tags/models/ | 1,709,530,822,000,000,000 | text/html | crawl-data/CC-MAIN-2024-10/segments/1707947476413.82/warc/CC-MAIN-20240304033910-20240304063910-00277.warc.gz | 933,525,068 | 29,184 | # What is Models: Definition and 400 Discussions
A model is an informative representation of an object, person or system. The term originally denoted the plans of a building in late 16th-century English, and derived via French and Italian ultimately from Latin modulus, a measure.
Representational models can be broadly divided into the concrete (e.g. physical form) and the abstract (e.g. behavioural patterns, especially as expressed in mathematical form). Of particular importance in the modern context, conceptual models are central to philosophy of science, as almost every scientific theory effectively embeds some kind of model of the physical or human sphere.
In commerce, a model might instead reference a specific version or configuration of a product offering, rather than functioning as a representation of something else.
In taxonomic settings (e.g. biology, architecture, art) a model is sometimes a particular instance of a set of related entities (species, built structures, artistic compositions) chosen as a convenient reference point around which to build discourse; such a model is almost always chosen to typify some central tendency of the group, exemplify the group's defining characteristic, or reify the group's historical lineage.
Kinds of models include:
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1. ### A Are there any theorems restricting possible QG candidates?
String theory, being such a theoretically successful theory as it is but with no experiment to single it out as THE model among alternatives, Im left to wonder, which models can be excluded? Are there essential no-go theorems regarding the physics of a theory for QG? Im aware of the...
2. ### Electric heat generation from parallel rods carrying current in an oil bath
I know that ##\dot e_{gen} = \frac {R_{e}i^2} {\pi r^2 L}## the thing is I don't know the value of i. I didn't write it, but another thing that the problem asks is to determine the flow of electric current. The model I came up with using heat generation due to electrical current is \frac...
3. ### I Models where all symmetries would be approximate?
I found this interesting discussion here in Physics Forums (https://www.physicsforums.com/threads/are-all-symmetries-in-physics-just-approximations.1005038/) where the topic of all symmetries being approximate is discussed Is there any model (for instance, some type of spacetime metric or...
4. ### Neural networks as mathematical models of intelligence
Why do almost all people not think that neural networks are the mathematical model of intelligence? I briefly explain what I understand: -A neuron is a mathematical object that takes numerical inputs from other nearby neurons, applies a nonlinear function (combining the input with numbers...
5. ### A Deriving Non-linear acoustic wave models, equilibrium state assumption
The standard derivation in obtaining a single wave equation involves making use of the heat equation with a Taylor expansion of the equation of state, then differentiating this equation and the continuity equation with respect to time, and combining with the divergence of the NS equation...
6. ### I Predicates and Models ... Goldrei
I am reading Goldrei's book: "Propositional and Predicate Calculus: A Model of Argument", Chapter 4: Predicates and Models. I need help in understanding Goldrei's answer to Exercise 4.5 (a) ... Exercise 4.5 together with Goldrei's solution reads as follows: Can someone please explain exactly...
7. ### I Linear Models vs Nonlinear Models
Hello, Models can be linear and nonlinear and I just learned that a "linear model" is not just a model where the dependent variable ##Y## is connected to independent variables ##X## raised to the 1st power... The model is called "linear" because the coefficients/parameters are not raised to...
8. ### I Do AEST (Absolute Euclidean Spacetime) models work?
I was reading a paper by J.M.C Montanus which was published in <low quality journal reference removed> in which he claims under AEST the new gravitational dynamics and electrodynamics are reformulated in close correspondence with classical physics, and subsequently leads to the correct...
9. ### I Hubble Parameter as function of time in universe models
This graph shows ##H## as a function of time related to the L-CDM model. Do we (@Jorrie) have similar graphs e.g. for ##\Lambda=0##; ##k=-1## critical, ##\Lambda=0##; ##k=0## open, ##\Lambda=0##; ##k=+1## closed? That would be great, thanks in advance.
10. ### I Some classical models of particles and quantum gauge theories
My article has been published in Quantum Reports. Expanded abstract: There is currently no consensus on the interpretation of quantum theory, so this article may be of interest as it contains a review and new results on some relevant mathematical models emulating well-known quantum theories...
11. ### I Trouble for physical collapse models?
https://www.quantamagazine.org/physics-experiments-spell-doom-for-quantum-collapse-theory-20221020/ Experiments Spell Doom for Decades-Old Explanation of Quantum Weirdness Physical-collapse theories have long offered a natural solution to the central mystery of the quantum world. But a series of...
12. ### A Exploring the Perception of Pain: Skeletal Models & Physics
I am not cooking up a torture device or a weapon. In fact, I have been spending time with skeletal models. I just want to be able to create the ability to perceive pain. Even if I were to try to work this out myself and get some kind of answer that relates to physics, how would I know for sure...
13. ### Ethical and social risks of harm from Language Models
I thought this paper might be of interest to those who are interested in how large language models such as GPT-3 pose various hazards. From the abstract: It is quite long but particularly attractive because it gives advice on how to read it for those who can only afford a minute or 10...
14. ### MCNP6 Fatal Error : Models required
Hi! so its me again. After previous problem already solved now i ran into another problem. now about BURN card. its said need model? what kind of model? I tried using .84c for all my material but doesn't seems to work! heres my code if anyone wants to try :-( c TWR-P...
15. ### I Direct limit of multiverse models of ZFC
Let ##(M_i)_{i\in I}## be a multiverse of models of ZFC. By that I mean: Each ##M_i## is a well-founded model of ZFC. ##(I,\leq_I)## is a partially ordered set, and whenever ##i\leq_I j##, there is an embedding ##\tau^j_i:M_i\rightarrow M_j## such that the image of ##M_i## is a transitive...
16. ### Questions about Circuit Models of Transmission Lines
This is for my graduate EM Theory class. My background is physics/optics, so I was able to understand when we solved maxwells eqs. for waves propagating between parallel conducting plates, but that lead into the lumped element circuit model of transmission lines which I don't understand. I've...
17. ### I Queueing Models: Generator Matrix for M/M/2/2 & M/M/2/4
Hello there, If we have M/M/C/K = M/M/2/2 (where note that the first M stands for memoryless arrival times for the packets (thus described by a Poisson process(lambda)), the second M stands for memoryless service times (i.e. described by an exponentially distributed(mu)), the number 2 for C...
18. ### Consider three models of the Mass distribution in the Milky Way
I attached a Jpeg with my attempted solution but I´m not sure if I´m on the right way... I hope for a correction in my calculations
19. ### I Why Are There So Few Quantum Time Machine Models?
As of today, there are plenty of time machine mathematical models based on general relativity theory (warp drives, wormholes), but few ones based on quantum physics. However, back in 2010, Seth Lloyd wrote: "quantum mechanics supports a variety of counter-intuitive phenomena which might allow...
20. ### MHB How many stickers did Angel and Kareem have altogether?
Angel and Kareem had some stickers. Angel had 5 times as many stickers as Kareem. After Angel gave 36 stickers to Kareem, both of them had an equal number of stickers. How many stickers did they both have altogether
21. ### MHB Bar Models with Ratios - HELP
I need help with how to use bar models with these kinda stuff. Thanks
22. ### B Is an infinite universe compatible with cyclic models?
Cyclic models for reference. I will take simple Big Bounce as an example of what I have in mind. In Big Bounce there periods of expansion and periods of contraction which result in a never-ending series of Big Bangs. However if Universe is infinite in extent this would require infinite amount...
23. ### I How well do cosmological models explain the observed µ vs. z data?
The following figure shows observed distance modulus (µ) vs. redshift (z) data (references of data sources are available): How well do cosmological models, such as ΛCDM and models based on non-expanding universe, explain these observed data? For explanation of terms, please see, Type Ia...
24. ### Impedance/admittance (acoustic) models for outdoor ground and seafloor
There are some mathematical models (eg Delany-Bazley) to calculate impedance of porous materials and these formulas give complex impedance values as a result. But I could not find any model to be used for seafloor (underwater ground modeling) or I don't know if existing models may be used. I...
25. ### Applications Involving Drying -- Using Kinetic Models
Hi, I am a mechanical student. I would like to ask are those drying kinetic equations for food drying applicable in drying a paperboard? Thankyou :)
26. ### Uncertainties in climate models
I have seen that many posters here seem to be very knowledgeable about the man made climate "emergency". So someone can surely point out a reference where all the sources of uncertainties for at least one specific model are provided with an estimate of their values (for examples, uncertainties...
27. ### A Exploring Planck 2015 Results on Power Law Potential Models
I am reading Planck 2015 results. In particular, I focused on "Power law potentials" subsection. The issues I have are 1. I do not understand why the validity of the model can be determined by the value of the ##B## mode. 2. Why the ##B## mode values ##\ln B = −11.6## and ##\ln B = −23.3## for...
28. ### Question about Spectral Estimation using AR Models
Hi, I was recently reading about spectral estimation with parametric methods, and specifically auto-regressive models. I came across the statement: "An AR(p) model can provide spectral estimates with p/2 peaks" and I was wondering why this was the case. I do apologize if this is the wrong forum...
29. ### A question about the parameters/constants entering climate models
Can someone point out to a resource where would be provided a list and description of the constants/parameters used in modern climate models. And the values used with their uncertainties. (PS: I know that any question related to global warming tends to trigger some people, I was called dumb...
30. ### A What are the parameters that are the same in CMB data for multiple models?
In cosmology, CMB tells a lot about which cosmological model can be acceptable or not. For instance we know that, whatever the cosmological model we use ##\theta_*## parameter will be always the same. Is there any other parameters that is listed in this picture is **model-independent** ?(i.e...
31. ### I Models and theories of laws of physics emerging from chaos?
Some physicists (like John A Wheeler, Holger B Nielsen or Ilya Prigogine) have proposed that all the laws of physics (including the most fundamental ones) emerged from a primordial chaos (for example, in the case of Wheeler, he proposed that laws of physics emerged from an initial random and...
32. ### I Probability models and entropy
Thinking of the common language notion of "entropy" as "uncertainty", how can running a simulation based on a probability model implement entropy increasing? After all, the simulation picks definite outcomes to happen, so (intuitively) there is less uncertainty about the future as definite...
33. ### Models for weather that include data from amateur stations?
I have the impression (I've not actually researched the matter) that some online weather services publish data from weather stations set up by amateurs. Do any organizations incorporate such data in their weather prediction models? I'd think that using such data would involve a sophisticated...
34. ### When are Lumped-element models used in the design process?
Hi everybody, Academic papers in mechanical engineering use often lumped-element (or lumped-parameter) models such as a typical quarter car model. However, books about the (mechanical) engineering design methodologies (such as by authors Dieter, Shigley, or Pahl-Beitz) seem to not mention this...
35. ### 3D Printing and "Watertight" Digital Models
Hello, I understand that CAD models (stl files) suitable for 3D printing must be "watertight" and not leaky in the polygon mesh. By analogy, if we filled the model with water, the water would not leak...This concept of watertightness means that there are no unintentional holes between the...
36. ### Material Models Sources: Ludwik, Holomon, Swift, Wok, etc.
Who can share the primary sources where material models are formulated: Ludwik, Holomon, Swift, Wok, Ludwikson, Hill and others?
37. ### A Advanced models for the Stern-Gerlach experiment
A detailed discussion of measurement in the Stern-Gerlach experiment can be given in the POVM setting; see this post.
38. ### I IAU Rotational Models: Sol Solar System Planet Info
I am developing my own project called orbital flight simulator myself. I was looking for some IAU rotational model about all planets (Sol solar system) through the Internet and my books but was unable find any information. Does anyone have good books or information (tables and algorithms like...
39. ### I Who was the first to find an initial singularity in GR models of the universe?
I have a question about the history of cosmology, hope its okay to ask here. Who was the first person since Einstein's Gr to point out a singularity in cosmology? I know Freidman talked of an expanding universe and Lematire a primeval atom. But were there any explicit mentions of the density of...
40. ### Policy for pandemic issues and how models shape it
https://www.sciencemag.org/news/2020/03/mathematics-life-and-death-how-disease-models-shape-national-shutdowns-and-other This shows how policy can be informed about differing effects of control policies in different environments. One of the bleak aspects of UK choices is shown as a graph...
42. ### How do I predict rogue waves using simple probability models ?
I need to predict an upcoming rogue wave or analyse old rogue wave events using simple probability models and real-time data for a physics high school project.
43. ### Relationship between Heat Capacity Cv for Different Models
I think the C_V for van der waals gas will be larger than ideal gas since it‘s a more precise description. However, for the relationship I cannot come up with a specific equation.
44. ### Computer models that predict the maximum power of a chemical reaction
Given a balanced chemical equation, can we predict using computer models the maximum power of the chemical reaction? Thanks.
45. ### How to characterize mathematical models for comparison
I am reviewing and comparing a wide range of mathematical models that are being applied to a specific realm of wildlife biology. For the comparison of these models, and to weigh advantages/disadvantages of different aspects with regard to application, I need to characterize each model. As I do...
46. ### A Friedmann-Robertson-Walker Models
Can we say that a universe with a radiation density (only) exists only in near a Big Bang time, and not a Big Crunch? Since it gets much smaller as time passes. For example in here: http://www.nat.vu.nl/~wimu/Varying-Constants-Pictures/Time-Scale-Universe.jpg We have different cosmological...
47. ### I Best models to describe molecules
Molecules don't really look like this with clearly defined objects and outlines. Remember that in the double slit experiments, we can't even model what happens between measurements, like how the electron behave between emitter and detector. So what is the best model to describe them? How...
48. ### I Confused by nonlocal models and relativity
Hello everyone! Recently I saw this paper: https://arxiv.org/pdf/1304.4801.pdf ("Any nonlocal model assuming “local parts” conflicts with relativity " by Antoine Suarez). He mentions standard experimental configuration with beam-splitters and detectors. Then he distinguishes possible models...
49. ### I Are all Cellular Automata models of universes?
Both Stephen Wolfram and nobel laureate Gerard 't Hooft think that the universe is a Cellular Automata. As far as I know, 't Hooft developped a series of frameworks to build different models of Cellular Automata and Wolfram also proposed a framework where network nodes could produce different...
50. ### Differing first-principle models for Maxwell-Boltzmann statistics?
Let's consider a simple scenario in Maxwell-Boltzmann statistics: 6 identical but distinguishable particles, and 9 quanta of energy, 9 indivisible units, to be distributed among the particles.The first model is like that of the wheels on a combination lock, or should I say "permutation lock"... | 3,846 | 17,450 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.578125 | 3 | CC-MAIN-2024-10 | latest | en | 0.929819 |
https://arzung.org/adding-integers-worksheet-pdf/ | 1,620,817,830,000,000,000 | text/html | crawl-data/CC-MAIN-2021-21/segments/1620243989693.19/warc/CC-MAIN-20210512100748-20210512130748-00524.warc.gz | 140,977,405 | 9,997 | # Adding integers worksheet pdf Most Effective
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Adding Integers Worksheet Pdf. 11 12 1 e. These worksheets are pdf files. 09102020 Adding integers worksheet pdf. Adding integers worksheet with answers pdf.
Adding And Subtracting Integers Worksheets Differentiated Adding And Subtracting Integers Subtracting Integers Integers Worksheet From pinterest.com
This page includes integers worksheets for comparing and ordering integers adding subtracting multiplying and dividing integers and order of operations with integers. These pdf worksheets provide abundant practice for 6th grade 7th grade and 8th grade students. Thermometer help students of grade 6 and grade 7 relate the adding and subtracting of integers with the temperature on a. Students find pairs of congruent shapes and add the numbers inside of them. These worksheets are printable pdf exercises of the. Find the sum of the.
### Printables Free Integer Word Problems Worksheet Integer Word Problems Worksheet Printable Fabul Word Problem Worksheets Free Math Worksheets Math Word Problems The dead sea the lowest elevation is 1.
The videos games quizzes and worksheets make excellent materials for math teachers math educators and parents. 1 9 10 j. -11 -5 12 2 10 -13 -8 -5 13 14 -7 15 11 15 -3 -1 -12 -1 -2 -15 10 -12 -5 7 13 -4 12 2 12 -13 -9 -1 9 -6 3. 21 posts related to adding integers worksheet grade 7. 14 4 10 m. 8 21 29 l.
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Adding Integers Find the sums of the integers. Students find pairs of congruent shapes and add the numbers inside of them. 04102020 Integers ranging from 20 to 20 are given in these pdf worksheets. If the signs are different then subtract smaller number from the largest number. Adding integers worksheet with answers pdf.
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Adding integers 85 96 11 80 57 137 86 38 48 22 41 19 18 45. 3 3 6 g. 8 21 29 l. These worksheets are pdf files. Add and subtract integers worksheet 2.
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Adding and subtracting integers word problems worksheet pdf addition and subtraction facts within 0 10 difference more than word problems. Students find pairs of congruent shapes and add the numbers inside of them. 15 7 8 i. Adding integers 85 96 11 80 57 137 86 38 48 22 41 19 18 45. Find the new reading in each thermometer.
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Number Line - Adding Integers Sheet 1 Use the number line to nd the sum. At the top of this worksheet there are many shapes with positive and negative numbers in them. 10 14 4 c. 12012021 Ordering integers worksheet for 7th grade children. 04102020 Integers ranging from 20 to 20 are given in these pdf worksheets.
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At the top of this worksheet there are many shapes with positive and negative numbers in them. 15 7 8 i. Students find pairs of congruent shapes and add the numbers inside of them. This packet is your notes for all of chapter 1. 10 14 4 c.
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In pdf for easy printing. Free integers positive and negative numbers worksheets adding subtracting multiplying dividing comparing. Add and subtract integers worksheet 2. Rules for Adding Integers Rule 1. Operations with integers With our adding and subtracting integers worksheets with answers PDF Multiplying and dividing integers worksheets your kids will discover simple ways to visualise and smartly work out math problems on integers following the four basic math operations.
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12012021 Ordering integers worksheet for 7th grade children. Worksheet 1 Worksheet 2 Worksheet 3 Worksheet 4 Worksheet 5 Worksheet 6. If the signs are different then subtract smaller number from the largest number. Adding and subtracting integers word problems worksheet pdf addition and subtraction facts within 0 10 difference more than word problems. If the signs are the same then add the numbers.
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5 8 3 d. These worksheets are pdf files. 12012021 Ordering integers worksheet for 7th grade children. 3 5 2 b. If the signs are different then subtract smaller number from the largest number.
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Adding Integers A Use an integer strategy to find each answer. It is expected you will take good notes and work the examples in class with your teacher in pencilIt is expected that you bring your packet to class every day and do not lose it. 5 8 3 d. Printables Free Integer Word Problems Worksheet Integer Word Problems Worksheet Printable Fabul Word Problem Worksheets Free Math Worksheets Math Word Problems The dead sea the lowest elevation is 1. 11 12 1 e.
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Find the new reading in each thermometer. Adding integers 85 96 11 80 57 137 86 38 48 22 41 19 18 45. 8 21 29 l. Addition of integers -10 to 10 Below are six versions of our grade 6 math worksheet on addition of integers with absolute value less than 10. At the top of this worksheet there are many shapes with positive and negative numbers in them.
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1 9 10 j. In pdf for easy printing. Printables Free Integer Word Problems Worksheet Integer Word Problems Worksheet Printable Fabul Word Problem Worksheets Free Math Worksheets Math Word Problems The dead sea the lowest elevation is 1. The videos games quizzes and worksheets make excellent materials for math teachers math educators and parents. Add and subtract integers worksheet 3.
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This page includes integers worksheets for comparing and ordering integers adding subtracting multiplying and dividing integers and order of operations with integers. 20 13 7 h. 14 4 10 m. Adding integers worksheet with answers pdf. Answers to Adding and Subtracting Integers 1 4 2 2 3 3 4 2 5 4 6 5 7 5 8 17 9 13 10 2 11 1 12 0 13 1 14 7 15 9 16 9 17 2 18 0 19 1 20 12 21 3 22 1 23 6 24 5 25 1 26 11 27 1 28 0 29 9 30 5 31 4 32 6.
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I g pa4l bl o urji mguhmtpsx xrxegsbexrcv le9de 6 x wmjamd1e5 fw ji wt4hq yiancf pi6neijt aea gprqev ya9l 3g neab fraa6 f worksheet by kuta software. 09102020 Adding integers worksheet pdf. 10 14 4 c. Answers to Adding and Subtracting Integers 1 4 2 2 3 3 4 2 5 4 6 5 7 5 8 17 9 13 10 2 11 1 12 0 13 1 14 7 15 9 16 9 17 2 18 0 19 1 20 12 21 3 22 1 23 6 24 5 25 1 26 11 27 1 28 0 29 9 30 5 31 4 32 6. Keep the same sign.
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This page includes Integers worksheets for comparing and ordering integers adding subtracting multiplying and dividing integers and order of operations with integers. 20 13 7 h. Keep the sign of the bigger number. The videos games quizzes and worksheets make excellent materials for math teachers math educators and parents. 8 21 29 l.
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-11 -5 12 2 10 -13 -8 -5 13 14 -7 15 11 15 -3 -1 -12 -1 -2 -15 10 -12 -5 7 13 -4 12 2 12 -13 -9 -1 9 -6 3. 20 13 7 h. P k2r0 s102 a jKJu etXai RSFo xfQttwnadroeK cL HLyC RE m HAyldlw Xrwiqgth Et8s Q 1rVeFs1enr evbe 0dNM v gMRaMdWeo TwAiUtxh N MIEn jffiIn1i lt re l sA plLgNe5b 7rGax t1 2Q Worksheet by Kuta Software LLC Kuta Software - Infinite Algebra 1 Name_____ Adding Positive and Negative Numbers Date_____ Period____. Free integers positive and negative numbers worksheets adding subtracting multiplying dividing comparing. Students find pairs of congruent shapes and add the numbers inside of them.
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These worksheets are pdf files. 8 21 29 l. 11 12 1 e. Thermometer help students of grade 6 and grade 7 relate the adding and subtracting of integers with the temperature on a. P k2r0 s102 a jKJu etXai RSFo xfQttwnadroeK cL HLyC RE m HAyldlw Xrwiqgth Et8s Q 1rVeFs1enr evbe 0dNM v gMRaMdWeo TwAiUtxh N MIEn jffiIn1i lt re l sA plLgNe5b 7rGax t1 2Q Worksheet by Kuta Software LLC Kuta Software - Infinite Algebra 1 Name_____ Adding Positive and Negative Numbers Date_____ Period____.
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3 5 2 b. _____ _____ Adding Integers 85 -96 -11 80 57 137 86 -38 48 22 -41 -19 -18 -45. Rule for Subtracting Integers Rule 1. P k2r0 s102 a jKJu etXai RSFo xfQttwnadroeK cL HLyC RE m HAyldlw Xrwiqgth Et8s Q 1rVeFs1enr evbe 0dNM v gMRaMdWeo TwAiUtxh N MIEn jffiIn1i lt re l sA plLgNe5b 7rGax t1 2Q Worksheet by Kuta Software LLC Kuta Software - Infinite Algebra 1 Name_____ Adding Positive and Negative Numbers Date_____ Period____. 3 5 2 b.
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http://www.conservapedia.com/index.php?title=Pareto_efficiency&diff=next&oldid=993131 | 1,532,271,363,000,000,000 | text/html | crawl-data/CC-MAIN-2018-30/segments/1531676593302.74/warc/CC-MAIN-20180722135607-20180722155607-00029.warc.gz | 414,256,917 | 7,650 | # Difference between revisions of "Pareto efficiency"
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In game theory and economics, the concept of Pareto efficiency (or Pareto optimality) is a method to judge the efficiency of a set of decisions made by the participants. It was named after Vilfredo Pareto. Paretto efficiency is different from and should not be confused with Nash equilibrium.
A decision set (a combination of all decisions made by all participants) is called strong Pareto optimal if there is no other set in the entire decision space (all possible decision sets) in which at least one participant is strictly better off and no participant is worse off than he was as a result of the current decision set. A decision set is called weak Pareto optimal if there is no other set in the entire decision space in which every participant is strictly better off than he was as a result of the current decision set. While a strong Pareto optimal set is necessarily weak Pareto optimal, the converse is not necessarily true.
If there exist a decision set where at least one participant's outcome improves without anybody else's outcome worsening, the new decision set Pareto dominates the old set.
## When Pareto efficiency is not the equilibrium state - Prisoner's dilemna
B A not confess confess not confess A: good / B: good A: bad / B: very good confess A: very good / B: bad A: OK / B: OK
In the one-stage game shown at the right side, prisoners A and B can concurrently choose between "not confess" and "confess". The result can either be "very good", "good", "OK", or "bad".
The green field ("not confess/not confess") is the Pareto optimal situation; the red field is the Nash equilibrium solution.
There exists no other decision set besides "not confess/not confess" that has an equal or better outcome for all participants. However, in "not confess/not confess" ("good" for A, "good" for B), A could switch to "confess". Assuming B does not change his decision, this improves A's result to "very good" while changing B's result to "bad". (There is no honor among thieves, so A is not concerned about B's welfare.) Knowing this, if B also changed his decision to "confess", B's result improves to "OK". However, A's result would then worsen, but only down to "OK" as well. Now at "confess/confess", if either A or B unilaterally changes to "not confess", his result worsens to "bad". Thus, "confess/confess", and not the Pareto optimum, would be the equilibrium outcome.
Generally in a game with finite steps, the equilibrium outcome may not necessarily be the Paretto efficient outcome. | 581 | 2,597 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.65625 | 3 | CC-MAIN-2018-30 | latest | en | 0.941116 |
http://www.chegg.com/homework-help/questions-and-answers/suppose-1st-1-4-distance-two-points-covered-average-velocity-18-m-s-average-velocity-remai-q1946757 | 1,472,353,046,000,000,000 | text/html | crawl-data/CC-MAIN-2016-36/segments/1471982932803.39/warc/CC-MAIN-20160823200852-00008-ip-10-153-172-175.ec2.internal.warc.gz | 369,809,867 | 13,327 | Suppose the 1st 1/4 of the distance between two points is covered with an average velocity of +18 m/s. The average velocity for the remainder of the trip is +51 m/s. What is the average velocity for the entire trip? | 54 | 215 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.8125 | 3 | CC-MAIN-2016-36 | latest | en | 0.967899 |
https://physics.stackexchange.com/questions/14652/fluid-mechanics-from-a-variational-principle | 1,628,106,074,000,000,000 | text/html | crawl-data/CC-MAIN-2021-31/segments/1627046154897.82/warc/CC-MAIN-20210804174229-20210804204229-00184.warc.gz | 427,151,247 | 40,134 | # Fluid Mechanics from a variational principle
It is possible to define a good variational principle to describe Fluid Mechanics? If so, what is the correct treatment of the issue. I guess something like:
$$I=\int d^4x \left(\frac{1}{2}\rho v^2-P-\rho g x\right).$$
• You should probably be more specific about what equation you want to reproduce. The full Navier-Stokes equations? Incompressible? Euler equations? Any of the above? Also, I know its just a first attempt, but the equation you wrote down has many flaws. – BebopButUnsteady Sep 14 '11 at 16:00
• I'm not an expert in the field, but I found a reference that claims this is possible. prl.aps.org/abstract/PRL/v58/i14/p1419_1 (behind a PRL paywall). – Gerben Sep 14 '11 at 17:29
• Thanks very much you both. BebopButUnsteady You are rigth, i meant Euler's equation. – Adolfo_Toloza Sep 15 '11 at 14:06
• A nice lagrangian treatment is available for incompressible potential flows with hydrostatic pressure, or for flows allowing one component of vorticity. Also, for a general Hamiltonian description one may resort to Clebsch variables, and then define the resultant lagrangian from these. One can check out some of Zakharov's reviews on the subject. – user8260 Apr 14 '12 at 22:27
This is the reason for the Lagrangian coordinates in fluid mechanics.
The velocity field is a momentum, so that the Lagrangian variational description needs the correpsonding coordinate. The corresponding coordinate is the map which tells you where each fluid particle ends up if you follow the flow up to time t. This is a diffeomorphism, and the Hamiltonian formulation is on a phase space of all diffeomorphisms and its tangent space, which is the velocity vector fields.
The kinetic energy is just the integral of the square of the velocity, and there is a pressure which is best put in by enforcing the constraint that the fluid is incompressible by Lagrange multipliers (if it is incompressible). The Lagrangian formulation is covered in many places. It is not particularly computationally convenient because the diffeomorphism generated by a flow is completely impossible to determine, and irrelevant because the diffeomorphisms are a homogenous group.
V.A. Arnold has a treatment of this point of view in his book "Topological Methods in Hydrodynamics", which is very good, and emphasizes the geometry.
Well, this is a huge topic, cf. e.g. Refs. 1-2 and e.g. this Phys.SE post.
1. The simplest action functional for fluid dynamics in the Lagrangian flow picture is \begin{align} I[{\bf r}] ~=~&\int \!\mathrm{d}\tau~\mathrm{d}^3{\bf a}~{\cal L},\cr {\cal L}~=~&\frac{1}{2}\dot{\bf r}^2 - \varepsilon\left(\rho({\bf a})^{-1}, S({\bf a})\right) -\phi({\bf r} ,\tau)) .\end{align}\tag{2.6} Here $${\bf r}={\bf r}({\bf a}, \tau)$$ are the position of a fluid parcel; $${\bf a}$$ is the labelling coordinate of the fluid parcel; $$\varepsilon$$ is specific internal energy; $$S$$ is the specific entropy; and $$\phi$$ is a specific potential energy. Its EL eqs are Newton's 2nd law for the fluid: \begin{align} -\ddot{\bf r}~\approx~&\rho^{-1}\nabla p +\nabla \phi, \cr p~:=~&\frac{\partial \varepsilon }{\partial (\rho^{-1})} .\end{align}\tag{2.11}
2. However, in practice one wants to use the Eulerian flow picture. This introduces relabelling symmetry with corresponding constraints. See e.g. Refs. 1-2 for details.
References:
1. R. Salmon, Hamiltonian Fluid Mechanics, Ann. Rev Fluid. Mech. (1988) 225. The pdf file can be downloaded from the author's webpage.
2. R.L. Seliger & G.B. Whitham, Variational principles in continuum mechanics, Proc. R. Soc. Lond. A305 (1968) 1 (Hat tip: tpg2114). | 1,020 | 3,659 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 7, "wp-katex-eq": 0, "align": 2, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.859375 | 3 | CC-MAIN-2021-31 | latest | en | 0.901536 |
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# When did the olympic schedule change from all games every 4 years to winter and summer every 2 years?
Updated: 9/28/2023
Wiki User
12y ago
The winter Olympics began in 1924 and through 1992 when the Winter Olympics were held in Albertville, France they occurred every 4 years in the same year as the summer Olympics. At that time it was determined that the Winter and Summer Olympics would occur every 4 years alternating every two years.
Therefore, in order to get onto a 2 year cycle, the Winter Olympics were held two years after the 1992 games in 1994 in Lillehammer, Norway. After 1994 they resumed the 4 year cycle, occurring in 1998, 2002, 2006 and 2010.
The Summer games maintained the 4 year cycle, and occurred 1996, 2000, 2004, 2008 and will occur again in 2012.
Wiki User
10y ago
Wiki User
12y ago
They didn't. The Winter Olympics are still held every four years, but as of 1994 Winter Olympic years are midway between Summer Olympic years. Before 1994, the Winter Olympics and Summer Olympics were held in the same years. The only Winter Olympics that were two years apart were the 1992 Games and the 1994 Games.
Wiki User
14y ago
because you were hyped up you hoe ask another question
Wiki User
12y ago
1994 ... the Winter and Summer Olympics were last held in the same year in 1992.
Wiki User
14y ago
No. They are held every 4 years!
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Q: When did the olympic schedule change from all games every 4 years to winter and summer every 2 years?
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Summer
### Which is bigger summer or winter Olympic?
probably summer it has more events but winter is gr8 too.
### What number is this 2008 Summer Olympics?
The modern Summer Olympic Games was started in 1896. There have been 28 Summer Olympic Games held. The modern Winter Olympic Games were started in 1924. There have been 20 Winter Olympic Games held.
### Where was the winter Olympics held in 2009?
No Olympic, Winter or Summer, was held in 2009.
### Why do you have a summer and a winter olympic games?
Not all the sports in the summer games can be played in the winter games, and vice verse.
### What is a topic sentence for summer and winter olympic games?
a good topic sentence would be the summer and winter olympic games are importent to the Olympics because these are some suporting details
### Is baseball in the winter Olympics?
No. Baseball is neither in the Winter nor Summer Olympic games.
### Is there a summer and a winter olympic torch?
No, there is not a summer and a winter olympic torch. There is only one torch. At the first olympic games ever held, the torch was lit, and it will never go out, so it just gets passed on to all of the olympic games that are held.
### Which winter olympic events US did not get a medal in 2007?
There were no Olympic Games in 2007. The summer games were in 2008 and the winter games were in 2010.
### Is table tennis played in the winter or summer Olympics?
Only in the Summer Olympic Games.
### How many many Olympic medals has Bulgaria won?
Bulgaria has won 213 Olympic medals including the Summer and Winter games. * 207 Summer * 6 Winter | 775 | 3,159 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.609375 | 3 | CC-MAIN-2024-38 | latest | en | 0.979276 |
http://openstudy.com/updates/5110628fe4b0d9aa3c48173a | 1,448,579,706,000,000,000 | text/html | crawl-data/CC-MAIN-2015-48/segments/1448398447860.26/warc/CC-MAIN-20151124205407-00293-ip-10-71-132-137.ec2.internal.warc.gz | 175,537,068 | 10,068 | ## Selena2345 2 years ago Solve The Equation.Then Check The Solution m+3(m-4)=16
1. timo86m
distribute the 3 first hint
2. Selena2345
can you show the whole work for the problem ?
3. timo86m
m+3(m-4)=16 m+3m-12=16 4m-12=16 4m=16+12 m=(16+12)/4 m=4+3=7
4. Ashleyisakitty
m + 3(-4 + m) = 16 m + (-4 * 3 + m * 3) = 16 m + (-12 + 3m) = 16 Reorder then combine like terms. -12 + 4m = 16 solve for m disturbute -12 + 12 + 4m = 16 + 12 Combine like terms 4m = 16 + 12 4m=28 divide each side by four M=?
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hello..sir..
1.what is the electric field at the centre of shpere having cavity at the distance r from centre.???
2.what is the electric field inside the cylindrical shell??
6 years ago
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Dear student,
Sphere having charge in the entire volume /Dielectric: Row* r/3 epsilon ( ) where is energy per unit volume and r is the distance from the centre.
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6 years ago
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More Questions On Electrostatics | 1,207 | 4,579 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.53125 | 3 | CC-MAIN-2017-04 | longest | en | 0.883227 |
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I have drawn my answers in paint, are they correct?
(4c) For the alphabet {0, 1} construct finite state automata corresponding to each of the following regular expressions:
(i) 0
(ii) 1 | 0
(iii) 0 * (1 | 0)
-
The first two are correct, although the first one might be able to be written as (depending on your convention)
``````(0) -- 0 --> ((1))
``````
The last one is also correct, but can be simplified to (whenever you have `ε` appearing, there is likely to be a way to compress the edges and states together to remove it)
`````` +- 0 -+
| |
v |
(0) ---+
/ \
1 0
\ /
v
((1))
``````
(Excuse my ascii diagrams. I'm using `(..)` for each state, and `((..))` for final states.)
Notice that the `0*` is basically a loop from a state to itself, since after reading a `0` the remaining regex to match is the same (as long as we aren't at the end of a string).
-
thank you for your clear explanations and further insight. – Danny Rancher Apr 26 '12 at 5:49 | 301 | 1,075 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.6875 | 3 | CC-MAIN-2014-52 | latest | en | 0.929829 |
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Question Number 55813 by amingolkar20@gmail.com last updated on 04/Mar/19
$$\frac{\mathrm{0}.\mathrm{8}}{{x}}=\frac{\mathrm{96}}{\mathrm{60}}\Rightarrow{x}=\mathrm{0}.\mathrm{5}\Rightarrow\mathrm{0}.\mathrm{8}−\mathrm{0}.\mathrm{5}=\mathrm{0}.\mathrm{3}\Rightarrow\mathrm{0}.\mathrm{4}−\mathrm{0}.\mathrm{3}=\mathrm{0}.\mathrm{1} \\$$
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November 8th, 2016, 03:25 AM #1
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logarithm properties
Hello,
How in this example log changed to exp? with which law?
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November 8th, 2016, 03:34 AM #2 Math Team Joined: Dec 2013 From: Colombia Posts: 7,305 Thanks: 2443 Math Focus: Mainly analysis and algebra $$\log_b x=y \implies b^y=x$$ Or, alternatively and equivalently $$b^{\log_b x}=x$$ Thanks from life24
November 8th, 2016, 03:42 AM #3 Senior Member Joined: Feb 2014 Posts: 112 Thanks: 1 Thank you but we have exponential.
November 8th, 2016, 03:47 AM #4 Math Team Joined: May 2013 From: The Astral plane Posts: 1,797 Thanks: 715 Math Focus: Wibbly wobbly timey-wimey stuff. What v8archie is trying to say is, just take the exponential of both sides. $\displaystyle \log(x) = y \implies x = e^y$ (This is assuming that log means "log with the base e.") -Dan Thanks from life24 Last edited by skipjack; November 8th, 2016 at 03:53 AM.
November 8th, 2016, 04:02 AM #5 Global Moderator Joined: Dec 2006 Posts: 18,951 Thanks: 1599 As exp is the inverse of log, one can remove log from the left-hand side and put exp in the right-hand side. Thanks from life24
November 8th, 2016, 04:22 AM #6
Math Team
Joined: Dec 2013
From: Colombia
Posts: 7,305
Thanks: 2443
Math Focus: Mainly analysis and algebra
Quote:
Originally Posted by life24 Thank you but we have exponential.
The $\log$ in the picture means $\log_e$ or $\ln$, the natural logarithm.
Tags logarithm, properties
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Contact - Home - Forums - Cryptocurrency Forum - Top | 635 | 2,012 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.453125 | 3 | CC-MAIN-2018-22 | latest | en | 0.897341 |
https://certifiedcalculator.com/how-to-calculate-time-between-dates-in-excel/ | 1,721,769,531,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763518115.82/warc/CC-MAIN-20240723194208-20240723224208-00888.warc.gz | 132,289,689 | 14,206 | How To Calculate Time Between Dates In Excel
Introduction: The How To Calculate Time Between Dates In Excel calculator is a handy tool for Excel users who need to determine the duration between two dates. Whether you are managing projects, tracking deadlines, or analyzing data, this calculator simplifies the process of calculating the time elapsed between two specific dates.
Formula: The calculator uses the difference in milliseconds between the inputted start and end dates. This difference is then converted to days by dividing it by the total number of milliseconds in a day (1000 * 3600 * 24).
How to Use:
1. Enter the start date using the date picker.
2. Input the end date using the date picker.
3. Click the "Calculate" button to get the calculated days between the two dates.
4. The result will display the number of days.
Example: For example, if the start date is January 1, 2023, and the end date is January 10, 2023, the calculator will provide the result as 9 days.
FAQs:
1. Q: Can I use this calculator for any date range? A: Yes, the calculator is suitable for any date range, allowing you to calculate the days between two specific dates.
2. Q: What format should I use for entering dates? A: Use the date picker and select the appropriate date format to ensure accurate calculations.
3. Q: What if the start date is after the end date? A: The calculator checks for valid input, and if the start date is after the end date, it will display "Invalid input."
4. Q: Is the result inclusive of the start and end dates? A: No, the result represents the number of full days between the start and end dates, excluding the partial days.
5. Q: Can I use this calculator for time intervals less than a day? A: No, this calculator calculates the difference in full days. For more granular time intervals, consider using Excel functions.
6. Q: Does this calculator account for leap years? A: Yes, the calculator considers leap years in its calculations, providing accurate results.
7. Q: Can I use this calculator for future dates? A: Yes, the calculator works for both past and future dates, providing the appropriate number of days.
8. Q: How precise are the calculations? A: The calculator provides a precise count of full days between the two dates, excluding any partial days.
9. Q: Can I share the calculated days between dates with others? A: Yes, feel free to share the calculated result with colleagues or team members working on date-sensitive projects.
10. Q: Is this calculator specifically for Excel users? A: While designed for Excel users, anyone can use this calculator to quickly determine the days between two dates.
Conclusion: The How To Calculate Time Between Dates In Excel calculator is a valuable resource for Excel users seeking an efficient way to calculate the duration between two dates. Whether you're managing schedules, analyzing project timelines, or simply tracking events, this calculator streamlines the process and enhances your Excel experience. Use it to save time and ensure accurate date calculations in your spreadsheets. | 645 | 3,078 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.234375 | 3 | CC-MAIN-2024-30 | latest | en | 0.855307 |
https://mcpt.ca/problem/jdcc15c5p3 | 1,719,256,241,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198865482.23/warc/CC-MAIN-20240624182503-20240624212503-00228.warc.gz | 343,334,877 | 9,789 | ## JDCC '15 Contest 5 P3 - Mazecrawler
View as PDF
Points: 10
Time limit: 2.0s
Memory limit: 64M
Author:
Problem type
For Mactoberfest, Mackenzie has decided to set up a maize maze for everyone to try and solve. Alex's teacher has just taken the class to try it out and the students quickly raced to solve the maze. However, Alex has realized that the longer he spends in the maze, the more class time he gets to skip!
The maze is set up as an grid of either walls (marked with #) or places he can walk (marked with .). Alex wants to take as long as he can to find his way out, however he needs to be careful. If his teacher catches him walking in circles, then she will suspend him! Obviously, Alex would hate being forced to skip school, so he won't visit any location more than once. Help Alex figure out the length of the longest path that he can take to exit the maze.
#### Input Specification
The first line of input provides the number of test cases, . test cases follow. Each test case starts with an integer . lines follow, each containing characters, which describe the maze. A character is either . (place Alex can walk), # (wall), A (Alex's starting location), or E (the exit).
#### Output Specification
For each test case, your program should output the length of the longest path that Alex can take to the exit.
#### Sample Input
3
4
A...
.##.
....
...E
5
A....
.....
###..
E##..
.....
5
E...#
##..#
###.#
##A.#
.....
#### Sample Output
12
19
9
#### Explanation for Sample
The paths are outlined with numbers modulo 10 below:
A123
.##4
8765
901E
A3478
12569
###10
E##23
87654
E87.#
##65#
###4#
##A3#
..12. | 433 | 1,637 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.578125 | 3 | CC-MAIN-2024-26 | latest | en | 0.936963 |
https://www.coursehero.com/file/5774673/HW1-2/ | 1,529,860,389,000,000,000 | text/html | crawl-data/CC-MAIN-2018-26/segments/1529267866984.71/warc/CC-MAIN-20180624160817-20180624180817-00215.warc.gz | 785,548,582 | 42,458 | HW1_2 - y 00 4 y 4 y = 0,y(0 = y(0 = 1 3 Section 17 Problem...
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Math 135, HW 1 Due Wednesday, January 14th 1. Find the general solutions of the following equations: (a) y 00 - y 0 = 0 (b) y 00 + y = 0 (c) y 00 + 4 y 0 + 4 y = 0 (d) y 00 + y = e x 2. Find the solution of the following initial value problem:
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Unformatted text preview: y 00 + 4 y + 4 y = 0 ,y (0) = y (0) = 1 3. Section 17, Problem 4 4. Section 17, Problem 8 5. Section 18, Problem 3 1...
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https://ligolang.org/docs/0.41.0/advanced/polymorphism/ | 1,653,080,799,000,000,000 | text/html | crawl-data/CC-MAIN-2022-21/segments/1652662534669.47/warc/CC-MAIN-20220520191810-20220520221810-00271.warc.gz | 418,589,760 | 7,406 | Version: 0.41.0
# Polymorphism
LIGO supports simple polymorphism when introducing declarations. This allows to write functions parametric on a type that can be later instantiated to concrete types.
## The identity function#
For any given type `t`, there is a canonical function of type `t -> t` (function from `t` to `t`): it takes an argument, and returns it immediately. For instance, we can write the identity function for `int` as follows:
let id = (x: int): int => x;
However, if we would want to use the same function on a different type, such as `nat`, we will need to write a new definition:
let idnat = (x : nat): nat => x;
If we read carefully, we see that there is almost no difference between `id` and `idnat`: it is just the type that changes, but for the rest, the body of the function remains the same.
Thanks to parametric polymorphism, we can write a single function declaration that works for both cases.
let id : <T>((x : T) => T) = x => x;
Here `T` is a type variable which can be generalised. In general, types prefixed with `_` are treated as generalisable.
We can then use this function directly in different types by just regular application:
const three_i : int = id(3);
const three_s : string = id("three");
During compilation, LIGO will monomorphise the polymorphic functions into specific instances, resulting in Michelson code that does not contain polymorphic function declarations anymore.
## Polymorphism with parametric types#
Polymorphism is especially useful when writing functions over parametric types, which include built-in types like lists, sets, and maps.
As an example, we will see how to implement list reversing parametrically on any type, rather than just on lists of a specific type.
Similar to the `id` example, we can introduce a type variable that can be generalised. We will write a direct version of the function using an accumulator, but the reader can experiment with different variations by using `List` combinators.
let rev : <T>((xs : list<T>) => list<T>) = xs => {
let rev : ((p : [list<T>, list<T>]) => list<T>) = ([xs, acc] : [list<T>, list<T>]) : list<T> =>
match(xs, list([
([] : list<T>) => acc,
([x,... xs] : list<T>) => rev([xs, list([x,...acc])])
]));
return rev([xs, (list([]) as list<T>)]);
};
We use an accumulator variable `acc` to keep the elements of the list processed, consing each element on it.
As with the identity function, we can then use it directly in different types:
const lint : list<int> = rev(list([1, 2, 3]));
const lnat : list<nat> = rev(list([(1 as nat), (2 as nat), (3 as nat)])); | 644 | 2,591 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.78125 | 3 | CC-MAIN-2022-21 | latest | en | 0.869068 |
https://www.scienceforums.net/topic/28102-ellipses-tilted-circles-circle-approximation/?tab=comments | 1,610,842,866,000,000,000 | text/html | crawl-data/CC-MAIN-2021-04/segments/1610703507971.27/warc/CC-MAIN-20210116225820-20210117015820-00218.warc.gz | 987,834,970 | 18,283 | Ellipses, tilted circles, circle approximation
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I have a machining problem that I am trying to solve, and it appears that math may be of assistance.
Basically, I have a 12mm cylinder and a piece of 10mm brass bar stock, and I want to cut a groove in the bar that approximates the curve of the cylinder fairly closely. Unfortunately, I don't have any tools that can work with a diameter as small as 12mm, so I thought that perhaps using a larger diameter circle, 'tilted' at an angle so it intersects the bar as an ellipse, might get me close enough.
(Of course, I never thought before about any formulae relating a 'tilted' circle to the defining particulars of its cross-sectional view based on the angle. Does viewing a circle at an angle result in a proper ellipse?)
That's probably incredibly unclear, so let me see if I can depict it. The attached images are, in order: the cylinder and the bar (with the desired groove marked in blue); the cutting tool (variable diameter, but not small enough); a top view of the tool and the bar; and an end-on view of the tool and the bar.
Obviously this method will only yield an approximation of the groove I need. The question is, however, what diameter and angle to use for the tool to get something 'good enough.' An ellipse with one focus 6mm from the end would probably do for starters..
Plus I learn a bit more about geometry..
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I wish I could help you but I'm feeling very well today:doh:. Anyways, a google search came up with this!
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Yes, I studied the Wikipedia article, but either it didn't answer my questions or else I'm too thick to understand how it did answer them. (Actually, the section on Semi-latus rectum and polar coordinates makes it clear that a 'tilted circle' is, in fact, a proper ellipse. One down..)
Thinking about this some more.. Given a tool diameter d, the foci would be d - 12mm apart, in order to give a 6mm distance from the nearest focus to an endpoint of the major axis. How to turn that into an angle measurement is still something I've not figured out, although the same section gives a clew. Figure out the eccentricity and the angle is easily calculated.
(I'm probably not awake enough to figure out what I'm doing wrong, but I'm also deducing that the constant sum of the distances to the foci is always equal to the length of the major axis.)
I went back to the Wikipedia article after a massive caffeine infusion, and I think I got a bit closer.
If the cutting tool is 50mm in diameter, and I want the least distance from a focus to an endpoint of the major axis to be 6mm, then using the formulae in the article we get:
1. $\varepsilon = \frac{c}{a} = \frac{(\frac{50}{2} - 6)}{25} = \frac{19}{25} = 0.76$
2. $\varepsilon = \sin{\psi} = 0.76$
3. $\psi = \arcsin{\varepsilon} = \arcsin{0.76} \approx 49.46\,^{\circ}$
4. $b = \sqrt{a^{2} \cdot (1 - \varepsilon^{2})} = \sqrt{625 \cdot (1 - 0.5776)} = \sqrt{264} \approx 16.25mm$
Which is a nice step along the way. However, the above will result in the semi-latus rectum (who says mathematicians don't have senses of humour?) being
$l = a \cdot (1 - \varepsilon^{2}) = 10.56mm$
so the width of the groove if it is 6mm deep will be 21.12mm. That's much too wide; the cylinder will roll around in it like cavemen carrying an egg (see the film Caveman ). Obviously I need to futz around with the diameter of the tool, the depth of the groove, and the eccentricity of the ellipse. (Since the cylinder is going to be soldered into the groove, it needn't mate perfectly -- just 'good enough.')
Apologies for 'thinking out loud' here, but perhaps this will be useful to someone else in the future.
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This thread was useful for me since I was trying to figure the same question on.
More specifically, I wanted to know how the minor axis of the projected ellipse varies with tilting angle Phi.
I'll take a look at the Wikipedia website here referenced to see whether the equations there are of any use (If not, I'll have to figure out the relationship myself).
I'm intuitively guessing that if (x^2)/a^2 + (y^2)/b^2=1, all you have to do is divide by cos(phi) which ever axis is reduced upon tilting, if tilting parallel to either of the ellipse axes that is.
For example, if the ellipse is ORIGINALLY A CIRCLE on a plane P, it's shape is:
(x^2)/R^2 + (y^2)/R^2=1
If tilting parallel to the y axis, then the circle will start becoming an ellipse by reducing its radius along the x direction:
(x^2)/(R*cos[phi])^2 + (y^2)/R^2=1
Which is the same as:
(x^2)/a^2 + (y^2)/b^2=1
After the following variable substitution:
a=R*cos[phi]
b=R
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Register a new account | 1,222 | 4,716 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.84375 | 4 | CC-MAIN-2021-04 | latest | en | 0.953775 |
https://www.physicsforums.com/threads/calculating-constant-speed-of-an-elevator-rising.449724/ | 1,611,194,186,000,000,000 | text/html | crawl-data/CC-MAIN-2021-04/segments/1610703522150.18/warc/CC-MAIN-20210121004224-20210121034224-00743.warc.gz | 917,459,926 | 13,308 | # Calculating Constant speed of an Elevator Rising
## Homework Statement
The motor for an elevator can produce 14kW of power. The elevator has a mass of 1100 kg, including its contents. At what constant speed will the elevator rise?
## Homework Equations
I'm not really sure. Probably Gravitational potential = mgh. Kinetic energy = 1/2mv^2 because its looking for speed.
## The Attempt at a Solution
I'm really not sure. It doesn't seem like enough information is given to solve for anything. There's probably some algebraic manipulation I'm missing.
Consider work done per second (14 kJ) - what increase in height does that correspond to (14kJ = mgh)?
-S
## Homework Statement
The motor for an elevator can produce 14kW of power. The elevator has a mass of 1100 kg, including its contents. At what constant speed will the elevator rise?
## Homework Equations
I'm not really sure. Probably Gravitational potential = mgh. Kinetic energy = 1/2mv^2 because its looking for speed.
## The Attempt at a Solution
I'm really not sure. It doesn't seem like enough information is given to solve for anything. There's probably some algebraic manipulation I'm missing. | 274 | 1,171 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.203125 | 3 | CC-MAIN-2021-04 | latest | en | 0.958487 |
https://www.unitsconverters.com/en/Centimeterpersquaresecond-To-Secondsfrom0to100kmperh/Unittounit-3423-3447 | 1,653,229,329,000,000,000 | text/html | crawl-data/CC-MAIN-2022-21/segments/1652662545548.56/warc/CC-MAIN-20220522125835-20220522155835-00638.warc.gz | 1,214,575,629 | 41,481 | Formula Used
1 Meter per Square Second = 100 Centimeter per Square Second
1 Meter per Square Second = 27.78 Seconds from 0 to 100 km per h
1 Centimeter per Square Second = 0.2778 Seconds from 0 to 100 km per h
## Centimeter per Square Seconds to Seconds from 0 to 100 km per hs Conversion
cm/s² stands for centimeter per square seconds and s stands for seconds from 0 to 100 km per hs. The formula used in centimeter per square seconds to seconds from 0 to 100 km per hs conversion is 1 Centimeter per Square Second = 0.2778 Seconds from 0 to 100 km per h. In other words, 1 centimeter per square second is 4 times smaller than a seconds from 0 to 100 km per h. To convert all types of measurement units, you can used this tool which is able to provide you conversions on a scale.
## Convert Centimeter per Square Second to Seconds from 0 to 100 km per h
How to convert centimeter per square second to seconds from 0 to 100 km per h? In the acceleration measurement, first choose centimeter per square second from the left dropdown and seconds from 0 to 100 km per h from the right dropdown, enter the value you want to convert and click on 'convert'. Want a reverse calculation from seconds from 0 to 100 km per h to centimeter per square second? You can check our seconds from 0 to 100 km per h to centimeter per square second converter.
How to convert Centimeter per Square Second to Seconds from 0 to 100 km per h?
The formula to convert Centimeter per Square Second to Seconds from 0 to 100 km per h is 1 Centimeter per Square Second = 0.2778 Seconds from 0 to 100 km per h. Centimeter per Square Second is 3.59971202303816 times Smaller than Seconds from 0 to 100 km per h. Enter the value of Centimeter per Square Second and hit Convert to get value in Seconds from 0 to 100 km per h. Check our Centimeter per Square Second to Seconds from 0 to 100 km per h converter. Need a reverse calculation from Seconds from 0 to 100 km per h to Centimeter per Square Second? You can check our Seconds from 0 to 100 km per h to Centimeter per Square Second Converter.
How many Meter per Square Second is 1 Centimeter per Square Second?
1 Centimeter per Square Second is equal to 0.2778 Meter per Square Second. 1 Centimeter per Square Second is 3.59971202303816 times Smaller than 1 Meter per Square Second.
How many Kilometer per Square Second is 1 Centimeter per Square Second?
1 Centimeter per Square Second is equal to 0.2778 Kilometer per Square Second. 1 Centimeter per Square Second is 3.59971202303816 times Smaller than 1 Kilometer per Square Second.
How many Micrometer per Square Second is 1 Centimeter per Square Second?
1 Centimeter per Square Second is equal to 0.2778 Micrometer per Square Second. 1 Centimeter per Square Second is 3.59971202303816 times Smaller than 1 Micrometer per Square Second.
How many Mile per Square Second is 1 Centimeter per Square Second?
1 Centimeter per Square Second is equal to 0.2778 Mile per Square Second. 1 Centimeter per Square Second is 3.59971202303816 times Smaller than 1 Mile per Square Second.
## Centimeter per Square Seconds to Seconds from 0 to 100 km per hs Converter
Units of measurement use the International System of Units, better known as SI units, which provide a standard for measuring the physical properties of matter. Measurement like acceleration finds its use in a number of places right from education to industrial usage. Be it buying grocery or cooking, units play a vital role in our daily life; and hence their conversions. unitsconverters.com helps in the conversion of different units of measurement like cm/s² to s through multiplicative conversion factors. When you are converting acceleration, you need a Centimeter per Square Seconds to Seconds from 0 to 100 km per hs converter that is elaborate and still easy to use. Converting Centimeter per Square Second to Seconds from 0 to 100 km per h is easy, for you only have to select the units first and the value you want to convert. If you encounter any issues to convert, this tool is the answer that gives you the exact conversion of units. You can also get the formula used in Centimeter per Square Second to Seconds from 0 to 100 km per h conversion along with a table representing the entire conversion.
Let Others Know | 1,012 | 4,262 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.828125 | 3 | CC-MAIN-2022-21 | latest | en | 0.779737 |
https://manasataramgini.wordpress.com/2019/03/10/packing-constants-for-polygonal-fractal-maps/ | 1,685,328,290,000,000,000 | text/html | crawl-data/CC-MAIN-2023-23/segments/1685224644574.15/warc/CC-MAIN-20230529010218-20230529040218-00169.warc.gz | 441,604,819 | 37,198 | ## Packing constants for polygonal fractal maps
Among the very first programs which we wrote in our childhood was one to generate the famous Sierpinski triangle as an attractor using the “Chaos Game” algorithm of Barnsley. A couple of years later we returned to it generalize it as a map in the complex plane. Consider the polynomial equation,
$z^m+1=0$, where integer $m=3,4,5...$
The roots of this equation, $z_j: z_1, z_2... z_m$, define the vertices of a $m$-sided polygon in the complex plan. For example, if $m=3$, we get an equilateral triangle defined by the roots $z_1= \tfrac{1}{2}+\tfrac{\sqrt{3}i}{2}, z_2= -1, z_3= \tfrac{1}{2}-\tfrac{\sqrt{3}i}{2}$.
With this in place the Chaos Game map is defined for a given $m$ as:
$z_{n+1}=r(z_n+z_j)$,
where $z_j$ is one of the $m$ roots chosen randomly with equal probability as the others in each iteration of the map and $0. If $r=1$ for any $m$ we get a random-walk structure (Figure 1).
Figure 1
For other $m, r$ we get chaotic maps and for particular values of $m, r$ we get attractors with a fractal structure. Thus, the Sierpinski triangle is obtained with $m=3, r=\tfrac{1}{2}$. This fills the triangle defined by $z_1, z_2, z_3$
Figure 2
For $m=4, r=\tfrac{1}{1+\sqrt{2}}$ we get the fractal street block (Figure 3).
Figure 3
We currently revisited this map because of a curious problem that emerges when we continue this operation as below for further polygons. For $m=5, r=1-\tfrac{1}{\phi}$ (where $\phi=\tfrac{1+\sqrt{5}}{2}$, the Golden Ratio) we get the fractal pentagons surrounding the interior penta-flake (Figure 4).
Figure 4
For $m=6, r=\tfrac{1}{3}$ we get the fractal hexagons surrounding the interior Koch’s snowflake (Figure 5).
Figure 5
For $m=7, r=\tfrac{1}{S}$ (where $S=2+2\cos\left(\tfrac{2\pi}{7}\right)$, the Silver constant. The Silver constant is an algebraic number which is the real root of the cubic $x^3-5x^2+6x-1$) we get the fractal heptagon necklace surrounding the interior hepta-flake (Figure 6).
Figure 6
For $m=8, r=\tfrac{1}{2+\sqrt{2}}$ we get the fractal octagon necklace (Figure 7).
Figure 7
For $m=9, r=\tfrac{1}{2+2\cos\left(\pi/9\right)}$ we get the fractal nonagon necklace (Figure 8).
Figure 8
For $m=10, r=\tfrac{1}{1+2\phi}$ we get the fractal decagon necklace (Figure 9).
Figure 9
For $m=11, r\approx 0.2209$ we get the fractal hendecagon necklace (Figure 10).
Figure 10
For $m=12, r=\tfrac{1}{3+\sqrt{3}}$ we get the fractal dodecagon necklace (Figure 11).
Figure 11
Given that these attractors are fractal, they have an infinite perimeter but occupy a finite area. Thus, one can define a common feature for the above attractors namely “tangency” of the fractal elements, i.e., each polygonal unit is distinct from its neighbor with the same scale-factor but at same time makes a contact with it like a tangent. While for the triangle and the square this definition is a bit murky, it is clearly visible from the pentagon onward. It can be contrasted with other fractal attractors obtained by this method where the elements overlap or are shared. For instance for $m=12, r=\tfrac{1}{2+2\cos\left(\pi/6\right)}$, we have the expected dodecad structure but two dodecad sub-elements are shared by each of the adjacent elements (Figure 12).
Figure 12
In the above examples (Figure 2-11) we have determined for each polygon the value of $r$ which results in a tangent attractor:
$m=3, r=\tfrac{1}{2}; m=4, r=\tfrac{1}{1+\sqrt{2}}; m=5, r=1-\tfrac{1}{\phi}; m=6, r=\tfrac{1}{3};\\ m=7, r=\tfrac{1}{S}; m=8, r=\tfrac{1}{2+\sqrt{2}}; m=9, r=\tfrac{1}{2+2\cos\left(\pi/9\right)}; \\ m=10, r=\tfrac{1}{1+2\phi}, ; m=11, r\approx 0.2209; m=12, r=\tfrac{1}{3+\sqrt{3}}$
For $m=5..8$ it is the reciprocal of $2+2\cos\left(\tfrac{2\pi}{m}\right)=4\cos^2\left(\tfrac{\pi}{m}\right)$, which are known as Beraha constants ( $B_n$) that appear in graph-coloring theory. However, for $m=9..12$ this principle clearly breaks down: e.g. for $m=12$, we see that $\tfrac{1}{B_{12}}$ yields the overlapping attractor (Figure 12). We have been able to obtain closed forms for the $r$ that yield tangent attractors for all $m$ except 11, where we report an empirically determined approximate value. What is the closed form expression for it? This leads to the question of whether there is a general formula to obtain our $r$ that results in tangency? To our knowledge these have not been answered.
This entry was posted in art, Scientific ramblings and tagged , , , , , , , , . Bookmark the permalink. | 1,442 | 4,519 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 41, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.84375 | 4 | CC-MAIN-2023-23 | latest | en | 0.773258 |
http://spmath7310.blogspot.com/2010/10/johns-sesame-street-video-post.html | 1,532,089,101,000,000,000 | text/html | crawl-data/CC-MAIN-2018-30/segments/1531676591596.64/warc/CC-MAIN-20180720115631-20180720135631-00116.warc.gz | 346,722,000 | 22,196 | ## Sunday, October 17, 2010
### JOHN'S SESAME STREET VIDEO POST
Group Members: John C., Alec M., Mark C., Brandon A.
Part One:
Two term ratios and Three term ratio- compares two or three quantities measured in the same units.
Example: Two term ratios, orange balls to purple balls 3:5
Three term ratios, orange balls to red balls to purple balls 3:2:5
Rates- compares two quantities measured in different units.
example: \$/orange= \$1.99/orange
Proportional reasoning- a relationship that says two ratios or rates are equal
example: x2
\$/h \$50/1h = \$100/2h
x2
Part Two:
Description: Lefty the salesman sells Ernie an "8"
Part Three:
1. Great post John!! It was good that you difined both two term and three term ratios. The video was great too.
2. Awesome Job John! I liked what Emily said, you defined two term and three term ratio. I liked how you colored important words. Awesome video, its good!
3. Amazing post John! I really like your video! It made me laugh, you guys brought in a lot of energy in to the video! I also like how you post is nice and organized. To me, you made it nice and organized by highlighting the important words and putting the next part in "bold". Keep it up!
4. Good job John! You guys had a really good video. Your post was nice and organized. You could of put a picture to explain it more but anyways good job, keep it up!
5. Great job John! I liked how you highlighted the important words and, of course, I liked your video. Next time try adding a picture or two to make your post better.
6. Nice post John, your post was really organized and neat. I liked the way you changed the color of the important words. I liked your video.
7. Good job!!!! i like how you highlighted the important words but the words could have been bigger and you could have put more space in between it also your examples could have been bigger and more colorful also i like your video
8. Good JOb JOhn.. I like your post. I think You and Alec did a good job. Next time try adding a picture to make you post even better.
9. Good Job John! I like your video. You and Alec were awesome. Next Time I think you should make the words on the papers more darker because it looked like they were sorta blank at some point of view. Other then that Good Job!
10. Awsome job John! I really like your video, it was very funny. I think for you to make your post better you should add a couple of pictures. Other than that great job !
11. Great job john!! your post was neat and your video is funny!! i like the color you put on your post it was good. Awesome job, and keep t up | 625 | 2,597 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.109375 | 3 | CC-MAIN-2018-30 | latest | en | 0.966782 |
https://mathematics-monster.com/symbols/Right-Tack.html | 1,721,756,302,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763518059.67/warc/CC-MAIN-20240723163815-20240723193815-00530.warc.gz | 341,185,515 | 6,541 | # Right Tack
## The Mathematical Symbol "Right Tack (⊢)"
homesitemapsymbolsright tack
The "Right Tack" Symbol (⊢)
The ⊢ symbol, commonly referred to as the "Right Tack" or "Turnstile", is a symbol of considerable significance in logic, mathematics, and computer science. It is traditionally used to represent entailment or provability.
## Usage of ⊢
The Right Tack symbol is often employed in various contexts, especially in the fields of formal logic and mathematical proof theory.
Example 1: Logical Entailment
In propositional logic, if $$A$$ and $$B$$ are statements, the expression $$A ⊢ B$$ means that $$B$$ can be logically inferred from $$A$$. It signifies that if $$A$$ is true, then $$B$$ must also be true.
Example 2: In Proof Theory
In proof theory, the turnstile symbol denotes provability. The expression $$\Gamma ⊢ \phi$$ means that the formula $$\phi$$ can be derived or proven from the set of formulas $$\Gamma$$.
## Significance in Mathematics and Logic
The ⊢ symbol has foundational importance in several areas:
• Formal Logic: It represents the relationship between hypotheses and conclusions in logical deductions.
• Proof Theory: The symbol is a staple in the notation of sequent calculus, a formal system for reasoning about proofs.
• Model Theory: It differentiates between syntactic provability and semantic entailment, often using a dual symbol (⊧).
• Computer Science: In formal methods, particularly in type theory and formal semantics, the turnstile is frequently used to specify the type or behavior of expressions or programs.
In summary, the ⊢ symbol is central to discussions and formalisms in logic and formal systems. It succinctly captures the essence of provability and entailment, concepts fundamental to rigorous mathematical and logical reasoning.
## Are You Good at Mathematical Symbols?
Do you know, or can you guess, the technical symbols? Well, let's see!
Gold
Silver
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• This test has questions.
• A correct answer is worth 5 points.
• You can get up to 5 bonus points for a speedy answer.
• Some questions demand more than one answer. You must get every part right.
• Beware! Wrong answers score 0 points.
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## Codes for the ⊢ Symbol
The Symbol ⊢ Alt Code Alt 8866 HTML Code ⊢ HTML Entity ⊢ CSS Code \22A2 Hex Code ⊢ Unicode U+22A2
## How To Insert the ⊢ Symbol
(Method 1) Copy and paste the symbol.
The easiest way to get the ⊢ symbol is to copy and paste it into your document.
Bear in mind that this is a UTF-8 encoded character. It must be encoded as UTF-8 at all stages (copying, replacing, editing, pasting), otherwise it will render as random characters or the dreaded �.
(Method 2) Use the "Alt Code."
If you have a keyboard with a numeric pad, you can use this method. Simply hold down the Alt key and type 8866. When you lift the Alt key, the symbol appears. ("Num Lock" must be on.)
(Method 3) Use the HTML Decimal Code (for webpages).
HTML TextOutput
<b>My symbol: ⊢</b>My symbol: ⊢
(Method 4) Use the HTML Entity Code (for webpages).
HTML TextOutput
<b>My symbol: ⊢</b>My symbol: ⊢
(Method 5) Use the CSS Code (for webpages).
CSS and HTML TextOutput
<style>
span:after {
content: "\22A2";}
</style>
<span>My symbol:</span>
My symbol: ⊢
(Method 6) Use the HTML Hex Code (for webpages and HTML canvas).
HTML TextOutput
<b>My symbol: ⊢</b>My symbol: ⊢
On the assumption that you already have your canvas and the context set up, use the Hex code in the format 0x22A2 to place the ⊢ symbol on your canvas. For example:
JavaScript Text
const x = "0x"+"E9"
ctx.fillText(String.fromCodePoint(x), 5, 5);
Output
(Method 7) Use the Unicode (for various, e.g. Microsoft Office, JavaScript, Perl).
The Unicode for ⊢ is U+22A2. The important part is the hexadecimal number after the U+, which is used in various formats. For example, in Microsoft Office applications (e.g. Word, PowerPoint), do the following:
TypeOutput
22A2
[Hold down Alt]
[Press x]
(The 22A2 turns into ⊢. Note that you can omit any leading zeros.)
In JavaScript, the syntax is \uXXXX. So, our example would be \u22A2. (Note that the format is 4 hexadecimal characters.)
JavaScript TextOutput
let str = "\u22A2"
document.write("My symbol: " + str)
My symbol: ⊢
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Use our handy widget to create a QR code for this page...or any page. | 1,217 | 4,820 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.71875 | 4 | CC-MAIN-2024-30 | latest | en | 0.895008 |
http://www.arenawp.com/2018/08/vectors-cross-product-of-2/ | 1,544,807,542,000,000,000 | text/html | crawl-data/CC-MAIN-2018-51/segments/1544376826145.69/warc/CC-MAIN-20181214162826-20181214184826-00298.warc.gz | 325,532,108 | 5,885 | # Vectors Cross Product Of 2
This post categorized under Vector and posted on August 16th, 2018.
The cross product of two vectors a and b is defined only in three-dimensional vectore and is denoted by a b.In physics sometimes the notation a b is used though this is avoided in mathematics to avoid confusion with the exterior product.Which Direction The cross product could point in the completely opposite direction and still be at right angles to the two other vectors so we have theIf you know exactly which file youd like to download or you want a file different from any listed below you can go directly to the Download Page to get it.
Notice that the dot product of two vectors is a number and not a vector. For 3 dimensional vectors we define the dot product similarlyMar 28 2005 Im not even sure such a thing exists P. Anyway if it does is it correct that it is Xc -Y Yc X (rotation 90 deg counter clockwise) CouldntDot Product A vector has magnitude (how long it is) and direction. Here are two vectors They can be multiplied using the Dot Product (also see Cross Product).. Calculating
Derivation of the formula to calculate the cross product of two vectors.As explained above a vector is often described by a set of vector components that add up to form the given vector. Typically these components are the projections of the vector on a set of mutually perpendicular reference axes (basis vectors).Follow us Share this page This section covers Introduction to Vectors Vector Operations Applications of Vectors Dot Product and Angle Between Two Vectors 3D Vectors Vectors in vectore (including Cross Product)
## Geometrical Interpretation Of The Magnitude Of The Cross Product
APA graphicysis Paper APA-2011-03 graphicle A Preliminary graphicessment of Specular Radar Cross Section Performance in the Chengdu J-20 Prototype [more]
## The Dot And Cross Product Pdf
If you know exactly which file youd like to download or you want a file different from any listed below you can go directly to the Download Page to [more]
## Vector Product J K B K J K B K C J Q
Two vectors are called orthogonal if their angle is a right angle. We see that angles are orthogonal if and only if v. w 0. Example To find the an [more] | 481 | 2,233 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.6875 | 4 | CC-MAIN-2018-51 | longest | en | 0.904484 |
http://html.rhhz.net/jckxjsgw/html/51490.htm | 1,721,325,462,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763514848.78/warc/CC-MAIN-20240718161144-20240718191144-00592.warc.gz | 16,525,361 | 13,034 | 初始缺陷对加筋板结构极限强度的影响研究
舰船科学技术 2017, Vol. 39 Issue (3): 29-35 PDF
Effect of initial imperfections on the ultimate strength of stiffened panels
SHI Xing-hua, BIAN Xuan-yi, QIAN Peng, WANG Peng-xiang
School of Naval Architecture and Ocean Engineering, Jiangsu University of Science and Technology, Zhenjiang 212003, China
Abstract: The ultimate strength of stiffened panel with three initial imperfections under uniaxial compression loading by the nonlinear finite element software ANSYS. Three initial imperfections, namely, initial deformation, dent is assumed to formed by the ball with different radius and different speed impacting on the stiffened plate and residual stress. One stiffened panel is introduced, the effect of three imperfections on the ultimate strength of stiffened panels. It is indicated that initial imperfections reduce the ultimate strength of stiffened panel, the effect of superposition of imperfections to ultimate strength i greater than that of only one imperfection to ultimate strength. Ultimate strength of stiffened panel decreases with the increase the depth of dent. Compared to initial deformation and dent, the reduction of residual stress to ultimate strength is greatest.
Key words: initial imperfections stiffened panels ultimate strength dent
0 引 言
1 初始缺陷 1.1 初始变形
${{{w}}_p} = \left( { - {w_p}} \right) \times \cos \frac{{m\pi x}}{a} \times \cos \frac{{n\pi y}}{b}\text{，}$ (1)
${{{w}}_{oh}} = \left( { - {w_{os}}} \right) \times \cos \frac{{m\pi x}}{a} \times \sin \frac{{n\pi z}}{{2h}}\text{，}$ (2)
${{{w}}_{oh}} = \left( { - {w_{oc}}} \right) \times \cos \frac{{n\pi x}}{a}\text{。}$ (3)
1.2 焊接残余应力
1.3 凹陷
Paik[8]经过研究和分析发现：在凹陷的幅值一定的情况下，凹陷形状对板格极限强度的影响很小。因此，本文加筋板上的所有凹陷全由球撞击而成。采用显式有限元程序 LS-DYNA 进行球与加筋板的碰撞过程的模拟，得出结构所有节点的位移改变量，选取加筋板结构的碰撞模型作为含凹陷结构极限强度的分析模型。
2 计算模型
图 1 加筋板计算模型 Fig. 1 Calculation model of stiffened panel
3 含初始缺陷结构极限承载力分析 3.1 初始变形和凹陷的叠加
图 2 含初始变形的加筋板变形和应力云图 Fig. 2 Deformation and the stress distribution of stiffened plate with initial deformation
图 3 加筋板的变形和应力云图（半径为 0.2 m） Fig. 3 Deformation and the stress distribution of stiffened plate（Radius of 0.2 m）
图 4 加筋板的变形和应力云图（半径为 0.25 m） Fig. 4 Deformation and the stress distribution of stiffened plate（Radius of 0.25 m）
图 5 加筋板的变形和应力云图（半径为 0.3 m） Fig. 5 Deformation and the stress distribution of stiffened plate（Radius of 0.3 m）
图 6 含初始缺陷加筋板的应力-应变曲线图 Fig. 6 The stress-strain curves of stiffened panels under initial imperfections
图 7 不同凹陷深度的加筋板应力-应变曲线 Fig. 7 The stress-strain curves of stiffened panels under different dent depths
图 8 加筋板的变形和应力云图（速度为 8 m/s） Fig. 8 Deformation and the stress distribution of stiffened plate（velocity of 8 m/s）
图 9 加筋板的变形和应力云图（速度为 9 m/s） Fig. 9 Deformation and the stress distribution of stiffened plate（velocity of 9 m/s）
图 10 加筋板的变形和应力云图（速度为 11 m/s） Fig. 10 Deformation and the stress distribution of stiffened plate（velocity of 11 m/s）
图 11 含初始缺陷加筋板的应力-应变曲线图 Fig. 11 The stress-strain curves of stiffened panels under initial imperfections
图 12 不同凹陷深度的加筋板应力-应变曲线 Fig. 12 The stress-strain curves of stiffened panels under different dent depths
3.2 三种初始缺陷的叠加
图 14 含初始缺陷的加筋板应力-应变曲线图 Fig. 14 The stress-strain curves of stiffened panels with initial imperfections
4 结 语
1）在考虑初始变形和凹陷对加筋板结构极限强度影响时发现，初始变形对结构的承载力影响最小，而凹陷对结构的承载力影响相对较大，凹陷对结构的承载力随着凹陷深度的增大而减小；
2）在考虑 3 种初始缺陷的影响时发现，残余应力严重影响结构的承载力，6 种模式下的结构只要含有残余应力，其承载力明显小于不含残余应力的。而在建造 FPSO 过程中所用的钢材都会经过焊接，这必然会在结构中残留残余应力，因此在校核结构强度时，不能忽视残余应力的影响；
3）初始缺陷的叠加对结构承载力的影响明显大于单独存在的情况。因此结构在建造运输等过程中，应该尽量避免在同一结构上造成缺陷的叠加，最大限度地保持结构的完整性。
[1] 张婧, 江小龙, 石晓彦, 等. 具有初始缺陷的裂纹加筋板剩余极限强度分析[J]. 哈尔滨工程大学学报. 2016, 37(7): 1–9. [2] 张婧, 施兴华, 顾学康. 具有初始缺陷的船体加筋板结构在复杂受力状态下的极限强度研究[J]. 中国造船. 2013, 54(1): 60–70. [3] 任慧龙, 郎舒妍, 任晨辉, 等. 带有初始缺陷的船体结构极限强度研究[J]. 舰船科学技术, 2015, 37(12): 38–41. REN Hui-long, LANG Shu-yan, REN Chen-hui, et al. Ultimate strength of hull structure with initial defect[J]. Ship Science and Technology, 2015, 37(12): 38–41. [4] PAIK J K, LEE J M, LEE D H. Ultimate strength of dented steel plates under axial compressive loads[J]. International Journal of Mechanical Sciences. 2003, 45(3): 433–448. [5] SAAD-ELDEEN S, GARBATOV Y, GUEDES SOARES C. Ultimate strength analysis of highly damaged plates[J]. Marine Structures, 2016, 45: 63–85 [6] CUI W, MANSOUR A E. Effects of welding distortions and residual stresses on the ultimate strength of long rectangular plates under uniaxial compression[J]. Mar Struct 1998(11): 251–269. [7] 汤夕春. 残余应力对H型钢梁柱构件极限承载力影响研究[D]. 武汉: 武汉理工大学, 2006. [8] PAIK J K. Ultimate strength of dented steel plates under edge shear loads[J]. Thin-Walled Structures. 2005, 43: 1475–1492. | 1,897 | 4,636 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.921875 | 3 | CC-MAIN-2024-30 | latest | en | 0.552448 |
http://www.decisionsciencenews.com/2016/10/28/off-switch-remember-line-circle-mean-think-binary/ | 1,601,135,455,000,000,000 | text/html | crawl-data/CC-MAIN-2020-40/segments/1600400244231.61/warc/CC-MAIN-20200926134026-20200926164026-00016.warc.gz | 167,831,077 | 15,051 | Main
## On-off switch: How to remember what the line and circle mean. Think binary.
Filed in Encyclopedia ,Ideas
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THINK ONE AND A ZERO
Is our new glue gun powered on or off?
We were recently in a hotel in Berlin Germany and the room heater had the line-circle (| O) symbol on it and we couldn’t remember whether line means on and circle means off, or the line means off and circle means on.
Quality German engineering made the heater silent so there was no way to tell by listening.
The next day we got home to find our new glue gun had arrived. Same problem. And glue guns take a few minutes to heat up so that’s annoying (and possibly dangerous)
Turns out it’s best not to think of it as a line and circle.
Think of it as a 1 and 0.
Recall your computer science, logic, electrical engineering, whatever classes:
0 is FALSE, low voltage, or off
1 is TRUE, high voltage, or on
Boom. Retained for life.
1. Daniel Reeves says:
The little perks of a CS degree. It never occurred to me that it could be ambiguous! Which is also a good example of the illusion of transparency π
October 31, 2016 @ 7:22 pm
2. dan says:
wouldn’t it be easier to just remember the 0 is like an O and means Off?
September 22, 2017 @ 11:43 am
3. dan says:
Doesn’t “On” also begin with O?
September 22, 2017 @ 11:56 am
4. steve says:
The Germans are wise enough to not use terms for ‘on’ and ‘off’ that may be confused with a zero. We messed up their language while moving it across the Channel.
September 23, 2017 @ 12:26 pm
5. Josh says:
That would make perfect sense if it looked like a 1 and a 0 not a line and a circle. Because logically you would think a circle is a closed loop, or a circuit that would be on and line is an open circuit.
December 3, 2017 @ 11:42 am
6. Naomi says:
I will never forget now. Thank you!!!
May 14, 2018 @ 4:16 pm
7. William Terry Hunefeld says:
YAY! BRILLIANT!!! THANKS!
May 29, 2018 @ 9:18 am
8. Dave says:
A classic example of “the curse of knowledge” in full force.
In a sense… it’s obviously obvious *if* everyone has the same background. But,.. wait… is that ever the case?
My vote is that this design and it’s continued use (in consumer products) is a glorious failure.
July 11, 2018 @ 4:19 pm
9. Tom Henry Sr says:
β0β can always stand for OFF and use βIβ to always mean IGNITION! Problem solved for life and all other conventions!
September 25, 2018 @ 4:20 pm
10. Graeme Harrison says:
What’s wrong with a tick or cross. Simple-
November 20, 2018 @ 4:39 pm
11. Gary LA says:
The current symbols are very nice and simple but I feel it should be a plus+ sign or light bulb symbol for “on” and maybe an O or Zero with a diagonal or horizontal line through it for “off” or “nothing”!?!?
December 4, 2018 @ 4:52 pm
12. Tom Winters says:
so 0 is like zero current is going through, and 1 means a current of 1 is going through, therefore that means On. It always looked like a circle and a line to me. I have been swearing about these meaningless symbols for years.
On keyboards, only the letter O is truly round. The number 0 is usually a bit of an oval shape. And the number 1 usually has a little tail at the top, even in European languages, and the letter I does not have a tail at the top. Therefore the O and I on these on/off switches do not register as the numbers 0 and 1 to people.
January 5, 2019 @ 12:59 pm
13. Ian says:
Is it not easier just to remember ‘one is on’ that’s what I have worked out from this off the cuff
April 29, 2019 @ 3:59 pm
14. Bocephus says:
Iβm with Graeme. Wouldβve been simpler to have used β+β for on and β-β for off.
June 15, 2019 @ 3:35 pm
15. edward leon wier says:
plus and minus are the superior symbols
June 20, 2019 @ 6:24 pm
16. Barry says:
If it takes that much thought, it’s a fail. It should be a longer continuous line and 2 shorter broken lines “—” , “- -” (tough to “draw” here), but obviously connected and open…
June 27, 2019 @ 3:24 pm
17. J Arnott says:
I think I seeing the – as being a wire that allows continuous flow of power, so by that interpretation the O represents a block of power.
July 19, 2019 @ 11:10 am
18. Robert Campbell says:
If you must have a non language based symbol, I think + for on and – for off is much easier to remember and would work much better. I can’t imagine anyone of normal intelligence being unsure about pressing + for on.
August 1, 2019 @ 11:29 am
19. Margaret H says:
Here are two options to help you remember…The number one has ‘on’ in the word one. So if you think of I and O, it’s a one and a zero. With ‘on’ in the word one, your switch is on.
The other option. When current/power comes into your appliance from the wall, it has to get to the appliance to be able to work. It has to come in from the wall and go out to the appliance. A straight line is the best way to do this…thus, ‘I’. If the current comes in from the wall, and the appliance is off, the current will just sit there and go around and around without ever making your appliance heat up, light up, or work…thus, ‘O’ where the power never gets to come out and go to the appliance to make it work.
Both are something I’ve used for years. Maybe it will help you.
August 7, 2019 @ 2:46 pm
20. Steve Williams says:
Sheesh. Just write ON or OFF on the confounded thing. Is that so hard? Who voted to have sterile, incomprehensible electronic-ese all throughout our lives, anyway?
August 10, 2019 @ 4:30 pm
21. Anonymous says:
How about thinking of O is “Off”
August 11, 2019 @ 8:10 am
22. HienN says:
The Chinese symbol for 1 is β-β.
So it wouldnβt make sense for them.
β+β and β-β makes more sense in my Opinion.
Everyone who says βOβ should be off.
Do you not spell the word βOnβ with an O?
September 4, 2019 @ 11:14 am
23. Anonymous says:
Whoβs every says the β|β should represent 1 as in on. Have never taken Chinese.
September 4, 2019 @ 11:19 am
24. Rob says:
How about just On & Off….
It’s not like both words have a lot of letters so just use them either on the switch or either side of when the switch is mounted.
September 20, 2019 @ 8:35 pm
25. dug says:
i work it as o for off i for ignition
October 12, 2019 @ 9:17 pm
I would think that a “check mark” for on and an “X” for off would be pretty well universally understood. Check means yes to power, X means no.
October 14, 2019 @ 12:02 pm
27. Allen Lewis says:
I have worked in the electronics industry for over 60 years. For at least 50 of those years they labeled on off switches with the word “OFF” if you wanted something off and “ON” if you wanted it on. Can’t go wrong there.
December 10, 2019 @ 7:01 pm
28. John Doe says:
Why not simply have a solid small circle marking on the side that is mean to be on, and no marking on the off side? Language independent, hard to misinterpret, simple.
January 16, 2020 @ 8:14 am
29. David Ireland says:
I hate the | & O markings! They tell me NOTHING! “Is the O ‘O’n or ‘O’ff?” We grew up with “On” and “Off”, why not just leave it that way?
February 16, 2020 @ 4:20 pm
30. Michael says:
Looks like a pipe to me, circle is not blocked so water can flow through so βoβ must be ON. Compacted, water canβt flow though so βlβ must be off. (Except backwards).
Not a good design.
April 20, 2020 @ 7:41 am
31. Niko says:
The world has gotten so dumb it has resorted to using hieroglyphics, so many icons and symbols. I don’t know what they all mean.
May 12, 2020 @ 11:29 am
### Write Comment
XHTML: <a href="" title=""> <abbr title=""> <acronym title=""> <b> <blockquote cite=""> <cite> <code> <del datetime=""> <em> <i> <q cite=""> <s> <strike> <strong> | 2,211 | 7,777 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.3125 | 3 | CC-MAIN-2020-40 | latest | en | 0.957539 |
https://lists.swift.org/pipermail/swift-evolution/Week-of-Mon-20170508/036523.html | 1,582,793,279,000,000,000 | text/html | crawl-data/CC-MAIN-2020-10/segments/1581875146665.7/warc/CC-MAIN-20200227063824-20200227093824-00487.warc.gz | 437,299,854 | 2,144 | # [swift-evolution] [Proposal][Discussion] Deprecate Tuple Shuffles
Mon May 8 03:24:11 CDT 2017
```I still have to disagree on that. Tuple patterns are not consistent in Swift.
Here is a small proof of my claim:
enum Foo {
case a(b: Int)
}
switch Foo.a(b: 10) {
case .a(b: let x):
print(x)
}
let tuple = (x: 2, y: 20)
switch tuple {
case (x: let a, y: let b):
print(a); print(b)
}
(x: let a, y: let b): (x: Int, y: Int) = tuple // Error!!!
Tuple destructuring only works using the shorthand pattern, which _can_ lead to all those puzzles from the discussion.
The shorthand form ‘Is good and beautiful’ (German proverb), but it can do more harm than it should. Personally I would entirely ban the shorthand version unless we’ve got a superior version of it without all these issues.
By the way not only tuples are affected by the mentioned puzzle:
enum Foo {
case sum(x: Int, y: Int)
}
switch Foo.sum(x: 3, y: 1) {
case let .sum(x: Int, y: Double):
print(Int + Double) // prints 4
}
-- | 286 | 1,003 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.578125 | 3 | CC-MAIN-2020-10 | latest | en | 0.826087 |
http://www.answers.com/topic/earl-grey | 1,555,764,658,000,000,000 | text/html | crawl-data/CC-MAIN-2019-18/segments/1555578529813.23/warc/CC-MAIN-20190420120902-20190420142902-00263.warc.gz | 198,724,144 | 18,574 | ## Results for: Earl-grey
In Personal Finance
# What are the 5Cs of credit?
5 C's of Credit refer to the factors that lenders of money evaluate to determine credit worthiness of a borrower. They are the following:. 1. Borrower's CHARACTER. 2. Borrow ( Full Answer )
In Acronyms & Abbreviations
# What does 5c stand for?
The Iphone 5C is Iphone 5Colorful 5c can also stand for thenumber 500 ("c" is the Roman numeral for 100) or for 5 degreesCelsius (centigrade) . +++ . "5c" can not stand fo ( Full Answer )
In Coins and Paper Money
# What animal is on a 5c coin?
There are multiple animals on 5 cent coins depending on the country and time period such as the Buffalo on the US "buffalo nickel", the Beaver on the Canadian nickel, etc.
In Math and Arithmetic
# What is -5c plus 9 and how?
You can't tell a thing about -5c+9 until you know what 'c' is. And every time 'c' changes, -5c+9 changes.
In Volume
# What is 5c in milliliters?
5cc? cc means cubic centimetres which is equal to ml, so 5ml. if you mean cl, then that is equal to 50ml
In Numerical Analysis and Simulation
# What is the answer for 5c equals -75?
The 'answer' is the number that 'c' must be, if 5c is really the same as -75. In order to find out what number that is, you could use 'algebra'. First, write the equatio ( Full Answer )
In iPhone 5
# How many pixels does the iPhone 5c have?
The iPhone 5c is 640 x 1136 pixels. That is about 326 pixels persquare inch (ppi).
In Temperature
# What is minus 5c in Fahrenheit?
(-5) degrees Celsius = 23 degrees Fahrenheit. Formula: [°F] = [°C] à 9 â 5 + 32
In iPhone 5
# How many inches is a iPhone 5c?
The screen is 4" big. The height is 4.9", width is 2.33" and thedepth is 0.35"
In iPhone 5
# How much does an iPhone 5c weigh?
The iPhone 5c weighs 4.65 ounches. It is heavier than the iPhone 5and 5s which weight 3.95. | 563 | 1,859 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.328125 | 3 | CC-MAIN-2019-18 | latest | en | 0.903975 |
http://www.americansocceranalysis.com/home/2015/7/19/usmnt-6-0-cuba-the-us-smokes-cuba | 1,495,565,094,000,000,000 | text/html | crawl-data/CC-MAIN-2017-22/segments/1495463607649.26/warc/CC-MAIN-20170523183134-20170523203134-00561.warc.gz | 416,393,718 | 18,584 | # USMNT 6-0 Cuba: The U.S. Smokes Cuba/July 19, 2015by Jared Young
By Jared Young (@jaredeyoung)
On Saturday the U.S.A. cruised to a 6-0 victory over Cuba in the Gold Cup quarterfinals and advanced to play Jamaica in the semifinals. When a country with the population and the financial resources of the U.S. pounds on a country whose players are much more intrigued with the idea of leaving the team, it’s hard to get too excited about the victory. It’s an even harder match to break down statistically. How do you analyze a drubbing? Let’s just all feel good, right? Believe it or not I’ve found some statistics that will sober you right up.
First let’s take a look inside a dominant performance. What does that look like? Here’s a look at the game funnel which looks at completed passes, possession, shots and shot quality in a comparative chart. The lines that are drawn represent how many of each statistic would be expected by an average team given the actual result of the immediate variable above it. For example, a team that completes 547 passes would normally have the ball for 58 minutes of the game (represented by the dot on the left). In this case the U.S. slightly underperformed.
Where the U.S. really outperformed the expectation was in both shots in the box and finishing. An average team that takes 17 shots would take 8.9 of those shots in the box. The U.S. managed 13 shots in the box and finished 6 of them. Their expected goals was 2.7. It was clearly a dominant performance across the board for the U.S.
But those with sharp memories might recall a team nicknamed El Tri also beat Cuba by a score of 6-0. There’s a greater than zero chance that the U.S. might face Mexico in the Gold Cup Final. Perhaps there’s a little something we can learn from looking at both games side by side. Here’s the tale of the tape from the two performances.
USMNTDif. v CubaMexicoDif. v Cuba
Passes Attempted 608 235 716 496
Completion Percentage 0.9 0.04 0.91 0.25
Possession 0.62 0.24 0.76 0.53
Passes Attempted in Final Third 142 50 274 228
Shots 17 8 44 41
Shots in the Box 13 10 32 31
Shots on Target 8 7 18 17
As you can see the Mexican performance was a far more dominant performance than the U.S.A’s. Does that matter? Probably not much, but it is a little sobering.
Next up for the U.S. is Jamaica, who has played exceptional defense during the tournament, pitching three straight shutouts. The Reggae Boyz bunkered in against Haiti, in a surprise move, showing their respect for the aggressive Haitian side. The tactic worked well as an early goal for Jamaica held up for a 1-0 win. Perhaps Jamaica will decide to play the same way against the U.S. If that’s the case, the U.S. will put together a game funnel much like they did against Cuba but there will be much fewer chances. As long as the U.S. respect the Jamaican counterattack they should be able to get past them and into the final. | 735 | 2,913 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.03125 | 3 | CC-MAIN-2017-22 | longest | en | 0.945335 |
https://books.google.com/books?id=CAoAAAAAYAAJ&hl=en | 1,521,918,050,000,000,000 | text/html | crawl-data/CC-MAIN-2018-13/segments/1521257650764.71/warc/CC-MAIN-20180324171404-20180324191404-00667.warc.gz | 569,384,119 | 11,599 | # Elements of Algebra
Hilliard, Gray, Little, and Wilkins, 1831 - Algebra - 304 pages
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Page 24 - Divide the first term of the dividend by the first term of the divisor, and write the result as the first term of the quotient. Multiply the whole divisor by the first term of the quotient, and subtract the product from the dividend.
Page 51 - A man was hired 50 days on these conditions. — that, for every day he worked, he should receive \$ '75, and, for every day he was idle, he should forfeit \$ '25 ; at the expiration of the time, he received \$ 27'50 ; how many days did he work...
Page 104 - It is founded on the following principle. The square root of the product of two or more factors, is equal to the product of the square roots of those factors.
Page 24 - Arrange the dividend and divisor with reference to a certain letter, and then divide the first term on the left of the dividend by the first term on the left of the divisor, the result...
Page 19 - To this result annex all the letters of the dividend, giving to each an exponent equal to the excess of its exponent in the dividend above that in the divisor.
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Page 3 - ... the product multiply the number of tens by one more than itself for the hundreds, and place the product of the units at the right of this product, for the tens and units. Thus...
Page 126 - The algebraic sum of the two roots is equal to the coefficient of the second term taken with the contrary sign.
Page 248 - ... to the sum of the extremes multiplied by half the number of terms. Rule. — Add the extremes together, and multiply their sum by half the number of terms ; the product will be the sum of the series.
Page 24 - Though there is some analogy between arithmetical and algebraical division, with respect to the manner in which the operations are disposed and performed, yet there is this essential difference between them, that in arithmetical division the figures of the quotient are obtained by trial, while in algebraical division the quotient obtained by dividing the first term of the partial dividend by the first term of the divisor is always one of the terms of the quotient sought. | 537 | 2,410 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.90625 | 4 | CC-MAIN-2018-13 | latest | en | 0.938238 |
https://betterlesson.com/lesson/resource/2081068/3-3-number-categories-review-docx | 1,498,467,480,000,000,000 | text/html | crawl-data/CC-MAIN-2017-26/segments/1498128320695.49/warc/CC-MAIN-20170626083037-20170626103037-00258.warc.gz | 743,583,661 | 23,675 | ## 3.3 Number Categories Review.docx - Section 3: Number Categories
3.3 Number Categories Review.docx
3.3 Number Categories Review.docx
# What Are Integers?
Unit 3: Integers and Rational Numbers
Lesson 4 of 17
## Big Idea: What are integers? How do integers connect with altitude, temperature, and football? Students work on understanding integers in multiple contexts.
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### Andrea Palmer
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