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https://www.physicsforums.com/threads/power-of-a-sound-source.817809/ | 1,508,357,723,000,000,000 | text/html | crawl-data/CC-MAIN-2017-43/segments/1508187823114.39/warc/CC-MAIN-20171018195607-20171018215607-00585.warc.gz | 980,980,678 | 16,308 | # Power of a sound source
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1. Jun 6, 2015
### nicholasH
1. The problem statement, all variables and given/known data
A sound source is placed at the top of a tall (h = 189.6m) radio tower. The source has a frequency of 740 Hz and an amplitude of 19.4 nm at point A. The air surrounding the tower has a density of 1.29 kgm-3 and sound travels through it with a velocity of 343 ms-1. Point A is 13.5 m above the source. You may ignore any reflections of the sound from the ground.
Calculate the average power leaving the source.
2. Relevant equations
P = (1/2)pAv(ws)^2
where p = density of air = 1.29
v = sound velocity = 343
s = maximum displacement (amplitude) = 19.4e-9
w = 2Pi*f = 2960*Pi
A = area of speaker
3. The attempt at a solution
It seems that this question is unsolvable without being supplied with the area of the speaker. Unless the amplitude at Point A somehow depends upon this area, however I'm sure that it depends solely upon the size of the speakers vibrations, not the area of the surface causing them.
Any help would be greatly appreciated.
2. Jun 7, 2015
### vela
Staff Emeritus
The intensity of a sound wave is given in units of power per area, so starting from your expression, you'd get
$$I = \frac PA = \frac 12 \rho v (\omega s)^2.$$ You're probably supposed to assume the speaker can be treated as a point source. How does the sound propagate away from the speaker and how does the intensity of sound vary with distance? | 390 | 1,462 | {"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} | 3.546875 | 4 | CC-MAIN-2017-43 | longest | en | 0.919766 |
https://es.mathworks.com/matlabcentral/answers/2099266-index-exceeds-the-number-of-array-elements-error-when-using-fsolve | 1,716,355,258,000,000,000 | text/html | crawl-data/CC-MAIN-2024-22/segments/1715971058531.78/warc/CC-MAIN-20240522040032-20240522070032-00533.warc.gz | 207,448,429 | 26,562 | # Index exceeds the number of array elements error when using fsolve
3 visualizaciones (últimos 30 días)
Kaelyn Smith el 26 de Mzo. de 2024
Movida: Matt J el 26 de Mzo. de 2024
I'm working on a project in which one part solves for the position solutions from a vector loop equation I generated. The code reads as follows:
%%position solution
%VLE: -R1 - R2 + R3 = 0
%defining fixed/knowns (m) - using average values of males (Table 2)
R1 = 0.4; %length of thigh
R2 = 0.4; %length of shin
th3 = 90*(pi/180); %converted to radians
%using fsolve for position solution *requires installation of optimization toolbox in MatLab
PAs = zeros(141,3); %empty array for th1 and R3, respectively, (unknowns) to be placed
for ii = 0:140 %to iteart through all possible input angles (degrees)
theta2 = ii*(pi/180); %converst to radians
PAs(ii+1,1) = theta2; %fills first spot in array with input value (th2) - knee angle of flexion
F1 = @(x) [-R1*cos(x(2)*(pi/180))-R2*cos(theta2); -R1*sin(x(2)*(pi/180))-R2*sin(theta2)+x(3)];
PAs(ii+1, [2 3]) = fsolve(F1, [0, 0.8]); %initial values (taken from standing leg)
end
th2 = PAs(:,1);
th1 = PAs(:,2);
r3 = PAs(:,3);
However, when I run it, I get an error reading "index exceeds number of array elements" and thus fsolve will not compute. Is anyone able to see any issues with my code that would cause this error?
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Stephen23 el 26 de Mzo. de 2024
Movida: Matt J el 26 de Mzo. de 2024
Your x0 is a two-element vector, so you told FSOLVE to call the function handle with a two-element vector. But then inside the function you try to access x(3), which thus does not exist.
If you expect the function handle to be called with a three-element vector, then x0 needs to have three elements.
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Kaelyn Smith el 26 de Mzo. de 2024
Movida: Matt J el 26 de Mzo. de 2024
Runs smoothly now, thank you!
Iniciar sesión para comentar.
R2023b
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# How to group variables in SPSS
### SPSS Statistical Software - Advanced Analytic
Find The Best Deals For Spss Statistical Software. Compare Prices Online And Save Today SPSS will not stop you from using a continuous variable as a splitting variable, but it is a bad idea to try to attempt this; SPSS will see each unique numeric value as a distinct category. In order to split the file, SPSS requires that the data be sorted with respect to the splitting variable 1 Choose Transform, Recode, Into Different Variables. 2 Put the variable you want to recode in the Input Variable → Output Variable box. In the Output Variable box, type in a name for the new (grouped) variable. For example, if you are grouping BMI you might use the name 'BMIgroup'. Click on Change. 3 Click on Old and New Values About Press Copyright Contact us Creators Advertise Developers Terms Privacy Policy & Safety How YouTube works Test new features Press Copyright Contact us Creators.
SPSS users often want to know how they can combine variables together. In this video Jarlath Quinn demonstrates how to use the compute procedure to calculate the mean of a number of variables to create one combined variable, and also how to use the count values procedure to count how many times a particular value occurs across a series of variables in order to create an overall count
In Statistica, usually the group is identified by a number (i.e. Group 1, 2 or 3) or by a categorical label, like MALE or FEMALE.These values are called codes and you can specify up to 1,000 of them.; In SPSS, grouping variables are defined on the worksheet and specified within a test window (for example, the Independent Samples T Test or Tests for Several Independent Samples window) Written and illustrated tutorials for the statistical software SPSS. Compare Means is best used when you want to compare several numeric variables with respect to one or more categorical variables. It is especially useful for summarizing numeric variables simultaneously across categories
Then, wave the Transform--Compute--Enter a name for the variable you will be calculating in the Targte variable box--sum(list all the variables by separating with comma here and close by brackets. The function group contains many useful, common functions that may be used for calculating values for new variables (e.g., mean, logarithm). To find a specific function, simply click one of the function groups in the Function Group list. You will now see a list of functions that belong to that function group in the Functions and Special. Old and New Values. Once you click Old and New Values, a new window where you will specify how to transform the values will appear.. 1 Old Value: Specify the type of value you wish to recode (e.g., a specific value, missing data, or a range of values) and the specific value to be recoded (e.g., a value of 1 or a range of 1-5).. When recoding variables, always handle the missing. Cases are aggregated based on the value of one or more break (grouping) variables. If you create a new, aggregated data file, the new data file contains one case for each group defined by the break variables. For example, if there is one break variable with two values, the new data file will contain only two cases
### Low Price Spss Statistical Software - On Sale No
1. The grouping variable must have at least two categories (groups); it may have more than two categories but a t test can only compare two groups, so you will need to specify which two groups to compare. You can also use a continuous variable by specifying a cut point to create two groups (i.e., values at or above the cut point and values below.
2. @Martin: Yes, I understand that I need to tinker with the syntax to choose the 'reference group' that I want in the independent variable. I did not know the exact SPSS syntax for this. That's why.
3. To create group-mean centered variables, we need to know the grouping variable, the list of the variables that we want to center and the suffix to the name of the new variables. (In this macro, we will use the variable names of the variables to be group-mean centered plus a suffix.
Drag and drop the dependent variable into the Test Variable(s) box, and the grouping variable into the Grouping Variable box; Click on Define Groups, and input the values that define each of the groups that make up the grouping variable (i.e., the coded value for Group 1 and the coded value for Group 2) Press Continue, and then click on OK to. Why would we need to recode? How do we recode? What if I need the syntax? I answer all these questions as efficiently as I can Recode a scale variable into a categorical variable using SPSS. For example, change the scale variable 'Age' into the categorical variable 'Age groups'.ASK.
How to Mean Center Predictors in SPSS? By Ruben Geert van den Berg under Regression. Also see SPSS Moderation Regression Tutorial.. For testing moderation effects in multiple regression, we start off with mean centering our predictors: mean centering a variable is subtracting its mean from each individual score. After doing so, a variable will have a mean of exactly zero but is not affected. I have an spss datafile which separated responses from two groups of participants on the same survey question into two variables in SPSS (i.e. Variable 1 = Males responses to question 1, and.
SPSS - Merge Categories of Categorical Variable By Ruben Geert van den Berg under Recoding Variables Summary. Merging some categories of a categorical variable in SPSS is not hard if you do it the right way. This tutorial demonstrates just that Rerunning our contingency table (not shown) confirms that SPSS now reports only 181 female cases working in marketing or sales. Also note that we now have 2 filter variables in our data and that's just fine but only 1 filter variable can be active at any time. Ok. Let's deactivate our new filter variable as well with FILTER OFF. Example 3 - Filter without Filter Variable 2. A new window will appear. Here you need to tell SPSS which data you want to include in the independent t-test. Add the test variable (Height in this case) into the Test Variable(s): window.Also, add the grouping variable (Group in this case) to the Grouping Variable: input.The window should now look like this combination of the groups created when two or more categorical variables interact. A good way to begin using crosstabs is to think about the data in question and to begin to form questions or hytpotheses relating to the categorical variables in the dataset. These might include Using SPSS for Nominal Data: Binomial and Chi-Squared Tests. This tutorial will show you how to use SPSS version 12.0 to perform binomial tests, Chi-squared test with one variable, and Chi-squared test of independence of categorical variables on nominally scaled data.. This tutorial assumes that you have
### Grouping Data - SPSS Tutorials - LibGuides at Kent State
1. The addition of a variable containing integers functioning as unique identifiers will sort out this issue. Add an ID. We're going to add a variable that will contain a set of number IDs by using the Transform -> Compute Variable menu item. The Compute Variable dialog box looks like this
2. How to assess differences between three groups in a pretest - posttest design using SPSS? 2 SPSS: 2 sample t-test: real data against fictional group with M=0 and SD=1
3. al variables (also called categorical or grouping variables) where participants fall into different groups or conditions (in this, audience presence groups), you need to tell SPSS what these groups are. To do this, you need to assign each group a name and number. The numerical code gets entered into the Data View sheet for each.
To add more variables, simply add more columns - one column per variable. The only variation to this is discussed later in this guide when we have to enter repeated measures. SPSS Statistics Defining Separate Groups. Separate groups are more commonly called between-subjects factors or independent groups This variable, mpgfd, will have two values: 0 if below the median mpg for its group (foreign/domestic) 1 if at/above the median mpg for its group (foreign/domestic). sort cases by foreign. examine variables = mpg by foreign /plot none /compare group / percentiles (5,10,25,50,75,95) haverage new variable column and give it the group label. - Variable View - Data View SPSS gives a lot of information, most which you don't need - Ignore what you don't need 1. Start SPSS from wherever you have it 2. Double click New Dataset at the top left 3. In the box on the right there are 10 people's names If the variable labels are not defined, variable names are used as labels. For multiple category sets, category labels come from the value labels of the first variable in the group. If categories missing for the first variable are present for other variables in the group, define a value label for the missing categories
I've finished my survey and have my outcome variable (whether someone has had military training) and predictor variables (the BFI personality matrix and DOSPERT risk matrix). I've exported my data from qualtrics into SPSS but I have 0 clue of how to group my variables together, as the BFI has 44 items and DOSPERT has 30 SPSS Variable Types and Formats By Ruben Geert van den Berg under Basics. Understanding SPSS variable types and formats allows you to get things done fast and reliably. Getting a grip on types and formats is not hard if you ignore the very confusing information under variable view.This tutorial will put you on the right track @Martin: Yes, I understand that I need to tinker with the syntax to choose the 'reference group' that I want in the independent variable. I did not know the exact SPSS syntax for this. That's why. It assumes that all variables in the model are interval and normally distributed. SPSS requires that each of the two groups of variables be separated by the keyword with. There need not be an equal number of variables in the two groups (before and after the with). manova read write with math science /discrim
Describe each group of stacked variables in the Variables to be Transposed section: a. Choose the Target Variable. SPSS has created generic names for these, which will be trans1, trans2, etc. b. Highlight the variables for the group in the list on the left, and use the arrow button to move them into box below Target Variable The instructions and examples will help guide you through establishing different types of variables for your particular research or analysis needs. Creating a new SPSS Statistics data file consists of two stages: defining the variables and entering the data. Defining the variables involves multiple processes and requires careful planning A multiple-response set is much like a new variable made of other variables you already have. A multiple-response set acts like a variable in some ways, but in other ways it doesn't. You define it based on the variables you've already defined, but it doesn't show up on the SPSS Variable View tab. It doesn't [ The best way to understand a dataset is to calculate descriptive statistics for the variables within the dataset. There are three common forms of descriptive statistics: 1. Summary statistics - Numbers that summarize a variable using a single number.Examples include the mean, median, standard deviation, and range In this case, we will make a total of two new variables (3 groups - 1 = 2). To do so in SPSS, we should first click on Transform and then Recode into Different Variables. Now, click on Groups, and then click on the highlighted arrow to move Groups to the empty window. Now, change the Name and the Label to Dum1, and click on Change
In SPSS Statistics, we entered the scores for cholesterol concentration, our dependent variable, under the variable name Cholesterol. Next, we created a grouping variable, called Group, which represented our independent variable. Since our independent variable had two groups - 'diet' and 'exercise' - we gave the diet group a value of 1 and. I am an SPSS novice, and I found this group recently when I was trying to determine how to combine two categorical into one variable in SPSS. I did not find an answer online, but I did eventually figure out how to do it. I decided to post it here to the benefit of others. I had one variable for Sex (1: Male; 2: Female) and one variable fo Centering Examples: SPSS and R. 1. The HLM package makes centering (either group- or grand-mean centering) very convenient and self-explanatory. Below, I show the steps I use in SPSS and R to center variables. Grand-mean centering in either package is relatively simple and only requires a couple line towards 'out-groups' can be fostered. The data can be found in the SPSS file: Week 4 data file.sav and looks like this: For an in-depth explanation of what each of the variables represent, revisit the Descriptive Statistics tutorial. When deciding what type of graph to produce, you first need to think about (1) th
### How to create grouped or banded variables in SPSS
•Key in values and labels for each variable •Run frequency for each variable •Check outputs to see if you have variables with wrong values. •Check missing values and physical surveys if you use paper surveys, and make sure they are really missing. •Sometimes, you need to recode string variables into numeric variables 1 SPSS Statistics Three-way ANOVA result. The primary goal of running a three-way ANOVA is to determine whether there is a three-way interaction between your three independent variables (i.e., a gender*risk*drug interaction). Essentially, a three-way interaction tests whether the simple two-way risk*drug interactions differ between the levels of gender (i.e., differ for males and females) How can I recode date intervals into a categorical variable? I have a very large data set with cases entered based on admission dates. These dates are all entered in an SPSS date variable which is called INDATE and formatted as dd.mm.yy. I want to code people according to their admission date (e.g 1 = admission between 11/1/92 and 10/31/93; 2= admission between 11/1/93 and 10/31/94; 3. A step by step guide to recoding AGE variables into generational groups in SPSS. Screenshots of every step is provided in an easy to follow tutorial of how to Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising
### How to combine variables in SPSS Statistics - Smart Vision
In the SPSS menu, select Analyze>Compare Means>One Sample T-test Select the variable(s) from the list you want to look at and click the button to move it into the Test Variable(s) area. Then enter the test value. In this example, we're testing the hypothesis that the median house value is 200,000 Creating dummy variables in SPSS Statistics Introduction. If you are analysing your data using multiple regression and any of your independent variables were measured on a nominal or ordinal scale, you need to know how to create dummy variables and interpret their results. This is because nominal and ordinal independent variables, more broadly known as categorical independent variables, cannot. a linear relationship between each pair of continuous dependent variables for each group of the independent categorical variable; multivariate normality; An Example: Two-Way MANOVA Test. This guide will explain, step by step, how to run the Two-way MANOVA test in SPSS statistical software by using an example Some functions, such as grpstats, accept multiple grouping variables specified as a cell array of grouping variables, for example, {G1,G2,G3}.In this case, the groups are defined by the unique combinations of values in the grouping variables. The order is decided first by the order of the first grouping variable, then by the order of the second grouping variable, and so on
### Grouping Data in SPSS - YouTub
The main reason for wanting to combine variables in SPSS is to allow two or more categorical variables to be treated as one. Alternatively, you may be trying to create a total awareness variable. The best way to learn how to recode variables in SPSS in order to combine them is to follow a step-by-step guide and refer to expert advice along the way Click OK and SPSS will produce dummy variables for all categories of the age group variable, as shown in Figure 8. Figure 8: New Variables Created From the Create Dummy Variable Dialog Box in SPSS. Now, we are ready to run the regression model with dummy variables
### Grouping Variable (Coding Variable) - Statistics How T
• Use SUM function to sum variables in SPSS e.g Transform / Compute Sum = SUM(v1,v2,v3,v4) The Syntax for this would be: COMPUTE sum = SUM(v1,v2,v3,v4) . EXECUTE . You can also do the following if you have more variables: COMPUTE sum_all=SUM(v1 TO v102). EXECUTE. If you don't use the SUM function and instead just use: SUM = V1 + V2 + V3 + V
• Example: Multiple Linear Regression in SPSS. Suppose we want to know if the number of hours spent studying and the number of prep exams taken affects the score that a student receives on a certain exam. To explore this, we can perform multiple linear regression using the following variables: Explanatory variables: Hours studied; Prep exams take
• The questionnaire contains 6 categories and each category has 8 questions. 8 items correspond to one variable which means that we have 6*8 = 48 questions in questionnaire. How do I combine the 8 different items into one variable, so that we will have 6 variables? How can I combine different items into one variable in SPSS
• An Example: How to run exploratory factor analysis test in SPSS. We collected data from students about their feeling before the exam. The students were asked to rate the following feelings on the scale from 1 to 5. We wanted to reduce the number of variables and group them into factors, so we used the factor analysis
• The table then shows one or more statistical tests commonly used given these types of variables (but not necessarily the only type of test that could be used) and links showing how to do such tests using SAS, Stata and SPSS
• When you have created the dataset by typing your data into SPSS, and after you have tested for the internal consistency of the scale (use Cronbach's α), it's time to create a new variable. Merging the variables. From the top menu bar in SPSS, select Transform -> Compute variable. You should now see the following dialogue box
• SPSS (The Statistical Package for the Social Sciences) software has been developed by IBM and it is widely used to analyse data and make predictions based on specific collections of data. SPSS is easy to learn and enables teachers as well as students to easily derive results with the help of a few commands
### Descriptive Stats by Group (Compare Means) - SPSS
• ation), which is the proportion of.
• The Group variable refers to which group each participant is in, so that '1' indicates the controls and '2' is assigned to the experimental group. In total, there are 40 individuals, 20 in each group. Below is a snapshot of some of the data within SPSS
• Independent variable, or grouping variable An Example in SPSS: Independent samples t-test Independent samples t-test uses to compare the mean value of a variable (for example, wage) measured in two different groups of people (for example, men and women) or different circumstances (for example, a union member or not a union member)
• 2. In the new Explore window, move the dependent variable (Protein X concentration) into the Dependent List box and the grouping variable (Treatment group) into the Factor List box. This is telling SPSS to give us the descriptive statistics for the Protein X concentration and to separate the outputs by the treatment group
### How do I combine 8 different items into one variable, so
Your variables should have: One independent variable with two or more levels (independent groups) so the test is more commonly used when you have three or more levels. On the other hand, for two levels, consider using the Mann Whitney U Test instead. Ordinal scale, Ratio Scale, or Interval scale dependent variables One Way ANOVA in SPSS Including Interpretation Click on Analyze -> Compare Means -> One-Way ANOVA. Drag and drop your independent variable into the Factor box and dependent variable into the Dependent List box. Click on Post Hoc, select Tukey, and press Continue. Click on Options, select Homogeneity of variance test, and press Continue
### Computing Variables - SPSS Tutorials - LibGuides at Kent
Splitting a data file in SPSS (e.g. by males and females) select the organize output by groups button 3) move the 'sex' variable to the field on the right so that the file is grouped based on sex 4) ok. From that point on, all analyses you do will be separated by sex (you'll get two t tests, boxes of descriptives etc) Sorry if this is a stupid question but I'm really struggling with this aspect of SPSS. I want to do a multiple regression for two predictor variables on one outcome variable. These variables are the result of three sets of questionnaire data and I don't know how to group each set of data into a single variable for each set
### How do I AGGREGATE in SPSS? - IB
It measures the correlations between two or more numeric variables. There are two types of correlations; bivariate and partial correlations. While Bivariate Correlations are computed using Pearson/Spearman Correlation Coefficient wherein it gives the measure of correlations between variables or rank orders This is the perfect tool if you wish to create tools based on the empirical distribution of a continuous variable you wish to recode into groups. (not useful for categorical variables you wish to recode). Note also that classification (cluster analysis) lets you create a categorical variable (classes, groups, partition), based on a multivariate. SPSS, prepare a codebook for the data set. • The codebook documents all of the items to be entered in the data set: -Variable names and labels -Variable types and formats -Coded values for categorical items -Missing value into SPSS. Now click Analyze, Classify, Hierarchical Cluster. Identify Name as the variable by which to label cases and Salary, FTE, Rank, Articles, and Experience as the variables. Indicate that you want to cluster cases rather than variables and want to display both statistics and plots. You may want to open the output in a ne
### Independent Samples t Test - SPSS Tutorials - LibGuides at
In this example, move the Section variable into the Grouping Variable box: You need to tell SPSS how to define the two groups. Click on the Define Groups button. The Define Groups dialog box appears: In the Group 1 text box, type in the value that determines the first group. In this example, the value of the 10 AM section is 10 The Split File command is used to separate the output of SPSS tests according to a group variable. The best example would be to split the output according to sex. By doing this in SPSS, through the use of the Split File command, you will get two separate outputs for subsequent analyses, one for males and the other for females Independent-Sample T Test dialogue box, enter the continuous variable fencetch in the Test Variable(s) field (4) by left-clicking the variable and left-clicking on the boxed arrow pointing to the Test Variable(s) field. Next, enter the discrete variable breed in the Grouping Variabel: field (5). To tell SPSS what values have been paired wit Next, select all three of the variables displayed in the window on the left, and click on the arrow key to transfer the variables to the window on the right. The SPSS default settings specify that Pearson Product-Moment correlation coefficients will be computed, and that two-tailed tests of significance will be reported
It must be in the form of rows=cases and columns=variables. SPSS can not be used with only the summarizing statistics (mean, standard deviation, sample size). Below left is the sample data. The sample mean is 38.6 and the sample standard deviation is 8.5. 2. Example: Suppose we want to test the claim that the population mean is larger than 35. As you can see, SPSS has created a new variable called Change, and filled it with difference scores (i.e., calculated by subtracting the PrePEF score from the FirstPostPEF score). At this point it's worth taking a look at the Variable View - just click on the tab towards the bottom of the screen - to check the properties of the. >How does one compare groups on nominal or ordinal variables? I want to know if the groups show significant differences in gender and education. How can one do it on SPSS? Google for the UCLA tutorial on using SPSS in data analysis. The names of SPSS procedures often match the names of the tests, such as t-test or ANOVA. -- Rich Ulric Next, move the dependent variables from the variable list on the left to the Test Variable(s) window using the arrow. Move female to the Grouping Variable box. Click Define Groups In this case, we specify the groups as 0 and 1, since our female variable lists males as 0 and females as 1 I have split my independent variable into 2 groups of high and low. I have 3 dependent variables of positive, negative, and neutral. I want to do a between groups comparison of high/low on each dependent variable. I have split my data on spss but not sure how to perform a t test with split data (high vs low) or which t test to perform However, we can compare the medians between the groups. In SPSS, we can compare the median between 2 or more independent groups by the following steps: Step 1. Open the dataset and identify the independent and dependent variables to use median test. Here, I use the Employee Data.sav which is in the installation directory of IBM-SPSS
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• What is not considered a “source” in google analytics by default?. | 5,930 | 27,334 | {"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-2021-39 | latest | en | 0.810301 |
https://gusto.com/resources/articles/benefits/health-insurance/how-calculate-fte-employee-number | 1,722,850,115,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722640436802.18/warc/CC-MAIN-20240805083255-20240805113255-00111.warc.gz | 232,255,511 | 19,369 | # How Do I Calculate My Full-Time Equivalent (FTE) Employee Number?
FTE stands for full-time equivalent, and it’s a way for employers to measure how many full-time employees they have, along with the number of part-time employees that can be translated into full-time terms.
And when you’re thinking about offering health benefits, you’ll see the FTE acronym flung around constantly.
The FTE calculation (and definition) can be confusing at first, so we’re here to help you make sense of it all. In this post, we’ll show you exactly how to calculate the number of full-time equivalents you have on your team.
Read on to learn how to calculate your full-time equivalent employee number, or if you’d rather watch a video that explains it, jump to bottom of this post.
## What is an FTE employee?
An FTE is a yardstick that measures the number of full-time hours being completed at your company. The number is tallied using your part-time and full-time employee count, in addition to a few simple calculations.
To reach your FTE count, you’ll have to translate the number of hours worked by your part-time employees to what they would look like on a full-time basis. After that, your full-time employees are folded into the final FTE count.
Is your team fully full-time? Then your FTE total is simply the number of employees you have on staff. If you also have part-timers on your team, then you’ll have to first convert their hours to full-time, and then add in your true full-timers.
## Why does my FTE number matter?
Your FTE number determines whether you’re seen as an applicable large employer, or ALE.
An ALE is not just a delicious beverage—it means that last year you had 50 or more employees, or a blend of full- and part-time workers that equaled 50 FTEs. Flip through your records to see what your team looked like a year ago.
If your company fits the ALE bill, it means you’re required to offer group health insurance under the Affordable Care Act’s employer mandate. Having ALE status also means that you need to send in your 1094-C and 1095-C forms describing the kind of coverage you provided to your team.
If you’re not an ALE, you can still give your team health insurance. In fact, 65 percent of small businesses that provide company-sponsored coverage have between five and 49 employees on staff.
## How do I calculate my FTE number?
It’s pretty easy. Grab a pencil, open your notebook, and we’ll show you exactly how to calculate your FTE count.
• Step 1: How many part-time workers do you have? According to the IRS, part-timers are those who work less than 130 hours a month, or 30 hours a week.
• Step 2: Write down the average number of hours each part-time employee works per week. Now, add them all together.
• Step 3: Take the result and divide it by 30.
• Step 4: Round down to the nearest whole number.
• Step 5: Add your full-time employee count to the number you got above.
• Step 6: You now have your FTE number. That’s it!
Here’s a quick formula that summarizes the FTE calculation above:
Your FTE number = (Total average of part-time hours worked per week / 30) + # of full-time employees
## FTEs in the wild
Now, let’s look at two examples of what calculating an FTE number might look like.
Let’s say you own a chain of movie theaters. To keep the show running, you employ a staff of 40 full-time employees and 20 part-timers. Each of your part-time employees works ten hours a week selling tickets and snacks, while your full-timers cram in an average of 30 hours a week on marketing, business development, and other showbiz-related tasks.
• To get to your FTE number, you first have to figure out the total weekly hours worked by your part-time employees [10 x 20 = 200].
• Then, you divide 200 by 30, which leaves you with 6.6. Now, round down. Add your full-time employee count to that number, and you get to an FTE number of 46. Therefore, you are not an ALE.
Great, but what if you’re in business for just a few months out of the year? Perhaps you also own a Halloween costume store that’s only open in September and October. During those two spooky months, you hire 60 seasonal workers. Since they work 120 days or less in a single year, you’re not considered an ALE here either.
## Video: Calculating your full-time equivalent employee number
Zeroing in on your full-time equivalent number is an important step to master when running your company. Once you figure out your FTE calculation, you’ll feel good knowing that you’re keeping your team compliant. | 1,045 | 4,520 | {"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} | 2.71875 | 3 | CC-MAIN-2024-33 | latest | en | 0.957898 |
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Guest Message by DevFuse
# Comparing gambling systems
49 replies to this topic
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Posted 18 November 2013 - 06:03 PM
Consider a gambling machine A. When you put in \$X and pull the handle, it will spit out (equally likely) either \$0.7*X, \$0.8*X, \$0.9*X, \$1.1*X, \$1.2*X, or \$1.5*X.
Now consider the following two ways of playing this machine:
Put in \$1, pull the handle, and keep whatever you get. Repeat.
Initially, put in \$1. Pull the handle, then put in whatever you get. Repeat.
Can you win money with this machine? Which is the better way to play? How can this be?
• 0
### #2 bonanova
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Posted 18 November 2013 - 07:13 PM
Spoiler for Looks like
• 0
Vidi vici veni.
### #3 Prime
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Posted 18 November 2013 - 09:07 PM
Spoiler for seems straightforward
Edited by Prime, 18 November 2013 - 09:14 PM.
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Past prime, actually.
### #4 plainglazed
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Posted 18 November 2013 - 09:25 PM
I really should know better than to chime in here -
Spoiler for less than proud and surely too simple
EDIT: I knew I shouldn't have tried to play with the big boys. See where I erred now and am with Prime.
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### #5 bonanova
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Posted 19 November 2013 - 08:44 AM
Spoiler for Not convinced
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Vidi vici veni.
### #6 phil1882
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Posted 19 November 2013 - 11:36 AM
hmmm
Spoiler for
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### #7 bonanova
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Posted 20 November 2013 - 09:50 AM
hmmm
Spoiler for
Spoiler for Understanding Method 2
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Vidi vici veni.
### #8 Rainman
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Posted 20 November 2013 - 06:06 PM
Spoiler for what is expected
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Posted 20 November 2013 - 06:12 PM
I temporarily changed this to unsolved to consider Rainman's thorough argument. Anyone else have thoughts?
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### #10 Prime
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Posted 20 November 2013 - 07:47 PM
I temporarily changed this to unsolved to consider Rainman's thorough argument. Anyone else have thoughts?
Change it back. The proof is coming.
• 0
Past prime, actually.
#### 0 user(s) are reading this topic
0 members, 0 guests, 0 anonymous users | 989 | 3,429 | {"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-2015-22 | latest | en | 0.891461 |
https://www.physicsforums.com/threads/conditional-expectation-on-an-indicator.778222/ | 1,571,453,953,000,000,000 | text/html | crawl-data/CC-MAIN-2019-43/segments/1570986688674.52/warc/CC-MAIN-20191019013909-20191019041409-00124.warc.gz | 1,046,676,084 | 17,498 | # Conditional expectation on an indicator
#### IniquiTrance
1. Homework Statement
Let $X$ and $Y$ be independent Bernoulli RV's with parameter $p$. Find,
$$\mathbb{E}[X\vert 1_{\{X+Y=0\}}]$$ and $$\mathbb{E}[Y\vert 1_{\{X+Y=0\}}]$$
2. Homework Equations
3. The Attempt at a Solution
I'm trying to show that,
$$\mathbb{E}[X+Y\vert 1_{\{X+Y=0\}}] = 0$$
by,
\begin{align*} \mathbb{E}[X+Y\vert 1_{\{X+Y=0\}}] &= \frac{\mathbb{E}[(X+Y)1_{\{X+Y=0\}}]}{\mathbb{P}[X+Y=0]} \\ &= \frac{0}{(1-p)^2} \\ &= 0 \end{align*}
Related Calculus and Beyond Homework Help News on Phys.org
#### haruspex
Homework Helper
Gold Member
2018 Award
$$\mathbb{E}[X\vert 1_{\{X+Y=0\}}]$$
I'm not familiar with the notation for the condition ($1_{\{X+Y=0\}}$). How does one read it? Can you post a link?
#### IniquiTrance
I'm not familiar with the notation for the condition ($1_{\{X+Y=0\}}$). How does one read it? Can you post a link?
It's the indicator of the event $\{X+Y=0\}$.
$$1_{\{X+Y=0\}}=\begin{cases}1, \qquad \text{if }X+Y=0; \\ 0, \qquad \text{otherwise.}\end{cases}$$
#### Ray Vickson
Homework Helper
Dearly Missed
1. Homework Statement
Let $X$ and $Y$ be independent Bernoulli RV's with parameter $p$. Find,
$$\mathbb{E}[X\vert 1_{\{X+Y=0\}}]$$ and $$\mathbb{E}[Y\vert 1_{\{X+Y=0\}}]$$
2. Homework Equations
3. The Attempt at a Solution
I'm trying to show that,
$$\mathbb{E}[X+Y\vert 1_{\{X+Y=0\}}] = 0$$
by,
\begin{align*} \mathbb{E}[X+Y\vert 1_{\{X+Y=0\}}] &= \frac{\mathbb{E}[(X+Y)1_{\{X+Y=0\}}]}{\mathbb{P}[X+Y=0]} \\ &= \frac{0}{(1-p)^2} \\ &= 0 \end{align*}
Basically, you are trying to show that the conditional distribution $f(k) \equiv P(X= k|X+Y=0), \; k=0,1,2, \ldots$ has mean zero; that is, that $\sum_{k=0}^{\infty} k f(k) = 0$. How do you suppose that could happen?
#### IniquiTrance
Basically, you are trying to show that the conditional distribution $f(k) \equiv P(X= k|X+Y=0), \; k=0,1,2, \ldots$ has mean zero; that is, that $\sum_{k=0}^{\infty} k f(k) = 0$. How do you suppose that could happen?
I think it is possible since both $X$ and $Y$ are Bernoulli, if their sum is 0, then $\mathbb{P}[X=0|X+Y=0]=1$. Then, $\sum_{k=0}^1kf(k)=0*1$.
#### Ray Vickson
Homework Helper
Dearly Missed
I think it is possible since both $X$ and $Y$ are Bernoulli, if their sum is 0, then $\mathbb{P}[X=0|X+Y=0]=1$. Then, $\sum_{k=0}^1kf(k)=0*1$.
Rather than "thinking it is possible" you need to actually prove it. But, at least you are on the right track---that is, your thinking is OK, and just needs to be firmed up. It is not difficult once you see what needs to be established.
"Conditional expectation on an indicator"
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• Solo and co-op problem solving | 1,107 | 2,962 | {"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": 2, "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} | 3.671875 | 4 | CC-MAIN-2019-43 | longest | en | 0.697393 |
https://physics.stackexchange.com/questions/453538/torques-in-euler-equation | 1,571,079,165,000,000,000 | text/html | crawl-data/CC-MAIN-2019-43/segments/1570986654086.1/warc/CC-MAIN-20191014173924-20191014201424-00343.warc.gz | 652,214,427 | 31,303 | Torques in Euler equation
The Euler equation is given by $$\mathbf I\dot{\boldsymbol \omega}+\boldsymbol\omega\times \mathbf I\boldsymbol\omega= \mathbf M.$$ Also see here. It explains that The expressions for the torque in the rotating and inertial frames are related by $$\mathbf M_{inert} = \mathbf Q \mathbf M$$ where $$\mathbf Q$$ is the rotation tensor (not rotation matrix), an orthogonal tensor related to the angular velocity vector by $${\displaystyle {\boldsymbol {\omega }}\times {\boldsymbol {v}}={\dot {\mathbf {Q} }}\mathbf {Q} ^{-1}{\boldsymbol {v}}}.$$ Isn't $$\mathbf M$$ just the torque we compute outside then transferred to one inside the inclined frame, i.e. using the Euler angle get the orientation of the body and express the torque with basis with the body frame. Why is it so complex in wikipedia, or I misunderstood?
The Euler equation
from the angular momentum $$L=I_{in}\,\omega_{in}$$
$$\Rightarrow$$
$$\frac{d}{dt} \left(I_{in}\,\omega\right)=M_{in}$$
with: $$I_{in}=R\,I_b\,R^T$$ $$\Rightarrow$$
$$L=I_{in}\,\omega_{in}=R\,I_b\,R^T\,\omega_{in}=R\,I_b\,\omega_b$$
R is the rotation matrix between inertial system (index in) and body coordinate system, (index b) ) we obtain:
$$\frac{d}{dt} \left(R\,I_{b}\,\omega_b\right)=M_{in}$$
$$\Rightarrow$$
$$\frac{d}{dt} \left(R\,I_{b}\,\omega_b\right)=R\,I_b\,\dot{\omega}_b+\dot{R}\,I_b\,\omega_b=M_{in}\tag 1$$
with $$\dot{R}=R\,\tilde{\omega}_b$$ in equation (1)
$$R\,I_b\,\dot{\omega}_b+R\,\tilde{\omega}_b\,I_b\,\omega_b=M_{in}\tag 2$$
multiply equation (2) from the left with $$R^T$$ we obtain (with $$R^T\,R=E$$ unity matrix):
$$I_b\,\dot{\omega}_b+\tilde{\omega}_b\,I_b\,\omega_b=R^T\,M_{in}\tag 3$$
with $$R^T\,M_{in}=M_{b}$$ and $$\tilde{\omega}\,u=\omega\times\,u$$ we get the EULER equations
$$\boxed{I_b\,\dot{\omega}_b+{\omega}_b\,\times \,(I_b\,\omega_b)=M_{b}}$$
or:
$$\boxed{I_{in}\,\dot{\omega}_{in}+{\omega}_{in}\,\times \,(I_{in}\,\omega_b)=M_{in}}$$
$$I_{in}=R\,I_b\,R^T$$ | 715 | 1,988 | {"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": 24, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.03125 | 4 | CC-MAIN-2019-43 | latest | en | 0.569902 |
https://math.stackexchange.com/questions/2748966/proving-that-l-xwwr-mid-x-w-in-0-1-is-not-regular | 1,558,877,698,000,000,000 | text/html | crawl-data/CC-MAIN-2019-22/segments/1558232259177.93/warc/CC-MAIN-20190526125236-20190526151236-00520.warc.gz | 550,904,156 | 31,031 | # Proving that $L=\{xww^r\mid x,w \in \{0,1\}^+\}$ is not regular
In the alphabet $\Sigma=\{0,1\}$, I need to prove that this language is not regular. I've tried using the pumping lemma, choosing the string $a(ab)^p(ba)^p$ for a given $p$, any possible choose of a decomposition $xyz$ of the string such that $|xy|<p$ is such that $xy$ is of the form $a(ab)^l$ or $a(ab)^la$. But there are so many possible forms for $y$ that I'm stuck here.
I know there are some similar questions like this, but they use some strange logic that if you can't apply some trick related to "extending" x then the lenguage is not regular, this trick works with languages like $\{wxw^r\mid w,x \in \{0,1\}^+\}$ but only because it's the same language with strings that start and end in the same character. | 232 | 786 | {"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} | 2.859375 | 3 | CC-MAIN-2019-22 | longest | en | 0.907437 |
https://us.metamath.org/ileuni/rmoeqd.html | 1,721,601,389,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763517796.21/warc/CC-MAIN-20240721213034-20240722003034-00860.warc.gz | 520,090,991 | 3,669 | Intuitionistic Logic Explorer < Previous Next > Nearby theorems Mirrors > Home > ILE Home > Th. List > rmoeqd GIF version
Theorem rmoeqd 2640
Description: Equality deduction for restricted at-most-one quantifier. (Contributed by Alexander van der Vekens, 17-Jun-2017.)
Hypothesis
Ref Expression
raleqd.1 (𝐴 = 𝐵 → (𝜑𝜓))
Assertion
Ref Expression
rmoeqd (𝐴 = 𝐵 → (∃*𝑥𝐴 𝜑 ↔ ∃*𝑥𝐵 𝜓))
Distinct variable groups: 𝑥,𝐴 𝑥,𝐵
Allowed substitution hints: 𝜑(𝑥) 𝜓(𝑥)
Proof of Theorem rmoeqd
StepHypRef Expression
1 rmoeq1 2632 . 2 (𝐴 = 𝐵 → (∃*𝑥𝐴 𝜑 ↔ ∃*𝑥𝐵 𝜑))
2 raleqd.1 . . 3 (𝐴 = 𝐵 → (𝜑𝜓))
32rmobidv 2622 . 2 (𝐴 = 𝐵 → (∃*𝑥𝐵 𝜑 ↔ ∃*𝑥𝐵 𝜓))
41, 3bitrd 187 1 (𝐴 = 𝐵 → (∃*𝑥𝐴 𝜑 ↔ ∃*𝑥𝐵 𝜓))
Colors of variables: wff set class Syntax hints: → wi 4 ↔ wb 104 = wceq 1332 ∃*wrmo 2420 This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 This theorem depends on definitions: df-bi 116 df-tru 1335 df-nf 1438 df-sb 1737 df-eu 2003 df-mo 2004 df-cleq 2133 df-clel 2136 df-nfc 2271 df-rmo 2425 This theorem is referenced by: (None)
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https://oeis.org/A361511 | 1,716,970,464,000,000,000 | text/html | crawl-data/CC-MAIN-2024-22/segments/1715971059221.97/warc/CC-MAIN-20240529072748-20240529102748-00419.warc.gz | 368,822,786 | 4,799 | The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
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A361511 a(1) = 1. Thereafter if a(n-1) is a novel term, a(n) = d(a(n-1)); otherwise, if a(n-1) is the t-th non-novel term, a(n) = a(n-1) + d(a(t)), where d is the divisor function A000005. 8
1, 1, 2, 2, 3, 2, 4, 3, 5, 2, 4, 6, 4, 7, 2, 4, 6, 8, 4, 7, 11, 2, 5, 7, 9, 3, 6, 10, 4, 8, 11, 13, 2, 4, 6, 8, 10, 13, 15, 4, 8, 12, 6, 9, 13, 15, 17, 2, 4, 7, 11, 15, 19, 2, 4, 8, 11, 15, 21, 4, 8, 11, 13, 17, 19, 21, 24, 8, 10, 12, 16, 5, 7, 9, 12, 16, 18, 6, 10, 14, 4, 7, 11, 13, 15, 17, 19, 23 (list; graph; refs; listen; history; text; internal format)
OFFSET 1,3 COMMENTS Inspired by A360179, but uses a simpler rule for non-novel terms. It is an obvious conjecture that every number eventually appears, but is there a proof? LINKS Michael De Vlieger, Table of n, a(n) for n = 1..40000 Michael De Vlieger, Scatterplot of a(n), n = 1..2^16, showing records in red, smallest missing numbers in blue (small until they enter sequence, then large), terms deriving from novel predecessors in gold, otherwise green. Michael De Vlieger, Plot that shows the increasing subsequences that form the rows when the sequence is regarded as an irregular triangle EXAMPLE The initial terms (in the third column, N = novel term, D = non-novel term): .n.a(n).....t .1,..1,.N, .2,..1,.D,..1 .3,..2,.N, .4,..2,.D,..2 .5,..3,.N, .6,..2,.D,..3 .7,..4,.N, .8,..3,.D,..4 .9,..5,.N, 10,..2,.D,..5 11,..4,.D,..6 12,..6,.N, 13,..4,.D,..7 14,..7,.N, 15,..2,.D,..8 16,..4,.D,..9 17,..6,.D,.10 18,..8,.N, 19,..4,.D,.11 20,..7,.D,.12 21,.11,.N, 22,..2,.D,.13 ... If n=8, for example, a(8) = 3 is a non-novel term, the 4th such, so a(9) = a(8) + d(a(4)) = 3 + d(2) = 5. Comment from Michael De Vlieger, Apr 08 2023 (Start) Can be read as an irregular triangle of increasing subsequences: 1; 1, 2; 2, 3; 2, 4; 3, 5; 2, 4, 6; 4, 7; 2, 4, 6, 8; 4, 7, 11; 2, 5, 7, 9; 3, 6, 10; 4, 8, 11, 13; 2, 4, 6, 8, 10, 13, 15; 4, 8, 12; 6, 9, 13, 15, 17; 2, 4, 7, 11, 15, 19; etc. (End) The rows end with the novel terms - see A361512, A361513 - and their lengths are given by A361514. MATHEMATICA nn = 120; c[_] = False; f[n_] := DivisorSigma[0, n]; a[1] = m = 1; Do[(If[c[#], a[n] = # + f[a[m]] ; m++, a[n] = f[#] ]; c[#] = True) &[a[n - 1]], {n, 2, nn}]; Array[a, nn] (* Michael De Vlieger, Apr 08 2023 *) CROSSREFS Cf. A000005, A360179, A361512-A361516, A362095. Sequence in context: A246029 A245564 A360179 * A345147 A214126 A205378 Adjacent sequences: A361508 A361509 A361510 * A361512 A361513 A361514 KEYWORD nonn,tabf AUTHOR N. J. A. Sloane, Apr 08 2023 STATUS approved
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Last modified May 29 03:48 EDT 2024. Contains 372921 sequences. (Running on oeis4.) | 1,359 | 3,167 | {"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} | 3.453125 | 3 | CC-MAIN-2024-22 | latest | en | 0.867695 |
https://proxies-free.com/ordinary-differential-equations-intuitive-explanation-for-one-of-the-conditions-in-kolmogorovs-predator-prey-theorem/ | 1,611,562,492,000,000,000 | text/html | crawl-data/CC-MAIN-2021-04/segments/1610703565376.63/warc/CC-MAIN-20210125061144-20210125091144-00361.warc.gz | 525,191,797 | 8,055 | # ordinary differential equations – Intuitive explanation for one of the conditions in Kolmogorov’s Predator-Prey theorem
I’m reading Nowak’s “Evolutionary dynamics”. In page 67 he introduces Kolmogorov’s Prey-predator equation, in the form
$$dot{x}=xFleft(x,yright)$$
$$dot{y}=yGleft(x,yright)$$
where $$F$$ and $$G$$ are $$C^{1}$$ functions. The variable $$x$$ is interpreted as the amount of prey while $$y$$ represents the amount of predators. A theorem by Kolmogorov is then stated – That this system has a stable equilibrium or a limit cycle if 8 conditions for $$F$$ and $$G$$ are met. One of these conditions is
$$xfrac{partial F}{partial x}+yfrac{partial F}{partial y}<0$$
And Nowak’s interpretation of this condition is that “For any given ratio of the two species, the rate of increase of prey is a decreasing function of population size”.
Can someone explain why this is a valid interpretation of the condition? | 241 | 928 | {"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": 10, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.921875 | 3 | CC-MAIN-2021-04 | latest | en | 0.82009 |
https://physics.stackexchange.com/questions/186517/definition-of-1-calorie | 1,561,589,571,000,000,000 | text/html | crawl-data/CC-MAIN-2019-26/segments/1560628000575.75/warc/CC-MAIN-20190626214837-20190627000837-00460.warc.gz | 533,496,632 | 35,825 | # Definition of 1 calorie
Why has the definition of 1 calorie been taken to be the energy required to heat 1 gram of water from 14.5 to 15.5 degree centigrade at standard pressure? Is there any specific reason for taking the temperature from 14.5 to 15.5?
• There are several definitions of calorie. See wiki page. – Gonenc Mogol May 28 '15 at 18:30
• Are you asking why some specific range was chosen, or are you asking why the starting point of 14.5 was chosen for the specific range? – BowlOfRed May 28 '15 at 18:33
• Pretty sure he's asking why the starting point is 14.5 degrees centigrade. As far as I know, no reason. I've always learned that it was the energy required to warm 1 gram of water by $1^{\circ}C$. – CoilKid May 28 '15 at 18:50
• I suspect this belongs on hsm.stackexchange ... our sister site for "history of science and math". – Floris May 28 '15 at 19:25
• That's one nice thing about water though, the different states have their own names. In my experience, when someone says "water" it is assumed they are referring to liquid $H_2O$ unless otherwise stated. Anyway, you make some good points. +1! – CoilKid May 28 '15 at 21:43 | 324 | 1,155 | {"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} | 2.671875 | 3 | CC-MAIN-2019-26 | latest | en | 0.938906 |
https://brilliant.org/problems/calciferous-cosine/ | 1,516,411,334,000,000,000 | text/html | crawl-data/CC-MAIN-2018-05/segments/1516084888341.28/warc/CC-MAIN-20180120004001-20180120024001-00654.warc.gz | 660,055,768 | 17,154 | # Calciferous Cosine
Geometry Level 2
$\large \cos { \left( \frac { \pi }{ 4 } +x \right) } +\cos { \left( \frac { \pi }{ 4 } -x \right) } =a$
$\large \cos { \left( \frac { 3\pi }{ 4 } +x \right) } -\cos { \left( \frac { 3\pi }{ 4 } -x \right) } =b$
$${ a }^{ 2 }+{ b }^{ 2 }=\ ?$$
× | 138 | 288 | {"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} | 2.671875 | 3 | CC-MAIN-2018-05 | longest | en | 0.109133 |
https://metanumbers.com/19634 | 1,631,874,641,000,000,000 | text/html | crawl-data/CC-MAIN-2021-39/segments/1631780055632.65/warc/CC-MAIN-20210917090202-20210917120202-00440.warc.gz | 439,337,978 | 7,275 | # 19634 (number)
19,634 (nineteen thousand six hundred thirty-four) is an even five-digits composite number following 19633 and preceding 19635. In scientific notation, it is written as 1.9634 × 104. The sum of its digits is 23. It has a total of 2 prime factors and 4 positive divisors. There are 9,816 positive integers (up to 19634) that are relatively prime to 19634.
## Basic properties
• Is Prime? No
• Number parity Even
• Number length 5
• Sum of Digits 23
• Digital Root 5
## Name
Short name 19 thousand 634 nineteen thousand six hundred thirty-four
## Notation
Scientific notation 1.9634 × 104 19.634 × 103
## Prime Factorization of 19634
Prime Factorization 2 × 9817
Composite number
Distinct Factors Total Factors Radical ω(n) 2 Total number of distinct prime factors Ω(n) 2 Total number of prime factors rad(n) 19634 Product of the distinct prime numbers λ(n) 1 Returns the parity of Ω(n), such that λ(n) = (-1)Ω(n) μ(n) 1 Returns: 1, if n has an even number of prime factors (and is square free) −1, if n has an odd number of prime factors (and is square free) 0, if n has a squared prime factor Λ(n) 0 Returns log(p) if n is a power pk of any prime p (for any k >= 1), else returns 0
The prime factorization of 19,634 is 2 × 9817. Since it has a total of 2 prime factors, 19,634 is a composite number.
## Divisors of 19634
1, 2, 9817, 19634
4 divisors
Even divisors 2 2 2 0
Total Divisors Sum of Divisors Aliquot Sum τ(n) 4 Total number of the positive divisors of n σ(n) 29454 Sum of all the positive divisors of n s(n) 9820 Sum of the proper positive divisors of n A(n) 7363.5 Returns the sum of divisors (σ(n)) divided by the total number of divisors (τ(n)) G(n) 140.121 Returns the nth root of the product of n divisors H(n) 2.6664 Returns the total number of divisors (τ(n)) divided by the sum of the reciprocal of each divisors
The number 19,634 can be divided by 4 positive divisors (out of which 2 are even, and 2 are odd). The sum of these divisors (counting 19,634) is 29,454, the average is 736,3.5.
## Other Arithmetic Functions (n = 19634)
1 φ(n) n
Euler Totient Carmichael Lambda Prime Pi φ(n) 9816 Total number of positive integers not greater than n that are coprime to n λ(n) 9816 Smallest positive number such that aλ(n) ≡ 1 (mod n) for all a coprime to n π(n) ≈ 2229 Total number of primes less than or equal to n r2(n) 8 The number of ways n can be represented as the sum of 2 squares
There are 9,816 positive integers (less than 19,634) that are coprime with 19,634. And there are approximately 2,229 prime numbers less than or equal to 19,634.
## Divisibility of 19634
m n mod m 2 3 4 5 6 7 8 9 0 2 2 4 2 6 2 5
The number 19,634 is divisible by 2.
• Semiprime
• Deficient
• Polite
• Square Free
## Base conversion (19634)
Base System Value
2 Binary 100110010110010
3 Ternary 222221012
4 Quaternary 10302302
5 Quinary 1112014
6 Senary 230522
8 Octal 46262
10 Decimal 19634
12 Duodecimal b442
20 Vigesimal 291e
36 Base36 f5e
## Basic calculations (n = 19634)
### Multiplication
n×y
n×2 39268 58902 78536 98170
### Division
n÷y
n÷2 9817 6544.67 4908.5 3926.8
### Exponentiation
ny
n2 385493956 7568788332104 148605590112529936 2917722156269412763424
### Nth Root
y√n
2√n 140.121 26.9776 11.8373 7.22107
## 19634 as geometric shapes
### Circle
Diameter 39268 123364 1.21106e+09
### Sphere
Volume 3.17041e+13 4.84426e+09 123364
### Square
Length = n
Perimeter 78536 3.85494e+08 27766.7
### Cube
Length = n
Surface area 2.31296e+09 7.56879e+12 34007.1
### Equilateral Triangle
Length = n
Perimeter 58902 1.66924e+08 17003.5
### Triangular Pyramid
Length = n
Surface area 6.67695e+08 8.9199e+11 16031.1
## Cryptographic Hash Functions
md5 4b94f01be364f47c025eecf9b80d5bfe 1ae0b9256b1e349ce9306005617051f475a1f1e3 da5b3e00daa27f785530691f2afd786d62e32ac98276adcf9576fb4496045f5c 50f345750502053d7738fb6831ca7265de8bf8e5f018057990fbdeec40bdfe69962eb8d33bb5f09111dcaacdb2dc996e28a429f84f5dea88d212071f95ebbb04 caa0a556d2c6e29a8083d5b1d988087ba51529c8 | 1,429 | 4,040 | {"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} | 3.828125 | 4 | CC-MAIN-2021-39 | latest | en | 0.820929 |
https://www.nag.com/numeric/cl/nagdoc_cl26.0/html/f16/f16pgc.html | 1,627,599,073,000,000,000 | text/html | crawl-data/CC-MAIN-2021-31/segments/1627046153897.89/warc/CC-MAIN-20210729203133-20210729233133-00250.warc.gz | 941,440,322 | 5,034 | f16 Chapter Contents
f16 Chapter Introduction
NAG Library Manual
# NAG Library Function Documentnag_dtbmv (f16pgc)
## 1 Purpose
nag_dtbmv (f16pgc) performs matrix-vector multiplication for a real triangular band matrix.
## 2 Specification
#include #include
void nag_dtbmv (Nag_OrderType order, Nag_UploType uplo, Nag_TransType trans, Nag_DiagType diag, Integer n, Integer k, double alpha, const double ab[], Integer pdab, double x[], Integer incx, NagError *fail)
## 3 Description
nag_dtbmv (f16pgc) performs one of the matrix-vector operations
$x←αAx or x←αATx,$
where $A$ is an $n$ by $n$ real triangular band matrix with $k$ subdiagonals or superdiagonals, $x$ is an $n$-element real vector and $\alpha$ is a real scalar.
## 4 References
Basic Linear Algebra Subprograms Technical (BLAST) Forum (2001) Basic Linear Algebra Subprograms Technical (BLAST) Forum Standard University of Tennessee, Knoxville, Tennessee http://www.netlib.org/blas/blast-forum/blas-report.pdf
## 5 Arguments
1: $\mathbf{order}$Nag_OrderTypeInput
On entry: the order argument specifies the two-dimensional storage scheme being used, i.e., row-major ordering or column-major ordering. C language defined storage is specified by ${\mathbf{order}}=\mathrm{Nag_RowMajor}$. See Section 2.3.1.3 in How to Use the NAG Library and its Documentation for a more detailed explanation of the use of this argument.
Constraint: ${\mathbf{order}}=\mathrm{Nag_RowMajor}$ or $\mathrm{Nag_ColMajor}$.
2: $\mathbf{uplo}$Nag_UploTypeInput
On entry: specifies whether $A$ is upper or lower triangular.
${\mathbf{uplo}}=\mathrm{Nag_Upper}$
$A$ is upper triangular.
${\mathbf{uplo}}=\mathrm{Nag_Lower}$
$A$ is lower triangular.
Constraint: ${\mathbf{uplo}}=\mathrm{Nag_Upper}$ or $\mathrm{Nag_Lower}$.
3: $\mathbf{trans}$Nag_TransTypeInput
On entry: specifies the operation to be performed.
${\mathbf{trans}}=\mathrm{Nag_NoTrans}$
$x←\alpha Ax$.
${\mathbf{trans}}=\mathrm{Nag_Trans}$ or $\mathrm{Nag_ConjTrans}$
$x←\alpha {A}^{\mathrm{T}}x$.
Constraint: ${\mathbf{trans}}=\mathrm{Nag_NoTrans}$, $\mathrm{Nag_Trans}$ or $\mathrm{Nag_ConjTrans}$.
4: $\mathbf{diag}$Nag_DiagTypeInput
On entry: specifies whether $A$ has nonunit or unit diagonal elements.
${\mathbf{diag}}=\mathrm{Nag_NonUnitDiag}$
The diagonal elements are stored explicitly.
${\mathbf{diag}}=\mathrm{Nag_UnitDiag}$
The diagonal elements are assumed to be $1$ and are not referenced.
Constraint: ${\mathbf{diag}}=\mathrm{Nag_NonUnitDiag}$ or $\mathrm{Nag_UnitDiag}$.
5: $\mathbf{n}$IntegerInput
On entry: $n$, the order of the matrix $A$.
Constraint: ${\mathbf{n}}\ge 0$.
6: $\mathbf{k}$IntegerInput
On entry: $k$, the number of subdiagonals or superdiagonals of the matrix $A$.
Constraint: ${\mathbf{k}}\ge 0$.
7: $\mathbf{alpha}$doubleInput
On entry: the scalar $\alpha$.
8: $\mathbf{ab}\left[\mathit{dim}\right]$const doubleInput
Note: the dimension, dim, of the array ab must be at least $\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{pdab}}×{\mathbf{n}}\right)$.
On entry: the $n$ by $n$ triangular band matrix $A$.
This is stored as a notional two-dimensional array with row elements or column elements stored contiguously. The storage of elements of ${A}_{ij}$, depends on the order and uplo arguments as follows:
• if ${\mathbf{order}}=\mathrm{Nag_ColMajor}$ and ${\mathbf{uplo}}=\mathrm{Nag_Upper}$,
${A}_{ij}$ is stored in ${\mathbf{ab}}\left[k+i-j+\left(j-1\right)×{\mathbf{pdab}}\right]$, for $j=1,\dots ,n$ and $i=\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,j-k\right),\dots ,j$;
• if ${\mathbf{order}}=\mathrm{Nag_ColMajor}$ and ${\mathbf{uplo}}=\mathrm{Nag_Lower}$,
${A}_{ij}$ is stored in ${\mathbf{ab}}\left[i-j+\left(j-1\right)×{\mathbf{pdab}}\right]$, for $j=1,\dots ,n$ and $i=j,\dots ,\mathrm{min}\phantom{\rule{0.125em}{0ex}}\left(n,j+k\right)$;
• if ${\mathbf{order}}=\mathrm{Nag_RowMajor}$ and ${\mathbf{uplo}}=\mathrm{Nag_Upper}$,
${A}_{ij}$ is stored in ${\mathbf{ab}}\left[j-i+\left(i-1\right)×{\mathbf{pdab}}\right]$, for $i=1,\dots ,n$ and $j=i,\dots ,\mathrm{min}\phantom{\rule{0.125em}{0ex}}\left(n,i+k\right)$;
• if ${\mathbf{order}}=\mathrm{Nag_RowMajor}$ and ${\mathbf{uplo}}=\mathrm{Nag_Lower}$,
${A}_{ij}$ is stored in ${\mathbf{ab}}\left[k+j-i+\left(i-1\right)×{\mathbf{pdab}}\right]$, for $i=1,\dots ,n$ and $j=\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,i-k\right),\dots ,i$.
If ${\mathbf{diag}}=\mathrm{Nag_UnitDiag}$, the diagonal elements of $\mathrm{AB}$ are assumed to be $1$, and are not referenced.
9: $\mathbf{pdab}$IntegerInput
On entry: the stride separating row or column elements (depending on the value of order) of the matrix $A$ in the array ab.
Constraint: ${\mathbf{pdab}}\ge {\mathbf{k}}+1$.
10: $\mathbf{x}\left[\mathit{dim}\right]$doubleInput/Output
Note: the dimension, dim, of the array x must be at least $\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,1+\left({\mathbf{n}}-1\right)\left|{\mathbf{incx}}\right|\right)$.
On entry: the right-hand side vector $b$.
On exit: the solution vector $x$.
11: $\mathbf{incx}$IntegerInput
On entry: the increment in the subscripts of x between successive elements of $x$.
Constraint: ${\mathbf{incx}}\ne 0$.
12: $\mathbf{fail}$NagError *Input/Output
The NAG error argument (see Section 2.7 in How to Use the NAG Library and its Documentation).
## 6 Error Indicators and Warnings
NE_ALLOC_FAIL
Dynamic memory allocation failed.
See Section 2.3.1.2 in How to Use the NAG Library and its Documentation for further information.
On entry, argument $〈\mathit{\text{value}}〉$ had an illegal value.
NE_INT
On entry, ${\mathbf{incx}}=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{incx}}\ne 0$.
On entry, ${\mathbf{k}}=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{k}}\ge 0$.
On entry, ${\mathbf{n}}=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{n}}\ge 0$.
NE_INT_2
On entry, ${\mathbf{pdab}}=〈\mathit{\text{value}}〉$, ${\mathbf{k}}=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{pdab}}\ge {\mathbf{k}}+1$.
NE_INTERNAL_ERROR
See Section 2.7.6 in How to Use the NAG Library and its Documentation for further information.
NE_NO_LICENCE
Your licence key may have expired or may not have been installed correctly.
See Section 2.7.5 in How to Use the NAG Library and its Documentation for further information.
## 7 Accuracy
The BLAS standard requires accurate implementations which avoid unnecessary over/underflow (see Section 2.7 of Basic Linear Algebra Subprograms Technical (BLAST) Forum (2001)).
## 8 Parallelism and Performance
nag_dtbmv (f16pgc) is not threaded in any implementation.
None.
## 10 Example
This example computes the matrix-vector product
$y=αAx$
where
$A = 1.0 0.0 0.0 0.0 2.0 2.0 0.0 0.0 0.0 3.0 3.0 0.0 0.0 0.0 4.0 4.0 ,$
$x = -1.0 2.0 -3.0 4.0$
and
$α=1.5 .$
### 10.1 Program Text
Program Text (f16pgce.c)
### 10.2 Program Data
Program Data (f16pgce.d)
### 10.3 Program Results
Program Results (f16pgce.r) | 2,456 | 6,941 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 104, "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-2021-31 | latest | en | 0.40629 |
https://www.physicsforums.com/threads/maximum-partial-sum-of-sequance-of-random-variables.418809/ | 1,544,607,233,000,000,000 | text/html | crawl-data/CC-MAIN-2018-51/segments/1544376823817.62/warc/CC-MAIN-20181212091014-20181212112514-00257.warc.gz | 1,005,700,793 | 13,778 | # Maximum partial sum of sequance of random variables
1. Jul 27, 2010
### shoomchool
Hi friends/colleagues,
Let X1, X2, ..., Xn be a sequence of independent, but NOT identically distributed random variables, with E(Xi)=0, and variance of each Xi being UNEQUAL but finite.
Let S be the vector of partial sum of Xs: Si=X1+X2+...+Xi.
Question: What is the limiting distribution of Maxi(Si), the maximum partial sum of X? By limiting distribution I mean as n grows to infinity.
I can also formulate this question slightly differently: is the limiting distribution of
partial sum of X a Brownian movement process? In that case the maximum partial sum is maximum distance of Brownian motions from its origin which has a closed formula.
If this question does not have answer with this assumptions, I need to know what additional assumptions I need to make.
Just in case, one more condition in this problem is that the variance function of X is a 'smooth' function in that If if Xi -> Xj then Var(Xi)->Var(Xj). | 242 | 1,011 | {"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} | 2.875 | 3 | CC-MAIN-2018-51 | latest | en | 0.932356 |
http://gamedev.stackexchange.com/questions/16235/how-can-i-make-water-appear-darker-with-depth-like-in-minecraft/16237 | 1,467,386,214,000,000,000 | text/html | crawl-data/CC-MAIN-2016-26/segments/1466783403502.46/warc/CC-MAIN-20160624155003-00150-ip-10-164-35-72.ec2.internal.warc.gz | 122,772,929 | 22,315 | # How can I make water appear darker with depth, like in Minecraft?
In Minecraft when you look at water the deeper you view the darker it gets. Does anyone know how to code something like that?
Minecraft with effect
similar game without effect
-
Isn't this done automagically since the material of the water cube is semi-transparent? – pek Aug 20 '11 at 22:01
I don't think so. I added a picture without the effect for comparison. – Xavier Aug 20 '11 at 22:05
Maybe it's an additive blend effect applied only on the water cubes? Again, this should be easy since the material is semi-transparent. – pek Aug 20 '11 at 22:11
you can also change the color of boxes according to the depth. – Ali.S Aug 20 '11 at 22:29
There are essentially two different approaches for lighting water based on depth:
# Voxel-Lighting
Minecraft uses voxel-based lighting, wich works by propagating light to adjacent cubes, lowering the brightness depending on the block type. Dark oceans are a side effect of this system.
Water blocks sunlight and reduces the light by 3 levels per block (instead of the default 1 level), wich means the brightness in an ocean for each distance from the surface is:
0 (surface): 15 (direct sunlight)
1: 12
2: 9
3: 6
4: 3
5 and below: 0 (darkness)
Source: Minecraft Wiki - Light
In games with a traditional lighting model, this effect can be created by measuring the amount of water that is between the light source and the ocean floor. The light is then faded based on this distance. There are a few methods for doing this:
## Direct Calculation
If you have a flat surface, you can easily calculate the distance the light travels in the water if you pass the surface normal away from body of water and the dot product of this normal and a surface position into the geometry shader.
The effective water distance is
where is the position of the vertex and is the angle between the light direction beneath the surface and the water's surface normal towards the body of water.
At sunset, only reaches a bit less than 50° because the light is refracted when entering the water.
Here's a blog post with a good explanation: The Digital Camera: Total Internal Reflection
Another post with more details: The Digital Camera: Snell’s Law of Refraction
If you're using a heightmap on a surface parallel to the water, becomes . The right factor equals 1 if the sun is directly above the water surface.
With a point light, you have to calculate for each vertex based on the relative position to the light source.
With a fixed water level or a fixed light direction, parts of the equation are constant and shouldn't be calculated in the shader for performance reasons.
### Pros:
• Fast and accurate
### Cons:
• Only works for flat water surfaces or only for light from directly above, as only one surface is normally taken into account. (The combination of a rough surface and tilted light could work to some extend with parallax mapping.)
• No caustics
If you render the water surface to a separate depth map (as seen from the light source), you can use that depth texture to calculate the distance the light travels in the water before hitting the surface.
To do this, you project each vertex into the light source's view projection in the vertex shader and do the texture lookup in the pixel shader.
If the surface is relatively flat, you should use a refracted light origin for better results.
### Pros:
• Works with relatively complex water geometry, as long as it doesn't occlude itself.*
• Can be reused for almost any kind of partially transparent volume.
### Cons:
• Slower than the direct calculation.
• Needs additional VRAM for the depth map.
• Not 100% accurate.
*You can determine the amount of water in front of the nearest solid surface by counting the depth from the light's POV as follows:
1. Render the solid geometry in your scene as normal. For each fragment, you add the depth value to the result texture.
2. Render the water's front-faces without updating the depth buffer and subtract the fragments' depths from the result.
3. Render the back-faces in the same way, but add the fragment depth to the result.
The result texture now contains the amount of water in front of the light in light-view-space, so the value must be transformed back before you use it. This method works to calculate the directional light (minus refraction), but will lead to incorrect ambient light if the surfaces are very irregular and there's a large amount of air between to bodies of water affecting the same fragments.
The pros and cons are the same as for normal shadow mapping, except that you need one more buffer while calculating depth and the performance is worse because you have to draw more geometry.
## Ray-Tracing
Ray tracing is by far the most accurate but also the most expensive solution for rendering transparent volumes. There are two ways of doing this: 1. Tracing from the ocean floor towards the surface and 2. Tracing from the light source towards the water. Multiple rays are needed for each point on the floor to calculate the brightness.
### Pros:
• Works correctly with every geometry.
• Correct caustics!
### Cons:
• Slow!
There are a few more things to take into account when rendering water:
## Fog
Light in water is scattered again while travelling to the observer, so you should blend it towards a solid color.
If the observer is submerged, you can just render fog based on the final result of the depth buffer. The fog color, but not its density should change with the observer's distance from the surface! (Minecraft only uses this part of the effect.)
If the observer looks at the water from above, you need to calculate the fog based on the depth difference between the surface and the geometry under water. The fog colour should get slightly darker with larger depth differences, but should only change to the point where the fog is fully opaque.
The fog colour should also depend on the view direction for each pixel, so it's slightly darker when looking down in both cases.
## Faking Caustics
If you use a seamless tiling 3D-Texture instead of a decal for fake caustics, you can avoid stretching on vertical surfaces. The strength of scattered light near the surface varies in three dimensions, so using a 2D-Texture usually produces stretching somewhere in the scene. You can model changing light angles by projecting the vertex positions of the floor into a different coordinate system.
Another possibility is to calculate the light density based on the surface position in the light's coordinate system, although that would most likely cost some performance.
The caustics should fade faster than the diffuse light with increasing depth.
Colours are scattered differently, so the light colour should change with increasing depth. This also prevents abrupt edges where, for example, a beach intersects the water surface.
## Angle of Incidence
Because of refraction, the light hits the ocean floor much steeper than it normally would. The Wikipedia article about Snell's law has formulae for angles and vectors.
-
I believe that the sky lighting effect in Minecraft is straight down - things get shaded by what is above them no matter where the sun is. Then local lighting from torches, etc. is applied with a dropoff effect - the farther away from the light source, the less light a cube gets.
If done this way, each layer of water would cumulatively shadow the layer below it, so each becomes progressively darker. Tree foliage provides shade like this, however it is not cumulative. You get the same shade under a tree whether it's 1 or 100 foliage cubes.
One clue that this is the method being used is that water doesn't get darker when farther away from the viewer - only as you go down. Yes, the fog effect does kick in at distance, but not the water dark effect.
So the basic formula for calculating lighting would be something like this in pseudo-code...
light_on_cube = 1.0
for each cube above target cube, from lowest to highest {
if cube being examined is tree foliage
light_on_cube = 0.5
else if cube being examined is water
light_on_cube = light_on_cube - 0.1
else if cube being examined is solid
light_on_cube = 0
}
This isn't perfect for calculating lighting under overhangs or in caves, as it would be pitch dark under an overhang using this method. But one could add in both local light sources (torches, fires, etc.) as well as treating sun lit blocks as light sources. Something like this might do it...
1. Calculate light from sun from directly above (via above pseudo-code) for each cube.
2. If a cube has a light source next to it, consider it fully lit (1.0)
3. If a cube is receiving no sun from directly above, give it some light based on how far away it is from a fully lit cube. Closer means more light, farther away means less (until zero).
The idea here is that if a cube is lit by the sun or a torch, the cube next to it is going to also be lit in some way. And the farther away you are from that lit cube, the less light there will be. It's sort of a kludge way to estimate diffuse lighting but I think (?) it would work.
-
Yeah, I'm pretty sure that's the ticket. I've done something similar in my game. – Byte56 Aug 21 '11 at 0:44
By the way I just added your blog to my google reader list Byte56 - developer blogs FTW! – Tim Holt Aug 21 '11 at 0:52
Oh, why thank you. Still off topic of this question, but I just read your blog about Professor Bailey's class. I was in that class last year! I'm fairly sure you gave that presentation last year too. I thought your name was familiar. Small world :) – Byte56 Aug 21 '11 at 5:35
Perhaps I'm misunderstanding the question, but why can't you just change the colour of the blocks depending on their depth?
If you have the depth d (in blocks, starting at 0) then a reasonable equation for brightness would be:
L = (1-m) e-kd+ m
Code: L = (1.0 - m) * exp(-k * d) + m;
k controls how fast it gets darker (higher = faster). A reasonable value would be 0.5.
m is the minimum brightness you want.
L varies from 0 to 1.
If you don't know how to change the colour of the blocks in whatever graphics API you are using then please ask that as a separate question (stating what API you use, and whether or not you are using shaders).
-
I simply didn't think of doing that. Just out of curiosity where did you get that equation? – Xavier Aug 21 '11 at 0:02
@Xavier: I just made it up. The e^-kd bit is just an exponential decay, which is a standard function for things that gradually tend toward zero over some value (depth). The multiplication by (1-m) and addition of m are just to scale and offset the decay so that it ends up at a minimum of m but still starts at 1. en.wikipedia.org/wiki/Exponential_decay – Peter Alexander Aug 21 '11 at 0:19
Thing is, the blocks of a deeper hue will only be seen if the blocks have alpha colours; in which case there is no need to change the block colour, the alpha will create the effect automagically. – Jonathan Connell Aug 22 '11 at 7:42
@Jonathan: You don't render the water blocks, you render the blocks on the sea bed with the colour darkening and then just have a single alpha layer on the water surface. – Peter Alexander Aug 22 '11 at 9:37
@Peter Alexander Ok, I assumed that in these block type games, even the water was made of blocks. – Jonathan Connell Aug 22 '11 at 9:57 | 2,564 | 11,440 | {"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} | 2.984375 | 3 | CC-MAIN-2016-26 | latest | en | 0.931704 |
http://stackoverflow.com/questions/101268/hidden-features-of-python/116580 | 1,469,536,695,000,000,000 | text/html | crawl-data/CC-MAIN-2016-30/segments/1469257824853.47/warc/CC-MAIN-20160723071024-00277-ip-10-185-27-174.ec2.internal.warc.gz | 230,641,525 | 41,523 | Dismiss
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# Hidden features of Python [closed]
What are the lesser-known but useful features of the Python programming language?
• Try to limit answers to Python core.
• Give an example and short description of the feature, not just a link to documentation.
• Label the feature using a title as the first line.
-
## locked by Bill the LizardMar 9 '12 at 23:54
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## closed as not constructive by David, Cody Gray, casperOneFeb 20 '12 at 20:09
As it currently stands, this question is not a good fit for our Q&A format. We expect answers to be supported by facts, references, or expertise, but this question will likely solicit debate, arguments, polling, or extended discussion. If you feel that this question can be improved and possibly reopened, visit the help center for guidance.If this question can be reworded to fit the rules in the help center, please edit the question.
Negative round
The `round()` function rounds a float number to given precision in decimal digits, but precision can be negative:
``````>>> str(round(1234.5678, -2))
'1200.0'
>>> str(round(1234.5678, 2))
'1234.57'
``````
Note: `round()` always returns a float, `str()` used in the above example because floating point math is inexact, and under 2.x the second example can print as `1234.5700000000001`. Also see the `decimal` module.
-
So often I have to round a number to a multiple. Eg, round 17 to a multiple of 5 (15). But Python's round doesn't let me do that! IMO, it should be structured as `round(num, precision=1) - round "num" to the nearest multiple of "precision"` – Wallacoloo May 16 '10 at 6:56
@wallacoloo what's the matter with (17 / 5)*5 ? Isn't it short and expressive? – silviot Aug 26 '10 at 19:39
@silviot try that with (19 / 5)*5. 19 rounded to the nearest 5 should be 20, right? But that seems to return 15. Also, that's relying on the integer division rules of Python 2.x. It won't work the same in 3.x. The most concise, correct solution imo is: `roundNearest = lambda n, m: round(float(n)/m)*m` – Wallacoloo Dec 17 '10 at 1:21
What about `(n+2)/5*5`? – Mikel Jan 23 '11 at 23:16
Or in general, `roundNearest = lambda n, m: (n + (m/2)) / m * m`. It's twice as fast as using `round(float)` on my system. – Mikel Jan 23 '11 at 23:50
Multiplying by a boolean
One thing I'm constantly doing in web development is optionally printing HTML parameters. We've all seen code like this in other languages:
``````class='<% isSelected ? "selected" : "" %>'
``````
In Python, you can multiply by a boolean and it does exactly what you'd expect:
``````class='<% "selected" * isSelected %>'
``````
This is because multiplication coerces the boolean to an integer (0 for False, 1 for True), and in python multiplying a string by an int repeats the string N times.
-
+1, that's a nice one. OTOH, as it's just a bit arcane, it's easy to see why you might not want to do this, for readability reasons. – SingleNegationElimination Dec 30 '09 at 23:38
I would write `bool(isSelected)` both for reliability and readability. – Marian May 29 '10 at 11:46
you could also use something like: `('not-selected', 'selected')[isSelected]` if you need an option for False value too.. – redShadow Jul 19 '10 at 13:37
Proper conditional expressions were added to Python in 2.5. If you're using 2.5+ you probably shouldn't use these tricks for readability reasons. – Peter Graham Jun 30 '11 at 2:12
Python's advanced slicing operation has a barely known syntax element, the ellipsis:
``````>>> class C(object):
... def __getitem__(self, item):
... return item
...
>>> C()[1:2, ..., 3]
(slice(1, 2, None), Ellipsis, 3)
``````
Unfortunately it's barely useful as the ellipsis is only supported if tuples are involved.
-
see stackoverflow.com/questions/118370/… for more info – molasses Sep 23 '08 at 0:33
That one's really hidden. +1 – gorsky Dec 18 '09 at 9:34
Actually, the ellipsis is quite useful when dealing with multi-dimensional arrays from `numpy` module. – Denilson Sá Aug 20 '10 at 20:33
This is supposed to be more useful in Python 3, where the ellipsis will become a literal. (Try it, you can type `...` in a Python 3 interpreter and it will return `Eillipsis`) – asmeurer Dec 28 '10 at 5:21
# re can call functions!
The fact that you can call a function every time something matches a regular expression is very handy. Here I have a sample of replacing every "Hello" with "Hi," and "there" with "Fred", etc.
``````import re
def Main(haystack):
# List of from replacements, can be a regex
finds = ('Hello', 'there', 'Bob')
replaces = ('Hi,', 'Fred,', 'how are you?')
def ReplaceFunction(matchobj):
for found, rep in zip(matchobj.groups(), replaces):
if found != None:
return rep
# log error
return matchobj.group(0)
named_groups = [ '(%s)' % find for find in finds ]
ret = re.sub('|'.join(named_groups), ReplaceFunction, haystack)
print ret
if __name__ == '__main__':
str = 'Hello there Bob'
Main(str)
# Prints 'Hi, Fred, how are you?'
``````
-
This is insane. I had no idea this existed. awesome. thanks a lot. – Jeffrey Jose May 27 '10 at 19:13
Never seen this before, but a better example might be `re.sub('[aeiou]', lambda match: match.group().upper()*3, 'abcdefghijklmnopqrstuvwxyz')` – Don Spaulding Mar 25 '11 at 17:14
tuple unpacking in python 3
in python 3, you can use a syntax identical to optional arguments in function definition for tuple unpacking:
``````>>> first,second,*rest = (1,2,3,4,5,6,7,8)
>>> first
1
>>> second
2
>>> rest
[3, 4, 5, 6, 7, 8]
``````
but a feature less known and more powerful allows you to have an unknown number of elements in the middle of the list:
``````>>> first,*rest,last = (1,2,3,4,5,6,7,8)
>>> first
1
>>> rest
[2, 3, 4, 5, 6, 7]
>>> last
8
``````
-
Quite haskellish :) cool one :) – pielgrzym Mar 26 '11 at 11:27
i like it , bummer it doesn't work in 2.7.. – wim Jul 26 '11 at 3:59
Multi line strings
One approach is to use backslashes:
``````>>> sql = "select * from some_table \
where id > 10"
>>> print sql
select * from some_table where id > 10
``````
Another is to use the triple-quote:
``````>>> sql = """select * from some_table
where id > 10"""
>>> print sql
select * from some_table where id > 10
``````
Problem with those is that they are not indented (look poor in your code). If you try to indent, it'll just print the white-spaces you put.
A third solution, which I found about recently, is to divide your string into lines and surround with parentheses:
``````>>> sql = ("select * from some_table " # <-- no comma, whitespace at end
"where id > 10 "
"order by name")
>>> print sql
select * from some_table where id > 10 order by name
``````
note how there's no comma between lines (this is not a tuple), and you have to account for any trailing/leading white spaces that your string needs to have. All of these work with placeholders, by the way (such as `"my name is %s" % name`).
-
have been looking for this for a long time – locojay Jun 18 '11 at 23:09
That's a gooood thing when writing long stuff in code, while keeping a low line length! – Joël Oct 27 '11 at 15:45
This answer has been moved into the question itself, as requested by many people.
-
+1 for amazingness, time and dedication here. – sqram Jul 16 '10 at 22:16
Can this answer be accepted, or be moved into the question? It would be nice to have such index at the top. – Denilson Sá Sep 24 '10 at 2:02
• The underscore, it contains the most recent output value displayed by the interpreter (in an interactive session):
```>>> (a for a in xrange(10000))
<generator object at 0x81a8fcc>
>>> b = 'blah'
>>> _
<generator object at 0x81a8fcc>
```
• A convenient Web-browser controller:
```>>> import webbrowser
>>> webbrowser.open_new_tab('http://www.stackoverflow.com')```
• A built-in http server. To serve the files in the current directory:
`python -m SimpleHTTPServer 8000`
• AtExit
`>>> import atexit`
-
Why not just SimpleHTTPServer? – Andrew Szeto Jul 9 '09 at 20:17
worth noting that the `_` is available only in interactive mode. when running scripts from a file, `_` has no special meaning. – SingleNegationElimination Nov 17 '09 at 18:52
@TokenMacGuy: Actually, you can define `_` to be a variable in a file (just in case you do want to go for obfuscated Python). – asmeurer Dec 28 '10 at 5:24
note: you can also use __ for the second-last and ___ for the third last – wim Jul 19 '11 at 11:22
@asmeurer I frequently use `_` as a name for variables I do not care about (eg `for _, desired_value, _ in my_tuple_with_some_irrelevant_values`). Yes, ike a prologger :) – brandizzi Sep 28 '11 at 18:51
### pow() can also calculate (x ** y) % z efficiently.
There is a lesser known third argument of the built-in `pow()` function that allows you to calculate xy modulo z more efficiently than simply doing `(x ** y) % z`:
``````>>> x, y, z = 1234567890, 2345678901, 17
>>> pow(x, y, z) # almost instantaneous
6
``````
In comparison, `(x ** y) % z` didn't given a result in one minute on my machine for the same values.
-
I've always wondered what the use case is for this. I haven't encountered one, but then again I don't do scientific computing. – bukzor Jul 30 '10 at 18:04
@buzkor: it's pretty useful for cryptography, too – Agos Jul 30 '10 at 23:23
Remember, this is the built-in `pow()` function. This is not the `math.pow()` function, which accepts only 2 arguments. – Denilson Sá Aug 4 '10 at 18:59
I remember stating very adamantly that I could not code cryptography in pure Python without this feature. This was in 2003, and so the version of Python I was working with was 2.2 or 2.3. I wonder if I was making a fool of myself and `pow` had that third parameter then or not. – Omnifarious Aug 21 '10 at 9:19
The cool thing here is that you can override this behavior in your own objects using `__pow__`. You just have to define an optional third argument. And for more information on where this would be used, see en.wikipedia.org/wiki/Modular_exponentiation. – asmeurer Dec 28 '10 at 5:30
You can easily transpose an array with zip.
``````a = [(1,2), (3,4), (5,6)]
zip(*a)
# [(1, 3, 5), (2, 4, 6)]
``````
-
Basically, `zip(*a)` unzips `a`. So if `b = zip(a)`, then `a == zip(*b)`. – asmeurer Dec 28 '10 at 5:27
map(None, *a) can come in handy if your tuples are of differing lengths: map(None, *[(1,2), (3,4,5), (5,)]) => [(1, 3, 5), (2, 4, None), (None, 5, None)] – hbn Jan 23 '11 at 21:37
Just found this feature at docs.python.org/library/functions.html and was about to share it on here. Looks like ya beat me to the chase. – Adam Fraser May 27 '11 at 21:51
The way I remember how this works is that "zip* turns a list of pairs in to a pair of lists" (and vice versa) – Adam Jan 10 '12 at 22:45
### enumerate with different starting index
`enumerate` has partly been covered in this answer, but recently I've found an even more hidden feature of `enumerate` that I think deserves its own post instead of just a comment.
Since Python 2.6, you can specify a starting index to `enumerate` in its second argument:
``````>>> l = ["spam", "ham", "eggs"]
>>> list(enumerate(l))
>>> [(0, "spam"), (1, "ham"), (2, "eggs")]
>>> list(enumerate(l, 1))
>>> [(1, "spam"), (2, "ham"), (3, "eggs")]
``````
One place where I've found it utterly useful is when I am enumerating over entries of a symmetric matrix. Since the matrix is symmetric, I can save time by iterating over the upper triangle only, but in that case, I have to use `enumerate` with a different starting index in the inner `for` loop to keep track of the row and column indices properly:
``````for ri, row in enumerate(matrix):
for ci, column in enumerate(matrix[ri:], ri):
# ci now refers to the proper column index
``````
Strangely enough, this behaviour of `enumerate` is not documented in `help(enumerate)`, only in the online documentation.
-
`help(enumerate)` has this proper function signature in python2.x, but not in py3k. I guess, a bug needs to be filled. – SilentGhost Oct 19 '10 at 10:10
`help(enumerate)` is definitely wrong in Python 2.6.5. Maybe they have fixed it already in Python 2.7. – Tamás Oct 19 '10 at 10:35
`help(enumerate)` from Python 3.1.2 says class enumerate(object) | enumerate(iterable) -> iterator for index, value of iterable, but the trick from the answer works fine. – Cristian Ciupitu Oct 19 '10 at 18:49
It looks like this was added in Python 2.6 as it does not work in Python 2.5. – Tamás Sep 23 '11 at 9:35
You can use property to make your class interfaces more strict.
``````class C(object):
def __init__(self, foo, bar):
self.foo = foo # read-write property
self.bar = bar # simple attribute
def _set_foo(self, value):
self._foo = value
def _get_foo(self):
return self._foo
def _del_foo(self):
del self._foo
# any of fget, fset, fdel and doc are optional,
# so you can make a write-only and/or delete-only property.
foo = property(fget = _get_foo, fset = _set_foo,
fdel = _del_foo, doc = 'Hello, I am foo!')
class D(C):
def _get_foo(self):
return self._foo * 2
def _set_foo(self, value):
self._foo = value / 2
foo = property(fget = _get_foo, fset = _set_foo,
fdel = C.foo.fdel, doc = C.foo.__doc__)
``````
In Python 2.6 and 3.0:
``````class C(object):
def __init__(self, foo, bar):
self.foo = foo # read-write property
self.bar = bar # simple attribute
@property
def foo(self):
'''Hello, I am foo!'''
return self._foo
@foo.setter
def foo(self, value):
self._foo = value
@foo.deleter
def foo(self):
del self._foo
class D(C):
@C.foo.getter
def foo(self):
return self._foo * 2
@foo.setter
def foo(self, value):
self._foo = value / 2
``````
-
It would be nice if your pre-2.6 and your 2.6 and 3.0 examples would actually present the exact same thing: classname is different, there are comments in the pre-2.6 version, the 2.6 and 3.0 versions don't contain initialization code. – Confusion Jan 10 '10 at 12:04
Many people don't know about the "dir" function. It's a great way to figure out what an object can do from the interpreter. For example, if you want to see a list of all the string methods:
``````>>> dir("foo")
['__add__', '__class__', '__contains__', (snipped a bunch), 'title',
'translate', 'upper', 'zfill']
``````
And then if you want more information about a particular method you can call "help" on it.
``````>>> help("foo".upper)
Help on built-in function upper:
upper(...)
S.upper() -> string
Return a copy of the string S converted to uppercase.
``````
-
dir() is essential for development. For large modules I've enhanced it to add filtering. See pixelbeat.org/scripts/inpy – pixelbeat Oct 12 '08 at 22:46
You can also directly use help: help('foo') – yuriks Dec 26 '08 at 18:44
If you use IPython, you can append a question mark to get help on a variable/method. – akaihola Jan 10 '09 at 3:50
see: An alternative to Python's dir(). Easy to type; easy to read! For humans only: github.com/inky/see – compie Jul 22 '10 at 18:26
I call this python's man pages and can also be implemented to work when 'man' is called rather than 'help' – inspectorG4dget Sep 22 '10 at 4:53
set/frozenset
Probably an easily overlooked python builtin is "set/frozenset".
Useful when you have a list like this, [1,2,1,1,2,3,4] and only want the uniques like this [1,2,3,4].
Using set() that's exactly what you get:
``````>>> x = [1,2,1,1,2,3,4]
>>>
>>> set(x)
set([1, 2, 3, 4])
>>>
>>> for i in set(x):
... print i
...
1
2
3
4
``````
And of course to get the number of uniques in a list:
``````>>> len(set([1,2,1,1,2,3,4]))
4
``````
You can also find if a list is a subset of another list using set().issubset():
``````>>> set([1,2,3,4]).issubset([0,1,2,3,4,5])
True
``````
As of Python 2.7 and 3.0 you can use curly braces to create a set:
``````myset = {1,2,3,4}
``````
as well as set comprehensions:
``````{x for x in stuff}
``````
For more details: http://docs.python.org/library/stdtypes.html#set
-
Also useful in cases where a dictionary were used only to test if a value is there. – Jacek Konieczny Mar 20 '10 at 10:20
I use set about as much as tuple and list. – L̲̳o̲̳̳n̲̳̳g̲̳̳p̲̳o̲̳̳k̲̳̳e̲̳̳ May 13 '10 at 20:42
for subsets, i believe it is `issubset` not `isasubset`. either way, the subset operator `<=` is nicer anyway. – wim Jul 19 '11 at 11:31
you can do dict comprehension too in python 2.7 like this { x:x*2 for x in range(3) } It's probably sort of confusing if you don't know what you are doing imho – Hassek Jul 25 '11 at 1:56
Built-in base64, zlib, and rot13 codecs
Strings have `encode` and `decode` methods. Usually this is used for converting `str` to `unicode` and vice versa, e.g. with `u = s.encode('utf8')`. But there are some other handy builtin codecs. Compression and decompression with zlib (and bz2) is available without an explicit import:
``````>>> s = 'a' * 100
>>> s.encode('zlib')
'x\x9cKL\xa4=\x00\x00zG%\xe5'
``````
Similarly you can encode and decode base64:
``````>>> 'Hello world'.encode('base64')
'SGVsbG8gd29ybGQ=\n'
>>> 'SGVsbG8gd29ybGQ=\n'.decode('base64')
'Hello world'
``````
And, of course, you can rot13:
``````>>> 'Secret message'.encode('rot13')
'Frperg zrffntr'
``````
-
Sadly this will stop working in Python 3 – Marius Gedminas Jun 18 '09 at 18:51
Oh, will it stop working? That's too bad :/. I was just thinking how great this feature was. Then I saw your comment. – FeatureCreep Jan 1 '10 at 20:56
Awe, the base64 one was pretty useful in interactive sessions handling data from the web. – L̲̳o̲̳̳n̲̳̳g̲̳̳p̲̳o̲̳̳k̲̳̳e̲̳̳ May 13 '10 at 20:39
In my opionion it's some type of en/decoding, but on the other side there should "only one way to it" and I think, that these things are better put in its own module! – Joschua Jun 23 '10 at 14:42
An interpreter within the interpreter
The standard library's code module let's you include your own read-eval-print loop inside a program, or run a whole nested interpreter. E.g. (copied my example from here)
``````\$ python
Python 2.5.1 (r251:54863, Jan 17 2008, 19:35:17)
[GCC 4.0.1 (Apple Inc. build 5465)] on darwin
>>> shared_var = "Set in main console"
>>> import code
>>> ic = code.InteractiveConsole({ 'shared_var': shared_var })
>>> try:
... ic.interact("My custom console banner!")
... except SystemExit, e:
... print "Got SystemExit!"
...
My custom console banner!
>>> shared_var
'Set in main console'
>>> shared_var = "Set in sub-console"
>>> import sys
>>> sys.exit()
Got SystemExit!
>>> shared_var
'Set in main console'
``````
This is extremely useful for situations where you want to accept scripted input from the user, or query the state of the VM in real-time.
TurboGears uses this to great effect by having a WebConsole from which you can query the state of you live web app.
-
``````>>> from functools import partial
>>> bound_func = partial(range, 0, 10)
>>> bound_func()
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
>>> bound_func(2)
[0, 2, 4, 6, 8]
``````
not really a hidden feature but partial is extremely useful for having late evaluation of functions.
you can bind as many or as few parameters in the initial call to partial as you want, and call it with any remaining parameters later (in this example i've bound the begin/end args to range, but call it the second time with a step arg)
-
I wish curryfication add a decent operator in python though. – fulmicoton Mar 17 '09 at 1:13
While debugging complex data structures pprint module comes handy.
Quoting from the docs..
``````>>> import pprint
>>> stuff = sys.path[:]
>>> stuff.insert(0, stuff)
>>> pprint.pprint(stuff)
[<Recursion on list with id=869440>,
'',
'/usr/local/lib/python1.5',
'/usr/local/lib/python1.5/test',
'/usr/local/lib/python1.5/sunos5',
'/usr/local/lib/python1.5/sharedmodules',
'/usr/local/lib/python1.5/tkinter']
``````
-
pprint is also good for printing dictionaries in doctests, since it always sorts the output by keys – akaihola Jan 10 '09 at 4:06
Python has GOTO
...and it's implemented by external pure-Python module :)
``````from goto import goto, label
for i in range(1, 10):
for j in range(1, 20):
for k in range(1, 30):
print i, j, k
if k == 3:
goto .end # breaking out from a deeply nested loop
label .end
print "Finished"
``````
-
Maybe it is best that this feature remains hidden. – James McMahon Oct 16 '08 at 12:32
Well, the actual hidden feature here is mechanism used to implement GOTO. – Constantin Oct 16 '08 at 15:21
Surely, for breaking out of a nested loop you can just raise an exception, no? – shylent Nov 14 '09 at 14:02
@shylent: Exceptions should be exceptional. For that reason they are optimized for the case that they are not thrown. If you expect the condition to occur in the course of normal processing, you should use another method – SingleNegationElimination Nov 17 '09 at 18:57
@shylent, the correct way to break out of a nested loop is to put the loop into a function, and return from the function – Christian Oudard Dec 16 '09 at 17:41
dict's constructor accepts keyword arguments:
``````>>> dict(foo=1, bar=2)
{'foo': 1, 'bar': 2}
``````
-
So long as the keyword arguments are valid Python identifiers (names). You can't use: dict(1="one", two=2 ...) because the "1" is not a valid identifier even though it's a perfectly valid dictionary key. – Jim Dennis Jun 25 '10 at 22:45
It's perfect for copy-and-update: base = {'a': 4, 'b': 5}; updated = dict(base, c=5) – Tomek Paczkowski Jan 12 '12 at 9:20
Sequence multiplication and reflected operands
``````>>> 'xyz' * 3
'xyzxyzxyz'
>>> [1, 2] * 3
[1, 2, 1, 2, 1, 2]
>>> (1, 2) * 3
(1, 2, 1, 2, 1, 2)
``````
We get the same result with reflected (swapped) operands
``````>>> 3 * 'xyz'
'xyzxyzxyz'
``````
It works like this:
``````>>> s = 'xyz'
>>> num = 3
``````
To evaluate an expression s * num interpreter calls s.__mul__(num)
``````>>> s * num
'xyzxyzxyz'
>>> s.__mul__(num)
'xyzxyzxyz'
``````
To evaluate an expression num * s interpreter calls num.__mul__(s)
``````>>> num * s
'xyzxyzxyz'
>>> num.__mul__(s)
NotImplemented
``````
If the call returns NotImplemented then interpreter calls a reflected operation s.__rmul__(num) if operands have different types
``````>>> s.__rmul__(num)
'xyzxyzxyz'
``````
-
+1 I knew about sequence multiplication, but the reflected operands are new to me. – Björn Pollex Sep 12 '10 at 7:53
@Space, it would be unpythonic to have `x * y != y * x`, after all :) – badp Sep 12 '10 at 17:59
In python you may have x * y != y * x (it's just enough to play with the 'mul' methods). – Roberto Liffredo Sep 12 '10 at 22:14
Seeing many questions about problems with `x= [] * 20`, i am thinking if it would be better to make shallow copies of the operands by default – warvariuc Mar 4 '12 at 19:23
Interleaving `if` and `for` in list comprehensions
``````>>> [(x, y) for x in range(4) if x % 2 == 1 for y in range(4)]
[(1, 0), (1, 1), (1, 2), (1, 3), (3, 0), (3, 1), (3, 2), (3, 3)]
``````
I never realized this until I learned Haskell.
-
way cool. docs.python.org/tutorial/… – jimmyorr Feb 11 '09 at 23:17
Not so cool, you are just having a list comprehension with two for loops. What is so surprising about that? – Olivier Verdier Feb 13 '10 at 21:10
@Olivier: there's an if between the two for loops. – Torsten Marek Feb 16 '10 at 11:50
@Torsten: well, the list comprehension comprises already a for .. if, so what is so interesting? You can write: `[x for i in range(10) if i%2 for j in range(10) if j%2]`, nothing especially cool or interesting. The if in the middle of your example has nothing to do with the second for. – Olivier Verdier Feb 16 '10 at 17:34
I was wondering, is there a way to do this with an else? `[ a for (a, b) in zip(lista, listb) if a == b else: '-' ]` – Austin Richardson Jul 14 '10 at 21:59
Getter functions in module operator
The functions `attrgetter()` and `itemgetter()` in module `operator` can be used to generate fast access functions for use in sorting and search objects and dictionaries
Chapter 6.7 in the Python Library Docs
-
s/Capter/Chapter/ – J.F. Sebastian Oct 3 '08 at 2:15
Rite :) Fixed it. – Ber Oct 5 '08 at 15:34
This answer deserves good examples, for instance in conjunction with `map()` – Jonathan Aug 29 '11 at 7:04
Obviously, the antigravity module. xkcd #353
-
Probably my most used module. After the soul module, of course. – sli Dec 30 '08 at 9:43
Which actually works. Try putting "import antigravity" in the newest Py3K. – Andrew Szeto Jun 5 '09 at 9:11
@Andrew Szeto... what does it do? – Jiaaro Dec 2 '09 at 18:13
@Jim Robert: It opens up the webbrowser to the xkcd site ;) – poke Mar 28 '10 at 13:53
the skynet module is quite useful too… – Tshirtman Mar 3 '12 at 0:38
Tuple unpacking:
``````>>> (a, (b, c), d) = [(1, 2), (3, 4), (5, 6)]
>>> a
(1, 2)
>>> b
3
>>> c, d
(4, (5, 6))
``````
More obscurely, you can do this in function arguments (in Python 2.x; Python 3.x will not allow this anymore):
``````>>> def addpoints((x1, y1), (x2, y2)):
... return (x1+x2, y1+y2)
(8, 5)
``````
-
For what it's worth, tuple unpacking in function definitions is going aaway in python 3.0 – Ryan Sep 29 '08 at 1:18
why is it going away? – interstar Nov 23 '08 at 11:47
Mostly because it makes the implementation really nasty, as far as I understand. (Eg.in inspect.getargs in the standard library - the normal path (no tuple args) is about 10 lines, and there are about 30 extra lines for handling tuple args (which only gets used occasionally).) Makes me sad though. – babbageclunk Nov 25 '08 at 14:17
Looks like they are removing some of the batteries in 3.0 :/ . – FeatureCreep Jan 1 '10 at 20:59
@yangyang: that was added. The only thing that was removed is the tuple unpacking in function definitions. Instead, you just move such unpacking to the first line of the function implementation. – ncoghlan Feb 1 '11 at 7:07
The Python Interpreter
``````>>>
``````
Maybe not lesser known, but certainly one of my favorite features of Python.
-
The #1 reason Python is better than everything else. </fanboi> – sli Dec 30 '08 at 9:48
Everything else you've seen. </smuglispweenie> – Matt Curtis Jun 29 '09 at 13:23
And it also has iPython which is much better than the default interpreter – juanjux Aug 11 '09 at 9:51
I wish I could use iPython like SLIME in all of its glory – daffywolf Dec 21 '09 at 4:22
### Referencing a list comprehension as it is being built...
You can reference a list comprehension as it is being built by the symbol '_[1]'. For example, the following function unique-ifies a list of elements without changing their order by referencing its list comprehension.
``````def unique(my_list):
return [x for x in my_list if x not in locals()['_[1]']]
``````
-
Nifty trick. Do you know if this is accepted behavior or is it more of a dirty hack that may change in the future? The underscore makes me think the latter. – Kiv Jan 1 '09 at 15:47
Interesting. I think it'd be a dirty hack of the locals() dictionary, but I'd be curious to know for sure. – Rory Jan 27 '09 at 23:12
not a good idea for algorithmic as well as practical reasons. Algorithmically, this will give you a linear search of the list so far on every iteration, changing your O(n) loop into O(n**2); much better to just make the list into a set afterwards. Practically speaking, it's undocumented, may change, and probably doesn't work in ironpython/jython/pypy . – llimllib Jun 18 '09 at 4:04
This is an undocumented implementation detail, not a hidden feature. It would be a bad idea to rely on this. – Marius Gedminas Jun 18 '09 at 18:48
If you want to reference the list as you're building it, use an ordinary loop. This is very implementation dependent - CPython uses a hidden name in the locals dict because it is convenient, but other implementations are under no obligation to do the same thing. – ncoghlan Feb 1 '11 at 7:02
Python sort function sorts tuples correctly (i.e. using the familiar lexicographical order):
``````a = [(2, "b"), (1, "a"), (2, "a"), (3, "c")]
print sorted(a)
#[(1, 'a'), (2, 'a'), (2, 'b'), (3, 'c')]
``````
Useful if you want to sort a list of persons after age and then name.
-
This is a consequence of tuple comparison working correctly in general, i.e. (1, 2) < (1, 3). – Constantin Oct 5 '08 at 9:43
This is useful for version tuples: (1, 9) < (1, 10). – Roger Pate Jun 27 '09 at 23:00
The unpacking syntax has been upgraded in the recent version as can be seen in the example.
``````>>> a, *b = range(5)
>>> a, b
(0, [1, 2, 3, 4])
>>> *a, b = range(5)
>>> a, b
([0, 1, 2, 3], 4)
>>> a, *b, c = range(5)
>>> a, b, c
(0, [1, 2, 3], 4)
``````
-
never seen this before, it's pretty nice! – MatToufoutu Jul 25 '10 at 18:01
which version? as this doesn't work in 2.5.2 – Dan D. Aug 26 '10 at 15:14
works with 3.1, but not with 2.7 – Paweł Prażak Jan 2 '11 at 19:09
Nice - been hoping for that! Shame the destructuring went. – hbn Jan 23 '11 at 21:47
The simplicity of :
``````>>> 'str' in 'string'
True
>>> 'no' in 'yes'
False
>>>
``````
is something i love about Python, I have seen a lot of not very pythonic idiom like that instead :
``````if 'yes'.find("no") == -1:
pass
``````
-
I'm conflicted about this, because it's inconsistent with the `in` behavior on other kinds of sequences. `1 in [3, 2, 1]` is `True`, but `[2, 1] in [3, 2, 1]` is `False`, and it could really be a problem if it were `True`. But that's what would be needed to make it consistent with the string behavior explained here. So I think the `.find()` approach is actually more Pythonic, although of course `.find()` ought to have returned `None` instead of -1. – Kragen Javier Sitaker Jan 12 '12 at 4:21
Also note: 'str' not in 'abc' #true – Kosta Jan 12 '12 at 9:31 | 9,108 | 30,014 | {"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-2016-30 | latest | en | 0.909411 |
https://crypto.stackexchange.com/questions/646/is-this-layered-xor-cipher-secure | 1,718,585,512,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198861674.39/warc/CC-MAIN-20240616233956-20240617023956-00527.warc.gz | 160,893,847 | 42,346 | Is this "layered" XOR cipher secure?
I am aware of the vulnerabilities of simple xor ciphers and recently I came across a block cipher that claims to solve those vulnerabilities.
The cipher goes as follows with both the block and key sizes at 256-bits: the key is separated into chunks of length 1 bit. Every bit in the plaintext is xored with every key chunk.
For example assume that the first bit of the plaintext is 1. Say that the key is 10100101010010101…
The operation that takes place is:
1 xor 1 = 0
0 xor 0 = 0
0 xor 1 = 1
1 xor 0 = 1
1 xor 0 = 1
This continues until the end of the key and the result becomes the first bit of the ciphertext.
Is this really as secure as advertised?
If not why?
If I understand right, your operation effectively is $$\forall i: c_i = p_i \oplus k_0 \oplus k_1 \oplus k_2 \oplus \dots \oplus k_n,$$ whith $c_i$ the ciphertext bits, $p_i$ the plaintext bits, and $k_j$ the key bits.
As $\oplus$ (this is XOR) is associative, this is equivalent to
$$k^* := k_0 \oplus k_1 \oplus k_2 \oplus \dots \oplus k_n,$$ $$\forall i: c_i = p_i \oplus k^*.$$
Now $k^*$ is either 0 or 1 - in the first case this operation is the identity, in the second case it is simple negation. Neither of those can be considered an encryption, and you effectively have a key space of 2 (= 1 bit).
Whoever told you this either wanted to play a joke with you, or knows nothing of cryptography (or both). Or I misunderstood your presention of the algorithm.
• Take your message and flip a coin. If it is heads, output the message. If it is tails, output the message with each bit flipped. Sounds secure :) Commented Sep 7, 2011 at 18:15
• You will still have to somehow securely send the value of the coin flip to the receiver, else he won't be in a better position than the attacker. Commented Sep 7, 2011 at 18:24
Unless you are badly (and I mean truly badly) misrepresenting the idea, it is one of the worse ideas I've seen in crypto in quite some time.
The first bit is effectively exclusive or'ed with the parity of the key; the ciphertext bit will be either the plaintext bit (if the key has an even number of '1' bits) or the complement of the first plaintext bit (if the key has an odd number of '1' bits). Now, what happens to the second plaintext bit? If it does through this same operation, the second ciphertext bit will be set to either the plaintext bit or its complement (using the exact same logic is the first bit).
Extending this, we see that the entire first ciphertext block will be either the plaintext block or its complement, with no other possibilities.
A "block cipher" that does either an identity transform or a complementation is worse than weak. The only good side I can see is that your key is secure; other than its parity, the attacker can't deduce anything about it :-)
• The parity is also everything an attacker needs to know about the key, though. Commented Sep 7, 2011 at 17:45
• With respect to the key space this would indeed be the worst possible encryption method. Commented Sep 7, 2011 at 20:26
• Well, no, these is something worse than something that transforms the plaintext in two different ways depending on the key... Commented Sep 7, 2011 at 20:29
In an effort to guess what the poster is saying, I tried to develop a "secure-as-possible" (but not really secure at all) cipher using only minor modifications of the above:
$Key = {k_0, k_1 ... k_m}$
$Plaintext = {p_0, p_1 ... p_n}$
$Ciphertext = {c_0, c_1 ... c_n}$
$\forall i: i \le m \rightarrow c_i = p_i \oplus k_i$
The first $m$ bits of ciphertext are the first $m$ bits of key xored with the first $m$ bits of plaintext.
$\forall i: i > m \rightarrow c_i = p_i \oplus p_{i-1} \oplus p_{i-2} ... \oplus p_{i-m} \oplus k_{i \mod m}$
The next $n$ bits of the ciphertext are the current plaintext bit xored with the last $m$ plaintext bits and the current key bit $k_{i \mod m}$.
The idea here is that the typical attack against a OTP-like scheme that reuses the key is slightly harder here (but still remains trivially easy).
• Hmm, some kind of plaintext-feedback mode? ;-) Commented Sep 7, 2011 at 20:11
• @paulo Ebermann - Exactly. What I really want to do is use the key as a seed to a PRNG but no PRNG is available so instead I built a really lame LFSR with really lame tap positions. Something better could be built by running a LFSR on the key with good tap positions but then I'm just reinventing a bad linear-stream cipher. Commented Sep 7, 2011 at 20:22 | 1,216 | 4,502 | {"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": 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} | 3.15625 | 3 | CC-MAIN-2024-26 | latest | en | 0.909691 |
https://goprep.co/q11-let-a-ll-2-3-1-2-b-cc-4-6-2-4-then-compute-ab-hence-i-1nkzu8 | 1,620,329,566,000,000,000 | text/html | crawl-data/CC-MAIN-2021-21/segments/1620243988759.29/warc/CC-MAIN-20210506175146-20210506205146-00628.warc.gz | 298,997,060 | 24,133 | Q. 115.0( 1 Vote )
# Let<span lang="EN
Given Data:
Matrices,
System of Equations: 2x + y = 4, 3x + 2y = 1
Calculation:
The std. system of equation is A’X = C
Therefore X = (A’)–1C = (A–1)’C
Here and
Now find A–1
AB=2I
Multiplying both sides by A–1
A–1AB=2A–1
Using X = (A’)–1C = (A–1)’C
Therefore x = 7 and y =–10.
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State True or FalMathematics - Exemplar | 266 | 887 | {"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-2021-21 | latest | en | 0.841082 |
https://playtaptales.com/numbers/novemoctogintaquadringentillion/ | 1,670,121,139,000,000,000 | text/html | crawl-data/CC-MAIN-2022-49/segments/1669446710953.78/warc/CC-MAIN-20221204004054-20221204034054-00364.warc.gz | 481,599,223 | 4,267 | A Novemoctogintaquadringentillion (1 Novemoctogintaquadringentillion) is 10 to the power of 1470 (10^1470). This is a truly astronomical number!
## How many zeros in a Novemoctogintaquadringentillion?
There are 1,470 zeros in a Novemoctogintaquadringentillion.
A Novemoctogintaquadringentillionaire is someone whos assets, net worth or wealth is 1 or more Novemoctogintaquadringentillion. It is unlikely anyone will ever be a true Novemoctogintaquadringentillionaire. If you want to be a Novemoctogintaquadringentillionaire, play Tap Tales!
## Is Novemoctogintaquadringentillion the largest number?
Novemoctogintaquadringentillion is not the largest number. Infinity best describes the largest possible number - if there even is one! We cannot comprehend what the largest number actually is.
1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000
## Big Numbers
This is just one of many really big numbers! | 1,208 | 2,821 | {"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-2022-49 | latest | en | 0.681574 |
https://chemistry.stackexchange.com/questions/164558/what-is-the-paramagnetic-susceptibility-of-sodium-at-around-room-temperature | 1,701,911,549,000,000,000 | text/html | crawl-data/CC-MAIN-2023-50/segments/1700679100626.1/warc/CC-MAIN-20231206230347-20231207020347-00658.warc.gz | 198,586,163 | 41,209 | # What is the paramagnetic susceptibility of sodium at around room temperature?
## Proposed solution:
This question comes from Tanner's manual Introduction to the Physics of Electrons in Solids, at the chapter dedicated to the application of the Fermi gas model. The Fermi energy is $$\mathsf{E}_F$$. The model used here is the free electron model, and the susceptibility is $$\mathcal{\chi} = \frac{\bf \mathcal{M}}{\bf B}$$
Assuming that the density of states at the Fermi level $$D(\mathsf{E}_F)$$ is approximated to: $$D(\mathsf{E}_F) = \frac{3N}{2} \mathsf{E}_F$$ where $$N$$ is the total number of electronic states. It is demonstrated that: $$\mathcal{\chi}=\frac{3n\mu_B^2}{2\mathsf{E}_F}$$ where $$n$$ is the number of conduction electrons per unit volume given to be $$n=2.5 \times 10^{28}\,m^{-3}$$, $$\mu_B$$ is the Bohr magneton given to be $$\mu_B = 9.3 \times 10^{-24}\,J\cdot T^{-1}$$, the Fermi energy for $$\ce{Na}$$ is $$\mathsf{E}_F = 5.2 \times 10^{-19}\,J$$, and therefore the susceptibility is $$\mathcal{\chi}=6.2\times 10^1\, MKS$$, which can be converted in SI by multiplication of $$4\pi \times 10^{-7}$$, so the result is $$\mathcal{\chi} = 7.8\times 10^{-5} \, SI$$
## Now my question:
This result is absolutely not consistent with the literature that states $$\mathcal{\chi} = 1.3\times 10^{-5} \, SI$$
What is the problem with Tanner or (most certainly) with my calculus ?
• Bohr magneton value is not correct and formula for free-electron susceptibility should be multiplied by susceptibility of vacuum. Apr 19, 2022 at 11:57
• @10ppb - The susceptibility of a vacuum is zero, so what we're really talking about here is the relative susceptibility (I believe) - I'm not sure there needs to be a term by which this is multiplied. I also see a calculated value of 3.1 eV (McQuarrie, Statistical Mechanics) for sodium, which is slightly off from what the OP has given. I believe the error lies as you indicated with the value for the Bohr magneton; and the number density given/computed. Apr 19, 2022 at 19:37
• The formula given for chi is not a correct SI formula. It should be multiplied by mu_zero = 4*pi*10^-7 H/m, whatever you want to call it. Apr 20, 2022 at 2:21
• Many thanks @ToddMinehardt, I corrected the question according to your suggestions. There is still a factor of 4 between both results but this must be understandable from the model, ... and not from my calculation mistakes ... Apr 29, 2022 at 18:31 | 717 | 2,457 | {"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": 16, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.46875 | 3 | CC-MAIN-2023-50 | longest | en | 0.855102 |
https://converths.com/how-many-inches-is-150-mm-unit-calculator/ | 1,709,477,453,000,000,000 | text/html | crawl-data/CC-MAIN-2024-10/segments/1707947476396.49/warc/CC-MAIN-20240303142747-20240303172747-00743.warc.gz | 187,528,231 | 48,267 | Couldn’t put your finger on unit of conversion – like 150 mm to inches? How many inches is 150mm?
## 150 mm is equal to 5.905 inches.
Numerator to Convert 150 mm to inches
## 150 mm equals how many inches?
Different units are employed by us for the purpose of length measuring all around the world. Several systems of measurement are widely agreed and used.
To name a few members, there is the metric system, Imperial units (also known as British Imperial), and the Chinese system of weights and measures. Each and every system of unit and conversion is common in various countries and regions.
## What is 150 mm to inches?
But 150mm equals how many inches? According to the basic formula, one inch is equal to 25.4 millimeters, and 1/25.4 inches equal 1 millimeter (or the same as: 1 out of 25.4 inches in 1 millimeter), we can calculate 32 mm to inches. Also check the 2 videos as follows for more details. Anyhoo how much is 150mm in inches?
# Way No. 1:
. 1 inch = 25.4 millimeters
150 mm = 150 ÷ 1 in = 150 ÷ 25.4 mm = 5.905 inches
150 millimeters = 5.905 inches
(PS: in = inch(plural: inches), mm = millimeter (plural: millimeters))
# Way No. 2:
. 1 inch = 25.4 millimeters
. 1 millimeter = 1/25.4 inches
150 mm = 150 x 1 mm = 150 x 1/25.4 in = 5.905 inches
150 millimeters = 5.905 inches
# Way No. 3: (Based on No. 2)
. 1 inch = 25.4 millimeters
. 1 millimeter = 1/25.4 inches = 0.03937 inch
150 mm = 150 x 1 mm = 150 x 0.03937 in = 5.905 inches
150 millimeters = 5.905 inches
## Different ways to convert mm to inches – Video
Do you agree with different methods? Which conversion do you want to tackle next?
Leave your comment below, share with a friend and never stop wondering.❤️ | 508 | 1,714 | {"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} | 3.734375 | 4 | CC-MAIN-2024-10 | latest | en | 0.892528 |
https://brilliant.org/problems/three-magnetically-coupled-coils/ | 1,513,184,759,000,000,000 | text/html | crawl-data/CC-MAIN-2017-51/segments/1512948529738.38/warc/CC-MAIN-20171213162804-20171213182804-00365.warc.gz | 522,826,864 | 12,087 | # Three Magnetically Coupled Coils
The frame shown on the left is made of material with magnetic permeability $$\mu >> \mu_0$$. The magnetic field in each segment of the frame is uniform and parallel to that segment. Coil circle has $$2 N$$ turns, coil square has $$N$$ turns, and coil triangle has $$N / 2$$ turns, where $$N >> 1$$ is an even integer. The dimensions of each segment of the frame are listed in the table below, where $$L >> \sqrt{A}$$:
Segment Length Cross-sectional Area $$IM$$ $$4 L$$ $$A$$ $$JN$$ $$4 L$$ $$2 A$$ $$KO$$ $$4 L$$ $$A$$ $$IJ$$ $$2.5 L$$ $$A$$ $$JK$$ $$2.5 L$$ $$A$$ $$MN$$ $$2.5 L$$ $$A$$ $$NO$$ $$2.5 L$$ $$A$$
The coils are connected as shown on the right to form a single equivalent inductance. The equivalent inductance can be expressed as:
$$\frac{X}{Y}\frac{\mu N^2 A}{L}$$
where $$X$$ and $$Y$$ are coprime positive integers. Determine $$X + Y$$.
× | 275 | 896 | {"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} | 2.859375 | 3 | CC-MAIN-2017-51 | longest | en | 0.847037 |
https://www.w3schools.in/category/c-program/ | 1,627,963,281,000,000,000 | text/html | crawl-data/CC-MAIN-2021-31/segments/1627046154420.77/warc/CC-MAIN-20210803030201-20210803060201-00398.warc.gz | 1,089,911,023 | 14,825 | # C Programs
## C Program to Print String
This C program is used to print a string on the screen input by the user. scanf function is used to obtain input and printf function is used to print the string on the screen
## C Program to Add n Number of Times
This C program adds n number of times which will be entered by the user.
## C Program to Generate Random Numbers
This C program generates numbers randomly using random function.
## C Program to Check whether the Given Number is a Palindromic
If a number, which when read in both forward and backward way is same, then such a number is called a palindrome number.
## C Program to Check whether the Given Number is a Prime
A prime number is a natural number that has only one and itself as factors.
## C Program to Find the Greatest Among Ten Numbers
This C Program is used to find the greatest among ten numbers. Program: #include <stdio.h> int main() { int a[10]; int i; int greatest; printf("Enter ten values:"); //Store 10 numbers in an array for (i = 0; i < 10; […]
## C Program to Find the Greatest Number of Three Numbers
This C Program is used to find the greatest number of three numbers. Program: #include <stdio.h> int main(){ int a, b, c; printf("Enter a,b,c: "); scanf("%d %d %d", &a, &b, &c); if (a > b && a > c) { […]
## C Program to Asks the User For a Number Between 1 to 9
C program which asks the user for a number between 1 to 9 and shows the number. If the user inputs a number out of the specified range, the program should show an error and prompt the user for a valid input.
## C Program to Check Whether the Given Number is Even or Odd
even numbers are perfectly divisible by 2. In this example, if else statement is used to check whether a number entered by the user is even or odd.
## C Program to Swapping Two Numbers Using Bitwise Operators
This C program is used to swapping two numbers, using bitwise operators.
## C Program to Display The Multiplication Table of a Given Number
This C program is used to display the multiplication table of a given number. Program: #include <stdio.h> int main() { int num, i = 1; printf(" Enter any Number:"); scanf("%d", &num); printf("Multiplication table of %d: ", num); while (i <= […]
## C Program to Calculate Simple Interest by Given Principle, Rate of Interest and Time
Simple interest is calculated by, sinterest=principletimerate/100 formula.
## C Program to Find Factorial
This C program calculates the factorial value using recursion.
## C Leap Year Program
C program code for Leap Year, this C program is used to check whether the given year of input is a leap year or not.
## C Program to Generate the Fibonacci Series
In the Fibonacci series, a number of the series is obtained by adding the last two numbers of the series.
## C Program to Print Without Semicolon
This C program is used to print on the screen without using a semicolon. Semicolon must be used after printf function, but we can avoid this, by using printf function with if, while or switch statements. | 709 | 3,032 | {"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-2021-31 | longest | en | 0.786207 |
https://physics.stackexchange.com/questions/540090/why-only-need-to-change-external-legs-in-minimal-subtraction-renormalization | 1,713,966,595,000,000,000 | text/html | crawl-data/CC-MAIN-2024-18/segments/1712296819273.90/warc/CC-MAIN-20240424112049-20240424142049-00612.warc.gz | 417,512,420 | 42,562 | # Why only need to change external legs in minimal-subtraction renormalization?
For the Ch. 27 in book QFT by Srednicki, in the modified minimal-subtraction renormalization scheme($$\overline{MS}$$), the residue for pole at $$-m_{ph}^2$$ is $$R$$, instead of one.
1. However, I can not understand why we need only change the external leg as:
• add a $$R^{1/2}$$ coefficient
• replace the Lagrangian mass $$m$$ as $$m_{ph}$$
but we don't need to change the internal legs.
1. Also, renormalization scheme means to determine the coefficient for counterterms, or say, determine the coefficient for $$Z_i$$ in Largranian: $$L=-\frac{1}{2}Z_\phi(\partial \phi)^2-\frac{1}{2}Z_mm\phi^2+\frac{1}{4!}Z_g g \phi^4\\=-\frac{1}{2}(\partial \phi_0)^2-\frac{1}{2}m_0\phi_0^2+\frac{1}{4!} g_0 \phi_0^4$$ according to the answer in Is the effective Lagrangian the bare Lagrangian?, I know that renormalized $$m$$ is not the physical mass, but the pole of propagator is. But I am confused that: since it seems like $$m_0$$ is just pole according to the second line of equation above, does this mean bare mass $$m_0$$ is actually the physical mass(the mass what we detected)? I think so because Srednicki says "bare parameters" must be independent of $$\mu$$" in Ch.28. But other book, such as p.323 Peskin, says bare mass is not not the values measured in experiments.
First, let me address the quick questions you have:
It seems like $$m_0$$ is just pole according to the second line of equation above, does this mean bare mass $$m_0$$ is actually the physical mass? And does the "physical mass" here means the mass what we detected?
No, $$m_0$$ is not the pole and it is not the physical mass. You can't just read off the pole from what appears in the Lagrangian.
Yes, the "physical mass" is the mass we can detect. If the theory have one-particle states, then the "physical" mass $$m_{\text{ph}}$$ is defined from the invariant of the momentum of the one-particle states $$k^2=-m_{\text{ph}}^2$$.
Now, let's clarify what is the pole and what are the differences between the renormalization scheme.
The pole:
In Srednicki's notations, the full propagator, defined via $$\mathbf{\Delta}(x-y)=i\langle 0|T\phi(x)\phi(y)|0\rangle$$ is given by the Lehmann-Kallen form (Eqn. 13.17): $$\tilde{\mathbf{\Delta}}(k^2)=\frac{1}{k^2+m_{\text{ph}}^2-i\epsilon} +\int ds\rho(s)\frac{1}{k^2+s-i\epsilon}$$ Here the renormalized field $$\phi(x)$$ is assumed to satisfy Eqn. (13.2): $$\langle k|\phi(0)|0\rangle=1$$
Looking at the first term of the exact propagator, the important point here is that it has a pole at $$k^2=-m_{\text{ph}}^2$$. This is the pole we are interested in, which define the physical mass.
On the other hand, you know that the full propagator in our perturbation theory is given in terms of the self-energy $$i\Pi(k^2)$$ by: $$\tilde{\mathbf{\Delta}}(k^2)=\frac{1}{k^2+m^2-\Pi(k^2)-i\epsilon}$$ where the self-energy can be computed by summing over the 1PI 2-point graphs.
One-shell scheme:
In the on-shell scheme, we want the renormalized mass $$m$$ to be the physical mass. That can be done by setting $$m=m_{\text{ph}}$$ and impose the certain conditions on $$\Pi(k^2)$$ such that the full propagator has a pole at $$k^2=-m_{\text{ph}}^2$$. This condition determines $$Z_m$$.
The second condition, $$\langle k|\phi(0)|0\rangle=1$$ is satisfied by requiring that the residue of the full propagator at the pole is $$1$$.
Minimal-subtraction Scheme:
In the (modified) minimal-subtraction scheme, all we care about is removing the infinities. $$Z_\phi$$ and $$Z_m$$ are chosen "minimally" such that the self-energy is finite.
The renormalized mass $$m$$ is not the physical mass. The pole is at $$k^2=-m_{\text{ph}}^2$$, not $$k^2=-m^2$$
And since the field has not been normalized "properly", the residue at the pole is $$R=|\langle k|\phi(0)|0\rangle|^2\neq 1$$.
• Thank you so much for your wonderful answer! But I am confused that if bare mass, e.g. $m_0$, is not the physical mass (something we detect), why we still say bare parameters must be independent of $\mu$, as in Ch.28 by Srednicki? Mar 29, 2020 at 17:24
• @MerlinZhang The intuitive picture is like this: The bare mass is the (physical) mass when there were no interaction ($g\rightarrow 0$). In the presence of the interaction, the free particle becomes "dressed" particle with physical mass $m_{ph}$. The difference between $m_0$ and $m_{ph}$ depends on $g$. So $m_0$ is some parameter we started off with. It shouldn't depend on anything. Mar 29, 2020 at 18:07
Point 1.
In the renormalized propagator the pole mass $$m_{ph}$$ is physical and independent of any subtraction scheme used to set the finite parts of the counterterms. In the on-shell subtraction scheme the finite parts of the counterterms are chosen so that $$m_{ren} = m_{ph}$$. In minimal subtraction $$m_{ren} \ne m_{ph}$$.
In minimal subtraction the lagrangian mass parameter is $$m_{ren}$$ and the LSZ formula has to be corrected by a $$R^{-1/2}$$ factor for each external particle because of the normalization of the field $$R^{-1/2} \phi (x)$$. The Green's function appearing in the LSZ formula already accounts for all of the interacting terms.
Point 2.
The bare Lagrangian is written in terms of bare (unrenormalized) fields and couplings, which are infinite. That is why of the renormalization procedure.
You write:
$$\phi_0 = \sqrt{Z_\phi} \phi_{ren}$$
$$m_0 = Z_m m_{ren}$$
$$g_0 = Z_g g_{ren}$$
The mass you detect is the pole mass, that is $$m_{ph}$$, which is related to the renormalized mass $$m_{ren}$$ as $$\Sigma_{ren} (m_{ph}) = m_{ren} - m_{ph}$$, where $$\Sigma_{ren} (m_{ph})$$ is the sum of all of the $$1PI$$ (one particle irreducible) graphs including the counterterms.
Here we will try to answer OP's title question, which seems spurred by the following paragraph above eq. (27.6) in Srednicki's book:
Finally, in the LSZ formula, each external line will contribute a factor of $$R$$ when the associated Klein-Gordon wave operator hits the external propagator and cancels its momentum-space pole, leaving behind the residue $$R$$. Combined with the correction factor of $$R^{−1/2}$$ for each field, we get a net factor of $$R^{1/2}$$ for each external line when using the $$\overline{\rm MS}$$ scheme. Internal lines each contribute a factor of $$(−i)/(k^2 + m^2)$$, where $$m$$ is the lagrangian-parameter mass, and each vertex contributes a factor of $$iZ_g g$$, where $$g$$ is the lagrangian-parameter coupling.
Srednicki is trying to say that the internal/amputated part of the connected correlator function in the LSZ formula can be calculated as a sum of amputated Feynman diagrams that are built from free propagators $$\Delta=1/(k^2 + m^2)$$, vertices $$ig$$, and counterterms as usual. Srednicki mentions indirectly the counterterms $$Z_g-1$$ for the vertex, but for some reason he does not mention the kinetic counterterm $$Z_{\phi}-1$$ and the mass counterterm $$Z_m-1$$, but of course they are also there.
The internal free propagators can typically not be re-summed into full/exact propagators a la this Phys.SE post; in particularly if they are part of a 1PI subdiagram, cf. my Phys.SE answer here.
On the other hand, the external legs are already re-summed into full/exact propagators $${\bf \Delta}~=~\frac{1}{k^2 + m^2-\Pi}~\simeq~\frac{R}{k^2 + m_{\rm ph}^2}$$ (which carry the residue factor $$R$$) in order to fit into the LSZ formalism. | 2,161 | 7,441 | {"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": 67, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.03125 | 3 | CC-MAIN-2024-18 | latest | en | 0.903553 |
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# The spectacular disintegration of a comet last year in full
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The spectacular disintegration of a comet last year in full [#permalink]
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The spectacular disintegration of a comet last year in full view of ground-and space-based telescopes provided new insights into how comets form and may thus force a rethinking of the role of comets in the delivery of organic compounds to the evolving Earth.
a) The spectacular disintegration of a comet last year in full view of ground-and space-based telescopes provided new insights into how comets form and may thus force
b) The spectacular disintegration of a comet last year in full view of ground-as well as space-based telescopes, provided new insights into how comets form and thus possibly forcing
c) When a comet's spectacular disintegration occurred in full view of ground-and space-based telescopes last year, it provided new insights into how comets form and thus may possibly force
d) Last year, in full view of ground-and space-based telescopes, a comet's spectacular disintegration provided new insights into how comets form and thus possibly forcing
e) Last year, in full view of ground-as well as space-based telescopes, the spectacular distegration of a comet has provided new insights into how comets form and may thus force
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25 Jan 2008, 22:02
Not sure. A, is it?
The spectacular disintegration of a comet last year in full view of ground-and space-based telescopes provided new insights into how comets form and may thus force a rethinking of the role of comets in the delivery of organic compounds to the evolving Earth.
a) The spectacular disintegration of a comet last year in full view of ground-and space-based telescopes provided new insights into how comets form and may thus force
b) The spectacular disintegration of a comet last year in full view of ground-as well as space-based telescopes, provided new insights into how comets form and thus possibly forcing --> Not parallel
c) When a comet's spectacular disintegration occurred in full view of ground-and space-based telescopes last year, it provided new insights into how comets form and thus may possibly force --> may possibly = redundant, occured = change the meaning of the original sentence.
d) Last year, in full view of ground-and space-based telescopes, a comet's spectacular disintegration provided new insights into how comets form and thus possibly forcing --> not parallel.
e) Last year, in full view of ground-as well as space-based telescopes, the spectacular distegration of a comet has provided new insights into how comets form and may thus force --> Incorrect : tense
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### Show Tags
26 Jan 2008, 00:09
This sentence has modifier issue –the spectacular disintegration of comet vs. in full view of ground-space-based telescopes. It is the comet’s spectacular disintegration that has provided new insights.
a) The spectacular disintegration of a comet last year in full view of ground-and space-based telescopes provided new insights into how comets form and may thus force (This choice restricting the meaning to views of telescopes – eliminate it)
b) The spectacular disintegration of a comet last year in full view of ground-as well as space-based telescopes, provided new insights into how comets form and thus possibly forcing (This choice restricting the meaning to views of telescopes – eliminate it)
c) When a comet's spectacular disintegration occurred in full view of ground-and space-based telescopes last year, it provided new insights into how comets form and thus may possibly force
(This is good one – this makes an assertion that the comet’s spectacular disintegration occurred in full view of telescopes – eliminate it)
d) Last year, in full view of ground-and space-based telescopes, a comet's spectacular disintegration provided new insights into how comets form and thus possibly forcing (full view is modifying the a comet's spectacular disintegration – Eliminate it)
e) Last year, in full view of ground-as well as space-based telescopes, the spectacular disintegration of a comet has provided new insights into how comets form and may thus force (full view modifying the spectacular disintegration) – Hold it
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26 Jan 2008, 02:44
The OA is A. Thanks a lot guys. you all have provided some good insights. I have a question for CaspAreaGuy. Would you please elaborate on the point you raised for option b? what did you mean by "as well as" can't mix with "x and y" cause that point you raised is new to me and need some more insight into that.
thanks
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26 Jan 2008, 02:54
hi tarek99,
pls disregard it. was in rush while reading it and confused it with constructions like ground-and-space telescopes.
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27 Jan 2008, 23:24
Hi Guys,
Can someone help me with what is being tested here??? I will appreciate your suggestions.
Thanks,
Re: SC: Comet [#permalink] 27 Jan 2008, 23:24
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Display posts from previous: Sort by | 1,649 | 6,794 | {"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} | 2.796875 | 3 | CC-MAIN-2017-22 | latest | en | 0.884397 |
https://andrescaicedo.wordpress.com/2008/11/18/ | 1,675,338,996,000,000,000 | text/html | crawl-data/CC-MAIN-2023-06/segments/1674764500017.27/warc/CC-MAIN-20230202101933-20230202131933-00656.warc.gz | 120,521,269 | 32,844 | ## 175- Partial fractions decomposition
November 18, 2008
[This post replaces the previous version from October 12, 2008. The new argument is significantly simpler than the one originally posted.]
I want to present here a Calculus II-level proof that the method of partial fractions decomposition works. I will actually show a more general result, which will greatly simplify the presentation and get rid of most problems of the somewhat awkward formulation below.
We need some notation:
• $\prod_{i=1}^n a_i$ means $a_1\times a_2\times\dots\times a_n$.
• $p(x)$, $q(x)$, etc, denote polynomials with real coefficients.
The proof that I show below is algorithmic in nature, meaning that it provides us with a method to find the relevant constants for any given specific polynomials $p$ and $q$. The constants we obtain are real numbers.
That the method of partial fractions decomposition works means that we can always find the relevant constants the method requires.
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## 175 -A problem from Homework sets 9, 10
November 18, 2008
I want to show here how to solve the following problem from this week’s homework set:
Starting with a given $x_0$, define the subsequent terms of a sequence by setting $x_{n+1}=x_n+\sin(x_n).$ Determine whether the sequence $\{x_n\}$ converges, and if it does, find its limit.
This is a nice simple example of a (discrete) dynamical system in one variable. It turns out that the sequence always converges, but the limit depends on the value of $x_0.$
• Case 1. $x_0=n\pi$ for some $n=0,\pm1,\pm2,\dots$
In this case $x_1=x_2=\dots=n\pi$, so the sequence trivially converges.
• Case 2. $2n\pi for some $n=0,\pm1,\pm2,\dots$
In this case I will show that $x_0 and that $\lim_{i\to\infty}x_i=(2n+1)\pi.$
First, notice that if $2n\pi, then we can write $x_i=2n\pi+t$ for some $t$ with $0 and $\sin(x_i)=\sin(t)>0$, so $x_{i+1}=x_i+\sin(x_i)>x_i.$
Second, recall that $\sin\theta<\theta$ for all $\theta>0$. You are probably familiar with this inequality from Calculus I; if not, one can prove it easily as follows: Let $f(\theta)=\sin(\theta)-\theta$, so $f(0)=0$. Also, $f'(\theta)=\cos(\theta)-1\le0$ for all $\theta$, so $f$ is always decreasing, and the result follows.
Also, recall that $\sin(t)=\sin(\pi-t)$, so
$x_{i+1}=x_i+\sin(x_i)=2n\pi+t+\sin(t)$ $=2n\pi+t+\sin(\pi-t)<2n\pi+t+(\pi-t)=(2n+1)\pi.$
We have shown (by induction) that the sequence $\{x_i\}_{i\ge0}$ is strictly increasing and bounded above (by $(2n+1)\pi$). Thus, it converges. If $L$ is its limit, then
$L=\lim_{i\to\infty}x_{i+1}=\lim_{i\to\infty}x_i+\sin(x_i)=L+\sin(L),$
so $\sin(L)=0$ and since $2n\pi, it follows that $L=(2n+1)\pi.$
• Case 3. $(2n+1)\pi for some $n=0,\pm1,\pm2,\dots$
In this case, $x_0>x_1>\dots$ and $\lim_{i\to\infty}x_i=(2n+1)\pi.$
The argument is very similar to the one for Case 2: If $(2n+1)\pi, then $\sin(x_i)<0$ so $x_{i+1}, and $x_i=(2n+1)\pi+t$ for some $t\in(0,\pi)$, so $\sin(x_i)=-\sin(t)>-t$ and therefore $x_{i+1}>(2n+1)\pi$. It follows that the sequence $\{x_i\}_{i\ge0}$ is decreasing and bounded below (by $(2n+1)\pi$), so it converges. As before, the limit must in fact be $(2n+1)\pi$, and we are done.
## 175, 275 -Homework 11 and suggestions for the week after Thanksgiving
November 18, 2008
Homework 11 is due Tuesday, December 2, at the beginning of lecture. The usual considerations apply.
In 175 we will try to cover this week until section 8.10, but probably won’t get that far. As mentioned last week, we will also cover additional topics that the book doesn’t mention or doesn’t treat in sufficient detail, once we are done with 8.10. These topics are uniform vs. pointwise convergence (including Wierstrass test), the behavior of the $p$-series $\displaystyle \sum_{n=1}^\infty\frac1{n^p}$ for $p=2,3,\dots$, and infinite products. I will distribute notes of the topics not covered in the book. If you want to read ahead, and would like some of the notes ahead of time, please let me know.
In 275 we will cover Chapter 14, probably this week we will cover until section 14.4. Particularly important are the notion of conservative field and Green’s theorem. Then we will continue with surface integrals and orientations, Stokes’s and the divergence theorems. This will probably take another week, maybe a bit more. If there is any time left afterwards, we will see Lagrange multipliers
Homework 11:
175: Do not use the solutions manual for any of these problems.
• Turn in the problems listed for Homework 10 that you still have pending.
• Section 8.6. Exercises 8, 25, 28, 37, 60.
• Section 8.7. Exercises 2, 4, 39-48.
Besides the exercises you have pending from last week, there are 17 new problems. Turn in the exercises you have pending, and at least 10 of the new problems. The others (at most 7) will be due December 9, together with the additional exercises for that week.
275:
• Turn in the problems listed for Homework 10 that you still have pending.
• Section 14.1. Exercises 1-8, 12, 16, 29.
• Section 14.2. Exercises 6, 8, 34, 41.
• Section 14.3. Exercises 2, 6, 12, 17, 20, 34, 38.
• Section 14.4. Exercises 2, 8, 18, 31-35.
Exercises 14.1.1-8 count as a single exercise. Besides the problems pending from last week, there are 23 exercises. Turn in at least 10 of these. The remaining problems (at most 13) will be due together with a few additional exercises on December 9.
## A characterization of continuity
November 18, 2008
Yesterday, Randall Holmes mentioned to me the following nice characterization of continuity for functions between Euclidean spaces.
Theorem. A function $f:{mathbb R}^nto{mathbb R}^m$ is continuous iff it preserves path-connectedness and compactness.
This is an easy exercise, but I don’t remember having seen the characterization before, so I figured I could as well write down the argument I found. It is clear that the result holds for a much wider class of spaces than the ${mathbb R}^n$, but to keep this post simple, I’ll just leave it this way.
Proof. For Euclidean spaces, continuity and sequential continuity coincide. Towards a contradiction, assume $x_i$ converges to $x$ but $f(x_i)$ does not converge to $f(x)$.
• Case 1. The range of ${f(x_i): ige 0}$ is infinite.
This quickly leads to a contradiction since ${f(x_i):ige 0}cup{f(x)}$ is a compact set: We may as well assume that the map $imapsto f(x_i)$ is injective, and since $f(x_i)$ does not converge to $f(x)$ we may in fact assume that all the $f(x_i)$ stay away from $f(x)$. The set ${f(x_i):ige 0}$ has an accumulation point, which cannot be $f(x)$ so it must be $f(x_m)$ for some $m$. But then the set ${f(x_i):i>m}cup{f(x)}$ is both compact and lacks one of its accumulation points, contradiction.
• Case 2. The range is finite.
We may as well assume all $x_i$ have the same image. Fix paths $A_i=[x_i,x_{i+1}]$ in ${mathbb R}^n$ that we can combine to get a path $bigcup_i A_icup{x}$ (for example, $A_i$ could simply be a segment). By preservation of path connectedness, any $A_i$ with range of size at least 2 in fact has range of size continuum. If infinitely many of the $A_i$ have infinite range, one easily reduces to Case 1. So we may assume all the $A_i$ have constant range, but then $bigcup_i A_icup{x}$ has a disconnected image. ${sf QED}$ | 2,192 | 7,284 | {"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": 85, "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} | 4.21875 | 4 | CC-MAIN-2023-06 | latest | en | 0.85686 |
https://admin.clutchprep.com/physics/practice-problems/83294/a-20-0-kg-cannonball-is-fired-from-a-cannon-with-muzzle-speed-of-1-000-m-s-at-an | 1,597,061,441,000,000,000 | text/html | crawl-data/CC-MAIN-2020-34/segments/1596439738674.42/warc/CC-MAIN-20200810102345-20200810132345-00589.warc.gz | 190,460,625 | 24,046 | # Problem: A 20.0-kg cannonball is fired from a cannon with muzzle speed of 1 000 m/s at an angle of 37.08 with the horizontal. A second ball is fired at an angle of 90.08. Use the isolated system model to find(a) the maximum height reached by each ball and(b) the total mechanical energy of the ball–Earth system at the maximum height for each ball. Let y =0 at the cannon.
⚠️Our tutors found the solution shown to be helpful for the problem you're searching for. We don't have the exact solution yet.
###### Problem Details
A 20.0-kg cannonball is fired from a cannon with muzzle speed of 1 000 m/s at an angle of 37.08 with the horizontal. A second ball is fired at an angle of 90.08. Use the isolated system model to find
(a) the maximum height reached by each ball and
(b) the total mechanical energy of the ball–Earth system at the maximum height for each ball. Let y =0 at the cannon. | 230 | 896 | {"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-2020-34 | latest | en | 0.899229 |
https://giftedanalysts.com/using-ardl-bounds-test-for-time-series-data-analysis/ | 1,720,897,976,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763514512.50/warc/CC-MAIN-20240713181918-20240713211918-00052.warc.gz | 249,588,189 | 24,607 | Please refer to the previous article on using Co-integration test and Fully Modified Ordinary Least Squares (FMOLS) here.
The characteristics of time series data make them not suitable for OLS directly, as such, the variables must be tested for stationarity that is, make their mean and variance equal in case they are not. Usually, a variable that is trending tends to have its mean and variance not equal (non-stationary). As such, the Augmented Dickey-Fuller test (ADF) is used to test for stationarity and make the variables to be stationary.
It is based on the result of the stationarity test, that we will know which method of analysis to go for. The following constitute the methods of analysis based on the stationarity test:
1. If all the variables are stationary at level, it means the mean and variance are equal without doing anything to them. In this case, the researcher can proceed to using the normal Ordinary Least Squares (OLS) to estimate the model and the result will be valid.
2. If some of the variables are stationary at level I(0) and some are stationary at first difference I(1), then the researcher will have to proceed to using ARDL bounds test to estimate the model.
3. If all the variables are stationary at first difference I(1), then Fully Modified Ordinary Least Square (FMOLS) is the appropriate method of analysis. You can download the PDF where FMOLS was explained here.
This article therefore explains the step by step methods of using ARDL bounds test to estimate the model if some of the variables are stationary at level I(0) while some are stationary at first difference I(1).
Testing for Stationarity
The model used for this is one in which Real GDP is a function of Savings Rate (SR), Prime Lending Rate (PLR) and Monetary Policy Rate (MPR). We can as such name is at the “Impact of Interest Rate on Economic Growth”. While SR, PLR and MPR are used as proxy to measure interest rate, real GDP is used as the measure of economic growth.
To test for stationarity;
1. Double Click on the variable
• Click on “View” and the illustration below will pop up
• Click on “Unit Root Test” and Check the button of “Trend and Intercept”
• Click on “OK” and the result will show as below:
From the result above, it can be seen that the Null hypothesis states that MPR has a unit root, which means that MPR is non stationary. The Probability value (P-value) of 0.1020 shows that we do not reject the null hypothesis since it is greater than all the levels of significance (1%, 5% and 10%). Since we need to make this stationary, we have to re-estimate MPR at first difference.
• Click on “View” again and then unit root test. From there, click on “first difference” this time around instead of “level”
• The result below will show:
From the result above, it can be seen that when we tested that stationarity of MPR at first difference, the P-value became 0.0000 which is less than all the levels of significance. Here, we can then reject our null hypothesis and say that MPR is stationary at first difference.
Now do the same thing for SR, PLR and RGDP. Before doing the same for RGDP however, you should log it. Two reasons can warrant you to log:
1. When the variable is not stationary at level and at first difference.
2. When you do not want the coefficients of your results to be large.
The command for logging a variable in E-views is genr lrgdp=log(rgdp). This explains that we are telling E-views to generate a variable named “lrgdp” and it should help us log the variable.
If you therefore do the same process of stationarity to the rest of the variables, you will notice that only PLR is stationary at level while the rest are stationary at first difference.
This will therefore make us estimate our model by making use of the Auto Regressive Distributive Lag (ARDL) bounds test.
Performing ARDL Bounds Test
To perform the bounds test, you should follow the steps below:
1. Hold the CTRL key and click on all the variables (let your dependent variable come first). Right click and open as an equation
• The table below will show
• Click on the drop down button that shows LS and click the last method that is ARDL
• The result below will be displayed
• Change the “Constant Level” to “Linear Trend” and click on OK. The result below will be displayed
• You do not need this result. As such, click on View – Coefficient Diagnostics – Bounds Test, as shown below:
• The result below will be displayed
From the result, there are some decision rules to follow before one can know the next method of analysis to follow. They are:
1. If the value of the F-statistic is greater than the upper bound (I1 Bound) of the chosen level of significance (in this case 5%), proceed to estimating co-integration and long run form.
2. If the value of F-statistics is less than the lower bound (I0 Bound) of the chosen level of significance, proceed to estimating ARDL at first difference. Here, you click on “Estimate” and add D in front of each of the variables [for example: D(LRGDP) D(PLR) D(SR) D(MPR)] and then click OK.
3. If the value of the F-statistics is in between the upper and lower bound of the chosen level of significance, then we go back to adjusting our lag to make sure the result is either greater than the upper bound or less than the lower bound.
4. In our case, the value of our F-statistics is 10.65974 and this is greater than the upper bound of our chosen level of significance (5.07). therefore, we proceed to estimating the short run and long run result of our model which is the same as the co-integration and long run form.
Based on the characteristics of our variables therefore, the appropriate method of analysis is not OLS, neither is it FMOLS but co-integration and long run form. Therefore, we have to run it.
Estimating the Short Run and Long Run relationship Among the Variables of Study
1. From the ARDL bounds test result displayed, click on View- Coefficient Diagnostics- Co-integration and long run form.
• The result below will be displayed:
The first result is the short run result. If you scroll down, you will see the long run result. The long run result shows how the variables will behave in the long run while the short run result shows how the variables will behave when adjusted by 1 year, 2 years and 3 years.
You can therefore interpret accordingly.
Conclusion
As it was explained, using OLS to estimate time series data will give wrong results because the Observational dependency, non- equal mean and variance as well as trending characteristics of the time series variables make them violate the Classical Linear Regression Model (CLRM) assumptions. As such, it is necessary to perform some pre-estimation tests as it is the result of these tests that will determine the appropriate methods of analysis.
• ### Kenechukwu Nwisienyi
Hi
Your illustration was explicit and straight to the point. Just what I needed to put me through in an analysis I am currently doing.
However, I noticed you didn’t test for stability of the model. Which stability test is most appropriate for the ardl? Thanks
• ### Abdulazeez Kuranga
Hi Kenechukwu,
You can use the Ramsey RESET test for the stability of the model. Just go to coefficient diagnostics just the way we did for the other tests. | 1,634 | 7,281 | {"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} | 3.078125 | 3 | CC-MAIN-2024-30 | latest | en | 0.93672 |
https://www.learncram.com/cbse/mcq-questions-for-class-10-science-magnetic-effects-of-electric-current-with-answers/ | 1,716,964,227,000,000,000 | text/html | crawl-data/CC-MAIN-2024-22/segments/1715971059206.29/warc/CC-MAIN-20240529041915-20240529071915-00405.warc.gz | 739,935,930 | 13,553 | # MCQ Questions for Class 10 Science Magnetic Effects of Electric Current with Answers
Free PDF Download of CBSE Class 10 Science Chapter 13 Magnetic Effects of Electric Current Multiple Choice Questions with Answers. MCQ Questions for Class 10 Science with Answers was Prepared Based on Latest Exam Pattern. Students can solve NCERT Class 10 Science Magnetic Effects of Electric Current Multiple Choice Questions with Answers to know their preparation level.
## Class 10 Science MCQs Chapter 13 Magnetic Effects of Electric Current
1. The magnetic field lines always begin from
(a) N-pole and end on S-pole.
(b) S-pole and end on N-pole.
(c) start from the middle and end at N-pole.
(d) start from the middle and end at S-pole.
2. The magnetic field is the strongest at
(a) middle of the magnet.
(b) north pole.
(c) south pole.
(d) both poles.
3. Material of the core of a strong magnet is
(a) aluminium
(b) soft iron
(c) copper
(d) steel
4. Magnetic lines of force inside current carrying solenoid are
(a) perpendicular to axis.
(b) along the axis and are parallel to each other.
(c) parallel inside the solenoid and circular at the ends.
(d) circular.
5. A soft iron bar is introduced inside a current carrying solenoid. The magnetic field inside the solenoid
(a) will become zero.
(b) will increase.
(c) will decrease.
(d) will remain unaffected.
6. An electric generator actually acts as
(a) a source of electric charge.
(b) a source of neat energy.
(c) an electromagnet.
(d) a converter of energy.
7. A magnetic field directed in north direction acts on an electron moving in east direction. The magnetic force on the electron will act
(a) vertically upwards.
(b) towards east.
(c) vertically downwards.
(d) towards north.
8. The direction of force on a current carrying conductor in a magnetic field is given by
(a) Fleming’s left hand rule.
(b) Fleming’s right hand rule.
(c) Right hand thumb rule.
(d) Left hand thumb rule.
9. The direction of induced current is given by
(a) Fleming’s right hand rule.
(b) Fleming’s left hand rule.
(c) Right hand thumb rule.
(d) Left hand thumb rule.
0. Switches are connected to
(a) live wire.
(b) neutral wire.
(c) earth wire.
(d) any one.
11. The most important safety method used for protecting home appliances from short-circuiting or Overloading is
(a) earthing
(b) use of stabilizers
(c) use of fuse
(d) use of electric meter
12. The best material to make permanent magnets is
(a) aluminium
(b) soft iron
(c) copper
(d) alnico
Fill in the Blanks
1. The magnetic field of a solenoid carrying a current is similar to that of a ……….. .
2. The direction of the induced current is given by ………..
3. A generator converts ……….. into ……….. .
4. In our houses, we receive AC electric power of ……….. V with a frequency of ……….. Hz.
5. The direction of magnetic force acting on a charged particle moving in a magnetic field can be found by ……….. .
6. According to Fleming’s left hand rule, if the first finger points in the direction of ……….., the second finger
in the direction of ……….., then the thumb will point in the direction of ……….. . | 754 | 3,098 | {"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} | 2.796875 | 3 | CC-MAIN-2024-22 | latest | en | 0.84761 |
https://se.mathworks.com/matlabcentral/cody/problems/1991-find-the-index-of-nth-maximum-of-a-row-vector-of-real-numbers/solutions/352288 | 1,607,025,971,000,000,000 | text/html | crawl-data/CC-MAIN-2020-50/segments/1606141732696.67/warc/CC-MAIN-20201203190021-20201203220021-00584.warc.gz | 475,042,167 | 17,615 | Cody
Problem 1991. Find the index of nth maximum of a row vector of real numbers
Solution 352288
Submitted on 15 Nov 2013
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
%% x = [2 4.5 3 1 3.33]; n = 4; y_correct = 1; assert(isequal(findMaxIndex(x,n),y_correct))
2 Pass
%% x = [2 4.5 3 1 3.33]; n = 5; y_correct = 4; assert(isequal(findMaxIndex(x,n),y_correct))
3 Pass
%% x = [2 4.5 3 1 3.33 eps inf 0.01]; n = 1; y_correct = 7; assert(isequal(findMaxIndex(x,n),y_correct))
4 Pass
%% x = [2 4.5 3 1 3.33 eps inf 0.01]; n = 8; y_correct = 6; assert(isequal(findMaxIndex(x,n),y_correct))
5 Pass
%% x = [2 4.5 3 1 3.33 eps inf 0.01 realmax realmin]; n = 2; y_correct = 9; assert(isequal(findMaxIndex(x,n),y_correct))
6 Pass
%% x = [-2.23 1 0 -6.65 2.63 -realmax inf 0]; n = 8 y_correct = 6; assert(isequal(findMaxIndex(x,n),y_correct))
n = 8
7 Pass
%% x = [2 4.5 3.33 3 1 3.33]; n = 2; y_correct = [3 6]; assert(isequal(findMaxIndex(x,n),y_correct))
8 Fail
%% x = [2 4.5 pi eps eps pi 0 pi 6]; n = 2; y_correct = [3 6 8]; assert(isequal(findMaxIndex(x,n),y_correct))
Error: Assertion failed.
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting! | 510 | 1,353 | {"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-2020-50 | latest | en | 0.523158 |
https://www.way2techin.com/2018/01/fractal-patterns-using-koch-curve.html | 1,585,818,365,000,000,000 | text/html | crawl-data/CC-MAIN-2020-16/segments/1585370506870.41/warc/CC-MAIN-20200402080824-20200402110824-00482.warc.gz | 1,236,832,356 | 41,880 | The Koch curve is a mathematical curve and one of the earliest fractal curves to have
been described. The progression for the area of the snowflake converges to 8/5 times the
area of the original triangle, while the progression for the curves perimeter diverges to
infinity.
The Koch curve can be constructed by starting with an equilateral triangle, then
recursively altering each line segment as follows:
1. divide the line segment into three segments of equal length.
2. draw an equilateral triangle that has the middle segment from step 1 as its base and
points outward.
3. remove the line segment that is the base of the triangle from step 2.
After one iteration of this process, the resulting shape is the outline of a hexagram.
#### Algorithm:
##### Input to the algorithm:
Direction(angle), length and iteration for drawing the Koch curve .
Output of the algorithm
Displaying the Koch Curve.
Data Variables
oldx, oldy : are static float coordinates for the vertex of triangle.
dir
: stores the angle of line segment.
len
: stores the length of line segment.
iter
: stores the number of iterations performed on triangle to produce th koch curve.
newX, newY : calculates new vertex coordinates for cuvre using oldx and oldy by
performing cosine and sine operations on dirRad.
Algorithm
1. Start
2. oldx=-0.7, oldy=0.5;
3. input dir, len and iter
4. dirRad = 0.0174533 * dir;
5. newX = oldx + len * cos(dirRad);
6. newY = oldy + len * sin(dirRad);
7. if (iter==0) { oldx = newX, oldy = newY; }
else{ decrement iter;
drawkoch(dir, len, iter) with dir as 60, -120 and 60 degrees; }
8. goto step no 7
9. Stop.
Output: Display koch curve.
```#include <GL/glut.h>
#include <math.h>
GLfloat oldx=-0.7,oldy=0.5;
void drawkoch(GLfloat dir,GLfloat len,GLint iter) {
GLdouble dirRad = 0.0174533 * dir;
GLfloat newX = oldx + len * cos(dirRad);
GLfloat newY = oldy + len * sin(dirRad);
if (iter==0) {
glVertex2f(oldx, oldy);
glVertex2f(newX, newY);
oldx = newX;
oldy = newY;
}
else {
iter--;
//draw the four parts of the side _/\_
drawkoch(dir, len, iter);
dir += 60.0;
drawkoch(dir, len, iter);
dir -= 120.0;
drawkoch(dir, len, iter);
dir += 60.0;
drawkoch(dir, len, iter);
}
}
void display(){
glClear( GL_COLOR_BUFFER_BIT );
glBegin(GL_LINES);
glColor3f(0.0, 1.0, 0.0);
drawkoch(0.0,0.04,3);
drawkoch(-120.0, 0.04, 3);
drawkoch(120.0,0.04,3);
glEnd();
glFlush();
}
int main(int argc, char** argv)
{
glutInit(&argc,argv);
glutInitDisplayMode(GLUT_SINGLE|GLUT_RGB);
glutInitWindowSize(500,500);
glutInitWindowPosition(0,0);
glutCreateWindow("Koch Curve");
glutDisplayFunc(display);
glutMainLoop();
}``` | 766 | 2,605 | {"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-2020-16 | longest | en | 0.745477 |
https://stats.stackexchange.com/questions/514963/does-the-wilcoxan-rank-sum-test-account-for-differences-in-sample-size | 1,718,206,312,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198861173.16/warc/CC-MAIN-20240612140424-20240612170424-00324.warc.gz | 518,886,061 | 40,016 | # Does the wilcoxan rank sum test account for differences in sample size?
I want to compare the overall mean weight between males and females in my biological sample. The weight is not normally distributed so I have used a Wilcoxan ranked sum test and found significant differences in weight between sexes. In this dataset, I have roughly 550 females and 350 males.
I also have a separate dataset where samples were taken using a separate sampling technique and I compared the exact same thing; weight between each sex and found no significant between sex but I had roughly 150 females and 50 males.
I want to compare results between sampling techniques but I'm cautious because of the differences in sample size between samples and between sex.
In an effort to correct for the lower sample size in the second method, I randomly sampled the same number of males and females from the first dataset and completed the same analysis 1000 times and found that ~600-800 times I found no significant differences in weight between sex.
• You are not going to have the same power to detect a M/F difference with the reduced number of observations. In terms of power, the most efficient design would be to have roughly equal sample sizes for both M and F. Having sample sizes 150 & 50 provides more info than 50 & 50, but not much more. "A chain is not stronger than it's weakest link." // Also, also huge re-sampled collections from a small dataset have no more information than the original small dataset. Re-sampling has its place in data analysis, but not in mysteriously creating info about the real world. Mar 21, 2021 at 21:26
You don't say anything about the actual weights you are dealing with. So I'll choose some hypothetical values for illustration. Suppose women have average weights about 230 (pounds) with standard deviation 45, and men averaging about 245 with SD 55.
Then respective sample sizes 150 and 50 may not be enough to detect the 15 lbs difference in gender weights. Then according to the following simulation in R, a little over half of the experiments according to these parameters would show a significant difference. (The power is the probability of detecting such a difference).
set.seed(2021)
pv = replicate(10^4,
wilcox.test(rnorm(150, 230, 45),
rnorm(50, 245, 55), alt="l")$p.val) mean(pv <+ .05) [1] 0.5502 # power of Wilcoxon rank sum test However, with the same weight distributions and sample sizes 550 and 350, you would almost certainly detect the difference in gender weights. set.seed(321) pv = replicate(10^4, wilcox.test(rnorm(550, 230, 45), rnorm(350, 245, 55), alt="l")$p.val)
mean(pv <+ .05)
[1] 0.9943
Note: There are procedures in most statistical software (and online) for the power of t tests (requiring normal data) where both samples are the same size. If sample sizes are different, then one can use formulas involving noncentral t distributions to compute power. However, I know of no such procedures for Wilcoxon signed rank tests. Thus, I have used simulation for this example.
• In 2nd dataset is it 150 (as in Comment above) or 50 (as in original Q) Males? Mar 22, 2021 at 2:39
• error on my part - should be 50 for males in the second set. I will edit my post Mar 22, 2021 at 2:41
• Attached is the data to provide context. The first Dataset; Male (n=350) mean=1.68 kg. with sd = 0.49. Female (n=550) mean=1.76 kg. with sd =0.46. The second dataset; Male (n=50) mean=1.63 kg. with sd=0.41. Female (n=150) mean = 1.72 kg. with sd=0.45. I entered my values into your simulation and had odd results. For dataset one with larger samples, a value=0 was given as the power multiple times. The second dataset had a slightly higher value of 0.0013. The way I Interpret that result states that the lower sample size dataset contains more power but hardly any power at all? Mar 22, 2021 at 2:42
• I reviewed the code and I placed the larger female means first and left the L in the alt argument therefore it explains why I was having issues. Mar 22, 2021 at 2:50 | 994 | 4,014 | {"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": 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} | 3.046875 | 3 | CC-MAIN-2024-26 | latest | en | 0.961589 |
https://www.flyingcoloursmaths.co.uk/secrets-of-the-mathematical-ninja-sines-and-cosines-near-45o/ | 1,582,927,722,000,000,000 | text/html | crawl-data/CC-MAIN-2020-10/segments/1581875147647.2/warc/CC-MAIN-20200228200903-20200228230903-00027.warc.gz | 730,013,913 | 15,344 | # Secrets of the Mathematical Ninja: Sines and cosines near 45º
This is the one area where I'm better with degrees than with radians - and I suspect that's only because I don't particularly notice when radian angles are close to $\frac{\pi}{4}$, but I do when degree angles are close to 45º.
This one's a trickier one than we've been looking at, but I'm sure you can manage; there's also a simple version: for angles very near 45º, 0.7 is a good guess for both sine and cosine. (In fact, $\sin(45º) = \cos(45º) = \frac{\sqrt{2}}{2} \simeq 0.707$, which is about 1% more than 0.7.)
However, such a rough answer for, say, $\sin(43º)$, would be unacceptable for the true mathematical ninja. So how can we adjust our answer?
Well... unless you're doing Further Maths, Taylor series probably don't concern you. Even if you are, you probably only get to see the more specific Maclaurin series. However, it's a useful little feller here:
$f(X + x) \simeq f(X) + x f^\prime(X)$.
Who to the what now? Well, what it means is, if you move a small distance from a known value, you can use the derivative to figure out a guess for the new answer. In this case, we have $X = 45º$, or - since we're doing calculus - $\frac{\pi}{4}$ radians.
When we're x radians away from π/4, this becomes:
$\sin(\frac{\pi}{4} + x) \simeq 0.707 ( 1 + x )$
$\cos(\frac{\pi}{4} + x) \simeq 0.707 ( 1 - x )$
Now we're in business - because we know that you can convert degrees to radians using the magic number $\frac{7}{400}$ - which is 1.75%. Can you see where this is going yet?
To work out $\sin(43º)$, you say 'it's two degrees below 45, so I need to minus 3.5% from sin(45º), which is 1% more than 0.7. So, it's 0.7 minus 2.5%, and 2.5% of 0.7 is about 0.02, making 0.68. (It's actually 0.682 - if I'd thought through the details a bit better, I'd have got that).
How about $\cos(40º)$? That's 5º below 45, so I need to add $5 \times 1.75% = 8.75%$ on to 0.707, or 9.75% onto 0.7. That'll be close enough to 0.77 as makes no odds - in fact, it's 0.766. Again, less lazy calculation would have got me closer, but not exactly there.
As an exercise, you can try applying the Taylor series near other known values of $\sin(x)$ and $\cos(x)$, even $\tan(x)$ if you're feeling brave1.
## Colin
Colin is a Weymouth maths tutor, author of several Maths For Dummies books and A-level maths guides. He started Flying Colours Maths in 2008. He lives with an espresso pot and nothing to prove.
1. Yes, it's in the formula book, it's $\sec^2(x)$ []
#### Share
This site uses Akismet to reduce spam. Learn how your comment data is processed. | 796 | 2,615 | {"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} | 4.28125 | 4 | CC-MAIN-2020-10 | longest | en | 0.940721 |
http://viettelhaiphong.vn/download/computational-methods-in-ordinary-differential-equations-introductory | 1,519,572,466,000,000,000 | text/html | crawl-data/CC-MAIN-2018-09/segments/1518891816647.80/warc/CC-MAIN-20180225150214-20180225170214-00625.warc.gz | 365,320,187 | 8,824 | # Download Computational Methods in Ordinary Differential Equations by J. D. Lambert PDF
By J. D. Lambert
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Extra info for Computational Methods in Ordinary Differential Equations (Introductory mathematics for scientists & engineers)
Sample text
0, and this is the first of the conditions (26). It should be observed that we have not made any use of the differential equation so far. } tends to some function y(x). Linear multistep methods I: basic theory 31 The second condition of (26) ensures that the function y(x) does in fact satisfy the differential equation. For, under the limiting process, (y,+ j - y,)/jh = jhy'(x) --+ j = 1, 2, ... ,(h), j = 1,2, ... ,(h) = 0. ,(h). Since L~=o et j = 0, we have, on dividing through by h, • L PJ,+ j=O j = • • y'(x) L jetj + L jetjcPj,,(h).
L = th(3/"+1 - . 2/,,) to compute a numerical solution/or the initial value problem of e"Xample 4. For this method, L:• aj = 0, J-O so that the first of the consistency conditions (26) is satisfied, but the second is not. } will <:onverge to a function y(x)as the steplength tends to zero, but this function y(x) will not be the solution of the initial value problem_ We observe that the failure of this inconsistent method is less dramatic than that of the zero-unstable method of example 4. This is because our inconsistent method is zero-stable and thus does not propagate errors in an explosive manner.
Since P2 = 0 for Euler's rule, the validity of (24) is verified. 2! 3! Y + ... (q-I)! y + .. 2! + (~! )h'A' + .. I I 1h4 A • + ... 3! J h2A2 = [exp (nhA)] { exp (hA) - I - hA - ""2 - thA[exp(hA) - I - hAJ} = [exp(nhA)][(1 - 1hA) exp (hA) - (I Also Y•• I - Y. = 1hA(y•• I + yJ + 1hA)]. , / 30 Computational methods in ordinary differential equations + thA) exp (nhA), or (1 - 4hA)y = (1. • "+ 1 Y. + 1] = by the localizing assumption (l - thA) exp [In = [exp(nhA)][(! '. = + I)hA]- that + thA) exp (nhA) thA)exp(hA) - (1 + 1M)] (1 -2'[y{x,); h], verifying (24). | 896 | 3,375 | {"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} | 3.125 | 3 | CC-MAIN-2018-09 | latest | en | 0.90338 |
https://git.sr.ht/~piotr-machura/sweep-ai/commit/2d45d6c985d47c35380b88016477b013670f1e58 | 1,669,599,736,000,000,000 | text/html | crawl-data/CC-MAIN-2022-49/segments/1669446710462.59/warc/CC-MAIN-20221128002256-20221128032256-00615.warc.gz | 321,205,430 | 6,263 | ## ~piotr-machura/sweep-ai
2d45d6c985d47c35380b88016477b013670f1e58 — Piotr Machura 10 months ago
```Fix random bomb placement
```
```2 files changed, 17 insertions(+), 11 deletions(-)
M sweep_ai/logic.py
M tests/test_logic.py
```
`M sweep_ai/logic.py => sweep_ai/logic.py +13 -11`
```@@ 6,6 6,7 @@ import numpy as np
#pylint: disable=invalid-name
+
class State:
"""Represents game state at any point in time.
@@ 31,7 32,7 @@ class State:
bombs: percentage of bombs to place
bomb_positions: exact bomb positions
- If `bomb_positions` are provided the `bombs` are ignored.
+ If `bomb_positions` are provided the `bombs` percentage is ignored.
"""
self.size = size
self.bomb = np.zeros((self.size, self.size), dtype=int)
@@ 40,21 41,23 @@ class State:
self.near = np.copy(self.bomb)
self.won: Optional[bool] = None
- # If the positions were not explicitly provided randomise them.
+ # If the positions were not explicitly provided randomise them
if bomb_positions is None:
- bomb_positions = list(
- zip(
- sample(range(self.size), k=int(self.size**2 * bombs)),
- sample(range(self.size), k=int(self.size**2 * bombs)),
- ))
-
- # Create the board based on the positions
+ # Reduce 'bombs' to [0, 1]
+ bombs = np.max([bombs, 0.])
+ bombs = np.min([bombs, 1.])
+ # Choose from all the possible positions
+ possible = [
+ (x, y) for x in range(self.size) for y in range(self.size)
+ ]
+ bomb_positions = sample(possible, k=round(self.size**2 * bombs))
+
+ # Place bombs
for x, y in bomb_positions:
self.bomb[x, y] = 1
for n_x, n_y in self.neighbors(x, y):
self.near[n_x, n_y] += 1
-
@property
def not_bomb(self):
"""The inverse of `self.bombs`."""
@@ 65,7 68,6 @@ class State:
"""The inverse of `self.revealed`."""
return (self.revealed + 1) % 2
-
def click(self, x: int, y: int):
"""Simulate a click on the `(x, y)` position.
```
`M tests/test_logic.py => tests/test_logic.py +4 -0`
```@@ 23,6 23,10 @@ def test_bombs():
[1, 1, 0, 1],
]))
+ for size, percentage in [(4, 0.25), (10, 0.1), (12, 0.34), (20, 0.1),]:
+ state = logic.State(size, percentage)
+ assert np.sum(state.bomb) == round(size**2 * percentage)
+
def test_neighbors():
state = logic.State(4)
``` | 721 | 2,403 | {"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-2022-49 | latest | en | 0.573658 |
http://au.metamath.org/mpegif/ltord2.html | 1,531,875,942,000,000,000 | text/html | crawl-data/CC-MAIN-2018-30/segments/1531676589980.6/warc/CC-MAIN-20180718002426-20180718022426-00598.warc.gz | 33,883,445 | 6,887 | Metamath Proof Explorer < Previous Next > Nearby theorems Mirrors > Home > MPE Home > Th. List > ltord2 Structured version Unicode version
Theorem ltord2 9556
Description: Infer an ordering relation from a proof in only one direction. (Contributed by Mario Carneiro, 14-Jun-2014.)
Hypotheses
Ref Expression
ltord.1
ltord.2
ltord.3
ltord.4
ltord.5
ltord2.6
Assertion
Ref Expression
ltord2
Distinct variable groups: , ,, ,, ,, ,, ,, ,,
Allowed substitution hints: (,) ()
Proof of Theorem ltord2
StepHypRef Expression
1 ltord.1 . . . 4
21negeqd 9300 . . 3
3 ltord.2 . . . 4
43negeqd 9300 . . 3
5 ltord.3 . . . 4
65negeqd 9300 . . 3
7 ltord.4 . . 3
8 ltord.5 . . . 4
98renegcld 9464 . . 3
10 ltord2.6 . . . 4
118ralrimiva 2789 . . . . . . 7
121eleq1d 2502 . . . . . . . 8
1312rspccva 3051 . . . . . . 7
1411, 13sylan 458 . . . . . 6
1514adantrl 697 . . . . 5
168adantrr 698 . . . . 5
17 ltneg 9528 . . . . 5
1815, 16, 17syl2anc 643 . . . 4
1910, 18sylibd 206 . . 3
202, 4, 6, 7, 9, 19ltord1 9553 . 2
215eleq1d 2502 . . . . . 6
2221rspccva 3051 . . . . 5
2311, 22sylan 458 . . . 4 | 513 | 1,108 | {"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-2018-30 | latest | en | 0.116776 |
https://knittystash.com/what-is-a-healthy-amount-of-credit-card-debt/ | 1,723,622,226,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722641104812.87/warc/CC-MAIN-20240814061604-20240814091604-00754.warc.gz | 259,634,988 | 38,998 | What is a Healthy Amount of Credit Card Debt
Your credit utilization ratio is a measure of how much credit you’re using compared to your total available credit. It’s calculated by dividing your total credit card balances by your total credit limits. A healthy credit utilization ratio is below 30%. Using more than 30% of your available credit can hurt your credit score.
• Divide your total credit card balances by your total credit limits.
• Multiply the result by 100 to get your credit utilization ratio as a percentage.
For example, if you have \$1,000 in credit card balances and \$5,000 in total credit limits, your credit utilization ratio would be 20% (1,000 / 5,000 * 100 = 20).
Credit Utilization Ratio Impact on Credit Score
0-10% Positive
10-30% Neutral
30-50% Negative
50%+ Very negative
Understanding Income and Debt Levels
Determining a healthy amount of credit card debt is not a fixed number but rather a personalized assessment based on your income and debt levels. It’s crucial to consider the following factors:
• Income: Calculate your net monthly income by subtracting taxes, insurance, and other deductions from your gross income.
• Debt-to-income ratio (DTI): This ratio measures how much of your income is spent on debt obligations. A DTI of 36% or less is generally considered healthy.
To determine your DTI, add up all your monthly debt payments, including credit cards, loans, and mortgages. Then, divide this total by your net monthly income. For instance, if your monthly debt payments total \$500 and your net income is \$2,000, your DTI would be 25% (\$500 / \$2,000 = 0.25 or 25%).
Managing Credit Card Debt
While there’s no definitive answer to “What is a healthy amount of credit card debt?”, it’s generally advisable to:
• Pay off your credit card balance in full each month to avoid interest charges.
• Keep your credit utilization ratio (CUR) below 30%. CUR is the percentage of your available credit that you’re using. Using more than 30% can negatively impact your credit score.
• Avoid carrying a balance on multiple high-interest credit cards.
• If you have difficulty managing credit card debt, consider seeking professional help from a credit counselor.
Recommended Credit Card Debt Levels
Based on the above considerations, the following table provides a general estimate of recommended credit card debt levels:
Income Level Recommended Credit Card Debt Limit
Below \$50,000 \$5,000 or less
\$50,000 to \$100,000 \$10,000 or less
\$100,000 to \$200,000 \$15,000 or less
\$200,000+ \$20,000 or less
Again, these are estimates and may vary depending on individual circumstances. It’s always recommended to prioritize debt repayment and maintain a healthy financial plan.
Credit Card Debt and Long-Term Financial Goals
Credit card debt can be a significant hurdle to achieving long-term financial goals. If managed responsibly, credit cards can provide convenience and financial flexibility. However, excessive debt can strain your budget, lower your credit score, and hinder your ability to save and invest for the future.
To ensure that credit card debt does not derail your financial plans, it is essential to develop a strategy for managing it effectively. This includes:
1. Create a budget: Track your income and expenses to determine how much you can afford to allocate towards debt repayment.
2. Prioritize high-interest debt: Focus on paying off cards with the highest interest rates first to minimize interest charges.
3. Make more than the minimum payment: Paying beyond the minimum required payment will reduce the amount of time it takes to become debt-free.
4. Explore debt consolidation options: If you have multiple credit card balances, consider consolidating them into a lower-interest loan to simplify repayment.
It’s important to note that the “healthy” amount of credit card debt varies depending on individual circumstances, income, and financial goals. However, general guidelines suggest aiming to keep your total credit card debt below 30% of your total available credit and monthly payments below 15% of your gross income.
Recommended Credit Card Debt Limits
Credit Card Usage Recommended Debt Limit
Emergency Expenses 0%
Short-Term Purchases Less than 30%
Long-Term Investments Avoid using credit cards
Remember, it is possible to manage credit card debt responsibly and achieve your financial goals. By understanding the potential impact of debt, creating a repayment plan, and making informed decisions about your credit card usage, you can maintain a healthy financial future.
Responsible Credit Card Usage Habits
• Pay your bills on time, every time.
• Keep your credit utilization ratio low (below 30%).
• Avoid carrying a balance from month to month.
• Only use credit cards for purchases you can afford to pay off.
• Monitor your credit reports regularly and dispute any errors.
By following these tips, you can use credit cards responsibly and avoid getting into debt.
And there you have it, folks! The truth about credit card debt and what’s considered healthy. Remember, it’s not about the amount of debt but how well you manage it. So keep track of your spending, pay down your balance on time, and you’ll be the master of your financial domain. Thanks for hanging out with me today. If you found this helpful, be sure to check back later for more financial wisdom. I’ll be here, dishing out the financial dirt that will help you conquer your finances and live the life you want. Cheers! | 1,142 | 5,493 | {"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} | 2.546875 | 3 | CC-MAIN-2024-33 | latest | en | 0.938186 |
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UCSD ECE 153 Handout #18 Prof. Young-Han Kim Thursday, November 6, 2008 Homework Set #5 Due: Thursday, November 20, 2008 1. Work on the midterm problems to make sure you understand everything clearly. 2. Read Sections 6.1–6.5 in the text. Try to work on all examples. 3. Which of the following matrices can be a covariance matrix? Justify your answer either by constructing a random vector X , as a function of the i.i.d. zero mean unit variance random variables Z 1 , Z 2 , and Z 3 , with the given covariance matrix, or by establishing a contradiction. (a) 1 2 0 2 (b) 2 1 1 2 (c) 1 1 1 1 2 2 1 2 3 (d) 1 1 2 1 2 3 2 3 3 4. Given a Gaussian random vector X N ( μ , Σ), where μ = (1 2 3) T and Σ = 9 0 0 0 4 1 0 1 1 . (a) What is P ( X 1 + X 2 + 2 X 3 < 0)? (b) Find the joint pdf on Y = A X , where A = 1 1 - 1 2 - 1 1 . 5. Packet switching. Let N P( λ ), i.e., Poisson with parameter λ , be the number of packets arriving at a switch per unit time. Each packet is routed to Output Port 1
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## This note was uploaded on 10/26/2011 for the course MATH 180C taught by Professor Eggers during the Winter '09 term at Aarhus Universitet.
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hw5 - UCSD ECE 153 Prof. Young-Han Kim Handout #18...
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Ask a homework question - tutors are online | 529 | 1,646 | {"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} | 3.015625 | 3 | CC-MAIN-2017-17 | longest | en | 0.834638 |
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10-27-2011 #1 yankees Guest Posts: n/a Tips For Games If any of you are trying to get high scores here are some tips for the games: Absolute Value Boxes- Make sure you know if each number is a positive number or a negative number. Call of Hierarchy- Be good with order of operations if your not very good at it the write down PEMDAS on a sheet of paper and keep it next to you. Order of Operations- Same thing as Call of Hierarchy. Plinko Probability- Answers the questions quickly and drop your chip a little bit to the side of the biggest number and don't get your chip stuck on the side. Solving Proportions- Memorize your multiplication and division facts. Baseball Exponents- Don't give up and keep going! Call of Geometry- Always try to get the ones on the top if your on that shape. Chopper Fractions & Decimals- Watch out for the middle and don't hit the top or the bottom! Circle Addition Equations- Try it on very hard so you get more points but make sure you click on them quickly! Coins Mystery- If you want use real coins to help you. I will post more later bye! Last edited by yankees; 12-30-2011 at 02:42 PM..
10-27-2011 #2 Mr. Hui Join Date: Mar 2005 Posts: 10,653 These tips are great. Thanks. __________________ Do Math and you can do Anything!
10-28-2011 #3 Jonathan W Guest Posts: n/a These are very helpful thanks!
10-28-2011 #4 yankees Guest Posts: n/a more Here are some more tips for games that are more popular. Deal or No Deal - Pick slowly and don't pick cases right next to each other. Geometric Shapes Avoider - Sometimes if you have Mozilla Firefox click during the game and there might be a glitch. Or you could get as many of the things that shrink your cursor and try to hide in one of the corners. Last edited by yankees; 12-30-2011 at 02:42 PM..
11-04-2011 #5
fatchicken21
Join Date: Nov 2011
Posts: 4
Quote:
Originally Posted by yankees If any of you are trying to get high scores here are some tips for the games: Absolute Value Boxes- Make sure you know if each number is a positive number or a negative number. Call of Hierarchy- Be good with order of operations if your not very good at it the write down PEMDAS on a sheet of paper and keep it next to you. Order of Operations- Same thing as Call of Hierarchy. Plinko Probability- Answers the questions quickly and drop your chip a little bit to the side of the biggest number and don't get your chip stuck on the side. Solving Proportions- Memorize your multiplication and division facts. Baseball Exponents- Don't give up and keep going! Call of Geometry- Always try to get the ones on the top if your on that shape. Chopper Fractions & Decimals- Watch out for the middle and don't hit the top or the bottom! Circle Addition Equations- Try it on very hard so you get more points but make sure you click on them quickly! Coins Mystery- If you want use real coins to help you. I will post more later bye!
thank you
11-19-2011 #6 Baseball Guest Posts: n/a Thank you "yankees". Very good tips!
11-22-2011 #7 zacmarz Join Date: Nov 2011 Posts: 944 Thanks
11-30-2011 #8 3.14159265 Join Date: Nov 2011 Posts: 11 Thank you very much yankees. I will see how good these tips work for me!
12-14-2011 #9
Knights2
Guest
Posts: n/a
Thanks!
Quote:
Originally Posted by yankees If any of you are trying to get high scores here are some tips for the games: Absolute Value Boxes- Make sure you know if each number is a positive number or a negative number. Call of Hierarchy- Be good with order of operations if your not very good at it the write down PEMDAS on a sheet of paper and keep it next to you. Order of Operations- Same thing as Call of Hierarchy. Plinko Probability- Answers the questions quickly and drop your chip a little bit to the side of the biggest number and don't get your chip stuck on the side. Solving Proportions- Memorize your multiplication and division facts. Baseball Exponents- Don't give up and keep going! Call of Geometry- Always try to get the ones on the top if your on that shape. Chopper Fractions & Decimals- Watch out for the middle and don't hit the top or the bottom! Circle Addition Equations- Try it on very hard so you get more points but make sure you click on them quickly! Coins Mystery- If you want use real coins to help you. I will post more later bye!
Thank you yankees! I will use your tip for Deal or No Deal.
- Knights2
12-29-2011 #10 bubbles101 Join Date: Dec 2011 Posts: 10 thank u so much absolutly USEFUL!!!!!!!!!
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## MCQ on Algebraic Equations and Simple Inequalities Worksheets 13 PDF Book Download
MCQ: Considering inequalities, nine is
1. < 11
2. < 5
3. < 7
4. > 14
A
MCQ: By solving equation a⁄4 + a⁄2 + a⁄6 = 5, value of 'a' will be
1. 7 5⁄11
2. 8 5⁄11
3. 5 5⁄11
4. 6 5⁄ 111
C
MCQ: By solving equation 6a⁄2 - 4a⁄3 - 2a⁄4 -4 =0, value of 'a' will be
1. 3 3⁄11
2. 2 3⁄9
3. 3 3⁄7
4. 4 3⁄13
C
MCQ: By solving inequality 1⁄3x > 6, answer will be
1. x > 20
2. x > 18
3. x > 22
4. x > 25
B
MCQ: If age of elder sister is 'a' and age of younger sister is 'b' then difference of ages is
1. 2(a + b)
2. 2a + 2b
3. a - b
4. 2(a - b)
C | 486 | 1,449 | {"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} | 3.734375 | 4 | CC-MAIN-2019-26 | latest | en | 0.828004 |
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### PRODUCT DESCRIPTION
Challenge your kid to use his knowledge about percentages in this fun game. Just roll the dice and race to calculate the percentage. Whoever gives the correct answer first earns a point and the first person to reach 15 points wins! In this game your kid will practice working out the percentages with the help of a calculator, a great tool for determining percentages.
Before getting started, it might help to briefly review how percentages work:
A percentage is a fraction or a part of a whole. Therefore, when working to find a percentage of a number, you will need to convert the percentage value to a decimal. For example, 25 % is equal to 0.25. You will multiply by the decimal amount to determine the percent. For example 25% of 60 is 0.25 x 60
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FREE | 288 | 1,136 | {"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} | 3.40625 | 3 | CC-MAIN-2017-09 | longest | en | 0.846485 |
https://ryansblog.xyz/post/5a3407c7-b2a7-42ed-9a0b-3e86fc2225f3 | 1,701,847,087,000,000,000 | text/html | crawl-data/CC-MAIN-2023-50/segments/1700679100583.31/warc/CC-MAIN-20231206063543-20231206093543-00282.warc.gz | 562,273,017 | 6,204 | # TurtleBot3 - Notes on Lidar HLS-LFCD-LDS
### Introduction
This post contains notes when learning the Lidar on TurtleBot3.
### Orientation of the Robot and the Lidar Coordinate System
The data from Lidar is a mapping from theta to distance. The theta is the position of the Lidar in a coordinate system. It's surprisingly hard to figure out this coordinate system. I still don't find any document that formally describes the zero degree axis of the Lidar on the TurtleBot3 robot. Here we will make some education guess based on materials found online. Of course, the only way to figure our the coordinate is to calibrate the Lidar.
First, we assume the photo on the TurtleBot3 website is the front of the robot. In the upper left part of the figure below, we can see that the rubber wheels are in front of the third stainless steel wheel. The bottom left part shows a bot in motion and the bottom right part of the figure shows the position of the lidar when the drive moves forward.
The upper right part of the figure shows the coordinate system of the lidar.
We could reasonably assume this coordinate system is also the coordinate system of the robot.
### LaserScan Message API
We digress a little here. TurtleBot3 is controlled by ROS, which defines a set of common APIs. For example, ROS defines the LaserScan message which can be used to report laser distance sensor data.
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# Single scan from a planar laser range-finder
#
# If you have another ranging device with different behavior (e.g. a sonar
# array), please find or create a different message, since applications
# the first ray in the scan.
#
# in frame frame_id, angles are measured around
# the positive Z axis (counterclockwise, if Z is up)
# with zero angle being forward along the x axis
float32 angle_min # start angle of the scan [rad]
float32 angle_max # end angle of the scan [rad]
float32 angle_increment # angular distance between measurements [rad]
float32 time_increment # time between measurements [seconds] - if your scanner
# is moving, this will be used in interpolating position
# of 3d points
float32 scan_time # time between scans [seconds]
float32 range_min # minimum range value [m]
float32 range_max # maximum range value [m]
float32[] ranges # range data [m] (Note: values < range_min or > range_max should be discarded)
float32[] intensities # intensity data [device-specific units]. If your
# device does not provide intensities, please leave
# the array empty.
Notes on intensities field found online
The intensities field should contain the measured intensity (i.e. brightness) of the reflected laser beams. This is, however, device specific and thus you cannot really make any assumptions about the values. In general, the higher the value, the brighter the reflected laser beam.
You can use the intensities to make some assumptions about the properties of the scanned material. E.g. it is used to detect reflectors and reflector tape, as there the intensity of the reflected beam is, in general, higher than from other material.
### HLS-LFCD-LDS Driver
The source code of the driver can be found here. We are interested in the part where the code publishes the Lidar data to ROS.
This code can be found in the hlds_laser_publisher.cpp file:
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while (ros::ok())
{
sensor_msgs::LaserScan::Ptr scan(new sensor_msgs::LaserScan);
laser.poll(scan);
rpms.data=laser.rpms;
laser_pub.publish(scan);
motor_pub.publish(rpms);
}
How does scan variable get populated? The fields of scan are set in the poll method in the script. We can also see in the code the communication is done through serial communication.
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...
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scan->ranges[359-index] = range / 1000.0;
scan->intensities[359-index] = intensity;
Becuase the sensor data is published directly, we should be able to get the sensor data without any ROS or TurtleBot3 packages. Here is the python code to read the Lidar data, it's a direct translation from the hlds_laser_publisher.cpp file (Some comments in the source code don't seem accurate so we just ignore them.)
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import os
import time
def clearScreen():
os.system('cls' if os.name == 'nt' else 'clear')
def convertByteToInt(byte):
return int.from_bytes(byte, 'big')
def getIntValueOfByte(byteArray, index):
return convertByteToInt(byteArray[index])
def getCurrentTimeInSecond():
return time.time()
class Lidar:
self.got_scan = False
self.lastDisplayTime = 0
def poll(self):
start_count = 0
raw_bytes = bytearray(2520)
good_sets = 0
motor_speed = 0
rpms = 0
while not self.got_scan:
if start_count == 0:
if raw_bytes[start_count] == 0xFA:
start_count = 1
elif start_count == 1:
if raw_bytes[start_count] == 0xA0:
start_count = 0
self.got_scan = True
toPrintResult = getCurrentTimeInSecond() - self.lastDisplayTime > 1
if toPrintResult:
self.lastDisplayTime = getCurrentTimeInSecond()
clearScreen()
print(">>> time = {}".format(self.lastDisplayTime))
for i in range(0, len(raw_bytes), 42):
if raw_bytes[i] == 0xFA and raw_bytes[i+1] == (0xA0 + int(i / 42)):
good_sets += 1
a = raw_bytes[i+3] << 8
b = raw_bytes[i+2]
motor_speed += a + b
rpms = int((a|b) / 10)
for j in range(i+4, i + 40, 6):
index = 6 * (int(i / 42)) + int((j - 4 - i) / 6)
byte0 = raw_bytes[j]
byte1 = raw_bytes[j + 1]
byte2 = raw_bytes[j + 2]
byte3 = raw_bytes[j + 3]
intensity = (byte1 << 8) + byte0
distRange = (byte3 << 8) + byte2
angle = 359 - index
if toPrintResult and distRange > 120 and distRange < 3500 and intensity > 3200:
print("theta = {}, range(m) = {}, intensity = {}, rpms = {}".format(359 - index, distRange / 1000.0, intensity, rpms))
else:
start_count = 0
if __name__ == '__main__':
import serial
baudrate = 230400
ser = serial.Serial('/dev/ttyUSB0', baudrate)
lidar = Lidar(ser)
while True:
lidar.poll()
lidar.got_scan = False
# ser.close()
----- END ----- | 1,752 | 6,195 | {"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} | 2.515625 | 3 | CC-MAIN-2023-50 | latest | en | 0.849034 |
https://www.coursehero.com/file/6662595/HW1v2/ | 1,516,174,701,000,000,000 | text/html | crawl-data/CC-MAIN-2018-05/segments/1516084886830.8/warc/CC-MAIN-20180117063030-20180117083030-00542.warc.gz | 882,571,371 | 81,545 | # HW1v2 - Homework#1 due week of Jan 31 Feb 1 Physics 375...
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Homework #1 – due week of Jan. 31 – Feb. 1 Physics 375 - Fuhrer Spring 2011 Show your work! 1) Suppose N = 9 students make the following measurements of the length of the classroom in meters: 5.056; 5.012; 5.084; 5.011; 5.113; 5.062; 5.099; 5.044; 5.055 Calculate the mean, standard deviation, and standard deviation of the mean for this sample distribution. Please do this by hand, rather than using software which automatically gives the values (and may be incorrect!) 2) You want to estimate the energy E stored in a capacitor, using the relation E = ½ CV 2 where C is the capacitance, and V the voltage across the capacitor. You measure the voltage across the capacitor to be 1.584 V with 0.7 % error, and the capacitor has a nominal value of 100 pF, with a 1.0 % error. 2A) What is the energy stored in the capacitor? 2B) What is your uncertainty in the energy? 2C) Which error, voltage or capacitance, contributes most to the uncertainty? 3) What does this script do?
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# Hands-On Math Chip Trading 1.1
Company: Ventura Educational Systems
Date Added: February 04, 2014 | Visits: 108
Hands-On Math: Chip Trading simulates the use of a popular math manipulative used to teach place value and addition and subtraction with regrouping.
Chip Trading is one of the best ways to help students place value. Students place chips representing one, ten, one hundred or one thousand on an interactive Playground to represent numbers. Chips can be regrouped or exchanged by dragging a virtual manipulative from one column to the next.
Using Hands-On Math: Chip Trading students can develop the following important mathematical concepts:
Place value concepts
Regrouping in the ones, tens and hundreds places
Naming numbers
Expanded notation
Hands-On Math: Chip Trading is a very useful way for student visualize images of numbers, intuitively understand place value and deepen their understanding of addition and subtraction. Use Chip Trading to have students represent numbers, as well as read and write the numbers. Rules for regrouping can be difficult for children. Use Chip Trading to illustrate regrouping by dragging and dropping chips from one column to another.
Multi-colored chips are used to represent numbers. Four types of chips are used Thousands, Hundreds, Tens and Ones.
Possible Topics:
Place Value
Subtraction
Regrouping
Expanded notation
By tapping an icon a randomly generated problem appears on the screen. Using Hands-On Math Chip Trading students enter the answer to the problem by moving chips in to columns. If an error occurs, specific feedback about the error is given. Progress toward learning objectives is tracked on the scoreboard.
-Explore place value.
-Learn when regrouping is needed.
Explore and Document
Activities at a variety of skill levels are also provided. Students are encouraged to document their discoveries in a journal. Here the students are asked to solve a problem that involves regrouping in the ones place. Students move chips to solve the problem. The scoreboard keeps track of how many problems are solved at each level.
Perfect for Small Group instruction
Environmentally Friendly Learning - (no need to photocopy activity pages for each student)
A Student-Centered Approach to Learning
Requirements: iOS 7.0 or later. Compatible with iPad.
Requirements: No special requirements Release Date: February 04, 2014 Platforms: iOS Users rating: 0/10
License: Shareware Cost: \$2.99 USD Size: 36.5 MB
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Hyperbolic functions
Calculation of hyperbolic functions
This content is licensed under Creative Commons Attribution/Share-Alike License 3.0 (Unported). That means you may freely redistribute or modify this content under the same license conditions and must attribute the original author by placing a hyperlink from your site to this work https://planetcalc.com/1116/. Also, please do not modify any references to the original work (if any) contained in this content.
This online calculator shows values of hyperbolic functions of given argument. The definitions of functions are below
Hyperbolic Functions
Digits after the decimal point: 2
Hyperbolic Functions
Hyperbolic sine
$\operatorname{sh}x=\frac{e^x-e^{-x}}{2}$
Hyperbolic cosine
$\operatorname{ch}x=\frac{e^x+e^{-x}}{2}$
Hyperbolic tangent
$\operatorname{th}x=\frac{\operatorname{sh}x}{\operatorname{ch}x} = \frac {e^x - e^{-x}} {e^x + e^{-x}} = \frac{e^{2x} - 1} {e^{2x} + 1}$
Hyperbolic cotangent
$\operatorname{cth}x=\frac{1}{\operatorname{th}x}$
Hyperbolic secant
$\operatorname{sech}x=\frac{1}{\operatorname{ch}x}$
Hyperbolic cosecant
$\operatorname{csch}x=\frac{1}{\operatorname{sh}x}$
Functions sh, ch, th, sech are continuous functions. Functions cth, csch are not defined for x=0.
Hyperbolic sine is increasing function passing through zero - $\operatorname{sh}0=0$.
Hyperbolic cosine is even function where $\operatorname{ch}0=1$ is the minimum. | 428 | 1,482 | {"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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 8, "/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} | 3.828125 | 4 | CC-MAIN-2019-09 | longest | en | 0.563038 |
http://zoi.utia.cas.cz/convolution-moment-invariants | 1,611,391,312,000,000,000 | text/html | crawl-data/CC-MAIN-2021-04/segments/1610703536556.58/warc/CC-MAIN-20210123063713-20210123093713-00696.warc.gz | 199,622,330 | 5,779 | ## Moment invariants to convolution
Some radiometric degradations of images, as a wrong focus, camera and/or scene motion, camera vibrations, and taking images through a turbulent medium such as atmosphere or water, can be described by combination of convolution and noise
where f(x,y) is an image function, h(x,y) is a point spread function (PSF) of the degradation, and n(x,y) is an additive random noise. If we have no limitation on PSF, invariants to such degradation cannot exist, on the other hand, the more constraints is satisfied by PSF, the more invariants can be constructed. All the above degradations can be described by a convolution with a centrosymmetric PSF, i.e. h(x,y)=h(-x,-y). In this case, we can construct the invariants by the following recursive formula.
If (p+q) is even, then
If (p+q) is odd, then
The blur invariants have their counterparts in Fourier domain, tangens of the phase of the Fourier spectrum of the image function is convolution invariant.
If we know the PSF satisfies some additional contraint, we can construct additional invariants. It is the case e.g. N-fold rotational symmetry, circular symmetry, or Gaussian PSF.
Sometimes, the convolution degradation is combined with some geometric degradation. We can use combined rotation and blur invariants or combined affine and blur invariants in these cases.
To demonstrate the performance of the above described invariants we apply them to the problem of template matching in a blurred and noisy scene. It was inspired by a remote sensing application area, we try to perform matching without any previous de-blurring by means of our blur invariants. We ran this experiment on real satellite images but the blur and noise were introduced artificially that gives us a possibility to control their amount and to quantitatively evaluate the results. We used the invariants normalized by a power of μ00 to image contrast and magnitude so they would have roughly the same range of values regardless of p and q.
The matching algorithm itself is straightforward. We search the blurred image g(x,y) and for each possible position of the template calculate the Euclidean distance in the space of blur invariants between the template and the corresponding window in g(x, y). The matching position of the template is determined by the minimum distance. The only user-defined parameter in the algorithm is the maximum order r of the invariants used. In this experiment we used r = 7, that means we applied 18 invariants from 3rd to 7th order. Three templates 48×48 were extracted from the 512×512 high-resolution SPOT image (City of Plzeň)
and contain significant local landmarks – the road crossing, the apartment block, and the confluence of two rivers
To simulate an acquisition by another sensor with a lower spatial resolution, the image was blurred by Gaussian masks of the size from 3×3 to 21×21 and corrupted by a Gaussian white noise with standard deviation ranging from 0 to 40 each. In all blurred and noisy frames, the algorithm attempted to localize the templates. As one can expect, the success rate of the matching depends on the amount of blur and on the noise level.
An example of a frame in which all three templates were localized correctly The results are summarized here
The boundary effect is important limitation of this method. Due to the blurring, the pixels laying near the boundary of the template inside the image are affected by those pixels laying outside the template. Since the invariants are calculated from a bounded area of the image where the blurring is not exactly a convolution, they are no longer invariant which might lead to mismatch.
Contact person: Jan Flusser , Tomáš Suk
Publications:
1. Flusser Jan, Suk Tomáš, Zitová Barbara: Moments and Moment Invariants in Pattern Recognition, Wiley & Sons Ltd., 2009 (in print).
2. Boldyš Jiří, Flusser Jan: Extension of Moment Features’ Invariance to Blur, Journal of Mathematical Imaging and Vision vol.32, 1 (2008), p. 227-238, Download PDF
3. Flusser Jan, Boldyš Jiří, Zitová Barbara: Moment forms invariant to rotation and blur in arbitrary number of dimensions, IEEE Transactions on Pattern Analysis and Machine Intelligence vol.25, 2 (2003), p. 234-246, Download PDF
4. Zitová Barbara, Flusser Jan: Invariants to convolution and rotation, Invariants for Pattern Recognition and Classification, p. 23-46, Eds: Rodrigues M. A ., World Scientific, (Singapore 2000)
5. Flusser Jan, Boldyš Jiří, Zitová Barbara: Invariants to convolution in arbitrary dimensions, Journal of Mathematical Analysis and Applications vol.13, 2 (2000), p. 101-113, Download PDF
6. Flusser Jan, Zitová Barbara: Combined invariants to linear filtering and rotation, International Journal of Pattern Recognition and Artificial Intelligence vol.13, 8 (1999), p. 1123-1136, Download PDF
7. Flusser Jan, Suk Tomáš: Degraded image analysis: An invariant approach, IEEE Transactions on Pattern Analysis and Machine Intelligence vol.20, 6 (1998), p. 590-603, Download PDF
8. Flusser Jan, Suk Tomáš: Classification of degraded signals by the method of invariants, Signal Processing vol.60, 2 (1997), p. 243-249, Download PDF
9. Flusser Jan, Suk Tomáš, Saic Stanislav: Recognition of images degraded by linear motion blur without restoration, Computing. Supplement vol.11, p. 37-51, Download PDF
10. Flusser Jan, Suk Tomáš, Saic Stanislav: Recognition of blurred images by the method of moments, IEEE Transactions on Image Processing vol.5, 3 (1996), p. 533-538, Download PDF
11. Flusser Jan, Suk Tomáš, Saic Stanislav: Image features invariant with respect to blur, Pattern Recognition vol.28, 11 (1995), p. 1723-1732, Download PDF
12. Flusser Jan, Suk Tomáš, Saic Stanislav: Moment-based features for description and recognition of blurred images, Theoretical Foundations of Computer Vision, p. 5, Eds: Klette R., Kropatsek W., Solina F., (Dagstuhl 1994), Theoretical Foundations of Computer Vision,
(Dagstuhl, DE, 14.03.1994-18.03.1994)
13. Flusser Jan, Suk Tomáš: Description and Recognition of Blurred Images by the Method of Blur Invariants, ÚTIA AV ČR, (Praha 1994)Research Report 1806
Relevant publications by other authors:
1. V. Ojansivu and J. Heikkilä, “Image registration using blur-invariant phase correlation,” IEEE Signal Processing Letters, vol. 14, no. 7, pp. 449–452, 2007.
2. A. Stern and N. Kopeika, “Analytical method to calculate optical transfer functions for image motion and vibrations using moments,” Journal of the Optical Society of America A, vol. 14, no. 2, pp. 388–396, 1997. | 1,555 | 6,558 | {"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-2021-04 | latest | en | 0.914108 |
https://www.cfd-online.com/Forums/openfoam-bugs/68140-alpha-alpha1-interfoam-interdymfoam-print.html | 1,513,426,112,000,000,000 | text/html | crawl-data/CC-MAIN-2017-51/segments/1512948587577.92/warc/CC-MAIN-20171216104016-20171216130016-00460.warc.gz | 720,348,623 | 2,334 | CFD Online Discussion Forums (https://www.cfd-online.com/Forums/)
- OpenFOAM Bugs (https://www.cfd-online.com/Forums/openfoam-bugs/)
- - alpha or alpha1 in interFoam & interDyMFoam (https://www.cfd-online.com/Forums/openfoam-bugs/68140-alpha-alpha1-interfoam-interdymfoam.html)
wavytracy September 8, 2009 06:45
alpha or alpha1 in interFoam & interDyMFoam
From the damBreak tutorial of version 1.5, fvSchemes looks like:
{
default Gauss linear;
}
divSchemes
{
div(rho*phi,U) Gauss limitedLinearV 1;
div(phi,gamma) Gauss vanLeer;
div(phirb,gamma) Gauss interfaceCompression;
}
Now, I was under the impresssion that gamma was replaced by alpha1 in version 1.6. Yet, here is the same excerpt from v1.6 damBreak tutorial, which contains alpha and alpha1:
{
default Gauss linear;
}
divSchemes
{
div(rho*phi,U) Gauss limitedLinearV 1;
div(phi,alpha) Gauss vanLeer;
div(phirb,alpha) Gauss interfaceCompression;
}
and it isn't even consistent - take a look at the same excerpt from interDyMFoam v1.6
{
default Gauss linear;
}
divSchemes
{
div(rho*phi,U) Gauss upwind;
div(phi,alpha) Gauss vanLeer;
div(phirb,alpha) Gauss interfaceCompression;
}
So what is the difference between alpha and alpha1. Am I misunderstanding something, or is this a bug?
Cheers,
Tracy.
henry September 9, 2009 02:54
alpha1 is the phase fraction of phase 1 in a multi-phase system, alpha in the control dictionaries refers to any phase. The reason for the "inconsistency" is to ensure that the discretisation schemes are the same for all phases.
H
wavytracy September 9, 2009 21:23
Thank you.
But the "inconsistency" refers to the line
in the controlDict of the interFoam tutorial,
compared to the line
in the controlDict of the interDyMFoam tutorial. | 503 | 1,748 | {"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} | 2.640625 | 3 | CC-MAIN-2017-51 | latest | en | 0.774014 |
https://www.kiddom.co/standards/616-nebraska-mathematics-learning-standards/grade-6 | 1,571,370,235,000,000,000 | text/html | crawl-data/CC-MAIN-2019-43/segments/1570986677884.28/warc/CC-MAIN-20191018032611-20191018060111-00490.warc.gz | 964,898,371 | 9,107 | Click on any standard to search for aligned resources. This data may be subject to copyright. You may download a CSV of the Nebraska Mathematics Learning Standards if your intention constitutes fair use.
Plan, assess, and analyze learning aligned to these standards using Kiddom.
#### MA 6.1.1.a
Show equivalence among common fractions, decimals and percents
#### MA 6.1.1.b
Compare and order positive and negative integers
#### MA 6.1.1.c
Identify integers less than 0 on a number line
#### MA 6.1.1.d
Represent large numbers using exponential notation (e.g., 1,000 = 103)
#### MA 6.1.1.e
Identify the prime factorization of numbers (e.g., 12 = 2 x 2 x 3 or 22 x 3)
#### MA 6.1.1.f
Classify numbers as natural, whole, or integer
#### MA 6.1.2.a
Use drawings, words, and symbols to explain the meaning of addition and subtraction of fractions
#### MA 6.1.2.b
Use drawings, words, and symbols to explain the meaning of addition and subtraction of decimals
#### MA 6.1.3.a
Multiply and divide positive rational numbers
#### MA 6.1.3.b
Select and apply the appropriate method of computation when problem solving (e.g., models, mental computation, paper-pencil, technology, divisibility rules)
#### MA 6.1.4
Use appropriate estimation methods to check the reasonableness of solutions for problems involving positive rational numbers
#### MA 6.2.1
Justify the classification of three dimensional objects
#### MA 6.2.2
Identify the ordered pair of a plotted point in the coordinate plane
#### MA 6.2.3
Perform and describe positions and orientation of shapes under single transformations (translation, rotation, reflection) not on a coordinate plane
#### MA 6.2.4
Identify two-dimensional drawings of three-dimensional objects
#### MA 6.2.5.a
Estimate and measure length with customary and metric units to the nearest 1/16 inch and mm
#### MA 6.2.5.b
Measure volume/capacity using the metric system
#### MA 6.2.5.c
Convert length, weight (mass), and liquid capacity from one unit to another within the same system
#### MA 6.2.5.d
Determine the perimeter of polygons
#### MA 6.2.5.e
Determine the area of parallelograms and triangles
#### MA 6.2.5.f
Determine the volume of rectangular prisms
#### MA 6.3.1.a
Describe and create simple algebraic expressions (e.g., one operation, one variable) from words and tables
#### MA 6.3.1.b
Use a variable to describe a situation with an equation (e.g., one-step, one variable)
#### MA 6.3.1.c
Identify relationships as increasing, decreasing, or constant
#### MA 6.3.2.a
Model contextualized problems using various representations (e.g., graphs, tables)
#### MA 6.3.2.b
Represent a variety of quantitative relationships using symbols and words
#### MA 6.3.3.a
Explain the multiplication property of equality (e.g., if a = b, then ac = bc)
#### MA 6.3.3.b
Evaluate numerical expressions containing multiple operations with respect to order of operations (e.g., 2 + 4 x 5)
#### MA 6.3.3.c
Evaluate simple algebraic expressions involving multiplication and division
#### MA 6.3.3.d
Solve one-step equations involving positive rational numbers
#### MA 6.3.3.e
Identify and explain the properties of equality used in solving one-step equations (e.g., addition, subtraction, division)
#### MA 6.4.1.a
Represent data using stem and leaf plots, histograms, and frequency charts
#### MA 6.4.1.b
Compare and interpret data sets and their graphical representations
#### MA 6.4.1.c
Find the mean, median, mode, and range for a set of data
#### MA 6.4.1.d
Compare the mean, median, mode, and range from two sets of data
#### MA 6.4.2
Make predictions based on data and create questions to further investigate the quality of the predictions
#### MA 6.4.2.a
Describe the theoretical probability of an event using a fraction, percentage, decimal, or ratio
#### MA 6.4.2.b
Compute theoretical probabilities for independent events
#### MA 6.4.2.c
Find experimental probability for independent events | 1,025 | 3,995 | {"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} | 3.65625 | 4 | CC-MAIN-2019-43 | latest | en | 0.771998 |
https://kartonedesign.it/temperature-conversion-worksheet-kelvin-celsius-fahrenheit-pdf.html | 1,618,765,090,000,000,000 | text/html | crawl-data/CC-MAIN-2021-17/segments/1618038507477.62/warc/CC-MAIN-20210418163541-20210418193541-00182.warc.gz | 430,179,319 | 14,225 | • Palomino truck campers for sale craigslist
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Here you will find our Temperature Conversion Worksheet page which will help your child to learn and practice converting between celsius and fahrenheit. On this webpage, you will find a range of measurement worksheets to help your child learn to convert between temperatures in Celsius(°C)...
# Temperature conversion worksheet kelvin celsius fahrenheit pdf
• To get temperatures in the Kelvin scale, add 273.15 degrees to the Celsius temperature: K = C + 273.15. To go from kelvins to degrees Celsius, do the opposite: Subtract 273.15 from the Kelvin temperature. Then you can convert the Celsius temperature to Fahrenheit if you want to. Here’s a quick temperature conversion system that may be easier ...
• Celsius, sometimes referred to as centigrade, is a unit for temperature measurement and a related temperature scale. It has got the name of its developer The decimals value is the number of digits to be calculated or rounded of the result of fahrenheit to celsius conversion. You can also check the...
• These three files allow you to convert a temperature between Celsius, Kelvin, and Fahrenheit. All included in this folder. Configured to run under the PRGM menu or MirageOS. tempconverter_75.zip: 1k: 12-03-08: CelcFahr Version 1.2 Simple unit converter that supports Farhenheit, Celsius, and Kelvin.
• Sep 21, 2013 · The units on the Kelvin scale are the same size as those of the Celsius scale, except that the Kelvin scale sets the lowest temperature at 0. Conversion rates. Fahrenheit to Celsius: Subtract 32 ...
• Aug 13, 2020 · Figure \(\PageIndex{1}\): A Comparison of the Fahrenheit, Celsius, and Kelvin Temperature Scales. Because the difference between the freezing point of water and the boiling point of water is 100° on both the Celsius and Kelvin scales, the size of a degree Celsius (°C) and a kelvin (K) are precisely the same.
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• This is a simple Celsius to Fahrenheit and Fahrenheit to Celsius temperature calculator. support negative temperature. very easy to use. farenheit celcius farenheit in celcius celcius to farenheit conversion farenheit celcius celcius to f convert farenheit to celcius from farenheit to celcius centigrade to farenheit celcius to f conversion fahrenheit to celsius converter 100 farenheit to ...
• Step 4 – Convert degrees kelvin into Fahrenheit. Now you have converted the TOA r into degrees kelvin. If you want to convert this into Celsius, you need to subtract 273.15 from the degrees kelvin. For Fahrenheit, multiply the degrees Celsius by 1.8 and then add 32. You can do this as one step within the Band Arithmetic function.
• Temperature scales conversion calculator for converting between Fahrenheit °F into Celsius °C ( Centigrade ) to Kelvin K, Reaumur This converter allows you to do instant conversions between various temperature measurements in °F, °C, K, °r, °R scales. You may enter whole numbers...
• Fahrenheit degrees = (9/5) X (Centigrade degrees) + 32 To convert between Celsius or Centigrade and Kelvin use the following formula: Kelvin degrees = Centigrade degrees + 273
• Use the above formulas above to convert the following: 1) 250 Kelvin to Celsius 2) 339 Kelvin to Celsius 3) 17 Celsius to Kelvin 4) 55 Celsius to Kelvin 5) 89.5 Fahrenheit to Celsius 6) 383 Kelvin to Fahrenheit o o o. Handout #2 1/27/09
• Apr 13, 2019 · Temperature Conversion Worksheet : Convert the following numbers from degrees Fahrenheit to degrees Celsius, … Thermometers : Types of Thermometers – The Liquid in Glass Thermometer, The mercury-in-glass thermometer, The alcohol-in-glass thermometer, General Equation for Temperature calculation using a liquid in glass thermometer, …
• To get temperatures in the Kelvin scale, add 273.15 degrees to the Celsius temperature: K = C + 273.15. To go from kelvins to degrees Celsius, do the opposite: Subtract 273.15 from the Kelvin temperature. Then you can convert the Celsius temperature to Fahrenheit if you want to. Here’s a quick temperature conversion system that may be easier ...
• The SI unit for temperature is the kelvin (K). Although 0 K is much colder than 0°C, a change of 1 K is equal to a change of 1°C. Three Temperature Scales 37˚ 310 212˚ 98.6˚ 32˚ 100˚ 20˚ 0˚ 373 293 273 68˚ Water boils Fahrenheit Celsius Kelvin Body temperature Room temperature Water freezes Temperature Conversions Table To convert ...
• Where: T c is temperature in Celsius T f is temperature in Fahrenheit To convert between degrees Fahrenheit (°F) and Kelvin (K): T f = (+ 32 5 9 ×(T 73.15 ) k −2) T K = (5 273.16 9 ×(T f − 32))+ Where: T f is temperature in Fahrenheit T K is temperature in Kelvin To convert between degrees Fahrenheit (°F) and Rankine (R): T f = T R ...
• Dec 24, 2020 · Because Fahrenheit degrees are 5/9 of a Celsius degree, it is easier to make more exact measurements without using fractions in the Fahrenheit scale. This scale continues to be used in the United States, although most other countries that use the metric system changed to Celsius in the 1960s and 1970s.
• This temperature conversion tool helps you convert from any temperature unit in an instance. When it comes to temperature conversion (often shortened to temp conversion), it is easy to convert Celsius to Kelvin, however if you want to convert Celsius to Fahrenheit, it becomes more tricky...
• To convert from Celsius to Fahrenheit temperatures, use the following formula: Temperature in °F = 1.8 x (Temperature in °C) + 32 In addition, there is another scale, used for scientific calculation, called the Kelvin scale. To convert between Celsius and Kelvin temperatures, simply add or subtract 273°:
• Aug 14, 2014 · where °F and °C are the temperatures in Fahrenheit and Celsius respectively. Plug 101.5 °F into the formula °C = 5 ⁄ 9 (101.5 – 32) °C = 5 ⁄ 9 (69.5) °C = 38.6 °C. Answer: The average body temperature of a cat in Celsius is 38.6 °C. For more help, try these other temperature conversion example problems: Convert Celsius to ...
• For example, if you want to know a temperature of 55 °F is equivalent to how many °C, you start by subtracting 32 from 55 °F as in 55-32 = 23, then multiply the answer by 5/9 or 0.55 as in 23 x 0.55 = 12.78 °C On the other hand, to convert temperature from Celsius to Fahrenheit the following conversion formula is used °F = 9 °C + 32 or ...
• Temperature Conversion between Fahrenheit and Celsius Formula: F = (9/5)C + 32 5F = 9C + 160 Example: 100F converted into C 5(100) = 9C + 160 500 - 160
• This makes Celsius (degC) and Fahrenheit (degF) affine units because they are both related to kelvin with an affine conversion. Rankine ( degR ) is defined in terms of kelvin with a zero linear offset and, therefore, is not an affine unit.
• Sep 20, 2018 · To convert °F into °C, you can take the °F temperature, subtract 32, and then divide by 1.8 to get °C. For example, 74°F -32 = 42, 42/1.8 = 23°C). Kelvin – The Kelvin scale was first proposed by Scottish Lord Kelvin as a scientific scale based on the concept of absolute zero, the temperature at which all movement in matter would stop or ...
• The formula to convert temperatures from Fahrenheit (F) to Kelvin (K) is K = 5/9(F - 32) + 273.15. Solve this formula for F. Referring to Problem 5, above, if the temperature is 300 ° Kelvin, what is the temperature in Fahrenheit? z - 6y + 2 = x + 2 xy = z + 2 3y - 2x = 5z + 2 equation x - 1/2y = 6z 3z + .5y = 11x 6x = y - z 15x + 2y = z 2z ...
• Nov 01, 2018 · Celsius to fahrenheit conversion chart celsius to fahrenheit chart gallery what is 120 c in gas mark oven temperatures conversion chart celsius to fahrenheit chart template 6 Best Temperature Conversion Chart Printable PrintableePrintable Temperature Conversion Charts6 Best Temperature Conversion Chart Printable PrintableeCelsius To Fahrenheit Conversion Chart Edit Fill Sign HandyTemperature ...
• Dec 17, 2015 · Ask the user to give the input of a temperature and then again ask the user to give the units of the temperature which was given input before. For now use Celsius and Fahrenheit. If the user has given the input as C then convert from Celsius to Fahrenheit and similarly if the user gives the input as F then convert from Fahrenheit to Celsius.
Temperature Difference Converter. Temperature Difference. C° °F. Kelvin - K. Another scale (common in science) is Kelvin, or the Absolute Temperature Scale. On the Kelvin scale the coldest temperature possible, -273 °C, has a value of 0 Kelvin (0 K) and is called the absolute zero.
Enter Celsius: automatically converts to Fahrenheit, Kelvin, Rankine & Reamur. Mathforum.org states that 32 degrees was the lowest temperature he recorded by mixing water with common salt, which was how the first ice cream freezers used to work.
Temperature Conversion Worksheet Answer Key | akademiexcel.com Online Library Temperature Conversion Worksheet Answer Key Temperature conversion work 2, Temperature conversion wksht key20130116152559536, Convert fahrenheit to celsius 1, Title fahrenheitcelsius temperature conversions, Reading thermometers in fahrenheit and celsius, Healthcare math
Temperature Conversion between Fahrenheit and Celsius Answers: Use Regular Formulas: i) = , ii) °F= to do temperature conversion, and use New Formulas: i) , ii) . to check your Answers. 1) 18 0C = 64.4 0F, 11) 50 0F = 10 0C,
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• Outward chakram build | 3,144 | 12,544 | {"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} | 2.609375 | 3 | CC-MAIN-2021-17 | latest | en | 0.752602 |
https://homework.cpm.org/category/CON_FOUND/textbook/ac/chapter/4/lesson/4.2.4/problem/4-105 | 1,713,447,884,000,000,000 | text/html | crawl-data/CC-MAIN-2024-18/segments/1712296817206.54/warc/CC-MAIN-20240418124808-20240418154808-00270.warc.gz | 268,970,244 | 14,939 | ### Home > AC > Chapter 4 > Lesson 4.2.4 > Problem4-105
4-105.
When Ellen started with Regina's favorite number and tripled it, the result was twelve more than twice the favorite number. Define a variable, write an equation, and then use the equation to find Regina's favorite number.
Define a variable.
$r$ = Regina's favorite number
Use the first sentence to write an equation.
Look at the important parts of the problem above.
$\color{blue}{3r} \color{purple}{=} \color{orange}{12} + \color{green}{2r}$
Solve for $r$. | 139 | 528 | {"found_math": true, "script_math_tex": 3, "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} | 3.78125 | 4 | CC-MAIN-2024-18 | latest | en | 0.822922 |
https://www.jiskha.com/questions/765875/I-keep-getting-28-19-for-this-problem-but-it-doesnt-check-with-the-solution-in | 1,539,812,711,000,000,000 | text/html | crawl-data/CC-MAIN-2018-43/segments/1539583511216.45/warc/CC-MAIN-20181017195553-20181017221053-00233.warc.gz | 976,384,743 | 5,614 | # MAth
I keep getting -28/19 for this problem, but it doesn't check with the solution in the back of the book. Help please..
solve the equation
7d-(1/2)(2d-4)=(-5/4)(d+4)
1. 0
1. 7 d - ( 1 / 2 ) ( 2 d - 4 ) = ( - 5 / 4 ) ( d + 4 )
7 d - ( 1 / 2 ) * 2 d - ( 1 / 2 ) * ( - 4 = ( - 5 / 4 ) * d + ( - 5 / 4 ) * 4
7 d - d + 2 = ( - 5 / 4 ) * d - 5
6 d + 2 = ( - 5 / 4 ) * d - 5
6 d + ( 5 / 4 ) d = - 5 - 2
( 24 / 4 ) d + ( 5 / 4 ) d = - 7
( 29 / 4 ) d = - 7 Multiply both sides by 4
29 d = - 28 Divide both sides by 29
d = - 28 / 29
posted by Anonymous
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http://ma.mathforcollege.com/youtube/06guassian/gaussian_04sle_determinantbackground.html | 1,627,627,039,000,000,000 | text/html | crawl-data/CC-MAIN-2021-31/segments/1627046153934.85/warc/CC-MAIN-20210730060435-20210730090435-00260.warc.gz | 27,799,747 | 4,417 | INTRODUCTION TO MATRIX ALGEBRA Transforming Matrix Algebra for the STEM Undergraduate HOME | TOPICS | VIDEOS | TEXTBOOK | PPT | QUIZZES | PROBLEM SET | CONTACT | MATH FOR COLLEGE | NUMERICAL METHODS
GAUSSIAN ELIMINATION (CHAPTER 06)
Determinant of a Matrix using Forward Elimination : Background
By Autar Kaw
TOPIC DESCRIPTION
Learn how to find the determinant of a matrix using forward elimination steps of Gaussian Elimination.
This video teaches you how to find the determinant of a matrix using forward steps of Gaussian Elimination.
ALL VIDEOS FOR THIS TOPIC
Naive Gaussian elimination: Theory: Part 1 of 2 [YOUTUBE 10:27] [TRANSCRIPT]
Naive Gaussian elimination: Theory: Part 2 of 2 [YOUTUBE 2:22] [TRANSCRIPT]
Naive Gauss Elimination Method: Example: Part 1 of 2 (Forward Elimination) [YOUTUBE 10:49] [TRANSCRIPT]
Naive Gauss Elimination Method: Example: Part 2 of 2 (Back Substitution) [YOUTUBE 6:40] [TRANSCRIPT]
Pitfalls of Naive Gauss Elimination Method: [YOUTUBE 7:20] [TRANSCRIPT]
Naive Gauss Elimination: Round-off Error Issues: Example: Part 1 of 3 [YOUTUBE 7:20] [TRANSCRIPT]
Naive Gauss Elimination: Round-off Error Issues: Example: Part 2 of 3 [YOUTUBE 7:40] [TRANSCRIPT]
Naive Gauss Elimination: Round-off Error Issues: Example: Part 3 of 3 [YOUTUBE 8:07] [TRANSCRIPT]
Gaussian Elimination With Partial Pivoting: Theory [YOUTUBE 10:39] [TRANSCRIPT]
Gaussian Elimination With Partial Pivoting: Example: Part 1 of 3 (Forward Elimination) [YOUTUBE 7:15] [TRANSCRIPT]
Gaussian Elimination With Partial Pivoting: Example: Part 2 of 3 (Forward Elimination) [YOUTUBE 10:08] [TRANSCRIPT]
Gaussian Elimination With Partial Pivoting: Example: Part 3 of 3 (Back Substitution) [YOUTUBE 6:18] [TRANSCRIPT]
Gaussian Elimination With Partial Pivoting: Round-off Error Issues: Example: Part 1 of 3 [YOUTUBE 8:58] [TRANSCRIPT]
Gaussian Elimination With Partial Pivoting: Round-off Error Issues: Example: Part 2 of 3 [YOUTUBE 8:17] [TRANSCRIPT]
Gaussian Elimination With Partial Pivoting: Round-off Error Issues: Example: Part 3 of 3 [YOUTUBE 5:48] [TRANSCRIPT]
Determinant of a Matrix Using Forward Elimination Method: Background [YOUTUBE 5:17] [TRANSCRIPT]
Determinant of a Matrix Using Forward Elimination Method: Example [YOUTUBE 10:07] [TRANSCRIPT]
COMPLETE RESOURCES
Get in one place the following: a textbook chapter, a PowerPoint presentation, individual YouTube lecture videos, worksheets to illustrate the method and its convergence, and multiple-choice questions on Gaussian Elimination. | 703 | 2,524 | {"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} | 3.65625 | 4 | CC-MAIN-2021-31 | latest | en | 0.647991 |
http://thermalfluidscentral.org/encyclopedia/index.php?title=Film_Boiling_Analysis_in_Porous_Media&diff=6411&oldid=4324 | 1,606,648,254,000,000,000 | text/html | crawl-data/CC-MAIN-2020-50/segments/1606141197593.33/warc/CC-MAIN-20201129093434-20201129123434-00280.warc.gz | 93,853,070 | 9,708 | # Film Boiling Analysis in Porous Media
(Difference between revisions)
Revision as of 15:58, 2 June 2010 (view source)← Older edit Revision as of 01:57, 9 July 2010 (view source)Newer edit → Line 1: Line 1: - Film boiling of liquid saturated in a porous medium at an initial temperature of {T_\infty } < {T_{sat}} next to a vertical, impermeable heated wall at a temperature of + [[Image:boiling_g_(1).gif|thumb|600 px|alt= Film boiling in porous media|
'''Film boiling in porous media.'''
]] - [[Image:boiling_g_(1).gif|thumb|600 px|alt= Film boiling in porous media|Figure 1: Film boiling in porous media.]] + Film boiling of liquid saturated in a porous medium at an initial temperature of ${T_\infty } < {T_{sat}}$ next to a vertical, impermeable heated wall at a temperature of ${T_w} > {T_{sat}}$ is analyzed (see figure). Vapor generated at the liquid-vapor interface flows upward due to buoyancy force. The liquid adjacent to the vapor layer is dragged upward by the vapor. The temperature at the liquid-vapor interface is at the saturation temperature. There are velocity and thermal boundary layers in the liquid phase adjacent to the vapor film. The solution of the film boiling problem requires solutions of vapor and liquid flow, as well as heat transfer in both the vapor and liquid phases. It is assumed that boundary layer approximations are applicable to the vapor film and to convection heat transfer in the liquid phase. It is further assumed that the vapor flow is laminar, two-dimensional; Darcy’s law is applicable in both the vapor and liquid phases. The continuity, momentum, and energy equations in the vapor film are - + - ${T_w} > {T_{sat}}$ is analyzed (see Fig. 1; [[#References|Cheng and Verma, 1981; Nield and Bejan, 1999]]). Vapor generated at the liquid-vapor interface flows upward due to buoyancy force. The liquid adjacent to the vapor layer is dragged upward by the vapor. The temperature at the liquid-vapor interface is at the saturation temperature. There are velocity and thermal boundary layers in the liquid phase adjacent to the vapor film. The solution of the film boiling problem requires solutions of vapor and liquid flow, as well as heat transfer in both the vapor and liquid phases. It is assumed that boundary layer approximations are applicable to the vapor film and to convection heat transfer in the liquid phase. It is further assumed that the vapor flow is laminar, two-dimensional; Darcy’s law is applicable in both the vapor and liquid phases. The continuity, momentum, and energy equations in the vapor film are +
$\frac{{\partial {u_v}}}{{\partial x}} + \frac{{\partial {v_v}}}{{\partial y}} = 0\qquad \qquad(1)$
$\frac{{\partial {u_v}}}{{\partial x}} + \frac{{\partial {v_v}}}{{\partial y}} = 0\qquad \qquad(1)$
Line 65: Line 63: - The above film boiling problem can be solved using a similarity solution like that for film condensation in porous media discussed in Section 8.5.2. The results + The above film boiling problem can be solved using a similarity solution like that for [[Film Condensation on an Inclined Wall|film condensation in porous media]]. - [[Image:boiling_j_(1).jpg|thumb|400 px|alt= Heat transfer for film boiling on a vertical wall in porous media|Figure 2: Heat transfer for film boiling on a vertical wall in porous media]] + ==References== - obtained by [[#References|Cheng and Verma (1981)]] are shown in Fig. 2. The dimensionless parameters used in Fig. 2 are defined as + Cheng, P., and Verma, A.K., 1981, “The Effect of Subcooling Liquid on Film Boiling about a Vertical Heated Surface in a Porous Medium,” ''International Journal of Heat and Mass Transfer'', Vol. 24, pp. 1151-1160. -
$\begin{array}{l} + Faghri, A., and Zhang, Y., 2006, ''Transport Phenomena in Multiphase Systems'', Elsevier, Burlington, MA - {\rm{N}}{{\rm{u}}_x} = \frac{{{h_x}x}}{{{k_{mv}}}} = \frac{{{{q''}_w}x}}{{{k_{mv}}({T_w} - {T_{sat}})}}\begin{array}{*{20}{c}} + - , & {{\rm{R}}{{\rm{a}}_{xv}} = \frac{{({\rho _\ell } - {\rho _v})gKx}}{{{\mu _v}{\alpha _{mv}}}}} \\ + - \end{array} \\ + - \begin{array}{*{20}{c}} + - {R = \frac{{{\rho _v}}}{{{\rho _\ell }}}\left[ {\frac{{{\mu _\ell }{\alpha _{mv}}({\rho _\ell } - {\rho _v}){c_{p\ell }}}}{{{\mu _v}{\alpha _{m\ell }}{\rho _\ell }{\beta _\ell }{h_{\ell v}}}}} \right],} & {{\rm{J}}{{\rm{a}}_v} = \frac{{{c_{p\ell }}({T_{sat}} - {T_\infty })}}{{{h_{\ell v}}}},} & {} \\ + - \end{array} \\ + - {\rm{J}}{{\rm{a}}_\ell } = \frac{{{c_{pv}}({T_w} - {T_{sat}})}}{{{h_{\ell v}}}} \\ + - \end{array}\qquad \qquad(13)$
+ - + - where Jakob numbers ${\rm{J}}{{\rm{a}}_v}$ and ${\rm{J}}{{\rm{a}}_\ell }$, measure the degrees of superheat in the vapor and subcooling in the liquid. For all cases shown in Fig. 2, the effect of liquid subcooling on the heat transfer is insignificant. The effect of vapor superheat on heat transfer is significant when ${\rm{J}}{{\rm{a}}_v}$ is less than 2. The following asymptotic result can be obtained from Fig. 2: + Faghri, A., Zhang, Y., and Howell, J. R., 2010, ''Advanced Heat and Mass Transfer'', Global Digital Press, Columbia, MO. - + -
$N{u_x} = 0.5642{\rm{Ra}}_{xv}^{1/2}{\begin{array}{*{20}{c}} + - , & {{\rm{Ja}}} \\ + - \end{array}_v} \to \infty \qquad \qquad(14)$
+ - + - + - ==References== + - + - Cheng, P., and Verma, A.K., 1981, “The Effect of Subcooling Liquid on Film Boiling about a Vertical Heated Surface in a Porous Medium,” ''International Journal of Heat and Mass Transfer'', Vol. 24, pp. 1151-1160. + Nield, D.A., and Bejan, A., 1999, ''Convection in Porous Media'', 2nd ed., Springer-Verlag, New York. Nield, D.A., and Bejan, A., 1999, ''Convection in Porous Media'', 2nd ed., Springer-Verlag, New York.
## Revision as of 01:57, 9 July 2010
Film boiling in porous media.
Film boiling of liquid saturated in a porous medium at an initial temperature of ${T_\infty } < {T_{sat}}$ next to a vertical, impermeable heated wall at a temperature of Tw > Tsat is analyzed (see figure). Vapor generated at the liquid-vapor interface flows upward due to buoyancy force. The liquid adjacent to the vapor layer is dragged upward by the vapor. The temperature at the liquid-vapor interface is at the saturation temperature. There are velocity and thermal boundary layers in the liquid phase adjacent to the vapor film. The solution of the film boiling problem requires solutions of vapor and liquid flow, as well as heat transfer in both the vapor and liquid phases. It is assumed that boundary layer approximations are applicable to the vapor film and to convection heat transfer in the liquid phase. It is further assumed that the vapor flow is laminar, two-dimensional; Darcy’s law is applicable in both the vapor and liquid phases. The continuity, momentum, and energy equations in the vapor film are
$\frac{{\partial {u_v}}}{{\partial x}} + \frac{{\partial {v_v}}}{{\partial y}} = 0\qquad \qquad(1)$
${u_v} = - \frac{K}{{{\mu _v}}}({\rho _\ell } - {\rho _v})g\qquad \qquad(2)$
${u_v}\frac{{\partial {T_v}}}{{\partial x}} + {v_v}\frac{{\partial {T_v}}}{{\partial y}} = {\alpha _{mv}}\frac{{{\partial ^2}{T_v}}}{{\partial {y^2}}}\qquad \qquad(3)$
where αmv is thermal diffusivity of the porous medium saturated with the vapor. The governing equations for the liquid boundary layer are
$\frac{{\partial {u_\ell }}}{{\partial x}} + \frac{{\partial {v_\ell }}}{{\partial y}} = 0\qquad \qquad(4)$
${u_\ell } = \frac{K}{{{\mu _\ell }}}{\rho _\infty }g{\beta _\ell }({T_\ell } - {T_\infty })\qquad \qquad(5)$
${u_\ell }\frac{{\partial {T_\ell }}}{{\partial x}} + {v_\ell }\frac{{\partial {T_\ell }}}{{\partial y}} = {\alpha _{m\ell }}\frac{{{\partial ^2}{T_\ell }}}{{\partial {y^2}}}\qquad \qquad(6)$
where ${\alpha _{m\ell }}$ is thermal diffusivity of the porous medium saturated with the liquid.
The boundary conditions at the heated wall (y = 0) are
${v_v} = 0\begin{array}{*{20}{c}} , & {y = 0} \\ \end{array}\qquad \qquad(7)$
$T = {T_w}\begin{array}{*{20}{c}} , & {y = 0} \\ \end{array}\qquad \qquad(8)$
It should be pointed out that uv is not equal to zero at the heating surface under Darcy’s law, i.e., slip occurs at the surface. The boundary condition in the liquid that is far from the heated surface is
${u_\ell } = 0\begin{array}{*{20}{c}} , & {y \to \infty } \\ \end{array}\qquad \qquad(9)$
${T_\ell } = {T_\infty }\begin{array}{*{20}{c}} , & {y \to \infty } \\ \end{array}\qquad \qquad(10)$
The mass balance at the liquid-vapor interface is [see eq. (10.152)]:
${\left( {\rho u\frac{{d\delta }}{{dx}} - \rho v} \right)_v} = {\left( {\rho u\frac{{d\delta }}{{dx}} - \rho v} \right)_\ell }\begin{array}{*{20}{c}} , & {y = {\delta _v}} \\ \end{array}\qquad \qquad(11)$
The temperature at the liquid-vapor interface is equal to the saturation temperature:
${T_v} = {T_\ell } = {T_{sat}}{\begin{array}{*{20}{c}} , & {y = \delta } \\ \end{array}_v}\qquad \qquad(12)$
The above film boiling problem can be solved using a similarity solution like that for film condensation in porous media.
## References
Cheng, P., and Verma, A.K., 1981, “The Effect of Subcooling Liquid on Film Boiling about a Vertical Heated Surface in a Porous Medium,” International Journal of Heat and Mass Transfer, Vol. 24, pp. 1151-1160.
Faghri, A., and Zhang, Y., 2006, Transport Phenomena in Multiphase Systems, Elsevier, Burlington, MA
Faghri, A., Zhang, Y., and Howell, J. R., 2010, Advanced Heat and Mass Transfer, Global Digital Press, Columbia, MO.
Nield, D.A., and Bejan, A., 1999, Convection in Porous Media, 2nd ed., Springer-Verlag, New York. | 2,902 | 9,520 | {"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": 14, "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-2020-50 | latest | en | 0.851765 |
https://k2bnewsletters.com/qa/is-age-a-continuous-variable.html | 1,619,189,221,000,000,000 | text/html | crawl-data/CC-MAIN-2021-17/segments/1618039594808.94/warc/CC-MAIN-20210423131042-20210423161042-00522.warc.gz | 432,230,670 | 8,725 | # Is Age A Continuous Variable?
## Is age discrete or continuous data?
Mondal[1] suggests that age can be viewed as a discrete variable because it is commonly expressed as an integer in units of years with no decimal to indicate days and presumably, hours, minutes, and seconds..
## Is gender an interval variable?
For example, gender is a nominal variable that can take responses male/female, which are the categories the nominal variable is divided into.
## What are the two types of categorical data?
There are two types of categorical data, namely; the nominal and ordinal data. Nominal Data: This is a type of data used to name variables without providing any numerical value.
## Is age an interval variable?
Variables that could have been measured as interval-level variables, such as age or income, have instead been made into categoric variables by creating categories that define specific ranges for the variables (e.g., for age, the categories are 18-24 years, 25-34 years, and so on).
## Is gender a continuous variable?
Gender can be a continuous variable, not just a categorical one: Comment on Hyde, Bigler, Joel, Tate, and van Anders (2019)
## Is annual income continuous or discrete?
An annual income of a person is a discrete variable. This implies it cannot be constant, but if it is more convenient for your program, you can consider it as a continuous attribute, because there are so many meanings for it, again. The profits will often be broken up into groups of polls and other data sets.
## How do you know if a variable is ordinal?
An ordinal variable is similar to a categorical variable. The difference between the two is that there is a clear ordering of the categories. For example, suppose you have a variable, economic status, with three categories (low, medium and high).
## What are examples of interval variables?
An interval scale is one where there is order and the difference between two values is meaningful. Examples of interval variables include: temperature (Farenheit), temperature (Celcius), pH, SAT score (200-800), credit score (300-850).
## Is Money discrete or continuous?
A continuous distribution should have an infinite number of values between \$0.00 and \$0.01. Money does not have this property – there is always an indivisible unit of smallest currency. And as such, money is a discrete quantity.
## Is age categorical nominal or ordinal?
Age can be both nominal and ordinal data depending on the question types. I.e “How old are you” is a used to collect nominal data while “Are you the first born or What position are you in your family” is used to collect ordinal data. Age becomes ordinal data when there’s some sort of order to it.
## Why is age a continuous variable?
Age is measured in units that, if precise enough, could be any number. Therefore the set they come from is infinite. For example, someone could be 22.32698457 years old or 22.32698459 years old. We could be infinitly accurate and use an infinite number of decimal places, therefore making age continuous.
## What type of variable is age?
In statistics, there are broadly 2 types of variables: Numerical variables: Numbers which should be treated as they usually are in mathematics. For example, age and weight would be considered numerical variables, while phone number and ZIP code would not be considered numerical variables.
## Is age continuous or categorical?
An Example: Age Age is, technically, continuous and ratio. A person’s age does, after all, have a meaningful zero point (birth) and is continuous if you measure it precisely enough. It is meaningful to say that someone (or something) is 7.28 year old.
## How do you know if something is discrete or continuous?
A discrete variable is a variable whose value is obtained by counting. A continuous variable is a variable whose value is obtained by measuring. A random variable is a variable whose value is a numerical outcome of a random phenomenon. A discrete random variable X has a countable number of possible values.
## Is Likert scale continuous or categorical?
All Answers (16) Categorical for a likert scale as it is an ordinal variable. There is some debate on this topic as some people choose to see it as a continuous variable. For our survey analysis, we chose to treat it like an ordinal variable and used ordinal regression. | 906 | 4,357 | {"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-2021-17 | latest | en | 0.921605 |
https://stats.stackexchange.com/questions/503547/probability-of-lottery-toto | 1,716,174,446,000,000,000 | text/html | crawl-data/CC-MAIN-2024-22/segments/1715971058147.77/warc/CC-MAIN-20240520015105-20240520045105-00387.warc.gz | 483,980,180 | 39,185 | # Probability of Lottery (TOTO)
I have just a question about probability/odds and combinatorics here.
Context:
• In Singapore, we have a lottery called Toto.
• Buyers can pick at least six numbers, from 1 to 49.
• Group 1 prize odds is 1 in 13,983,816 (49c6), where the buyer must win all 6 numbers bought
Question:
• Why is Group 2 odds 1 in 2,330,636, where the buyer must win 5 numbers plus an additional number?
• I figured it was from (49c6)/6 but have no idea why)
• Would be great if anyojne could give insights to Group 3 to 7 as well
According to the definition given in the wiki page, we play six numbers and an additional one (so, 6+1). Group 2 win is achieved when 5 of your 6 chosen numbers and the separated number matches the given 5+1. Number of total cases of this 5+1 is simply C(49,6). But, out of your 6+1 play, you can generate six (5+1) sets by choosing any 5 of the first 6 numbers. That makes your odds 6 in C(49,6), i.e. 1 in 2330636.
For Group 1, 3, 5 and 7, that is, with "$$k$$ numbers" match, the odds of winning (denoted as $$W(k)$$) is
$$W(k)=\frac{C_{49}^{6}}{C_6^k \times C_{42}^{6-k}}$$, where $$k$$ is integers from 3 to 6.
For instance, when $$k=4$$, $$W(4) = \frac{C_{49}^{6}}{C_6^4 \times C_{42}^2}=1082.76$$, same as given by the link of Toto.
For Group 2, 4 and 6, that is, with "$$k$$ numbers plus the additional number" match, the odds of winning (denoted as $$W_+(k)$$) is
$$W_+(k) = \frac{C_{49}^{6}}{C_6^k \times C_{42}^{5-k}}$$, where $$k$$ is integers from 3 to 5.
For instance, when $$k=4$$, $$W_+(4) = \frac{C_{49}^{6}}{C_6^4 \times C_{42}^1}=22196.53$$, same as given by the link of Toto. | 581 | 1,650 | {"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": 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": 12, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.3125 | 4 | CC-MAIN-2024-22 | latest | en | 0.909966 |
https://slidetodoc.com/percent-composition-empirical-molecular-formulas-percent-composition-the/ | 1,722,850,684,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722640436802.18/warc/CC-MAIN-20240805083255-20240805113255-00230.warc.gz | 424,247,807 | 11,673 | # Percent Composition Empirical Molecular Formulas Percent Composition The
• Slides: 22
Percent Composition Empirical & Molecular Formulas
Percent Composition • The percent by mass of each element in the compound
Percent Composition Example 1 • Determine the percent composition of calcium carbonate, Ca. CO 3.
Percent Composition Example 2 • Determine the percent composition of magnesium nitrate, Mg(NO 3)2.
Empirical Formula • A chemical formula showing the simplest ratio of elements in a compound
Molecular Formula • A formula that shows the actual number of each element in a compound.
Empirical & Molecular Formula Ethyne, C 2 H 2 Styrene, C 8 H 8 • Empirical Formula • Molecular Formula
Empirical Formula Example 3 A compound is found to contain 25. 9% nitrogen and 74. 1% oxygen. Determine the empirical formula.
Empirical Formula Example 4 • What is the empirical formula for a compound which contains 67. 1% zinc and the rest oxygen?
Empirical Formula Example 5 • Find the empirical formula of a compound that contains 2. 374% H, 14. 14% C, and 83. 48% Cl.
Empirical Formula Example 6 • A compound contains 57. 54% C, 3. 45% H, and 39. 01% F. What is its empirical formula?
Molecular Formula Example 7 • Calculate the molecular formula of a compound whose molar mass is 60. 0 g/mol and the empirical formula is CH 4 N.
Molecular Formula Example 8 • A compound is found to contain 50. 05 % sulfur and 49. 95 % oxygen by weight. • What is the empirical formula for this compound? • The molecular weight for this compound is 64. 07 g/mol. What is its molecular formula? | 394 | 1,591 | {"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} | 2.65625 | 3 | CC-MAIN-2024-33 | latest | en | 0.8005 |
http://lesswrong.com/lw/v9/aiming_at_the_target/ | 1,455,278,857,000,000,000 | text/html | crawl-data/CC-MAIN-2016-07/segments/1454701163729.14/warc/CC-MAIN-20160205193923-00046-ip-10-236-182-209.ec2.internal.warc.gz | 121,487,882 | 27,531 | # Aiming at the Target
8 26 October 2008 04:47PM
Previously in seriesBelief in Intelligence
Previously, I spoke of that very strange epistemic position one can occupy, wherein you don't know exactly where Kasparov will move on the chessboard, and yet your state of knowledge about the game is very different than if you faced a random move-generator with the same subjective probability distribution - in particular, you expect Kasparov to win. I have beliefs about where Kasparov wants to steer the future, and beliefs about his power to do so.
Well, and how do I describe this knowledge, exactly?
In the case of chess, there's a simple function that classifies chess positions into wins for black, wins for white, and drawn games. If I know which side Kasparov is playing, I know the class of chess positions Kasparov is aiming for. (If I don't know which side Kasparov is playing, I can't predict whether black or white will win - which is not the same as confidently predicting a drawn game.)
More generally, I can describe motivations using a preference ordering. When I consider two potential outcomes, X and Y, I can say that I prefer X to Y; prefer Y to X; or find myself indifferent between them. I would write these relations as X > Y; X < Y; and X ~ Y.
Suppose that you have the ordering A < B ~ C < D ~ E. Then you like B more than A, and C more than A. {B, C}, belonging to the same class, seem equally desirable to you; you are indifferent between which of {B, C} you receive, though you would rather have either than A, and you would rather have something from the class {D, E} than {B, C}.
When I think you're a powerful intelligence, and I think I know something about your preferences, then I'll predict that you'll steer reality into regions that are higher in your preference ordering.
Think of a huge circle containing all possible outcomes, such that outcomes higher in your preference ordering appear to be closer to the center. Outcomes between which you are indifferent are the same distance from the center - imagine concentric rings of outcomes that are all equally preferred. If you aim your actions and strike a consequence close to the center - an outcome that ranks high in your preference ordering - then I'll think better of your ability to aim.
The more intelligent I believe you are, the more probability I'll concentrate into outcomes that I believe are higher in your preference ordering - that is, the more I'll expect you to achieve a good outcome, and the better I'll expect the outcome to be. Even if a powerful enemy opposes you, so that I expect the final outcome to be one that is low in your preference ordering, I'll still expect you to lose less badly if I think you're more intelligent.
What about expected utilities as opposed to preference orderings? To talk about these, you have to attribute a probability distribution to the actor, or to the environment - you can't just observe the outcome. If you have one of these probability distributions, then your knowledge of a utility function can let you guess at preferences between gambles (stochastic outcomes) and not just preferences between the outcomes themselves.
The "aiming at the target" metaphor - and the notion of measuring how closely we hit - extends beyond just terminal outcomes, to the forms of instrumental devices and instrumental plans.
Consider a car - say, a Toyota Corolla. The Toyota Corolla is made up of some number of atoms - say, on the (very) rough order of ten to the twenty-ninth. If you consider all the possible ways we could arrange those 1029 atoms, it's clear that only an infinitesimally tiny fraction of possible configurations would qualify as a working car. If you picked a random configurations of 1029 atoms once per Planck time, many ages of the universe would pass before you hit on a wheeled wagon, let alone an internal combustion engine.
(When I talk about this in front of a popular audience, someone usually asks: "But isn't this what the creationists argue? That if you took a bunch of atoms and put them in a box and shook them up, it would be astonishingly improbable for a fully functioning rabbit to fall out?" But the logical flaw in the creationists' argument is not that randomly reconfiguring molecules would by pure chance assemble a rabbit. The logical flaw is that there is a process, natural selection, which, through the non-chance retention of chance mutations, selectively accumulates complexity, until a few billion years later it produces a rabbit. Only the very first replicator in the history of time needed to pop out of the random shaking of molecules - perhaps a short RNA string, though there are more sophisticated hypotheses about autocatalytic hypercycles of chemistry.)
Even restricting our attention to running vehicles, there is an astronomically huge design space of possible vehicles that could be composed of the same atoms as the Corolla, and most of them, from the perspective of a human user, won't work quite as well. We could take the parts in the Corolla's air conditioner, and mix them up in thousands of possible configurations; nearly all these configurations would result in a vehicle lower in our preference ordering, still recognizable as a car but lacking a working air conditioner.
So there are many more configurations corresponding to nonvehicles, or vehicles lower in our preference ranking, than vehicles ranked greater than or equal to the Corolla.
A tiny fraction of the design space does describe vehicles that we would recognize as faster, more efficient, and safer than the Corolla. Thus the Corolla is not optimal under our preferences, nor under the designer's own goals. The Corolla is, however, optimized, because the designer had to hit an infinitesimal target in design space just to create a working car, let alone a car of Corolla-equivalent quality. The subspace of working vehicles is dwarfed by the space of all possible molecular configurations for the same atoms. You cannot build so much as an effective wagon by sawing boards into random shapes and nailing them together according to coinflips. To hit such a tiny target in configuration space requires a powerful optimization process. The better the car you want, the more optimization pressure you have to exert - though you need a huge optimization pressure just to get a car at all.
This whole discussion assumes implicitly that the designer of the Corolla was trying to produce a "vehicle", a means of travel. This assumption deserves to be made explicit, but it is not wrong, and it is highly useful in understanding the Corolla.
Planning also involves hitting tiny targets in a huge search space. On a 19-by-19 Go board there are roughly 1e180 legal positions (not counting superkos). On early positions of a Go game there are more than 300 legal moves per turn. The search space explodes, and nearly all moves are foolish ones if your goal is to win the game. From all the vast space of Go possibilities, a Go player seeks out the infinitesimal fraction of plans which have a decent chance of winning.
You cannot even drive to the supermarket without planning - it will take you a long, long time to arrive if you make random turns at each intersection. The set of turn sequences that will take you to the supermarket is a tiny subset of the space of turn sequences. Note that the subset of turn sequences we're seeking is defined by its consequence - the target - the destination. Within that subset, we care about other things, like the driving distance. (There are plans that would take us to the supermarket in a huge pointless loop-the-loop.)
In general, as you live your life, you try to steer reality into a particular region of possible futures. When you buy a Corolla, you do it because you want to drive to the supermarket. You drive to the supermarket to buy food, which is a step in a larger strategy to avoid starving. All else being equal, you prefer possible futures in which you are alive, rather than dead of starvation.
When you drive to the supermarket, you aren't really aiming for the supermarket, you're aiming for a region of possible futures in which you don't starve. Each turn at each intersection doesn't carry you toward the supermarket, it carries you out of the region of possible futures where you lie helplessly starving in your apartment. If you knew the supermarket was empty, you wouldn't bother driving there. An empty supermarket would occupy exactly the same place on your map of the city, but it wouldn't occupy the same role in your map of possible futures. It is not a location within the city that you are really aiming at, when you drive.
Human intelligence is one kind of powerful optimization process, capable of winning a game of Go or turning sand into digital computers. Natural selection is much slower than human intelligence; but over geological time, cumulative selection pressure qualifies as a powerful optimization process.
Once upon a time, human beings anthropomorphized stars, saw constellations in the sky and battles between constellations. But though stars burn longer and brighter than any craft of biology or human artifice, stars are neither optimization processes, nor products of strong optimization pressures. The stars are not gods; there is no true power in them.
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Comment author: 26 October 2008 06:03:20PM 2 points [-]
I agree, generally, but I've got a quibble with your last paragraph. I'm tentatively in agreement that stars are not, qua stars, optimization processes, but I'm less certain that stars do not contain optimization processes. And I'm tentatively certain that stars are the products of strong optimization pressures; how likely is star formation? Doesn't cosmological/astronomical evolution (i.e. the 'rules' by which it occurs) count as a (powerful) form of selection? There are innumerable dust clouds in the visible universe that never became stars.
Have you read 'A New Kind of Science' (yes, it's a pretentious title) by Stephen Wolfram? He has a number of interesting discussions of intelligence. Your recent posts re: intelligence and optimization processes remind me of Wolfram's statement (I'm greatly paraphrasing) that a sufficiently general definition of intelligence (in terms of information processing and something akin to your optimization processes) would necessarily include all kinds of entities that we would not categorize as intentional.
Comment author: 17 June 2012 12:41:16PM -2 points [-]
Stars are a strictly accidental, natural formation given gravity and non-homogenous, sufficiently large gas clouds. That's that.
Nuclear computing is a whole different matter. If you can overcome the thermodynamic activity at upwards of 15 billion kelvin, then it is definitely a possibility. Personally I would assign higher probability to concentric dyson-sphere brains.
Comment author: 21 July 2012 10:35:52PM 1 point [-]
I'm curious what you think about this after reading these 17 pages from the book I mentioned. The point I was making relied on the idea (or perspective) that everything already is computing. The point then being that the physical processes within stars might be sufficiently advanced computationally that they could be considered, in some sense, intelligent.
Comment author: 22 July 2012 11:51:13AM -2 points [-]
Intelligence is optimization power. Boltzmann brains don't have a lot.
Comment author: 26 October 2008 06:23:21PM 0 points [-]
Comment author: 26 October 2008 06:24:26PM 0 points [-]
Comment author: 26 October 2008 07:12:39PM 1 point [-]
How do you avoid conflating intelligence with power? (Or do you, in fact, think that the two are best regarded as different facets of the same thing?) I'd have more ability to steer reality into regions I like if I were cleverer -- but also if I were dramatically richer or better-connected.
Comment author: 26 October 2008 07:30:11PM 0 points [-]
Re intelligence vs. power: think about it as quality of engine vs. how you apply the engine. You can have a perfect car, and still drown it in a pool. Quality of engine is abstract knowledge about it, it's not derived from performance of that engine on a specific race track. If you are highly intelligent, but get hit by a stone fallen from the sky, it doesn't mean that it was your preferred outcome. When the outcome turns out wrong each time, it shows that your abstract knowledge was wrong, but quality of engine is not outcome itself.
Comment author: 26 October 2008 07:44:52PM 0 points [-]
Comment author: 26 October 2008 07:47:50PM 4 points [-]
Kenny, compared to cumulative processes like natural selection that mutate and select over and over - let alone human intelligence that navigates a compressed search space - to select one star cloud out of a million possibles is only 20 bits of information at most. And considering the variance between star clouds, that 20 bits of information won't go very far. You can't expect to find complex functionally optimized machinery within stars on the order of what exists in the smallest bacterium. If evolution has not gotten started anywhere else in the galaxy, then I fully expect that the rest of the entire Milky Way contains less interesting complexity than one Earth butterfly.
See e.g. "No Evolutions for Corporations or Nanodevices".
Comment author: 26 October 2008 07:49:16PM 0 points [-]
Vladimir, if I understand both you and Eliezer correctly you're saying that Eliezer is saying not "intelligence is reality-steering ability" but "intelligence is reality-steering ability modulo available resources". That makes good sense, but that definition is only usable in so far as you have some separate way of estimating an agent's available resources, and comparing the utility of what might be very different sets of available resources. (Compare a nascent superintelligent AI, with no ability to influence the world directly other than by communicating with people, with someone carrying a whole lot of powerful weapons. Who has the better available resources? Depends on context -- and on the intelligence of the two.) Eliezer, I think, is proposing a way of evaluating the "intelligence" of an agent about which we know very little, including (perhaps) very little about what resources it has.
Put differently: I think Eliezer's given a definition of "intelligence" that could equally be given as a definition of "power", and I suspect that in practice using it to evaluate intelligence involves applying some *other* notion of what counts as intelligence and what counts as something else. (E.g., we've already decided that how much money you have, or how many nuclear warheads you have at your command, don't count as "intelligence".)
Comment author: 17 June 2012 12:50:01PM 0 points [-]
If you have two agent source codes A and B both provided with resource amount R (detailing computational architecture and tools such as telepresence robots and nanotech) then you will observe that if A is a stronger optimizer than B, A will get more done in less time, or alternately hit a much higher preferred world.
If you have one agent source code C and run two instances, one with resources M and one with resources N, then if M > N, then agent running on M will dominate the agent running on N.
"Intelligence" is cleverness of source code, "Power" is the available resources. A really clever agent can outdo a stupid one even if ludicrously handicapped, resource wise. A stupid agent with powerful nanotech dominates a clever agent with human servants.
Comment author: 26 October 2008 07:55:28PM 0 points [-]
Comment author: 26 October 2008 08:22:57PM 1 point [-]
This is very similar to an earlier post. Eliezer, go faster. I, for one, am waiting for some non-trivial FAI math - is there any?
Comment author: 26 October 2008 08:30:41PM 0 points [-]
Stars are optimisation processes. They maximise entropy production. See the work of R. C. Dewar. Dewar's work was based on the work of E. T. Jaynes in this area.
Comment author: 26 October 2008 09:09:48PM 3 points [-]
Vladimir, there's plenty of non-trivial decision theory math that other people have invented.
If I were going to write up a piece of novel FAI math, it would be my general theory of Newcomblike problems, but the last time I tried that it started turning into a book. But that would be the main thing that I would do, if it got to the point that impressing people with at least one piece of elegant math turned into a high enough priority.
Comment author: 26 October 2008 09:56:20PM 0 points [-]
The state spaces of both chess and go have to be expanded to include "previous history". In the case of go, this is to avoid the ko problem -- moves that would produce the exact same board state as a previous state are forbidden. Chess, well, see a chess rule book, or wikipedia.
Comment author: 26 October 2008 09:58:30PM 0 points [-]
When you drive to the supermarket, you aren't really aiming for the supermarket, you're aiming for a region of possible futures in which you don't starve.
The first time you head to the supermarket it might be trying to stop starving, but after you have done it for a few times, it becomes an in grained habit. And you might be heading to the super market, because you always head to the super market on a saturday. You might do so even if it becomes knowably sub optimal for starvation prevention, because you aren't re-evaluating the economics of doing so.
This is a known and exploited facet of humans, hence special offers to get you buying food for a bit, to hope it becomes a habit.
I however sometimes spend far too long making food buying decisions (i.e. more time spent if I was working for that time than I might save).
If your AI was making a decision to buy bread vs making it would it calculate the nutrition of store bought bread, cost of petrol and bread, wear and tear on the car etc vs the time taken to make bread, energy costs of cooking it, ingredient costs, wear and tear on oven, cost to repair or replace oven etc every time one of these values changed or would it use cached results?
Of course if the AI was going to be truly powerful it would be able to predict the secondary effects of choices it made, would the money it spent in avoiding starvation be in the hands of other people trying to avoid starvation of people in general, i.e. giving it to people spending it to encourage research and actions that lead to the avoidance of food shortages in the future (either through lobbying government or directly depending what was more influential). I sometimes feel I need a very Powerful AGI just to buy my groceries.
Comment author: 26 October 2008 10:28:24PM 0 points [-]
I think it's worth mentioning that Kasparov will have a harder time accurately predicting your moves than you will have predicting his. Each of you knows that Kasparov will win, but this will much more likely be due to a blunder on your part than a brilliancy on his. He may well reason, "sooner or later this patzer is going to hang a piece", but he will have no way of knowing when.
Comment author: 26 October 2008 10:41:21PM 0 points [-]
You cannot even drive to the supermarket without planning - it will take you a long, long time to arrive if you make random turns at each intersection.
Eliezer, what do you mean by "planning"? The word needs a technical definition. (So does "optimisation", for that matter, by people on both sides of the claim that stars are, or are not, optimisers.)
Reaching goals does not necessarily involve planning. Water reaches the foot of a hill without planning. The room thermostat maintains the temperature without planning. It is said that no plan of battle survives contact with the enemy. I have a simulation of a robot that walks over uneven terrain and hunts food particles. That robot does no planning. I know: I created it. (Neither does it optimise, learn, adapt, remember, or predict. It merely works.) I know my way around the town I live in, and do not need to make any plan to reach the supermarket. I only need to know what to do at each point of the journey. In a strange town I would use a map and make a plan, but the plan would have to be continually updated according to conditions encountered.
To leap from observing the accomplishment of goals to "planning" is an anthropomorphisation of the sort that you have condemned in people working on AI, except when planning, technically defined, is demonstrated to actually be present in the mechanism. If "planning" does not mean some particular sort of mechanism, then you might as well call it "emergence", or "pixies".
you try to steer reality into a particular region of possible futures.
By "steering" I understand continually correcting your course to maintain the approach to your goal. Steering is not planning. The thermostat steers the temperature and the robot steers to its prey without planning. Steering without planning is possible; planning without steering is useless. Relying on a plan makes it unreliable.
Anyone can test this. Give someone directions in the form of a plan of which way to go at each intersection. Don't tell them the destination you're aiming them at. Have them execute the plan and tell you where they got to.
Comment author: 26 October 2008 11:42:14PM 0 points [-]
Will, you still seem to think Eliezer is saying "do what an optimal agent would, even when doing so is not optimal." No.
[Richard] Anyone can test this. Give someone directions in the form of a plan of which way to go at each intersection. Don't tell them the destination you're aiming them at. Have them execute the plan and tell you where they got to.
But then they're not optimizing for a goal they can be said to have. If a street is closed, they won't reach the destination, as they would if they knew what the destination was.
Comment author: 27 October 2008 07:39:51AM 0 points [-]
+1 to Will Pearson and Richard Kennaway. Humans mostly follow habit instead of optimizing.
Eliezer, this is interesting:
> my general theory of Newcomblike problems
Some kind of bounded rationality? Could you give us a taste?
Comment author: 27 October 2008 08:12:09AM 0 points [-]
Vladimir: Some kind of bounded rationality? Could you give us a taste?
I was wondering the same thing. I'd be less interested in a decision theory for sub-Omegas and more interested in one for Omegas.
Comment author: 27 October 2008 09:45:58AM 0 points [-]
Tim Tyler: Stars are optimisation processes. They maximise entropy production.
No, at least, not by the definition of "optimisation processes" that Eliezer uses. Stars don't plan to maximize entropy productions, gravity doesn't plot a course down a hill so that a ball reaches the lowest point. Both can get stuck in a local maxima. Reread the post about Kasparov, and try to come up with a corresponding story about stars. Elizier is not talking about the same kind of thing as you are.
Comment author: 27 October 2008 11:31:17AM 1 point [-]
No, at least, not by the definition of "optimisation processes" that Eliezer uses.
You are being ridiculous - "optimisation process" is a perfectly standard term.
Stars don't plan to maximize entropy productions.
"Planning" is not part of the definition of what constitutes an optimisation process.
Comment author: 27 October 2008 12:59:59PM 0 points [-]
an outcome that ranks high in your preference ordering
Well if Garry's wins are in the centre of your preference ordering circle of course you'll lose! Some fighting spirit please!
Oh, and if something maximising entropy is a valid optimisation process, then surely everything is an optimisation process and the term becomes useless? Optimisation processes lead (locally) away from maximal entropy, not towards it, right?
Comment author: 27 October 2008 01:25:36PM 0 points [-]
Emile, you've mixed up "optimization process" and "intelligence". According to your post, Eliezer wouldn't consider evolution an optimization process. He does; he doesn't consider it intelligent.
Comment author: 27 October 2008 03:21:14PM 0 points [-]
Oh, and if something maximising entropy is a valid optimisation process, then surely everything is an optimisation process and the term becomes useless?
Not really. A salt crystal is not an optimisation process - at least not on conventional timescales. However, certainly optimisation is a widespread, "universal" phenomena - driving most change in the universe and all self-organising systems - including biological ones.
Optimisation processes lead (locally) away from maximal entropy, not towards it, right?
That description certainly fits a star. The star is locally ordered (it's a big, dense ball of matter), but it creates global disorder - in the form of heat and radiation.
However, I don't think there is a general statement you can make about what optimisation processes do to "local" entropy levels. For a counter-example, consider gas expanding to fill a box. That is surely an optimisation process, and we know what solution it will converge on. However, there is no associated "optimising agent" using a heat pump to perform work to execute the task - and consequently there are not really any "local" increases in entropy occurring.
Comment author: 27 October 2008 03:29:05PM 0 points [-]
there are not really any "local" increases in entropy occurring.
I meant "decreases", of course. There might be local decreases if self-organising systems formed (e.g. if the gas became turbulent, and formed eddies), but that gets us into the realm of pedantic nit-picking.
Comment author: 27 October 2008 03:34:38PM 0 points [-]
Tim: I'm not offering a definition of "optimization process" or "intelligence", I'm just pointing out that when you say "gravity is an optimization process", or "stars are optimization processes", you're missing the whole point of the Kasparov post.
There's a difference between the unpredictability of a ball rolling down a hill, and the unpredictability of Kasparov's chess moves. This difference is not obvious.
Comment author: 27 October 2008 03:36:54PM 0 points [-]
Nick Tarleton: But then they're not optimizing for a goal they can be said to have. If a street is closed, they won't reach the destination, as they would if they knew what the destination was.
Neither will the person who has that goal, if they ignore the goal having made the plan.
People habitually overestimate the necessity of planning. Planning can be useful, but it is never enough, often unnecessary, and sometimes actively harmful.
Comment author: 27 October 2008 04:37:35PM 0 points [-]
You know, I've been thinking that I'm having trouble saying exactly what a "preference" is.
"that which an optimization process selects for" would seem to more or less declare everything an optimization process.
Anyone got a decent reduction on the notion of a preference itself? I'm kinda annoyed that I don't seem to be able to quite work that out.
Comment author: 27 October 2008 04:58:01PM 1 point [-]
I'm just pointing out that when you say [...] "stars are optimization processes", you're missing the whole point of the Kasparov post.
I was addressing the sentence: "But though stars burn longer and brighter than any craft of biology or human artifice, stars are neither optimization processes, nor products of strong optimization pressures." - which, IMHO, is factually inaccurate. I do not see any evidence that I am missing anything.
Comment author: 27 October 2008 05:26:14PM 0 points [-]
"Preferences" is just another name for the values of agents.
Comment author: 27 October 2008 05:53:51PM 0 points [-]
Tim Tyler:
Yes, I understood that. I meant can you reduce it to non-mind? Besides, evolution is an optimization process, and I wouldn't call it an agent that has values.
Either way, the point is that it's just moving my confusion from the word "preferences" to the word "values".
If I then say "those things an agent wants", then I'm just stuck at the word "want" again. It's not a reduction, just a repeated renaming of the same black box.
Comment author: 27 October 2008 06:58:26PM 0 points [-]
"Values" is another name for components of a utility function. One area where things get fuzzy is when you get to decide whether something qualifies as an agent or not - but that is a traditional problem which lies beyond the scope of this post.
Comment author: 27 October 2008 07:49:35PM 0 points [-]
Tim: no, I'd think of it in reverse, that a utility function is a very special type of encoding for a set of preferences.
Again, I'm not denying that I think I have an intuitive sense of what I think I mean by the term. It's just that when I try to reduce it from something mind to something non mind, the best I can come up with is stuff like "that which an optimization process selects for"
At which point I have to declare everything an optimization process in some sense. (=I'm actually semisorta tempted to do this, to talk about optimization power as a property of processes in general, rather than distinguishing certain types of processes as optimization processes. This way I think I'd have a reasonably serviceable reduction of the notion of a preference. Except then with intelligent agents that aren't logically omnicient and, say, can't yet fully compute their morality (or primality or whatever as appropriate) and thus in a sense don't actually fully know their preferences.
Well, there's hopefully enough here to illustrate my confusion sufficiently that you or someone who's actually worked out the correct answer can help me out here. I'm annoyed that I don't know this. :)
Comment author: 04 November 2008 05:21:20PM 0 points [-]
FYI -- the best chess player of the past 10 years has been a guy called Anand, and he is the best rapid chess player of all time. Maybe some day people will stop talking about Kasparov who retired a few years ago!
Comment author: 27 November 2008 08:51:31AM 0 points [-]
I was brought to full view of the picture in your last paragraph and I have to say.....You could have made this much shorter and much easier to understand (Especially for those "lacking"). Otherwise about half of that article is just you spinning your wheels going nowhere. Don't get me wrong, the idea is interesting, but for the most part it could have been expressed with,
"There are an infinite amount of possibilities for anything to happen. That said, in our day to day routines only our own intelligence,experiences, and knowledge can determine the amount of success that we have in our lives."
Right? It's similar to poetry, as I say, "If it has to be explained to you by someone more knowledgeable then it defeats the point of expressing yourself"
Comment author: 27 November 2008 08:53:49AM 0 points [-]
I was brought to full view of the picture in your last paragraph and I have to say.....You could have made this much shorter and much easier to understand (Especially for those "lacking"). Otherwise about half of that article is just you spinning your wheels going nowhere. Don't get me wrong, the idea is interesting, but for the most part it could have been expressed with,
"There are an infinite amount of possibilities for anything to happen. That said, in our day to day routines only our own intelligence,experiences, and knowledge can determine the amount of success that we have in our lives."
Right? It's similar to poetry, as I say, "If it has to be explained to you by someone more knowledgeable then it defeats the point of expressing yourself" | 7,003 | 31,632 | {"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} | 2.625 | 3 | CC-MAIN-2016-07 | longest | en | 0.966514 |
https://getrevising.co.uk/revision-cards/additional_sciencephysics_chapter_2 | 1,534,811,558,000,000,000 | text/html | crawl-data/CC-MAIN-2018-34/segments/1534221217901.91/warc/CC-MAIN-20180820234831-20180821014831-00568.warc.gz | 691,664,803 | 15,039 | GCSE AQA Additional Science-Physics Chapter 2
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• Created by: Mel
• Created on: 24-05-12 09:45
## Forces between objects
Forces are measured in newtons (N)
Objects ALWAYS exert equal and opposite forces on each other.
e.g. If you place a book on a table the weight of the book will act vertically downwards on the table. The table will exert an equal and opposite reaction force upwards on the book.
The motive force on a car is the force that makes it move. This force is due to friction between the ground and the tyre of each drive wheel. Friction acts where the tyre is in contact with the ground.
Force (N) = Mass (kg) x acceleration (m/s^2)
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## Resultant force
Most objects have more than one force acting on them. The 'resultant force' is the single force that would have the same effect on the object as all the original forces acting together. When the resultant force on an object is zero:
• if the object is at rest it will stay at rest
• if the object is moving it will carry on moving at the same speed and in the same direction
When the resultant force on an object is not zero there will be an acceleration in the direction of the force.
• If the object is at rest it will accelerate in the direction of the resultant force
• If the object is moving in the same direction as the resultant force it will accelerate in that direction
• If the object is moving in the opposite direction to the resultant force it will decelerate
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## Force and Acceleration
A resultant force always causes an acceleration.
If there is no acceleration in a particular situation the resultant force must be zero. An object can accelerate by changing its direction even if it is going at a constant speed. So a resultant force is needed to make an object change direction.
Resultant Force (N) = Mass (kg) x Acceleration m/s2
The bigger the mass of an object, the bigger the force needed to give it a particular acceleration.
The velocity of the object decreases (i.e. it decelerates) if the resultant force is opposite in direction. We say its accelerates is negative because it is opposite in direction to its velocity
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If a vehicle is travelling at a steady speed the resultant force on it is zero because the motive force of its engine is balanced by the resistive forces. The driving forces are equal and opposite to the frictional forces.
The faster the speed of a vehicle, the bigger the deceleration needed to bring it to rest in a particular distance, so the bigger the braking force needed.
The stopping distance of a vehicle is the distance it travels during the driver's reaction time (the thinking distance) plus the distance it travels under the braking force (the braking distance).
The thinking distance is increased if the driver is tired or under the influence of alcohol or drugs.
The braking distance can be increased by poorly maintained roads, weather conditions and the condition of the car. For example, worn tyres or worn brakes will increase braking distance.
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## Falling Objects
If an object falls freely, the resultant force acting on oit is the force of gravity. We call the force of gravity 'weight', and the acceleration 'the acceleration due to gravity'.
Weight (N) = Mass (kg) x Gravitational Field Strength (N/Kg)
When an object falls through a fluid (e.g. air), the fluid exerts frictional forces (e.g. air resistance) on it, resisting its motion. The faster the object falls, the bigger the frictional force becomes. Eventually it will be equal to the weight of the object. The resultant force is now zero, so the body stops accelerating and moves at a constant velocity called 'terminal velocity'.
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These are brilliant revision notes if you are studying for the GCSE AQA Additional Science exam. They are nicely laid out and highlighted key terms.
They are printable so you can add them to your own notes.
I really think these will help you with your revision of this topic to ensure you understand these equations- which are fairly simple but can seem a bit daunting at first.
## Similar Physics resources:
See all Physics resources »See all Forces and Motion resources » | 913 | 4,235 | {"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} | 4.15625 | 4 | CC-MAIN-2018-34 | longest | en | 0.907072 |
https://physics-network.org/what-is-centrifugal-force-in-simple-words/ | 1,680,224,487,000,000,000 | text/html | crawl-data/CC-MAIN-2023-14/segments/1679296949506.62/warc/CC-MAIN-20230330225648-20230331015648-00415.warc.gz | 510,511,746 | 18,613 | # What is centrifugal force in simple words?
Definition of centrifugal force : the apparent force that is felt by an object moving in a curved path that acts outwardly away from the center of rotation — compare centripetal force.
## What is centrifugal force explain with example?
Meanwhile, the centrifugal force is an apparent outward force on an object that is moving in a circle. An example of centrifugal force would be the sensation you have when riding a merry-go-round that makes you want to fly outwards.
## Is centrifugal force real in physics?
The centrifugal force is very real if you are in a rotating reference frame. It causes objects in a rotating frame of reference to accelerate away from the center of rotation. Washing machines, uranium enrichment centrifuges, and biology lab centrifuges all depend on the reality of the centrifugal force .
## What are 5 centrifugal forces examples?
• Drifting.
• Weight at Poles and Equator.
• A Stone Tied to a Thread.
• Merry-Go-Round.
• Centrifugal Pumps.
• Washing Machine.
• Centrifugal Clutches.
## What is a good example of a centrifugal force?
When a car in motion takes a sudden turn towards the left, passengers in a car experience an outward push. This is due to the centrifugal force acting on passengers.
## What is the principle of centrifugal force?
In accordance with Newton’s third law of motion, the body in curved motion exerts an equal and opposite force on the other body. This reactive force is exerted by the body in curved motion on the other body that provides the centripetal force and its direction is from that other body toward the body in curved motion.
## What is difference between centrifugal and centripetal?
So, the two key differences: centripetal is real and pushing towards the center of the circle. Centrifugal is fake and pushes away from the center.
## What are the three main characteristics of centrifugal force?
Characteristics of Centrifugal Force: It is an imaginary force or pseudo force. It is experienced in non – inertial frame of reference. The magnitude of the centripetal force is equal to that of the centripetal force. It is always directed away from the centre of the circle along the radius.
## Is centrifugal force the same as gravity?
Gravity is not centrifugal force. The direction of gravity is opposite to that of centrifugal force. The gravitational force pulls the object towards the centre of Earth. Centrifugal force acts radially outwards and it tries to fling the object away.
## Do we feel centrifugal force on Earth?
Because the rotation of the earth is very smooth and doesn’t change, the centripetal acceleration we feel is very nearly constant. This means that the (small) centrifugal force from the rotation gets added to gravity to make up the “background force” we don’t notice.
## Can you feel centrifugal force in space?
The net force on the spaceship is also zero (no air resistance in space), so the spaceship will continue to orbit on its own without the use of any propulsion. The reason you don’t feel centrifugal force is because it isn’t a real force. It is a fictitious force.
## Why is there no centrifugal force on Earth?
Since the equator spins fast in response to the earth, it results in a large centrifugal force. However, at the poles, there is no spinning at all. Hence, the centrifugal force at the poles is zero. Since the Earth is rotating there is more centrifugal force at the equator rather than at the poles.
## Is wind a centrifugal force?
An illustration of wind (black arrows) as it moves around a circular low-pressure center. The centrifugal force acting on the moving air is in cyan (blue-green). As air is pushed toward the center of a low-pressure center, is curves, creating an outward-directed centrifugal force.
## Does centrifugal force affect gravity?
Since centrifugal force points outwards from the center of rotation, it tends to cancel out a little bit of earth’s gravity. If the earth were not spinning, you would be heavier as you would feel the full force of gravity.
## Which device works under centrifugal force?
A centrifuge is a device that uses centrifugal force to separate various components of a fluid. This is achieved by spinning the fluid at high speed within a container, thereby separating fluids of different densities (e.g. cream from milk) or liquids from solids.
## What is the purpose of a centrifugal?
Their main purpose is to transfer fluids through an increase in pressure. Centrifugal pumps can have different structures, but their operating principle and fluid dynamic characteristics are always the same. Schematically, centrifugal pumps are formed of an impeller that rotates inside the casing.
## What is the SI unit of centrifugal force?
Centrifugal force is a vector quantity. The centrifugal force equals the product of mass and the centrifugal acceleration of the body. The name of the SI unit for centrifugal force is a newton.
## What’s the opposite of centrifugal force?
According to Newton’s third law of motion, for every action there is an equal and opposite reaction. The centripetal force, the action, is balanced by a reaction force, the centrifugal ( center-fleeing ) force. The two forces are equal in magnitude and opposite in direction.
## Why centrifugal force is called pseudo force?
The centrifugal force is a pseudo-force because if the centripetal force ceased for an object in circular motion, the centrifugal force the body is “feeling” would instantly disappear, and the object would travel tangentially to its line of motion.
## What are the two examples of centrifugal force?
Examples of Centrifugal Force When a car in motion takes a sudden turn towards left, passengers in a car experiences an outward push to the right. this is due to the centrifugal force acting on passengers. 2. A bucket full of water is rotated in vertical circle at a particular speed, so that water dose not fall.
## What are the advantages of centrifugal?
Centrifugal chemical pumps rank high in energy efficiency compared to other pumping technologies. This puts them at a significant advantage over other pump styles. Their efficiency reduces costs both short term and over the lifespan of each unit. This high-efficiency operation also reduces the strain on energy systems.
## Is centrifugal force energy?
In order to move the mass m closer to the axis work must be done against the centrifugal force. Therefore the mass gains potential energy as it moves inwards, eg at the expense of its kinetic energy. Centrifugal force is like another force of gravity, acting radially outwards instead of vertically downwards.
## What is the effect of centrifugal force?
The effects of these forces may be classified in three main phases: first, the general sensations of the apparent increase in weight of the body; secondly, the loss of vision or “blacking-out “; thirdly, the loss of consciousness which is infrequent and is usually preceded by a period of ” black-out”.
## Is centrifugal force an illusion?
The best proof that the centrifugal force is an illusion is the direction the bucket will fly if you let go of it: If there really was an outward-pulling force, it should fly away along the line connecting you and the bucket. In reality, it will fly along a line perpendicular to that.
## How much centrifugal force can a human withstand?
Unprotected humans can usually withstand between 3 and 3.5 gs of centrifugal force, Cohen says. “This assumes the person is able to relax. But most people tend to tense up, which makes it more difficult for the body to withstand g force over a period of time,” says Cohen. | 1,603 | 7,670 | {"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} | 3.40625 | 3 | CC-MAIN-2023-14 | latest | en | 0.904725 |
https://calculator.academy/body-to-fat-ratio-calculator/ | 1,652,770,833,000,000,000 | text/html | crawl-data/CC-MAIN-2022-21/segments/1652662517018.29/warc/CC-MAIN-20220517063528-20220517093528-00273.warc.gz | 210,610,510 | 61,852 | Enter the total body weight (lbs) and the fat weight (lbs) into the Body to Fat Ratio Calculator. The calculator will evaluate and display the Body to Fat Ratio.
## Body to Fat Ratio Formula
The following formula is used to calculate the Body to Fat Ratio.
BFR = BW / F
• Where BFR is the Body to Fat Ratio
• BW is the total body weight (lbs)
• F is the fat weight (lbs)
## How to Calculate Body to Fat Ratio?
The following example problems outline how to calculate Body to Fat Ratio.
Example Problem #1:
1. First, determine the total body weight (lbs).
• The total body weight (lbs) is given as: 160.
2. Next, determine the fat weight (lbs).
• The fat weight (lbs) is provided as: 40.
3. Finally, calculate the Body to Fat Ratio using the equation above:
BFR = BW / F
The values given above are inserted into the equation below and the solution is calculated:
BFR = 160 / 40 = 4.00:1
Example Problem #2:
For this problem, the variables required are provided below:
total body weight (lbs) = 200
fat weight (lbs) = 50 | 260 | 1,032 | {"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} | 3.4375 | 3 | CC-MAIN-2022-21 | longest | en | 0.862045 |
http://www.newton.dep.anl.gov/askasci/phy00/phy00996.htm | 1,419,044,265,000,000,000 | text/html | crawl-data/CC-MAIN-2014-52/segments/1418802769328.92/warc/CC-MAIN-20141217075249-00134-ip-10-231-17-201.ec2.internal.warc.gz | 696,386,440 | 3,846 | Electric and Magnetic Attraction Differences ```Name: Julia Status: educator Grade: 4-5 Location: WI Country: N/A Date: 10/31/2005 ``` Question: If static electricity (i.e. a wool-rubbed balloon making your hair stick up) attracts objects due to the negative charge being built up, then why won't the negative pole of a magnet attract the same objects? Replies: Dear Julia, Magnets do not attract (or repel) stationary charges since the magnetic force is quite different from the electric force, although it is closely related. Stationary charges are not affected by magnetic fields. Moving charges passing through a magnetic field do feel a force, but the force is perpendicular to the magnetic field line. This is unlike the electric force, which is parallel to the electric field lines. Since electric field lines radiate from electric charges, the electric force will attract charges toward (or away from) the charge producing the electric field. Since magnetic field lines radiate from the poles of a magnet and the magnetic force is perpendicular to the field lines (as well as perpendicular to the velocity of the charge), a charge passing in front of a pole will have its direction changed, but will not be attracted to or repelled from the pole. Best, Dick Plano, Professor of Physics emeritus, Rutgers University Julia, North and South poles of a magnet are not in any way electric. They are not positive and negative charges of any sort. Every atom is a tiny magnet. If you attach a coil of wire to a battery so that electric current runs through the coil, the coil becomes magnetic (i.e. an electromagnet). In the same way, the motion and spin of the particles inside an atom cause the atom to be magnetized. In a standard magnet, many of the atoms "face the same direction". Their tiny magnetic fields work together to produce a large magnetic field. Neither pole of a magnet is positive or negative. The poles just tell you which way the atoms face. Dr. Ken Mellendorf Physics Instructor Illinois Central College Click here to return to the Physics Archives
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Update: June 2012 | 545 | 2,542 | {"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} | 3.140625 | 3 | CC-MAIN-2014-52 | latest | en | 0.915105 |
https://euphonics.org/12-3-1-simulating-a-tanpura-or-bray-harp/ | 1,726,441,160,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700651668.26/warc/CC-MAIN-20240915220324-20240916010324-00648.warc.gz | 218,833,750 | 26,584 | # 12.3.1 Simulating a tanpura or bray harp
Following the approach of Valette and Cuesta [1], the simplest model for the buzzing bridge of a tanpura or a bray harp is sketched in Fig. 1. A string has fixed ends at $x=0$ and $x=L_1$, and can execute small transverse vibration with displacement $w(x,t)$. At $x=L_2$ there is a rigid stop which might be in line with the string’s equilibrium position or might be offset by a small distance $y_1$. During contact the short piece of string between $L_2$ and $L_1$ is assumed to be in its static equilibrium position, because any residual vibration there will be rapidly damped out: in the case of the tanpura, by contact with the cotton jivari thread. In Fig. 1, the solid line shows a typical string displacement when out of contact, while the dashed line shows an in-contact case. Note that for clarity this figure shows a rather large distance between the stop and the end of the string, but in real instruments that distance is very short.
When the string is not in contact with the stop, we can express the displacement as a modal sum in the form
$$w_1(x,t)=\sum_n{\sin \dfrac{n \pi x}{L_1} (a_n \cos \omega_n t + b_n \sin \omega_n t)} \tag{1}$$
whereas when it is in contact we can write
$$w_2(x,t)=\sum_n{\sin \dfrac{n \pi x}{L_2} (c_n \cos \Omega_n t + d_n \sin \Omega_n t)} \tag{2}$$
where in the second case the expression only applies for $0 \le x \le L_2$. The natural frequencies of the full string, without the stop, are $\omega_n$, while those the string would have if it was permanently fixed at the stop are $\Omega_n$. Suitable expressions for these frequencies were derived from section 5.4.3, incorporating the inharmonicity effect of bending stiffness in the string. For simplicity, damping has been omitted from equations (1) and (2): it does not play a significant role in the process of switch-over when contact is made or lost, which we will deal with next. However, allowance for small damping will be incorporated in the final simulation model.
At a moment when contact with the stop is made or lost, we need to relate the two expressions (1) and (2) by requiring that the displacement and velocity of the string for $0 \le x \le L_2$ are the same whether calculated from $w_1$ or $w_2$. The two requirements are
$$\sum_n{\sin \dfrac{n \pi x}{L_1} (a_n \cos \omega_n t + b_n \sin \omega_n t)}$$
$$\mathrm{~~~~~~~~~~~~~~}=\sum_n{\sin \dfrac{n \pi x}{L_2} (c_n \cos \Omega_n t + d_n \sin \Omega_n t)} \tag{3}$$
and
$$\sum_n{\sin \dfrac{n \pi x}{L_1} \omega_n (b_n \cos \omega_n t \mathrm{~} – \mathrm{~} a_n \sin \omega_n t)}$$
$$\mathrm{~~~~~~~~~~~~~~} =\sum_n{\sin \dfrac{n \pi x}{L_2} \Omega_n (d_n \cos \Omega_n t \mathrm{~} – \mathrm{~} c_n \sin \Omega_n t)} . \tag{4}$$
Since we have used sinusoidal shapes in both expressions, this amounts to calculating the Fourier series decomposition of $w_1$ and $\dot{w}_1$ in terms of the sine functions used to express $w_2$. The method was explained in section 2.2.1: we need to multiply both equations through by $\sin m \pi x/L_2$, integrate over the range of $x$ from $0$ to $L_2$, and take advantage of the orthogonality of the sine functions.
For equation (3), the result is
$$c_m \cos \Omega_m t + d_m \sin \Omega_m t \mathrm{~~~~~~~~~~~~~~}$$
$$\mathrm{~~~~~~~~~~~~~~} = \dfrac{2}{L_2}\sum_n{I_{mn} (a_n \cos \omega_n t + b_n \sin \omega_n t)} \tag{5}$$
where
$$I_{mn}=\int_0^{L_2}{ \sin \dfrac{n \pi x}{L_1} \sin \dfrac{m \pi x}{L_2} dx} . \tag{6}$$
The corresponding result from equation (4) is
$$d_m \cos \Omega_m t \mathrm{~} – \mathrm{~} c_m \sin \Omega_m t \mathrm{~~~~~~~~~~~~~~~~~~~~~~}$$
$$\mathrm{~~~~~~~~~~~~~~} = \dfrac{2}{L_2 \Omega_m}\sum_n{I_{mn} \omega_n (b_n \cos \omega_n t \mathrm{~} – \mathrm{~} a_n \sin \omega_n t)} . \tag{7}$$
The integral $I_{mn}$ can be evaluated straightforwardly, making use of the trigonometric identity
$$\sin A \sin B = \dfrac{1}{2} [\cos(A-B) – \cos(A+B)] , \tag{8}$$
to give
$$I_{mn} = \dfrac{L_1 L_2}{2 \pi}\left[ \dfrac{\sin \frac{\pi(n L_2 – m L_1)}{L_1}}{n L_2 \mathrm{~} – \mathrm{~}m L_1} – \dfrac{\sin \frac{\pi(n L_2 + m L_1)}{L_1}}{n L_2 +m L_1}\right] . \tag{9}$$
We can write these results in a compact form by defining vectors $\underline{A}$, $\underline{B}$, $\underline{C}$ and $\underline{D}$ with components given by
$$A_n=a_n \cos \omega_n t+b_n \sin \omega_n t \tag{10}$$
$$B_n=\omega_n(b_n \cos \omega_n t-a_n \sin \omega_n t) \tag{11}$$
$$C_n=c_n \cos \Omega_n t+d_n \sin \Omega_n t \tag{12}$$
$$D_n=\Omega_n(d_n \cos \Omega_n t-c_n \sin \Omega_n t) \tag{13}$$
and writing $I$ for the matrix with components $I_{mn}$: then equations (5) and (7) become
$$\underline{C} = \dfrac{2}{L_2} I \mathrm{~} \underline{A} \tag{14}$$
and
$$\underline{D} = \dfrac{2}{L_2} I \mathrm{~} \underline{B} . \tag{15}$$
Now we can describe the sequence of the simulation. Suppose we begin with an excitation of the string which is upwards, away from the stop. That means that the initial motion is out of contact, and our initial conditions define the coefficients $a_n$ and $b_n$. We then proceed by evaluating equation (1) at each time step (and at this stage we can insert the exponential factors necessary to describe the damping of each string mode). If $w_1(L_2,t)$ is still such that the string lies above the stop, we are still out of contact and we proceed to the next time step.
But when $w_1(L_2,t)$ lies below the position of the stop, contact has been made. We need to transfer attention to equation (2), so we need to know the values of $c_n$ and $d_n$. From the known values of $a_n$ and $b_n$, we calculate $C_n$ and $D_n$ from equations (14) and (15), then invert equations (12) and (13) to give
$$c_n=C_n \cos \Omega_n t-\dfrac{D_n}{\Omega_n} \sin \Omega_n t \tag{16}$$
$$d_n=\dfrac{D_n}{\Omega_n} \cos \Omega_n t+C_n \sin \Omega_n t . \tag{17}$$
Now at each time step we evaluate equation (2) (with the added damping terms) to give the string motion, then check whether contact has been lost. The condition for loss of contact is that the force on the stop is upwards rather than downwards in Fig. 1, so contact is lost the first time we find
$$T \left.\dfrac{\partial w_2}{\partial x} \right|_{x=L_2} < 0 \tag{18}$$
where $T$ is the tension of the string. This time, we know the values of $c_n$ and $d_n$, and we need to calculate corresponding values of $a_n$ and $b_n$. We can find $A_n$ and $B_n$ by inverting equations (14) and (15):
$$\underline{A} = \dfrac{L_2}{2} I^{-1} \underline{C} \tag{19}$$
and
$$\underline{B} = \dfrac{L_2}{2} I^{-1} \underline{D} , \tag{20}$$
then finally invert equations (10) and (11) to obtain
$$a_n=A_n \cos \omega_n t-\dfrac{B_n}{\omega_n} \sin \omega_n t \tag{21}$$
$$b_n=\dfrac{B_n}{\omega_n} \cos \omega_n t+A_n \sin \omega_n t . \tag{22}$$
The string is then out of contact again, and we repeat the process until the desired simulation time is reached.
The simulations in section 12.3 used this model, with parameter values loosely based on a tanpura. The string length was $L_2=0.99 \mathrm{~m}$, the distance $L_1-L_2$ was 5 mm and the string was assumed to be made of brass with a diameter 0.4 mm. The nominal tuned frequency was 73.4 Hz. Damping was included using the model developed in Chapter 5 and applied to a clavichord string in section 12.2.4. The resulting Q-factor, as a function of frequency, is shown in Fig. 2. For the cases shown in section 12.3, the stop was positioned exactly on the equilibrium line of the string. The sampling rate was 44.1 kHz, for convenience of audio sound demonstrations.
[1] C. Valette and C. Cuesta, “Mécanique de la corde vibrante”, Hermés, Paris (1993). A summary in English is given by C. Valette, “The mechanics of vibrating strings”, Chapter 4 of “Mechanics of musical instruments”, ed. A. Hirschberg, J. Kergomard and G. Weinreich; CISM Courses and Lectures no. 355, Springer-Verlag (1995). | 2,527 | 7,927 | {"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} | 3.796875 | 4 | CC-MAIN-2024-38 | latest | en | 0.898575 |
http://educationask.com/general/539-general.html | 1,619,050,647,000,000,000 | text/html | crawl-data/CC-MAIN-2021-17/segments/1618039554437.90/warc/CC-MAIN-20210421222632-20210422012632-00356.warc.gz | 26,896,326 | 2,721 | # A mixture of 50 litres of milk and water contain 10% of water. How much water must be added to make water?
Question:conti..20% in the given mixture?
choice
a)5.5 litres
b)6.5 litres
c)6 litres
d)6.25 litres
e)6.75 litres
10% of 50L is 5L
a) 5.5L + 5L = 10.5L of 55.5L = 10.5%
b) 6.5L + 5L = 11.5L of 56.5L = 20.4%
c) 6L + 5L = 11L of 56L = 19.6%
d) 6.25L + 5L = 11.25L of 56.25L = 20.0%
e) 6.75L + 5L = 11.75L of 56.75L = 20.7% | 225 | 434 | {"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} | 3.921875 | 4 | CC-MAIN-2021-17 | longest | en | 0.760098 |
http://nrich.maths.org/public/leg.php?code=106&cl=2&cldcmpid=2569 | 1,500,993,786,000,000,000 | text/html | crawl-data/CC-MAIN-2017-30/segments/1500549425254.88/warc/CC-MAIN-20170725142515-20170725162515-00074.warc.gz | 236,961,378 | 8,574 | # Search by Topic
#### Resources tagged with Cubes similar to Bands and Bridges: Bringing Topology Back:
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### There are 36 results
Broad Topics > 3D Geometry, Shape and Space > Cubes
### Dice, Routes and Pathways
##### Stage: 1, 2 and 3
This article for teachers discusses examples of problems in which there is no obvious method but in which children can be encouraged to think deeply about the context and extend their ability to. . . .
### Christmas Boxes
##### Stage: 3 Challenge Level:
Find all the ways to cut out a 'net' of six squares that can be folded into a cube.
### Cubist Cuts
##### Stage: 3 Challenge Level:
A 3x3x3 cube may be reduced to unit cubes in six saw cuts. If after every cut you can rearrange the pieces before cutting straight through, can you do it in fewer?
### Drilling Many Cubes
##### Stage: 3 Challenge Level:
A useful visualising exercise which offers opportunities for discussion and generalising, and which could be used for thinking about the formulae needed for generating the results on a spreadsheet.
### Tic Tac Toe
##### Stage: 3 Challenge Level:
In the game of Noughts and Crosses there are 8 distinct winning lines. How many distinct winning lines are there in a game played on a 3 by 3 by 3 board, with 27 cells?
### Troublesome Dice
##### Stage: 3 Challenge Level:
When dice land edge-up, we usually roll again. But what if we didn't...?
### Dicey
##### Stage: 2 Challenge Level:
A game has a special dice with a colour spot on each face. These three pictures show different views of the same dice. What colour is opposite blue?
### Take Ten
##### Stage: 3 Challenge Level:
Is it possible to remove ten unit cubes from a 3 by 3 by 3 cube made from 27 unit cubes so that the surface area of the remaining solid is the same as the surface area of the original 3 by 3 by 3. . . .
### Icosian Game
##### Stage: 3 Challenge Level:
This problem is about investigating whether it is possible to start at one vertex of a platonic solid and visit every other vertex once only returning to the vertex you started at.
### How Many Dice?
##### Stage: 3 Challenge Level:
A standard die has the numbers 1, 2 and 3 are opposite 6, 5 and 4 respectively so that opposite faces add to 7? If you make standard dice by writing 1, 2, 3, 4, 5, 6 on blank cubes you will find. . . .
### Painted Faces
##### Stage: 2 Challenge Level:
Imagine a 3 by 3 by 3 cube made of 9 small cubes. Each face of the large cube is painted a different colour. How many small cubes will have two painted faces? Where are they?
### Cube Drilling
##### Stage: 2 Challenge Level:
Imagine a 4 by 4 by 4 cube. If you and a friend drill holes in some of the small cubes in the ways described, how many will not have holes drilled through them?
### Marbles in a Box
##### Stage: 3 Challenge Level:
How many winning lines can you make in a three-dimensional version of noughts and crosses?
### Counting Triangles
##### Stage: 3 Challenge Level:
Triangles are formed by joining the vertices of a skeletal cube. How many different types of triangle are there? How many triangles altogether?
### All in the Mind
##### Stage: 3 Challenge Level:
Imagine you are suspending a cube from one vertex (corner) and allowing it to hang freely. Now imagine you are lowering it into water until it is exactly half submerged. What shape does the surface. . . .
### Painting Cubes
##### Stage: 3 Challenge Level:
Imagine you have six different colours of paint. You paint a cube using a different colour for each of the six faces. How many different cubes can be painted using the same set of six colours?
### Next Size Up
##### Stage: 2 Challenge Level:
The challenge for you is to make a string of six (or more!) graded cubes.
### Holes
##### Stage: 1 and 2 Challenge Level:
I've made some cubes and some cubes with holes in. This challenge invites you to explore the difference in the number of small cubes I've used. Can you see any patterns?
### Painted Cube
##### Stage: 3 Challenge Level:
Imagine a large cube made from small red cubes being dropped into a pot of yellow paint. How many of the small cubes will have yellow paint on their faces?
### Construct-o-straws
##### Stage: 2 Challenge Level:
Make a cube out of straws and have a go at this practical challenge.
### Green Cube, Yellow Cube
##### Stage: 2 Challenge Level:
How can you paint the faces of these eight cubes so they can be put together to make a 2 x 2 cube that is green all over AND a 2 x 2 cube that is yellow all over?
### Nine Colours
##### Stage: 3 Challenge Level:
Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?
### Three Cubed
##### Stage: 2 Challenge Level:
Can you make a 3x3 cube with these shapes made from small cubes?
### A Puzzling Cube
##### Stage: 2 Challenge Level:
Here are the six faces of a cube - in no particular order. Here are three views of the cube. Can you deduce where the faces are in relation to each other and record them on the net of this cube?
### Triple Cubes
##### Stage: 1 and 2 Challenge Level:
This challenge involves eight three-cube models made from interlocking cubes. Investigate different ways of putting the models together then compare your constructions.
### Four Layers
##### Stage: 1 and 2 Challenge Level:
Can you create more models that follow these rules?
### Three Sets of Cubes, Two Surfaces
##### Stage: 2 Challenge Level:
How many models can you find which obey these rules?
### Making Maths: Link-a-cube
##### Stage: 2 Challenge Level:
Make a cube with three strips of paper. Colour three faces or use the numbers 1 to 6 to make a die.
### Thinking 3D
##### Stage: 2 and 3
How can we as teachers begin to introduce 3D ideas to young children? Where do they start? How can we lay the foundations for a later enthusiasm for working in three dimensions?
### Changing Areas, Changing Volumes
##### Stage: 3 Challenge Level:
How can you change the surface area of a cuboid but keep its volume the same? How can you change the volume but keep the surface area the same?
### Cubic Conundrum
##### Stage: 2, 3 and 4 Challenge Level:
Which of the following cubes can be made from these nets?
### The Third Dimension
##### Stage: 1 and 2 Challenge Level:
Here are four cubes joined together. How many other arrangements of four cubes can you find? Can you draw them on dotty paper?
### Christmas Presents
##### Stage: 2 Challenge Level:
We need to wrap up this cube-shaped present, remembering that we can have no overlaps. What shapes can you find to use?
### Classifying Solids Using Angle Deficiency
##### Stage: 3 and 4 Challenge Level:
Toni Beardon has chosen this article introducing a rich area for practical exploration and discovery in 3D geometry
### Cubes
##### Stage: 1 and 2 Challenge Level:
Investigate the number of faces you can see when you arrange three cubes in different ways.
### Paper Folding - Models of the Platonic Solids
##### Stage: 2, 3 and 4
A description of how to make the five Platonic solids out of paper. | 1,700 | 7,181 | {"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} | 4.15625 | 4 | CC-MAIN-2017-30 | longest | en | 0.910658 |
https://wizedu.com/questions/5?page=4 | 1,718,727,249,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198861762.73/warc/CC-MAIN-20240618140737-20240618170737-00056.warc.gz | 542,581,299 | 11,907 | A lab is testing the amount of a certain active chemical compound in a particular drug...
A lab is testing the amount of a certain active chemical compound in a particular drug that has been recently developed. The manufacturer claims that the average amount of the chemical is 110 mg. It is known that the standard deviation in the amount of the chemical is 7 mg.
A random sample of 21 batches of the new drug is tested and found to have a sample mean concentration of 104.5 mg of the active chemical.
a)Calculate the 95% confidence interval for the mean amount of the active chemical in the drug. Give your answers to 2 decimal places.
≤ μ ≤
b)At a significance level α = 0.05, the null hypothesis that the population mean amount of the active chemical in the drug is 110 mg is
In: Statistics and Probability
An entrepreneur examines monthly sales (in $1,000s) for 40 convenience stores in Rhode Island. (You may... An entrepreneur examines monthly sales (in$1,000s) for 40 convenience stores in Rhode Island. (You may find it useful to reference the appropriate table: z table or t table)
Excel data
Sales Sqft 140 1810 160 2500 80 1010 180 2170 140 2310 110 1320 90 1130 110 1500 130 1950 80 1010 110 1770 140 1840 140 2330 140 2490 120 1550 120 1900 210 2320 120 1700 180 2500 170 2380 160 1880 120 1780 120 1610 90 1230 140 1920 100 1260 90 1260 190 2470 130 2420 110 1550 100 1260 140 2230 100 1500 140 1970 120 1530 120 1800 110 1520 170 2210 100 1440 110 1470
a. Select the null and the alternative hypotheses in order to test whether average sales differ from $130,000. • H0: μ = 130,000; HA: μ ≠ 130,000 • H0: μ ≥ 130,000; HA: μ < 130,000 • H0: μ ≤ 130,000; HA: μ > 130,000 b-1. Calculate the value of the test statistic. (Negative value should be indicated by a minus sign. Round intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.) b-2. Find the p-value. • p-value < 0.01 • 0.01 ≤ p-value < 0.02 • 0.02 ≤ p-value < 0.05 • 0.05 ≤ p-value < 0.10 • p-value ≥ 0.10 c. At α = 0.05 what is your conclusion? Do average sales differ from$130,000?
• Reject H0; average sales differ from $130,000. • Reject H0; average sales do not differ from$130,000.
• Do not reject H0; average sales differ from $130,000. • Do not reject H0; average sales do not differ from$130,000.
In: Statistics and Probability
AlwaysRain Irrigation, Inc., would like to determine capacity requirements for the next four years. Currently two...
AlwaysRain Irrigation, Inc., would like to determine capacity requirements for the next four years. Currently two production lines are in place for making bronze and plastic sprinklers. Three types of sprinklers are available in both bronze and plastic: 90-degree nozzle sprinklers, 180-degree nozzle sprinklers, and 360-degree nozzle sprinklers. Management has forecast demand for the next four years as follows:
YEARLY DEMAND 1 (IN 000s) 2 (IN 000s) 3 (IN 000s) 4 (IN 000s) Plastic 90 31 40 52 53 Plastic 180 14 16 17 14 Plastic 360 52 52 63 65 Bronze 90 6 6 5 15 Bronze 180 2 2 5 13 Bronze 360 10 12 11 22
Both production lines can produce all the different types of nozzles. The bronze machines needed for the bronze sprinklers require three operators and can produce up to 18,000 sprinklers. The plastic injection molding machine needed for the plastic sprinklers requires four operators and can produce up to 300,000 sprinklers. Three bronze machines and only one injection molding machine are available.
What are the capacity requirements for the next four years? (Assume that there is no learning.) (Enter the demand values in thousands. Round your answers to 2 decimal places.)
Year 1 Year 2 Year 3 Year 4 Plastic Demand for plastic sprinklers Percentage of capacity used % % % % Machine requirements Labor requirements Bronze Demand for bronze sprinklers Percentage of capacity used % % % % Machine requirements Labor requirements
In: Statistics and Probability
How to determine quartile
How to determine quartile
In: Statistics and Probability
A manufacturing shop is designed to operate most efficiently at an output of 580 units per...
A manufacturing shop is designed to operate most efficiently at an output of 580 units per day. In the past month the plant averaged 510 units per day.
What was their capacity utilization rate last month? (Round your answer to 1 decimal place.)
Capacity utilization rate %
In: Statistics and Probability
Question text In a random sample of 200 people, 32 people have blue eyes (characteristic B)....
Question text
In a random sample of 200 people, 32 people have blue eyes (characteristic B). Which of the following 95% confidence intervals estimate the true proportion pp of measurements in the population with characteristic B?
Select one:
a. (0.109, 0.211)
c. (0.431, 0.712)
d. (0.561, 0.912)
In: Statistics and Probability
The score of 24 randomly selected exams in a geometry class are given below: 72 85...
The score of 24 randomly selected exams in a geometry class are given below:
72 85 62 88 75 65 76 99 74 67 83 50 98 78 90 70 80 55 78 77 70 80 68 60
It has been reported that the mean score of all geometry exams is less than 78. Test the validity of the report at α = 0.02 by using the data given above.
(a) Clearly, state H0 and H1, identify the claim and type of test.
H0 :
H1 :
b) Find and name all related critical values, draw the distribution, and clearly mark and shade the critical region(s).
(c) Find the computed test statistic and the P-value.
C.T.S. :
P-Value :
(d) Use non-statistical terminology to state your final conclusion about the claim.
It has also been reported that the standard deviation of all scores in a geometry exam is 10. Test the validity of the report at α = 0.01 by using the data given above.
(e) Clearly, state H0 and H1, identify the claim and type of test.
H0 :
H1 :
(f) Find and name all related critical values, draw the distribution, clearly mark and shade the critical region(s).
(g) Find the computed test statistic and the P-value.
C.T.S. :
P-Value :
(h) Use non-statistical terminology to state your final conclusion about the claim.
In: Statistics and Probability
The average driving distance (yards) and driving accuracy(percent of drives that land in the fairway) for...
Player Distance (yards) Accuracy (%) The average driving distance (yards) and driving accuracy(percent of drives that land in the fairway) for 8 golfers are recorded in the table to the right. Complete parts a through e below. 1 316.1316.1 44.6 2 303.3 51.7 3 309.4 47.5 4 311.6 40.6 5 295.3 55.4 6 290.4 58.9 7 295.8 56.2 8 304.3 49.5
a. Write the equation of a straight-line model relating driving accuracy (y) to driving distance (x). Choose the correct answer below.
A.y =β1x
B.y=β1x2+β0
C.y=β1x+ε
D.y=β0+β1x+ε
b. Fit the model, part
a,to the data using simple linear regression. Give the least squares prediction equation.ModifyingAbove y with caretyequals= 250.3plus+Left parenthesis negative 0.6587 right parenthesis(−0.6587)x
c. Interpret the estimated y-intercept of the line.
A.Since a drive with 0% accuracy is outside the range of the sample data, the y-intercept has no practical interpretation.
B.For each additional yard in distance, the accuracy is estimated to change by the value of the y-intercept.
C.For each additional percentage in accuracy, the distance is estimated to change by the value of they-intercept.
D.Since a drive with distance 0 yards is outside the range of the sample data, the y-intercept has no practical interpretation.
d. Interpret the estimated slope of the line. Choose the correct answer below.
A.Since a drive with distance 0 yards is outside the range of the sample data, the slope has no practical interpretation.
B.For each additional percentage in accuracy, the distance is estimated to change by the value of the slope.
C.For each additional yard in distance, the accuracy is estimated to change by the value of the slope.
D.Since a drive with 0% accuracy is outside the range of the sample data, the slope has no practical interpretation.
In: Statistics and Probability
Are America's top chief executive officers (CEOs) really worth all that money? One way to answer...
Are America's top chief executive officers (CEOs) really worth all that money? One way to answer this question is to look at row B, the annual company percentage increase in revenue, versus row A, the CEO's annual percentage salary increase in that same company. Suppose that a random sample of companies yielded the following data: B: Percent for company 2 5 29 8 21 14 13 12 A: Percent for CEO -1 5 21 13 12 18 9 8 Do these data indicate that the population mean percentage increase in corporate revenue (row B) is different from the population mean percentage increase in CEO salary? Use a 1% level of significance. Will you use a left tailed, right tailed, or two tailed test? Select one: a. two tailed test b. right tailed test c. left tailed test
In: Statistics and Probability
The heights of 18-year-old men are approximately normally distributed with mean 68 inches and standard deviation...
The heights of 18-year-old men are approximately normally distributed with mean 68 inches and standard deviation 3 inches. What is the probability that the average height of a sample of twenty 18-year-old men will be less than 69 inches? Round your answer to four decimal places.
In: Statistics and Probability
The (simulated) data (mg decrease per decilitre of blood) for the Omega-3 group is stored in...
The (simulated) data (mg decrease per decilitre of blood) for the Omega-3 group is stored in Table A1, and the data for the control group is stored in Table A2. You are required to calculate a 95% confidence interval for the average difference in cholesterol reduction and to test the hypothesis that there was no difference between the two diets in average reduction of cholesterol.
1. How many patients were in each diet group?
2. What was the mean (decrease) in cholesterol for the Omega-3 group of patients?
3. What was the standard deviation in that group? LABORATORY ASSIGNMENTS INTRODUCTORY STATISTICS LABORATORY 37
4. What was the mean (decrease) in cholesterol for the control group of patients?
5. What was the standard deviation in the control group?
6. What is the estimated difference of means?
7. Standard error of the difference between means 2 2 2 1 2 1 n s n s = + What is the standard error of the difference of means?
b) Calculate the margin of error of the estimated difference of means. For this large-sample 95% confidence interval we can approximate with a z value which is z0.025 = 1.96. Calculate the confidence interval as difference between means ± margin of error.
8. What is the margin of error of the estimated difference?
9. What is the lower limit for the 95% confidence interval of the difference in cholesterol reduction between Omega-3 and control diets?
10. What is the upper limit?
DATA A1:
86.6
73.9
99.4
67.9
82.3
80.3
82.8
77.9
76.8
85.9
62.5
34
120.9
57
114.9
83.7
103.5
67.4
86.1
87.6
104.2
123
91.7
95.2
95.8
90.7
72.9
72.9
62
98.1
70
77.3
34.8
58
66.7
100.6
98.6
75
52.9
54
42.1
86.7
68.9
68.8
76
87.1
99.2
119.3
88.5
90.9
DATA A2
52.5 38.6 60.7 90.8 57.9 38.6 31.9 35.2 27.7 31.5 39.4 80.4 61.1 88.1 37.5 43.5 35.6 81.6 55.2 66.7 56.3 47.4 105.2 51.7 35.8 58.9 24.5 92.8 55 52.5 110.2 86.5 30.7 50.8 58.2 75.1 73.9 12.5 23.3 96.6 55.6 102.9 103 50.2 88.7 53.7 41.5 24.7 80.3 84.4
In: Statistics and Probability
To study how social media may influence the products consumers buy, researchers collected the opening weekend...
To study how social media may influence the products consumers buy, researchers collected the opening weekend box office revenue (in millions of dollars) for 23 recent movies and the social media message rate (average number of messages referring to the movie per hour). The data are available below. Conduct a complete simple linear regression analysis of the relationship between revenue (y) and message rate (x).
Message Rate
Revenue (\$millions)
1363.2
146
1219.2
79
681.2
67
583.6
37
454.7
35
413.9
34
306.2
21
289.8
18
245.1
18
163.9
17
148.9
16
147.4
15
147.3
15
123.6
14
118.1
13
108.9
13
100.1
12
90.3
11
89.1
6
70.1
6
56.2
5
41.6
3
8.4
1
The least squares regression equation is ModifyingAbove y with caret=________+ ( _______ )x. (Round to three decimal places as needed.)
PrintDone
In: Statistics and Probability
1. A population of values has a normal distribution with μ=182.1 and σ=28.9. You intend to...
1. A population of values has a normal distribution with μ=182.1 and σ=28.9. You intend to draw a random sample of size n=117.
Find the probability that a single randomly selected value is less than 187.7.
P(X < 187.7) =
Find the probability that a sample of size n=117is randomly selected with a mean less than 187.7.
P(¯x < 187.7) =
2.
CNNBC recently reported that the mean annual cost of auto insurance is 1045 dollars. Assume the standard deviation is 211 dollars. You take a simple random sample of 69 auto insurance policies.
Find the probability that a single randomly selected value is less than 977 dollars.
P(X < 977) =
Find the probability that a sample of size n=69= is randomly selected with a mean less than 977 dollars.
P(¯xx¯ < 977) =
In: Statistics and Probability
Very Bad Drugs Corp believes that their new drug, Brain Boost, increases focus and alertness by...
Very Bad Drugs Corp believes that their new drug, Brain Boost, increases focus and alertness by 15%. Answer the following:
(a)Formulate a set of two hypotheses to test their claim in words and symbols.
(b) What would a Type 1 error be?
(c) What would a Type 2 error be?
In: Statistics and Probability
Q2: Do social recommendations increase ad effectiveness? A study of online viewers who arrived at an...
Q2: Do social recommendations increase ad effectiveness? A study of online viewers who arrived at an advertising video for a particular brand by following a social media recommendation link to viewers who arrived at the same video by web browsing. Data were collected on whether the viewer could correctly recall the brand being advertised after seeing the video. The results were:
Yes No
Recommendation 407 150
Browsing 193 91
Determine whether brand recall is higher following a social media recommendation than with only web browsing at alpha=.05.
1. What is the claim from the question? What are Null and Alternative Hypothesis for this problem?
2. What kind of test do you want to use?
A. Two Samples Independent Population T Test with Equal Variance
B. Two Samples related Population T Test
C. Two Samples Independent Population T Test with Unequal Variance
D. Two Sample Proportion Z Test
E. Two Sample Variance F Test
3. Calculate Test Statistics
4. Find Critical Value(s) and appropriate degree of freedom if necessary Test Statistics:
5. Find P-value
6. What is the conclusion that you could make? Clearly write down the conclusion and business statement and illustrate what type error you could make.
In: Statistics and Probability | 4,127 | 15,232 | {"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": 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} | 3.125 | 3 | CC-MAIN-2024-26 | latest | en | 0.744227 |
https://cn.maplesoft.com/support/help/maple/view.aspx?path=GraphTheory/SpecialGraphs/CirculantGraph&L=C | 1,726,249,788,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700651535.66/warc/CC-MAIN-20240913165920-20240913195920-00366.warc.gz | 150,233,457 | 22,132 | CirculantGraph - Maple Help
GraphTheory[SpecialGraphs]
CirculantGraph
construct circulant graph
Calling Sequence CirculantGraph(n, k)
Parameters
n - positive integer k - positive integer or list of positive integers
Description
• The CirculantGraph(n,k) command returns the circulant graph on n vertices with jump parameter k.
Definition
• The circulant graph is a graph on n vertices in which vertex i is connected to vertices i-j and i+j for each j in k.
Examples
> $\mathrm{with}\left(\mathrm{GraphTheory}\right):$
> $\mathrm{with}\left(\mathrm{SpecialGraphs}\right):$
> $\mathrm{C_7_12}≔\mathrm{CirculantGraph}\left(7,\left[1,2\right]\right)$
${\mathrm{C_7_12}}{≔}{\mathrm{Graph 1: an undirected graph with 7 vertices and 14 edge\left(s\right)}}$ (1)
> $\mathrm{DrawGraph}\left(\mathrm{C_7_12}\right)$
Compatibility
• The GraphTheory[SpecialGraphs][CirculantGraph] command was introduced in Maple 2019. | 270 | 931 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 5, "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} | 3.046875 | 3 | CC-MAIN-2024-38 | latest | en | 0.45975 |
www.restaurant-alte-muehle.de | 1,686,028,716,000,000,000 | text/html | crawl-data/CC-MAIN-2023-23/segments/1685224652235.2/warc/CC-MAIN-20230606045924-20230606075924-00723.warc.gz | 1,059,205,796 | 7,392 | calculate rpm of mill
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# calculate rpm of mill
• ### Speed and Feed Calculator
The proper speed and feed help improve tool life and remove material at the optimal rate. Find SFM, IPM, RPM, and more here.
• ### How To Calculate Rpm Of Mill In Cement Plant
How To Calculate Cement Mill Critical Speed. How to calculate rpm of mill in cement plant. The paper also Mill speed rpm GM in I chamber 107 t Critical speed 76 GM in II chamber 217 t • Empty heights of both the chambers measured to calculate the ball charge, filling and estimate the power consumption at mill shaft. .
• ### How To Calculate Rpm Of Mill In Cement Plant
How To Calculate Rpm Of Mill In Cement Plant; How To Calculate Rpm Of Mill In Cement Plant . We provide you with all accessories of mining machinery and equipment produced by our company, with complete models, reliable performance, stability and durability. Ensure the first time to meet customer parts replacement needs, reduce customer downtime maintenance …
• ### how to calculate rpm of mill in cement plant
how to calculate rpm of mill in cement plant. September 1, 2022 CONCRETE MANUAL BATCHING AND MIXING CHECKING BATC H PLANT OPERATION Check to ensure accuracy and dependable operati on of the proposed equipment and methods prior to the start of concreting operations and after ma king any changes in the …
• ### Formula for Face Milling
Formulae for Face Milling. Cutting Speed(vc) *Divide by 1000 to change to m from mm. DC(mm);Cutter Diameter π():Pi n(min-1):Main Axis Spindle Speed vc(m/min):Cutting Speed . Check the item you want to calculate, input values in the two boxes, and then press the Calculate button. DC(mm) n(min-1) vc(m/min) （Problem） What is the cutting speed when …
For forms, calculate values with a factor of 1 This function is blocking, and should not be used in async functions A qualified cosmetic surgeon 86603P – 3W Notice that if we know the pitch (P) and the wire diameter (W), then for any G-code G76 is a cnc cycle which is used for thread cutting on cnc machines G-code G76 is a cnc cycle which is used for thread cutting on cnc machines. …
• ### Face Milling Formulas
This is a list of formulas used in face milling. This page explains the formulas for calculating the cutting speed (vc), feed per tooth (f), table feed (Vf), machining time (Tc), net power for face milling (Pc), and Kc values, giving examples to help your understanding. "Introduction to Machining" is a site where users can learn about machining.
• ### Metric Milling Formulas
You are viewing the milling formulas for metric units, if you'd like to view the milling formulas for english units please click here. Symbol Chart. D = Depth of Cut (in millimeters) d = Diameter of Cutter (in millimeters) T = Number of Teeth in Cutter : W = Width of Cut (in millimeters) K = Constant (cubic inches per minute per HPc) = Revolutions per Minute: = …
• ### What RPM should you mill aluminum?
· RPM recommendations based on First Guess Speeds for various drill bit diameters. 1/8 (.125″); tool steel. 45-60. 1528. cast Iron. 50-125. 2139. aluminum and alloys.
• ### Calculate Rpm Of Mill
How Do You Calculate The Rpm Of An End Mill Answerstoall. May 08, 2022 How do you calculate the RPM of an end mill? To calculate RPMs, the formula is RPM x CSS Dia. CSS is the Constant Surface Speed in Surface Feet per Minute. Dia. is the diameter of the cutting tool you are using (or the diameter of the workpiece you are cutting on a lathe).
• ### how to calculate rpm of mill in cement plant
Cement mill notebook - SlideShare. 7 Jan 2022 Calculation of the Critical Mill Speed: G: weight of a grinding ball in kg. w: Angular velocity of the …
• ### Wind Turbine Calculator – WindCycle
This wind turbine calculator is a comprehensive tool for determining the power output, revenue, and torque of either a horizontal-axis (HAWT) or vertical-axis turbine (VAWT). You only need to input a few basic parameters to check the efficiency of your turbine and how much it can earn you. You can use our tool as either a HAWT or a VAWT
• ### How can I calculate the rotational speed of a wind turbine?
generally, a 20kW wind turbine has a 9-12m Rotor Diameter, TSR=6 and your wind speed is 9m/s, so i calculated RPM for this turbine: 9m Rotor : RPM. 10m Rotor: RPM. 12m Rotor: 85
• ### how can we calculate the rpm of ball mill
ball mill rpm calculation for quartz material 49 Ratings The Gulin product line consisting of more than 30 machines sets the standard for our industry We plan to help you meet your needs with our equipment with our distribution and product support system and the continual introduction and updating of products Milling Speed. Design of horizontal ball mills for improving the rate of . …
• ### Free Speeds & Feeds Calculator (Milling, Turning, Drilling)
For grooving application – Choose grooving for shallow grooving and parting for deep grooving. What to Get: If you need only the cutting speed [1], select "Speeds Only", and you will be asked to enter fewer parameters. Mode – Advanced / Simple: In simple mode, you need to enter fewer parameters, and the calculator will rely on the
• ### how to calculate rpm of mill in cement plantstonecrusher
Raw mills usually operate at 72-74% critical speed and cement mills at 74-76%. calculation of the critical mill speed g weight of a grinding ball in angular velocity of the mill tube in radial/ 2**(n/60) di inside mill diameter in meter (effective mill diameter).n revolution per minute in rpm. More
• ### How To Calculate Rpm Of A Motor To Ball Mill
SC Milling parameters. 19904 rpm 500 1000 314 8 If the maximum speed of the milling motor is lower than the calculated value the maximum speed of the milling motor needs to be inserted into the formula for the feed calculation The end mill feed rate is calculated with the following formula vf n z fz
• ### Ball Mill Design/Power Calculation
· The approximate horsepower HP of a mill can be calculated from the following equation: HP = (W) (C) (Sin a) (2π) (N)/ 33000. where: W = weight of charge. C = distance of centre of gravity or charge from centre of mill in feet. a = dynamic angle of repose of the charge. N = mill speed in RPM. HP = A x B x C x L. Where.
• ### Spindle Speed Calculator with steps
· To determine spindle speed, use the following steps: Enter the diameter of the part, D = 30 mm. Fill in the cutting speed, V = 7 m/min. Calculation is done using the spindle speed formula: N_s= dfrac {V cdot 1000} {pi cdot D} N_s = dfrac {7 cdot 1000} {pi cdot 30} = rpm. The preceding paragraph illustrates how to determine the
• ### Ball Mill Parameter Selection & Calculation
· 1 Calculation of ball mill capacity. The production capacity of the ball mill is determined by the amount of material required to be ground, and it must have a certain margin when designing and selecting. There are many factors affecting the production capacity of the ball mill, in addition to the nature of the material (grain size, hardness, density, temperature and …
• ### How To Calculate Table Rpm In Vertical Raw Mill
Ball Mill Design Power Calculation. Jun 19, 2022 The ball mill motor power requirement calculated above as 1400 HP is the power that must be applied at the mill drive in order to grind the tonnage of feed from one size distribution. The following shows how the size or select the matching mill required to draw this power is calculated from known
• ### How To Calculate Rpm Of Mill In Cement Plant
1 calculation of ball mill capacity. the production capacity of the ball mill is determined by the amount of material required to be ground, and it must have a certain margin when designing and selecting. there are many factors affecting the production capacity of the ball mill, in addition to the nature of the material grain size, hardness, density, temperature and.
• ### How To Calculate Table Rpm In Vertical Raw Mill
Milling Speed And Feed Calculator. Milling speed and feed calculator milling operations remove material by feeding a workpiece into a rotating cutting tool with sharp teeth such as an end mill or face mill calculations use the desired tool diameter number of teeth cutting speed and cutting feed which should be chosen based on the specific cutting conditions including the …
• ### How Can We Calculate The Rpm Of Ball Mill-ball Mill
Ball Mill Rpm Calculation Introduction To The Mill Mit. A ball mill critical speed actually ball rod ag or sag is the speed at which the centrifugal forces equal gravitational forces at the mill shells inside surface and no balls will fall from its position onto the shell the imagery below helps explain what goes on inside a mill as speed varies lab report 1 and 2 practical 1 ball
• ### mininghow to calculate rpm of mill in cement plant
mininghow to calculate rpm of mill in cement plant Description. aixergee - Process Optimization for the Cement Industry. Jul 09, 2022· Alfonsstr. 44 52070 Aachen Tel. +49 241 4134492-50 [email protected] Process Optimization for the Cement Industry. Get Price →
• ### How to calculate planetry ball mill parmeters?
· Cordierite was synthesized by the reaction sintering using a high-energy ball milling process. After a high-energy ball milling for 32hr, the reaction temperature of cordierite was reduced to 1350
• ### how to calculate rpm of mill in cement plant
.:. Mill Critical Speed Determination. Enter the measured mill rotation in revolutions per minute. Result #1: This mill would need to spin at RPM to be at 100% critical speed. Result #2: This mill's measured RPM is % of critical speed. Calculation Backup: the formula used for Critical Speed is: N c =()
• ### How to calculate the RPMs and Speeds using as slitting saw on a mill?
· This means the speed of the cutting surface will be fairly high even at low RPM compared to an end mill. For example, the Surface Feet per Minute cutting speed (SFM) for high speed steel is about 67 SFM*. For a 2" diameter slitting saw with 110 teeth cutting 12L14 steel, the calculations would be as follows: RPM = (SFM x 12) ÷ (Tool Diameter x
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• crusher pef 500 | 2,476 | 10,615 | {"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-2023-23 | latest | en | 0.839357 |
https://kidsworksheetfun.com/exponential-growth-and-decay-worksheet-answer-key-algebra-2/ | 1,701,635,232,000,000,000 | text/html | crawl-data/CC-MAIN-2023-50/segments/1700679100508.53/warc/CC-MAIN-20231203193127-20231203223127-00523.warc.gz | 400,095,671 | 25,126 | # Exponential Growth And Decay Worksheet Answer Key Algebra 2
Exponential growth and decay word problem displaying top 8 worksheets found for this concept. Within the frayer model students will explore equations real world examples tables graphsi used the information provided to compare and contrast growth a.
Exponential Functions Anchor Chart Growth And Decay Anchor Charts Exponential Growth
### A2 3 3 explain and use the laws of fractional and negative exponents understand exponential functions and use these functions in problems involving exponential growth and decay.
Exponential growth and decay worksheet answer key algebra 2. The inside of the foldable is organized with two frayer models. If growth or decay is occurring by a fixed percentage during each period of time use the formula y a 1 r t or y a 1 r t. The positive constant r is called either the growth rate for.
A2 3 4 graph an exponential function of the form f x ab x. 20 exponential growth and decay worksheet algebra 2 exponential functions algebra worksheet by pecktabo math exponential functions 20 problems 4 determine whether it is an exponential function given an equation 2 determine whether it is linear or exponential given a table 3 evaluate given x value 4 match the function to the graph 2 graph the exponential function describe the domain and rang. This foldable provides an introduction to exponential growth decay.
A2 3 4 graph an exponential function of the form f x ab x. 0 3 or 30 2. Some of the worksheets for this concept are exponential growth and decay exponential growth and decay exponential growth and decay work growth decay word problem key exponential growth and decay lesson reteach exponential functions growth and decay exponential logarithmic applications.
College algebra worksheet 2 exponential growth and decay problems if a certain quantity a is growing continuously at rate r then a may be written as a function of time as follows a a0ert. For scientific applications use the formula y ae kt or y ae kt. 0 25 or 25 4.
0 02 or 2 3. If a is decaying continuously at rate r then a may be written as follows a a0e rt. Some of the worksheets for this concept are exponential growth and decay word problems exponential growth and decay exponential growth and decay work exp growth decay word probs growth decay word problem key college algebra work 2 exponential growth and decay word problems interest.
A2 3 3 explain and use the laws of fractional and negative exponents understand exponential functions and use these functions in problems involving exponential growth and decay. Problem solving exponential growth and decay displaying top 8 worksheets found for this concept. Exponential growth and decay.
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Graphing Exponential Functions Cheat Sheet Functions Math Exponential Functions School Algebra | 895 | 4,750 | {"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-2023-50 | latest | en | 0.782822 |
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# Weird differential equation- help please? Watch
1. The equation is:
Okay, here's what I did so far... I'm not sure if it's mathematically valid introducing an imaginary term, but it was all I could think of..
The answer given by Wolfram is
... Help anyone? How on earth are you supposed to get that answer?
2. You introduced the i term to make the integral look like an arcsin. There's a related standard integral ..
Wolfram has given you a big hint - if you know about hyperbolics you're OK.
3. (Original post by ian.slater)
You introduced the i term to make the integral look like an arcsin. There's a related standard integral ..
Wolfram has given you a big hint - if you know about hyperbolics you're OK.
This a question from my textbook (the answer given in the back of the book is COMPLETELY different by the way), but the hyperbolic functions aren't actually covered in my course... hence why I was pretty shocked by this answer
Would you mind elaborating on your point please? I don't understand, isn't the derivative of just ? So the derivative of would just be ... I know pretty much nothing about hyperbolics, sorry :/
4. (Original post by innerhollow)
This a question from my textbook (the answer given in the back of the book is COMPLETELY different by the way), but the hyperbolic functions aren't actually covered in my course... hence why I was pretty shocked by this answer
Would you mind elaborating on your point please? I don't understand, isn't the derivative of just ? So the derivative of would just be ...
Try substituting y = cosh(t).
You're right about the derivative.
There are lots of interesting similarities between trig functions and the hyperbolic trigs - which is why your original approach was so good.
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https://www.transtutors.com/questions/consider-an-asset-that-costs-130-today-you-are-going-to-hold-it-for-1-year-and-then--4930045.htm | 1,582,904,247,000,000,000 | text/html | crawl-data/CC-MAIN-2020-10/segments/1581875147234.52/warc/CC-MAIN-20200228135132-20200228165132-00348.warc.gz | 899,391,312 | 16,180 | # Consider an asset that costs $130 today. You are going to hold it for 1 year and then sell it... 1 answer below » Consider an asset that costs$130 today. You are going to hold it for 1 year and then sell it. Suppose that there is a 25 percent chance that it will be worth $100 in a year, a 25 percent chance that it will be worth$120 in a year, and a 50 percent chance that it will be worth $160 in a year. Instructions: In part a, round your answer to 3 decimal places. In parts b and d, round your answers to 2 decimal places. If you are entering any negative numbers be sure to include a negative sign (-) in front of those numbers. a. What is its average expected rate of return? b. Next, figure out what the investment’s average expected rate of return would be if its current price were$140 today.
c. Does the increase in the current price increase or decrease the asset’s average expected rate of return?
(Click to select) Decrease Increase
d. At what price would the asset have a zero average expected rate of return?
This is the last question in the assignment. To submit, use Alt + S. To access other questions, proceed to the question map button.Ne
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https://kr.mathworks.com/matlabcentral/answers/1597184-dijkstra-algoritm-coding-on-multileg-itineraries | 1,721,622,504,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763517823.95/warc/CC-MAIN-20240722033934-20240722063934-00559.warc.gz | 304,917,143 | 29,354 | # Dijkstra algoritm coding on multileg itineraries
조회 수: 2 (최근 30일)
Davide Spano 2021년 11월 27일
편집: Davide Spano 2021년 11월 29일
Hi to everybody, I'm a fresh newby in this forum and actually to Matlab too.
I'm looking for a solution to a problem I heard would be resolvable with the Dijkstra algoritm, but I am not really sure if it would be the real solution.
My problem is the following:
1. I got a list of 764 ocurrencies (Variables: Code, County_name, Lon, Lat);
2. an another matrix with the distances between pairwise of 32 nodes
3. The geodesic distance between pairwise of any singular origin/destination (764) and the nodes
I need to perform the calculation tha allow me to find the minimum distance between all the pairwise of the 764 ocurrencies passing by the two of the 32 nearest nodes
I'm working on it for a very lasting time, and also if I can conceptualise that in my mind, I'm looking to a good solution that could allow to me to manage all the new 500k+ and I think the Dijkstra algoritm would be a good solution, but I can't find right way to code it.
Hope someone could help, thanks
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### 채택된 답변
Yongjian Feng 2021년 11월 27일
Dijkstra algorithm actually gives you the seudo-code of the implementation. Just need to translate that seudo-code into matlab. What do you mean "the right way" then?
##### 댓글 수: 3이전 댓글 1개 표시이전 댓글 1개 숨기기
Yongjian Feng 2021년 11월 27일
My understanding is that Dijkstra's algorithm doesn't need node values. The nodes need indices to identify them, but no values needed.
But I think Dijkstra's algorithm uses fixed source node. Or say it gives you only the shortest pathes between the selected source node and another node.
If you want any pair of nodes, you might need to look at Floyd's algorithm.
Davide Spano 2021년 11월 29일
편집: Davide Spano 2021년 11월 29일
Hi Yongjian!
I was having a look at Floyd's algorithm you suggested me on saturday, I think it also is not what I am looking for.
Think a moment about my problem in this way:
I got a matrix with 8 columns. The first two are the coordinates of the origin point (lon, lat), the second pair are the coordianate of the nearest train station, the third pair are those of the train station nearest tothe destination point, and the last pair are those of the destination point.
The occurrences are all the pairs of origin and destination points ((n*(n-1))/2)) with n=764 that I already have in an excel worksheet.
The aim of the challenge is to calculate the distance in the following way
Origin to Dep Station + Dep Stat to Arr Stat + Arr Stat to Dest.
with Dep Stat to Arr Stat = train line in Km (I have already calculate too for each pairs of train stations that are in number of 32)
when Dep Stat = Arr Stat then "train line"=1
Finally compare and chose the minimum between this multileg route and a geodesic distance.
I was thinking to write down the code as :
%define an optimal route to point Or to point Dst using a train leg
for each i in origin
leg1=geodist(origin, DepSt)
leg2= for each j in TrainStation
if Kj=Kj
then Kj+kj=1
else kj+kj="line lenght"
end
end
for each i in destination
leg3=geodist (ArrST,Destination)
end
multileg = leg1+leg2+leg3
end
%define a variable named optimalroute
optrt= min(geodist(o,d), multileg(o,d))
Now, I am aware that this sintax would never run, but this is an another way to try to define the problem with I am coping, but I am also aware I am really bad at coding.
Thanks, for any suggestion you cold give me.
D.
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A104178 Decimal expansion of log_10(3+2*sqrt(2)). 4
7, 6, 5, 5, 5, 1, 3, 7, 0, 6, 7, 5, 7, 2, 6, 1, 5, 6, 6, 3, 8, 7, 9, 9, 0, 4, 8, 3, 8, 4, 0, 1, 2, 2, 2, 6, 4, 7, 7, 4, 4, 4, 7, 3, 7, 4, 1, 4, 1, 3, 6, 5, 9, 7, 1, 1, 1, 9, 1, 1, 1, 4, 2, 0, 1, 1, 3, 5, 4, 2, 5, 1, 0, 8, 7, 9, 5, 6, 2, 7, 9, 0, 7, 8, 5, 9, 0, 1, 4, 7, 4, 1, 3, 8, 7, 6, 8, 9, 3, 7, 4, 9, 1, 7, 8 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET 0,1 LINKS G. C. Greubel, Table of n, a(n) for n = 0..10000 Eric Weisstein's World of Mathematics, Delannoy Number Eric Weisstein's World of Mathematics, Schroeder Number EXAMPLE 0.76555137067572615663879904838401222647744473741413659711191114201... MATHEMATICA RealDigits[ Log[10, 3 + 2Sqrt[2]], 10, 111][[1]] (* Robert G. Wilson v *) PROG (PARI) log(3 + 2*sqrt(2))/log(10) \\ G. C. Greubel, Mar 27 2018 (Magma) Log(3+2*Sqrt(2))/Log(10); // G. C. Greubel, Mar 27 2018 CROSSREFS Cf. A114470, A114472. Sequence in context: A182209 A120634 A178753 * A092874 A198109 A059751 Adjacent sequences: A104175 A104176 A104177 * A104179 A104180 A104181 KEYWORD nonn,cons AUTHOR N. J. A. Sloane, Dec 24 2005 EXTENSIONS More terms from Robert G. Wilson v, Dec 28 2005 STATUS approved
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# Scientists typically do their most creative work before the
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Scientists typically do their most creative work before the age of forty. It is commonly
thought that this happens because aging by itself brings about a loss of creative
capacity
. However, studies show that a disproportionately large number of the
scientists who produce highly creative work beyond the age of forty entered their
field at an older age than is usual.
Since by the age of forty the large majority of
scientists have been working in their field for at least fifteen years, the studies’ finding
strongly suggests that the real reason why scientists over forty rarely produce highly
creative work is not that they have simply aged but rather that they generally have
spent too long in a given field.
In the argument given, the two portions in boldface play which of the following roles?
A. The first is the position that the argument as a whole opposes; the second is an
objection that has been raised against a position defended in the argument.
B. the first is a claim that has been advanced in support of a position that the
argument opposes; the second is a finding that has been used in support of that
position.
C. The first is an explanation that the argument challenges; the second is a finding
that has been used in support of that explanation.
D. The first is an explanation that the argument challenges; the second is a finding on
which that challenge is based.
E. The first is an explanation that the argument defends; the second is a finding that
has been used to challenge that explanation.
Last edited by JCLEONES on 12 Feb 2008, 07:51, edited 1 time in total.
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Re: Boldfaced CR - Creative work [#permalink]
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11 Feb 2008, 16:53
JCLEONES wrote:
Scientists typically do their most creative work before the age of forty. It is commonly
thought that this happens because aging by itself brings about a loss of creative
capacity. However, studies show that a disproportionately large number of the
scientists who produce highly creative work beyond the age of forty entered their
field at an older age than is usual. Since by the age of forty the large majority of
scientists have been working in their field for at least fifteen years, the studies’ finding
strongly suggests that the real reason why scientists over forty rarely produce highly
creative work is not that they have simply aged but rather that they generally have
spent too long in a given field.
In the argument given, the two portions in boldface play which of the following roles?
A. The first is the position that the argument as a whole opposes; the second is an
objection that has been raised against a position defended in the argument.
B. the first is a claim that has been advanced in support of a position that the
argument opposes; the second is a finding that has been used in support of that
position.
C. The first is an explanation that the argument challenges; the second is a finding
that has been used in support of that explanation.
D. The first is an explanation that the argument challenges; the second is a finding on
which that challenge is based.
E. The first is an explanation that the argument defends; the second is a finding that
has been used to challenge that explanation.
Please repost with the bolds. Thx
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Re: Boldfaced CR - Creative work [#permalink]
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12 Feb 2008, 07:53
Post corrected. Thanks
GMATBLACKBELT wrote:
JCLEONES wrote:
Scientists typically do their most creative work before the age of forty. It is commonly
thought that this happens because aging by itself brings about a loss of creative
capacity. However, studies show that a disproportionately large number of the
scientists who produce highly creative work beyond the age of forty entered their
field at an older age than is usual. Since by the age of forty the large majority of
scientists have been working in their field for at least fifteen years, the studies’ finding
strongly suggests that the real reason why scientists over forty rarely produce highly
creative work is not that they have simply aged but rather that they generally have
spent too long in a given field.
In the argument given, the two portions in boldface play which of the following roles?
A. The first is the position that the argument as a whole opposes; the second is an
objection that has been raised against a position defended in the argument.
B. the first is a claim that has been advanced in support of a position that the
argument opposes; the second is a finding that has been used in support of that
position.
C. The first is an explanation that the argument challenges; the second is a finding
that has been used in support of that explanation.
D. The first is an explanation that the argument challenges; the second is a finding on
which that challenge is based.
E. The first is an explanation that the argument defends; the second is a finding that
has been used to challenge that explanation.
Please repost with the bolds. Thx
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Re: Boldfaced CR - Creative work [#permalink]
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12 Feb 2008, 09:05
D makes more sense to me.
D. The first is an explanation that the argument challenges; the second is a finding on
which that challenge is based.
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Re: Boldfaced CR - Creative work [#permalink]
### Show Tags
13 Feb 2008, 01:03
D
Scientists typically do their most creative work before the age of forty. It is commonly
thought that this happens because aging by itself brings about a loss of creative
capacity
. However, studies show that a disproportionately large number of the
scientists who produce highly creative work beyond the age of forty entered their
field at an older age than is usual.
Since by the age of forty the large majority of
scientists have been working in their field for at least fifteen years, the studies’ finding
strongly suggests that the real reason why scientists over forty rarely produce highly
creative work is not that they have simply aged but rather that they generally have
spent too long in a given field.
In the argument given, the two portions in boldface play which of the following roles?
A. The first is the position that the argument as a whole opposes; the second is an
objection that has been raised against a position defended in the argument.
B. the first is a claim that has been advanced in support of a position that the
argument opposes; the second is a finding that has been used in support of that
position
.
C. The first is an explanation that the argument challenges; the second is a finding
that has been used in support of that explanation.
D. The first is an explanation that the argument challenges; the second is a finding on
which that challenge is based. - the best.
E. The first is an explanation that the argument defends; the second is a finding that
has been used to challenge that explanation.
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Re: Boldfaced CR - Creative work [#permalink]
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13 Feb 2008, 20:20
d
Kudos [?]: 35 [0], given: 0
Re: Boldfaced CR - Creative work [#permalink] 13 Feb 2008, 20:20
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# Scientists typically do their most creative work before the
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https://findatwiki.com/Design_of_experiments | 1,717,070,857,000,000,000 | text/html | crawl-data/CC-MAIN-2024-22/segments/1715971667627.93/warc/CC-MAIN-20240530114606-20240530144606-00043.warc.gz | 218,556,204 | 36,336 | # Design of experiments
The design of experiments (DOE or DOX), also known as experiment design or experimental design, is the design of any task that aims to describe and explain the variation of information under conditions that are hypothesized to reflect the variation. The term is generally associated with
experiments in which the design introduces conditions that directly affect the variation, but may also refer to the design of quasi-experiments, in which natural
conditions that influence the variation are selected for observation.
In its simplest form, an experiment aims at predicting the outcome by introducing a change of the preconditions, which is represented by one or more independent variables, also referred to as "input variables" or "predictor variables." The change in one or more independent variables is generally hypothesized to result in a change in one or more dependent variables, also referred to as "output variables" or "response variables." The experimental design may also identify control variables that must be held constant to prevent external factors from affecting the results. Experimental design involves not only the selection of suitable independent, dependent, and control variables, but planning the delivery of the experiment under statistically optimal conditions given the constraints of available resources. There are multiple approaches for determining the set of design points (unique combinations of the settings of the independent variables) to be used in the experiment.
statistical power and sensitivity
.
Correctly designed experiments advance knowledge in the natural and social sciences and engineering, with design of experiments methodology recognised as a key tool in the successful implementation of a Quality by Design (QbD) framework.[1] Other applications include marketing and policy making. The study of the design of experiments is an important topic in metascience.
## History
### Statistical experiments, following Charles S. Peirce
A theory of statistical inference was developed by Charles S. Peirce in "Illustrations of the Logic of Science" (1877–1878)[2] and "A Theory of Probable Inference" (1883),[3] two publications that emphasized the importance of randomization-based inference in statistics.[4]
#### Randomized experiments
Charles S. Peirce randomly assigned volunteers to a
blinded, repeated-measures design to evaluate their ability to discriminate weights.[5][6][7][8]
Peirce's experiment inspired other researchers in psychology and education, which developed a research tradition of randomized experiments in laboratories and specialized textbooks in the 1800s.[5][6][7][8]
#### Optimal designs for regression models
Gergonne in 1815. In 1918, Kirstine Smith published optimal designs for polynomials of degree six (and less).[10][11]
### Sequences of experiments
The use of a sequence of experiments, where the design of each may depend on the results of previous experiments, including the possible decision to stop experimenting, is within the scope of sequential analysis, a field that was pioneered[12] by Abraham Wald in the context of sequential tests of statistical hypotheses.[13] Herman Chernoff wrote an overview of optimal sequential designs,[14] while adaptive designs have been surveyed by S. Zacks.[15] One specific type of sequential design is the "two-armed bandit", generalized to the multi-armed bandit, on which early work was done by Herbert Robbins in 1952.[16]
## Fisher's principles
A methodology for designing experiments was proposed by Ronald Fisher, in his innovative books: The Arrangement of Field Experiments (1926) and The Design of Experiments (1935). Much of his pioneering work dealt with agricultural applications of statistical methods. As a mundane example, he described how to test the lady tasting tea hypothesis, that a certain lady could distinguish by flavour alone whether the milk or the tea was first placed in the cup. These methods have been broadly adapted in biological, psychological, and agricultural research.[17]
Comparison
In some fields of study it is not possible to have independent measurements to a traceable metrology standard. Comparisons between treatments are much more valuable and are usually preferable, and often compared against a scientific control or traditional treatment that acts as baseline.
Randomization
Random assignment is the process of assigning individuals at random to groups or to different groups in an experiment, so that each individual of the population has the same chance of becoming a participant in the study. The random assignment of individuals to groups (or conditions within a group) distinguishes a rigorous, "true" experiment from an observational study or "quasi-experiment".[18] There is an extensive body of mathematical theory that explores the consequences of making the allocation of units to treatments by means of some random mechanism (such as tables of random numbers, or the use of randomization devices such as playing cards or dice). Assigning units to treatments at random tends to mitigate confounding, which makes effects due to factors other than the treatment to appear to result from the treatment.
The risks associated with random allocation (such as having a serious imbalance in a key characteristic between a treatment group and a control group) are calculable and hence can be managed down to an acceptable level by using enough experimental units. However, if the population is divided into several subpopulations that somehow differ, and the research requires each subpopulation to be equal in size, stratified sampling can be used. In that way, the units in each subpopulation are randomized, but not the whole sample. The results of an experiment can be generalized reliably from the experimental units to a larger statistical population of units only if the experimental units are a random sample from the larger population; the probable error of such an extrapolation depends on the sample size, among other things.
Statistical replication
Measurements are usually subject to variation and
peer-reviewed journal or widely cited, the researcher is independent of the original experiment, the researcher must first try to replicate the original findings using the original data, and the write-up should state that the study conducted is a replication study that tried to follow the original study as strictly as possible.[20]
Blocking
Blocking is the non-random arrangement of experimental units into groups (blocks) consisting of units that are similar to one another. Blocking reduces known but irrelevant sources of variation between units and thus allows greater precision in the estimation of the source of variation under study.
Orthogonality
Orthogonality concerns the forms of comparison (contrasts) that can be legitimately and efficiently carried out. Contrasts can be represented by vectors and sets of orthogonal contrasts are uncorrelated and independently distributed if the data are normal. Because of this independence, each orthogonal treatment provides different information to the others. If there are T treatments and T – 1 orthogonal contrasts, all the information that can be captured from the experiment is obtainable from the set of contrasts.
Multifactorial experiments
Use of multifactorial experiments instead of the one-factor-at-a-time method. These are efficient at evaluating the effects and possible interactions of several factors (independent variables). Analysis of experiment design is built on the foundation of the analysis of variance, a collection of models that partition the observed variance into components, according to what factors the experiment must estimate or test.
## Example
This example of design experiments is attributed to Harold Hotelling, building on examples from Frank Yates.[21][22][14] The experiments designed in this example involve combinatorial designs.[23]
Weights of eight objects are measured using a
independent
. Denote the true weights by
${\displaystyle \theta _{1},\dots ,\theta _{8}.\,}$
We consider two different experiments:
1. Weigh each object in one pan, with the other pan empty. Let Xi be the measured weight of the object, for i = 1, ..., 8.
2. Do the eight weighings according to the following schedule—a weighing matrix:
${\displaystyle {\begin{array}{lcc}&{\text{left pan}}&{\text{right pan}}\\\hline {\text{1st weighing:}}&1\ 2\ 3\ 4\ 5\ 6\ 7\ 8&{\text{(empty)}}\\{\text{2nd:}}&1\ 2\ 3\ 8\ &4\ 5\ 6\ 7\\{\text{3rd:}}&1\ 4\ 5\ 8\ &2\ 3\ 6\ 7\\{\text{4th:}}&1\ 6\ 7\ 8\ &2\ 3\ 4\ 5\\{\text{5th:}}&2\ 4\ 6\ 8\ &1\ 3\ 5\ 7\\{\text{6th:}}&2\ 5\ 7\ 8\ &1\ 3\ 4\ 6\\{\text{7th:}}&3\ 4\ 7\ 8\ &1\ 2\ 5\ 6\\{\text{8th:}}&3\ 5\ 6\ 8\ &1\ 2\ 4\ 7\end{array}}}$
Let Yi be the measured difference for i = 1, ..., 8. Then the estimated value of the weight θ1 is
${\displaystyle {\widehat {\theta }}_{1}={\frac {Y_{1}+Y_{2}+Y_{3}+Y_{4}-Y_{5}-Y_{6}-Y_{7}-Y_{8}}{8}}.}$
Similar estimates can be found for the weights of the other items:
{\displaystyle {\begin{aligned}{\widehat {\theta }}_{2}&={\frac {Y_{1}+Y_{2}-Y_{3}-Y_{4}+Y_{5}+Y_{6}-Y_{7}-Y_{8}}{8}}.\\[5pt]{\widehat {\theta }}_{3}&={\frac {Y_{1}+Y_{2}-Y_{3}-Y_{4}-Y_{5}-Y_{6}+Y_{7}+Y_{8}}{8}}.\\[5pt]{\widehat {\theta }}_{4}&={\frac {Y_{1}-Y_{2}+Y_{3}-Y_{4}+Y_{5}-Y_{6}+Y_{7}-Y_{8}}{8}}.\\[5pt]{\widehat {\theta }}_{5}&={\frac {Y_{1}-Y_{2}+Y_{3}-Y_{4}-Y_{5}+Y_{6}-Y_{7}+Y_{8}}{8}}.\\[5pt]{\widehat {\theta }}_{6}&={\frac {Y_{1}-Y_{2}-Y_{3}+Y_{4}+Y_{5}-Y_{6}-Y_{7}+Y_{8}}{8}}.\\[5pt]{\widehat {\theta }}_{7}&={\frac {Y_{1}-Y_{2}-Y_{3}+Y_{4}-Y_{5}+Y_{6}+Y_{7}-Y_{8}}{8}}.\\[5pt]{\widehat {\theta }}_{8}&={\frac {Y_{1}+Y_{2}+Y_{3}+Y_{4}+Y_{5}+Y_{6}+Y_{7}+Y_{8}}{8}}.\end{aligned}}}
The question of design of experiments is: which experiment is better?
The variance of the estimate X1 of θ1 is σ2 if we use the first experiment. But if we use the second experiment, the variance of the estimate given above is σ2/8. Thus the second experiment gives us 8 times as much precision for the estimate of a single item, and estimates all items simultaneously, with the same precision. What the second experiment achieves with eight would require 64 weighings if the items are weighed separately. However, note that the estimates for the items obtained in the second experiment have errors that correlate with each other.
Many problems of the design of experiments involve combinatorial designs, as in this example and others.[23]
## Avoiding false positives
False positive conclusions, often resulting from the pressure to publish or the author's own confirmation bias, are an inherent hazard in many fields.[24]
Use of
false positives in the data collection phase. When a double-blind design is used, participants are randomly assigned to experimental groups but the researcher is unaware of what participants belong to which group. Therefore, the researcher can not affect the participants' response to the intervention.[25]
Experimental designs with undisclosed
P-hacking can be prevented by preregistering researches, in which researchers have to send their data analysis plan to the journal they wish to publish their paper in before they even start their data collection, so no data manipulation is possible.[29][30]
Another way to prevent this is taking a double-blind design to the data-analysis phase, making the study triple-blind, where the data are sent to a data-analyst unrelated to the research who scrambles up the data so there is no way to know which participants belong to before they are potentially taken away as outliers.[25]
Clear and complete
replication of results.[31]
## Discussion topics when setting up an experimental design
An experimental design or randomized clinical trial requires careful consideration of several factors before actually doing the experiment.[32] An experimental design is the laying out of a detailed experimental plan in advance of doing the experiment. Some of the following topics have already been discussed in the principles of experimental design section:
1. How many factors does the design have, and are the levels of these factors fixed or random?
2. Are control conditions needed, and what should they be?
3. Manipulation checks: did the manipulation really work?
4. What are the background variables?
5. What is the sample size? How many units must be collected for the experiment to be generalisable and have enough
power
?
6. What is the relevance of interactions between factors?
7. What is the influence of delayed effects of substantive factors on outcomes?
8. How do response shifts affect self-report measures?
9. How feasible is repeated administration of the same measurement instruments to the same units at different occasions, with a post-test and follow-up tests?
10. What about using a proxy pretest?
11. Are there
lurking variables
?
12. Should the client/patient, researcher or even the analyst of the data be blind to conditions?
13. What is the feasibility of subsequent application of different conditions to the same units?
14. How many of each control and noise factors should be taken into account?
The independent variable of a study often has many levels or different groups. In a true experiment, researchers can have an experimental group, which is where their intervention testing the hypothesis is implemented, and a control group, which has all the same element as the experimental group, without the interventional element. Thus, when everything else except for one intervention is held constant, researchers can certify with some certainty that this one element is what caused the observed change. In some instances, having a control group is not ethical. This is sometimes solved using two different experimental groups. In some cases, independent variables cannot be manipulated, for example when testing the difference between two groups who have a different disease, or testing the difference between genders (obviously variables that would be hard or unethical to assign participants to). In these cases, a quasi-experimental design may be used.
In the pure experimental design, the independent (predictor) variable is manipulated by the researcher – that is – every participant of the research is chosen randomly from the population, and each participant chosen is assigned randomly to conditions of the independent variable. Only when this is done is it possible to certify with high probability that the reason for the differences in the outcome variables are caused by the different conditions. Therefore, researchers should choose the experimental design over other design types whenever possible. However, the nature of the independent variable does not always allow for manipulation. In those cases, researchers must be aware of not certifying about causal attribution when their design doesn't allow for it. For example, in observational designs, participants are not assigned randomly to conditions, and so if there are differences found in outcome variables between conditions, it is likely that there is something other than the differences between the conditions that causes the differences in outcomes, that is – a third variable. The same goes for studies with correlational design (Adér & Mellenbergh, 2008).
## Statistical control
It is best that a process be in reasonable statistical control prior to conducting designed experiments. When this is not possible, proper blocking, replication, and randomization allow for the careful conduct of designed experiments.[33] To control for nuisance variables, researchers institute control checks as additional measures. Investigators should ensure that uncontrolled influences (e.g., source credibility perception) do not skew the findings of the study. A
manipulation check
is one example of a control check. Manipulation checks allow investigators to isolate the chief variables to strengthen support that these variables are operating as planned.
One of the most important requirements of experimental research designs is the necessity of eliminating the effects of
intervening variables (a variable in between the supposed cause (X) and the effect (Y)), and anteceding variables (a variable prior to the supposed cause (X) that is the true cause). When a third variable is involved and has not been controlled for, the relation is said to be a zero order
relationship. In most practical applications of experimental research designs there are several causes (X1, X2, X3). In most designs, only one of these causes is manipulated at a time.
## Experimental designs after Fisher
Some efficient designs for estimating several main effects were found independently and in near succession by Raj Chandra Bose and K. Kishen in 1940 at the Indian Statistical Institute, but remained little known until the Plackett–Burman designs were published in Biometrika in 1946. About the same time, C. R. Rao introduced the concepts of orthogonal arrays as experimental designs. This concept played a central role in the development of Taguchi methods by Genichi Taguchi, which took place during his visit to Indian Statistical Institute in early 1950s. His methods were successfully applied and adopted by Japanese and Indian industries and subsequently were also embraced by US industry albeit with some reservations.
In 1950, Gertrude Mary Cox and William Gemmell Cochran published the book Experimental Designs, which became the major reference work on the design of experiments for statisticians for years afterwards.
Developments of the theory of linear models have encompassed and surpassed the cases that concerned early writers. Today, the theory rests on advanced topics in linear algebra, algebra and combinatorics.
As with other branches of statistics, experimental design is pursued using both
frequentist statistics studies the sampling distribution while Bayesian statistics updates a probability distribution
on the parameter space.
Some important contributors to the field of experimental designs are
Some discussion of experimental design in the context of system identification (model building for static or dynamic models) is given in[40] and.[41]
## Human participant constraints
Laws and ethical considerations preclude some carefully designed experiments with human subjects. Legal constraints are dependent on jurisdiction. Constraints may involve institutional review boards, informed consent and confidentiality affecting both clinical (medical) trials and behavioral and social science experiments.[42] In the field of toxicology, for example, experimentation is performed on laboratory animals with the goal of defining safe exposure limits for humans.[43] Balancing the constraints are views from the medical field.[44] Regarding the randomization of patients, "... if no one knows which therapy is better, there is no ethical imperative to use one therapy or another." (p 380) Regarding experimental design, "...it is clearly not ethical to place subjects at risk to collect data in a poorly designed study when this situation can be easily avoided...". (p 393)
## References
1. ^ "The Sequential Nature of Classical Design of Experiments | Prism". prismtc.co.uk. Retrieved 10 March 2023.
2. .
3. ^ Peirce, Charles Sanders (1883). "A Theory of Probable Inference". In C. S. Peirce (Ed.), Studies in logic by members of the Johns Hopkins University (p. 126–181). Little, Brown and Co (1883)
4. . Indeed, Pierce's work contains one of the earliest explicit endorsements of mathematical randomization as a basis for inference of which I am aware (Peirce, 1957, pages 216–219
5. ^ a b Peirce, Charles Sanders; Jastrow, Joseph (1885). "On Small Differences in Sensation". Memoirs of the National Academy of Sciences. 3: 73–83.
6. ^ a b of
S2CID 52201011
.
7. ^ a b
S2CID 143685203
.
8. ^ a b Trudy Dehue (December 1997). "Deception, Efficiency, and Random Groups: Psychology and the Gradual Origination of the Random Group Design".
S2CID 23526321
.
9. .
10. .
11. .
12. ^ Johnson, N.L. (1961). "Sequential analysis: a survey." Journal of the Royal Statistical Society, Series A. Vol. 124 (3), 372–411. (pages 375–376)
13. ^ Wald, A. (1945) "Sequential Tests of Statistical Hypotheses", Annals of Mathematical Statistics, 16 (2), 117–186.
14. ^ a b Herman Chernoff, Sequential Analysis and Optimal Design, SIAM Monograph, 1972.
15. . (pages 151–180)
16. .
17. ) "To biologists, he was an architect of the 'modern synthesis' that used mathematical models to integrate Mendelian genetics with Darwin's selection theories. To psychologists, Fisher was the inventor of various statistical tests that are still supposed to be used whenever possible in psychology journals. To farmers, Fisher was the founder of experimental agricultural research, saving millions from starvation through rational crop breeding programs." p.54.
18. ^ Dr. Hani (2009). "Replication study". Archived from the original on 2 June 2012. Retrieved 27 October 2011.
19. S2CID 27838472
, retrieved 27 October 2011
20. .
21. .
22. ^ a b Jack Sifri (8 December 2014). "How to Use Design of Experiments to Create Robust Designs With High Yield". youtube.com. Retrieved 11 February 2015.
23. S2CID 26793416
.
24. ^
PMID 31536248.{{cite journal}}: CS1 maint: numeric names: authors list (link
)
25. .
26. ^ "Science, Trust And Psychology in Crisis". KPLU. 2 June 2014. Archived from the original on 14 July 2014. Retrieved 12 June 2014.
27. ^ "Why Statistically Significant Studies Can Be Insignificant". Pacific Standard. 4 June 2014. Retrieved 12 June 2014.
28. PMID 29531091
.
29. ^ "Pre-Registering Studies – What Is It, How Do You Do It, and Why?". www.acf.hhs.gov. Retrieved 29 August 2023.
30. ^ Chris Chambers (10 June 2014). "Physics envy: Do 'hard' sciences hold the solution to the replication crisis in psychology?". theguardian.com. Retrieved 12 June 2014.
31. ^ Ader, Mellenberg & Hand (2008) "Advising on Research Methods: A consultant's companion"
32. ^ Bisgaard, S (2008) "Must a Process be in Statistical Control before Conducting Designed Experiments?", Quality Engineering, ASQ, 20 (2), pp 143–176
33. .
34. .
35. ^ Walpole, Ronald E.; Myers, Raymond H.; Myers, Sharon L.; Ye, Keying (2007). Probability & statistics for engineers & scientists (8 ed.). Upper Saddle River, NJ: Pearson Prentice Hall. .
36. ^ Myers, Raymond H.; Montgomery, Douglas C.; Vining, G. Geoffrey; Robinson, Timothy J. (2010). Generalized linear models : with applications in engineering and the sciences (2 ed.). Hoboken, N.J.: Wiley. .
37. ^ Box, George E.P.; Hunter, William G.; Hunter, J. Stuart (1978). Statistics for Experimenters : An Introduction to Design, Data Analysis, and Model Building. New York: Wiley. .
38. ^ Box, George E.P.; Hunter, William G.; Hunter, J. Stuart (2005). Statistics for Experimenters : Design, Innovation, and Discovery (2 ed.). Hoboken, N.J.: Wiley. .
39. .
40. .
41. ^ Moore, David S.; Notz, William I. (2006). Statistics : concepts and controversies (6th ed.). New York: W.H. Freeman. pp. Chapter 7: Data ethics. .
42. ^ Ottoboni, M. Alice (1991). The dose makes the poison : a plain-language guide to toxicology (2nd ed.). New York, N.Y: Van Nostrand Reinhold. .
43. .
### Sources
• Peirce, C. S. (1877–1878), "Illustrations of the Logic of Science" (series), Popular Science Monthly, vols. 12–13. Relevant individual papers:
• (1878 March), "The Doctrine of Chances", Popular Science Monthly, v. 12, March issue, pp. 604–615. Internet Archive Eprint.
• (1878 April), "The Probability of Induction", Popular Science Monthly, v. 12, pp. 705–718. Internet Archive Eprint.
• (1878 June), "The Order of Nature", Popular Science Monthly, v. 13, pp. 203–217.Internet Archive Eprint.
• (1878 August), "Deduction, Induction, and Hypothesis", Popular Science Monthly, v. 13, pp. 470–482. Internet Archive Eprint.
• (1883), "A Theory of Probable Inference", Studies in Logic, pp. 126–181, Little, Brown, and Company. (Reprinted 1983, John Benjamins Publishing Company, ) | 5,566 | 24,021 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 4, "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} | 2.59375 | 3 | CC-MAIN-2024-22 | latest | en | 0.931929 |
http://acm.zju.edu.cn/onlinejudge/showProblem.do?problemId=4498 | 1,563,500,161,000,000,000 | text/html | crawl-data/CC-MAIN-2019-30/segments/1563195525973.56/warc/CC-MAIN-20190719012046-20190719034046-00192.warc.gz | 4,751,617 | 2,722 | Welcome to ZOJ
Problem Sets Information Select Problem Runs Ranklist
ZOJ Problem Set - 3543
Number String
Time Limit: 5 Seconds Memory Limit: 65536 KB
The signature of a permutation is a string that is computed as follows: for each pair of consecutive elements of the permutation, write down the letter 'I' (increasing) if the second element is greater than the first one, otherwise write down the letter 'D' (decreasing). For example, the signature of the permutation {3,1,2,7,4,6,5} is "DIIDID".
Your task is as follows: You are given a string describing the signature of many possible permutations, find out how many permutations satisfy this signature.
Note: For any positive integer n, a permutation of n elements is a sequence of length n that contains each of the integers 1 through n exactly once.
#### Input
Each test case consists of a string of 1 to 1000 characters long, containing only the letters 'I', 'D' or '?', representing a permutation signature.
Each test case occupies exactly one single line, without leading or trailing spaces.
Proceed to the end of file. The '?' in these strings can be either 'I' or 'D'.
#### Output
For each test case, print the number of permutations satisfying the signature on a single line. In case the result is too large, print the remainder modulo 1000000007.
```II
ID
DI
DD
?D
??```
```1
2
2
1
3
6```
#### Hint
Permutation {1,2,3} has signature "II".
Permutations {1,3,2} and {2,3,1} have signature "ID".
Permutations {3,1,2} and {2,1,3} have signature "DI".
Permutation {3,2,1} has signature "DD".
"?D" can be either "ID" or "DD".
"??" gives all possible permutations of length 3.
Author: HONG, Qize
Contest: The 2011 ACM-ICPC Asia Dalian Regional Contest
Submit Status | 460 | 1,745 | {"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-2019-30 | latest | en | 0.797099 |
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Transcript of Hyperbolic Geometry for mjb/cs553/Handouts/hyperbolic... 1 mjb –February 28, 2019 Computer...
• 1
mjb – February 28, 2019 Computer Graphics
1
Hyperbolic Geometry for Visualization
hyperbolic.ppts
Mike Bailey [email protected]
mjb – February 28, 2019 Computer Graphics
2 Zooming and Panning Around a Complex 2D Display
• Standard (Euclidean) geometry zooming forces much of the information off the screen
• This eliminates the context from the zoomed-in display
• This problem can be solved with hyperbolic methods if we are willing to give up Euclidean geometry
• 2
mjb – February 28, 2019 Computer Graphics
3 Usual Zooming in Euclidean Space
123,101 line strips 446,585 points
mjb – February 28, 2019 Computer Graphics
4 Zooming in Polar Hyperbolic Space
• 3
mjb – February 28, 2019 Computer Graphics
5 Polar Hyperbolic Equations
(X,Y)
R
Θ
R’ = R / (R+K)
Θ’ = Θ
X’ = R’cosΘ’ Y’ = R’sinΘ’
Overall theme: something divided by something else a little bigger
1'lim 0
R K
0'lim
R K
then:' RR
R K
Because
mjb – February 28, 2019 Computer Graphics
6
YXR 22
)(tan 1 X Y
KR RR
'
KR X
R X
KR RRX
cos''
' 'sin R Y YY R R K R R K
Polar Hyperbolic Equations Don’t Actually Need to use Trig
Coordinates moved to outer edge when K = 0
Coordinates moved to center when K = ∞
• 4
mjb – February 28, 2019 Computer Graphics
7
KR XX
'
Cartesian Hyperbolic Equations – Treat X and Y Independently
KR YY
'
KX
XX 22
'
KY
YY 22
'
{ {Polar
Cartesian
Coordinates moved to outer edge when K = 0
Coordinates moved to center when K = ∞
mjb – February 28, 2019 Computer Graphics
8 Zooming in Cartesian Hyperbolic Space
• 5
mjb – February 28, 2019 Computer Graphics
9 The Problem with T-Intersections
mjb – February 28, 2019 Computer Graphics
10 The Problem with T-Intersections
Your code computes the hyperbolic transformation here and here, and OpenGL draws a straight line between them. But, this point had its hyperbolic transformation computed separately, and doesn’t match up with the straight line.
This kind of situation is called a T-intersection, and crops up all the time in computer graphics, even though we don’t want it to.
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mjb – February 28, 2019 Computer Graphics
11 A Solution to the T-Intersection Problem
Break this line up into several (many?) sub-pieces, and perform the Hyperbolic Transformation on each intermediate point.
This makes that straight line into a curve, as it should be. But, how many line segments should we use?
0 1( ) (1 )P t t P tP t = 0., .01, .02, .03, …
mjb – February 28, 2019 Computer Graphics
12 A More Elegant Approach is to Recursively Subdivide
void DrawHyperbolicLine( P0, P1 ) {
Compute point
Convert point A to Hyperbolic Coordinates, calling it A’
Convert P0 and P1 to Hyperbolic Coordinates P0’, P1’
Compute point
Compare A’ and B if( they are “close enough” ) {
Draw the line P0’-P1’ } else {
DrawHyperbolicLine( P0, A ); DrawHyperbolicLine( A, P1 );
} }
0 1
2. P PA
0 1' '' 2.
P PB
Subdividing to render a curve or surface correctly is a recurring theme in computer graphics.
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mjb – February 28, 2019 Computer Graphics
13Hyperbolic Corvallis (Streets, Buildings, Parks)
Kelley Engineering
Center
mjb – February 28, 2019 Computer Graphics
14
http://www.sott.net/articles/show/215021-Hyperbolic-map-of-the-internet-will-save-it-from-COLLAPSE | 1,131 | 3,543 | {"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} | 3.5 | 4 | CC-MAIN-2022-21 | latest | en | 0.799121 |
http://www.gradesaver.com/textbooks/math/calculus/calculus-early-transcendentals-8th-edition/appendix-a-numbers-inequalities-and-absolute-values-a-exercises-page-a9/15 | 1,524,201,344,000,000,000 | text/html | crawl-data/CC-MAIN-2018-17/segments/1524125937114.2/warc/CC-MAIN-20180420042340-20180420062340-00044.warc.gz | 445,111,889 | 12,668 | ## Calculus: Early Transcendentals 8th Edition
$x\geq-1$
Considering the inequality rules: $-a\geq b = a\leq-b$ and if $a>b$ then $a-c > b-c$ then: $1-x\leq2$ $=1-1 -x\leq 2-1$ $=-x\leq1$ $=x\geq-1$ | 97 | 199 | {"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} | 3.828125 | 4 | CC-MAIN-2018-17 | latest | en | 0.427446 |
https://search.r-project.org/CRAN/refmans/covKCD/html/covCSE.html | 1,701,588,805,000,000,000 | text/html | crawl-data/CC-MAIN-2023-50/segments/1700679100489.16/warc/CC-MAIN-20231203062445-20231203092445-00170.warc.gz | 569,900,559 | 1,926 | covCSE {covKCD} R Documentation
## Empirical Bayes core shrinkage covariance estimator
### Description
Estimate a covariance matrix by adaptively shrinking the core.
### Usage
covCSE(data, n = NULL, p1 = NULL, p2 = NULL, tol = 1e-08)
### Arguments
data either a numeric n*p1*p2 array consisting of n data matrices each of dimension p1*p2, or a p1*p2 covariance matrix of data of this type. If the latter, the values of n, p1 and p2 must be specified. n the sample size. p1 the row dimension of the data matrices. p2 the column dimension of the data matrices. tol the convergence tolerance of the iterative algorithm.
### Value
a covariance matrix of the same dimension as S. The attribute w of S gives the shrinkage weight on the Kronecker covariance of S.
Peter Hoff
### Examples
p1<-4 ; p2<-3 ; n<-20
# create a matrix Y with separable covariance
Sig1<-rWishart(1,p1,diag(p1))[,,1]
Sig2<-rWishart(1,p2,diag(p2))[,,1]
Y<-array(rnorm(n*p1*p2),dim=c(n,p1,p2))
Y<-aperm( apply(Y,c(1,3),function(y){ msqrt(Sig1)%*%y } ),c(2,1,3))
Y<-aperm( apply(Y,c(1,2),function(y){ msqrt(Sig2)%*%y } ),c(2,3,1))
# covariance
S<-mcov(Y)
covCSE(S,n,p1,p2)
# now an unstructured covariance
S<-rWishart(1,p1*p2,diag(p1*p2))[,,1]
covCSE(S,n,p1,p2)
[Package covKCD version 0.1 Index] | 419 | 1,281 | {"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} | 2.90625 | 3 | CC-MAIN-2023-50 | latest | en | 0.519869 |
https://www.slideserve.com/Rita/the-assumptions-of-anova | 1,531,836,917,000,000,000 | text/html | crawl-data/CC-MAIN-2018-30/segments/1531676589726.60/warc/CC-MAIN-20180717125344-20180717145344-00268.warc.gz | 972,952,781 | 20,127 | The Assumptions of ANOVA
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# The Assumptions of ANOVA - PowerPoint PPT Presentation
The Assumptions of ANOVA. Dennis Monday Gary Klein Sunmi Lee May 10, 2005. Major Assumptions of Analysis of Variance . The Assumptions Independence Normally distributed Homogeneity of variances Our Purpose Examine these assumptions Provide various tests for these assumptions Theory
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## PowerPoint Slideshow about 'The Assumptions of ANOVA' - Rita
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### The Assumptions of ANOVA
Dennis Monday
Gary Klein
Sunmi Lee
May 10, 2005
Major Assumptions of Analysis of Variance
• The Assumptions
• Independence
• Normally distributed
• Homogeneity of variances
• Our Purpose
• Examine these assumptions
• Provide various tests for these assumptions
• Theory
• Sample SAS code (SAS, Version 8.2)
• Consequences when these assumptions are not met
• Remedial measures
Normality
• Why normal?
• ANOVA is anAnalysis of Variance
• Analysis of two variances, more specifically, the ratio of two variances
• Statistical inference is based on the F distribution which is given by the ratio of two chi-squared distributions
• No surprise that each variance in the ANOVA ratio come from a parent normal distribution
• Calculations can always be derived no matter what the distribution is. Calculations are algebraic properties separating sums of squares. Normality is only needed for statistical inference.
NormalityTests
• Wide variety of tests we can perform to test if the data follows a normal distribution.
• Mardia (1980) provides an extensive list for both the univariate and multivariate cases, categorizing them into two types
• Properties of normal distribution, more specifically, the first four moments of the normal distribution
• Shapiro-Wilk’s W (compares the ratio of the standard deviation to the variance multiplied by a constant to one)
• Goodness-of-fit tests,
• Kolmogorov-Smirnov D
• Cramer-von Mises W2
• Anderson-Darling A2
NormalityTests
procunivariate data=temp normal plot;
var expvar;
run;
procunivariate data=temp normal plot;
var normvar;
run;
Tests for Normality
Test --Statistic--- -----p Value------
Shapiro-Wilk W 0.731203 Pr < W <0.0001
Kolmogorov-Smirnov D 0.206069 Pr > D <0.0100
Cramer-von Mises W-Sq 1.391667 Pr > W-Sq <0.0050
Anderson-Darling A-Sq 7.797847 Pr > A-Sq <0.0050
Tests for Normality
Test --Statistic--- -----p Value------
Shapiro-Wilk W 0.989846 Pr < W 0.6521
Kolmogorov-Smirnov D 0.057951 Pr > D >0.1500
Cramer-von Mises W-Sq 0.03225 Pr > W-Sq >0.2500
Anderson-Darling A-Sq 0.224264 Pr > A-Sq >0.2500
Stem Leaf # Boxplot
22 1 1 |
20 7 1 |
18 90 2 |
16 047 3 |
14 6779 4 |
12 469002 6 |
10 2368 4 |
8 005546 6 +-----+
6 228880077 9 | |
4 5233446 7 | |
2 3458447 7 *-----*
0 366904459 9 | + |
-0 52871 5 | |
-2 884318651 9 | |
-4 98619 5 +-----+
-6 60 2 |
-8 98557220 8 |
-10 963 3 |
-12 584 3 |
-14 853 3 |
-16 0 1 |
-18 4 1 |
-20 8 1 |
----+----+----+----+
Multiply Stem.Leaf by 10**-1
Normal Probability Plot
8.25+
| *
|
|
| *
|
| *
| +
4.25+ ** ++++
| ** +++
| *+++
| +++*
| ++****
| ++++ **
| ++++*****
| ++******
0.25+* * ******************
+----+----+----+----+----+----+----+----+----+----+
Normal Probability Plot
2.3+ ++ *
| ++*
| +**
| +**
| ****
| ***
| **+
| **
| ***
| **+
| ***
0.1+ ***
| **
| ***
| ***
| **
| +***
| +**
| +**
| ****
| ++
| +*
-2.1+*++
+----+----+----+----+----+----+----+----+----+----+
-2 -1 0 +1 +2
Stem Leaf # Boxplot
8 0 1 *
7
7
6
6 1 1 *
5
5 2 1 *
4 5 1 0
4 4 1 0
3 588 3 0
3 3 1 0
2 59 2 |
2 00112234 8 |
1 56688 5 |
1 00011122223444 14 +--+--+
0 55555566667777778999999 23 *-----*
0 000011111111111112222222233333334444444 39 +-----+
----+----+----+----+----+----+----+----
Consequences of Non-Normality
• F-test is very robust against non-normal data, especially in a fixed-effects model
• Large sample size will approximate normality by Central Limit Theorem (recommended sample size > 50)
• Simulations have shown unequal sample sizes between treatment groups magnify any departure from normality
• A large deviation from normality leads to hypothesis test conclusions that are too liberal and a decrease in power and efficiency
Remedial Measures for Non-Normality
• Data transformation
• Be aware - transformations may lead to a fundamental change in the relationship between the dependent and the independent variable and is not always recommended.
• Don’t use the standard F-test.
• Modified F-tests
• Adjust the degrees of freedom
• Rank F-test (capitalizes the F-tests robustness)
• Randomization test on the F-ratio
• Other non-parametric test if distribution is unknown
• Make up our own test using a likelihood ratio if distribution is known
Independence
• Independent observations
• No correlation between error terms
• No correlation between independent variables and error
• Positively correlated data inflates standard error
• The estimation of the treatment means are more accurate than the standard error shows.
Independence Tests
• If we have some notion of how the data was collected, we can check if there exists any autocorrelation.
• The Durbin-Watson statistic looks at the correlation of each value and the value before it
• Data must be sorted in correct order for meaningful results
• For example, samples collected at the same time would be ordered by time if we suspect results could depend on time
Independence Tests
procglm data=temp;
class trt;
model y = trt / p;
output out=out_ds r=resid_var;
run;
quit;
data out_ds;
set out_ds;
time = _n_;
run;
procgplot data=out_ds;
plot resid_var * time;
run;
quit;
procglm data=temp;
class trt;
model y = trt / p;
output out=out_ds r=resid_var;
run;
quit;
data out_ds;
set out_ds;
time = _n_;
run;
procgplot data=out_ds;
plot resid_var * time;
run;
quit;
First Order Autocorrelation 0.00479029
Durbin-Watson D 1.96904290
First Order Autocorrelation 0.90931
Durbin-Watson D 0.12405
Remedial Measures for Dependent Data
• First defense against dependent data is proper study design and randomization
• Designs could be implemented that takes correlation into account, e.g., crossover design
• Look for environmental factors unaccounted for
• Add covariates to the model if they are causing correlation, e.g., quantified learning curves
• If no underlying factors can be found attributed to the autocorrelation
• Use a different model, e.g., random effects model
• Transform the independent variables using the correlation coefficient
Homogeneity of Variances
• Eisenhart (1947) describes the problem of unequal variances as follows
• the ANOVA model is based on the proportion of the mean squares of the factors and the residual mean squares
• The residual mean square is the unbiased estimator of 2, the variance of a single observation
• The between treatment mean squares takes into account not only the differences between observations, 2,just like the residual mean squares, but also the variance between treatments
• If there was non-constant variance among treatments, we can replace the residual mean square with some overall variance, a2, and a treatment variance, t2, which is some weighted version of a2
• The “neatness” of ANOVA is lost
Homogeneity of Variances
• The omnibus (overall) F-test is very robust against heterogeneity of variances, especially with fixed effects and equal sample sizes.
• Tests for treatment differences like t-tests and contrasts are severely affected, resulting in inferences that may be too liberal or conservative.
Tests for Homogeneity of Variances
• Levene’s Test
• computes a one-way-anova on the absolute value (or sometimes the square) of the residuals, |yij – ŷi| with t-1, N – t degrees of freedom
• Considered robust to departures of normality, but too conservative
• Brown-Forsythe Test
• a slight modification of Levene’s test, where the median is substituted for the mean (Kuehl (2000) refers to it as the Levene (med) Test)
• The Fmax Test
• Proportion of the largest variance of the treatment groups to the smallest and compares it to a critical value table
• Tabachnik and Fidell (2001) use the Fmax ratio more as a rule of thumb rather than using a table of critical values.
• Fmax ratio is no greater than 10
• Sample sizes of groups are approximately equal (ratio of smallest to largest is no greater than 4)
• No matter how the Fmax test is used, normality must be assumed.
Tests for Homogeneity of Variances
procglm data=temp;
class trt;
model y = trt;
means trt / hovtest=levene hovtest=bf;
run;
quit;
procglm data=temp;
class trt;
model y = trt;
means trt / hovtest=levene hovtest=bf;
run;
quit;
Homogeneous Variances
The GLM Procedure
Levene's Test for Homogeneity of Y Variance
ANOVA of Squared Deviations from Group Means
Sum of Mean
Source DF Squares Square F Value Pr > F
TRT 1 10.2533 10.2533 0.60 0.4389
Error 98 1663.5 16.9747
Brown and Forsythe's Test for Homogeneity of Y Variance
ANOVA of Absolute Deviations from Group Medians
Sum of Mean
Source DF Squares Square F Value Pr > F
TRT 1 0.7087 0.7087 0.56 0.4570
Error 98 124.6 1.2710
Heterogenous Variances
The GLM Procedure
Levene's Test for Homogeneity of y Variance
ANOVA of Squared Deviations from Group Means
Sum of Mean
Source DF Squares Square F Value Pr > F
trt 1 10459.1 10459.1 36.71 <.0001
Error 98 27921.5 284.9
Brown and Forsythe's Test for Homogeneity of y Variance
ANOVA of Absolute Deviations from Group Medians
Sum of Mean
Source DF Squares Square F Value Pr > F
trt 1 318.3 318.3 93.45 <.0001
Error 98 333.8 3.4065
Tests for Homogeneity of Variances
• SAS (as far as I know) does not have a procedure to obtain Fmax (but easy to calculate)
• More importantly:
VARIANCE TESTS ARE ONLY FOR ONE-WAY ANOVA
WARNING: Homogeneity of variance testing and Welch's ANOVA are only available for unweighted one-way models.
Tests for Homogeneity of Variances(Randomized Complete Block Design and/or Factorial Design)
• In a CRD, the variance of each treatment group is checked for homogeneity
• In factorial/RCBD, each cell’s variance should be checked
H0: σij2 = σi’j’2, For all i,j where i ≠ i’, j ≠ j’
Tests for Homogeneity of Variances(Randomized Complete Block Design and/or Factorial Design)
• Approach 1
• Code each row/column to its own group
• Run HOVTESTS as before
• Approach 2
• Recall Levene’s Test and Brown-Forsythe Test are ANOVAs based on residuals
• Find residual for each observation
• Run ANOVA
data newgroup;
set oldgroup;
if block = 1 and treat = 1 then newgroup = 1;
if block = 1 and treat = 2 then newgroup = 2;
if block = 2 and treat = 1 then newgroup = 3;
if block = 2 and treat = 2 then newgroup = 4;
if block = 3 and treat = 1 then newgroup = 5;
if block = 3 and treat = 2 then newgroup = 6;
run;
procglm data=newgroup;
class newgroup;
model y = newgroup;
means newgroup / hovtest=levene hovtest=bf;
run;
quit;
procsort data=oldgroup; by treat block; run;
procmeans data=oldgroup noprint; by treat block;
var y;
output out=stats mean=mean median=median;
run;
data newgroup;
merge oldgroup stats;
by treat block;
resid = abs(mean - y);
if block = 1 and treat = 1 then newgroup = 1;
………
run;
procglm data=newgroup;
class newgroup;
model resid = newgroup;
run; quit;
Tests for Homogeneity of Variances(Repeated-Measures Design)
• As there is only one score per cell, the variance of each cell cannot be computed. Instead, four assumptions need to be tested/satisfied
• Compound Symmetry
• Homogeneity of variance in each column
• σa12 = σa22 =σa32
• Homogeneity of covariance between columns
• σa1a2=σa2a3= σa3a1
• No A x S Interaction (Additivity)
• Sphericity
• Variance of difference scores between pairs are equal
• σYa1-Ya2= σYa1-Ya3= σYa2-Ya3
Tests for Homogeneity of Variances(Repeated-Measures Design)
• Usually, testing sphericity will suffice
• Sphericity can be tested using the Mauchly test in SAS
procglm data=temp;
class sub;
model a1 a2 a3 = sub / nouni;
repeated as 3 (123) polynomial / summary printe;
run; quit;
Sphericity Tests
Mauchly's
Variables DF Criterion Chi-Square Pr > ChiSq
Transformed Variates 2 Det = 0 6.01 .056
Orthogonal Components 2 Det = 0 6.03 .062
• If there is only one score per cell, homogeneity of variances needs to be shown for the marginals of each column and each row
• Each factor for a latin-square
• Whole plots and subplots for split-plot
• If there are repititions, homogeneity is to be shown within each cell like RCBD
• If there are repeated-measures, follow guidelines for sphericity, compound symmetry and additivity as well
Remedial Measures for Heterogeneous Variances
• Studies that do not involve repeated measures
• If normality is not violated, a weighted ANOVA is suggested (e.g., Welch’s ANOVA)
• If normality is violated, the data transformation necessary to normalize data will usually stabilize variances as well
• If variances are still not homogeneous, non-ANOVA tests might be your option
• Studies with repeated measures
• For violations of sphericity
• modify the degrees of freedom have been suggested.
• Greenhouse-Geisser
• Huynh and Feldt
• Only do specific comparisons (sphericity does not apply since only two groups – sphericity implies more than two)
• MANOVA
• Use an MLE procedure to specify variance-covariance matrix
Other Concerns
• Outliers and influential points
• Data should always be checked for influential points that might bias statistical inference
• Use scatterplots of residuals
• Statistical tests using regression to detect outliers
• DFBETAS
• Cook’s D
References
• Casella, G. and Berger, R. (2002). Statistical Inference. United States: Duxbury.
• Cochran, W. G. (1947). Some Consequences When the Assumptions for the Analysis of Variances are not Satisfied. Biometrics. Vol. 3, 22-38.
• Eisenhart, C. (1947). The Assumptions Underlying the Analysis of Variance. Biometrics. Vol. 3, 1-21.
• Ito, P. K. (1980). Robustness of ANOVA and MANOVA Test Procedures. Handbook of Statistics 1: Analysis of Variance (P. R. Krishnaiah, ed.), 199-236. Amsterdam: North-Holland.
• Kaskey, G., et al. (1980). Transformations to Normality. Handbook of Statistics 1: Analysis of Variance (P. R. Krishnaiah, ed.), 321-341. Amsterdam: North-Holland.
• Kuehl, R. (2000). Design of Experiments: Statistical Principles of Research Design and Analysis, 2nd edition. United States: Duxbury.
• Kutner, M. H., et al. (2005). Applied Linear Statistical Models, 5th edition. New York: McGraw-Hill.
• Mardia, K. V. (1980). Tests of Univariate and Multivariate Normality. Handbook of Statistics 1: Analysis of Variance (P. R. Krishnaiah, ed.), 279-320. Amsterdam: North-Holland.
• Tabachnik, B. and Fidell, L. (2001). Computer-Assisted Research Design and Analysis. Boston: Allyn & Bacon. | 4,329 | 15,374 | {"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} | 3.65625 | 4 | CC-MAIN-2018-30 | latest | en | 0.850319 |
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## Pixar in a Box
### Unit 6: Lesson 2
Mathematics of depth of field
# Circle of confusion calculation
## Problem
Below is a diagram for calculating the radius of a circle of confusion, B, C. E represents the center of the lens and D represents the top of the aperture. A is where the rays from a particular point intersect. F, G is a line passing through A that is perpendicular to the image plane and to the lens.
Click and drag the angles below to match angles of the same size.
Stuck?
Stuck? | 166 | 721 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 6, "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} | 2.625 | 3 | CC-MAIN-2023-06 | latest | en | 0.906328 |
https://www.jiskha.com/display.cgi?id=1339869134 | 1,503,483,610,000,000,000 | text/html | crawl-data/CC-MAIN-2017-34/segments/1502886118195.43/warc/CC-MAIN-20170823094122-20170823114122-00278.warc.gz | 896,483,057 | 3,788 | # physics
posted by .
You have a mass of 71 kg and are on a 51-degree slope hanging on to a cord with a breaking strength of 165 newtons. What must be the coefficient of static friction to 2 decimal places between you and the surface for you to be saved from the fire?
In the previous problem if the coefficient of static friction is zero, to the nearest tenth of a degree, what would the incline angle have to be in order for the cord not to break?
• physics -
x: 0= m•g•sinα-T-F(fr),
y: 0 = - m•g•cos α +N.
F(fr) =k•N=k• m•g•cos α,
F(fr) = m•g•sinα – T,
k• m•g•cos α = m•g•sinα – T,
k= tan α – T/m•g•cos α =
=tan51º- 165/71•9.8•cos51 =
= 0.86.
If k=0,
tan α = T/m•g•cos α,
sin α/ cos α = T/m•g•cos α,
sin α = T/m•g =167/71•9.8 =0.24
α =13.88º
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https://askoranswerme.com/4476/ | 1,618,639,562,000,000,000 | text/html | crawl-data/CC-MAIN-2021-17/segments/1618038101485.44/warc/CC-MAIN-20210417041730-20210417071730-00470.warc.gz | 217,917,526 | 8,986 | # What is the formula of torque?
What is the formula of torque?
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Description : List the different methods to produce damping torque.
Answer : Methods of providing damping torque in indicating type instruments: 1) Air friction damping. 2) Fluid friction damping. 3) Eddy current damping.
Description : State the function of controlling torque. Write two types of it.
Answer : Function of Controlling Torque: To restrict the motion of pointer / spindle and stop the pointer at the relevant position to get correct reading. To bring back pointer to zero ... measurement is removed. Types of Controlling Torque: 1. Spring control method 2.Gravity control method
Description : Ideally, the damping torque should be (1) Proportional to velocity of the moving system and operating current. (2) Proportional to the velocity of the moving system but independent of operating ... operating current. (4) Independent of the velocity of the moving system and operating current.
Answer : Ideally, the damping torque should be Proportional to the velocity of the moving system but independent of operating current.
Description : The meter which does not have any component in it to provide control torque is (A) Electrodynamometer for current measurement (B) Electrodynamometer for voltage measurement (C) Electrodynamometer for power measurement. (D) Electrodynamometer for power factor measurement.
Answer : The meter which does not have any component in it to provide control torque is Electrodynamometer for power factor measurement.
Description : The torque produced in wattmeter is proportional to
Description : The shaft torque of a d.c. motor is less than its armature torque because of .......... losses.
Answer : The shaft torque of a d.c. motor is less than its armature torque because of rotational losses.
Description : The maximum torque of d.c. motors is limited by?
Answer : The maximum torque of d.c. motors is limited by commutation.
Answer : In a meggar controlling torque is provided by coil.
Answer : In a portable instrument, the controlling torque is provided by spring.
Answer : Torque developed by a D.C. motor depends upon magnetic field, active length of the conductor, current flow through the conductors, number of conductors, radius of armature.
← Prev Question Next Question → | 1,843 | 8,512 | {"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-2021-17 | longest | en | 0.868663 |
eduproz.in | 1,685,812,699,000,000,000 | text/html | crawl-data/CC-MAIN-2023-23/segments/1685224649302.35/warc/CC-MAIN-20230603165228-20230603195228-00539.warc.gz | 265,118,767 | 18,003 | # Python Program to Print the Fibonacci Sequence (with Explanation)
Python Program to Print the Fibonacci Sequence: The Fibonacci series is a well-known mathematical sequence that has fascinated mathematicians and computer scientists alike. It is a sequence of numbers where each number is the sum of the two preceding ones, starting with 0 and 1. In this blog post, we will explore different ways to print the Fibonacci series using Python.
We will cover a range of methods, from simple loops to advanced generators, each with its own advantages and disadvantages. Whether you are a beginner or an experienced programmer, you will find something useful in this blog post to help you better understand the Fibonacci series and how to generate it in Python.
## Python Program to Print the Fibonacci Sequence
The Fibonacci series is a sequence of numbers where each number is the sum of the two preceding ones. In mathematical terms, it can be defined as F(n) = F(n-1) + F(n-2), where F(0) = 0 and F(1) = 1. So let’s discuss the “Python Program to Print the Fibonacci Sequence” in different ways.
### Fibonacci Sequence Using Recursion
One of the simplest ways to print the Fibonacci series is by using recursion. In this method, we define a function that calls itself recursively to generate the next number in the series.
``````def fibonacci(n):
if n <= 1:
return n
else:
return fibonacci(n-1) + fibonacci(n-2)
terms = 10
if terms <= 0:
print("Please enter a positive integer.")
else:
print("Fibonacci sequence:")
for i in range(terms):
print(fibonacci(i))
``````
Explanation:
The function takes an integer `n` as input, which represents the number of terms in the sequence to generate. If `n` is less than or equal to 1, the function returns n, which is either 0 or 1 depending on the value of `n`. Otherwise, the function recursively calls itself twice, passing in `n-1` and `n-2` as arguments, and returns the sum of the two results.
The code then sets the variable `terms` to 10, which represents the number of terms to generate in the sequence. If `terms` is less than or equal to 0, the code prints a message asking the user to enter a positive integer.
Otherwise, the code prints a message indicating that it is printing the Fibonacci sequence and uses a `for` loop to generate and print each term in the sequence.
The `for` loop iterates over a range of integers from 0 to `terms - 1`, and calls the `fibonacci` function to generate the value of each term in the sequence. The value of each term is then printed to the console using the `print` function.
### Fibonacci Sequence Using While Loop
Another way to print the Fibonacci series is by using a loop. In this method, we start with the first two numbers in the series (0 and 1) and generate the next numbers by adding the previous two numbers.
``````terms = 10
n1, n2 = 0, 1
count = 0
if terms <= 0:
print("Please enter a positive integer.")
elif terms == 1:
print("Fibonacci sequence upto",terms,":")
print(n1)
else:
print("Fibonacci sequence:")
while count < terms:
print(n1)
nth = n1 + n2
n1 = n2
n2 = nth
count += 1
``````
Explanation:
The code sets the variable `terms` to 10, which represents the number of terms to generate in the sequence. It then sets `n1` and `n2` to 0 and 1 respectively, which are the first two numbers in the sequence. The variable `count` is initialized to 0, which will be used to keep track of how many terms have been generated so far.
If `terms` is less than or equal to 0, the code prints a message asking the user to enter a positive integer. If `terms` is 1, the code prints a message indicating that it is printing the Fibonacci sequence up to the first term, which is simply 0.
If `terms` is greater than 1, the code enters a `while` loop that will continue to generate terms in the sequence until `count` is equal to `terms`. In each iteration of the loop, the code prints the value of `n1`, which is the current term in the sequence. It then calculates the next term in the sequence, which is the sum of `n1` and `n2`, and stores it in a variable called `nth`.
Finally, the code updates `n1` and `n2` to be the previous two terms in the sequence, and increments `count` to keep track of how many terms have been generated so far. This code is a more efficient way to generate the Fibonacci sequence because it uses a loop instead of recursion, and it only needs to store two variables at any given time instead of an entire sequence of numbers.
### Fibonacci Sequence Using List and for loop
We can also use a list to store the Fibonacci series and print the elements of the list.
``````def fibonacci(n):
fib= [0, 1]
for i in range(2, n):
fib.append(fib[i-1] + fib[i-2])
return fib
terms = 10
if terms <= 0:
print("Please enter a positive integer.")
else:
print("Fibonacci sequence:")
series = fibonacci(terms)
for num in series:
print(num)``````
Explanation:
The code defines a function called `fibonacci` that takes an integer `n` as input, which represents the number of terms in the sequence to generate. The function initializes a list called `fib` with the first two numbers in the sequence, 0 and 1. It then enters a `for` loop that iterates over a range of integers from 2 to `n-1`, and appends the sum of the previous two numbers in the sequence to the list.
After the loop completes, the function returns the list of numbers in the Fibonacci sequence. The code then sets the variable `terms` to 10, which represents the number of terms to generate in the sequence. If `terms` is less than or equal to 0, the code prints a message asking the user to enter a positive integer.
Otherwise, the code prints a message indicating that it is printing the Fibonacci sequence and calls the `fibonacci` function to generate the sequence. The resulting list of numbers is stored in a variable called `series`, which is then printed to the console using a `for` loop that iterates over the elements in the list and prints each one.
### Fibonacci Sequence Using Generators
Generators are a powerful feature in Python that allows us to create iterators. We can use a generator to generate the Fibonacci series and print its elements.
``````def fibonacci():
a, b = 0, 1
while True:
yield a
a, b = b, a + b
terms = 10
fib = fibonacci()
if terms <= 0:
print("Please enter a positive integer.")
else:
print("Fibonacci sequence:")
for i in range(terms):
print(next(fib))
``````
Explanation:
The `fibonacci()` function defines two variables `a` and `b` and initializes them to 0 and 1, respectively. Then it enters an infinite loop, where it yields the current value of `a` in each iteration using the `yield` keyword. After that, it updates the values of `a` and `b` by swapping them and adding them together.
The `terms` variable is initialized with the number of terms of the Fibonacci sequence that we want to generate. Then, the function creates a Fibonacci sequence generator object `fib` using the `fibonacci()` function. If `terms` is less than or equal to zero, it prints an error message, indicating that the input is invalid.
Otherwise, it prints a message indicating that it is going to print the Fibonacci sequence and enters a loop where it iterates over `terms` and calls the `next()` function on the `fib` generator object to get the next value of the sequence, which it prints to the console using the `print()` function.
## Conclusion
In this blog post, we discussed the “Python Program to Print the Fibonacci Sequence” in different ways. We explored recursion, loops, lists, and generators to generate the series. Each method has its own advantages and disadvantages, and we should choose the method that suits our needs best. | 1,809 | 7,682 | {"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} | 3.65625 | 4 | CC-MAIN-2023-23 | latest | en | 0.862098 |
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# Is it Possible for Excel to Do something like ths?
Topic closed. 4 replies. Last post 10 years ago by DrDan.
Page 1 of 1
Member #19992
August 9, 2005
2867 Posts
Offline
Posted: July 17, 2007, 10:13 am - IP Logged
I want to break down a number in pick 3 to every possible combination...
Example 026
I want to break this number into forming 026, 062, 260, 206, 620, and 602
And if thats not enough I would like to know how I could transfer these numbers to a chart once a number is hit.
Say 026 was called and I want to chart all box hits, is there a way to first create all 6 box plays and have them go to their coresponding spot on the chart by just typing in the 026 in an area?
We are all Lucky... just some of us don't realize it!
New Member
Trenton, Missouri
United States
Member #48846
January 11, 2007
2 Posts
Offline
Posted: July 19, 2007, 6:07 am - IP Logged
Rakster,
Not sure what you're asking for concerning the Charts but this is what I did.
Column A 026
Column B =(CONCATENATE(LEFT(A1,1),MID(A1,2,1),RIGHT(A1,1)))*1
Column C =(CONCATENATE(LEFT(A1,1),RIGHT(A1,1),MID(A1,2,1)))*1
Column D =(CONCATENATE(MID(A1,2,1),LEFT(A1,1),RIGHT(A1,1)))*1
Column E =(CONCATENATE(MID(A1,2,1),RIGHT(A1,1),LEFT(A1,1)))*1
Column F =(CONCATENATE(RIGHT(A1,1),LEFT(A1,1),MID(A1,2,1)))*1
Column G =(CONCATENATE(RIGHT(A1,1),MID(A1,2,1),LEFT(A1,1)))*1
The formulas can be on a different page as long as the "A1" points to your Number "026".
DrDan
Member #19992
August 9, 2005
2867 Posts
Offline
Posted: July 19, 2007, 9:58 am - IP Logged
Rakster,
Not sure what you're asking for concerning the Charts but this is what I did.
Column A 026
Column B =(CONCATENATE(LEFT(A1,1),MID(A1,2,1),RIGHT(A1,1)))*1
Column C =(CONCATENATE(LEFT(A1,1),RIGHT(A1,1),MID(A1,2,1)))*1
Column D =(CONCATENATE(MID(A1,2,1),LEFT(A1,1),RIGHT(A1,1)))*1
Column E =(CONCATENATE(MID(A1,2,1),RIGHT(A1,1),LEFT(A1,1)))*1
Column F =(CONCATENATE(RIGHT(A1,1),LEFT(A1,1),MID(A1,2,1)))*1
Column G =(CONCATENATE(RIGHT(A1,1),MID(A1,2,1),LEFT(A1,1)))*1
The formulas can be on a different page as long as the "A1" points to your Number "026".
DrDan
Thank you Doc... this is exactly what I was looking for!
We are all Lucky... just some of us don't realize it!
United States
Member #16612
June 2, 2005
3493 Posts
Offline
Posted: July 19, 2007, 1:57 pm - IP Logged
I hope that combination hits.
New Member
Trenton, Missouri
United States
Member #48846
January 11, 2007
2 Posts
Offline
Posted: July 19, 2007, 8:57 pm - IP Logged
What I said:
Not sure what you're asking for concerning the Charts but this is what I did.
Column A 026
Column B =(CONCATENATE(LEFT(A1,1),MID(A1,2,1),RIGHT(A1,1)))*1
Column C =(CONCATENATE(LEFT(A1,1),RIGHT(A1,1),MID(A1,2,1)))*1
Column D =(CONCATENATE(MID(A1,2,1),LEFT(A1,1),RIGHT(A1,1)))*1
Column E =(CONCATENATE(MID(A1,2,1),RIGHT(A1,1),LEFT(A1,1)))*1
Column F =(CONCATENATE(RIGHT(A1,1),LEFT(A1,1),MID(A1,2,1)))*1
Column G =(CONCATENATE(RIGHT(A1,1),MID(A1,2,1),LEFT(A1,1)))*1
The formulas can be on a different page as long as the "A1" points to your Number "026".
What I should have said!!
Format columns A thru G as "Custom '000'".
Column A Lottery draw 026
Column B =CONCATENATE(LEFT(A1,1),MID(A1,2,1),RIGHT(A1,1))
Column C =CONCATENATE(LEFT(A1,1),RIGHT(A1,1),MID(A1,2,1))
Column D =CONCATENATE(MID(A1,2,1),LEFT(A1,1),RIGHT(A1,1))
Column E =CONCATENATE(MID(A1,2,1),RIGHT(A1,1),LEFT(A1,1))
Column F =CONCATENATE(RIGHT(A1,1),LEFT(A1,1),MID(A1,2,1))
Column G =CONCATENATE(RIGHT(A1,1),MID(A1,2,1),LEFT(A1,1))
The formulas can be on a different page as long as the "A1" points to your Number "026".
Sorry for the confusion. Hope this helps.
DrDan
Page 1 of 1 | 1,465 | 3,802 | {"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 | 3 | CC-MAIN-2017-04 | longest | en | 0.712645 |
http://ricardo.ecn.wfu.edu/~cottrell/OPE/archive/0001/0012.html | 1,560,898,797,000,000,000 | text/html | crawl-data/CC-MAIN-2019-26/segments/1560627998844.16/warc/CC-MAIN-20190618223541-20190619005541-00202.warc.gz | 146,322,582 | 3,105 | # [OPE-L:2009] Re: Re: Re: A possible paradox in the theory of value
From: Jurriaan Bendien (djjb99@worldonline.nl)
Date: Sun Jan 02 2000 - 16:57:43 EST
I am trying to follow this argument, but I will say I object to "farmers"
being treated as "unskilled labour". This could make sense in some
metaphorical way. but real farmers are very rarely unskilled labourers !!!
Cheers
Jurriaan
At 08:24 PM 1/2/00 GMT, you wrote:
>At 08:37 02/01/00 +1100, ope-l@galaxy.csuchico.edu wrote:
>>I think you're double-counting the 500K hours for the production of the
>>means of subsistence of the operators. If I'm paid a wage of \$1,000, and
>>then spend it all on commodities, then it counts just as \$1,000.
>>
>
>Here is a reproduction table that illustrates what I mean. There is
>no double counting.
>There are 5 productive activities producing cake, bread, corn, bakers
>and farmers. Farmers stand in for unskilled labour. The economy maintains
>10 farmers using as inputs 10 unskilled humans ( column h ) and
>15 tons of bread ( col br).
>Bakers stand in as skilled labour in the example, the economy produces
>a gross output of 10 bakers, using 10 people to do so, but one of the
>bakers is retained to represent the cost of training new bakers. Again
>the bakers consume 15 tons of bread.
>The production of material products then uses one or other of the two
>class of labour plus corn as an input.
>
>
> inputs
> output b f c h br val tot v Profit price
>cake tons 20 4 20 1.00 20 4.45 1.0
>bread tons 30 5 30 0.91 27 5.55 0.9
>corn tons 60 10 10 0.47 28 10 0.5
>bakers 10 1 10 15 2.62 26 1.5
>farmers 10 10 15 2.36 24 1.4
>b= bakers, f=farmers, c= corn, h=humans, br=bread
>
>The surplus product takes the form of cake 20 tons of which have a value
>of 1 person per ton.
>
>The commodities are assumed to sell at their value, whereas the labour
>is purchased for the cost of its reproduction. The values are given
>by all the labour directly and indirectly necessary for their reproduction.
>Thus the value of a farmer is 2.36 persons, that of a baker 2.62 persons, but
>they are paid only 1.4 and 1.5 respectively.
>
>The profit of 20 is just sufficient for the capitalists to purchase
>and eat all the cake produced.
>
>
>The question is not one of double counting but whether one treats the
>costs of reproducing labour as part of the value of what it produces.
>If the costs of training enter into the value of the product, so should
>the costs of feeding.
>
>If one adopts this approach, one can do the accounting quite consitently.
>One ends up with the value of annual profits being equal to the working
>population. ( Note that when dealing with value accounts per annum, the
>dimension is persons since it is the result of cancelling out person years
>per year to give persons ).
>
>It would be interesting to check whether this method of accounting
>or Marx's method leads to a more accurate prediction of prices.
>
>
>Paul Cockshott (clyder@gn.apc.org)
>
>
>
This archive was generated by hypermail 2b29 : Mon Jan 31 2000 - 07:00:05 EST | 880 | 3,052 | {"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} | 3.125 | 3 | CC-MAIN-2019-26 | latest | en | 0.863558 |
https://www.codeproject.com/Articles/12821/Writing-Custom-BizTalk-Functoids?fid=260632&df=90&mpp=10&sort=Position&spc=None&tid=3429855 | 1,498,332,706,000,000,000 | text/html | crawl-data/CC-MAIN-2017-26/segments/1498128320323.17/warc/CC-MAIN-20170624184733-20170624204733-00230.warc.gz | 846,770,046 | 27,071 | 12,999,609 members (117,066 online)
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Posted 25 Jan 2006
# Writing Custom BizTalk Functoids
, 25 Jan 2006
Rate this:
An article on how to write custom BizTalk functoids.
## Introduction to Functoids
I am sure you have heard about functions, but what about functoids? Functoids or BizTalk functoids are, in a way, small reusable functions that you build just like functions. These are like operations that you need to perform specific tasks on data. BizTalk comes with a good collection of readymade functoids. But you will frequently face situations where you desire a simple functionality. Let us say, you want to validate a credit card number, it will be great if we can build a functoid which can take in a credit card number and credit card type, and return true or false. This will be a very good scenario for writing a functoid of your own.
## Scenario
As a learning exercise, I suggest building a functoid which calculates the perimeter of a rectangle for a fencing company. The logic of the functoid implementation is really concise:
`2 x (length + breadth)`
## A Bird's Eye View of the Steps
To create a BizTalk functoid, we need to briefly do the following:
• Derive our functoid from `Microsoft.BizTalk.BaseFunctoids`.
• Give it all resource strings like function name, function bitmaps to be displayed in the mapper, tool tip text, and description.
• Give it a unique GUID and a functoid ID.
• Specify what category the functoid belongs to (Math, Logical, String etc..).
• Specify input and output parameters.
• Specify the input and output connection types.
• Specify the function to call.
## Getting Down to Business ..
I have broken down the activity into a series of logical steps.
### Step 1: Creating your functoid project
You need to create a functoid as a class library. So we need to select a class library project to begin. Make sure you give a proper namespace name for it as we will need this to load the functoid later, using Reflection. We will use `Custom.Biztalk.MathFunctoid` as the namespase in our example:
### Step 2: Signing the DLL with a key
You need to have a strong name for this assembly to get it loaded into the toolbox. So create a strong name and sign it:
`C:\Samples\MathFunctoid > sn -k mathFunctoid.snk`
Once you have the strong key generated, insert the line below to the AssemblyInfo.cs:
`[assembly: AssemblyKeyFile("..\\..\\mathFunctoid.snk")]`
### Step 3: Give a unique ID for this assembly
We need to give a unique ID for this assembly. Using GUIDGEN from the Visual Studio prompt, generate a new GUID and add the following to the AssemblyInfo.cs:
`[assembly: Guid("5DE500CC-45BC-454b-A23D-24449899042C")]`
### Step 4: Add the class skeleton
We need to have a class to implement this functionality, so add a class and call it `CPerimeter` (or any meaningful name of your choice):
Once the class is added, add the following lines in the namespace inclusion section at the top of your class file:
```using Microsoft.BizTalk.BaseFunctoids;
using System.Reflection;
using System.Globalization;
using System.Resources;```
### Step 6: Add references to BizTalk base functoids
In the project references, add a reference to Microsoft.BizTalk.BaseFunctoids.dll. This DLL implements all the base classes we need to create a functoid.
### Step 7: Add a resource file
In Visual Studio, go to File->Add New Item->Resource File.
I named the resource file Mathresource.resx for this example. Now, add the following resource strings and specify their custom descriptions:
Resource ID Value Explanation `IDS_CONVERTINTFUNCTOID_ID` 6123 A value greater than 6000 `IDS_FUNCTOID_NAME` “Perimeter” The functoid description in toolbox `IDS_MATHFUNCTOID_TOOLTIP` “Calculates the perimeter of a rectangle” What appears on the tool tip `IDS_MATH_DESCRIPTION` “Calculates the perimeter” Description of functoid in VS `IDS_PERIMETERFUNCTOID_EXCEPTION` "Perimeter functoid threw an exception" Description of exception to the Biztalk subsystem
Now, create a 16 x 16 bitmap and add that to the resource file, and reference it as `IDS_MATH_BITMAP` using the Resource Editor.
### Step 8: Implement the class
To implement this class, we derive our class from `BaseFunctoid`. And in the class, we load the resource file, and set the different parameters like functoid name, tool tip text, and parameters for the functoid.
```public class CPerimeter : BaseFunctoid
{
static ResourceManager resmgr = new
ResourceManager("Custom.Biztalk.MathFunctoid" +
".MathResource", Assembly.GetExecutingAssembly());
public CPerimeter():base()
{
int functoidID;
functoidID = System.Convert.ToInt32(
resmgr.GetString("IDS_CONVERTINTFUNCTOID_ID"));
this.ID = functoidID;
// This has to be a number greater than 6000
SetupResourceAssembly("Custom.Biztalk.MathFunctoid" +
".MathResource", Assembly.GetExecutingAssembly());
//Set Resource strings , bitmaps
SetName("IDS_FUNCTOID_NAME");
SetTooltip("IDS_MATHFUNCTOID_TOOLTIP");
SetDescription("IDS_MATH_DESCRIPTION");
SetBitmap("IDS_MATH_BITMAP");
// Minimum and maximum parameters
// that the functoid accepts
this.SetMinParams(2);
this.SetMaxParams(2);
/// Function name that needs to be
/// called when this Functoid is invoked.
/// Put this in GAC
SetExternalFunctionName(GetType().Assembly.FullName,
"Custom.Biztalk.MathFunctoid.CPerimeter",
"CalcPerimeter");
//Category for this functoid.
this.Category = FunctoidCategory.Math;
//Input and output Connection type
this.OutputConnectionType =
ConnectionType.AllExceptRecord ;
}
}```
### Step 9: Implement the function logic
Now, we implement the functoid logic for the function name specified in the above step, using `SetExternalFunctionName`. The code below trims the incoming values. This is done because in XML, string data that are numerals could contain white spaces.
```public string CalcPerimeter(string RectangleLength,
{
int ilength = 0;
int ibreadth = 0;
int iPerimeter = 0;
ResourceManager resmgr = new ResourceManager("Custom." +
"Biztalk.MathFunctoid.MathResource",
Assembly.GetExecutingAssembly());
//Remove whitespace
RectangleLength = RectangleLength.Trim();
if ( IsNumeric(RectangleLength) && IsNumeric(RectangleBreadth) )
{
try
{
ilength = Convert.ToInt32(RectangleLength,
System.Globalization.CultureInfo.InvariantCulture);
System.Globalization.CultureInfo.InvariantCulture);
iPerimeter = 2 * (ilength + ibreadth);
}
catch
{
throw new Exception(string.Format(resmgr.GetString(
"IDS_PERIMETERFUNCTOID_EXCEPTION"),
RectangleLength + " " +
}
}
return iPerimeter.ToString() ;
}```
### Step 10: Compile and Deploy
You are now ready to build and deploy your functoid. Once it is built, copy the Custom.Biztalk.MathFunctoid.dll to Drive:\Program Files\Microsoft BizTalk Server 2004\Developer Tools\Mapper Extensions.
Now, make the DLL available in the GAC, using the following command line operation:
`C:\> gacutil /if Copy the Custom.Biztalk.MathFunctoid.dll`
### Step 11: Adding the functoid to the ToolBox
Open a BizTalk project and go to toolbox, and then right click on the toolbox. Go to Add/Remove items, select the Functoids tab, and browse to Custom.Biztalk.MathFunctoid.dll in the mapper extension folder, and check it.
You should now see your functoid in the toolbox under the list of Mathematical functoids (because we set the category as Math, remember?).
### Step 12: Take a deep breath!
Congrats, you just finished your first custom BizTalk functoid and I am sure it wont be your last!
## Points of Interest
### Testing the functoid
I have included a small map to test the functoid. You can download this project in the source available for download at the top of this article. It is titled customFunctoid Map.
### Gotcha's
You cannot insert a bitmap directly into the resource editor, you will have to use ResEditor to do it. The ResEditor can be found here: C:\Program Files\Microsoft Visual Studio .NET 2003\SDK\v1.1\Samples\Tutorials\resourcesandlocalization\reseditor.
### Exceptions
You might get an exception that the functoid was not found.
```Exception Caught: Functoid not found:
guid({5DE500CC-45BC-454b-A23D-24449899042C}) funcid(6123)```
This happens when you GAC the DLL but forget to copy it to the mapper extension folder.
## History
• Version 1.0 - January 22, 2006.
This article has no explicit license attached to it but may contain usage terms in the article text or the download files themselves. If in doubt please contact the author via the discussion board below.
A list of licenses authors might use can be found here
## About the Author
Architect United States
Abhilash is from Kerala, South India. He is presently working as an Integration Consultant for many fortune 500 companies in his current role at Neudesic
Abhilash has been programming since he got his first PC, when they used to load BASIC using tapes. He got his first real PC in 1994 - a 286 with a 40 MB hard disk, 1 MB RAM, and a 5.25 " FDD with a HGA graphics card.
Pascal was his first favorite programming language. And he thought at one time that it was the greatest language. He never really got on to the Delphi wagon, but went with C++, and then progressively VC++ SDK, MFC, COM, and then eventually chose C# as his preferred language once .NET came along. With the emergence of SOA into mainstream, Abhilash chose BizTalk as his SOA realization tool of preference. He opines that BizTalk helps implement SOA; by so clearly separating the message and the underlying implementation, and connect apps purely based on contracts. This is what many classic technologies like IDL tried to do, but somewhere, the point got lost. BizTalk is his tool of choice for EAI. Abhilash has worked in various platforms including Win32,.NET,Linux, and Mainframes and has professional experience in embedded development and voice telephony.This helps him understand the EAI domain better.
His passions include programming, blogging ,cricket and chess. He likes to troll MS user groups and used to run a site www.biztalkcafe.com as a hobby. The site has a forum, so if you work with BizTalk server, he would like to hear about your experiences there.
He was awarded Biztalk Server MVP in April of 2006.
His life events gets recorded here www.abhilash.in. You can connect with him on Linkedin
## Comments and Discussions
View All Threads First Prev Next
Lifetime of a Functoid Inverso16-Apr-10 22:40 Inverso1 6-Apr-10 22:40
Last Visit: 31-Dec-99 18:00 Last Update: 24-Jun-17 9:31 Refresh 1
General News Suggestion Question Bug Answer Joke Praise Rant Admin
Use Ctrl+Left/Right to switch messages, Ctrl+Up/Down to switch threads, Ctrl+Shift+Left/Right to switch pages. | 2,562 | 10,756 | {"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-2017-26 | latest | en | 0.844968 |
https://ask.sagemath.org/users/23165/radmir/?sort=recent | 1,696,043,915,000,000,000 | text/html | crawl-data/CC-MAIN-2023-40/segments/1695233510575.93/warc/CC-MAIN-20230930014147-20230930044147-00018.warc.gz | 130,896,291 | 5,508 | 2016-09-05 15:09:02 +0200 received badge ● Student (source) 2016-09-05 11:33:39 +0200 asked a question how to sum up the function over all permutations of variables in associative non-commutative algebra in sage i need to sum up $\lambda_{\sigma}(a_{\sigma(1)}a_{\sigma(2)}a_{\sigma(3)}-a_{\sigma(3)}a_{\sigma(4)}a_{\sigma(5)})$ over all $\sigma\in S_5$ where $a_i$ are elements of associative non-commutative algebra. the result should be $E_1a_1a_2a_3a_4a_5+\cdots+E_{120}a_5a_4a_3a_2a_1$ and i need to express $E_i$ in terms of $\lambda_{\sigma}$. actualy my tartget is to find non-zero solution of $E_i=0$ for all $i$. 2016-09-05 11:33:39 +0200 asked a question how to sum up the function over all permutations of variables in associative non-commutative algebra hello, i need to sum up $\lambda_{\sigma}(a_{\sigma(1)}a_{\sigma(2)}a_{\sigma(3)}-a_{\sigma(3)}a_{\sigma(4)}a_{\sigma(5)})$ over all $\sigma\in S_5$ where $a_i$ are elements of associative non-commutative algebra. the result should be $E_1a_1a_2a_3a_4a_5+\cdots+E_{120}a_5a_4a_3a_2a_1$ and i need to express $E_i$ in terms of $\lambda_{\sigma}$. actualy my tartget is to find non-zero solution of $E_i=0$ for all $i$. | 438 | 1,184 | {"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} | 3.28125 | 3 | CC-MAIN-2023-40 | latest | en | 0.716515 |
http://www.jiskha.com/display.cgi?id=1369713865 | 1,495,778,315,000,000,000 | text/html | crawl-data/CC-MAIN-2017-22/segments/1495463608642.30/warc/CC-MAIN-20170526051657-20170526071657-00155.warc.gz | 669,797,072 | 3,842 | # chemistry
posted by on .
18.5g Al is submerged in 20.2g of water with a total temperature of 27°C. How much energy in joules is absorbed by the Al if the temperature changes to 32°C ?
• chemistry - ,
This is similar to a limiting reagent problem. Al can absorb only as much heat as the water has to release; therefore, you must work two problems and determine if the water has enough heat to release for the Al to absorb all of it or not.
q Al = mass Al x specific heat Al x delta T. Solve for q.
or
q H2O = mass H2O x specific heat H2O x delta T.
### Answer This Question
First Name: School Subject: Answer:
### Related Questions
More Related Questions
Post a New Question | 171 | 685 | {"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-2017-22 | latest | en | 0.929578 |
https://convertoctopus.com/528-months-to-seconds | 1,611,411,707,000,000,000 | text/html | crawl-data/CC-MAIN-2021-04/segments/1610703538082.57/warc/CC-MAIN-20210123125715-20210123155715-00181.warc.gz | 287,083,426 | 8,236 | ## Conversion formula
The conversion factor from months to seconds is 2629746, which means that 1 month is equal to 2629746 seconds:
1 mo = 2629746 s
To convert 528 months into seconds we have to multiply 528 by the conversion factor in order to get the time amount from months to seconds. We can also form a simple proportion to calculate the result:
1 mo → 2629746 s
528 mo → T(s)
Solve the above proportion to obtain the time T in seconds:
T(s) = 528 mo × 2629746 s
T(s) = 1388505888 s
The final result is:
528 mo → 1388505888 s
We conclude that 528 months is equivalent to 1388505888 seconds:
528 months = 1388505888 seconds
## Alternative conversion
We can also convert by utilizing the inverse value of the conversion factor. In this case 1 second is equal to 7.2019860242753E-10 × 528 months.
Another way is saying that 528 months is equal to 1 ÷ 7.2019860242753E-10 seconds.
## Approximate result
For practical purposes we can round our final result to an approximate numerical value. We can say that five hundred twenty-eight months is approximately one billion three hundred eighty-eight million five hundred five thousand eight hundred eighty-eight seconds:
528 mo ≅ 1388505888 s
An alternative is also that one second is approximately zero times five hundred twenty-eight months.
## Conversion table
### months to seconds chart
For quick reference purposes, below is the conversion table you can use to convert from months to seconds
months (mo) seconds (s)
529 months 1391135634 seconds
530 months 1393765380 seconds
531 months 1396395126 seconds
532 months 1399024872 seconds
533 months 1401654618 seconds
534 months 1404284364 seconds
535 months 1406914110 seconds
536 months 1409543856 seconds
537 months 1412173602 seconds
538 months 1414803348 seconds | 451 | 1,792 | {"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-2021-04 | latest | en | 0.808051 |
https://www.urionlinejudge.com.br/judge/en/profile/14451?direction=asc&sort=Ranks.runtime | 1,597,502,751,000,000,000 | text/html | crawl-data/CC-MAIN-2020-34/segments/1596439740848.39/warc/CC-MAIN-20200815124541-20200815154541-00200.warc.gz | 861,386,874 | 5,941 | # PROFILE
Check out all the problems this user has already solved.
Problem Problem Name Ranking Submission Language Runtime Submission Date
1019 Time Conversion 05613º 4019949 C 0.000 4/4/16, 1:39:25 PM
1001 Extremely Basic 07670º 2889586 C 0.000 9/22/15, 7:31:15 PM
1007 Difference 04985º 2890153 C 0.000 9/22/15, 8:45:32 PM
1011 Sphere 07317º 4019741 C 0.000 4/4/16, 12:56:32 PM
1012 Area 06702º 4019792 C 0.000 4/4/16, 1:18:49 PM
1016 Distance 06048º 4019910 C 0.000 4/4/16, 1:34:52 PM
1014 Consumption 06808º 4019841 C 0.000 4/4/16, 1:26:10 PM
1001 Extremely Basic 05187º 0495471 C++ 0.000 2/21/14, 3:04:02 PM
1006 Average 2 04888º 2890089 C 0.000 9/22/15, 8:36:28 PM
1010 Simple Calculate 07678º 4019606 C 0.000 4/4/16, 12:51:49 PM
1009 Salary with Bonus 07825º 4019585 C 0.000 4/4/16, 12:36:52 PM
1008 Salary 04689º 2890379 C 0.000 9/22/15, 9:30:05 PM
1002 Area of a Circle 06053º 2889682 C 0.000 9/22/15, 7:42:13 PM
1003 Simple Sum 05989º 2889723 C 0.000 9/22/15, 7:47:39 PM
1020 Age in Days 05884º 4019981 C 0.000 4/4/16, 1:44:00 PM
1035 Selection Test 1 05366º 4124538 C 0.000 4/15/16, 10:23:16 AM
1021 Banknotes and Coins 03117º 4024585 C 0.000 4/4/16, 11:07:07 PM
1017 Fuel Spent 00007º 1335743 C 0.000 11/17/14, 9:44:33 AM
1036 Bhaskara's Formula 05022º 4124589 C 0.000 4/15/16, 10:39:24 AM
1015 Distance Between Two Points 06571º 4019865 C 0.000 4/4/16, 1:29:20 PM
1018 Banknotes 00007º 1335796 C 0.000 11/17/14, 10:03:16 AM
1005 Average 1 05024º 2889850 C 0.000 9/22/15, 8:02:40 PM
1004 Simple Product 05797º 2889797 C 0.000 9/22/15, 7:54:13 PM
1013 The Greatest 06413º 4019820 C 0.000 4/4/16, 1:22:06 PM
1021 Banknotes and Coins 00386º 16576873 C# 0.020 12/3/19, 12:46:51 AM
1005 Average 1 02791º 16565277 C# 0.024 12/1/19, 11:09:20 PM
1009 Salary with Bonus 02180º 16565356 C# 0.024 12/1/19, 11:23:34 PM
1017 Fuel Spent 01704º 16576118 C# 0.024 12/2/19, 11:26:29 PM
1006 Average 2 02618º 16565296 C# 0.024 12/1/19, 11:12:06 PM
1008 Salary 02459º 16565339 C# 0.024 12/1/19, 11:20:11 PM
1 of 3 | 1,011 | 2,009 | {"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-2020-34 | latest | en | 0.302615 |
http://www.functionx.com/csharp2/topics/math4.htm | 1,529,658,807,000,000,000 | text/html | crawl-data/CC-MAIN-2018-26/segments/1529267864387.54/warc/CC-MAIN-20180622084714-20180622104714-00156.warc.gz | 412,786,226 | 3,707 | Mathematics in C#: Trigonometry
Introduction
A circle is a group or series of distinct points drawn at an exact same distance from another point referred to as the center. The distance from the center C to one of these equidistant points is called the radius, R. The line that connects all of the points that are equidistant to the center is called the circumference of the circle. The diameter is the distance between two points of the circumference to the center; in other words, a diameter is double the radius.
To manage the measurements and other related operations, the circumference is divided into 360 portions. Each of these portions is called a degree. The unit used to represent the degree is the degree, written as ˚. Therefore, a circle contains 360 degrees, that is 360˚. The measurement of two points A and D of the circumference could have 15 portions of the circumference. In this case, this measurement would be represents as 15˚.
The distance between two equidistant points A and B is a round shape geometrically defined as an arc. An angle, ө, is the ratio of the distance between two points A and B of the circumference divided by the radius R. This can be written as:
Therefore, an angle is the ratio of an arc over the radius. Because an angle is a ratio and not a “physical” measurement, which means an angle is not a dimension, it is independent of the size of a circle. Obviously this angle represents the number of portions included by the three points. A better unit used to measure an angle is the radian or rad.
A cycle is a measurement of the rotation around the circle. Since the rotation is not necessarily complete, depending on the scenario, a measure is made based on the angle that was covered during the rotation. A cycle could cover part of the circle in which case the rotation would not have been completed. A cycle could also cover the whole 360˚ of the circle and continue there after. A cycle is equivalent to the radian divided by 2 * Pi.
The Pi Constant
The word п, also written as Pi, is a constant number used in various mathematical calculations. Its approximate value is 3.1415926535897932. The calculator of Windows represents it as 3.1415926535897932384626433832795. Borland had included its value in the math.h library as M_PI 3.14159265358979323846.
A diameter is two times the radius. In geometry, it is written as 2R. In C++, it is written as 2 * R or R * 2 (because the multiplication is symmetric). The circumference of a circle is calculated by multiplying the diameter to Pi, which is 2Rп, or 2 * R * п or 2 * R * Pi.
To perform conversions between the degree and the radian, you can use the formula:
360˚ = 2п rad which is equivalent to 1 rad = 360˚ / 2п = 57.3˚.
The Cosine of a Value
Consider the following geometric figure:
Consider AB the length of A to B, also referred to as the hypotenuse. Also consider AC the length of A to C which is the side adjacent to point A. The cosine of the angle at point A is the ratio AC/AB. That is, the ratio of the adjacent length, AC, over the length of the hypotenuse, AB:
The returned value, the ratio, is a double-precision number between –1 and 1.
To calculate the cosine of an angle, the Math class provides the Cos() method. Its syntax is:
`public static double Cos(double d);`
Here is an example:
```using System;
class Program
{
static int Main()
{
int number = 82;
Console.WriteLine("The cosine of {0} is {1}", number, Math.Cos(number));
return 0;
}
}```
This would produce:
```The cosine of 82 is 0.949677697882543
Press any key to continue . . .```
The Sine of a Value
Consider AB the length of A to B, also called the hypotenuse to point A. Also consider CB the length of C to B, which is the opposite side to point A. The sine represents the ratio of CB/AB; that is, the ratio of the opposite side, CB over the hypotenuse AB.
To calculate the sine of a value, you can call the Sin() method of the Math class. Its syntax is:
`public static double Sin(double a);`
Here is an example:
```using System;
class Program
{
static int Main()
{
double number = 82.55;
Console.WriteLine("The sine of {0} is {1}", number, Math.Sin(number));
return 0;
}
}```
This would produce:
```The sine of 82.55 is 0.763419622322519
Press any key to continue . . .```
Tangents
Consider AC the length of A to C. Also consider BC the length of B to C. The tangent is the result of BC/AC; that is, the ratio of BC over AC. To assist you with calculating the tangent of of a number, the Math class is equipped with a method named Tan whose syntax is:
`public static double Tan(double a);`
Here is an example:
```using System;
class Program
{
static int Main()
{
uint number = 225;
Console.WriteLine("The tangent of {0} is {1}", number, Math.Tan(number));
return 0;
}
}```
This would produce:
```The tangent of 225 is -2.53211499233434
Press any key to continue . . .```
The Arc Tangent
Consider BC the length of B to C. Also consider AC the length of A to C. The arc tangent is the ratio of BC/AC. To calculate the arc tangent of a value, you can use the Math.Atan() method. Its syntax is
`public static double Atan(double d);`
Here is an example:
```using System;
class Program
{
static int Main()
{
short number = 225;
Console.WriteLine("The arc tangent of {0} is {1}",
number, Math.Atan(number));
return 0;
}
}```
This would produce:
```The arc tangent of 225 is 1.56635191161394
Press any key to continue . . .``` | 1,358 | 5,461 | {"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} | 4.46875 | 4 | CC-MAIN-2018-26 | latest | en | 0.966005 |
https://mail.gap-system.org/pipermail/forum/2008/002077.html | 1,556,065,162,000,000,000 | text/html | crawl-data/CC-MAIN-2019-18/segments/1555578616424.69/warc/CC-MAIN-20190423234808-20190424020808-00112.warc.gz | 465,000,842 | 2,139 | # [GAP Forum] Use GAP to Compute Hom(G1, G2)?
Jeffrey Rolland rollandj at uwm.edu
Sat Feb 9 01:37:07 GMT 2008
```Alexander Hulpke wrote:
> Dear GAP Forum,
>
>
>> I am trying to compute the set of all homomorphisms from a group G1
>> [which is the semi-direct product of the integeres Z with the binary
>> icosahedral group P (also known as SL(2,5) and the Poincare group)] to
>> the group P (the Poincare group again) - Hom(G1, P). This sort of
>> problem seems right up GAP's alley.
>>
>> I have a presentatiion for G1: <z, s, t| s^3(st)^(-2), t^5(st^(-2),
>> zs(s^2ts^2t^3z)^(-1), zt(s^5ts^2tz)^(-1)>.
>
> The easiest seems to be to find all quotients of G1 that are isomorphic
> to a subgroup of SL(2,5). (There is some redundancy in this and for
> bigger cases other methods would be better. However in this case
> everything else is far more work for the user.)
<snip>
> Careful: This group has no quotient isomorphic to A_5 and thus cannot
> have SL(2,5) as quotient. So its probably not the group you want.
<snip>
> Best,
>
> Alexander Hulpke
<snip>
Prof. Hulpke,
Oops! You are right. I actually want all homomorhphisms to Out(P) = Z_2.
I know you can just send z from the Z in G1 to 1 in Z_2 and the s and t
from the P in G1 to 0 in Z_2, but I needed to know if there were any
other homs. Sorry, it's been a long time since I looked at this, and I
forgot what I needed. I put this on the back burner until I realized GAP
may be able to do this.
At any rate, your post should give me what I need. Thanks.
Sincerely,
--
Jeffrey Rolland
<rollandj at uwm.edu>
``` | 506 | 1,582 | {"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-2019-18 | latest | en | 0.932862 |
https://www.alextoys.pl/ALEcrusher/30559.html | 1,621,323,458,000,000,000 | text/html | crawl-data/CC-MAIN-2021-21/segments/1620243989756.81/warc/CC-MAIN-20210518063944-20210518093944-00479.warc.gz | 635,193,852 | 7,224 | crusher how to calculate the cost of returns
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### Crusher How To Calculate The Cost Of Returns
To calculate the average total cost per hour, divide the annual total cost by the number of total hours that the machine is used. Evaluating Alternatives to Machine Ownership For some machinery investment decisions, machinery own-ership and operating cost are calculated for comparisons to the current custom rate. If the capital invested in a ...
### crusher how to calculate the cost of returns
At 40 returns per year, this equates to an annual cost of \$113,780. The improvement team proposed a project to reduce the amount of returned products by 25 percent to 30 per year, which would lead to a cost of \$85,335 per year.
### Crusher How To Calculate The Cost Of Returns
USDA has estimated annual production costs and returns and published accounts for major field crop and livestock enterprises since 1975. Cost and return estimates are reported for the United States and major production regions for corn, soybeans, wheat, cotton, grain sorghum, rice, peanuts, oats, barley, milk, hogs, and cow-calf. These cost and return accounts are "historical" accounts based ...
### Calculate Crusher Run 2" minus | cubic yards / Tons
#1 Simple and Easy to Calculate. The return on investment metric is frequently used because it's so easy to calculate. Only two figures are required – the benefit and the cost. Because a "return" can mean different things to different people, the ROI formula is easy to use, as there is not a strict definition of "return".
### Calculating ROI to Realize Project Value
With no fees, you would have \$57,434.91. With a two percent annual fee, you would accumulate \$31,329.84, a 45.45 percent reduction. So the two percent annual fee cut your total return almost in half! Use the Investment Fee Calculator to see the effect of fees on total returns.
### USDA ERS - Commodity Costs and Returns
Mar 31, 2020· The rate of return for the stock is thus a \$30 gain per share, divided by the \$60 cost per share, or 50%. On the other hand, consider an investor that …
### crusher how to calculate the cost of returns
Crusher Run Calculator; Crusher Run Calculator * Calculator is provided for informational purposes only, and the result is only estimates. Area 1: Width (Feet) Length (Feet) Depth (Inches) Area 2: Width (Feet) Length (Feet) Depth (Inches) Area 3: Width (Feet) Length (Feet) …
### How to Calculate Machinery Ownership and Operating Costs
Calculate your earnings and more. Meeting your long-term investment goal is dependent on a number of factors. This not only includes your investment capital and rate of return, but inflation ...
### Annualized Return Calculator
Type in inches and feet of your project and calculate the estimated amount of Base material in cubic yards, cubic feet and Tons, that your need for your project. The Density of Crusher Run 2" minus: 2,410 lb/yd³ or 1.21 t/yd³ or 0.8 yd³/t
### Gravel Calculator – Square Footage Area
How Much Cost Of Gravel? Homeowners will need about 200 square feet of coverage which costs around \$350 with most homeowners spending between \$300 and \$400 for smaller project. For this size of project, consider purchasing pea gravel in bags of 0.5 cubic feet.
### Investment Fee Calculator - See How Fees Reduce Your Returns
Calculating ROI to Realize Project Value - iSixSigma. At 40 returns per year, this equates to an annual cost of \$113,780. The improvement team proposed a project to reduce the amount of returned products by 25 percent to 30 per year, which would lead to a cost of \$85,335 per year.
### USDA ERS - Commodity Costs and Returns
how to calculate crusher fuel. how to calculate crusher fuel. how to calculate weight loss when lifting. the owning and operating costs of dump trucks world. diesel exhaust fluid or def, is an addition to your costs in scr based engines, but in the long run the cost just about zeroes out thanks to fuel economy gains, mack says.
### How Much Crushed Stone Do You Need? A Sure-Fire Formula
You are quite excited, but there is just one problem: It requires crushed stone, and you have no clue how to calculate how much you will need. Crushed stone is a material that is typically used as a base or underlayment, upon which the stuff that actually shows -- for example, the concrete of a patio -- will rest.
### Cost of Homeownership Calculator - NerdWallet
Annualized Return Calculator. The Annualized Return Calculator computes the annualized return of an investment held for a specified number of years.. Annualized Return = ((Ending value of investment / Beginning value of investment) ^ (1 / Number years held)) - 1
### How to Calculate Machinery Ownership and Operating Costs
USDA has estimated annual production costs and returns and published accounts for major field crop and livestock enterprises since 1975. Cost and return estimates are reported for the United States and major production regions for corn, soybeans, wheat, cotton, grain sorghum, rice, peanuts, oats, barley, milk, hogs, and cow-calf. These cost and return accounts are "historical" accounts based ...
### Average Return Calculator
To calculate the average total cost per hour, divide the annual total cost by the number of total hours that the machine is used. Evaluating Alternatives to Machine Ownership For some machinery investment decisions, machinery own-ership and operating cost are calculated for comparisons to the current custom rate. If the capital invested in a ...
### Crusher Run Calculator - BJS Nursery
Aug 31, 2020· To calculate net returns, total returns and total costs must be considered. Total returns for a stock result from capital gains and dividends. Total costs would include the initial purchase price ...
### Crusher How To Calculate The Cost Of Returns
It will calculate any one of the values from the other three in the CAPM formula. CAPM (Capital Asset Pricing Model) In finance, the CAPM (capital asset pricing model) is a theory of the relationship between the risk of a security or a portfolio of securities and the expected rate of return … | 1,852 | 8,695 | {"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} | 3.140625 | 3 | CC-MAIN-2021-21 | latest | en | 0.91813 |
https://homework.cpm.org/category/CCI_CT/textbook/int3/chapter/11/lesson/11.2.1/problem/11-57 | 1,571,453,507,000,000,000 | text/html | crawl-data/CC-MAIN-2019-43/segments/1570986688674.52/warc/CC-MAIN-20191019013909-20191019041409-00385.warc.gz | 515,085,332 | 15,712 | ### Home > INT3 > Chapter 11 > Lesson 11.2.1 > Problem11-57
11-57.
1. Add or subtract the following rational expressions. Be sure to look for factors before trying to determine a common denominator, and simplify your answers, if possible. Homework Help ✎
This is addition of fractions. What are the steps for adding fractions?
Factor.
$\frac{4x}{(x+2)(x-4)} +\frac{4}{x-4}$
To make common denominators, multiply the second term by the Giant One below.
$\frac{4x}{(x+2)(x-4)} +\frac{4(x+2)}{(x+2)(x-4)}$
Add the numerators and keep the denominators the same.
$\frac{8x+8}{(x+2)(x-4)}$
Refer to part (a).
$\frac{1}{x+2}$ | 202 | 628 | {"found_math": true, "script_math_tex": 4, "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} | 3.84375 | 4 | CC-MAIN-2019-43 | longest | en | 0.761518 |
https://www.convertunits.com/from/astronomical+unit/to/bee+space | 1,660,434,652,000,000,000 | text/html | crawl-data/CC-MAIN-2022-33/segments/1659882571989.67/warc/CC-MAIN-20220813232744-20220814022744-00135.warc.gz | 632,366,026 | 17,217 | ## ››Convert astronomical unit to bee space
astronomical unit bee space
How many astronomical unit in 1 bee space? The answer is 4.3449816297359E-14.
We assume you are converting between astronomical unit and bee space.
You can view more details on each measurement unit:
astronomical unit or bee space
The SI base unit for length is the metre.
1 metre is equal to 6.6845871226706E-12 astronomical unit, or 153.84615384615 bee space.
Note that rounding errors may occur, so always check the results.
Use this page to learn how to convert between astronomical units and bee space.
Type in your own numbers in the form to convert the units!
## ››Quick conversion chart of astronomical unit to bee space
1 astronomical unit to bee space = 23015057029385 bee space
2 astronomical unit to bee space = 46030114058769 bee space
3 astronomical unit to bee space = 69045171088154 bee space
4 astronomical unit to bee space = 92060228117538 bee space
5 astronomical unit to bee space = 1.1507528514692E+14 bee space
6 astronomical unit to bee space = 1.3809034217631E+14 bee space
7 astronomical unit to bee space = 1.6110539920569E+14 bee space
8 astronomical unit to bee space = 1.8412045623508E+14 bee space
9 astronomical unit to bee space = 2.0713551326446E+14 bee space
10 astronomical unit to bee space = 2.3015057029385E+14 bee space
## ››Want other units?
You can do the reverse unit conversion from bee space to astronomical unit, or enter any two units below:
## Enter two units to convert
From: To:
## ››Definition: Astronomical unit
The astronomical unit (AU or au or a.u. or sometimes ua) is a unit of length. It is approximately equal to the mean distance between the Earth and Sun. The currently accepted value of the AU is 149 597 870 691 ± 30 metres (about 150 million kilometres or 93 million miles).
The symbol "ua" is recommended by the Bureau International des Poids et Mesures, but in the United States and other anglophone countries the reverse usage is more common. The International Astronomical Union recommends "au" and international standard ISO 31-1 uses "AU".
## ››Metric conversions and more
ConvertUnits.com provides an online conversion calculator for all types of measurement units. You can find metric conversion tables for SI units, as well as English units, currency, and other data. Type in unit symbols, abbreviations, or full names for units of length, area, mass, pressure, and other types. Examples include mm, inch, 100 kg, US fluid ounce, 6'3", 10 stone 4, cubic cm, metres squared, grams, moles, feet per second, and many more! | 644 | 2,587 | {"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} | 2.640625 | 3 | CC-MAIN-2022-33 | latest | en | 0.773381 |
https://quizlet.com/11370311/8th-grade-earth-science-ch-17a-set-2-flash-cards/ | 1,524,180,929,000,000,000 | text/html | crawl-data/CC-MAIN-2018-17/segments/1524125937074.8/warc/CC-MAIN-20180419223925-20180420003925-00164.warc.gz | 678,917,092 | 55,851 | 27 terms
# 8th Grade Earth Science CH 17A set 2
Earthquakes
###### PLAY
P Waves, S Waves, L Waves
Three types of Earthquake Waves
P Waves
First waves to reach sensors -- can go anywhere
S Waves
Second waves to reach sensors -- Do not go through core
Core is liquid
Why do second waves probably not go through core
L Waves
Slowest and most destructive waves -- travel on surface
Calculated by finding difference between arrival of P and S waves
How do you find the distance to an earthquake
Sensor is farther from epicenter
What is indicated by a bigger interval between the arrival of the waves at the sensor
Triangulation
How is location found by sensors since one cannot pinpoint location
Computers
Today location is quickly found by using...
Depth of focus
What can be found by studying arrival times of all three waves
Amplitude and Wavelength
What do all waves have in common
Fault
Feature of earth's surface -- first thought to cause earthquakes, then thought to be result, now known to be feature caused by movement of tectonic plates
San Andreas Fault
most well-known fault -- type is strike-slip between the Pacific and North American tectonic plates
70 km or deeper
How deep does a quake need to be before it will not be felt -- thought to be quakes along fault line where one plate is sub ducting under other plates
save lives not property
Why are prediction techniques being developed -- also why are building materials and methods being improved
Fault lines
What is identified in earthquake-prone areas
How long before scientists might be able to predict earthquakes
Where, When, Magnitude
What will be predicted
Pacific Rim or Ring of Fire
Circum-Pacific and Alpine Himalayan volcano belts are also known as
90%
How many earthquakes occur in Circum-Pacific or Alpine Himalayan
Volcanoes
What often trigger earthquakes
Volcanoes
what is sometimes preceded by an earthquake -- not known if the earthquake causes it though
Note places where lots occur and then see what gap between is and how often they occurred in the past
Today's prediction method
knowledge of deeper terrain (inner layers)
What is needed to understand why and when earthquakes will be happening
Being prepared
What is the next best line of defense if you aren't able to predict earthquakes
California
What state is often described as about to fall off into the ocean
No known reason
Multitude of sensors installed in California show that pressure sometimes builds up and then dissipates without an earthquake | 532 | 2,492 | {"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-2018-17 | latest | en | 0.954009 |
https://community.fabric.microsoft.com/t5/Desktop/Referencing-Unrelated-Data/td-p/36854 | 1,726,071,701,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700651390.33/warc/CC-MAIN-20240911152031-20240911182031-00662.warc.gz | 159,284,946 | 52,028 | cancel
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New Member
## Referencing Unrelated Data
Hi,
I am a newbie to DAX and I am working on Forecasting and need to reference the "TL APPROVALS" from the previous "Payment_No". Everything I have tried has resulted in something similar to what you see in the "Last PMT Approvals" below. Can someone please help me find a DAX formula that will work to give me the desired results I have placed in the last column of the table below? TIA
Order Co DATE (Year) Order Co MONTH partner_prog_id Payment_No TL APPROVALS Last PMT Approvals I want the Last PMT Approvals to give these results 2015 05-MAY 1 0 1,312 1,832 1 685 1,832 1,312 2 314 1,832 685 3 192 1,832 314 4 143 1,832 192 5 108 1,832 143 05-MAY Total 2,754 1,832 06-JUN 1 0 947 1,324 1 537 1,324 947 2 242 1,324 537 3 145 1,324 242 4 106 1,324 145 5 77 1,324 106 06-JUN Total 2,054 1,324 77 2015 Total 4,808 3,156 Grand Total 4,808 3,156
3 REPLIES 3
Memorable Member
Looks like you have a join happening on date rather than payment number, hence the PMT approvals summing at a month level rather than a payment level.
Make a calculated column with a related() function to make sure the pmt approval data is coming across properly, and then make the measure based on that (more long winded but you know the join is working by seeing the column). You can then just sumx() to get latest pmt approvals.
// if this is a solution please mark as such. Kudos always appreciated.
New Member
Samdthompson,
I am really just trying to reference the response from the previous payment so if you are looking at the row with Payment_No 1 I could use a formula that would say =if(Payment_No 0 approvals = 0, 0, 1). I have thought about using the approval date and just look back to last month but that doesn't work because Payment_No 0 is a 14 day trial. That would mean looking back 1 month would give you approvals on Payment_No 0 and some of Payment_No 1. Any suggestions?
Thanks!
Microsoft Employee
@prices35
To get the expected output, you can either create a new column in the "Data page" or in the "Edit query page".
```Column = SUMX(FILTER(Sheet1,
EARLIER(Sheet1[Payment_No])=Sheet1[Payment_No]+1
&&
EARLIER(Sheet1[Order Co DATE (Year)])=Sheet1[Order Co DATE (Year)]
&&
EARLIER(Sheet1[Order Co MONTH])=Sheet1[Order Co MONTH]
&&
EARLIER(Sheet1[partner_prog_id])=Sheet1[partner_prog_id]
)
,Sheet1[TL APPROVALS])```
In Data page
In Edit quries
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Top Kudoed Authors | 863 | 3,074 | {"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-2024-38 | latest | en | 0.915452 |
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