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https://en.wikibooks.org/wiki/Engineering_Analysis/Matrix_Forms
|
[
"Engineering Analysis/Matrix Forms\n\nMatrices that follow certain predefined formats are useful in a number of computations. We will discuss some of the common matrix formats here. Later chapters will show how these formats are used in calculations and analysis.\n\nDiagonal Matrix\n\nA diagonal matrix is a matrix such that:\n\n$a_{ij}=0,i\\neq j$",
null,
"In otherwords, all the elements off the main diagonal are zero, and the diagonal elements may be (but don't need to be) non-zero.\n\nCompanion Form Matrix\n\nIf we have the following characteristic polynomial for a matrix:\n\n$|A-\\lambda I|=\\lambda ^{n}+a_{n-1}\\lambda ^{n-1}+\\cdots +a_{1}\\lambda ^{1}+a_{0}$",
null,
"We can create a companion form matrix in one of two ways:\n\n${\\begin{bmatrix}0&0&0&\\cdots &0&-a_{0}\\\\1&0&0&\\cdots &0&-a_{1}\\\\0&1&0&\\cdots &0&-a_{2}\\\\0&0&1&\\cdots &0&-a_{3}\\\\\\vdots &\\vdots &\\vdots &\\ddots &\\vdots &\\vdots \\\\0&0&0&\\cdots &1&-a_{n-1}\\end{bmatrix}}$",
null,
"Or, we can also write it as:\n\n${\\begin{bmatrix}-a_{n-1}&-a_{n-2}&-a_{n-3}&\\cdots &a_{1}&a_{0}\\\\0&0&0&\\cdots &0&0\\\\1&0&0&\\cdots &0&0\\\\0&1&0&\\cdots &0&0\\\\0&0&1&\\cdots &0&0\\\\\\vdots &\\vdots &\\vdots &\\ddots &\\vdots &\\vdots \\\\0&0&0&\\cdots &1&0\\end{bmatrix}}$",
null,
"Jordan Canonical Form\n\nTo discuss the Jordan canonical form, we first need to introduce the idea of the Jordan Block:\n\nJordan Blocks\n\nA jordan block is a square matrix such that all the diagonal elements are equal, and all the super-diagonal elements (the elements directly above the diagonal elements) are all 1. To illustrate this, here is an example of an n-dimensional jordan block:\n\n${\\begin{bmatrix}a&1&0&\\cdots &0\\\\0&a&1&\\cdots &0\\\\0&0&a&\\cdots &0\\\\\\vdots &\\vdots &\\vdots &\\ddots &\\vdots \\\\0&0&a&\\cdots &1\\\\0&0&0&\\cdots &a\\end{bmatrix}}$",
null,
"Canonical Form\n\nA square matrix is in Jordan Canonical form, if it is a diagonal matrix, or if it has one of the following two block-diagonal forms:\n\n${\\begin{bmatrix}D&0&\\cdots &0\\\\0&J_{1}&\\cdots &0\\\\\\vdots &\\vdots &\\ddots &\\vdots \\\\0&0&\\cdots &J_{n}\\end{bmatrix}}$",
null,
"Or:\n\n${\\begin{bmatrix}J_{1}&0&\\cdots &0\\\\0&J_{2}&\\cdots &0\\\\\\vdots &\\vdots &\\ddots &\\vdots \\\\0&0&\\cdots &J_{n}\\end{bmatrix}}$",
null,
"The where the D element is a diagonal block matrix, and the J blocks are in Jordan block form."
] |
[
null,
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|
https://dev.to/miccwan/leetcode-practice-2-51pg
|
[
"## DEV Community",
null,
"Micc Wan\n\nPosted on • Updated on\n\n# Leetcode Challenge #2\n\nIt has been two days since the last post. I found out that the study plan is supposed to be done daily. It unlocks new problem set everyday. So I'll just try to finish two days at a time (at least for the part I) and see if I need to adjust my schedule when I get to the second part .\n\n## Today's problems\n\nToday's topic: `Two pointers`\n\nID Name Difficulty Problem Solution\n167 Two Sum II - Input Array Is Sorted medium link link\n\nThe topic for Day 2~5 is `Two pointers`. I'm not familiar with this word but I think the binary search method I used last time is a kind of two pointers.\n\nI'm gonna skip problems 977, 283, 167 since they are actually pretty easy and the solutions were intuitive.\n\n### 189. Rotate Array\n\nThe problem is really interesting.\nSome simple methods like slice+concat or rotate from the end costs too much space (O(n) and O(k) respectively).\nIt tooks me some time to come up with an O(1) space solution (though they are all O(n) time).\nThe main idea is:\nIf you move the nums to nums[k], and move the original nums[k] to nums[2*k], ...(under modulo n, of course), it will come back to nums at some point. But in some cases, this cycle does not contain all of the numbers. More precisely, only indexes in the form `0 + m * gcd(n, k)` will be included. So we need to repeat the same procedure but starts from `1 ~ gcd(n, k)`.\n\ne.g. consider `n = 9, k = 6`\n\n``````0 -> 6 -> 3 -> 0 -> ...\n1 -> 7 -> 4 -> 1 -> ...\n2 -> 8 -> 5 -> 2 -> ...\n``````\n\nThe resulting code:\n\n``````var rotate = function (nums, k) {\nconst g = gcd(nums.length, k);\n\nfor (let i = 0; i < g; i++) {\nlet j = i;\nlet tmp = nums[j];\nlet next;\nwhile (next != i) {\nnext = (j + k) % nums.length;\n[nums[next], tmp] = [tmp, nums[next]];\nj = next;\n}\n}\n};\n``````\n\nThis solution is some kind of inflexible. So I checked leetcode discussion and found a beautiful magic. The key concept is:\n`rotate(n, k) = reverse(0, n-1) + reverse(0, k-1) + reverse(k, n-1)`\n\ne.g. consider `n = 7, n = 3`\n\n`````` [1, 2, 3, 4, 5, 6, 7] // original\n-> [7, 6, 5, 4, 3, 2, 1] // reverse(0, 6)\n-> [5, 6, 7, 4, 3, 2, 1] // reverse(0, 2)\n-> [5, 6, 7, 1, 2, 3, 4] // reverse(3, 6)\n``````\n\nI haven't figured out how this magic was discovered, but it was really shocking for me.\n\nAnother two pointer problem I picked today is:\n\nID Name Difficulty Problem Solution\n\nUnexpectedly, this problem took me about 40 minutes. According to the constraint, `n < 10^5`, O(n^2) is not acceptable. So brute force enumeration is not good enough.\n\nAfter tackled with many examples, I noticed that the area formula `(l - r) * Math.min(height[l], height[r])` only takes the minimum of the heights into account. Some greedy algorithm that prioritize the smaller height might come in handy in this case.\n\nThe final algorithm becomes:\nStarts from the most outer pair, record the area value and shrink the smaller side inward until it found some larger height. If the new area is bigger, update the record. Then repeat the steps again and again until the two pointers coinside. Note that if the heights of the both sides are the same, we have to shrink them at the same time, since the area will never get larger if only one side is shrinked.\n\nEach time we shrink the border, the width of the container will become smaller. So we only needs to focus on maximizing the heights. The greedy algorithm works due to the property of area formula.\n\nThe complexities are O(n) time and O(1) space, since the process of shrinking border will be done in total of n-1 times and calculating the area is O(1).\n\n## Conclusion\n\nThe five problems above took me about 1.5 hrs, due to the unexpected difficulty of the last problem. Also, they are more difficult than the problems last time. The proof of correctness for the last algorithm even require some mathematical techniques, e.g. Loop invariant. But this series is not an algorithm tutorial, sorry I will skip those details.\n\nSo that's my challenge today, hope u enjoy. :)\n\n<-- Previous | Home | Next -->",
null,
""
] |
[
null,
"https://res.cloudinary.com/practicaldev/image/fetch/s--FKaeZ8eX--/c_imagga_scale,f_auto,fl_progressive,h_420,q_auto,w_1000/https://dev-to-uploads.s3.amazonaws.com/uploads/articles/dwzo8k8i00g3uyihe1kc.png",
null,
"https://res.cloudinary.com/practicaldev/image/fetch/s--ZTIqDcq---/c_fill,f_auto,fl_progressive,h_50,q_auto,w_50/https://dev-to-uploads.s3.amazonaws.com/uploads/user/profile_image/892277/b14dcee2-ce22-4167-a0ed-38a461066457.jpeg",
null
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|
https://brandewinder.com/2010/02/06/Recalculate-cells-before-reading-from-a-worksheet/
|
[
"# Recalculate cells before reading from a worksheet\n\nI am currently working on a project which extends an Excel VSTO add-in model I had developed a few months back. This is a joint project, and my add-in has to interact with a classic Excel worksheet model, which got me worried. The original model read data from Excel into a C# object, which handles the heavy-duty computation, and writes back results to a spreadsheet once it is done. The modified model has to proceed in 2 steps: perform a partial read of the inputs, compute some outputs, feed them into the worksheet model, read some results from that worksheet, resume computations and write out the final outputs.\n\nThe reason I was worried is that the spreadsheet I have to interact with is a bit slow, and I was concerned about a race condition type of problem. What if the add-in attempted to read data from the worksheet, before Excel had time to update the values in the worksheet?\n\nIn order to check whether there was a problem, I created a small test case. I first wrote a VBA function which was on purpose very slow:\n\nPublic Function SlowFunction(arg As String) As String\n\nWaitFor 10\nSlowFunction = arg\n\nEnd Function\n\nPublic Function WaitFor(seconds As Integer)\n\nDim startTime As Double\nstartTime = timer\n\nDo While timer < startTime + seconds\nLoop\n\nEnd Function\n\n\nThe SlowFunction simply takes a string as input, calls the WaitFor function, which stays busy for a few seconds, and returns the input string after 10 seconds have elapsed. This allowed me to artificially create an extremely inefficient worksheet: when the input cell A1 is modified, the output cell A2 is updated only 10 seconds later.",
null,
"The next step was to create a tiny VSTO project, which changed the value in cell A1, and read the value in cell A2 right after – the question being, what would happen? Would it read the value before it has changed, or wait for the update to occur before reading it? Or would it crash?\n\npublic bool Run()\n{\nvar workbook = excel.ActiveWorkbook;\nvar worksheet = (Worksheet)workbook.ActiveSheet;\n\nvar inputRange = worksheet.get_Range(\"Input\", Type.Missing);\nvar initial = inputRange.Value2.ToString();\nvar modified = initial + \" (Changed)\";\ninputRange.Value2 = modified;\n\nvar outputRange = worksheet.get_Range(\"Output\", Type.Missing);\n}\n\n\nI was honestly not sure what to expect when I ran this, but the result was what I hoped it would be: the Run() method reads the updated value. As a result, though, it has to wait for Excel to get its job done, and is held up for 10 seconds.\n\nNow when a workbook becomes heavy and slow, it is quite common to modify its behavior and set Calculation to Manual instead of Automatic. In that case, when the user modifies an input value, cells which depend on that value are not immediately recalculated, and the workbook remains in a “stale” state, until the user requests an recalculation, by hitting the F9 key. So I proceeded to set my clumsy workbook to Manual Calculation:",
null,
"In this case, running the same code results in reading stale, non-updated values.\n\nTo address that issue, one possible solution is to check whether Excel is done with its calculations, and trigger a recalculation if required, by inserting the following code before the read:\n\ninputRange.Value2 = modified;\n\nif (excel.CalculationState != XlCalculationState.xlDone)\n{\nworksheet.Calculate();\n}\n\nvar outputRange = worksheet.get_Range(\"Output\", Type.Missing);"
] |
[
null,
"https://mathias-brandewinder.github.io//assets/2010-02-06-SlowWorkbook_thumb.png",
null,
"https://mathias-brandewinder.github.io//assets/2010-02-06-ManualCalculation_thumb.png",
null
] |
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|
https://www.electronicsforu.com/electronics-projects/matlab-image-deblurring-hough-transform
|
[
"# Image Processing Using MATLAB: Image Deblurring and Hough Transform (Part 4 of 4)\n\nDr Anil Kumar Maini is former director, Laser Science and Technology Centre, a premier laser and optoelectronics R&D laboratory of DRDO of Ministry of Defence--Varsha Agrawal is a senior scientist with Laser Science and Technology Centre (LASTEC), a premier R&D lab of DRDO\n\n18876\n\n## Read Part 3\n\nImage pre-processing and identification of certain shaped objects in the image is explained here using Image Deblurring and Hough Transform.\n\nImage deblurring removes distortion from a blurry image using knowledge of the point spread function (PSF). Image deblurring algorithms in Image Processing Toolbox include Wiener, and regularised filter deconvolution, blind, Lucy-Richardson, as well as conversions between point spread and optical transfer functions. These functions help correct blurring caused by out-of-focus optics, camera or subject movement during image capture, atmospheric conditions, short exposure time and other factors.\n\ndeconvwnr function deblurs the image using Wiener filter, while deconvreg function deblurs with a regularised filter. deconvlucy function implements an accelerated, damped Lucy-Richardson algorithm and deconvblind function implements the blind deconvolution algorithm, which performs deblurring without the knowledge of PSF. We discuss here how to deblur an image using Wiener and regularised filters.\n\n## Deblurring using Wiener filter\n\nWiener deconvolution can be used effectively when frequency characteristics of the image and additive noise are known to some extent. In the absence of noise, Wiener filter reduces to an ideal inverse filter.\n\ndeconvwnr function deconvolves image I using Wiener filter algorithm, returning deblurred image J as follows:\n\nJ = deconvwnr(I,PSF,NSR)\n\nwhere image I can be an N-dimensional array, PSF the point-spread function with which image I was convolved, and NSR the noise-to-signal power ratio of the additive noise. NSR can be a scalar or a spectral-domain array of the same size as image I. NSR=0 is equivalent to creating an ideal inverse filter.\n\nImage I can be of class uint8, uint16, int16, single or double. Other inputs have to be of class double. Image J has the same class as image I.\n\nThe following steps are taken to read ‘Image_2.tif’, blur it, add noise to it and then restore the image using Wiener filter.\n\n1. The syntax to read image (Image_2.tif) into the MATLAB workspace and display it is:\n>> I=im2double(imread(‘Image_2.tif’));\n>>imshow(I)",
null,
"Fig. 1: Image read into the MATLAB workspace\n\nFig. 1 shows the image generated by imshow function.\n\n2. h=fspecial(‘motion’, len, theta) returns a filter to approximate the linear motion of a camera by len pixels, with an angle of theta degrees in a counter-clockwise direction. The filter becomes a vector for horizontal and vertical motions. The default value of len is 9 and that of theta is 0, which corresponds to a horizontal motion of nine pixels. B=imfilter(A,h) filters multidimensional array A with multidimensional filter h. Array A can be logical or non-sparse numeric array of any class and dimension. Result B has the same size and class as A. The syntax is:\n>> LEN=21;\n>> THETA=11;\n>> PSF=fspecial(‘motion’,LEN,THETA);\n>> blurred=imfilter(I,PSF,’conv’,’circular’);\n>>figure,imshow(blurred)",
null,
"Fig. 2: Image after filtering with multidimensional filter\n\nFig. 2 shows the image generated by imshow function.\n\n3. J=imnoise(I,’gaussian’,M,V) adds Gaussian white noise of mean M and variance V to image I:\n>>noise_mean=0;\n>>noise_var=0.002;\n>>blurred_noise=imnoise(blurred,’gaussian’,\nnoise_mean,noise_var);\n>>figure, imshow(blurred_noise)",
null,
"Fig. 3: Image generated after addition of Gaussian white noise\n\nFig. 3 shows the image generated by imshow function.\n\n4. As mentioned above, J=deconvwnr (I,PSF,NSR) deconvolves image I using Wiener filter algorithm, returning deblurred image J. The following commands generate a deblurred image using NSR of zero:\n>>estimated_nsr=0;\n>> wnr2=deconvwnr(blurred_noise,PSF,\nestimated_nsr);\n>>figure,imshow(wnr2)",
null,
"Fig. 4: Deblurred image using NSR of zero\n\nFig. 4 shows the image generated by imshow function.\n\n5. The following commands generate a deblurred image using NSR calculated from the image:\n>>estimated_nsr=noise_var/var(I(:));\n>> wnr3=deconvwnr(blurred_noise,PSF,\nestimated_nsr);\n>>figure,imshow(wnr3)",
null,
"Fig.5: Restored image from the blurred and noisy image using estimated NSR generated from the image\n\nFig. 5 shows the restored image from the blurred and noisy image using estimated NSR generated from the image.\n\nDeblurring with a regularised filter\n\nA regularised filter can be used effectively when limited information is known about the additive noise.\n\nJ=deconvreg(I, PSF) deconvolves image I using regularised filter algorithm and returns deblurred image J. The assumption is that image I was created by convolving a true image with a point-spread function and possibly by adding noise. The algorithm is a constrained optimum in the sense of least square error between the estimated and true images under requirement of preserving image smoothness.\n\nImage I can be an N-dimensional array.\nVariations of deconvreg function are given below:\n\n• J = deconvreg(I, PSF, NOISEPOWER)\nwhere NOISEPOWER is the additive noise power. The default value is 0.\n\n• J = deconvreg(I, PSF, NOISEPOWER, LRANGE)\nwhere LRANGE is a vector specifying range where the search for the optimal solution is performed.\n\nThe algorithm finds an optimal Lagrange multiplier LAGRA within LRANGE range. If LRANGE is a scalar, the algorithm assumes that LAGRA is given and equal to LRANGE; the NP value is then ignored. The default range is between [1e-9 and 1e9].\n\n• J = deconvreg(I, PSF, NOISEPOWER, LRANGE, REGOP)\n\nwhere REGOP is the regularisation operator to constrain deconvolution. The default regularisation operator is Laplacian operator, to retain the image smoothness. REGOP array dimensions must not exceed image dimensions; any non-singleton dimensions must correspond to the non-singleton dimensions of PSF.\n\n[J, LAGRA] = deconvreg(I, PSF,…) outputs the value of Lagrange multiplier LAGRA in addition to the restored image J.\n\nIn a nutshell, there are optional arguments supported by deconvreg function. Using these arguments you can specify the noise power value, the range over which deconvreg should iterate as it converges on the optimal solution, and the regularisation operator to constrain the deconvolution."
] |
[
null,
"https://www.electronicsforu.com/wp-contents/uploads/2018/05/image-generated-by-imshow-function-500x377.jpg",
null,
"https://www.electronicsforu.com/wp-contents/uploads/2018/05/Image-after-filtering-with-multidimensional-filter-500x375.jpg",
null,
"https://www.electronicsforu.com/wp-contents/uploads/2018/05/Image-generated-after-addition-of-Gaussian-white-noise-500x399.jpg",
null,
"https://www.electronicsforu.com/wp-contents/uploads/2018/05/Deblurred-image-using-NSR-of-zero-500x383.jpg",
null,
"https://www.electronicsforu.com/wp-contents/uploads/2018/05/Restored-image-from-the-blurred-and-noisy-image-using-estimated-NSR-generated-from-the-image-500x375.jpg",
null
] |
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https://maharashtraboardsolutions.in/maharashtra-board-12th-commerce-maths-solutions-chapter-5-ex-5-2-part-2/
|
[
"# Maharashtra Board 12th Commerce Maths Solutions Chapter 5 Index Numbers Ex 5.2\n\nBalbharati Maharashtra State Board 12th Commerce Maths Solution Book Pdf Chapter 5 Index Numbers Ex 5.2 Questions and Answers.\n\n## Maharashtra State Board 12th Commerce Maths Solutions Chapter 5 Index Numbers Ex 5.2\n\nCalculate Laspeyres, Paasche’s, Dorbish-Bowely’s, and Marshall-Edegworth’s Price Index Numbers in Problems 1 and 2.\n\nQuestion 1.",
null,
"Solution:",
null,
"",
null,
"",
null,
"Question 2.",
null,
"Solution:",
null,
"",
null,
"Calculate Walsh’s Price Index Number in Problems 3 and 4.\n\nQuestion 3.",
null,
"Solution:",
null,
"Question 4.",
null,
"Solution:",
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"",
null,
"",
null,
"",
null,
"Question 5.\nIf p01(L) = 90, and p01(P) = 40, find p01(D – B) and p01(F)\nSolution:",
null,
"Question 6.\nIf Σp0q0 = 140, Σp0q1 = 200, Σp1q0 = 350, Σp1q1 = 460, find Laspeyre’s Paasche’s Dorbish-Bowley’s and Marshall- Edgeworth’s Price Index Numbers.\nSolution:",
null,
"Question 7.\nGiven that Laspeyre’s and Dorbish-Bowley’s Price Index Numbers are 160.32 and 164.18 respectively. Find Paasche’s Price Index Number.\nSolution:",
null,
"Question 8.\nGiven that Σp0q0 = 220, Σp0q1 = 380, Σp1q1 = 350 is Marshall-Edgeworth’s Price Index Number is 150, find Laspeyre’s Price Index Number.\nSolution:",
null,
"Question 9.\nFind x in the following table if Laspeyres and Paasche’s Price Index Numbers are equal.",
null,
"Solution:",
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"",
null,
"",
null,
"Question 10.\nIf Laspeyre’s Price Index Number is four times Paasche’s Price Index Number, then find the relation between Dorbish-Bowley’s and Fisher’s Price Index Numbers.\nSolution:",
null,
"Question 11.\nIf Dorbish-Bowley’s and Fisher’s Price Index Numbers are 5 and 4, respectively, then find Laspeyres and Paasche’s Price Index Numbers.\nSolution:",
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"",
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""
] |
[
null,
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null,
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null,
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null,
"https://maharashtraboardsolutions.guru/wp-content/uploads/2022/01/Maharashtra-Board-12th-Commerce-Maths-Solutions-Chapter-5-Index-Numbers-Ex-5.2-Q3.png",
null,
"https://maharashtraboardsolutions.guru/wp-content/uploads/2022/01/Maharashtra-Board-12th-Commerce-Maths-Solutions-Chapter-5-Index-Numbers-Ex-5.2-Q3.1.png",
null,
"https://maharashtraboardsolutions.guru/wp-content/uploads/2022/01/Maharashtra-Board-12th-Commerce-Maths-Solutions-Chapter-5-Index-Numbers-Ex-5.2-Q4.png",
null,
"https://maharashtraboardsolutions.guru/wp-content/uploads/2022/01/Maharashtra-Board-12th-Commerce-Maths-Solutions-Chapter-5-Index-Numbers-Ex-5.2-Q4.1.png",
null,
"https://maharashtraboardsolutions.guru/wp-content/uploads/2022/01/Maharashtra-Board-12th-Commerce-Maths-Solutions-Chapter-5-Index-Numbers-Ex-5.2-Q4.2.png",
null,
"https://maharashtraboardsolutions.guru/wp-content/uploads/2022/01/Maharashtra-Board-12th-Commerce-Maths-Solutions-Chapter-5-Index-Numbers-Ex-5.2-Q4.3.png",
null,
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null,
"https://maharashtraboardsolutions.guru/wp-content/uploads/2022/01/Maharashtra-Board-12th-Commerce-Maths-Solutions-Chapter-5-Index-Numbers-Ex-5.2-Q5.png",
null,
"https://maharashtraboardsolutions.guru/wp-content/uploads/2022/01/Maharashtra-Board-12th-Commerce-Maths-Solutions-Chapter-5-Index-Numbers-Ex-5.2-Q6.png",
null,
"https://maharashtraboardsolutions.guru/wp-content/uploads/2022/01/Maharashtra-Board-12th-Commerce-Maths-Solutions-Chapter-5-Index-Numbers-Ex-5.2-Q7.png",
null,
"https://maharashtraboardsolutions.guru/wp-content/uploads/2022/01/Maharashtra-Board-12th-Commerce-Maths-Solutions-Chapter-5-Index-Numbers-Ex-5.2-Q8.png",
null,
"https://maharashtraboardsolutions.guru/wp-content/uploads/2022/01/Maharashtra-Board-12th-Commerce-Maths-Solutions-Chapter-5-Index-Numbers-Ex-5.2-Q9.png",
null,
"https://maharashtraboardsolutions.guru/wp-content/uploads/2022/01/Maharashtra-Board-12th-Commerce-Maths-Solutions-Chapter-5-Index-Numbers-Ex-5.2-Q9.1.png",
null,
"https://maharashtraboardsolutions.guru/wp-content/uploads/2022/01/Maharashtra-Board-12th-Commerce-Maths-Solutions-Chapter-5-Index-Numbers-Ex-5.2-Q9.2.png",
null,
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"https://maharashtraboardsolutions.guru/wp-content/uploads/2022/01/Maharashtra-Board-12th-Commerce-Maths-Solutions-Chapter-5-Index-Numbers-Ex-5.2-Q10.png",
null,
"https://maharashtraboardsolutions.guru/wp-content/uploads/2022/01/Maharashtra-Board-12th-Commerce-Maths-Solutions-Chapter-5-Index-Numbers-Ex-5.2-Q11.png",
null,
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|
https://jemrare.com/tag/factorize-2x2-%E2%88%92-8x-%E2%88%92-42/
|
[
"# Factorize 2×2 − 8x − 42\n\n## Question 3: Factorize 2×2 − 8x − 42\n\nQuestion 3: Factorize 2×2 − 8x − 42 Factorization exercises , factorization examp... »\n\nInsert math as\n$${}$$"
] |
[
null
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|
https://www.nature.com/articles/s41598-017-08750-z?error=cookies_not_supported&code=02a33075-63bd-4b19-bda2-ecdbacf6d9f7
|
[
"Non-diffraction propagation of acoustic waves in a rapidly modulated stratified medium\n\nAbstract\n\nA rapidly modulated stratified medium with a large mass density modulation depth (LMMD) is proposed to achieve non-diffraction propagation (NDP) of acoustic waves. It is found that the NDP in LMMD medium is independent of the incident angle and can be operated in a broad-band manner. Such an NDP is robust and is unhampered by medium losses. An effective medium theory (EMT) is developed for acoustic waves propagating in the LMMD medium based on the first-principles method. The LMMD EMT is verified by using the transfer-matrix method (TMM) for both propagating and evanescent waves. Furthermore, we discuss the influence of the geometry on NDP, and finite element simulations are conducted to verify the NDP in the LMMD medium.\n\nIntroduction\n\nNon-diffraction propagation (NDP) of acoustic waves in spatially modulated media has been widely studied theoretically and experimentally because of the potential applications in wave beaming, acoustic waveguides, and subwavelength imaging1,2,3,4,5,6,7,8,9,10,11,12,13,14. The NDP of the wave beam shows flat equifrequency contours (EFCs) in the band structure; hence, the efficient NDP with a small angular divergence requires long flat EFCs15,16,17,18,19,20,21. In general, NDP appears only in a small range of incident angles on the flat segments of the EFCs and is very sensitive to the frequency of the incident waves; these features hinder the further actual applications of NDP. Therefore, many studies have been carried out to expand both the incident angle and the working frequency for NDP10,11,12,13,14. For example, in phononic crystals, the filling ratios or the form of the scatterer could broaden the frequency region of NDP10, 11. A rectangular phononic crystal is more favourable for expanding the incident angle range compared to a triangular one13, 14.\n\nRecently, Rizza and Ciattoni22, 23 proposed a novel and robust regime for NDP when the transverse magnetic (TM) waves propagate in rapidly modulated stratified media with a large dielectric modulation depth (Kapitza medium)24. The rapid and large modulation of permittivity strongly suppresses the longitudinal component of the electric field, thus slowing down diffraction of the TM waves. Such a design is capable of achieving all-angle self-collimation, including the evanescent waves at any frequency, resulting in NDP. It is well known that the acoustic equations in a fluid are identical in form to the single polarization Maxwell equations via a variable exchange that also preserves the boundary conditions in a two-dimensional geometry. In many cases, the two acoustic parameters (mass density and bulk modulus) could be analogous to the two parameters (electric permittivity and magnetic permeability) in the electromagnetic problem25. Extending the concept from optics, the NDP of acoustic waves may occur in a rapidly modulated stratified medium.\n\nIn this paper, we propose a rapidly modulated stratified medium with a large mass density modulation depth (LMMD) that is capable of achieving broad-band NDP for all incident angles. An effective medium model for the LMMD medium is deduced based on the first-principles method because the very deep and rapidly modulated mass density variation entails a medium homogenization that cannot be described by the standard effective medium theory (EMT). The EMT for the LMMD medium is verified by using the transfer-matrix method (TMM) for both propagating and evanescent waves. It is found that the large mass density modulation leads to non-diffraction propagation of acoustic waves that is robust and cannot be hampered by medium losses. Furthermore, we discuss the influence of the geometry on NDP, and finite element simulations are conducted to verify NDP in the LMMD medium.\n\nResults\n\nEffective medium theory based on the first-principles method\n\nAn anisotropic acoustic metamaterial often possesses an anisotropic mass density tensor ρ and a scalar bulk modulus κ 26. Here, we only consider an inviscid fluid-like metamaterial with zero shear modulus. The anisotropic mass density tensor ρ should be expressed as diagonal $$\\,{\\boldsymbol{\\rho }}=diag[{\\rho }_{x},{\\rho }_{y},{\\rho }_{z}]$$. The propagation of acoustic waves in this material is governed by the conservation of momentum and mass equations of a general form26,\n\n$$\\{\\begin{array}{c}\\nabla p=-{\\boldsymbol{\\rho }}\\frac{\\partial v}{\\partial t}\\\\ \\nabla \\cdot {\\boldsymbol{v}}=-\\frac{1}{\\kappa }\\frac{\\partial p}{\\partial t}\\end{array}\\,,$$\n(1)\n\nwhere p is the hydrostatic pressure field, and v is the velocity field. Inside the metamaterial, the two-dimensional pressure field p and velocity field $${\\boldsymbol{v}}=({v}_{x},{v}_{z})$$ are related by the motion equations, where time dependence e iwt has been assumed:\n\n$$\\{\\begin{array}{c}{\\partial }_{x}p=i\\omega {\\rho }_{x}{v}_{x}\\\\ {\\partial }_{z}p=i\\omega {\\rho }_{z}{v}_{z}\\\\ {\\partial }_{x}{v}_{x}+{\\partial }_{z}{v}_{z}=i\\omega p/\\kappa \\end{array}.$$\n(2)\n\nHere, we consider a specific medium periodically modulated along the z-axis whose relative mass density $${\\rho }_{r}={\\rho }_{x}/{\\rho }_{0}={\\rho }_{z}/{\\rho }_{0}$$ 0 is the mass density of the background medium) permits the Fourier series expansion\n\n$${\\rho }_{r}={\\rho }_{m}+\\sum _{n\\ne 0}({a}_{n}+\\frac{{b}_{n}}{\\eta }){e}^{in(\\frac{K}{\\eta })z},$$\n(3)\n\nwhere ρ m is the average of the relative mass density ρ r , ($${a}_{n}+{b}_{n}/\\eta$$) is the Fourier coefficient, $$2\\pi \\eta /K$$ is the spatial period, and η is a dimensionless parameter. The propagation of acoustic waves is now characterized by two very different scales, i.e., a macroscopic one (the radiation wavelength) and a microscopic one (the mass density modulation period). To describe this problem, we will rely on a two-scale expansion of the fields27, 28. The physical problem is described by two variables: a slow coordinate z (macroscopic) and a fast coordinate $$Z=z/\\eta$$ (microscopic) representing the rapid variations of the material at the scale of the basic cell, measured by η. It is natural to allow each acoustic field component to separately depend on the slow coordinate z and fast coordinate Z, allowing for decomposition of each component as a Taylor expansion up to first order in η,\n\n$$H(x,z,Z)=[{\\bar{H}}^{(0)}(x,z)+{\\tilde{H}}^{(0)}(x,z,Z)]+\\eta [{\\bar{H}}^{(1)}(x,z)+{\\tilde{H}}^{(1)}(x,z,Z)],$$\n(4)\n\nwhere H = p, v x , or v z , and the superscript (0) or (1) indicates the order of each term. The overline and tilde label the averaged and rapidly varying contributions to each order, respectively. After substituting Eq. (4) into Eq. (2) and noting that $${\\partial }_{z}={\\partial }_{z}+\\frac{1}{\\eta }{\\partial }_{Z}$$, each equation yields a power series in η whose various orders are the superposition of slowly varying (independent of Z) and fast (dependent on Z) contributions. For each order, the averaged and rapidly varying contributions can be independently balanced. From the lowest order $${\\eta }^{-1}$$, $${{\\bar{v}}_{x}}^{(0)}=0$$, $${{\\tilde{v}}_{x}}^{(0)}=0$$, $${{\\tilde{v}}_{z}}^{(0)}=0$$, and $${\\tilde{p}}^{(0)}=\\frac{\\omega {\\rho }_{0}}{K}\\sum _{n\\ne 0}\\frac{{b}_{n}}{n}{e}^{inKZ}{{\\bar{v}}_{z}}^{(0)}$$ can be obtained. From the order $${\\eta }^{0}$$ of the third line of Eq. (2), we obtain\n\n$${\\partial }_{z}{{\\bar{v}}_{z}}^{(0)}=i\\omega \\frac{1}{\\kappa }{\\bar{p}}^{(0)},$$\n(5)\n$${\\partial }_{Z}{{\\tilde{v}}_{z}}^{(1)}=i\\omega \\frac{1}{\\kappa }{\\tilde{p}}^{(0)},$$\n(6)\n$${{\\tilde{v}}_{z}}^{(1)}=\\frac{{k}_{0}^{2}}{{K}^{2}}\\sum _{n\\ne 0}\\frac{{b}_{n}}{{n}^{2}}{e}^{inKZ}{{\\bar{v}}_{z}}^{(0)}.$$\n(7)\n\nFrom the slowly varying part of the order $${\\eta }^{0}$$ for the second line of Eq. (2) and Eq. (7), we obtain\n\n$${\\partial }_{z}{\\bar{p}}^{(0)}=i\\omega {\\rho }_{0}{\\rho }_{r}^{eff}{{\\bar{v}}_{z}}^{(0)},$$\n(8)\n\nwhere\n\n$${\\rho }_{r}^{eff}={\\rho }_{m}+\\frac{{k}_{0}^{2}}{{K}^{2}}\\sum _{n\\ne 0}\\frac{{b}_{-n}{b}_{n}}{{n}^{2}}.\\,$$\n(9)\n\nTherefore, the pressure field and velocity field in a rapidly modulated stratified medium only have slowly varying terms, i.e., $$p\\approx {\\bar{p}}^{(0)}(x,z)$$ and $${\\boldsymbol{v}}\\approx {{\\bar{v}}_{z}}^{(0)}{\\hat{e}}_{z}$$. The two-dimensional motion equations of Eq. (2) become one-dimensional motion equations of Eqs (5) and (8); then, the acoustic waves propagating in the LMMD medium can be simulated by these in an effective homogeneous medium with uniform effective mass density $${\\rho }_{0}{\\rho }_{r}^{eff}$$. It is obvious that, regardless of the medium losses, the effective mass density is not even defined and the velocity field component $${v}_{x}$$ vanishes because the density is not assumed to be real. Therefore, the NDP within the LMMD medium is very robust and cannot be hampered, even in the presence of medium losses. The effective mass density of Eq. (9) has two contributions: the former corresponds to the average mass density, and the latter corresponds to the rapidly varying part of the density modulation. The proposed EMT is fundamentally different from the standard EMT29, whose effective mass densities are $${\\rho }_{x}\\,=\\,< {\\rho }^{-1}{ > }^{-1}$$ and $${\\rho }_{z}\\,=\\, < \\rho >$$. When $${b}_{n}=0$$, i.e., without the large modulation depth contribution to the density, Eq. (3) for the LMMD medium is the same as that for the standard EMT.\n\nNumerical demonstrations\n\nTo check the prediction of the proposed EMT, let us consider the reflection and transmission of acoustic plane waves from a slab filled with the LMMD medium. Figure 1 shows that the acoustic waves with an incident angle θ propagate from air into the layered LMMD medium slab. The mass density modulation is along the z-axis with a period of $$\\Lambda =\\eta {\\lambda }_{0}$$. Here, $${\\lambda }_{0}=2\\pi /{k}_{0}$$ is the incident wavelength, and η is the small parameter. The slab thickness L is a multiple of the period $$\\eta {\\lambda }_{0}$$, and the unit cell consists of N homogeneous layers with a thickness of $$\\eta {\\lambda }_{0}/N$$. The structural parameters of the layered LMMD medium can be designed according to the incident wavelength, which means that we can achieve the NDP at any desired frequency. Based on Eq. (3), the mass density of the jth layer in the unit cell ($$j=1,\\ldots ,N$$) can be expressed as\n\n$${\\rho }_{r}={\\rho }_{m}+(\\frac{1}{\\eta }+i\\delta \\rho )\\cos \\,[\\frac{2\\pi }{N}(j-1)],$$\n(10)\n\nwhere ρ m is the mean value of the mass density, and $$\\delta \\rho$$ (not large) is responsible for the modulation of medium absorption. Figure 2 shows the transmissivities ($$T={|{p}_{t}|}^{2}/{|{p}_{i}|}^{2}$$) of the acoustic plane waves through the layered LMMD medium slabs with various thicknesses L as a function of $${k}_{x}/{k}_{0}=sin\\theta$$. The acoustic waves with an incident angle θ propagate from air into the layered slab. The material parameters $${\\rho }_{m}=0.05+0.05i$$, $$\\delta \\rho =0.025$$, $$N=10$$, and $$\\eta =1/60$$. Figure 2(a),(b),(c), and (d) represent the results for the slab with various thicknesses of $$20\\eta {\\lambda }_{0}$$, 40$$\\eta {\\lambda }_{0}$$, $$80\\eta {\\lambda }_{0}$$, and $$100\\eta {\\lambda }_{0}$$, respectively. The solid lines show the transmissivities calculated by using the transfer-matrix method (TMM), which are the exact results. The dashed lines represent the results based on the proposed effective medium theory for LMMD (LMMD EMT). Based on Eq. (5) and Eq. (8), the transmissivity can be expressed as\n\n$$T={|\\cos ({k}_{z}L)-iFsin({k}_{z}L)|}^{-2},$$\n(11)\n\nwhere $${k}_{z}={k}_{0}\\sqrt{{\\rho }_{r}^{eff}}$$ and $$F=[\\sqrt{{\\rho }_{r}^{eff}}cos\\theta +\\frac{1}{\\sqrt{{\\rho }_{r}^{eff}}cos\\theta }]/2$$. Inserting the Fourier coefficients of the considered density profile into Eq. (9), we can obtain $${\\rho }_{r}^{eff}$$. The dash-dotted lines show the profiles of the transmissivity evaluated by using the standard effective medium theory (standard EMT). It is obvious that the results based on the LMMD EMT match well with the exact results, whereas the standard EMT is not suitable for the LMMD medium. Even within the longwave approximation regime, the standard EMT is inadequate for the layered LMMD medium because the contributions arising from the rapidly varying periodic density oscillations become important in the LMMD medium.\n\nWe further investigate the validity of the LMMD EMT for $${k}_{x} > {k}_{0}$$. In this condition, the scattering of acoustic waves should encompass evanescent waves. The quantity $$T={|{p}_{t}|}_{z=L}^{2}/{|{p}_{i}|}_{z=0}^{2}$$ represents the above discussed slab transmissivity for $$|{k}_{x}| < {k}_{0}$$ and the efficiency in transporting evanescent waves for $$|{k}_{x}| > {k}_{0}$$. Figure 3(a) shows the logarithmic plot of T as a function of the ($${k}_{x}/{k}_{0}$$) value. The material parameters are identical to those considered in Fig. 2. The thickness of the slab is fixed at $$100\\eta {\\lambda }_{0}$$. The solid, dashed, and dash-dotted lines show the results obtained by using the TMM, LMMD EMT, and standard EMT, respectively. It is obvious that the LMMD EMT predictions agree well with the exact ones for both propagating and evanescent waves, whereas the standard EMT is inadequate for the LMMD medium. In addition, it is noted that medium absorption plays a very detrimental role in the NDP30. Figures 3(b) and (c) show the logarithmic plot of T for the LMMD medium slab for various absorptions with $${\\rho }_{m}=0.05+0.005i$$ and $$\\delta \\rho =0.0025$$ and with $${\\rho }_{m}=0.05+0.5i$$ and $$\\delta \\rho =0.25$$, respectively. The other material parameters are the same as those of Fig. 3(a). In these two situations, the results obtained by using the LMMD EMT approach match well with the exact ones, whereas the ones based on the standard EMT fail. Therefore, the proposed LMMD EMT is very robust against the medium losses, and this feature is very important in the NDP.\n\nLet us continue to discuss the NDP properties of the LMMD medium slab. It is well known that the NDP of the wave beams exhibits equifrequency contours (EFCs), and the long and flat EFCs correspond to a more efficient NDP. The layered LMMD medium is a periodic structure along the z-axis with the period $$\\Lambda =\\eta {\\lambda }_{0}$$. According to Bloch’s theorem, the field amplitude matrix has $${\\boldsymbol{\\Psi }}(z+\\Lambda )={e}^{i{k}_{z}\\Lambda }{\\boldsymbol{\\Psi }}(z)$$. Moreover, according to the transfer-matrix method, $${\\boldsymbol{\\Psi }}(z+\\Lambda )=T{\\boldsymbol{\\Psi }}(z)$$. Substituting $${\\boldsymbol{\\Psi }}(z+\\Lambda )={\\boldsymbol{T}}\\Psi (z)$$ into $${\\boldsymbol{\\Psi }}(z+\\Lambda )={e}^{i{k}_{z}\\Lambda }{\\boldsymbol{\\Psi }}(z)$$, we obtain $$|{\\boldsymbol{T}}-{e}^{i{k}_{z}\\Lambda }{\\boldsymbol{I}}|=0$$. Here, I is a $$2\\times 2$$ unit matrix. Thus, the EFCs can be obtained by solving the eigenvalues of the matrix $${\\boldsymbol{T}}$$. Figure 4(a) shows the EFCs of the LMMD medium with $${\\rho }_{m}=0.05+0.05i$$ and $$\\delta \\rho =0.025$$, which are obtained by imposing the above Bloch condition on the field amplitudes evaluated through the TMM. The solid, dashed, dash-dotted, and dash-dot-dot lines represent the EFCs for $$\\eta =1/100$$, $$\\eta =1/60$$, $$\\eta =1/40$$, and $$\\eta =1/20$$, respectively. When $$\\eta =1/100$$, the ($${k}_{z}/{k}_{0}$$) of the LMMD medium almost remains constant for the various ($${k}_{x}/{k}_{0}$$), indicating perfect NDP. It is obvious that the efficiency of the NDP in the LMMD medium will be reduced with increasing $$\\eta$$. As $$\\eta$$ increases to 1/20, the EFC of the LMMD medium effectively deviates from the constant non-diffracting value of ($${k}_{z}/{k}_{0}$$) approximately for $$|{k}_{x}| > 5{k}_{0}$$, and hence, the diffraction is not fully suppressed. Note that, according to the LMMD EMT, the $${k}_{z}$$ $$({k}_{z}={k}_{0}\\sqrt{{\\rho }_{r}^{eff}})$$ of LMMD medium should remain a constant value for any $${k}_{x}$$, thereby ensuring perfect NDP. Therefore, the proposed EMT and the NDP for the LMMD medium are not suitable for the case with a large $$\\eta$$, especially for evanescent waves. We also examine the influence of the number of layers N in the unit cell on the NDP of the LMMD medium. In Fig. 4(b), the solid, dashed, and dash-dotted lines represent the EFCs of LMMD medium with the number of layers N of 14, 10, and 6, respectively. Here, $${\\rho }_{m}=0.05+0.05i$$, $$\\delta \\rho =0.025$$, and $$\\eta =1/60$$. As N = 14, the EFC of the LMMD medium is very long and flat. It is found that the efficiency of NDP of the LMMD medium is reduced with decreasing number of layers, as shown in Fig. 4(b).\n\nFinally, full-wave simulations of the finite element method (FEM) are used to simulate wave propagations in the LMMD medium. Figure 5(a) shows the acoustic wave propagation in air. The Gaussian beam propagates from the left side in the air, and the width of the wave beam broadens appreciably over the propagation distance. Figure 5(b),(c), and (d) show the Gaussian beam launched from a distance of 0.73 $${\\lambda }_{0}$$ into the LMMD medium without absorption at the incident angles of $$0^\\circ$$, $$45^\\circ$$, and $$85^\\circ$$, respectively. Here, $${\\rho }_{m}=0.05$$ and δρ = 0. Figure 5(e),(f), and (g) represent the Gaussian beam propagating from air into the LMMD medium with absorption at the incident angles of 0°, 45°, and 85°, respectively. Here, $${\\rho }_{m}=0.05+0.05i$$ and δρ = 0.025. The source is aimed at the centre of the left air-LMMD interface of the structure when the incident angle is 0° and at the bottom corner when the incident angle is 45° or 85°. It can be seen clearly that the Gaussian beam propagates through the LMMD medium without a visible divergence, even when the incident angle is as large as 85°, and the diffractions are fully suppressed both in the lossless and lossy LMMD media. Therefore, all-angle NPD can be realized in the LMMD medium, which is also robust against the medium losses. In addition, we investigate the frequency response of the LMMD medium. Figure 6 shows the full widths at half maximum (FWHMs) of the input Gaussian waves (solid line) and the output waves (scattered circles) through the LMMD medium (thickness of 7.5 $${\\lambda }_{0}$$) as a function of frequency. By contrast, the dashed line represents the FWHMs of Gaussian waves after propagating a two-wavelength distance in air. The Gaussian waves with frequencies from 2 kHz to 3 kHz will be tested. The structural parameters of the layered LMMD medium used are the same as those for 2.5 kHz, which is chosen only for convenience. It is found that the FWHMs of the output waves through the LMMD medium are almost unchanged compared to those of the input waves, whereas the FWHMs of Gaussian waves will reach 40 cm after propagating only a two-wavelength distance in air. Therefore, the NDP in the LMMD medium could be well maintained in a broadband range.\n\nDiscussion\n\nThe proposed LMMD EMT based on the first-principles method can well explain the broad-band all-angle acoustic non-diffraction propagation in the LMMD medium. The effective mass density of the proposed LMMD EMT is the sum of the average mass density and a contribution from the rapidly varying part of the density modulation. The rapid and large modulation of mass density should strongly suppress the transverse component of the velocity field and slow down diffraction of acoustic waves. As the modulation of the mass density becomes large in comparison with the mean value, the acoustic wave evolution will be affected not only by the value of the mass density but also by additional important contributions arising from the rapidly varying periodic density oscillations. Under this condition, the standard EMT is unsuitable for the layered LMMD medium, even within the longwave approximation regime.\n\nThe LMMD medium based on our theory is composed of layered fluid-like metamaterials with different mass densities. Fluid-like metamaterials can dynamically behave (in the homogenization limit) as true fluid materials. Many methods have been proposed to realize fluid-like metamaterials. For example, Torrent and Sánchez-Dehesa26 proposed a design of a fluid-like metamaterial based on the homogenization properties of a solid structure composed of cylindrical scatters. Li et al.31 experimentally used brass fins embedded on a brass substrate to realize a fluid-like metamaterial. A 2D multilayered fluid-fluid structure can be obtained inside a planar wave guide made of aluminium, in which a circular cavity is drilled with an embedded corrugated structure32. Moreover, fluid-like metamaterials with negative mass density can be obtained by using membrane-type metamaterials with simple constructs33, 34. Furthermore, the recent rapid increases in additive manufacturing and nanoscale manufacturing are very beneficial to fabricating complex and small-scale metamaterials25. Therefore, we believe that the multilayered LMMD medium could be realized by fluid-like metamaterials.\n\nIn conclusion, an LMMD medium has been proposed that is capable of realizing the non-diffraction propagation of acoustic waves. An EMT for the LMMD medium was derived from the first-principles method via the transfer-matrix method for both propagating and evanescent waves. It is found that the NDP in the LMMD medium is independent of the incident angle and can be operated in a broad-band manner. The influence of the geometry on the NDP in the LMMD media was investigated in detail. A smaller η and a larger N can ensure longer and flatter EFCs of the LMMD medium, indicating better NDP. This stratified medium may be useful for subwavelength imaging, wave beaming, and acoustic waveguides.\n\nMethods\n\nThe numerical simulations are performed by using the finite element method based on COMSOL Multiphysics software. The background medium is air, which has mass density and speed of sound of 1.25 kg/m3 and 343 m/s, respectively. The frequency of the incident acoustic waves is 2.5 kHz in the finite element calculations. An LMMD medium slab with $$L=450\\eta {\\lambda }_{0}$$ is investigated, and the parameters are N = 10 and $$\\eta =1/60$$. The unit cell with a thickness of $$\\Lambda =\\eta {\\lambda }_{0}$$ consists of N homogeneous layers. The mass density of the jth layer in the unit cell ($$j=1,\\ldots ,10$$) along the z direction is given according to Eq. (10). The Gaussian beam with a FWHM of 9.6 cm propagates from the air into the LMMD medium. The average of the relative mass density ρ r is $${\\rho }_{m}$$, where $${\\rho }_{m}=0.05$$ and $$\\delta \\rho =0$$ for the lossless case and $${\\rho }_{m}=0.05+0.05i$$ and $$\\delta \\rho =0.025$$ for the lossy case in the numerical simulations. Periodic boundary conditions are imposed in the x direction, and radiation boundary conditions are set for the remaining boundaries. The largest mesh element size is lower than one tenth of the incident wavelength, and the further refined meshes are applied in the domain of the unit cells of the microstructure.\n\nReferences\n\n1. 1.\n\nPérez-Arjona, I. et al. Theoretical prediction of the nondiffractive propagation of sonic waves through periodic acoustic media. Phys. Rev. B 75, 014304 (2007).\n\n2. 2.\n\nEspinosa, V. et al. Subdiffractive propagation of ultrasound in sonic crystals. Phys. Rev. B 76, 140302(R) (2007).\n\n3. 3.\n\nSánchez-Morcillo, V. J. et al. Propagation of sound beams behind sonic crystals. Phys. Rev. B 80, 134303 (2009).\n\n4. 4.\n\nLi, J. et al. Acoustic beam splitting in two-dimensional phononic crystals using self-collimation effect. J. Appl. Phys. 118, 144903 (2015).\n\n5. 5.\n\nCicek, A., Kaya, O. A. & Ulug, B. Acoustic waveguiding by pliable conduits with axial cross sections as linear waveguides in two-dimensional sonic crystals. J. Acoust. Soc. Am. 134, 3613 (2013).\n\n6. 6.\n\nLi, B., Deng, K. & Zhao, H. P. Acoustic guiding and subwavelength imaging with sharp bending by sonic crystal. Appl. Phys. Lett. 99, 051908 (2011).\n\n7. 7.\n\nChen, L. S., Kuo, C. H. & Ye, Z. Acoustic imaging and collimating by slabs of sonic crystals made from arrays of rigid cylinders in air. Appl. Phys. Lett. 85, 1072 (2004).\n\n8. 8.\n\nHe, Z. J. et al. Subwavelength imaging of acoustic waves by a canalization mechanism in a two dimensional phononic crystal. Appl. Phys. Lett. 93, 233503 (2008).\n\n9. 9.\n\nJia, H. et al. Subwavelength imaging by a simple planar acoustic superlens. Appl. Phys. Lett. 97, 173507 (2010).\n\n10. 10.\n\nShi, J. J., Lin, S. C. S. & Huang, T. S. Wide-band acoustic collimating by phononic crystal composites. Appl. Phys. Lett. 92, 111901 (2008).\n\n11. 11.\n\nWu, L. Y., Chen, L. W. & Wu, M. L. The nondiffractive wave propagation in the sonic crystal consisting of rectangular rods with a slit. J. Phys.: Condens. Matter 20, 295229 (2008).\n\n12. 12.\n\nSoliveres, E. et al. Simultaneous self-collimation of fundamental and second-harmonic in sonic crystals. Appl. Phys. Lett. 99, 151905 (2011).\n\n13. 13.\n\nCicek, A., Kaya, O. A. & Ulug, B. Wide-band all-angle acoustic self-collimation by rectangular sonic crystals with elliptical bases. J. Phys. D: Appl. Phys. 44, 205104 (2011).\n\n14. 14.\n\nTsai, C. N. & Chen, L. W. The manipulation of self-collimated beam in phononic crystals composed of orientated rectangular inclusions. Appl. Phys. A 122, 659 (2016).\n\n15. 15.\n\nYu, X. & Fan, S. Bends and splitters for self-collimated beams in photonic crystals. Appl. Phys. Lett. 83, 3251 (2003).\n\n16. 16.\n\nIliew, R. et al. Diffractionless propagation of light in a low-index photonic-crystal film. Appl. Phys. Lett. 85, 5854 (2004).\n\n17. 17.\n\nLiang, W. Y. et al. Super-broadband non-diffraction guiding modes in photonic crystals with elliptical rods. J. Phys. D: Appl. Phys. 43, 075103 (2010).\n\n18. 18.\n\nXu, Y. et al. The all-angle self-collimating phenomenon in photonic crystals with rectangular symmetry. J. Opt. A: Pure Appl. Opt. 10, 085201 (2008).\n\n19. 19.\n\nWu, Z. H. et al. All-angle self-collimation in two-dimensional rhombic-lattice photonic crystals. J. Opt. 14, 015002 (2012).\n\n20. 20.\n\nNoori, M., Soroosh, M. & Baghban, H. All-angle self-collimation in two-dimensional square array photonic crystals based on index contrast tailoring. Optical Engineering 54(3), 037111 (2015).\n\n21. 21.\n\nChuang, Y. C. & Suleski, T. J. Complex rhombus lattice photonic crystals for broadband all-angle self-collimation. J. Opt. 12, 035102 (2010).\n\n22. 22.\n\nRizza, C. & Ciattoni, A. Effective medium theory for Kapitza stratified media: diffractionless propagation. Phys. Rev. Lett. 110, 143901 (2013).\n\n23. 23.\n\nRizza, C. & Ciattoni, A. Kapitza homogenization of deep gratings for designing dielectric metamaterials. Opt. Lett. 38(18), 3658–3660 (2013).\n\n24. 24.\n\nKapitza, P. Dynamic stability of the pendulum with vibrating suspension point. J. Exp. Theor. Phys. 21, 588 (1951).\n\n25. 25.\n\nCummer, S. A., Christensen, J. & Alù, A. Controlling sound with acoustic metamaterials. Nat. Rev. Mater. 1, 16001 (2016).\n\n26. 26.\n\nTorrent, D. & Sánchez-Dehesa, J. Anisotropic mass density by two-dimensional acoustic metamaterials. New J. Phys. 10, 023004 (2008).\n\n27. 27.\n\nSanders, J. A. & Verhulst, F. Averaging methods in nonlinear dynamical systems (Springer-Verlag, Berlin, 1985).\n\n28. 28.\n\nFelbacq, D. et al. Two-scale approach to the homogenization of membrane photonic crystals. J. Nanophoton. 2, 023501 (2008).\n\n29. 29.\n\nSchoenberg, M. & Sen, P. N. Properties of a periodically stratified acoustic half-space and its relation to a Biot fluid. J. Acoust. Soc. Am. 73, 61 (1983).\n\n30. 30.\n\nLi, X., He, S. & Jin, Y. Subwavelength focusing with a multilayered Fabry-Perot structure at optical frequencies. Phys. Rev. B 75, 045103 (2007).\n\n31. 31.\n\nLi, J. et al. Experimental demonstration of an acoustic magnifying hyperlens. Nature Mater. 8, 931 (2009).\n\n32. 32.\n\nTorrent, D. & Sánchez-Dehesa, J. Anisotropic mass density by radially periodic fluid structures. Phys. Rev. Lett. 105, 174301 (2010).\n\n33. 33.\n\nYang, Z. et al. Membrane-Type Acoustic Metamaterial with Negative Dynamic Mass. Phys. Rev. Lett. 101, 204301 (2008).\n\n34. 34.\n\nPark, C. M. et al. Amplification of Acoustic Evanescent Waves Using Metamaterial Slabs. Phys. Rev. Lett. 107, 194301 (2011).\n\nAcknowledgements\n\nThis work was supported by the National Basic Research Program of China (2017YFA0303700), the National Natural Science Foundation of China under Grant Nos 11574148, 11674175, and 11674172, the Major Project of Nature Science Research for Colleges and Universities in Jiangsu Province under Grant No. 15KJA140002, the Postdoctoral Science Foundation funded project of China under Grant No. 2016M601765, the Jiangsu Planned Projects for Postdoctoral Research Funds under Grant No. 1601190B, and the Fundamental Research Funds for the Central Universities (020414380001).\n\nAuthor information\n\nX.Z., Q.W., and Y.C. performed the analytical and numerical simulations. X.Z. and D.W. conceived the idea and wrote the manuscript. D.W. and X.L. conceived and supervised the manuscript. All authors contributed to the discussions.\n\nCorrespondence to Da-Jian Wu or Xiao-Jun Liu.\n\nEthics declarations\n\nCompeting Interests\n\nThe authors declare that they have no competing interests.\n\nPublisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.\n\nRights and permissions\n\nReprints and Permissions"
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https://www.arxiv-vanity.com/papers/1908.07408/
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"# Mixed-Timescale Beamforming and Power Splitting for Massive MIMO Aided SWIPT IoT Network\n\nXihan Chen, Hei Victor Cheng, An Liu, Kaiming Shen, and Min-Jian Zhao This work was supported by the Science and Technology Program of Shenzhen, China, under Grant JCYJ20170818113908577, and the National Natural Science Foundation of China under Project No. 61571383. The work of An Liu was supported by the China Recruitment Program of Global Young Experts. Xihan Chen, An Liu and Min-Jian Zhao are with the College of Information Science and Electronic Engineering, Zhejiang University, Hangzhou 310027, China (e-mail: , , ). Hei Victor Cheng, and Kaiming Shen are with the Electrical and Computer Engineering Department, University of Toronto, Toronto, ON M5S 3G4, Canada (e-mail: , ).\n###### Abstract\n\nTraditional simultaneous wireless information and power transfer (SWIPT) with power splitting assumes perfect channel state information (CSI), which is difficult to obtain especially in the massive multiple-input-multiple-output (MIMO) regime. In this letter, we consider a mixed-timescale joint beamforming and power splitting (MJBP) scheme to maximize general utility functions under a power constraint in the downlink of a massive MIMO SWIPT IoT network. In this scheme, the transmit digital beamformer is adapted to the imperfect CSI, while the receive power splitters are adapted to the long-term channel statistics only due to the consideration of hardware limit and signaling overhead. The formulated optimization problem is solved using a mixed-timescale online stochastic successive convex approximation (MO-SSCA) algorithm. Simulation results reveal significant gain over the baselines.\n\nSWIPT, massive MIMO, mixed-timescale joint beamforming and power splitting, online stochastic successive convex approximation.\n\n## I Introduction\n\nThe Internet of Things (IoT) is a revolutionary communication paradigm to provide massive connectivity for the next-generation wireless cellular networks. The limited battery life of devices poses a significant challenge for designing green and sustainable IoT. One promising solution is to leverage the simultaneous wireless information and power transfer (SWIPT) with radio frequency to prolong the IoT network, due to its ability to provide cost-effective and perpetual power source . This requires receiver circuits to decode information and harvest energy from the same received signal independently and simultaneously, which renders SWIPT impractical.\n\nTo overcome these limitations, the telecommunication industry is increasingly turning towards power splitting (PS), a receiver architecture that divides the received signal into two streams of different power for decoding information and harvesting energy. Based on the PS architecture, considers a multiuser joint beamforming and power splitting design problem under QoS constraints and proposes a semidefinite relaxation-based algorithm. To further reduce the computational complexity, an second-order cone programming relaxation method is proposed in . Recently, combines the SWIPT and massive multiple-input-multiple-output (MIMO) to further improve the spectral and energy efficiency of IoT networks. The aforementioned works focus on optimizing the weighted sum of objective function under perfect CSI, which is difficult to obtain in the massive MIMO regime due to the large number of antennas and the limited pilot sequences . In such scenarios, it is more reasonable to consider a mixed-timescale optimization of the long-term performance of the network, which only requires imperfect CSI plus the knowledge of channel statistics . To the best of our knowledge, this is first work on mixed-timescale optimization for massive MIMO aided SWIPT IoT network.\n\nContribution of this letter includes the algorithm design for mixed-timescale joint beamforming and power splitting (MJBP) scheme for the downlink transmission of massive MIMO aided SWIPT IoT network, to maximize a general network utility. Specifically, the digital beamformer is adapted to the imperfect CSI, while the power spiltters are adapted to the long-term channel statistics due to the consideration of hardware limit and signaling overhead. We propose a mixed-timescale online stochastic successive convex approximation (MO-SSCA) algorithm to solve this joint optimization problem. Simulations verify the advantages of the proposed MJBP scheme over the baselines.\n\n## Ii System Model and Problem Formulation\n\nConsider the downlink of a massive MIMO aided SWIPT IoT network, where the base station (BS) is equipped with antennas to simultaneously serve single-antenna IoT devices. As illustrated in Fig. 1, the BS employs digital beamformer to spatially multiplex devices and manage the multi-device interference, while device applies the power splitter () to coordinate information decoding and energy harvesting from the received signal. With MJBP, both the digital beamformer and the power splitters are optimized at the BS. Furthermore, the digital beamformer is adapted to instantaneous CSI. For the power splitter implemented at each device, it is adapted to long-term channel statistics due to following reasons: 1) the hardware capability of the IoT device is limited, and thus the power splitter cannot be changed frequently due to hardware limitations ; 2) such design can reduce the signaling overhead of sending to the corresponding device, especially when the number of devices is large.\n\nWe consider flat fading channels with block fading model, but the proposed algorithm can be easily modified to cover the frequency selective channels. The channel is assumed to be constant within each block of length . In this case, the received signal splitted to the information decoder (ID) of device is given by where is the data symbol for device , is the additive noise (AN) at the PS of device , and is the AN introduced by the ID at device . Meanwhile, the received signal splitted to the energy harvester (EH) is given by\n\nAn achievable ergodic rate at device is given by\n\n ^r∘k(ρk,F) =EH[log2(1+Γk(ρk,F,H))] −1TK∑m=1log2(1+Tρkσ2k+δkVar(hHkfm), (1)\n\nwhere is the SINR of device with\n\n Γk(ρk,F,H)=ρk|hHkfk|2ρk(∑Km≠k|hHkfm|2+σ2k)+δ2k.\n\nIn practice, perfect CSI is challenging to obtain due to device mobility, processing latency and other limitations. Thus, we model the channel imperfection as where is the estimated channel from from BS to device , is the channel error independent of , and is the variance of the channel error. Consequently, the achievable rate is obtained by replacing in (1) with . For convenience, we let , and . Further, we define as the collection of short-term optimization variables for all possible estimated channel states , where is the feasible set of .\n\nProposition 1 : The ergodic rate at device is bounded as , and\n\n ¯¯¯rk(ρk,Θ)−1TK∑m=1log2(1+TPmaxδ2kE^H,ϕk[||^hk+ϕk||2]).\n\nHere the lower bound follows from the properties of variance and the Cauchy–Schwarz inequality. From Proposition 1, optimizing the lower and upper bound provide the same optimal solution. Moreover, as verified in Fig. 2, we find that both bounds are tight. Therefore, we optimize the lower (upper) bound of the ergodic rate at each device as it is more tractable for optimization.",
null,
"Fig. 2: Cumulative distribution function (CDF) of the lower and upper bound of ergodic rate at each device. The detailed setup is given in Section IV.\n\nThe average harvested power conditioned on imperfect CSI of device follows a non-linear function and can be expressed as where\n\n ^e∘k(ρk,F|^hk,ϕk)=(Ψk−SkΩk)/(1−Ωk),\n\nwhere is a constant denoting the maximum harvested power at the th device, , , and parameter and are constants related to the circuit specifications, and is the input RF power for the th device. Then, the average harvested power of user is defined as .\n\nWe are interested in a mixed-timescale joint optimization of digital beamformer and power splitter to balance the average ergodic rate and the average harvested power. This can be formulated as the following network utility maximization problem:\n\n P:maxρ∈Φ,ΘK∑k=1g(¯¯¯ηk(ρk,Θ)), (2)\n\nwhere with the corresponding weight is a weighted sum of the average ergodic rate and the harvested power, is the feasible set of power splitters. The utility function is a continuously differentiable and concave function of . Moreover, is non-decreasing w.r.t. and its derivative is Lipschitz continuous.\n\n## Iii Online Optimization Algorithm\n\nIn this section, we propose a MO-SSCA algorithm to solve the mixed-timescale stochastic non-convex optimization problem , and summarize it in Algorithm 1. In MO-SSCA, we focus on a coherence time of channel statistics, where the time is divided into frames and each frame consists of time slots. At beginning, the BS initializes the MO-SSCA algorithm with power splitter and a weight vector . In subsequent, and are updated once at the end of each frame. Then we elaborate the implementation details of the iteration of the MO-SSCA algorithm at the -th frame.\n\n### Iii-a Short-term FP-BCD Algorithm\n\nAt time slot within the -th frame, BS obtains the estimated channel by uplink channel training. Based upon the current , , and , we can obtain digital beamforming by maximizing the a weighted sum of the average data rate and the average harvested power conditioned on imperfect CSI, which can be formulated as\n\n P2(ρ,v,^H):maxF∈ΛK∑k=1vk¯¯¯η∘k(ρk,F|^hk),\n\nwhere with and , and is solved at time slot .\n\nSince the objective function contains expectation operators, it does not have a closed-form expression. To address the challenge, we resort to the Sample Average Approximation (SAA) method . Specifically, a total of samples are generated for independently drawn from the distribution , and the -th sample of is defined as In this case, the SAA version of is formulated as where .\n\nHowever, solving problem is still challenging due to the nonlinear fractional term in and coupling in the power constraint. To this end, we apply the Lagrangian dual transform method to recast problem into a more tractable yet equivalent form, using the following lemma.\n\n###### Lemma 1.\n\nThe optimal digital beamforming solves the problem in (1) if and only if it solves\n\n maxF∈Λ1NN∑n=1K∑k=1f(F,qnk,ϕnk) (3)\n\nwhere with , and is the optimal auxiliary variable introduced for each ratio term.\n\nIn subsequent, we use the complex quadratic transformation to equivalently recast problem (3) as\n\n maxF∈Λ,w,q1NN∑n=1K∑k=1^rk(F,qnk,ϕnk,wnk)+^e∘k(F,qnk,ϕnk,wnk) (4)\n\nwhere\n\n ^rk(F,qnk,ϕnk,wnk)≜√vkρk(1+qnk)Re{fHk~hk,n(wnk)H} +(wnk)Hwnk(ρk(Γnk+σ2k)+δ2k)−qnk+log2(1+qnk).\n\nwith , and with is the auxiliary variable vector. Observing that the constraints are separable with respect to the three blocks of variables, i.e., , and , we shall focus on designing a fractional programming block coordinate descent (FP-BCD) algorithm to find a stationary point of problem (4), and summarize it in Algorithm 2. For problem (4), this amounts to the following steps:\n\n#### Iii-A1 Optimization of q\n\nThe optimal is given by\n\n (qnk)∗=ρk|~hHk,nfk|2ρk(Γnk−|~hHk,nfk|2+σ2k)+δ2k. (5)\n\n#### Iii-A2 Optimization of w\n\nBy applying the first-order optimal condition, the optimal admits a closed-form solution as:\n\n (wnk)∗=(ρk(Γnk+σ2k)+δ2k)−1√ρkvk(1+qnk)~hHk,nfk. (6)\n\n#### Iii-A3 Optimization of F\n\nThe subproblem w.r.t. is nonconvex due to the involvement of the non-linear energy harvesting model. To overcome this difficulty, we first transform it into a more tractable yet equivalent form by the introduction of new auxiliary variables and some manipulations, which can be expressed as\n\n P4:maxF∈Λ,αnk≥01NN∑n=1K∑k=1^rk(F,qnk,ϕnk,wnk)+ςnk (7) s.t.ln(1/(αnk+Ωnk)−1)+dkK∑m=1|(^hk+ϕnk)Hfm|2+ck≥0,\n\nwhere , and . Note that the constraint in problem is nonconvex. Thus, we apply the the majorization minimization (MM) method to approximate this nonconvex constraint using its first-order Taylor expansion as\n\n maxF∈Λ,αnk≥01NN∑n=1K∑k=1^rk(F,qnk,ϕnk,wnk)+ςnk (8) s.t.dkK∑m=1(^hk+ϕnk)H(~fm~fHm+~fm¯¯¯fHm+¯¯¯fm~fHm)(^hk+ϕnk) +ln(1/(~ςnk+Ωnk)−1)+ςnk−~ςnk(~ςnk+Ωnk−1)(~ςnk+Ωnk)+ck≥0,\n\nwhere and represents the last iteration of and , and . Note that problem (8) is convex, which can be efficiently solved by the CVX toolbox .\n\n### Iii-B Long-term Optimization\n\nBefore the end of -th frame, device obtains a full channel sample and channel error sample . Based on , and , we preserve the partial concavity of the original function and add the proximal regularization, to construct the concave surrogate function , resulting in the following\n\n ¯¯¯gt(ρk)=g(~ηtk)+(utk)T(ρk−ρtk)−τ|ρk−ρtk|2, (9)\n\nwhere is a postive constant; the recursive approximation of the weighted sum of the data rate and the harvested power is given by\n\n ~ηtk=(1−αt)~ηt−1k+αtNN∑n=1∑i∈Tt^η∘k(ρtk,Ft(i)|^hik,ϕnk(i))|Tt|,\n\nwith , and is a step-sizes sequence to be properly chosen; the recursive approximation of the partial derivative is given by\n\n utk=(1−αt)ut−1k+αtJρk(ρtk,Ft(i)|^htk,ϕtk)∇¯¯ηkg(~ηtk),\n\nwith , is the gradient of w.r.t. at and . Moreover, the weight vector is updated as\n\n vt+1k=(1−βt)vtk+βt¯vtk, (10)\n\nwith , where is a step-sizes sequence satisfying , . Moreover, the optimal power splitting ratio for device can be obtained by solving the following quadratic optimization problem, i.e.,\n\n maxρk∈Φ ¯gt(ρk). (11)\n\nBy applying the first-order optimality condition, it yields the closed-form solution where denotes the projection onto the feasible region . Consequently, the long-term variable is updated as\n\n ρt+1k=(1−βt)ρtk+βt¯ρtk. (12)\n\nRemark 1 : Note that the stationary weight vector has captured the nature of the utility function. However, it is difficult to obtain , since it in turn depends on the stationary solution . Therefore, the basic idea of the proposed algorithm is to iteratively update the long-term variable and the weight vector such that and converge to a stationary solution and the corresponding stationary weight vector , respectively.\n\n### Iii-C Convergence Analysis\n\nThe following theorem states that Algorithm 2 converges to a stationary point of up to certain convergence error which vanishes to zero exponentially as .\n\n###### Theorem 2 (Convergence of Algorithm 2).\n\nSuppose problem has a discrete set of stationary points, denoted by . Let denote the limiting point of the sequence generated by Algorithm 2 with input parameter and sample number . Then for every small positive number , there exist positive constants and , independent of , such that\n\n Pr⎧⎪⎨⎪⎩minF∈F∗(ρ,v,^H)∥FN(ρ,v,^H)−F(ρ,v,^H)∥≥ϵ⎫⎪⎬⎪⎭≤p(ϵ,N),\n\nfor sufficiently large, where .\n\n###### Proof:\n\nSpecifically, the proposed FP-BCD algorithm falls in the MM framework and similar proof is provided in . From Theorem 4.4 in , every limiting point of sequence generated by the short-term FP-BCD algorithm is a stationary point of problem , where problem is the sample average approximation of problem with samples. As stated in , problem is equivalent to problem w.p.1 when approaches to infinity, due to the classical law of large number for random functions. That is to say, as , any stationary point of is also a stationary point of problem w.r.1. When is finite, Algorithm 2 converges to approximate stationary points of problem with the exponential convergence rate . This is consequence of , Theorem 3.1, which provides a general convergence result for the original problem that satisfies the following assumptions: (a) The feasible set of optimization variables is a nonempty closed convex set; (b) The objective function of the original problem is continuously differentiable on the feasible set for any given random system states, and its gradient is Lipchitz continuous. Clearly, problem satisfies the aforementioned assumption (a) and (b). This completes the proof. ∎\n\nBased on Theorem 2, the convergence of the proposed MO-SSCA algorithm is summarized in the following theorem.\n\n###### Theorem 3 (Convergence of the Algorithm 1).\n\nGiven problem (2), suppose that in (9) and the step-sizes and are chosen so that\n\n1. , for some ,\n\n2. , , ,\n\n3. .\n\nLet denote the sequence of iterates generated by Algorithm 1, where . Then every limit point of almost surely satisfies\n\n v∗=∇¯¯ηg(¯¯¯η∗), (13)\n (ρ−ρ∗)T∇Tρg(¯¯¯η(ρ∗,ΘN(v∗,ρ∗)))≤0,∀ρ∈Φ, (14)\n\nwhere , and Moreover, it satisfies\n\n (F−FN(i))TJF(ρ∗,FN(i)|^H(i))∇¯¯¯ηg(¯¯¯η∗)≤e(N), (15)\n\nwhere is the Jacobian matrix of the vector w.r.t. at and , and satisfies almost surely.\n\n###### Proof:\n\nBased on Theorem 2, Theorem 3 can be proven by a similar approach in . Thus, we omit the details due to the limited space. ∎\n\nAccording to equation (15) in Theorem 3, it implies that the short-term solution found by Algorithm 2 must satisfy the stationary condition approximately with certain error that converges to zero exponentially as . Moreover, the limiting point generated by Algorithm 1 also satisfies the stationary conditions in (13) and (14), respectively. Thus, Algorithm 1 converges to stationary solutions of the mixed-timescale optimization problem . Note that since converges to zero exponentially, Algorithm 2 with a small can already achieve a good performance and avoids excessive computational complexity.\n\n## Iv Simulation Results and Discussions\n\nWe consider a single-cell of radius m, where BS is equipped with antennas. There are 12 devices randomly distributed in the cell. We adopt a geometric channel model with a half-wavelength space ULA for simulations . The channel between BS and device is given by , where is the array response vector, ’s are Laplacian distributed with an angular spread , , are randomly generated from an exponential distribution and normalized such that , is the average channel gain determined by the pathloss model , and is the distance between BS and device in meters. We consider channel paths for each device. The transmit power budget for BS is dBm. We set , mW, , , , dB, dBm and dBm. There are time slots in each frame and the slot size is 2 ms. The coherence interval , which corresponds to a coherence time of 2 ms and a coherence bandwidth of 200 kHz . The coherence time for the channel statistics is assumed to be 10 s. We use the average sum utility as an example to illustrate the advantages of the proposed scheme. Two schemes are included as baselines: 1) maximum ratio transmission (MRT) scheme, which is obtained by fixing the MRT beamformer ; 2) zero-forcing (ZF) scheme, which is obtained by fixing the ZF beamformer . The power splitters of both MRT and ZF scheme are obtained by the long-term optimization.",
null,
"Fig. 3: (a) Utility performance versus SNR. (b) Tradeoff comparison for different schemes (M=64,K=12, and SNR=10 dB).\n\nIn Fig 3, we plot the utility performance versus the signal-to-noise ratio (SNR). We can see that as the SNR increases, the average sum utility of all schemes increases gradually. It is observed that the average sum utility achieved by the proposed MJBP scheme is higher than that achieved by the other schemes for moderate and large SNR. This indicates that the proposed MJBP scheme can better mitigate the multi-device interference to achieve better tradeoff between the average ergodic rate and the average harvested power, which is further validated in Fig 3.",
null,
"Fig. 4: (a) Utility performance versus the number of devices K. (b) Utility performance versus the number of antennas M.\n\nIn Fig 4, we plot the utility performance versus the number of devices . We observe that the proposed MJBP scheme achieves significant gain over MRT scheme and ZF scheme, which demonstrates the importance of mixed-timescale joint optimization. Moreover, as the number of devices increases, the performance gap between the proposed MJBP scheme and other competing schemes becomes larger.\n\nIn Fig 4, we plot the utility performance versus the number of antennas at BS. It shows that the performance of all these schemes is monotonically increasing with the number of antennas. Again, it is seen that the proposed MJBP scheme outperforms all the other schemes for all regime.\n\n## V Conclusion\n\nIn this letter, we considered mixed-timescale joint beamforming and power splitting (MJBP) scheme in the downlink transmission of massive MIMO aided SWIPT IoT network to maximize the network utility under the power budget constraint. We proposed a MO-SSCA algorithm to find stationary solutions of the mixed-timescale non-convex stochastic optimization problem. Simulations verify that the proposed MJBP scheme achieves significant gain over existing schemes.\n\n## References\n\n• M. Swan, “Sensor mania! the Internet of things, wearable computing, objective metrics, and the quantified self 2.0,” J. Sens. Actuator Netw, vol. 1, no. 3, pp. 217–253, 2012.\n• R. Zhang and C. K. HO, “MIMO broadcasting for simultaneous wireless information and power transfer,” IEEE Trans. Wireless Commun., vol. 12, no. 5, pp. 1989–2001, May 2013.\n• Q. Shi, L. Liu, W. Xu, and R. Zhang, “Joint transmit beamforming and receive power splitting for MISO SWIPT systems,” IEEE Trans. Wireless Commun., vol. 13, no. 6, pp. 3269–3280, Apr 2014.\n• Q. Shi, W. Xu, T. Chang, Y. Wang, and E. Song, “Joint beamforming and power splitting for MISO interference channel with SWIPT: An SOCP relaxation and decentralized algorithm,” IEEE Trans. Signal Process., vol. 62, no. 23, pp. 6194–6208, Dec 2014.\n• G. Dong, H. Zhang, and D. Yuan, “Optimal downlink transmission in Massive MIMO enabled SWIPT systems with zero-forcing precoding,” IEEE Global Commun. Conf., Dec 2014.\n• G. Caire, “On the ergodic rate lower bounds with applications to masssive MIMO,” IEEE Trans. Wireless Commun., vol. 17, no. 5, pp. 3258–3268, May 2018.\n• A. Liu, X. Chen, W. Yu, V. Lau, and M. Zhao, “Two-timescale hybrid compression and forward for massive MIMO aided C-RAN,” IEEE Trans. Signal Process., vol. 67, no. 9, pp. 2484–2498, Mar 2019.\n• E. Boshkovska, D. Ng, N. Zlatanov, and R. Schober, “Practical non-linear energy harvesting model and resource allocation for SWIPT systems,” IEEE Commun. Lett., vol. 19, no. 12, pp. 2082–2085, Dec. 2015.\n• A. Shapiro, D. Dentcheva, and A. Ruszczynski, Lecture on stochastic programming: modeling and theory. SIAM, 2009.\n• K. Shen and W. Yu, “Fractional programming for communication systems – Part II: Uplink scheduling via matching,” IEEE Trans. Signal Process., vol. 66, no. 10, pp. 2631–2644, Mar 2018.\n• M. W. Jacobson and J. A. Fessler, “An expanded theoretical treatment of iteration-dependent majorize-minimize algorithms,” IEEE Transactions on Image Processing, vol. 16, no. 10, pp. 2411–2422, Oct 2007.\n• “CVX Research, Inc. CVX: Matlab software for disciplined convex programming, version 2.0 beta.” Sep, 2012. [Online]. Available: http://cvxr.com/cvx.\n• K. Shen, W. Yu, L. Zhao, and D. P. Palomar, “Optimal of MIMO device-to-device networks via matrix fractional programming: A minorization-maximization approach,” arXiv.org:1808.05678, 2019.\n• H. Sun and H. Xu, “A note on uniform exponential convergence of sample average approximation of random functions,” J. Math. Anal. Appl, pp. 698–708, 2012.\n• Technical Specification Group Radio Access Network; Further Advancements for E-UTRA Physical Layer Aspects, 3GPP TR 36.814. [Online]. Available: http://www.3gpp.org\n• T. Marzetta, E. G. Larsson, H. Yang, and H. Ngo, Fundamentals of Massive MIMO. Cambridge, U.K.: Cambridge University Press, 2016."
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"https://media.arxiv-vanity.com/render-output/4953088/x2.png",
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"https://media.arxiv-vanity.com/render-output/4953088/x3.png",
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http://josephgedwards.info/multiplication-word-problems-worksheets/grade-2-word-problems-worksheets-multiplication-and-division-word-problems-worksheets-for-2nd-grade/
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[
"# Grade 2 Word Problems Worksheets Multiplication And Division Word Problems Worksheets For 2nd Grade",
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"grade 2 word problems worksheets multiplication and division word problems worksheets for 2nd grade.\n\ngrade 4 algebra worksheets word problems examples of multiplication multiplying decimals pdf decimal worksheet 5,multiplication word problems worksheets for grade 2 pdf mystery pictures coloring task cards 6,multiplication word problems worksheets year 2 for grade pdf 5,multiplying decimal word problems worksheet grade 5 multiplication worksheets 4 multi step 4th,grade 2 word problems worksheets multiplication and division 5 pdf 3rd for 2nd,multi step multiplication word problems 4th grade worksheets and division 6 5 pdf 2 problem solving 4,multiplication and division word problems worksheets for grade 2 6 multiplying decimals pdf third all math,multiplication word problems worksheets grade 5 pdf math 4 and division 3rd,multiplication and division word problems worksheets 3rd grade pdf simple addition subtraction multiplying fractions,multiplication and division word problems worksheets grade 6 math for 3 learning 2 problem 2nd."
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https://annahutch.github.io/PhD/17Apr.html
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[
"## Corrected Coverage Matching Estimate\n\n• This alternative corrected coverage estimate uses only those simulated credible sets where the number of variants matches that of the original credible set to be corrected.\n\n• I am running simulations to implement this method on credible sets with $$nvar < 4$$ (to ensure we are not conditioning on a particularly implausible event - e.g. exactly 120 variants in the set).\n\n• Our standard corrected coverage estimate uses 1000 simulations for each SNP considered causal. Since the matching estimate cuts out SNPs (and we don’t want our estimate to be based only on a handful of samples) I increase the number of simulations for each SNP considered causal to 10K (although this leads to some considered causal SNPs with 10K simulations and some with a handful).\n\n• To get our final corrected coverage estimate, we need to deal with unbalanced samples. To do this, we take a single average by stacking the ‘covered’ binary indicator for each credible set (where the nvar matches what we want). We then make a pp.vect vector of the corresponding posterior probabilities. The length of both of these vectors is sum(nsims). This means that those simulations which have more data (because they have the correct nvar) will be up weighted.\n\n• The simulations are in /APRIL/trim_sims/",
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"It seems that this matching method is not very accurate. Perhaps we could limit its use to high power scenarios (large $$\\mu$$, e.g. for PTPN22 $$\\mu=20$$)."
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[
null,
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",
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.9112871,"math_prob":0.9882329,"size":1420,"snap":"2020-45-2020-50","text_gpt3_token_len":302,"char_repetition_ratio":0.12076271,"word_repetition_ratio":0.008733625,"special_character_ratio":0.21478873,"punctuation_ratio":0.07392996,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9672961,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-11-29T04:45:52Z\",\"WARC-Record-ID\":\"<urn:uuid:42123aa3-0cb7-4001-9b1c-3fed1f0d9c2c>\",\"Content-Length\":\"1049339\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:c85539c0-6309-4d64-a2c2-32f19f1be131>\",\"WARC-Concurrent-To\":\"<urn:uuid:39ff42cf-f560-45d3-9183-58e5a49acb68>\",\"WARC-IP-Address\":\"185.199.110.153\",\"WARC-Target-URI\":\"https://annahutch.github.io/PhD/17Apr.html\",\"WARC-Payload-Digest\":\"sha1:6T25X2CH5PYC7M6SUJVYXAB4XAGI3MOX\",\"WARC-Block-Digest\":\"sha1:6GXY37U5WFUC2JNZIS5VJEXM7AMK3WLO\",\"WARC-Truncated\":\"length\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-50/CC-MAIN-2020-50_segments_1606141196324.38_warc_CC-MAIN-20201129034021-20201129064021-00047.warc.gz\"}"}
|
https://www.litscape.com/word_analysis/primost
|
[
"# primost in Scrabble®\n\nThe word primost is playable in Scrabble®, no blanks required.\n\nPRIMOST\n(94 = 44 + 50)\nTOPRIMS\n(94 = 44 + 50)\nIMPORTS\n(94 = 44 + 50)\n\n## Seven Letter Word Alert: (3 words)\n\nimports, primost, toprims\n\nPRIMOST\n(94 = 44 + 50)\nPRIMOST\n(92 = 42 + 50)\nPRIMOST\n(92 = 42 + 50)\nPRIMOST\n(92 = 42 + 50)\nPRIMOST\n(86 = 36 + 50)\nPRIMOST\n(86 = 36 + 50)\nPRIMOST\n(86 = 36 + 50)\nPRIMOST\n(86 = 36 + 50)\nPRIMOST\n(86 = 36 + 50)\nPRIMOST\n(83 = 33 + 50)\nPRIMOST\n(80 = 30 + 50)\nPRIMOST\n(78 = 28 + 50)\nPRIMOST\n(78 = 28 + 50)\nPRIMOST\n(76 = 26 + 50)\nPRIMOST\n(76 = 26 + 50)\nPRIMOST\n(76 = 26 + 50)\nPRIMOST\n(76 = 26 + 50)\nPRIMOST\n(76 = 26 + 50)\nPRIMOST\n(74 = 24 + 50)\nPRIMOST\n(74 = 24 + 50)\nPRIMOST\n(74 = 24 + 50)\nPRIMOST\n(74 = 24 + 50)\nPRIMOST\n(74 = 24 + 50)\nPRIMOST\n(74 = 24 + 50)\nPRIMOST\n(72 = 22 + 50)\nPRIMOST\n(72 = 22 + 50)\nPRIMOST\n(72 = 22 + 50)\nPRIMOST\n(72 = 22 + 50)\nPRIMOST\n(72 = 22 + 50)\nPRIMOST\n(69 = 19 + 50)\nPRIMOST\n(67 = 17 + 50)\nPRIMOST\n(66 = 16 + 50)\nPRIMOST\n(66 = 16 + 50)\nPRIMOST\n(65 = 15 + 50)\nPRIMOST\n(65 = 15 + 50)\nPRIMOST\n(65 = 15 + 50)\nPRIMOST\n(65 = 15 + 50)\nPRIMOST\n(65 = 15 + 50)\nPRIMOST\n(64 = 14 + 50)\nPRIMOST\n(63 = 13 + 50)\nPRIMOST\n(63 = 13 + 50)\nPRIMOST\n(63 = 13 + 50)\n\nPRIMOST\n(94 = 44 + 50)\nTOPRIMS\n(94 = 44 + 50)\nIMPORTS\n(94 = 44 + 50)\nPRIMOST\n(92 = 42 + 50)\nIMPORTS\n(92 = 42 + 50)\nIMPORTS\n(92 = 42 + 50)\nTOPRIMS\n(92 = 42 + 50)\nPRIMOST\n(92 = 42 + 50)\nPRIMOST\n(92 = 42 + 50)\nTOPRIMS\n(92 = 42 + 50)\nTOPRIMS\n(86 = 36 + 50)\nPRIMOST\n(86 = 36 + 50)\nPRIMOST\n(86 = 36 + 50)\nIMPORTS\n(86 = 36 + 50)\nTOPRIMS\n(86 = 36 + 50)\nPRIMOST\n(86 = 36 + 50)\nIMPORTS\n(86 = 36 + 50)\nPRIMOST\n(86 = 36 + 50)\nTOPRIMS\n(86 = 36 + 50)\nPRIMOST\n(86 = 36 + 50)\nIMPORTS\n(86 = 36 + 50)\nIMPORTS\n(86 = 36 + 50)\nTOPRIMS\n(86 = 36 + 50)\nTOPRIMS\n(86 = 36 + 50)\nIMPORTS\n(86 = 36 + 50)\nIMPORTS\n(86 = 36 + 50)\nTOPRIMS\n(86 = 36 + 50)\nIMPORTS\n(84 = 34 + 50)\nIMPORTS\n(84 = 34 + 50)\nTOPRIMS\n(84 = 34 + 50)\nTOPRIMS\n(84 = 34 + 50)\nTOPRIMS\n(83 = 33 + 50)\nPRIMOST\n(83 = 33 + 50)\nIMPORTS\n(83 = 33 + 50)\nIMPORTS\n(80 = 30 + 50)\nTOPRIMS\n(80 = 30 + 50)\nPRIMOST\n(80 = 30 + 50)\nIMPORTS\n(78 = 28 + 50)\nPRIMOST\n(78 = 28 + 50)\nTOPRIMS\n(78 = 28 + 50)\nPRIMOST\n(78 = 28 + 50)\nIMPORTS\n(78 = 28 + 50)\nTOPRIMS\n(78 = 28 + 50)\nIMPORTS\n(76 = 26 + 50)\nTOPRIMS\n(76 = 26 + 50)\nPRIMOST\n(76 = 26 + 50)\nIMPORTS\n(76 = 26 + 50)\nPRIMOST\n(76 = 26 + 50)\nPRIMOST\n(76 = 26 + 50)\nPRIMOST\n(76 = 26 + 50)\nPRIMOST\n(76 = 26 + 50)\nTOPRIMS\n(76 = 26 + 50)\nIMPORTS\n(76 = 26 + 50)\nTOPRIMS\n(76 = 26 + 50)\nTOPRIMS\n(74 = 24 + 50)\nTOPRIMS\n(74 = 24 + 50)\nPRIMOST\n(74 = 24 + 50)\nTOPRIMS\n(74 = 24 + 50)\nIMPORTS\n(74 = 24 + 50)\nIMPORTS\n(74 = 24 + 50)\nTOPRIMS\n(74 = 24 + 50)\nPRIMOST\n(74 = 24 + 50)\nPRIMOST\n(74 = 24 + 50)\nIMPORTS\n(74 = 24 + 50)\nIMPORTS\n(74 = 24 + 50)\nIMPORTS\n(74 = 24 + 50)\nPRIMOST\n(74 = 24 + 50)\nPRIMOST\n(74 = 24 + 50)\nTOPRIMS\n(74 = 24 + 50)\nIMPORTS\n(74 = 24 + 50)\nTOPRIMS\n(74 = 24 + 50)\nPRIMOST\n(74 = 24 + 50)\nIMPORTS\n(72 = 22 + 50)\nTOPRIMS\n(72 = 22 + 50)\nIMPORTS\n(72 = 22 + 50)\nPRIMOST\n(72 = 22 + 50)\nTOPRIMS\n(72 = 22 + 50)\nTOPRIMS\n(72 = 22 + 50)\nTOPRIMS\n(72 = 22 + 50)\nPRIMOST\n(72 = 22 + 50)\nPRIMOST\n(72 = 22 + 50)\nPRIMOST\n(72 = 22 + 50)\nIMPORTS\n(72 = 22 + 50)\nPRIMOST\n(72 = 22 + 50)\nTOPRIMS\n(72 = 22 + 50)\nIMPORTS\n(72 = 22 + 50)\nIMPORTS\n(72 = 22 + 50)\nTOPRIMS\n(69 = 19 + 50)\nPRIMOST\n(69 = 19 + 50)\nTOPRIMS\n(69 = 19 + 50)\nIMPORTS\n(69 = 19 + 50)\nIMPORTS\n(69 = 19 + 50)\nPRIMOST\n(67 = 17 + 50)\nTOPRIMS\n(66 = 16 + 50)\nIMPORTS\n(66 = 16 + 50)\nPRIMOST\n(66 = 16 + 50)\nPRIMOST\n(66 = 16 + 50)\nTOPRIMS\n(65 = 15 + 50)\nTOPRIMS\n(65 = 15 + 50)\nTOPRIMS\n(65 = 15 + 50)\nPRIMOST\n(65 = 15 + 50)\nIMPORTS\n(65 = 15 + 50)\nPRIMOST\n(65 = 15 + 50)\nTOPRIMS\n(65 = 15 + 50)\nPRIMOST\n(65 = 15 + 50)\nTOPRIMS\n(65 = 15 + 50)\nPRIMOST\n(65 = 15 + 50)\nPRIMOST\n(65 = 15 + 50)\nIMPORTS\n(65 = 15 + 50)\nIMPORTS\n(65 = 15 + 50)\nIMPORTS\n(65 = 15 + 50)\nIMPORTS\n(65 = 15 + 50)\nTOPRIMS\n(64 = 14 + 50)\nIMPORTS\n(64 = 14 + 50)\nPRIMOST\n(64 = 14 + 50)\nIMPORTS\n(63 = 13 + 50)\nIMPORTS\n(63 = 13 + 50)\nTOPRIMS\n(63 = 13 + 50)\nPRIMOST\n(63 = 13 + 50)\nPRIMOST\n(63 = 13 + 50)\nPRIMOST\n(63 = 13 + 50)\nTOPRIMS\n(63 = 13 + 50)\nTOPRIMS\n(63 = 13 + 50)\nIMPORTS\n(63 = 13 + 50)\nTOPRIMS\n(62 = 12 + 50)\nIMPORTS\n(62 = 12 + 50)\nTOPRIM\n(39)\nTOPRIM\n(39)\nIMPORT\n(39)\nIMPORT\n(39)\nROMPS\n(36)\nPRISM\n(36)\nPROMS\n(36)\nPRIMO\n(36)\nPRIMO\n(36)\nPRISM\n(36)\nPROMS\n(36)\nSTOMP\n(36)\nSTOMP\n(36)\nTOPRIM\n(33)\nROMP\n(33)\nPROM\n(33)\nPRIM\n(33)\nPROM\n(33)\nTOPRIM\n(33)\nMOPS\n(33)\nTOPRIM\n(33)\nIMPORT\n(33)\nIMPORT\n(33)\nIMPORT\n(33)\nTOPRIM\n(33)\nIMPORT\n(33)\nPRIM\n(33)\nIMPORT\n(32)\nTOPRIM\n(32)\nTOPRIM\n(30)\nTOPRIM\n(30)\nIMPORT\n(30)\nSTOMP\n(30)\nPROMS\n(30)\nPRISM\n(30)\nPROMS\n(30)\nIMPORT\n(30)\nPROMS\n(30)\nMOIST\n(30)\nSPORT\n(30)\nMORTS\n(30)\nOMITS\n(30)\nTRIPS\n(30)\nPRISM\n(30)\nSTOMP\n(30)\nPRISM\n(30)\nSPIRO\n(30)\nPRISM\n(30)\nSTOMP\n(30)\nSPRIT\n(30)\nPOSIT\n(30)\nROMPS\n(30)\nPRIMO\n(30)\nPRIMO\n(30)\nROMPS\n(30)\nTRIMS\n(30)\nPRIMO\n(30)\nSTRIP\n(30)\nSTORM\n(30)\nPORTS\n(30)\nROMPS\n(30)\nSTROP\n(30)\nIMPS\n(27)\nPROMS\n(27)\nPRIMO\n(27)\nPROMS\n(27)\nPRIMO\n(27)\nPOTS\n(27)\nTRIP\n(27)\nTRIM\n(27)\nPRISM\n(27)\nPRISM\n(27)\nMOPS\n(27)\nPRISM\n(27)\n\n# primost in Words With Friends™\n\nThe word primost is playable in Words With Friends™, no blanks required.\n\nTOPRIMS\n(104 = 69 + 35)\nPRIMOST\n(104 = 69 + 35)\nPRIMOST\n(104 = 69 + 35)\nIMPORTS\n(104 = 69 + 35)\nIMPORTS\n(104 = 69 + 35)\nPRIMOST\n(104 = 69 + 35)\nTOPRIMS\n(104 = 69 + 35)\n\n## Seven Letter Word Alert: (3 words)\n\nimports, primost, toprims\n\nPRIMOST\n(104 = 69 + 35)\nPRIMOST\n(104 = 69 + 35)\nPRIMOST\n(104 = 69 + 35)\nPRIMOST\n(98 = 63 + 35)\nPRIMOST\n(98 = 63 + 35)\nPRIMOST\n(98 = 63 + 35)\nPRIMOST\n(87 = 52 + 35)\nPRIMOST\n(87 = 52 + 35)\nPRIMOST\n(87 = 52 + 35)\nPRIMOST\n(86 = 51 + 35)\nPRIMOST\n(80 = 45 + 35)\nPRIMOST\n(80 = 45 + 35)\nPRIMOST\n(80 = 45 + 35)\nPRIMOST\n(77 = 42 + 35)\nPRIMOST\n(69 = 34 + 35)\nPRIMOST\n(65 = 30 + 35)\nPRIMOST\n(65 = 30 + 35)\nPRIMOST\n(65 = 30 + 35)\nPRIMOST\n(65 = 30 + 35)\nPRIMOST\n(65 = 30 + 35)\nPRIMOST\n(63 = 28 + 35)\nPRIMOST\n(63 = 28 + 35)\nPRIMOST\n(63 = 28 + 35)\nPRIMOST\n(63 = 28 + 35)\nPRIMOST\n(63 = 28 + 35)\nPRIMOST\n(61 = 26 + 35)\nPRIMOST\n(61 = 26 + 35)\nPRIMOST\n(61 = 26 + 35)\nPRIMOST\n(61 = 26 + 35)\nPRIMOST\n(61 = 26 + 35)\nPRIMOST\n(61 = 26 + 35)\nPRIMOST\n(61 = 26 + 35)\nPRIMOST\n(58 = 23 + 35)\nPRIMOST\n(57 = 22 + 35)\nPRIMOST\n(56 = 21 + 35)\nPRIMOST\n(56 = 21 + 35)\nPRIMOST\n(54 = 19 + 35)\nPRIMOST\n(54 = 19 + 35)\nPRIMOST\n(53 = 18 + 35)\nPRIMOST\n(53 = 18 + 35)\nPRIMOST\n(53 = 18 + 35)\nPRIMOST\n(53 = 18 + 35)\nPRIMOST\n(53 = 18 + 35)\nPRIMOST\n(52 = 17 + 35)\nPRIMOST\n(52 = 17 + 35)\nPRIMOST\n(52 = 17 + 35)\nPRIMOST\n(52 = 17 + 35)\nPRIMOST\n(51 = 16 + 35)\nPRIMOST\n(50 = 15 + 35)\nPRIMOST\n(50 = 15 + 35)\nPRIMOST\n(50 = 15 + 35)\nPRIMOST\n(50 = 15 + 35)\nPRIMOST\n(50 = 15 + 35)\nPRIMOST\n(49 = 14 + 35)\nPRIMOST\n(49 = 14 + 35)\nPRIMOST\n(49 = 14 + 35)\nPRIMOST\n(49 = 14 + 35)\nPRIMOST\n(48 = 13 + 35)\n\nTOPRIMS\n(104 = 69 + 35)\nPRIMOST\n(104 = 69 + 35)\nPRIMOST\n(104 = 69 + 35)\nIMPORTS\n(104 = 69 + 35)\nIMPORTS\n(104 = 69 + 35)\nPRIMOST\n(104 = 69 + 35)\nTOPRIMS\n(104 = 69 + 35)\nTOPRIMS\n(98 = 63 + 35)\nPRIMOST\n(98 = 63 + 35)\nPRIMOST\n(98 = 63 + 35)\nIMPORTS\n(98 = 63 + 35)\nPRIMOST\n(98 = 63 + 35)\nPRIMOST\n(87 = 52 + 35)\nPRIMOST\n(87 = 52 + 35)\nIMPORTS\n(87 = 52 + 35)\nTOPRIMS\n(87 = 52 + 35)\nPRIMOST\n(87 = 52 + 35)\nTOPRIMS\n(87 = 52 + 35)\nIMPORTS\n(87 = 52 + 35)\nIMPORTS\n(87 = 52 + 35)\nTOPRIMS\n(87 = 52 + 35)\nIMPORTS\n(86 = 51 + 35)\nTOPRIMS\n(86 = 51 + 35)\nIMPORTS\n(86 = 51 + 35)\nPRIMOST\n(86 = 51 + 35)\nTOPRIMS\n(86 = 51 + 35)\nIMPORTS\n(80 = 45 + 35)\nIMPORTS\n(80 = 45 + 35)\nIMPORTS\n(80 = 45 + 35)\nIMPORTS\n(80 = 45 + 35)\nIMPORTS\n(80 = 45 + 35)\nPRIMOST\n(80 = 45 + 35)\nPRIMOST\n(80 = 45 + 35)\nPRIMOST\n(80 = 45 + 35)\nTOPRIMS\n(80 = 45 + 35)\nTOPRIMS\n(80 = 45 + 35)\nTOPRIMS\n(80 = 45 + 35)\nTOPRIMS\n(80 = 45 + 35)\nTOPRIMS\n(80 = 45 + 35)\nIMPORTS\n(77 = 42 + 35)\nTOPRIMS\n(77 = 42 + 35)\nPRIMOST\n(77 = 42 + 35)\nTOPRIMS\n(77 = 42 + 35)\nIMPORTS\n(77 = 42 + 35)\nTOPRIMS\n(69 = 34 + 35)\nIMPORTS\n(69 = 34 + 35)\nIMPORTS\n(69 = 34 + 35)\nTOPRIMS\n(69 = 34 + 35)\nPRIMOST\n(69 = 34 + 35)\nIMPORT\n(66)\nTOPRIM\n(66)\nTOPRIM\n(66)\nIMPORTS\n(65 = 30 + 35)\nTOPRIMS\n(65 = 30 + 35)\nPRIMOST\n(65 = 30 + 35)\nTOPRIMS\n(65 = 30 + 35)\nPRIMOST\n(65 = 30 + 35)\nPRIMOST\n(65 = 30 + 35)\nTOPRIMS\n(65 = 30 + 35)\nIMPORTS\n(65 = 30 + 35)\nPRIMOST\n(65 = 30 + 35)\nTOPRIMS\n(65 = 30 + 35)\nIMPORTS\n(65 = 30 + 35)\nPRIMOST\n(65 = 30 + 35)\nIMPORTS\n(65 = 30 + 35)\nTOPRIMS\n(63 = 28 + 35)\nTOPRIMS\n(63 = 28 + 35)\nTOPRIMS\n(63 = 28 + 35)\nIMPORTS\n(63 = 28 + 35)\nIMPORTS\n(63 = 28 + 35)\nTOPRIMS\n(63 = 28 + 35)\nPRIMOST\n(63 = 28 + 35)\nIMPORTS\n(63 = 28 + 35)\nIMPORTS\n(63 = 28 + 35)\nPRIMOST\n(63 = 28 + 35)\nPRIMOST\n(63 = 28 + 35)\nPRIMOST\n(63 = 28 + 35)\nPRIMOST\n(63 = 28 + 35)\nPRIMOST\n(61 = 26 + 35)\nPRIMOST\n(61 = 26 + 35)\nIMPORTS\n(61 = 26 + 35)\nPRIMOST\n(61 = 26 + 35)\nPRIMOST\n(61 = 26 + 35)\nTOPRIMS\n(61 = 26 + 35)\nTOPRIMS\n(61 = 26 + 35)\nTOPRIMS\n(61 = 26 + 35)\nPRIMOST\n(61 = 26 + 35)\nTOPRIMS\n(61 = 26 + 35)\nPRIMOST\n(61 = 26 + 35)\nTOPRIMS\n(61 = 26 + 35)\nTOPRIMS\n(61 = 26 + 35)\nTOPRIMS\n(61 = 26 + 35)\nIMPORTS\n(61 = 26 + 35)\nPRIMOST\n(61 = 26 + 35)\nIMPORTS\n(61 = 26 + 35)\nIMPORTS\n(61 = 26 + 35)\nIMPORTS\n(61 = 26 + 35)\nIMPORTS\n(61 = 26 + 35)\nIMPORTS\n(61 = 26 + 35)\nTOPRIM\n(60)\nIMPORT\n(60)\nTOPRIM\n(60)\nIMPORT\n(60)\nTOPRIMS\n(58 = 23 + 35)\nIMPORTS\n(58 = 23 + 35)\nIMPORTS\n(58 = 23 + 35)\nTOPRIMS\n(58 = 23 + 35)\nPRIMOST\n(58 = 23 + 35)\nTOPRIMS\n(58 = 23 + 35)\nIMPORTS\n(58 = 23 + 35)\nPROMS\n(57)\nPRIMO\n(57)\nPROMS\n(57)\nROMPS\n(57)\nSTOMP\n(57)\nPRISM\n(57)\nPRIMOST\n(57 = 22 + 35)\nPRIMO\n(57)\nPRISM\n(57)\nSTOMP\n(57)\nTOPRIMS\n(56 = 21 + 35)\nPRIMOST\n(56 = 21 + 35)\nPRIMOST\n(56 = 21 + 35)\nPRIMOST\n(54 = 19 + 35)\nROMP\n(54)\nPRIMOST\n(54 = 19 + 35)\nPROM\n(54)\nIMPORTS\n(54 = 19 + 35)\nPROM\n(54)\nTOPRIMS\n(54 = 19 + 35)\nPRIM\n(54)\nIMPORTS\n(54 = 19 + 35)\nMOPS\n(54)\nTOPRIMS\n(54 = 19 + 35)\nPRIM\n(54)\nIMPORTS\n(53 = 18 + 35)\nIMPORTS\n(53 = 18 + 35)\nTOPRIMS\n(53 = 18 + 35)\nTOPRIMS\n(53 = 18 + 35)\nPRIMOST\n(53 = 18 + 35)\nTOPRIMS\n(53 = 18 + 35)\nTOPRIMS\n(53 = 18 + 35)\nPRIMOST\n(53 = 18 + 35)\nIMPORTS\n(53 = 18 + 35)\nIMPORTS\n(53 = 18 + 35)\nPRIMOST\n(53 = 18 + 35)\nPRIMOST\n(53 = 18 + 35)\nIMPORTS\n(53 = 18 + 35)\nIMPORTS\n(53 = 18 + 35)\nPRIMOST\n(53 = 18 + 35)\nPRIMOST\n(52 = 17 + 35)\nTOPRIMS\n(52 = 17 + 35)\nTOPRIMS\n(52 = 17 + 35)\nIMPORTS\n(52 = 17 + 35)\nIMPORTS\n(52 = 17 + 35)\nPRIMOST\n(52 = 17 + 35)\nIMPORTS\n(52 = 17 + 35)\nTOPRIMS\n(52 = 17 + 35)\nPRIMOST\n(52 = 17 + 35)\nPRIMOST\n(52 = 17 + 35)\nPRIMOST\n(51 = 16 + 35)\nIMPORTS\n(51 = 16 + 35)\nTOPRIMS\n(51 = 16 + 35)\nTOPRIMS\n(51 = 16 + 35)\nIMPORTS\n(51 = 16 + 35)\nPRIMOST\n(50 = 15 + 35)\nPRIMOST\n(50 = 15 + 35)\nIMPORTS\n(50 = 15 + 35)\nTOPRIMS\n(50 = 15 + 35)\nIMPORTS\n(50 = 15 + 35)\nTOPRIMS\n(50 = 15 + 35)\nTOPRIMS\n(50 = 15 + 35)\nIMPORTS\n(50 = 15 + 35)\nIMPORTS\n(50 = 15 + 35)\nTOPRIMS\n(50 = 15 + 35)\nPRIMOST\n(50 = 15 + 35)\nPRIMOST\n(50 = 15 + 35)\nTOPRIMS\n(50 = 15 + 35)\nTOPRIMS\n(50 = 15 + 35)\nPRIMOST\n(50 = 15 + 35)\nIMPORTS\n(50 = 15 + 35)\nTOPRIMS\n(50 = 15 + 35)\nIMPORTS\n(50 = 15 + 35)\nTOPRIMS\n(49 = 14 + 35)\nIMPORTS\n(49 = 14 + 35)\nTOPRIMS\n(49 = 14 + 35)\nPRIMOST\n(49 = 14 + 35)\nTOPRIMS\n(49 = 14 + 35)\nPRIMOST\n(49 = 14 + 35)\nPRIMOST\n(49 = 14 + 35)\nPRIMOST\n(49 = 14 + 35)\nIMPORTS\n(49 = 14 + 35)\nIMPORTS\n(49 = 14 + 35)\nTOPRIM\n(48)\nTOPRIM\n(48)\nOMITS\n(48)\nMOIST\n(48)\nSPRIT\n(48)\nIMPORT\n(48)\nSTROP\n(48)\n\n# Word Growth involving primost\n\nos most\n\nrim prim primo\n\n## Longer words containing primost\n\n(No longer words found)"
] |
[
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.54457736,"math_prob":1.0000099,"size":430,"snap":"2020-10-2020-16","text_gpt3_token_len":129,"char_repetition_ratio":0.3004695,"word_repetition_ratio":0.2413793,"special_character_ratio":0.2,"punctuation_ratio":0.13513513,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":1.0000077,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-02-18T05:13:04Z\",\"WARC-Record-ID\":\"<urn:uuid:852b5336-43ee-4c1a-9cc6-d3269bb43cab>\",\"Content-Length\":\"148795\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:08ab7a42-242a-45fb-9362-bb097625faac>\",\"WARC-Concurrent-To\":\"<urn:uuid:5352fe1e-41df-4d70-8e4a-3afa821d6c66>\",\"WARC-IP-Address\":\"104.18.51.165\",\"WARC-Target-URI\":\"https://www.litscape.com/word_analysis/primost\",\"WARC-Payload-Digest\":\"sha1:DYNJFLZX3MKMZSHR7Y5P6G5537CVIPZV\",\"WARC-Block-Digest\":\"sha1:SMQ4C7ETCWZWPIJ5VMB32WMONW22I5PF\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-10/CC-MAIN-2020-10_segments_1581875143505.60_warc_CC-MAIN-20200218025323-20200218055323-00182.warc.gz\"}"}
|
https://codeforces.com/blog/entry/90939
|
[
"### the_nightmare's blog\n\nBy the_nightmare, history, 20 months ago,",
null,
"1527A - And Then There Were K\n\nAuthor: loud_mouth\nIdea: Bignubie\n\nEditorial\nSolution (Loud_mouth)\nSolution (the_nightmare)\n\n1527B1 - Palindrome Game (easy version)\n\nAuthor: DenOMINATOR\nIdea: shikhar7s\n\nEditorial\nSolution (DenOMINATOR)\nSolution (shikhar7s)\n\n1527B2 - Palindrome Game (hard version)\n\nAuthor: DenOMINATOR\nIdea:DenOMINATOR\n\nEditorial\nSolution(Greedy) (DenOMINATOR)\nSolution(DP) (DenOMINATOR)\n\n1527C - Sequence Pair Weight\n\nAuthor: sharabhagrawal25\nIdea: rivalq\n\nEditorial\nSolution (sharabhagrawal25)\nSolution (mallick630)\n\n1527D - MEX Tree\n\nAuthor: mallick630\nIdea: CoderAnshu\n\nEditorial\nSolution (shikhar7s)\nSolution (the_nightmare)\n\n1527E - Partition Game\n\nAuthor: rivalq\nIdea: rivalq\n\nEditorial\nSolution (rivalq)\nSolution (the_nightmare)",
null,
"Tutorial of Codeforces Round #721 (Div. 2)",
null,
"",
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"Comments (77)\n| Write comment?\n » contest was the_nightmare\n• » » haha, nice one XD\n » nightmare round\n » How to solve E using divide and conquer DP? (and especially how to maintain the cost around?)\n• » » 20 months ago, # ^ | ← Rev. 2 → link here is my code for divide and conquer techniquei took the idea from the code given below and understood it linkbasically what we are doing here is we are maintaining a persistent segment tree on every ith index which will provide us with the information that if we consider a segment of [i,j] then what will be its cost. The basic idea here is to use segment tree with range updates and point query.You could see from my code how to update ranges its pretty straightforward.now that we can find out the cost of any segment in log(n)complexity all we have to do is calculate the dp which can be calculated with the help of divide and conquer the only hard part of this method was the persistent segment tree part which was difficult to understand and actually think by yourself(atleast for me it was very new idea)\n » In problem B1, when all the elements of the string is 1, then how Bob wins?\n• » » It is given in the input section that string $s$ contains at least one $0$\n• » » » But for this, why Draw is not the correct answer?\n• » » » » Yes, technically it should be DRAW but to avoid confusion we omitted that case\n• » » » » » 19 months ago, # ^ | ← Rev. 2 → i have implemented dp for B2, but it's giving me incorrect output, pls help me find the bug const int N = 1e3; ll dp[N/2 + 1][N/2 + 1]; void solve() { int n; cin >> n; string s; cin >> s; int cnt00 {}, cnt01 {}, mid {}, rev {}; for(int i = 0; i < n - 1 - i; i++) { if (s[i] == s[n - 1 - i] && s[i] == '0') { cnt00++; } if (s[i] != s[n - 1 - i]) { cnt01++; } } if (n % 2 && s[n/2] == '0') { mid = 1; } if (dp[cnt01][cnt00][mid][rev] < 0) { cout << \"ALICE\" << '\\n'; } else if (dp[cnt01][cnt00][mid][rev] > 0) { cout << \"BOB\" << '\\n'; } else { cout << \"DRAW\" << '\\n'; } } int main() { fastio(); for(int i = 0; i <= N/2; i++) { for(int j = 0; j <= N/2; j++) { for(int mid = 0; mid < 2; mid++) { for(int rev = 0; rev < 2; rev++) { dp[i][j][mid][rev] = INF; } } } } dp = 0; for(int i = 0; i <= N/2; i++) { for(int j = 0; j <= N/2; j++) { for(int mid = 0; mid < 2; mid++) { for(int rev = 0; rev < 2; rev++) { // i -> cnt of symmetric 01 pairs // j -> cnt of symmetric 00 pairs if (i > 0) { dp[i][j][mid][rev] = min(dp[i][j][mid][rev], 1-dp[i-1][j][mid]); } if (j > 0) { dp[i][j][mid][rev] = min(dp[i][j][mid][rev], 1-dp[i+1][j-1][mid]); } if (mid > 0) { dp[i][j][mid][rev] = min(dp[i][j][mid][rev], 1-dp[i][j]); } if (rev == 0 && i > 0) { dp[i][j][mid][rev] = min(dp[i][j][mid][rev], -dp[i][j][mid]); } } } } } int tc = 1; cin >> tc; while(tc--) { solve(); } } \n » orz\n » Does someone know of any problem similar to C?\n » 20 months ago, # | ← Rev. 2 → what is the time complexity in B2 dp approach. 1.is it O(n^2) for one test case as it depends on no of 00 pairs and no of 01 pairs? 2.also if n^2 per test case how it passes the judge in 1 sec as n^2*t=1e9 ?\n• » » We precompute the dp and use it to answer all test cases\n• » » Dp is pre-computed not run for each test case\n » Alternative solution to A: SpoilerKeep doing $n=n$ & $(n-1)$ while $n$ & $(n-1)>0$. Print $n-1$.\n• » » I think this will TLE in python\n• » » » It does not. PyPy 3 submission: 116877296\n• » » Yes, you can do that too, but it would take too much time and result in TLE\n• » » » 20 months ago, # ^ | ← Rev. 2 → The complexity is logn for this so it won't TLE. At each iteration, you're setting at least 1 set bit to 0.\n• » » 20 months ago, # ^ | ← Rev. 2 → Hey! I am not able to understand why I am getting TLE for this solution :( Solutionll ans=n; while(n--){ ans=ans&n; if(ans==0){cout<\n » 20 months ago, # | ← Rev. 3 → MY ISSUE PLEASE HELP ( PROBLM B1) !!ok when the number of zeros are even for example example 0 0 0 0 0 0 A pay1 1 0 0 0 0 0 B reverse 0 0 0 0 0 1 A pay1 1 0 0 0 0 1 B pay1 1 1 0 0 0 1 A reverse 1 0 0 0 1 1 B pay1 1 1 0 0 0 1 A reverse 1 0 0 0 1 1 B pay1 1 1 0 0 1 1 A pay1 1 1 1 0 1 1 B reverse 1 1 0 1 1 1 A pays1 1 1 1 1 1 1 isn't this optimal here every 4 changes means DRAW and extra 1,2,3 means BOB winsAnd when zeros are odd: this part of editorial its not clear to me :( Alice will change s[n/2] from '0' to '1' and play with the same strategy as Bob did in the above case. This way Bob will spend 1 dollar more than Alice resulting in Alice's win. example 0 1 0 1 0 1 0 1 0 A pay1 0 1 0 1 1 1 0 1 0 B pay1 0 1 1 1 1 1 0 1 0 A reverse 0 1 0 1 1 1 1 1 0 B pay1 0 1 1 1 1 1 1 1 0 A pay1 1 1 1 1 1 1 1 1 0 B reverse 1 1 1 1 1 1 1 1 1 in this case every 2 means DRAW and its repeating pattern of pay1 as AB BA AB BA then if cnt_of_0 is odd and cnt_of_0/2 is odd we will have 1 zero extra which will be paid by B means ALICE wins.but if cnt_of_0/2 is even we will have 1 zero extra which will be paid by A means BOB wins.PLEASEEEEE HELPPPPPPP!!UPD: Understood!!How to solve this. Thanks everyone\n• » » Actually, for example $000000$ game goes-$A$ pay $1$ $100000$$B pay 1 100001$$A$ pay $1$ $100101$$B pay 1 101101$$A$ pay $1$ $111101$$B reverse 101111$$A$ pay $1$ $111111$$B$ winsNow, analyse $010101010$\n » After spending about 20-25 minutes I understood the logic of problem C ( yes I'm still a noob), but I was wondering how does one come up with that logic during contests ( I know practice, practice practice) but I suck at dp and I've been trying to improve it, so if anyone has dp sheets that can build my foundation it'll be of great help thanks :), I've been doing classic dp problems like knapsack, longest common subsequence type questions and even started with matrix chain multiplication recently.\n• » » The states are easier to come up during contests if you really try to, most probably you just take what the problem asks and derive subtasks as a prefix, eg: Kadane-ish (or multiple prefixes across multiple sequences, eg: LCS), suffix, subarray of the original sequence, eg: matrix chain multiplication. I'm sure after a lot of $practice$, things would become somewhat more intuitive and reflexive.\n » Alternative solution to E:First steps are also coming up with the $dp$ and writing the brute-force transition formula. Then, by considering $last(a_{r + 1})$, we can prove the following property: $c(l - 1, r) + c(l, r + 1) \\leq c(l - 1, r + 1) + c(l, r)$ Therefore, $c$ satisfies Quadrilateral Inequality, where a divide-and-conquer solution works in $O(nk\\log n)$ time.Note that calculating $c$ needs a two pointers trick similar to 868F - Yet Another Minimization Problem.\n• » » I am using divide and conquer dp optimization for problem E. can you help me why i am getting TLE code\n• » » » for(int k = mid; k >= optl; k--) { $k$ should be enumerated from $optr$ to $optl$, not $mid$ to $optl$. Otherwise, the parameter optr is unused.\n• » » How to prove complexity of two pointers trick?\n » Anyone please, help me to understand..For problem B1 help me to figure out the answer for this test case 00100\n• » » ALICE — 10100 BOB — 10101 ALICE- 10111 BOB — 11101 (REVERSE) ALICE — 11111ALICE --> 3 BOB -->1 BOB WINS\n• » » » Why it is not possible?ALICE — 10100 BOB — 00101(REVERSE) ALICE- 10101 BOB — 11101 ALICE — 10111(REVERSE) BOB — 11111ALICE --> 2 BOB -->2 DRAW\n• » » » » it's not that you can't do that . you can .But you know what , the word optimal is mentioned in the question, means if i got a chance to play then i tried my best to win , so if bob put a 1 in the string instead of reversing he will land in the winning position , instead of a draw. You can't just brute force and say bob or alice win or its a draw. its not mandiatory that if i have a chance to reverse the string then i have to reverse it , so that i will be relived from that 1 dollar penalty, you can't do that .\n » rivalq the_nightmare I am confused in the editorial for E. Aren't the k mentioned in the dp transitions and the k mentioned in the big oh notation different?\n• » » Yes they are different. The one in dp transitions you can regard as a temp variable.\n » 20 months ago, # | ← Rev. 2 → Problem B2 — Palindrome Hard Please explain this case for string: 1000 A reverses -> 0001 (A=0 B=0) B pays -> 1001 (A=0 B=1) A pays -> 1101 (A=1 B=1) B reverses -> 1011 (A=1 B=1) A pays -> 1111 (A=2 B=1) So BOB should win. But by the above code, it's making Alice the winner. Please guide me where I am doing a mistake in the implementation.\n• » » Alice can win this way:A pays -> 1001B pays -> 1101A reverses -> 1011B pays -> 1111B = 2 A = 1, so Alice wins. Bob has no other moves.\n• » » » According to you Alice wins..But according to Jyotirmaya Bob wins...So what is the exact ans...Both of you correct.\n• » » » » Alice wants to win right? So she would do exactly what I stated. Bob has no other move than just to lose. It is not logical to make a move that will allow your oponent to win.\n » 20 months ago, # | ← Rev. 2 → In fact , some users of the Chinese online judge : Luogu said that the difficulty of these problems is not monotonically increasing and they suggested that you should have changed the order of problem B and C. the_nightmare\n• » » 20 months ago, # ^ | ← Rev. 2 → There is only one additional case to be dealt in B2 if you look at the editorial. That would explain why they considered B2 as easier probably.. and dp is not what most div 2 contestants used.\n• » » Basically, we have to put together B1 and B2 due to contest restrictions due to which we are not able to swap B2 and C. But we have provided the scoring according to difficulty B(750+1500) total 2250 and C only 1500.\n• » » » In problem D's editorial shouldn't it be \"We will always break before or on reaching root\" instead of \"Note that we will always break at the root as it is marked visited in the initial step.\"\n » The term \"Contiguous Subarray\" is much more quicker to grasp than \"Subsegment\".Hope future authors see this :) Nice Contest btw\n• » » but you know what you got something to learn.\n• » » I mixed subsegment with subsquence, and it wasted me lots of time to solve this problem in a wrong way\n » Could someone please write a simpler edit for Problem-C, I have gone over it a lot of times but am still confused as to why the question creator went for:value[a[i]] += (i + 1);please help me out with the logic. I understood the task but couldn't implement it that well and now I'm even more confused.\n• » » I think (i+1) refers to the total number of subarrays ending at i. Since we are using 0 indexing, so +1 for the adjustment.\n• » » Consider and element i. Now if take an element j such that a[i]==a[j] and j < i then subarray a[j-i] will occur as part of all subarray's from i = 0 to j i.e j + 1 times. So value[a[i]] += i + 1\n• » » » Oh now i get it, thank you so much\n• » » » » Happy to help\n• » » » I was confused over this part. Thanks now,I got it.\n » Can someone help me with my solution :My idea: Maintain a path and its endpoints. Maintain a 'visited' array which denotes whether or not this node is in current path. Consider 0 as base case and mark it visited and initialize both the endpoints to 0. Iterate from 0 to i In order to find if there can be a path having all nodes [0, i] we just need to check if the endpoints of path having all of [0, i-1] can be extended to i, so move from ith node to its parent till we find a node that is in the path that includes the nodes [0, i-1], that is first visited node. If this node happens to be one of the endpoints then extend the path and update endpoints else there can be no such path that includes all of [0, i] nodes and we dont need to check this for following i's. I am unable to figure out why this gives TLE ! https://codeforces.com/contest/1527/submission/116924323\n»\n\n# include<bits/stdc++.h>\n\nusing namespace std;\n\nint main(){\n\nint t;\ncin>>t;\n\nwhile(t--){\nint n;\ncin>>n;\nstring s;\ncin>>s;\nint count=0;\nif(n==1&&s=='0'){\ncout<<\"BOB\"<<'\\n';\ncontinue;\n}\nfor(int i=0;i<s.length();i++){\ns[i]=='0'?count+=1:count=count;\n}\nif(count%2==0){\ncout<<\"BOB\"<<'\\n';\n}\nelse{\ncout<<\"ALICE\"<<'\\n';\n}\n\n}\n\n}\n\n• » » This is my logic, you can use to improve your code 116814530\n• » » » Thanks\n » Nice explanation of problem B2\n » 20 months ago, # | ← Rev. 2 → Can someone give a small test for those codes which fail test case 5 by printing 1 instead of 0 at 1923rd position for problem D? Submission\n• » » 20 months ago, # ^ | ← Rev. 2 → I got that error by incorrectly calculating in the tree \"0 -- 2 -- 1\" the number of pairs with mex == 2 (there are 0).\n » In problem A I am getting wrong output format Expected integer, but \"2.68435e+008\" found Solutionlong long n;cin>>n; long long ans=log2(n); cout<\n• » » pow() returns a double, while the expected output is an integer, hence the WA. Also as anubh4v stated, pow() (and log2() too) can be imprecise at times, leading to incorrect rounding of the number.\n• » » » I will keep that in mind. Thanks\n » Can someone explain me how does the dynamic programming solution for B2 works?From my understanding of the problem when we consider alice we add positively, when we consider bob we add negatively. But how does that happen in code? How does the code distinguish bob from alice? And how does it simulate turns?In other words: can someone explain me how the simulation of the game occurs during the bottom up transitions of the editorial / given code?Thanks in advance.\n• » » Because dp[i][j][k][l] is the optimal answer for a state where i is the number of 00, j is the number of 01 or 10, and k = 1 denotes if the middle position in case of odd length string is 0 and l = 1 denotes that in the last turn other person reversed the sting thus we can not reverse. For all the states, we will assume that the current turn is of Alice and to compute the answer for that state, we will add negative of the transition states, which will denote Bob's optimal score.\n » can anyone pls tell why i am getting time limit exceeded on test case 7 in problem D MEX TREE i am just doing a dfs traversal once to calculate subtree sizes and then iterating from 1 to n and marking not visited nodes as visited in my current path and calculating answer for each mex value.my submission link https://codeforces.com/contest/1527/submission/116996030\n » In Problem D: as mentioned in the editorial that we need to \"update the subtree sizes as we move up to parent recursively\", we don't need to do this. When (l!=r) we will always choose the other parent. Only when we are calculating MEX1 (the previous l was equal to r) so we have to update the size of 0 subtree only once.\n• » » Yoir solution simplified the question mqnyfolds. Thanks anadii!\n » I do not know if this approach has been covered for E using divide and conquer dp. To get cost of current interval, maintain global 2 pointers on the array, sum variable and array of deque. Fit the pointer for each query. Amortized complexity over per level of dp should be N*log(N). So with K layers it becomes K*N*log(N).\n » the_nightmare's solution for D will TLE for the following case. https://drive.google.com/file/d/1K-1sb5ls2PP0lKiGQf5dy9BVuqMBvReG/view?usp=sharing\n » Problem 1527C - Sequence Pair Weight could have been done greedily (and imo it's easier). Let $d(x, y)$ denote the number of segments which contain elements at indices $x$ and $y$ (indices start from 0 so $x,y \\in {0, 1, 2, \\dots, n-1}$). It is easy to see that if $y > x$ then $d(x, y) = (x+1)*(n-y)$. This allows obvious $O(n^2)$ solution, but it can be done faster in $O(n)$. Let's say we have a vector $v$ and we are at it's $i$-th element. Then, we can calculate the answer as: $d(v_0, v_i) + d(v_1, v_i) + \\dots + d(v_{i-1}, v_i)$which is just $(v_0+1)*(n-v_i) + (v_1+1)*(n-v_i) + \\dots + (v_{i-1}+1)*(n-v_i)$and this can be simplified to: $(v_1 + v_2 + v_3 + \\dots + v_{i-1} + i-1) * (n-v_i)$Which you can easily calculate while iterating through the vector. Code: 124839948\n• » » Shouldn't it be $(v_0 + v_1 + v_2 + v_3 + \\text{...} + v_{i-1} + i) \\times (n-v_i)$?\n » I think more short solution for A: https://codeforces.com/contest/1527/submission/127546267\n » in b1 can anyone explain output for this string 01011010 i am getting draw\n » 7 months ago, # | ← Rev. 3 → in problem C let the array be, 1 3 1 2 1 when we take subarray , 1 3 1 2 1 weight will be 3 {(1,2),(2,5),(1,5)} 3 1 2 1 then weight will be 1 { (3,5) }but according to editorial the weight of second one will be 3.anyone please reply ?\n• » » I ran the same code. Its giving correct answer : 7\n• » » » can you please explain me ? how is it possible\n• » » » » Check input format"
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https://www.lmfdb.org/EllipticCurve/Q/1600g4/
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"Show commands for: Magma / SageMath / Pari/GP\n\n## Minimal Weierstrass equation\n\nmagma: E := EllipticCurve([0, 1, 0, -3633, -129137]); // or\n\nmagma: E := EllipticCurve(\"1600g4\");\n\nsage: E = EllipticCurve([0, 1, 0, -3633, -129137]) # or\n\nsage: E = EllipticCurve(\"1600g4\")\n\ngp: E = ellinit([0, 1, 0, -3633, -129137]) \\\\ or\n\ngp: E = ellinit(\"1600g4\")\n\n$$y^2 = x^{3} + x^{2} - 3633 x - 129137$$\n\n## Mordell-Weil group structure\n\n$$\\Z\\times \\Z/{2}\\Z$$\n\n### Infinite order Mordell-Weil generator and height\n\nmagma: Generators(E);\n\nsage: E.gens()\n\n $$P$$ = $$\\left(253, 3900\\right)$$ $$\\hat{h}(P)$$ ≈ 3.37158164614\n\n## Torsion generators\n\nmagma: TorsionSubgroup(E);\n\nsage: E.torsion_subgroup().gens()\n\ngp: elltors(E)\n\n$$\\left(73, 0\\right)$$\n\n## Integral points\n\nmagma: IntegralPoints(E);\n\nsage: E.integral_points()\n\n$$\\left(73, 0\\right)$$, $$\\left(253, 3900\\right)$$\n\nNote: only one of each pair $\\pm P$ is listed.\n\n## Invariants\n\n magma: Conductor(E); sage: E.conductor().factor() gp: ellglobalred(E) Conductor: $$1600$$ = $$2^{6} \\cdot 5^{2}$$ magma: Discriminant(E); sage: E.discriminant().factor() gp: E.disc Discriminant: $$-4000000000000$$ = $$-1 \\cdot 2^{14} \\cdot 5^{12}$$ magma: jInvariant(E); sage: E.j_invariant().factor() gp: E.j j-invariant: $$-\\frac{20720464}{15625}$$ = $$-1 \\cdot 2^{4} \\cdot 5^{-6} \\cdot 109^{3}$$ Endomorphism ring: $$\\Z$$ (no Complex Multiplication) Sato-Tate Group: $\\mathrm{SU}(2)$\n\n## BSD invariants\n\n magma: Rank(E); sage: E.rank() Rank: $$1$$ magma: Regulator(E); sage: E.regulator() Regulator: $$3.37158164614$$ magma: RealPeriod(E); sage: E.period_lattice().omega() gp: E.omega Real period: $$0.297715280512$$ magma: TamagawaNumbers(E); sage: E.tamagawa_numbers() gp: gr=ellglobalred(E); [[gr[i,1],gr[i]] | i<-[1..#gr[,1]]] Tamagawa product: $$8$$ = $$2\\cdot2^{2}$$ magma: Order(TorsionSubgroup(E)); sage: E.torsion_order() gp: elltors(E) Torsion order: $$2$$ magma: MordellWeilShaInformation(E); sage: E.sha().an_numerical() Analytic order of Ш: $$1$$ (exact)\n\n## Modular invariants\n\n#### Modular form1600.2.a.c\n\nmagma: ModularForm(E);\n\nsage: E.q_eigenform(20)\n\ngp: xy = elltaniyama(E);\n\ngp: x*deriv(xy)/(2*xy+E.a1*xy+E.a3)\n\n$$q - 2q^{3} - 2q^{7} + q^{9} + 2q^{13} + 6q^{17} + 4q^{19} + O(q^{20})$$\n\n magma: ModularDegree(E); sage: E.modular_degree() Modular degree: 2304 $$\\Gamma_0(N)$$-optimal: no Manin constant: 1\n\n#### Special L-value\n\nmagma: Lr1 where r,Lr1 := AnalyticRank(E: Precision:=12);\n\nsage: r = E.rank();\n\nsage: E.lseries().dokchitser().derivative(1,r)/r.factorial()\n\ngp: ar = ellanalyticrank(E);\n\ngp: ar/factorial(ar)\n\n$$L'(E,1)$$ ≈ $$2.0075427511$$\n\n## Local data\n\nmagma: [LocalInformation(E,p) : p in BadPrimes(E)];\n\nsage: E.local_data()\n\ngp: ellglobalred(E)\n\nprime Tamagawa number Kodaira symbol Reduction type Root number ord($$N$$) ord($$\\Delta$$) ord$$(j)_{-}$$\n$$2$$ $$2$$ $$I_4^{*}$$ Additive 1 6 14 0\n$$5$$ $$4$$ $$I_6^{*}$$ Additive 1 2 12 6\n\n## Galois representations\n\nThe image of the 2-adic representation attached to this elliptic curve is the subgroup of $\\GL(2,\\Z_2)$ with Rouse label X10b.\n\nThis subgroup is the pull-back of the subgroup of $\\GL(2,\\Z_2/2^2\\Z_2)$ generated by $\\left(\\begin{array}{rr} 3 & 0 \\\\ 2 & 3 \\end{array}\\right),\\left(\\begin{array}{rr} 3 & 3 \\\\ 2 & 3 \\end{array}\\right)$ and has index 12.\n\nmagma: [GaloisRepresentation(E,p): p in PrimesUpTo(20)];\n\nsage: rho = E.galois_representation();\n\nsage: [rho.image_type(p) for p in rho.non_surjective()]\n\nThe mod $$p$$ Galois representation has maximal image $$\\GL(2,\\F_p)$$ for all primes $$p$$ except those listed.\n\nprime Image of Galois representation\n$$2$$ B\n$$3$$ B\n\n## $p$-adic data\n\n### $p$-adic regulators\n\nsage: [E.padic_regulator(p) for p in primes(3,20) if E.conductor().valuation(p)<2]\n\n$$p$$-adic regulators are not yet computed for curves that are not $$\\Gamma_0$$-optimal.\n\n## Iwasawa invariants\n\n $p$ Reduction type $\\lambda$-invariant(s) $\\mu$-invariant(s) 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 add ordinary add ordinary ss ordinary ordinary ordinary ordinary ordinary ordinary ordinary ordinary ordinary ordinary - 3 - 3 1,1 1 1 1 1 1 1 1 1 1 1 - 1 - 0 0,0 0 0 0 0 0 0 0 0 0 0\n\nAn entry - indicates that the invariants are not computed because the reduction is additive.\n\n## Isogenies\n\nThis curve has non-trivial cyclic isogenies of degree $$d$$ for $$d=$$ 2, 3 and 6.\nIts isogeny class 1600g consists of 4 curves linked by isogenies of degrees dividing 6.\n\n## Growth of torsion in number fields\n\nThe number fields $K$ of degree up to 7 such that $E(K)_{\\rm tors}$ is strictly larger than $E(\\Q)_{\\rm tors}$ $\\cong \\Z/{2}\\Z$ are as follows:\n\n$[K:\\Q]$ $K$ $E(K)_{\\rm tors}$ Base-change curve\n2 $$\\Q(\\sqrt{-30})$$ $$\\Z/6\\Z$$ Not in database\n$$\\Q(\\sqrt{-1})$$ $$\\Z/2\\Z \\times \\Z/2\\Z$$ Not in database\n4 $$\\Q(i, \\sqrt{30})$$ $$\\Z/2\\Z \\times \\Z/6\\Z$$ Not in database\n4.2.1600.1 $$\\Z/4\\Z$$ Not in database\n6 6.2.186624000.3 $$\\Z/6\\Z$$ Not in database\n\nWe only show fields where the torsion growth is primitive. For each field $K$ we either show its label, or a defining polynomial when $K$ is not in the database."
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https://advancesincontinuousanddiscretemodels.springeropen.com/articles/10.1186/s13662-020-02759-x
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[
"Theory and Modern Applications\n\n# Dynamics of a stochastic population model with Allee effects under regime switching\n\n## Abstract\n\nA stochastic single-species model with Allee effects under regime switching is developed and detected in the present study. First, extinction and persistence of the model are dissected. Subsequently, sufficient criteria are offered to ensure that the model possesses a unique ergodic stationary distribution. Finally, the theoretical outcomes are employed to evaluate the evolution of the African wild dog (Lycaon pictus) in Africa, and some significant functions of stochastic perturbations are exposed.\n\n## 1 Introduction\n\nThe Allee effect, which is depicted by a relationship between the per capita growth rate and the population size, is a universal biological phenomenon [2, 11, 14]. Allee effects happen while populations rely on cooperation or aggregation to hunt, to prevent capture, or to bring up their young [11, 14]. For instance, the African wild dogs usually form cooperative groups to hunt , suricate (Suricata suricatta) and Pacific salmon (Oncorhynchus spp.) form groups to prevent capture [6, 20]. The significance of Allee effects has been admitted in a lot of biological subjects (for example, eco-epidemiology , biological invasions , and population ecology ), and numerous mathematical frameworks have been put forward to dissect the role of Allee effects (see, e.g., [5, 11, 14, 21]). Especially, Takeuchi took advantage of the following equation to test the impacts of Allee effects on the evolution of a population:\n\n$$\\frac{\\mathrm{d}\\varPsi }{\\mathrm{d}t}=\\varPsi \\biggl[r+ \\frac{\\mu \\varPsi }{1+\\lambda \\varPsi } - \\frac{\\varPsi ^{2}}{1+\\lambda \\varPsi } \\biggr],$$\n(1)\n\nwhere $$\\varPsi =\\varPsi (t)$$ means the population size; r indicates the intrinsic growth rate; $$\\mu >0$$ is the Allee threshold under which the population will become extinct; $$\\lambda >0$$ depicts the environmental carrying capacity.\n\nAll species in natural environments undulate in an essentially random way, and randomness brings a hazard of extinction . Commonly, puny undulations and medium undulations are two classes of usual undulations in the environments . We first appraise the former. Several authors (see, e.g., [1, 9, 10, 1517]) have proffered that the puny undulations often act on the parameters in a system, and one could take advantage of the white noise to approximately depict the puny undulations. In this way, in model (1)\n\n$$r\\rightarrow r+\\eta _{1} \\dot{\\xi _{1}}(t),\\qquad \\mu \\rightarrow \\mu + \\eta _{2} \\dot{\\xi _{2}}(t),$$\n\nand accordingly,\n\n$$\\mathrm{d}\\varPsi =\\varPsi \\biggl[r+\\frac{\\mu \\varPsi }{1+\\lambda \\varPsi }- \\frac{\\varPsi ^{2}}{1+\\lambda \\varPsi } \\biggr]\\,\\mathrm{d}t+\\eta _{1} \\varPsi \\,\\mathrm{d}\\xi _{1}(t)+\\frac{\\eta _{2}\\varPsi ^{2}}{1+\\lambda \\varPsi } \\,\\mathrm{d}\\xi _{2}(t),$$\n(2)\n\nwhere $$\\eta _{i}^{2}$$ means the intensity of the white noise, $$\\{\\xi (t)\\}_{t\\geq 0}=\\{(\\xi _{1}(t), \\xi _{2}(t))\\}_{t\\geq 0}$$ indicates a Wiener process defined on a complete probability space $$(\\varOmega , {\\{\\mathcal{F}_{t}}\\}_{t\\geq 0}, \\mathrm{P})$$ which obeys the usual conditions.\n\nNext we appraise the medium undulations (for instance, the medium variations of rainfall and temperature) which are often encountered by the species. When these medium undulations emerge, the parameter values in a system often jump. For instance, Choristoneura fumiferana (Clemens) reproduces 50% more eggs at 25C than at 15C . These medium undulations cannot be portrayed by (2) [12, 1517]. Mathematically, one may employ a finite-state Markov chain to portray these medium undulations [12, 13, 1517]. Denote by $$\\theta =\\theta (t)$$ a right-continuous irreducible Markov chain which is independent of $$\\{\\xi (t)\\}_{t\\geq 0}$$. Then we can deduce from Eq. (2) that\n\n$$\\mathrm{d}\\varPsi =\\varPsi \\biggl[r(\\theta )+ \\frac{\\mu (\\theta )\\varPsi }{1+\\lambda (\\theta )\\varPsi } - \\frac{\\varPsi ^{2}}{1+\\lambda (\\theta )\\varPsi } \\biggr]\\,\\mathrm{d}t+\\eta _{1}( \\theta )\\varPsi \\,\\mathrm{d}\\xi _{1}(t) + \\frac{\\eta _{2}(\\theta )\\varPsi ^{2}}{1+\\lambda (\\theta )\\varPsi } \\,\\mathrm{d}\\xi _{2}(t).$$\n(3)\n\nDuring recent decades, there has been growing interest in extinction, persistence, and stability of population models . However, little research has been conducted to appraise these behaviors of (2) and (3). The present study detects these behaviors of (2): we first dissect the extinction and persistence of model (2) in Sect. 2, and then offer sufficient criteria to ensure that model (3) possesses a unique ergodic stationary distribution (UESD) in Sect. 3; in Sect. 4, we make use of the theoretical outcomes to evaluate the evolution of the African wild dog (Lycaon pictus) in Africa and expose some significant functions of puny undulations and medium undulations.\n\n## 2 Extinction and permanence\n\nLet $$\\varTheta =\\{1,\\ldots,N\\}$$ and $$\\varGamma =(\\gamma _{mj})_{N\\times N}$$ mean the state space and the generator of $$\\theta (t)$$, respectively, i.e.,\n\n$$P\\bigl\\{ \\theta (t+\\Delta t)=j|\\theta (t)=m\\bigr\\} = \\textstyle\\begin{cases} \\gamma _{mj}\\Delta t+o(\\Delta t), & \\mbox{if } j\\neq m; \\\\ 1+\\gamma _{mm}\\Delta t+o(\\Delta t), & \\mbox{if } j=m, \\end{cases}$$\n\nwhere $$\\gamma _{mj}\\geq 0$$ means the transition rate from state m to state j if $$j\\neq m$$, and $$\\gamma _{mm}=-\\sum_{j=1,j\\neq m}^{N}\\gamma _{mj}$$ for $$m=1,2,\\ldots,N$$, see for more details. Note that $$\\theta (t)$$ is irreducible, then (see, e.g., ) it has a stationary distribution which is denoted by $$\\sigma =(\\sigma _{1},\\ldots,\\sigma _{N})$$. Let $$\\mathbb{R}_{+}^{0}=\\{x\\in \\mathbb{R}|x>0\\}$$. Define $$f^{u}=\\max_{m\\in \\varTheta }\\{f(m)\\}$$, $$f^{l}=\\min_{m\\in \\varTheta }\\{f(m) \\}$$. By standard procedures (see, e.g., ), one can testify the following.\n\n### Lemma 1\n\nFor any$$(\\varPsi (0),\\theta (0))\\in \\mathbb{R}_{+}^{0}\\times \\varTheta$$, Eq. (3) possesses a pathwise unique global solution$$(\\varPsi (t),\\theta (t))\\in \\mathbb{R}_{+}^{0}\\times \\varTheta$$almost surely (a.s.).\n\nWe first offer the criteria for extinction of Eq. (3).\n\n### Theorem 1\n\n$$\\bar{\\chi }+\\bar{\\varPi }<0\\Rightarrow$$$$\\lim_{t\\rightarrow +\\infty }\\varPsi (t)=0$$, $$a.s$$., namely, $$\\varPsi (t)$$becomes extinct, where\n\n\\begin{aligned}& \\bar{\\chi }=\\sum_{m\\in \\varTheta }\\sigma _{m} \\chi (m),\\qquad \\chi (m)=r(m)- \\frac{\\eta _{1}^{2}(m)}{2}, \\\\& \\bar{\\varPi }=\\sum _{m\\in \\varTheta }\\sigma _{m} \\biggl[\\frac{\\mu (m)}{\\lambda (m)} - \\frac{2(\\sqrt{1+\\lambda (m)\\mu (m)}-1)}{\\lambda ^{2}(m)} \\biggr]. \\end{aligned}\n\n### Proof\n\nWe can deduce from the ergodicity of θ that\n\n$$\\lim_{t\\rightarrow +\\infty }t^{-1} \\int _{0}^{t} \\biggl[\\chi \\bigl( \\theta (s) \\bigr)+\\frac{\\mu (\\theta (s))}{\\lambda (\\theta (s))} - \\frac{2(\\sqrt{1+\\lambda (\\theta (s))\\mu (\\theta (s))}-1)}{\\lambda ^{2}(\\theta (s))} \\biggr]\\,\\mathrm{d}s =\\bar{\\chi }+\\bar{\\varPi }.$$\n(4)\n\nNotice that\n\n$$\\min_{x>0} \\biggl\\{ \\frac{\\mu (\\cdot )+\\lambda (\\cdot )x^{2}}{1+\\lambda (\\cdot )x} \\biggr\\} = \\frac{2(\\sqrt{1+\\lambda (\\cdot )\\mu (\\cdot )}-1)}{\\lambda (\\cdot )}.$$\n\nThen the Itô formula (see, e.g., ) implies that\n\n\\begin{aligned}[b] \\ln \\varPsi (t)-\\ln \\varPsi (0)& = \\int _{0}^{t} \\biggl[\\chi \\bigl( \\theta (s) \\bigr)+ \\frac{\\mu (\\theta (s))\\varPsi (s)-\\varPsi ^{2}(s)}{1+\\lambda (\\theta (s))\\varPsi (s)} \\biggr]\\,\\mathrm{d}s \\\\ &\\quad {}-\\frac{1}{2} \\int _{0}^{t} \\frac{\\eta _{2}^{2}(\\theta (s))\\varPsi ^{2}(s)}{(1+\\lambda (\\theta (s))\\varPsi (s))^{2}} \\,\\mathrm{d}s + \\sum_{i=1}^{2} L_{i}(t) \\\\ & = \\int _{0}^{t} \\biggl[\\chi \\bigl(\\theta (s)\\bigr)+ \\frac{\\mu (\\theta (s))}{\\lambda (\\theta (s))} - \\frac{\\mu (\\theta (s))+\\lambda (\\theta (s))\\varPsi ^{2}(s)}{\\lambda (\\theta (s)) (1+\\lambda (\\theta (s))\\varPsi (s))} \\biggr]\\,\\mathrm{d}s \\\\ &\\quad {}- \\frac{1}{2} \\int _{0}^{t} \\frac{\\eta _{2}^{2}(\\theta (s))\\varPsi ^{2}(s)}{(1+\\lambda (\\theta (s))\\varPsi (s))^{2}} \\,\\mathrm{d}s + \\sum_{i=1}^{2} L_{i}(t) \\\\ & \\leq \\int _{0}^{t} \\biggl[\\chi \\bigl(\\theta (s)\\bigr)+ \\frac{\\mu (\\theta (s))}{\\lambda (\\theta (s))} - \\frac{2(\\sqrt{1+ \\lambda (\\theta (s))\\mu (\\theta (s))}-1)}{\\lambda ^{2}(\\theta (s))} \\biggr]\\,\\mathrm{d}s \\\\ &\\quad {} -\\frac{1}{2} \\int _{0}^{t} \\frac{\\eta _{2}^{2}(\\theta (s))\\varPsi ^{2}(s)}{(1+ \\lambda (\\theta (s))\\varPsi (s))^{2}} \\,\\mathrm{d}s+ \\sum_{i=1}^{2} L_{i}(t), \\end{aligned}\n(5)\n\nwhere\n\n$$L_{1}(t)= \\int _{0}^{t}\\eta _{1}\\bigl(\\theta (s)\\bigr)\\,\\mathrm{d}\\xi _{1}(s),\\qquad L_{2}(t)= \\int _{0}^{t} \\frac{\\eta _{2}(\\theta (s))\\varPsi (s)}{1+\\lambda (\\theta (s))\\varPsi (s)} \\,\\mathrm{d}\\xi _{2}(s).$$\n\nCompute the quadratic variation of $$L_{2}(t)$$:\n\n$$\\bigl\\langle L_{2}(t),L_{2}(t)\\bigr\\rangle = \\int _{0}^{t} \\frac{\\eta _{2}^{2}(\\theta (s))\\varPsi ^{2}(s)}{(1+\\lambda (\\theta (s))\\varPsi (s))^{2}} \\,\\mathrm{d}s.$$\n\nIn accordance with the exponential martingale inequality (see, e.g., ), we can deduce that\n\n$$\\mathrm{P} \\biggl\\{ \\sup_{0\\leq t\\leq k} \\biggl[L_{2}(t)- \\frac{1}{2} \\bigl\\langle L_{2}(t),L_{2}(t)\\bigr\\rangle \\biggr]>2\\ln k \\biggr\\} \\leq 1/k^{2}.$$\n\nAccordingly, Borel–Cantelli’s lemma (see, e.g., ) manifests that, for almost all $$\\omega \\in \\varOmega$$, one can find an integer $$k^{\\ast }=k^{\\ast }(\\omega )$$ such that, for $$k\\geq k^{\\ast }$$,\n\n$$\\sup_{0\\leq t\\leq k} \\biggl[L_{2}(t)-\\frac{1}{2} \\bigl\\langle L_{2}(t),L_{2}(t) \\bigr\\rangle \\biggr]\\leq 2 \\ln k.$$\n\nFor this reason,\n\n$$L_{2}(t)\\leq 2\\ln k+\\frac{1}{2}\\bigl\\langle L_{2}(t),L_{2}(t)\\bigr\\rangle =2 \\ln k+ \\frac{1}{2} \\int _{0}^{t} \\frac{\\eta _{2}^{2}(\\theta (s))\\varPsi ^{2}(s)}{(1+\\lambda (\\theta (s))\\varPsi (s))^{2}} \\,\\mathrm{d}s,\\quad 0\\leq t\\leq k, k\\geq k^{\\ast }.$$\n\nUtilizing this inequality to (5) gives that, for $$0\\leq t\\leq k$$, $$k\\geq k^{\\ast }$$,\n\n\\begin{aligned} \\ln \\varPsi (t)-\\ln \\varPsi (0) \\leq& \\int _{0}^{t} \\biggl[\\chi \\bigl(\\theta (s)\\bigr)+ \\frac{\\mu (\\theta (s))}{\\lambda (\\theta (s))} - \\frac{2(\\sqrt{1+\\lambda (\\theta (s))\\mu (\\theta (s))}-1)}{\\lambda ^{2}(\\theta (s))} \\biggr]\\,\\mathrm{d}s \\\\ &{}+L_{1}(t)+2 \\ln k. \\end{aligned}\n\nAccordingly, for $$0< k-1\\leq t\\leq k$$, $$k\\geq k^{\\ast }$$,\n\n\\begin{aligned} t^{-1}\\ln \\varPsi (t)-t^{-1}\\ln \\varPsi (0) \\leq& t^{-1} \\int _{0}^{t} \\biggl[ \\chi \\bigl(\\theta (s) \\bigr)+\\frac{\\mu (\\theta (s))}{\\lambda (\\theta (s))} - \\frac{2(\\sqrt{1+\\lambda (\\theta (s))\\mu (\\theta (s))}-1)}{\\lambda ^{2}(\\theta (s))} \\biggr]\\,\\mathrm{d}s \\\\ &{}+t^{-1}L_{1}(t) +\\frac{2\\ln k}{k-1}. \\end{aligned}\n(6)\n\nObviously,\n\n$$\\lim_{t\\rightarrow +\\infty }t^{-1}L_{1}(t)=0,\\quad \\mbox{a.s.}$$\n(7)\n\nUtilizing (4) and (7) to (6) causes $$\\limsup_{t\\rightarrow +\\infty }t^{-1}\\ln \\varPsi (t)\\leq \\bar{ \\chi }+\\bar{\\varPi }<0$$, a.s. As a result, for any $$\\epsilon >0$$, there is $$T>0$$ such that, for any $$t\\geq T$$,\n\n$$t^{-1}\\ln \\varPsi (t)\\leq \\bar{\\chi }+\\bar{\\varPi }+\\epsilon .$$\n\nThat is to say,\n\n$$\\varPsi (t)\\leq e^{(\\bar{\\chi }+\\bar{\\varPi }+\\epsilon )t}.$$\n\nLet ϵ be sufficiently small such that $$\\bar{\\chi }+\\bar{\\varPi }+\\epsilon <0$$, then $$\\lim_{t\\rightarrow +\\infty }\\varPsi (t)=0$$. □\n\nIn order to test stochastic permanence (SP) of model (3), we do some preparations. Suppose that $$(X(t),\\theta (t))$$ follows the equation below:\n\n$$\\mathrm{d}X=u_{1} (X,\\theta )\\,\\mathrm{d}t+u_{2} (X, \\theta )\\,\\mathrm{d}\\xi _{1}(t) +u_{3} (X,\\theta ) \\,\\mathrm{d}\\xi _{2}(t).$$\n\nLet $$U(X,m)$$ be a function which is twice continuously differentiable. Define an operator $$\\mathcal{L}$$ as follows:\n\n$$\\mathcal{L}U(X,m)=U_{X}(X,m)u_{1}(X,m)+ \\frac{u_{2}^{2}(X,m)+u_{3}^{2}(X,m)}{2}U_{XX}(X,m)+\\sum_{j\\in \\varTheta } \\gamma _{mj}U(X,j).$$\n\n### Definition 1\n\n()\n\nModel (3) is called SP if, for $$\\forall \\varepsilon \\in (0,1)$$, one can find a couple of constants $$f_{1}= f_{1}(\\varepsilon )$$ and $$f_{2}= f_{2}(\\varepsilon )$$ such that, for $$\\forall (\\varPsi (0),\\theta (0))\\in \\mathbb{R}_{+}^{0}\\times \\varTheta$$,\n\n$$\\liminf_{t\\rightarrow +\\infty }\\mathrm{P}\\bigl\\{ \\varPsi (t)\\geq f_{1} \\bigr\\} \\geq 1-\\varepsilon ,\\qquad \\liminf_{t\\rightarrow + \\infty } \\mathrm{P}\\bigl\\{ \\varPsi (t)\\leq f_{2}\\bigr\\} \\geq 1-\\varepsilon.$$\n(8)\n\n### Lemma 2\n\n()\n\nThere is a solution to$$\\varGamma x=\\upsilon$$ $$\\sigma \\upsilon =0$$, where$$\\upsilon \\in \\mathbb{R}^{N}$$.\n\n### Theorem 2\n\n$$\\bar{\\chi }>0\\Rightarrow$$model (3) is SP.\n\n### Proof\n\nLet\n\n$$U_{1}(\\varPsi )=1/\\varPsi ^{2},\\quad \\varPsi \\in \\mathbb{R}_{+}^{0}.$$\n\nWe can deduce from Itô’s formula that\n\n\\begin{aligned} \\mathrm{d}U_{1}(\\varPsi )& =2U_{1}(\\varPsi ) \\biggl[ \\frac{\\varPsi ^{2}}{1+\\lambda (\\theta )\\varPsi }- \\frac{\\mu (\\theta )\\varPsi }{1+\\lambda (\\theta )\\varPsi }-r( \\theta ) \\biggr] \\,\\mathrm{d}t \\\\ &\\quad {}+3 \\biggl(\\eta _{1}^{2}( \\theta )U_{1}(\\varPsi )+ \\frac{\\eta _{2}^{2}(\\theta )}{(1+\\lambda (\\theta )\\varPsi )^{2}} \\biggr) \\,\\mathrm{d}t \\\\ &\\quad {} -2\\eta _{1}(\\theta )U_{1}(\\varPsi )\\,\\mathrm{d}\\xi _{1}(t) -\\frac{2\\eta _{2}(\\theta )}{\\varPsi (1+\\lambda (\\theta )\\varPsi )} \\,\\mathrm{d}\\xi _{2}(t). \\end{aligned}\n\nExamine the equation $$\\varGamma x=-2\\chi +\\bar{\\chi }(2,\\ldots,2)^{\\mathrm{T}}$$, where $$\\chi =(\\chi (1),\\ldots,\\chi (N))^{\\mathrm{T}}$$. In accordance with Lemma 2, it possesses a solution which is denoted by $$(\\alpha _{1},\\ldots,\\alpha _{N})^{\\mathrm{T}}$$. Accordingly,\n\n$$\\frac{1}{2}\\sum_{j\\in \\varTheta } \\gamma _{mj}\\alpha _{j}+\\chi (m)=\\bar{ \\chi }.$$\n(9)\n\nChoose sufficiently small $$\\varpi \\in (0,1)$$ which fulfills that, for every $$m\\in \\varTheta$$,\n\n$$1-\\alpha _{m}\\varpi >0,\\qquad \\bar{\\chi }-\\varpi \\eta _{1}^{2}(m)+ \\frac{\\alpha _{m}\\varpi }{2(1-\\alpha _{m}\\varpi )}\\sum _{j\\in \\varTheta } \\gamma _{mj}\\alpha _{j}>0.$$\n\nThen (9) implies that\n\n\\begin{aligned} \\chi (m)-\\frac{1}{2(1-\\alpha _{m}\\varpi )\\varpi }\\sum _{j\\in \\varTheta } \\gamma _{mj}(1-\\alpha _{j} \\varpi ) &=\\chi (m)+ \\frac{1}{2(1-\\alpha _{m}\\varpi )}\\sum_{j\\in \\varTheta } \\gamma _{mj} \\alpha _{j} \\\\ &=\\bar{\\chi }+ \\frac{\\alpha _{m}\\varpi }{2(1-\\alpha _{m}\\varpi )}\\sum_{j\\in \\varTheta } \\gamma _{mj}\\alpha _{j}. \\end{aligned}\n(10)\n\nLet\n\n$$U_{2}(\\varPsi ,m)=(1-\\alpha _{m}\\varpi ) \\bigl(1+U_{1}(\\varPsi )\\bigr)^{\\varpi }.$$\n\nWe can deduce from Itô’s formula that\n\n\\begin{aligned} \\mathrm{d}U_{2}(\\varPsi ,\\theta )& = \\mathcal{L}U_{2}( \\varPsi ,\\theta )\\,\\mathrm{d}t-2\\eta _{1}( \\theta ) (1-\\alpha _{m}\\varpi )U_{1}( \\varPsi ) \\bigl(1+U_{1}(\\varPsi )\\bigr)^{\\varpi -1}\\,\\mathrm{d}\\xi _{1}(t) \\\\ &\\quad {} - \\frac{2\\eta _{2}(\\theta )(1-\\alpha _{m}\\varpi )}{\\varPsi (1+\\lambda (\\theta )\\varPsi )}U_{1}( \\varPsi ) \\bigl(1+U_{1}( \\varPsi )\\bigr)^{\\varpi -1}\\,\\mathrm{d}\\xi _{2}(t), \\end{aligned}\n\nthen taking the expectation gives\n\n$$\\mathbb{E}U_{2}\\bigl(\\varPsi (t),\\theta (t)\\bigr)=U_{2} \\bigl(\\varPsi (0),\\theta (0)\\bigr)+ \\mathbb{E} \\int _{0}^{t}\\mathcal{L}U_{2}\\bigl( \\varPsi (s),\\theta (s)\\bigr) \\,\\mathrm{d}s,$$\n\nwhere\n\n\\begin{aligned}& \\mathcal{L}U_{2}(\\varPsi ,m) \\\\ & \\quad =2(1-\\alpha _{m}\\varpi )\\varpi \\bigl(1+U_{1}(\\varPsi ) \\bigr)^{ \\varpi -2} \\\\ & \\qquad {}\\times \\biggl\\{ \\bigl(1+U_{1}(\\varPsi )\\bigr) \\biggl[U_{1}(\\varPsi ) \\biggl( \\frac{\\varPsi ^{2}}{1+\\lambda (m)\\varPsi }- \\frac{\\mu (m)\\varPsi }{1+\\lambda (m)\\varPsi }-r(m)+3\\eta _{1}^{2}(m)/2 \\biggr) \\\\ & \\qquad {} + \\frac{3\\eta _{2}^{2}(m)}{2(1+\\lambda (m)\\varPsi )^{2}} \\biggr]+(\\varpi -1) \\biggl[\\eta _{1}^{2}(m)U_{1}^{2}( \\varPsi )+ \\frac{\\eta _{2}^{2}(m)}{(1+\\lambda (m)\\varPsi )^{2}}U_{1}(\\varPsi ) \\biggr] \\biggr\\} \\\\ & \\qquad {} +\\bigl(1+U_{1}(\\varPsi )\\bigr)^{\\varpi }\\sum _{j\\in \\varTheta } \\gamma _{mj}(1-\\alpha _{j} \\varpi ) \\\\ & \\quad =2(1-\\alpha _{m}\\varpi )\\varpi \\bigl(1+U_{1}(\\varPsi ) \\bigr)^{ \\varpi -2} \\biggl\\{ - \\bigl[\\chi (m)-\\varpi \\eta _{1}^{2}(m) \\bigr]U_{1}^{2}( \\varPsi ) \\\\ & \\qquad {} + \\biggl(3\\eta _{1}^{2}(m)/2-r(m)+ \\frac{1}{1+\\lambda (m)\\varPsi }+ \\frac{\\eta _{2}^{2}(m)(\\varpi +0.5)}{(1+\\lambda (m)\\varPsi )^{2}} \\biggr)U_{1}( \\varPsi ) \\\\ & \\qquad {}+ \\frac{1}{1+\\lambda (m)\\varPsi }+ \\frac{3\\eta _{2}^{2}(m)}{2(1+\\lambda (m)\\varPsi )^{2}} -\\frac{\\mu (m)}{\\varPsi (1+\\lambda (m)\\varPsi )} \\bigl(1+U_{1}( \\varPsi ) \\bigr) \\biggr\\} \\\\ & \\qquad {}+ \\bigl(1+U_{1}(\\varPsi )\\bigr)^{\\varpi }\\sum _{j \\in \\varTheta }\\gamma _{mj}(1-\\alpha _{j} \\varpi ) \\\\ & \\quad =2(1-\\alpha _{m}\\varpi )\\varpi \\bigl(1+U_{1}(\\varPsi ) \\bigr)^{ \\varpi -2} \\biggl\\{ - \\biggl[ \\chi (m)-\\varpi \\eta _{1}^{2}(m)- \\frac{\\sum_{j\\in \\varTheta }\\gamma _{mj}(1-\\alpha _{j}\\varpi )}{2(1-\\alpha _{m}\\varpi )\\varpi } \\biggr]U_{1}^{2}( \\varPsi ) \\\\ & \\qquad {} + \\biggl[3\\eta _{1}^{2}(m)/2-r(m)+ \\frac{\\varPsi }{1+\\lambda (m)}+ \\frac{\\eta _{2}^{2}(m)(\\varpi +0.5)}{(1+\\lambda (m)\\varPsi )^{2}}+ \\frac{\\sum_{j\\in \\varTheta }\\gamma _{mj}(1-\\alpha _{j}\\varpi )}{(1-\\alpha _{m}\\varpi )\\varpi } \\biggr]U_{1}(\\varPsi ) \\\\ & \\qquad {} +\\frac{1}{1+\\lambda (m)\\varPsi }+ \\frac{3\\eta _{2}^{2}(m)}{2(1+\\lambda (m)\\varPsi )^{2}} + \\frac{\\sum_{j\\in \\varTheta }\\gamma _{mj}(1-\\alpha _{j}\\varpi )}{2(1-\\alpha _{m}\\varpi )\\varpi } \\\\ & \\qquad {}- \\frac{\\mu (m)}{1+\\lambda (m)\\varPsi } \\varPsi ^{-1} \\bigl(1+U_{1}(\\varPsi ) \\bigr) \\biggr\\} \\\\ & \\quad =2(1-\\alpha _{m}\\varpi )\\varpi \\bigl(1+U_{1}(\\varPsi ) \\bigr)^{ \\varpi -2} \\biggl\\{ - \\biggl[ \\bar{\\chi }-\\varpi \\eta _{1}^{2}(m)+ \\frac{\\alpha _{m}\\varpi }{2(1-\\alpha _{m}\\varpi )}\\sum _{j\\in \\varTheta } \\gamma _{mj}\\alpha _{j} \\biggr]U_{1}^{2}(\\varPsi ) \\\\ & \\qquad {} + \\biggl[3\\eta _{1}^{2}(m)/2-r(m)+ \\frac{1}{1+\\lambda (m)\\varPsi }+ \\frac{\\eta _{2}^{2}(m)(\\varpi +0.5)}{(1+\\lambda (m)\\varPsi )^{2}} \\\\ & \\qquad {}+ \\frac{\\sum_{j\\in \\varTheta }\\gamma _{mj}(1-\\alpha _{j}\\varpi )}{(1-\\alpha _{m}\\varpi )\\varpi } \\biggr]U_{1}(\\varPsi )+\\frac{1}{1+\\lambda (m)\\varPsi }+ \\frac{3\\eta _{2}^{2}(m)}{2(1+\\lambda (m)\\varPsi )^{2}} \\\\ & \\qquad {} + \\frac{\\sum_{j\\in \\varTheta }\\gamma _{mj}(1-\\alpha _{j}\\varpi )}{2(1-\\alpha _{m}\\varpi )\\varpi } - \\frac{\\mu (m)}{1+\\lambda (m)\\varPsi } \\varPsi ^{-1} \\bigl(1+U_{1}(\\varPsi ) \\bigr) \\biggr\\} . \\end{aligned}\n\nChoose sufficiently small $$\\delta \\in \\mathbb{R}_{+}^{0}$$ which fulfills that, for each $$m\\in \\varTheta$$,\n\n$$g_{1}=:\\bar{\\chi }-\\varpi \\eta _{1}^{2}(m)+ \\frac{\\alpha _{m}\\varpi }{2(1-\\alpha _{m}\\varpi )}\\sum _{j\\in \\varTheta } \\gamma _{mj}\\alpha _{j}- \\frac{\\delta }{2\\varpi }>0.$$\n(11)\n\nLet\n\n$$U_{3}(\\varPsi ,m)= e^{\\delta t}U_{2}(\\varPsi ,m).$$\n\nWe can deduce from Itô’s formula that\n\n$$\\mathbb{E}U_{3}\\bigl(\\varPsi (t),\\theta (t)\\bigr)=U_{2} \\bigl( \\varPsi (0),\\theta (0)\\bigr)+\\mathbb{E} \\int _{0}^{t}\\mathcal{L} \\bigl[e^{ \\delta s}U_{2} \\bigl(\\varPsi (s),\\theta (s)\\bigr) \\bigr]\\,\\mathrm{d}s,$$\n\nwhere\n\n\\begin{aligned} &\\mathcal{L}\\bigl[U_{3}(\\varPsi ,m)\\bigr] \\\\ &\\quad = 2 e^{\\delta t}(1-\\alpha _{m}\\varpi ) \\varpi \\bigl(1+U_{1}(\\varPsi )\\bigr)^{\\varpi -2} \\\\ &\\qquad {}\\times\\biggl\\{ - \\biggl[ \\bar{ \\chi }-\\varpi \\eta _{1}^{2}(m)-\\frac{\\delta }{2\\varpi }+ \\frac{\\alpha _{m}\\varpi }{2(1-\\alpha _{m}\\varpi )}\\sum_{j\\in \\varTheta } \\gamma _{mj}\\alpha _{j} \\biggr]U_{1}^{2}( \\varPsi ) \\\\ &\\qquad {} + \\biggl[3\\eta _{1}^{2}(m)/2-r(m)+ \\frac{1}{1+\\lambda (m)\\varPsi }+ \\frac{\\eta _{2}^{2}(m)(\\varpi +0.5)}{(1+\\lambda (m)\\varPsi )^{2}} \\\\ &\\qquad {}+ \\frac{1}{(\\sum_{j\\in \\varTheta }\\gamma _{mj}(1-\\alpha _{j}\\varpi )-\\alpha _{m}\\varpi )\\varpi }+ \\frac{\\delta }{\\varpi } \\biggr]U_{1}(\\varPsi ) \\\\ &\\qquad {} +\\frac{1}{1+\\lambda (m)\\varPsi }+ \\frac{3\\eta _{2}^{2}(m)}{2(1+\\lambda (m)\\varPsi )^{2}}+ \\frac{\\sum_{j\\in \\varTheta }\\gamma _{mj}(1-\\alpha _{j}\\varpi )}{2(1-\\alpha _{m}\\varpi )\\varpi } \\\\ &\\qquad {}+ \\frac{\\delta }{2\\varpi }-\\frac{\\mu (m)}{1+\\lambda (m)\\varPsi } \\varPsi ^{-1} \\bigl(1+U_{1}(\\varPsi ) \\bigr) \\biggr\\} \\\\ &\\quad \\leq 2 e^{\\delta t}(1-\\alpha _{m}\\varpi )\\varpi \\bigl(1+U_{1}( \\varPsi )\\bigr)^{\\varpi -2} \\\\ &\\qquad {}\\times\\biggl\\{ - \\biggl[ \\bar{ \\chi }-\\varpi \\eta _{1}^{2}(m)- \\frac{\\delta }{2\\varpi }+ \\frac{\\alpha _{m}\\varpi }{2(1-\\alpha _{m}\\varpi )}\\sum_{j\\in \\varTheta } \\gamma _{mj}\\alpha _{j} \\biggr]U_{1}^{2}( \\varPsi ) \\\\ &\\qquad {} + \\biggl[3\\eta _{1}^{2}(m)/2-r(m)+ \\frac{1}{1+\\lambda (m)\\varPsi }+ \\frac{\\eta _{2}^{2}(m)(\\varpi +0.5)}{(1+\\lambda (m)\\varPsi )^{2}} \\\\ &\\qquad {}+ \\frac{\\sum_{j\\in \\varTheta }\\gamma _{mj}(1-\\alpha _{j}\\varpi )}{(1-\\alpha _{m}\\varpi )\\varpi }+ \\frac{\\delta }{\\varpi } \\biggr]U_{1}(\\varPsi ) \\\\ &\\qquad {} +\\frac{1}{1+\\lambda (m)\\varPsi }+ \\frac{3\\eta _{2}^{2}(m)}{2(1+\\lambda (m)\\varPsi )^{2}}+ \\frac{\\sum_{j\\in \\varTheta }\\gamma _{mj}(1-\\alpha _{j}\\varpi )}{2(1-\\alpha _{m}\\varpi )\\varpi } + \\frac{\\delta }{2\\varpi } \\biggr\\} \\\\ &\\quad =e^{\\delta t}(1-\\alpha _{m}\\varpi )2\\varpi \\bigl(1+U_{1}( \\varPsi )\\bigr)^{\\varpi -2} \\bigl\\{ -g_{1}U_{1}^{2}(\\varPsi )+g_{2}U_{1}( \\varPsi )+g_{3} \\bigr\\} , \\end{aligned}\n\nand\n\n\\begin{aligned}& g_{2}=3\\eta _{1}^{2}(m)/2-r(m)+ \\frac{1}{1+\\lambda (m)\\varPsi }+ \\frac{\\eta _{2}^{2}(m)(\\varpi +0.5)}{(1+\\lambda (m)\\varPsi )^{2}} + \\frac{\\sum_{j\\in \\varTheta }\\gamma _{mj}(1-\\alpha _{j}\\varpi )}{(1-\\alpha _{m}\\varpi )\\varpi }+ \\frac{\\delta }{\\varpi }, \\\\& g_{3}=\\frac{1}{1+\\lambda (m)\\varPsi }+ \\frac{3\\eta _{2}^{2}(m)}{2(1+\\lambda (m)\\varPsi )^{2}}+ \\frac{\\sum_{j\\in \\varTheta }\\gamma _{mj}(1-\\alpha _{j}\\varpi )}{2(1-\\alpha _{m}\\varpi )\\varpi } +\\frac{\\delta }{2\\varpi }. \\end{aligned}\n\nDefine\n\n$$Q(\\varPsi ,m)= 2\\varpi \\bigl(1+U_{1}(\\varPsi ) \\bigr)^{\\varpi -2} \\bigl\\{ -g_{1}U_{1}^{2}( \\varPsi )+g_{2}U_{1}(\\varPsi )+g_{3} \\bigr\\} .$$\n(12)\n\nAccording to (11), $$g_{1}>0$$, then $$Q(\\varPsi ,m)$$ is upper bounded on $$\\mathbb{R}_{+}^{0}\\times \\varTheta$$, that is to say, $$\\sup_{\\varPsi \\in \\mathbb{R}_{+}^{0},m\\in \\varTheta }\\{Q( \\varPsi ,m)\\}<+\\infty$$. Define $$\\bar{Q}_{1}=\\sup_{\\varPsi \\in \\mathbb{R}_{+}^{0},m\\in \\varTheta }\\{Q(\\varPsi ,m)\\}$$. Accordingly,\n\n\\begin{aligned} \\mathbb{E}U_{3}\\bigl(\\varPsi (t),\\varpi (t)\\bigr)&=(1-\\alpha _{m}\\varpi )\\mathbb{E}\\bigl[e^{ \\delta t}\\bigl(1+U_{1} \\bigl(\\varPsi (t)\\bigr)\\bigr)^{\\varpi }\\bigr] \\\\ &\\leq (1-\\alpha _{m} \\varpi ) \\bigl(1+U_{1}\\bigl( \\varPsi (0)\\bigr)\\bigr)^{\\varpi }+(1- \\alpha _{m}\\varpi )\\bar{Q}_{1}\\bigl(e^{\\delta t}-1 \\bigr)/ \\delta , \\end{aligned}\n\nwhich indicates that\n\n$$\\limsup_{t\\rightarrow +\\infty }\\mathbb{E} \\bigl[U_{1}^{\\varpi }\\bigl( \\varPsi (t)\\bigr)\\bigr]\\leq \\limsup _{t\\rightarrow +\\infty }\\mathbb{E}\\bigl[\\bigl(1+U_{1}\\bigl( \\varPsi (t)\\bigr)\\bigr)^{\\varpi }\\bigr]\\leq \\bar{Q}_{1}/\\delta =: \\bar{Q}_{2}.$$\n(13)\n\nFor this reason,\n\n$$\\limsup_{t\\rightarrow +\\infty }\\mathbb{E}\\bigl[\\varPsi ^{-2\\varpi }(t)\\bigr] \\leq \\bar{Q}_{2}.$$\n\nLet $$f_{1}=(\\varepsilon /\\bar{Q}_{2})^{0.5/\\varpi }$$. We can deduce from Chebyshev’s inequality (see, e.g., ) that\n\n$$\\mathrm{P}\\bigl\\{ \\varPsi (t)< f_{1}\\bigr\\} =\\mathrm{P}\\bigl\\{ \\varPsi ^{-2\\varpi }(t)> f_{1}^{-2 \\varpi }\\bigr\\} \\leq \\mathbb{E} \\bigl[\\varPsi ^{-2\\varpi }(t)\\bigr]/ f_{1}^{-2\\varpi }= f_{1}^{2 \\varpi } \\mathbb{E}\\bigl[\\varPsi ^{-2\\varpi }(t) \\bigr].$$\n\nAccordingly,\n\n$$\\limsup_{t\\rightarrow +\\infty }\\mathrm{P}\\bigl\\{ \\varPsi (t)< f_{1} \\bigr\\} \\leq f_{1}^{2\\varpi }\\bar{Q}_{2}= \\varepsilon .$$\n\nFor this reason,\n\n$$\\liminf_{t\\rightarrow +\\infty }\\mathrm{P}\\bigl\\{ \\varPsi (t)\\geq f_{1} \\bigr\\} \\geq 1-\\varepsilon .$$\n\nNow let us test $$\\limsup_{t\\rightarrow +\\infty }\\mathrm{P}\\{\\varPsi (t)> f_{2} \\}\\leq \\varepsilon$$. Let\n\n$$U(\\varPsi )=\\varPsi ^{\\beta },\\quad \\varPsi >0, \\beta \\in (0,1).$$\n\nTaking advantage of Itô’s formula results in\n\n\\begin{aligned} \\mathrm{d}U(\\varPsi ) =&\\beta \\varPsi ^{\\beta } \\biggl[r(\\theta )+0.5( \\beta -1) \\biggl(\\eta _{1}^{2}( \\theta )+ \\frac{\\eta _{2}^{2}(\\theta )\\varPsi ^{2}}{(1+\\lambda (\\theta )\\varPsi )^{2}} \\biggr) \\\\ &{}+\\frac{\\mu (\\theta )\\varPsi }{1+\\lambda (\\theta )\\varPsi }- \\frac{\\varPsi ^{2}}{1+\\lambda (\\theta )\\varPsi } \\biggr]\\,\\mathrm{d}t \\\\ &{} +\\beta \\eta _{1}(\\theta )\\varPsi ^{\\beta }\\,\\mathrm{d}\\xi _{1}(t)+ \\frac{\\beta \\eta _{2}(\\theta )\\varPsi ^{\\beta +1}}{1+\\lambda (\\theta )\\varPsi } \\,\\mathrm{d}\\xi _{2}(t) \\\\ \\leq& \\beta \\varPsi ^{\\beta } \\biggl[r(\\theta )+ \\frac{\\mu (\\theta )\\varPsi }{1+\\lambda (\\theta )\\varPsi }- \\frac{\\varPsi ^{2}}{1+\\lambda (\\theta )\\varPsi } \\biggr]\\,\\mathrm{d}t \\\\ &{}+\\beta \\eta _{1}(\\theta ) \\varPsi ^{\\beta }\\,\\mathrm{d}\\xi _{1}(t)+ \\frac{\\beta \\eta _{2}(\\theta )\\varPsi ^{\\beta +1}}{1+\\lambda (\\theta )\\varPsi } \\,\\mathrm{d}\\xi _{2}(t). \\end{aligned}\n\nFor this reason,\n\n\\begin{aligned} \\mathrm{d}\\bigl(e^{t} U(\\varPsi )\\bigr) =&e^{t} U(\\varPsi )\\,\\mathrm{d}t+e^{t} \\,\\mathrm{d}U(\\varPsi ) \\\\ \\leq& e^{t} \\varPsi ^{\\beta }\\,\\mathrm{d}t+e^{t} \\beta \\varPsi ^{\\beta } \\biggl[r(\\theta )+ \\frac{\\mu (\\theta )\\varPsi }{1+\\lambda (\\theta )\\varPsi }- \\frac{\\varPsi ^{2}}{1+\\lambda (\\theta )\\varPsi } \\biggr]\\,\\mathrm{d}t \\\\ &{}+e^{t}\\beta \\eta _{1}(\\theta )\\varPsi ^{\\beta }\\,\\mathrm{d} \\xi _{1}(t)+ \\frac{e^{t}\\beta \\eta _{2}(\\theta )\\varPsi ^{\\beta +1}}{1+\\lambda (\\theta )\\varPsi } \\,\\mathrm{d}\\xi _{2}(t) \\\\ =&\\beta e^{t}\\varPsi ^{\\beta } \\biggl[1/\\beta +r(\\theta )+ \\frac{\\mu (\\theta )\\varPsi }{1+\\lambda (\\theta )\\varPsi }- \\frac{\\varPsi ^{2}}{1+\\lambda (\\theta )\\varPsi } \\biggr]\\,\\mathrm{d}t \\\\ &{} +e^{t} \\beta \\eta _{1}(\\theta )\\varPsi ^{\\beta } \\,\\mathrm{d}\\xi _{1}(t)+ \\frac{e^{t}\\beta \\eta _{2}(\\theta )\\varPsi ^{\\beta +1}}{1+\\lambda (\\theta )\\varPsi } \\,\\mathrm{d}\\xi _{2}(t) \\\\ \\leq& \\beta e^{t} \\varPsi ^{\\beta } \\biggl[1/\\beta +r^{u}+\\mu ^{u}/ \\lambda ^{l}- \\frac{\\varPsi ^{2}}{1+\\lambda ^{u}\\varPsi } \\biggr]\\,\\mathrm{d}t \\\\ &{}+e^{t} \\beta \\eta _{1}(\\theta )\\varPsi ^{\\beta }\\,\\mathrm{d} \\xi _{1}(t)+ \\frac{e^{t}\\beta \\eta _{2}(\\theta )\\varPsi ^{\\beta +1}}{1+\\lambda (\\theta )\\varPsi } \\,\\mathrm{d}\\xi _{2}(t) \\\\ \\leq& C e^{t} \\,\\mathrm{d}t+e^{t} \\beta \\eta _{1}(\\theta ) \\varPsi ^{\\beta }\\,\\mathrm{d}\\xi _{1}(t)+ \\frac{e^{t}\\beta \\eta _{2}(\\theta )\\varPsi ^{\\beta +1}}{1+\\lambda (\\theta )\\varPsi } \\,\\mathrm{d}\\xi _{2}(t), \\end{aligned}\n\nwhere $$C>0$$ is a constant. This implies that $$\\limsup_{t\\rightarrow +\\infty }\\mathbb{E}[\\varPsi ^{\\beta }(t)] \\leq C$$. Then we can deduce from Chebyshev’s inequality that $$\\limsup_{t\\rightarrow +\\infty }\\mathrm{P}\\{\\varPsi (t)> f_{2} \\}\\leq \\varepsilon$$. □\n\n## 3 Stationary distribution\n\nNow we provide sufficient criteria to ensure that model (3) possesses a UESD.\n\n### Lemma 3\n\n(, Theorem 3.13)\n\nLet$$\\varLambda (y;t)=(\\varPsi (t),\\theta (t))$$be an$$\\mathbb{R}^{n}\\times \\varTheta$$-valued stochastic process, where$$y=(\\varPsi (0),\\theta (0))$$. Let$$F \\times \\varTheta \\subset \\mathbb{R}^{n}\\times \\varTheta$$be a domain. Then$$\\varLambda (y;t)$$is positive recurrent with respect to$$F \\times \\varTheta$$if and only if, for arbitrary$$m\\in \\varTheta$$, there is a nonnegative function$$W(\\varPsi , m)$$: $$F^{c}\\rightarrow \\mathbb{R}$$such that, for some$$a>0$$,\n\n$$\\mathcal{L}W(\\varPsi ,m)\\leq -a,\\quad (\\varPsi ,m)\\in F^{c}\\times \\varTheta ,$$\n\nwhere$$F^{c}$$represents the complement ofF.\n\n### Lemma 4\n\n(, Theorems 4.3 and 4.4)\n\nIf$$\\varLambda (y;t)$$is positive recurrent with respect to a domain, then it has a UESD.\n\n### Theorem 3\n\n$$\\bar{\\chi }>0\\Rightarrow$$model (3) possesses a UESD.\n\n### Proof\n\nChoose sufficiently small $$\\zeta \\in (0,1)$$ which obeys\n\n$$1- \\frac{\\zeta }{2}\\alpha ^{u}>0,\\qquad \\bar{\\chi }- \\frac{\\zeta }{2}\\bigl(\\eta _{1}^{2} \\bigr)^{u} +\\frac{\\zeta }{2}\\min_{m\\in \\varTheta } \\biggl\\{ \\frac{\\alpha _{m}(\\bar{\\chi }-\\chi (m))}{1-\\zeta \\alpha _{m}/2} \\biggr\\} >0,$$\n(14)\n\nwhere $$\\alpha _{m}$$ abides by (9), $$\\alpha ^{u}=\\max_{m\\in \\varTheta }\\{\\alpha _{m}\\}$$ and $$(\\eta _{1}^{2})^{u}=\\max_{m\\in \\varTheta }\\{\\eta _{1}^{2}(m)\\}$$. Let\n\n$$U_{4}(\\varPsi ,m)= (1-\\zeta \\alpha _{m}/2 )\\varPsi ^{-\\zeta }+\\varPsi , \\quad \\varPsi \\in \\mathbb{R}_{+}^{0}.$$\n\nWe can deduce that\n\n\\begin{aligned} &\\mathcal{L}U_{4}(\\varPsi ,m) \\\\ &\\quad =-\\zeta \\biggl(1-\\frac{\\zeta \\alpha _{m}}{2} \\biggr)\\varPsi ^{- \\zeta } \\biggl(r(m)+\\frac{\\mu (m)\\varPsi }{1+\\lambda (m)\\varPsi }- \\frac{\\varPsi ^{2}}{1+\\lambda (m)\\varPsi } \\biggr) \\\\ &\\qquad {}+ \\frac{\\eta _{1}^{2}(m)}{2} \\zeta (\\zeta +1) \\biggl(1-\\frac{\\zeta \\alpha _{m}}{2} \\biggr)\\varPsi ^{- \\zeta } \\\\ &\\qquad {} +\\frac{\\eta _{2}^{2}(m)}{2(1+\\lambda (m)\\varPsi )^{2}} \\zeta (\\zeta +1) \\biggl(1-\\frac{\\zeta \\alpha _{m}}{2} \\biggr) \\varPsi ^{- \\zeta +2} -\\zeta \\varPsi ^{-\\zeta }\\sum _{j\\in \\varTheta } \\gamma _{mj} \\frac{\\alpha _{j}}{2} \\\\ &\\qquad {} +\\varPsi \\biggl(r(m)+ \\frac{\\mu (m)\\varPsi }{1+\\lambda (m)\\varPsi }- \\frac{\\varPsi ^{2}}{1+\\lambda (m)\\varPsi } \\biggr) \\\\ &\\quad =-\\zeta \\biggl(1-\\frac{\\zeta \\alpha _{m}}{2} \\biggr)\\varPsi ^{- \\zeta } \\biggl(r(m)-\\frac{1}{2}\\eta _{1}^{2}(m)- \\frac{\\zeta }{2}\\eta _{1}^{2}(m) \\biggr) \\\\ &\\qquad {}- \\zeta \\biggl(1-\\frac{\\zeta \\alpha _{m}}{2} \\biggr)\\varPsi ^{-\\zeta } \\biggl(1+ \\frac{\\zeta \\alpha _{m}/2}{1-\\zeta \\alpha _{m}/2} \\biggr)\\sum_{j \\in \\varTheta } \\gamma _{mj}\\frac{\\alpha _{j}}{2} \\\\ &\\qquad {} -\\zeta \\biggl(1-\\frac{\\zeta \\alpha _{m}}{2} \\biggr) \\varPsi ^{1-\\zeta } \\biggl( \\frac{\\mu (m)}{1+\\lambda (m)\\varPsi }- \\frac{\\varPsi }{1+\\lambda (m)\\varPsi }- \\frac{\\eta _{2}^{2}(m)(\\zeta +1)\\varPsi }{2(1+\\lambda (m)\\varPsi )^{2}} \\biggr) \\\\ &\\qquad {} +\\varPsi \\biggl(r(m)+ \\frac{\\mu (m)\\varPsi }{1+\\lambda (m)\\varPsi }- \\frac{\\varPsi ^{2}}{1+\\lambda (m)\\varPsi } \\biggr) \\\\ &\\quad =-\\zeta \\biggl(1-\\frac{\\zeta \\alpha _{m}}{2} \\biggr)\\varPsi ^{- \\zeta } \\biggl( \\chi (m)+\\frac{1}{2}\\sum_{j\\in \\varTheta } \\gamma _{mj} \\alpha _{j}-\\frac{\\zeta }{2}\\eta _{1}^{2}(m)+ \\frac{\\zeta \\alpha _{m}/2}{1-\\zeta \\alpha _{m}/2}\\sum _{j\\in \\varTheta } \\gamma _{mj}\\frac{\\alpha _{j}}{2} \\biggr) \\\\ &\\qquad {} -\\zeta \\biggl(1-\\frac{\\zeta \\alpha _{m}}{2} \\biggr) \\varPsi ^{1-\\zeta } \\biggl( \\frac{\\mu (m)}{1+\\lambda (m)\\varPsi }- \\frac{\\varPsi }{1+\\lambda (m)\\varPsi }- \\frac{\\eta _{2}^{2}(m)(\\zeta +1)\\varPsi }{2(1+\\lambda (m)\\varPsi )^{2}} \\biggr) \\\\ &\\qquad {} +\\varPsi \\biggl(r(m)+ \\frac{\\mu (m)\\varPsi }{1+\\lambda (m)\\varPsi }- \\frac{\\varPsi ^{2}}{1+\\lambda (m)\\varPsi } \\biggr) \\\\ &\\quad =-\\zeta \\biggl(1-\\frac{\\zeta \\alpha _{m}}{2} \\biggr)\\varPsi ^{- \\zeta } \\biggl( \\bar{\\chi }-\\frac{\\zeta }{2}\\eta _{1}^{2}(m)+ \\frac{\\zeta \\alpha _{m}/2}{1-\\zeta \\alpha _{m}/2}\\bigl(\\bar{\\chi }-\\chi (m)\\bigr) \\biggr) \\\\ &\\qquad {} -\\zeta \\biggl(1-\\frac{\\zeta \\alpha _{m}}{2} \\biggr) \\varPsi ^{1-\\zeta } \\biggl( \\frac{\\mu (m)}{1+\\lambda (m)\\varPsi }- \\frac{\\varPsi }{1+\\lambda (m)\\varPsi }- \\frac{\\eta _{2}^{2}(m)(\\zeta +1)\\varPsi }{2(1+\\lambda (m)\\varPsi )^{2}} \\biggr) \\\\ &\\qquad {} +\\varPsi \\biggl(r(m)+ \\frac{\\mu (m)\\varPsi }{1+\\lambda (m)\\varPsi }- \\frac{\\varPsi ^{2}}{1+\\lambda (m)\\varPsi } \\biggr). \\end{aligned}\n\nNote that\n\n\\begin{aligned}& \\lim_{\\varPsi \\rightarrow 0^{+}}\\zeta \\biggl(1- \\frac{\\zeta \\alpha _{m}}{2} \\biggr)\\varPsi \\biggl( \\frac{\\mu (m)}{1+\\lambda (m)\\varPsi }-\\frac{\\varPsi }{1+\\lambda (m)\\varPsi }- \\frac{\\eta _{2}^{2}(m)(\\zeta +1)\\varPsi }{2(1+\\lambda (m)\\varPsi )^{2}} \\biggr)=0, \\\\& \\lim_{\\varPsi \\rightarrow 0^{+}}\\varPsi ^{1+\\zeta } \\biggl(r(m)+ \\frac{\\mu (m)\\varPsi }{1+\\lambda (m)\\varPsi }- \\frac{\\varPsi ^{2}}{1+\\lambda (m)\\varPsi } \\biggr)=0. \\end{aligned}\n\nHence\n\n$$\\lim_{\\varPsi \\rightarrow 0^{+}} \\frac{\\mathcal{L}U_{4}(\\varPsi ,m)}{\\varPsi ^{-\\zeta }}=-\\zeta \\biggl(1- \\frac{\\zeta \\alpha _{m}}{2} \\biggr) \\biggl(\\bar{\\chi }-\\frac{\\zeta }{2} \\eta _{1}^{2}(m)+\\frac{\\zeta \\alpha _{m}/2}{1-\\zeta \\alpha _{m}/2}\\bigl( \\bar{\\chi }-\\chi (m)\\bigr) \\biggr)=:-h_{m}.$$\n\nBy (14), $$h_{m}>0$$, therefore\n\n$$\\lim_{\\varPsi \\rightarrow 0^{+}} \\frac{\\mathcal{L}U_{4}(\\varPsi ,m)}{h_{m}\\varPsi ^{-\\zeta }}=-1.$$\n(15)\n\nFurthermore,\n\n$$\\lim_{\\varPsi \\rightarrow +\\infty } \\frac{\\mathcal{L}U_{4}(\\varPsi ,m)}{\\frac{\\varPsi ^{3}}{1+\\lambda (m)\\varPsi }}=-1.$$\n(16)\n\nOn the basis of (15) and (16), one can find $$a_{1}<1$$ such that, for $$\\varPsi \\in (0, a_{1}]\\cup [1/a_{1},+\\infty )$$, $$\\mathcal{L}U_{4}(\\varPsi ,m)\\leq -1$$. Accordingly, for $$\\forall (\\varPsi ,m) \\in \\{(0, a_{1}]\\cup [1/a_{1},+\\infty )\\}\\times \\varTheta$$,\n\n$$\\mathcal{L}U_{4}(\\varPsi ,m)\\leq -1.$$\n\nWe then deduce from Lemma 3 and Lemma 4 that model (3) possesses a UESD. □\n\n## 4 Real world applications\n\nIn this section we employ the theoretical outcomes (i.e., Theorems 1, 2, and 3) to evaluate the evolution of the African wild dog (Lycaon pictus) in Africa. In accordance with prior investigations [4, 9], $$r\\in [-0.19,0.49]$$, $$\\mu =3$$, and $$\\lambda \\in [3,52]$$. The present study chooses $$\\varTheta =\\{1,2\\}$$, $$r\\equiv 0.15$$, $$\\mu \\equiv 3$$, $$\\lambda \\equiv 25$$, $$\\eta _{1}^{2}(1)=0.6$$, $$\\eta _{1}^{2}(2)=0.2$$, $$\\eta _{2}^{2}\\equiv 0.16$$. Hence\n\n\\begin{aligned}& \\chi (1)=r(1)-\\eta _{1}^{2}(1)/2=-0.15,\\qquad \\chi (2)=0.05, \\\\& \\bar{\\varPi }=\\varPi (1)=\\varPi (2)=\\mu /\\lambda -2(\\sqrt{1+\\lambda \\mu }-1)/ \\lambda ^{2}=0.095. \\end{aligned}\n\nDue to the fact that $$\\chi (1)+\\varPi (1)<0$$, Theorem 1 implies that the dogs in state 1 become extinct (see Fig. 1(a), which manifests that the extinction happens in about 85 years), and accordingly, state 1 is an extinction state. At the same time, note that $$\\chi (2)>0$$, Theorem 2 and Theorem 3 indicate that this species in state 2 is SP and possesses a UESD (see Fig. 1(b)), and accordingly, state 2 is a persistence state. Figures 1(a) and 1(b) reflect that the puny undulations on the growth rate bring a hazard of extinction for the dogs. Let us now choose different values of σ.\n\n1. (i)\n\nLet $$\\sigma =(0.8,0.2)$$. Compute that $$\\bar{\\chi }+\\bar{\\varPi }=-0.015<0$$. Thus Theorem 1 implies that the dogs in system (3) become extinct (see Fig. 1(c), which manifests that the extinction happens in about 105 years).\n\n2. (ii)\n\nLet $$\\sigma =(0.2,0.8)$$. Compute that $$\\bar{\\chi }=0.01>0$$. Thus Theorem 2 and Theorem 3 indicate that this species in system (3) is SP and possesses a UESD (see Fig. 1(d)).\n\nFigures 1(c) and 1(d) reflect that if the medium undulations expend much time on the extinction states such that $$\\bar{\\chi }+\\bar{\\varPi }<0$$, then the dogs are in danger; if the medium undulations expend much time on the persistence states such that $$\\bar{\\chi }>0$$, then the dogs are secure.\n\n## 5 Conclusions\n\nEvaluating the functions of environmental undulations on the evolution of species is an attractive topic in ecology . The present study has taken advantage of the white noise and the Markovian switching to portray the puny undulations and medium undulations in the environment, respectively, and has put forward a stochastic population model with Allee effects under regime switching. For this model, the criteria for extinction, persistence, and the existence of a UESD have been offered. The findings uncover that these properties of system (3) highly correlate with the environmental undulations.\n\n• Since\n\n\\begin{aligned}& \\bar{\\chi }=\\sum_{m\\in \\varTheta }\\sigma _{m} \\chi (m), \\qquad \\bar{\\varPi }= \\sum_{m\\in \\varTheta }\\sigma _{m} \\biggl[\\frac{\\mu (m)}{\\lambda (m)} - \\frac{2(\\sqrt{1+\\lambda (m)\\mu (m)}-1)}{\\lambda ^{2}(m)} \\biggr], \\\\& \\chi (m)=r(m)-\\frac{\\eta _{1}^{2}(m)}{2}, \\end{aligned}\n\nthen for each $$m\\in \\varTheta$$\n\n$$\\frac{\\mathrm{d}(\\bar{\\chi }+\\bar{\\varPi })}{\\mathrm{d}\\eta _{1}^{2}(m)}=- \\frac{\\sigma _{m}}{2}\\leq 0.$$\n\nAccordingly, the puny undulations on the growth rate bring a hazard of extinction. This is consistent with the prior studies (see, e.g., ).\n\n• If the Markov chain $$\\theta (t)$$ expends much time on the persistence states such that $$\\bar{\\chi }>0$$, then model (3) is persistent and possesses a UESD; if $$\\theta (t)$$ expends much time on the extinction states such that $$\\bar{\\chi }+\\bar{\\varPi }<0$$, then the species represented by system (3) is dangerous.\n\nAt the end of this paper, we would like to mention that we have not examined the case $$\\bar{\\chi }+\\bar{\\varPi }>0>\\bar{\\chi }$$. In this case, the results are too complicated to research at the present stage. This issue deserves a fuller treatment in subsequent analyses.\n\n## References\n\n1. Aguirre, P., González-Olivares, E., Torres, S.: Stochastic predator–prey model with Allee effect on prey. Nonlinear Anal., Real World Appl. 14, 768–779 (2013)\n\n2. Allee, W.: Animal Aggregations: A Study in General Sociology. University of Chicago Press, Chicago (1931)\n\n3. Arctic Climate Impact Assessment: Impacts of a Warming Arctic—Arctic Climate Impact Assessment. Cambridge University Press, Cambridge (2004)\n\n4. Bach, L., Pedersen, R., Hayward, M., Stagegaard, J., Loeschcke, V., Pertoldi, C.: Assessing re-introductions of the African Wild dog (Lycaon pictus) in the Limpopo Valley Conservancy, South Africa, using the stochastic simulation program VORTEX. J. Nat. Conserv. 18, 237–246 (2010)\n\n5. Boukal, D., Berec, L.: Single-species models of the Allee effect: extinction boundaries, sex ratios and mate encounters. J. Theor. Biol. 218, 375–394 (2002)\n\n6. Clutton-Brock, T., Gaynor, D., McIlrath, G., MacColl, A., et al.: Predation, group size and mortality in a cooperative mongoose, Suricata suricatta. J. Anim. Ecol. 68, 672–683 (1999)\n\n7. Courchamp, F., Berec, L., Gascoigne, J.: Allee Effects in Ecology and Conservation. Oxford University Press, London (2008)\n\n8. Cushing, J., Hudson, J.: Evolutionary dynamics and strong Allee effects. J. Biol. Dyn. 6, 941–958 (2012)\n\n9. Jovanović, M., Krstić, M.: The influence of time-dependent delay on behavior of stochastic population model with the Allee effect. Appl. Math. Model. 39, 733–746 (2015)\n\n10. Jovanović, M., Krstić, M.: Extinction in stochastic predator–prey population model with Allee effect on prey. Discrete Contin. Dyn. Syst., Ser. B 22, 2651–2667 (2017)\n\n11. Kang, Y.: Dynamics of a generalized Ricker–Beverton–Holt competition model subject to Allee effects. J. Differ. Equ. Appl. 22, 687–723 (2016)\n\n12. Li, X., Jiang, D., Mao, X.: Population dynamical behavior of Lotka–Volterra system under regime switching. J. Comput. Appl. Math. 232, 427–448 (2009)\n\n13. Li, D., Liu, M.: Invariant measure of a stochastic food-limited population model with regime switching. Math. Comput. Simul. 178, 16–26 (2020)\n\n14. Liebhold, A., Bascompte, J.: The Allee effect, stochastic dynamics and the eradication of alien species. Ecol. Lett. 6, 133–140 (2003)\n\n15. Liu, M., Bai, C.: Optimal harvesting of a stochastic mutualism model with regime-switching. Appl. Math. Comput. 375, 125040 (2020)\n\n16. Liu, M., Deng, M.: Analysis of a stochastic hybrid population model with Allee effect. Appl. Math. Comput. 364, 124582 (2020)\n\n17. Liu, C., Li, H., Cheung, L.: Weak persistence of a stochastic delayed competition system with telephone noise and Allee effect. Appl. Math. Lett. 103, 106186 (2020)\n\n18. Mao, X., Yuan, C.: Stochastic Differential Equations with Markovian Switching. Imperial College Press, London (2006)\n\n19. Panik, M.: Stochastic Differential Equations: An Introduction with Applications in Population Dynamics Modeling. Wiley, New York (2017)\n\n20. Rinella, D., Wipfli, M., Stricker, C., et al.: Pacific salmon (Oncorhynchus spp.) runs and consumer fitness: growth and energy storage in stream-dwelling salmonids increase with salmon spawner density. Can. J. Fish. Aquat. Sci. 69, 73–84 (2012)\n\n21. Takeuchi, Y.: Global Dynamical Properties of Lotka–Volterra Systems. World Scientific, Singapore (1996)\n\n22. Tobin, P., Berec, L., Liebhold, A.: Exploiting Allee effects for managing biological invasions. Ecol. Lett. 14, 615–624 (2011)\n\n23. Wang, K.: Stochastic Mathematical Biology Models. Science Press, Beijing (2010)\n\n24. Yin, G., Zhu, C.: Hybrid Switching Diffusions: Properties and Applications. Springer, New York (2010)\n\n### Acknowledgements\n\nWe are very grateful to the referees for their careful reading and very valuable comments, which led to an improvement of our paper.\n\n### Availability of data and materials\n\nData sharing not applicable to this article as no datasets were generated or analysed during the current study.\n\n## Funding\n\nML thanks the National Natural Science Foundation of P.R. China (No. 11771174) and the Natural Science Foundation of Jiangsu Province (No. BK20170067), and “Qinglan Project” of Jiangsu Province, P.R. China.\n\n## Author information\n\nAuthors\n\n### Contributions\n\nWMJ mainly finished the writing of the whole content of the paper. ML mainly finished the establishment of the model. All authors read and approved the final manuscript.\n\n### Corresponding author\n\nCorrespondence to Weiming Ji.\n\n## Ethics declarations\n\n### Competing interests\n\nThe authors declare that they have no competing interests.\n\n## Rights and permissions",
null,
""
] |
[
null,
"https://advancesincontinuousanddiscretemodels.springeropen.com/track/article/10.1186/s13662-020-02759-x",
null
] |
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http://jsxgraph.org/wiki/index.php?title=Extended_mean_value_theorem&oldid=6757
|
[
"# Extended mean value theorem\n\nThe extended mean value theorem (also called Cauchy's mean value theorem) is usually formulated as:\n\nLet\n\n$f, g: [a,b] \\to \\mathbb{R}$\n\nbe continuous functions that are differentiable on the open interval $(a,b)$. If $g'(x)\\neq 0$ for all $x\\in(a,b)$, then there exists a value $\\xi \\in (a,b)$ such that\n\n$\\frac{f'(\\xi)}{g'(\\xi)} = \\frac{f(b)-f(a)}{g(b)-g(b)}.$\n\nRemark: It seems to be easier to state the extended mean value theorem in the following form:\n\nLet\n\n$f, g: [a,b] \\to \\mathbb{R}$\n\nbe continuous functions that are differentiable on the open interval $(a,b)$. Then there exists a value $\\xi \\in (a,b)$ such that\n\n$f'(\\xi)\\cdot (g(b)-g(a)) = g'(\\xi) \\cdot (f(b)-f(b)).$\n\nThis second formulation avoids the need that $g'(x)\\neq 0$ for all $x\\in(a,b)$ and is therefore much easier to handle numerically.\n\nThe proof is similar, just use the function\n\n$h(x) = f(x)\\cdot(g(b)-g(a)) - (g(x)-g(a))\\cdot(f(b)-f(a))$\n\nand apply Rolle's theorem.\n\nVisualization The extended mean value theorem says that given the curve\n\n$C: [a,b]\\to\\mathbb{R}, \\quad t \\mapsto (f(t), g(t))$\n\nwith the above prerequisites for $f$ and $g$, there exists a $\\xi$ such that the tangent to the curve in the point $C(\\xi)$ is parallel to the secant through $C(a)$ and $C(b)$.\n\n### The underlying JavaScript code\n\nvar board = JXG.JSXGraph.initBoard('box', {boundingbox: [-5, 10, 7, -6], axis:true});\nvar p = [];\n\np = board.create('point', [0, -2], {size:2});\np = board.create('point', [-1.5, 5], {size:2});\np = board.create('point', [1, 4], {size:2});\np = board.create('point', [3, 3], {size:2});\n\n// Curve\nvar fg = JXG.Math.Numerics.Neville(p);\nvar graph = board.create('curve', fg, {strokeWidth:3, strokeOpacity:0.5});\n\n// Secant\nline = board.create('line', [p, p], {strokeColor:'#ff0000', dash:1});\n\nvar df = JXG.Math.Numerics.D(fg);\nvar dg = JXG.Math.Numerics.D(fg);\n\n// Usually, the extended mean value theorem is formulated as\n// df(t) / dg(t) == (p.X() - p.X()) / (p.Y() - p.Y())\n// We can avoid division by zero with that formulation:\nvar quot = function(t) {\nreturn df(t) * (p.Y() - p.Y()) - dg(t) * (p.X() - p.X());\n};\n\nvar r = board.create('glider', [\nfunction() { return fg(JXG.Math.Numerics.root(quot, (fg() + fg) * 0.5)); },\nfunction() { return fg(JXG.Math.Numerics.root(quot, (fg() + fg) * 0.5)); },\ngraph], {name: 'C(ξ)', size: 4, fixed:true, color: 'blue'});\n\nboard.create('tangent', [r], {strokeColor:'#ff0000'});"
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[
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https://socratic.org/questions/what-are-some-examples-of-decomposition-reactions
|
[
"# What are some examples of decomposition reactions?\n\nJan 19, 2015\n\nDecomposition reactions are chemical reactions in which a more complex molecule breaks down to make simpler ones. There are three types of decomposition reactions:\n\nThermal decomposition reactions;\nElctrolytic decomposition reactions;\nPhoto decomposition reactions.\n\nThermal decomposition - such reactions are usually endothermic, since energy in the form of heat is required to break the bonds of the more complex molecule. Examples include\n\n$C a C {O}_{3 \\left(s\\right)} + \\text{heat} \\to C a {O}_{\\left(s\\right)} + C {O}_{2 \\left(g\\right)}$ - calcium carbonate decomposes into calcium oxide and carbon dioxide when heated;\n\n$2 K C l {O}_{3 \\left(s\\right)} + \\text{heat} \\to 2 K C {l}_{\\left(s\\right)} + 3 {O}_{2 \\left(g\\right)}$ - potassium chlorate decomposes into potassium chloride and oxygen gas when ehated;\n\n$2 F e {\\left(O H\\right)}_{3} + \\text{heat} \\to F {e}_{2} {O}_{3} + 3 {H}_{2} O$ -ferric dioxide decomposes into ferric oxide and water when heated;\n\nElectrolytic decomposition - such reactions occur when an electric current is passed through an aqueous solution of a compound. Two classic examples are the electrolysis of water",
null,
"$2 {H}_{2} {O}_{\\left(l\\right)} \\to 2 {H}_{2 \\left(g\\right)} + {O}_{2 \\left(g\\right)}$ - water decomposes into hydrogen and oxygen in the presence of an electric current;\n\nand the decomposition of sodium chloride",
null,
"$2 N a C {l}_{\\left(l\\right)} \\to 2 N {a}_{\\left(l\\right)} + C {l}_{2 \\left(g\\right)}$ - molten sodium chloride will decompose into molten sodium and chlorine gas;\n\nPhoto decomposition - these reactions occur in the presence of light (photons). Examples include\n\n$2 A g C {l}_{\\left(s\\right)} + \\text{sunlight} \\to 2 A {g}_{\\left(s\\right)} + C {l}_{2 \\left(g\\right)}$ - silver chloride decomposes into silver and chlorine in the presence of sunlight;\n\n$2 A g B {r}_{\\left(s\\right)} + \\text{sunlight} \\to 2 A {g}_{\\left(s\\right)} + 2 C {l}_{2 \\left(g\\right)}$ - silver bromide decomposes into silver and chlorine in the presence of sunlight;\n\nAs a rule of thumb, most decomposition reactions are endothermic, since energy, either in the form of heat, electric current, or sunlight must be provided in order to break the bonds of the more complex molecule."
] |
[
null,
"https://d2jmvrsizmvf4x.cloudfront.net/a5HCiPwbT3uuFXqdgdXV_electrolysis.jpg",
null,
"https://d2jmvrsizmvf4x.cloudfront.net/9Q67HEB7RPq6ArUHb0wC_20_5.gif",
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http://www.cngyhl.cn/buy/show.php?itemid=320
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[
"",
null,
"# 自动包装机械,专业包装机械,专业机械,定制包装机械,定制机械,\n\n## 距离截止时间还剩：长期采购\n\n• 需求数量：1000\n• 包装需求：\n• 所在地：广东\n• 已有605人浏览",
null,
"• 暂无相关资料！\n\n### 产品详细说明\n\nr r r r r r r\nr r r r r r r r\n r r 售后服务：凡购买本公司的产品后,我们派专业技术人员到贵公司安装，调试及操作培训，至贵公司技术工能熟练操作。我公司的所有产品从你购买日起，保修期为一年，在保修期内，我公司派专业技术人员及时上门无偿维护，一切费用由我公司承担。实行终身跟宗服务制。我们以先进的专业技术和优良售后服务为客户解决一切后顾之忧，一旦承诺，终身相随。机器免费汽运到需方单位，需技术人员上门的能当天出发的，绝不拖到第二天。一年后配件如因使用不当造成破损，只收取成本费。r r r HS-250B HS-250D HS-250S 枕式包装机r",
null,
"r r r (一)主要性能和结构特点r 1.双变频器控制，袋长即设即切，无需调节空走，一步到位，省时省膜。r 2.人机界面，参数设定方便快捷。r 3.故障自诊断功能，故障显示一目了然。r 4.高感度光电眼色标跟踪，数字化输入封切位置，使封切位置更加准确。r 5.温度独立PID控制，更好适合各种包装材质。r 6.定位停机功能，不粘刀，不浪费包膜。r 7.传动系统简洁，工作更可靠，维护保养更方便。r 8.所有控制由软件实现，方便功能调整和技术升级，永不落后。 r r\nr r\n\nr r\n\nr\nr\n\nr r\n\nr r r r r r r\nr r r r r r r r\n r r r r (r r 二)适用范围r 适合于饼干、米通、雪饼、蛋黄派、巧克力、面包、方便面、月饼、药品、日用品、工业零件、纸盒或托盘等各类有规则物体的包装. r r",
null,
"r r r r",
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null,
"r r r r\nr r\n\nr r\n\nr\nr\n\nr r\n\nr r r r r r r\nr r r r r r r r\n r r r (三)选配装置r 1.打码机r 2.直纹中封轮r 3.网纹端封模r 4.超大触摸屏 r r\nr r\n\nr\nr\n\nr\nr\n\nr\nr\n\nr r r r r r r\nr r r r r r r r\nr\n\nr\nr (\n)技术规格 r\n\nr r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r\n r r 机型 r r r r HS-250Br r r r HS-250Dr r r r HS-250Sr r r r 薄膜宽度 r r r r Max.250mmr r r r Max.180mmr r r r 制袋长度r r r r 65～190mmr 120～280mmr r r r 90～220mmr r r r 45-90mmr r r r 制袋宽度r r r r 30～110mmr r r r 30-80mmr r r r 产品高度r r r r Max.40mmr r r r Max. 55mmr r r r Max.35mmr r r r 膜卷直径r r r r Max.320mmr r r r 包装速度r r r r 40～230包/分r r r r 60-330包/分r r r r 电源规格r r r r 220V,50/60HZ,2.4KVAr r r r 机器尺寸r r r r (L)3770×(W)670×(H)1450r r r r 机器质量r r r r 800Kgr r r r 备 注r r r r r r 有充气装置r r r r r r\nr\n\nr\nr\n\nr\nr r\n\nr\nr\n\nr\nr\n\nr\nr\n\nr\nr\nr\n\n1000 价格面议 广东\n\n### 相关询价单推荐\n\n• #### 高品质洗衣机械，工业\n\n采购数量100",
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null,
"价格需求：\n\n包装需求：\n\n来自[全国]的采购商\n\n已有548人浏览\n\n立即报价\n\n有效期至：长期有效\n\n• #### 自动包装机械,专业包\n\n采购数量1000",
null,
"价格需求：\n\n包装需求：\n\n来自[全国]的采购商\n\n已有605人浏览\n\n立即报价\n\n有效期至：长期有效"
] |
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null,
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null,
"http://i05.c.aliimg.com/img/ibank/2014/930/170/1525071039_108642416.jpg",
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"http://i04.c.aliimg.com/img/ibank/2013/212/422/1082224212_108642416.jpg",
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|
https://www.nag.com/numeric/nl/nagdoc_latest/clhtml/g01/g01conts.html
|
[
"# NAG CL InterfaceG01 (Stat)Simple Calculations on Statistical Data\n\nSettings help\n\nCL Name Style:\n\nG01 (Stat) Chapter Introduction – A description of the Chapter and an overview of the algorithms available.\n\nFunction\nMark of\nIntroduction\n\nPurpose\nMean, variance, skewness, kurtosis, etc., one variable, from frequency table\ng01aec 6 nag_stat_frequency_table\nFrequency table from raw data\ng01alc 4 nag_stat_five_point_summary\nFive-point summary (median, hinges and extremes)\ng01amc 9 nag_stat_quantiles\nQuantiles of a set of unordered values\ng01anc 23 nag_stat_quantiles_stream_fixed\nCalculates approximate quantiles from a data stream of known size\ng01apc 23 nag_stat_quantiles_stream_arbitrary\nCalculates approximate quantiles from a data stream of unknown size\ng01atc 24 nag_stat_summary_onevar\nComputes univariate summary information: mean, variance, skewness, kurtosis\ng01auc 24 nag_stat_summary_onevar_combine\nCombines multiple sets of summary information, for use after g01atc\ng01bjc 4 nag_stat_prob_binomial\nBinomial distribution function\ng01bkc 4 nag_stat_prob_poisson\nPoisson distribution function\ng01blc 4 nag_stat_prob_hypergeom\nHypergeometric distribution function\ng01dac 7 nag_stat_normal_scores_exact\nNormal scores, accurate values\ng01dcc 7 nag_stat_normal_scores_var\nNormal scores, approximate variance-covariance matrix\ng01ddc 4 nag_stat_test_shapiro_wilk\nShapiro and Wilk's $W$ test for Normality\ng01dhc 4 nag_stat_ranks_and_scores\nRanks, Normal scores, approximate Normal scores or exponential (Savage) scores\ng01eac 4 nag_stat_prob_normal\nProbabilities for the standard Normal distribution\ng01ebc 1 nag_stat_prob_students_t\nProbabilities for Student's $t$-distribution\ng01ecc 1 nag_stat_prob_chisq\nProbabilities for ${\\chi }^{2}$ distribution\ng01edc 1 nag_stat_prob_f\nProbabilities for $F$-distribution\ng01eec 1 nag_stat_prob_beta\nUpper and lower tail probabilities and probability density function for the beta distribution\ng01efc 1 nag_stat_prob_gamma\nProbabilities for the gamma distribution\ng01emc 7 nag_stat_prob_studentized_range\nComputes probability for the Studentized range statistic\ng01epc 7 nag_stat_prob_durbin_watson\nComputes bounds for the significance of a Durbin–Watson statistic\ng01erc 7 nag_stat_prob_vonmises\nComputes probability for von Mises distribution\ng01etc 7 nag_stat_prob_landau\nLandau distribution function\ng01euc 7 nag_stat_prob_vavilov\nVavilov distribution function\ng01ewc 25 nag_stat_prob_dickey_fuller_unit\nComputes probabilities for the Dickey–Fuller unit root test\ng01eyc 7 nag_stat_prob_kolmogorov1\nComputes probabilities for the one-sample Kolmogorov–Smirnov distribution\ng01ezc 7 nag_stat_prob_kolmogorov2\nComputes probabilities for the two-sample Kolmogorov–Smirnov distribution\ng01fac 4 nag_stat_inv_cdf_normal\nDeviates for the Normal distribution\ng01fbc 1 nag_stat_inv_cdf_students_t\nDeviates for Student's $t$-distribution\ng01fcc 1 nag_stat_inv_cdf_chisq\nDeviates for the ${\\chi }^{2}$ distribution\ng01fdc 1 nag_stat_inv_cdf_f\nDeviates for the $F$-distribution\ng01fec 1 nag_stat_inv_cdf_beta\nDeviates for the beta distribution\ng01ffc 1 nag_stat_inv_cdf_gamma\nDeviates for the gamma distribution\ng01fmc 7 nag_stat_inv_cdf_studentized_range\nComputes deviates for the Studentized range statistic\ng01ftc 7 nag_stat_inv_cdf_landau\nLandau inverse function $\\Psi \\left(x\\right)$\ng01gbc 6 nag_stat_prob_students_t_noncentral\nComputes probabilities for the non-central Student's $t$-distribution\ng01gcc 6 nag_stat_prob_chisq_noncentral\nComputes probabilities for the non-central ${\\chi }^{2}$ distribution\ng01gdc 6 nag_stat_prob_f_noncentral\nComputes probabilities for the non-central $F$-distribution\ng01gec 6 nag_stat_prob_beta_noncentral\nComputes probabilities for the non-central beta distribution\ng01hac 1 nag_stat_prob_bivariate_normal\nProbability for the bivariate Normal distribution\ng01hbc 6 nag_stat_prob_multi_normal\nComputes probabilities for the multivariate Normal distribution\ng01hcc 23 nag_stat_prob_bivariate_students_t\nComputes probabilities for the bivariate Student's $t$-distribution\ng01hdc 24 nag_stat_prob_multi_students_t\nComputes the probability for the multivariate Student's $t$-distribution\ng01jcc 7 nag_stat_prob_chisq_noncentral_lincomb\nComputes probability for a positive linear combination of ${\\chi }^{2}$ variables\ng01jdc 7 nag_stat_prob_chisq_lincomb\nComputes lower tail probability for a linear combination of (central) ${\\chi }^{2}$ variables\ng01kac 9 nag_stat_pdf_normal\nCalculates the value for the probability density function of the Normal distribution at a chosen point\ng01kfc 9 nag_stat_pdf_gamma\nCalculates the value for the probability density function of the gamma distribution at a chosen point\ng01kkc 23 nag_stat_pdf_gamma_vector\nComputes a vector of values for the probability density function of the gamma distribution\ng01kqc 23 nag_stat_pdf_normal_vector\nComputes a vector of values for the probability density function of the Normal distribution\ng01lbc 24 nag_stat_pdf_multi_normal_vector\nComputes a vector of values for the probability density function of the multivariate Normal distribution\ng01mbc 7 nag_stat_mills_ratio\nComputes reciprocal of Mills' Ratio\ng01mtc 7 nag_stat_pdf_landau\nLandau density function $\\varphi \\left(\\lambda \\right)$\ng01muc 7 nag_stat_pdf_vavilov\nVavilov density function ${\\varphi }_{V}\\left(\\lambda ;\\kappa ,{\\beta }^{2}\\right)$\nCumulants and moments of quadratic forms in Normal variables\nMoments of ratios of quadratic forms in Normal variables, and related statistics\ng01ptc 7 nag_stat_pdf_landau_moment1\nLandau first moment function ${\\Phi }_{1}\\left(x\\right)$\ng01qtc 7 nag_stat_pdf_landau_moment2\nLandau second moment function ${\\Phi }_{2}\\left(x\\right)$\ng01rtc 7 nag_stat_pdf_landau_deriv\nLandau derivative function ${\\varphi }^{\\prime }\\left(\\lambda \\right)$\ng01sac 23 nag_stat_prob_normal_vector\nComputes a vector of probabilities for the standard Normal distribution\ng01sbc 23 nag_stat_prob_students_t_vector\nComputes a vector of probabilities for the Student's $t$-distribution\ng01scc 23 nag_stat_prob_chisq_vector\nComputes a vector of probabilities for ${\\chi }^{2}$ distribution\ng01sdc 23 nag_stat_prob_f_vector\nComputes a vector of probabilities for $F$-distribution\ng01sec 23 nag_stat_prob_beta_vector\nComputes a vector of probabilities for the beta distribution\ng01sfc 23 nag_stat_prob_gamma_vector\nComputes a vector of probabilities for the gamma distribution\ng01sjc 23 nag_stat_prob_binomial_vector\nComputes a vector of probabilities for the binomial distribution\ng01skc 23 nag_stat_prob_poisson_vector\nComputes a vector of probabilities for the Poisson distribution\ng01slc 23 nag_stat_prob_hypergeom_vector\nComputes a vector of probabilities for the hypergeometric distribution\ng01tac 23 nag_stat_inv_cdf_normal_vector\nComputes a vector of deviates for the standard Normal distribution\ng01tbc 23 nag_stat_inv_cdf_students_t_vector\nComputes a vector of deviates for Student's $t$-distribution\ng01tcc 23 nag_stat_inv_cdf_chisq_vector\nComputes a vector of deviates for ${\\chi }^{2}$ distribution\ng01tdc 23 nag_stat_inv_cdf_f_vector\nComputes a vector of deviates for $F$-distribution\ng01tec 23 nag_stat_inv_cdf_beta_vector\nComputes a vector of deviates for the beta distribution\ng01tfc 23 nag_stat_inv_cdf_gamma_vector\nComputes a vector of deviates for the gamma distribution\ng01wac 24 nag_stat_moving_average\nComputes the mean and standard deviation using a rolling window\ng01zuc 7 nag_stat_init_vavilov\nInitialization function for g01muc and g01euc"
] |
[
null
] |
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|
https://www.geogebra.org/m/PB5wwqh3
|
[
"# The pencil of conics\n\nSuppose we are given two conic equations and . Then the pencil of conics is the set of curves with equations , where and are arbitrary numbers.\nDrag around the foci that define the hyperbola and ellipse. You can also drag the conics around."
] |
[
null
] |
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|
https://es.mathworks.com/help/matlab/ref/matlab.unittest.qualifications.verifiable.verifytrue.html
|
[
"# verifyTrue\n\nClass: matlab.unittest.qualifications.Verifiable\nPackage: matlab.unittest.qualifications\n\nVerify value is true\n\n## Syntax\n\n``verifyTrue(testCase,actual)``\n``verifyTrue(testCase,actual,diagnostic)``\n\n## Description\n\nexample\n\n````verifyTrue(testCase,actual)` verifies that the value of `actual` is logical `1` (`true`).```\n\nexample\n\n````verifyTrue(testCase,actual,diagnostic)` also associates the diagnostic information in `diagnostic` with the qualification.```\n\n## Input Arguments\n\nexpand all\n\nTest case, specified as a `matlab.unittest.qualifications.Verifiable` object. Because the `matlab.unittest.TestCase` class subclasses `matlab.unittest.qualifications.Verifiable` and inherits its methods, `testCase` is typically a `matlab.unittest.TestCase` object.\n\nValue to test, specified as a value of any data type. Although you can provide a value of any data type, the test fails if `actual` is not a logical scalar with a value of `true`.\n\nDiagnostic information to display when the qualification passes or fails, specified as a string array, character array, function handle, or array of `matlab.automation.diagnostics.Diagnostic` objects.\n\nDepending on the test runner configuration, the testing framework can display diagnostics when the qualification passes or fails. By default, the framework displays diagnostics only when the qualification fails. You can override the default behavior by customizing the test runner. For example, use a `DiagnosticsOutputPlugin` instance to display both failing and passing event diagnostics.\n\nExample: `\"My Custom Diagnostic\"`\n\nExample: `@dir`\n\n## Attributes\n\n `Sealed` `true`\n\nTo learn about attributes of methods, see Method Attributes.\n\n## Examples\n\nexpand all\n\nCreate a test case for interactive testing.\n\n```testCase = matlab.unittest.TestCase.forInteractiveUse; ```\n\nTest `true`.\n\n```verifyTrue(testCase,true) ```\n```Verification passed. ```\n\nTest `false`.\n\n```verifyTrue(testCase,false) ```\n```Verification failed. --------------------- Framework Diagnostic: --------------------- verifyTrue failed. --> The value must evaluate to \"true\". Actual Value: logical 0 ------------------ Stack Information: ------------------ In C:\\work\\TestMATLABLogicalFunctionsExample.m (TestMATLABLogicalFunctionsExample) at 16 ```\n\nWhen you test using `verifyTrue`, the test fails if the actual value is not of type `logical`.\n\nCreate a test case for interactive testing.\n\n```testCase = matlab.unittest.TestCase.forInteractiveUse; ```\n\nTest the value `1`. The test fails because the value is of type `double`.\n\n```verifyTrue(testCase,1,\"Value must be a logical scalar.\") ```\n```Verification failed. ---------------- Test Diagnostic: ---------------- Value must be a logical scalar. --------------------- Framework Diagnostic: --------------------- verifyTrue failed. --> The value must be logical. It is of type \"double\". Actual Value: 1 ------------------ Stack Information: ------------------ In C:\\work\\TestANonzeroNumericValueExample.m (TestANonzeroNumericValueExample) at 14 ```\n\nWhen you test using `verifyTrue`, the test fails if the actual value is nonscalar.\n\nCreate a test case for interactive testing.\n\n```testCase = matlab.unittest.TestCase.forInteractiveUse; ```\n\nTest the value `[true true]`. The test fails because the value is nonscalar.\n\n```verifyTrue(testCase,[true true]) ```\n```Verification failed. --------------------- Framework Diagnostic: --------------------- verifyTrue failed. --> The value must be scalar. It has a size of [1 2]. Actual Value: 1×2 logical array 1 1 ------------------ Stack Information: ------------------ In C:\\work\\TestLogicalArraysExample.m (TestLogicalArraysExample) at 15 ```\n\n## Tips\n\n• `verifyTrue` is a convenience method. For example, `verifyTrue(testCase,actual)` is functionally equivalent to the following code.\n\n```import matlab.unittest.constraints.IsTrue testCase.verifyThat(actual,IsTrue) ```\n• `verifyTrue` might not provide the same level of strictness adhered to by other constraints such as `IsEqualTo`. In this example, the test using `verifyTrue` passes, but the test using `verifyEqual` fails.\n\n```actual = 5; expected = uint8(5); testCase = matlab.unittest.TestCase.forInteractiveUse; verifyTrue(testCase,isequal(actual,expected)) % Test passes verifyEqual(testCase,actual,expected) % Test fails ```\n\nIn general, `verifyTrue` runs faster than `IsEqualTo` but is less strict and provides less diagnostic information in the event of a failure.\n\n• An alternative to `verifyTrue` is the `verifyReturnsTrue` method. `verifyTrue` runs faster and is easier to use, but `verifyReturnsTrue` provides slightly better diagnostic information. In this example, both tests fail, but the second test displays the function handle as part of the diagnostics.\n\n```actual = 1; expected = 2; testCase = matlab.unittest.TestCase.forInteractiveUse; verifyTrue(testCase,isequal(actual,expected)) verifyReturnsTrue(testCase,@()isequal(actual,expected))```\n• Use verification qualifications to produce and record failures without throwing an exception. Since verifications do not throw exceptions, all test content runs to completion even when verification failures occur. Typically, verifications are the primary qualification for a unit test, since they typically do not require an early exit from the test. Use other qualification types to test for violation of preconditions or incorrect test setup:\n\n• Use assumption qualifications to ensure that the test environment meets preconditions that otherwise do not result in a test failure. Assumption failures result in filtered tests, and the testing framework marks the tests as `Incomplete`. For more information, see `matlab.unittest.qualifications.Assumable`.\n\n• Use assertion qualifications when the failure condition invalidates the remainder of the current test content, but does not prevent proper execution of subsequent tests. A failure at the assertion point renders the current test as `Failed` and `Incomplete`. For more information, see `matlab.unittest.qualifications.Assertable`.\n\n• Use fatal assertion qualifications to abort the test session upon failure. These qualifications are useful when the failure is so fundamental that continuing testing does not make sense. Fatal assertion qualifications are also useful when fixture teardown does not restore the environment state correctly, and aborting testing and starting a fresh session is preferable. For more information, see `matlab.unittest.qualifications.FatalAssertable`.\n\n## Version History\n\nIntroduced in R2013a"
] |
[
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|
https://percentagecalculator.pro/How-much-is_65_percent-of_1400_Pounds
|
[
"# 65 percent of 1400 Pounds\n\n### Percentage Calculator\n\nWhat is % of Answer:\n\n### Percentage Calculator 2\n\nis what percent of ? Answer: %\n\n### Percentage Calculator 3\n\nis % of what? Answer:\n\nWe think you reached us looking for answers like: What is 65 (65%) percent (%) of 1400 (1400)? Or may be: 65 percent of 1400 Pounds. See the solutions to these problems below.\n\n## How to work out percentages - Step by Step\n\nHere are the solutions to the questions stated above:\n\n### 1) What is 65% of 1400?\n\nAlways use this formula to find a percentage:\n\n% / 100 = Part / Whole replace the given values:\n\n65 / 100 = Part / 1400\n\nCross multiply:\n\n65 x 1400 = 100 x Part, or\n\n91000 = 100 x Part\n\nNow, divide by 100 and get the answer:\n\nPart = 91000 / 100 = 910\n\n### 2) 65 is what percent of 1400?\n\nUse again the same percentage formula:\n\n% / 100 = Part / Whole replace the given values:\n\n% / 100 = 65 / 1400\n\nCross multiply:\n\n% x 1400 = 65 x 100\n\nDivide by 1400 and get the percentage:\n\n% = 65 x 100 / 1400 = 4.6428571428571%"
] |
[
null
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{"ft_lang_label":"__label__en","ft_lang_prob":0.82637036,"math_prob":0.99378383,"size":819,"snap":"2019-13-2019-22","text_gpt3_token_len":261,"char_repetition_ratio":0.16564417,"word_repetition_ratio":0.0882353,"special_character_ratio":0.43956044,"punctuation_ratio":0.11445783,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.999813,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-05-24T05:37:28Z\",\"WARC-Record-ID\":\"<urn:uuid:c02afae7-13de-4b5c-a89a-0b10b387fad2>\",\"Content-Length\":\"26830\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:6718b281-6580-45a5-b76e-0d736c15f00d>\",\"WARC-Concurrent-To\":\"<urn:uuid:b64a98e8-046a-4b60-ad28-bef02ce08835>\",\"WARC-IP-Address\":\"104.18.32.170\",\"WARC-Target-URI\":\"https://percentagecalculator.pro/How-much-is_65_percent-of_1400_Pounds\",\"WARC-Payload-Digest\":\"sha1:SUBJIRGF6RFQB6M4CBB7LOO3DSDRQ3EU\",\"WARC-Block-Digest\":\"sha1:VZBFUT6MBX2RATU5TN5YLKZBSTIGS67Q\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-22/CC-MAIN-2019-22_segments_1558232257514.68_warc_CC-MAIN-20190524044320-20190524070320-00029.warc.gz\"}"}
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https://geek-workshop.com/thread-38486-1-1.html
|
[
"##",
null,
"帐号 自动登录 找回密码 密码 注册\n 搜索\n\n# 8F328U在使用 delayMicroseconds()時會很不準",
null,
"发表于 2019-4-18 14:58:27 | 显示全部楼层 |阅读模式\n 本帖最后由 eddiewwm 于 2019-4-18 15:11 编辑 實測 8F328U在使用 delayMicroseconds()時會很不準，會快很多，delay 1000us時，得出的約是 765us。 可參考網上的文章 https://www.arduino.cn/thread-12468-1-1.html 作出改進。 LGT 原來在 wiring.c 中的設定為： /* Delay for the given number of microseconds. Assumes a 1, 8, 12, 16, 20 or 24 MHz clock. */ void delayMicroseconds(unsigned int us) { // call = 4 cycles + 2 to 4 cycles to init us(2 for constant delay, 4 for variable) // calling avrlib's delay_us() function with low values (e.g. 1 or // 2 microseconds) gives delays longer than desired. //delay_us(us); #if F_CPU >= 24000000L // for the 24 MHz clock for the aventurous ones, trying to overclock // zero delay fix if (!us) return; // = 3 cycles, (4 when true) // the following loop takes a 1/6 of a microsecond (4 cycles) // per iteration, so execute it six times for each microsecond of // delay requested. us *= 6; // x6 us, = 7 cycles // account for the time taken in the preceeding commands. // we just burned 22 (24) cycles above, remove 5, (5*4=20) // us is at least 6 so we can substract 5 us -= 5; //=2 cycles #elif F_CPU >= 20000000L // for the 20 MHz clock on rare Arduino boards // for a one-microsecond delay, simply return. the overhead // of the function call takes 18 (20) cycles, which is 1us __asm__ __volatile__ ( \"nop\" \"\\n\\t\" \"nop\" \"\\n\\t\" \"nop\" \"\\n\\t\" \"nop\"); //just waiting 4 cycles if (us <= 1) return; // = 3 cycles, (4 when true) // the following loop takes a 1/5 of a microsecond (4 cycles) // per iteration, so execute it five times for each microsecond of // delay requested. us = (us << 2) + us; // x5 us, = 7 cycles // account for the time taken in the preceeding commands. // we just burned 26 (28) cycles above, remove 7, (7*4=28) // us is at least 10 so we can substract 7 us -= 7; // 2 cycles #elif F_CPU >= 16000000L // for the 16 MHz clock on most Arduino boards // for a one-microsecond delay, simply return. the overhead // of the function call takes 14 (16) cycles, which is 1us if (us <= 1) return; // = 3 cycles, (4 when true) // the following loop takes 1/4 of a microsecond (4 cycles) // per iteration, so execute it four times for each microsecond of // delay requested. us <<= 2; // x4 us, = 4 cycles // account for the time taken in the preceeding commands. // we just burned 19 (21) cycles above, remove 5, (5*4=20) // us is at least 8 so we can substract 5 us -= 5; // = 2 cycles, #elif F_CPU >= 12000000L // for the 12 MHz clock if somebody is working with USB // for a 1 microsecond delay, simply return. the overhead // of the function call takes 14 (16) cycles, which is 1.5us if (us <= 1) return; // = 3 cycles, (4 when true) // the following loop takes 1/3 of a microsecond (4 cycles) // per iteration, so execute it three times for each microsecond of // delay requested. us = (us << 1) + us; // x3 us, = 5 cycles // account for the time taken in the preceeding commands. // we just burned 20 (22) cycles above, remove 5, (5*4=20) // us is at least 6 so we can substract 5 us -= 5; //2 cycles #elif F_CPU >= 8000000L // for the 8 MHz internal clock // for a 1 and 2 microsecond delay, simply return. the overhead // of the function call takes 14 (16) cycles, which is 2us if (us <= 2) return; // = 3 cycles, (4 when true) // the following loop takes 1/2 of a microsecond (4 cycles) // per iteration, so execute it twice for each microsecond of // delay requested. us <<= 1; //x2 us, = 2 cycles // account for the time taken in the preceeding commands. // we just burned 17 (19) cycles above, remove 4, (4*4=16) // us is at least 6 so we can substract 4 us -= 4; // = 2 cycles #else // for the 1 MHz internal clock (default settings for common Atmega microcontrollers) // the overhead of the function calls is 14 (16) cycles if (us <= 16) return; //= 3 cycles, (4 when true) if (us <= 25) return; //= 3 cycles, (4 when true), (must be at least 25 if we want to substract 22) // compensate for the time taken by the preceeding and next commands (about 22 cycles) us -= 22; // = 2 cycles // the following loop takes 4 microseconds (4 cycles) // per iteration, so execute it us/4 times // us is at least 4, divided by 4 gives us 1 (no zero delay bug) us >>= 2; // us div 4, = 4 cycles #endif // busy wait __asm__ __volatile__ ( \"1: sbiw %0,1\" \"\\n\\t\" // 2 cycles \"brne 1b\" : \"=w\" (us) : \"0\" (us) // 2 cycles ); // return = 4 cycles } 复制代码 針對 8F328U 板用的是 16MHz主頻 作出了以下的更改 #elif F_CPU >= 16000000L ....... us = (us << 2) ; // x5 us, = 7 cycles delay 1000us 時得到的是 ： us = (us << 2); // x ==> 765us us = (us << 2) + us; // x ==> 954us us *= 6; // x ==> 1140us 在不作任何改動下，就祇能乘以系數 1.31 作補償了。\n\n 本版积分规则 回帖后跳转到最后一页\n\nGMT+8, 2019-11-19 14:20 , Processed in 0.042862 second(s), 24 queries ."
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https://stats.stackexchange.com/questions/367372/compare-ks-test-and-wasserstein-distance-or-earth-movers-distance
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[
"# Compare KS test and Wasserstein distance or Earth mover's distance\n\nConsider two sets of data points A and B. Both these data points are from mixture of unknown number of Gaussians. The mean of the Gaussians are little different for each set (there may have few overlap or very close separated mean values). However for both cases the variance of all the Gaussians are small. Now, if we give a set of data point say C, how to estimate C is from A or from from B? I understand there are many methods to do so: is there a way tell the most efficient method? This is a very board question, so specifically can we compare the KS test https://en.wikipedia.org/wiki/Kolmogorov%E2%80%93Smirnov_test and https://en.wikipedia.org/wiki/Wasserstein_metric for this problem? Is there a way to prove that KS test/Wasserstein metric would give better estimate?\n\nIt appears to me that Cumulative distribution is not smooth so Wasserstein metric would be better, is it true?\n\n• A few questions. 1) You refer to A and B as sets of distributions, then later as distributions themselves--which case are you asking about? 2) What does it mean to to estimate whether a distribution is from another distribution? 3) Since you use the word estimate, are these distributions themselves fit to sampled datapoints? It might help clarify things to say a little more about the goals of this analysis Sep 18, 2018 at 2:54\n• @user20160 Thanks a lot, very good point. Is it clear now? Sep 18, 2018 at 3:01\n• Yes, it's clearer now. Two remaining questions. 1) Are A and B known to be generated by different distributions? 2) \"how to estimate C is from A or from from B?\" Does this mean you want to determine whether C was generated by the same distribution that generated A or the one that generated B? On a related note: do you know that C was definitely generated by one of these two distributions (but are uncertain as to which)? Sep 18, 2018 at 3:54\n• @user20160 Yes to 1). A and B are known to generate from different distribution (physically different but close) 2) yes, I want to know from where C was generated. Yes, it must be generated either form A or B no other. Sep 18, 2018 at 3:59\n• Sep 18, 2021 at 22:49"
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http://mymathforum.com/algebra/9008-momentum.html
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[
"Algebra Pre-Algebra and Basic Algebra Math Forum\n\n October 9th, 2009, 05:34 PM #1 Newbie Joined: Oct 2009 Posts: 2 Thanks: 0 Momentum? The question: In reconstructing an automobile accident, investigators study the total momentum, both before and after the accident, of the vehicles involved. The total momentum of two vehicles moving in the same direction is found by multiplying the weight of each vehicle by its speed and then adding the results. For example, if one vehicle weighs 3000 pounds and is traveling at 35 miles per hour, and another weighs 2500 pounds and is traveling at 45 miles per hour in the same direction, then the total momentum is 3000 multiplied by 35 + 2500 multiplied by 45 = 217,500. In this exercise we study a collision in which a vehicle weighing 3720 pounds ran into the rear of a vehicle weighing 2480 pounds. (a) After the collision, the larger vehicle was traveling at 30 miles per hour, and the smaller vehicle was traveling at 50 miles per hour. Find the total momentum of the vehicles after the collision. 235600 (b) The smaller vehicle was traveling at 20 miles per hour before the collision, but the speed V, in miles per hour, of the larger vehicle before the collision is unknown. Find a formula expressing the total momentum of the vehicles (B) before the collision as a function of V. B= (c) The principle of conservation of momentum states that the total momentum before the collision equals the total momentum after the collision. Using this principle with parts (a) and (b), determine at what speed the larger vehicle was traveling before the collision. (Enter your answer to the nearest whole number.) ___mph",
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"October 9th, 2009, 08:28 PM #2 Global Moderator Joined: Dec 2006 Posts: 21,105 Thanks: 2324 Where are you stuck?",
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"Tags momentum",
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"Thread Tools",
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"Show Printable Version",
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"Email this Page Display Modes",
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"Linear Mode",
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"Switch to Hybrid Mode",
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"Switch to Threaded Mode",
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"Similar Threads Thread Thread Starter Forum Replies Last Post Nazz Algebra 6 January 14th, 2014 03:10 PM boomer029 Physics 0 October 16th, 2012 09:47 PM azizlwl Physics 4 March 24th, 2012 04:37 AM johnny Physics 5 February 9th, 2008 06:28 PM axelle Physics 1 December 18th, 2007 07:08 AM\n\n Contact - Home - Forums - Cryptocurrency Forum - Top",
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https://viva64.com/en/w/v724/
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[
" V724. Converting integers or pointers to BOOL can lead to a loss of high-order bits. Non-zero value can become 'FALSE'.",
null,
"",
null,
"# V724. Converting integers or pointers to BOOL can lead to a loss of high-order bits. Non-zero value can become 'FALSE'.\n\nThe analyzer has detected an issue when casting pointers or integer variables to the BOOL type may cause a loss of the most significant bits. As a result, a non-zero value which actually means TRUE may unexpectedly turn to FALSE.\n\nIn programs, the BOOL (gboolean, UBool, etc.) type is interpreted as an integer type. Any value other than zero is interpreted as true, and zero as false. Therefore, a loss of the most significant bits resulting from type conversion will cause an error in the program execution logic.\n\nFor example:\n\n``````typedef long BOOL;\n__int64 lLarge = 0x12300000000i64;\nBOOL bRes = (BOOL) lLarge;``````\n\nIn this code, a non-zero variable is truncated to zero when being cast to BOOL, which renders it FALSE.\n\nHere are a few other cases of improper type conversion:\n\n``````int *p;\nsize_t s;\nlong long w;\nBOOL x = (BOOL)p;\nBOOL y = s;\nBOOL z = (BOOL)s;\nBOOL q = (BOOL)w;``````\n\nTo fix errors like these, we need to perform a check for a non-zero value before BOOL conversion.\n\nHere are the various ways to fix these issues:\n\n``````int *p;\nsize_t s;\nlong long w;\nBOOL x = p != nullptr;\nBOOL y = s != 0;\nBOOL z = s ? TRUE : FALSE;\nBOOL q = !!w;``````\n According to Common Weakness Enumeration, potential errors found by using this diagnostic are classified as CWE-197.\n You can look at examples of errors detected by the V724 diagnostic.\n\n411\n14 100\n\n### Do you make errors in the code?",
null,
""
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https://mathhelpboards.com/threads/specific-example-of-eisensteins-theorem-using-r-z.4899/
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[
"# Specific example of Eisenstein's Theorem using R = Z\n\n#### Peter\n\n##### Well-known member\nMHB Site Helper\nEisenstein's Criterion is stated in Dummit and Foote as follows: (see attachment)\n\n-----------------------------------------------------------------------------------\n\nProposition 13 (Eisenstein's Criterion) Let P be a prime ideal of the integral domain R and let\n\n[TEX] f(x) = x^n + a_{n-1}x^{n-1} + ... ... + a_1x + a_0 [/TEX]\n\nbe a polynomial in R[x] (here [TEX] n \\ge 1[/TEX] )\n\nSuppose [TEX] a_{n-1}, ... ... a_1, a_0 [/TEX] are all elements of P and suppose [TEX] a_0 [/TEX] is not an element of [TEX] P^2 [/TEX].\n\nThen f(x) is irreducible in R[x]\n\n------------------------------------------------------------------------------------\n\nThe beginning of the proof reads as follows:\n\nProof: Suppose f(x) were reducible, say f(x) = a(x)b(x) in R[x] where a(x) and b(x) are nonconstant polynomials.\n\nReducing the equation modulo P and using the assumptions on the coefficients of f(x) we obtain the equation [TEX] x^n = \\overline{a(x)b(x)}[/TEX] in (R/P)[x] where the bar denotes polynomials with coefficients reduced modulo P... .,.. etc. etc.\n\n-----------------------------------------------------------------------------------\n\nI will now take a specific example with R= Z as the integral domain concerned and P = (3) as the prime ideal in Z.\n\nAlso take (for example) $$\\displaystyle f(x) = x^3 + 9x^2 + 21x + 9 = (x+3) (x^2 +6x + 3)$$\n\nNow as the proof requires, reduce f(x) mod P\n\nNow using D&F Proposition 2 (see attached) - namely $$\\displaystyle R[x]/(I) \\cong R/I)[x]$$ we have\n\n$$\\displaystyle Z[x]/(3) \\cong (Z/(3))[x]$$\n\nand so we to obtain $$\\displaystyle \\overline{f(x)}$$ we simply reduce the coefficients of f(x) by mod 3\n\nSince $$\\displaystyle 9, 21 \\in \\overline{0}$$\n\nwe have $$\\displaystyle \\overline{f(x)} = \\overline{x^3}$$\n\nThe coset $$\\displaystyle \\overline{f(x)}$$ would include elements such as $$\\displaystyle x^3 + 3, x^3 + 6x^2 + 24x - 3, ... ...$$ and so on.\n\nCan someone please confirm my working in this particular case of the Eisenstein proof is correct?\n\nPeter\n\n[This post is also on MHF]\n\nLast edited:\n\n#### Opalg\n\n##### MHB Oldtimer\nStaff member\nTo discuss this example in terms of Eisenstein's Criterion, you need to point out that neither the hypothesis nor the conclusion of Eisenstein's theorem is satisfied here. The coefficients $9$ and $21$ are both multiples of $3$, but the constant term $9$ is a multiple of $3^2$ (contrary to Eisenstein's Criterion). And the polynomial $f(x)$ is not irreducible because it factorises as $(x+3) (x^2 +6x + 3)$.\n\n#### Peter\n\n##### Well-known member\nMHB Site Helper\nTo discuss this example in terms of Eisenstein's Criterion, you need to point out that neither the hypothesis nor the conclusion of Eisenstein's theorem is satisfied here. The coefficients $9$ and $21$ are both multiples of $3$, but the constant term $9$ is a multiple of $3^2$ (contrary to Eisenstein's Criterion). And the polynomial $f(x)$ is not irreducible because it factorizes as $(x+3) (x^2 +6x + 3)$.\nThanks Opalg.\n\nRegarding my specific example, I think that my post was not completely clear in what I was attempting to demonstrate. I was taking a specific example and following the D&F proof on D&F page 310 - see attached - which assumes that f(x) is reducible and then proceeds to reduce f(x) modulo P. So, I took a reducible polynomial that (I thought) followed the Eisenstein rules for coefficients and then was focussed on showing how this led to the equation $$\\displaystyle f(x) = \\overline{a(x)b(x)}$$ when f(x) is reduced modulo P.\n\nMind you as you point out I was wrong in allowing $$\\displaystyle a_0 \\in P^2$$. I am not sure it would really alter my exercise in establishing $$\\displaystyle f(x) = \\overline{a(x)b(x)}$$but I probably should have taken (say) $$\\displaystyle f(x) = x^3 + 9x^2 + 24x + 18 = (x +3)(x^2 + 6x + 6)$$ and then moved on (in parallel with or following the steps of D&F's proof to show that $$\\displaystyle f(x) = \\overline{a(x)b(x)}$$ - since it is these steps that bother me.\n\n*** Reflecting on the proof, I am confused by the following:\n\nIn D&F page 310 (see attached) we find the following:\n\n\"Suppose F(x) were reducible, say f(x) = a(x)b(x) in R[x], where a(x) and b(x) are nonconstant polynomials. Reducing the equation modulo P and using the assumptions on the coefficients we obtain the equation $$\\displaystyle f(x) = \\overline{a(x)b(x)}$$ in (R/P)[x] ... ... etc\n\nMy confusion is as follows:\n\nP is a prime ideal in R (in my specific example P + (3) is a prime ideal in R = Z)\n\nBUT!\n\nP is not an ideal in R[x] --> so how can we reduce the equation f(x) = a(x)b(x) which is in R[x] by an ideal P which is not even in R[x]???\n\nI would be extremely grateful if someone could clarify this situation for me\n\nPeter"
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http://msubbu.in/ChemicalEngg_Resources/qb/appmath/appmath-problems.htm
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[
"### Applied Mathematics in Chemical Engineering\n\n1. Three tanks of 10,000 gal capacity are each arranged so that when water is fed into the first tank an equal quantity of solution overflows from the first tank to the second tank, likewise from the second to the third, and from third to some point out of the system. Agitators keep the contents of each tank uniform in concentration. To start, let each of the tanks be full of a solution of concentration Co lb/gal. Run water into the first tank at 50 gpm, and let the overflows function as above. Calculate the time required to reduce the concentration in the first tank to Co/10. Calculate the concentrations in the other two tanks at this time.\n2. A tank contains 100 ft3 of fresh water; 2 ft3 of brine, having a concentration of 1 % salt, is run into the tank per minute, and the mixture, kept uniform by mixing, runs out at the rate of 1 ft3/min. What will be the exit brine concentration when the tank contains 150 ft3 of brine?\n3. In an experimental study of saponification of methyl acetate by sodium hydroxide, it is found that 25% of the ester is converted to alcohol in 12 min when the initial concentrations of both ester and caustic are 0.01 M. What conversion of ester would be obtained in 1 hr if the initial ester concentration were 0.025 M and the initial caustic concentration were 0.015 M ?\n4. In a chemical reaction involving two substances, the velocity of transformation dx/dt at any time t is known to be equal to the product (0.9 - x) (0.4 - x). Express x interms of t, given that when t = 300, x = 0.3.\n5. A tank of volume 0.5 m3 is filled with brine containing 40 kg of dissolved salt. Water runs into the tank at the rate of 1.4 X 10-4 m3/sec and the mixture, kept uniform by stirring, runs out at the same rate. How much salt is in the tank after two hours?\n6. The number N of bacteria in a culture grows at a rate proportional to N. N = 100 at t = 0 and N = 332 at t = 1 hr. Find the value of N after 1.5 hrs.\n7. A compressed-air vessel has a volume of 10 ft3. Cooling coils hold its temperature constant at 70oF. The pressure now in the vessel is 100 psia. Air is flowing in at the rate of 10 lb/hr. How fast is the pressure increasing?\n8. A lake has a surface area of 100 km2. One river is bringing water into the lake at a rate of 10,000 m3/s, while another is taking water out at 8000m3/s. Evaporation and seepage are negligible. How fast is the level of the lake rising or falling? Answer: 72mm/h\n9. A vacuum chamber has a volume of 10 ft3. When the vacuum pump is running, the steady-state pressure in the chamber is 0.1 lbf/in2. The pump is shut off, and the following pressure-time data are observed:\n```Time after shutoff, min\tPressure, psia\n0\t\t0.1\n10\t\t1.1\n20\t\t2.1\n30\t\t3.1\n```\n\nCalculate the rate of air leakage into the vacuum chamber when the pump is running. Air may be assumed to be a perfect gas. The air temperature may be assumed constant at 70oF. Answer: 0.0051 lb/min.\n\n10. The tank in fig1 is cylindrical and has a vertical axis. Its horizontal cross-sectional area is 100 ft2. The hole in the bottom has a cross-sectional area of 1 ft2. The interface between the gasoline and the water remains perfectly horizontal at all times. The interface is now 10 ft above the bottom. How soon will gasoline start to flow out the bottom? Assume frictionless flow. Sp.gr of gasoline:0.72 . Answer: 36.5 sec.\n11.",
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"Fig1\n\n12. A tank has 1000 m3 of salt solution. The salt concentration is 10 kg/m3. At time zero, salt-free water starts to flow into the tank at a rate of 10 m3/min. Simultaneously salt solution flows out of the tank at 10 m3/min, so that the volume of the solution in the tank is always 1000 m3. A mixer in the tank keeps the concentration of of salt in the entire tank constant; the concentration in the effluent is the same at the concentration in the tank. What is the concentration in the effluent as a function of time?\n13. Repeat the above problem, with the change that there is a layer of solid salt on the bottom of the tank, which is steadily dissolving into the solution at a rate of 5 kg/min.\n14. Rework problem 11, with the change that the outflow is only 9 m3/min and the total volume of liquid contained in the tank is thus increasing by 1 m3/min.\n15. The \"heat capacity\" of my house is 3300 kJ/oC. That is, 3300 kJ raises the temperature of my house 1oC. The heater in my house can supply heat at a maximum rate of 5.2 x 104 kJ/hr.\n(a) I return from vacation to a cold house. The inside temperature is 5oC and the outside temperature is -15oC (minus 15 deg C). I set the heater at its maximum rate at 8:00 pm. At what time will the temperature in my house be 20oC?\n(b) Heat escapes from my house through conduction through the walls and roof. The rate of heat loss, qloss in kJ/hr, is proportional to the difference between the inside temperature and the outside temperature:\nqloss = k(Tinside - Toutside)\nwhere k = 740 kJ/(oC.hr). Repeat the calculation in (a), but include heat loss by conduction through the walls and roof.\n16. (a) Calculate the concentration of pollutant in the lake as a function of time (in kg pollutant / m3 water).\n\nVolume of water in lake = Vlake = 4 x 109 m3\n\nFlow rate of river = Qriver = 12 x 106 m3/day\nConcentration of X in river = [X] = 6.5 x 10-6 kg/m3 water\n\n(b)The pollutant decomposes to inert substances at a rate proportional to its concentration in water:\n\nRate of decomposition of pollutant = -k[X]\n\n[X] has units of (kg X)/(m3 water) and k is a constant with units (m3 water)/day.\n\nCalculate the concentration of pollutant in the lake as a function of time (in kg pollutant / m3 water) when decomposition is included.\n\n17. The reaction of chemical P to chemical Q releases heat:\n\nP à Q + 770 kJ/mole.\n\nBecause pure P reacts explosively, the reaction is conducted in a dilute water solution. Consider a batch reactor (no flow in or out) initially charged with 1.0 kg of water and 0.12 mole of P (= 0.013 kg P) at 50oC. Thus [P]o = 0.12 mole/kg water. The reactor is thermally insulated.\n(a) Calculate the temperature in the reactor after P has completely reacted to form Q. You may assume that the heat capacity of the dilute solution is the same as that of water.\n\n18. (b) Obtain mathematical expression for the temperature in the reactor as a function of [P].\n\n(c) The rate of the reaction P à Q increases as the temperature increases. Under the conditions here the rate is approximately proportional to the temperature:\n\nrate of reaction = d[P] / dt = - aT[P]\nsuch that a is a constant. Derive an expression for [P] as a function of time. Note that T is a function of time. Note also that T is a function of [P].\n\n19. Surge tanks are often used to smooth flow rate fluctuations in liquid streams flowing between chemical processes. Consider a liquid surge tank with one inlet (flowing from process I) and one outlet stream (flowing to process II). Assume that the density is constant. Find how the volume of the tank varies as a function of time, if the inlet and oulet flowrates vary.\n(dV/dt = Fi - F)\n\n20. Surge drums are often used as intermediate storage capacity for gas streams that are transferred between chemical process units. Consider a drum, where qi is the inlet molar flow rate and q is the outlet molar flow rate. Develop a model that describes the variation of pressure in the tank with time. Assume that the tank is maintained in isothermal conditions.\n\n21. Consider a perfectly mixed stirred-tank heater, with a single feed stream and a single product stream. Assuming that the flowrate and temperature of the inlet stream can vary, that the tank is perfectly insulated, and the rate of heat added per unit time (Q) can vary, develop a model to find the tank temperature as a function of time. State your assumptions.\n\n22. Assume that two chemical species, A and B, are in a solvent feed stream entering a liquid-phase reactor that is maintained at a constant temperature. Two species react inversibly to form a third species, P. Find the reactor concentration of each species as a function of time.\n\n© M.Subramanian, Lecturer, Chemical Engg, SVCE, Sriperumbudur - 602105, Tamil Nadu, INDIA"
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"http://msubbu.in/ChemicalEngg_Resources/qb/appmath/twofluiddrain.gif",
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http://www.computerchess.org.uk/ccrl/4040/cgi/engine_details.cgi?match_length=30&print=Details&each_game=1&eng=Sting%20SF%209.9%2064-bit
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[
"Contents: CCRL 40/15 Downloads and Statistics January 25, 2020 Testing summary: Total: 1'116'816 games played by 2'606 programs White wins: 386'579 (34.6%) Black wins: 286'858 (25.7%) Draws: 443'379 (39.7%) White score: 54.5%\n\n## Engine Details\n\n Options Show each game results\nSting SF 9.9 64-bit (3012+16\n−17\n)Quote\n Authors: Marco Costalba, Joona Kiiski, Stockfish team members Links: Homepage, Development Versions, Testing Framework\nStockfish was originally based on Glaurung by Tord Romstad.\nThis is one of the 107 Stockfish versions we tested: Compare them!\n Opponent Elo Diff Results Score LOS Perf – Komodo 8 64-bit 3205 +16−16 (+193) 8.5 − 31.5(+0−23=17) 21.3%8.5 / 40 0.0% +8 = 0 = 0 = 0 = = 0 = 0 = 0 0 = 0 = 0 = 0 = = = = = 0 0 0 0 0 0 0 0 = 0 = 0 0 0 0 – Komodo 12.1.1 MCTS 64-bit 4CPU 3183 +17−16 (+171) 10 − 40(+2−32=16) 20.0%10.0 / 50 0.0% −39 = 1 0 = 0 0 0 = 0 = = 0 0 0 0 0 0 0 0 0 = = 0 0 0 = 0 = 0 0 0 = 0 0 0 1 0 = = 0 0 = 0 = 0 0 0 = 0 = – Andscacs 0.93 64-bit 3171 +13−13 (+159) 9.5 − 22.5(+3−16=13) 29.7%9.5 / 32 0.0% +27 = 0 0 0 = = = 0 0 0 = 0 0 0 = 0 0 0 = = 0 1 0 = = = 0 1 = 1 0 = – Houdini 4 64-bit 3168 +10−10 (+156) 6.5 − 33.5(+1−28=11) 16.3%6.5 / 40 0.0% −91 0 = 0 = 0 0 0 0 = 0 = 0 0 0 0 = = 0 0 0 0 0 0 0 = 0 = 0 0 = 0 0 0 0 = = 0 0 1 0 – Fire 4 64-bit 3146 +11−11 (+134) 8.5 − 31.5(+2−25=13) 21.3%8.5 / 40 0.0% −62 0 = = 0 = 0 0 0 0 0 0 = = 0 = = 0 0 0 = 0 = 0 1 1 0 0 0 0 = 0 = 0 = 0 = 0 0 0 0 – Gull 3 64-bit 3121 +7−7 (+109) 12 − 28(+5−21=14) 30.0%12.0 / 40 0.0% −24 = = 1 = = 0 0 0 = 0 = 0 0 1 = = = 0 0 = 0 1 = 0 0 = 0 0 1 = = 0 1 0 0 0 0 0 0 0 – Chiron 4 64-bit 3115 +9−9 (+103) 8.5 − 23.5(+1−16=15) 26.6%8.5 / 32 0.0% −38 = = 0 = = = = = = 0 0 0 0 = 0 1 0 = 0 = 0 0 0 = 0 = 0 0 0 = = 0 – Strelka 5.5 64-bit 3104 +7−6 (+92) 10 − 22(+2−14=16) 31.3%10.0 / 32 0.0% −21 = = = 0 = = 1 0 = 0 0 0 = 0 = = 0 = 0 0 = 0 = = = 0 = = 0 0 1 0 – Fritz 16 64-bit 3102 +11−11 (+90) 13.5 − 18.5(+6−11=15) 42.2%13.5 / 32 0.0% +43 0 = 0 = = 0 0 0 0 1 1 = 1 = 0 = 1 1 = 0 = 1 = 0 0 = = 0 = = = = – Critter 1.6a 64-bit 3101 +7−7 (+89) 11.5 − 28.5(+2−19=19) 28.8%11.5 / 40 0.0% −41 = = = 0 = 0 0 0 1 = = 0 0 0 = = = 0 0 0 0 0 = = = 0 0 0 = 0 = 0 0 = 1 = = = = 0 – Komodo 12.1.1 MCTS 64-bit 3081 +16−16 (+69) 15 − 25(+9−19=12) 37.5%15.0 / 40 0.0% −17 = = 0 0 = 0 = = 1 0 0 = 0 = 0 0 0 1 0 = 0 1 0 = 0 1 0 1 0 1 = 1 0 0 0 = 0 1 1 = – Texel 1.07 64-bit 3075 +12−12 (+63) 9 − 23(+1−15=16) 28.1%9.0 / 32 0.0% −71 0 = = 0 0 = = = 0 = = 0 = 0 = 1 0 0 = 0 = 0 0 0 = 0 = = = 0 = 0 – Laser 1.5 64-bit 3073 +14−15 (+61) 14.5 − 17.5(+10−13=9) 45.3%14.5 / 32 0.0% +29 = 0 = 1 = = 1 = 0 0 0 1 0 0 1 1 0 = = = 0 0 1 1 1 = 1 0 1 0 0 0 – BlackMamba 2.0 64-bit 3057 +10−10 (+45) 18.5 − 21.5(+8−11=21) 46.3%18.5 / 40 0.0% +24 = 0 0 = 1 1 0 = 1 1 = = 0 0 0 = = = = 0 1 = 1 = = = = = 0 0 0 = = = 1 0 = = = 1 – Stockfish 2.1.1 64-bit 3053 +15−15 (+41) 14 − 18(+2−6=24) 43.8%14.0 / 32 0.0% +9 = = = = 1 = = = = = = = = 0 1 = 0 = = 0 = 0 = = = = 0 = = 0 = = – Ethereal 9.65 64-bit 3042 +17−17 (+30) 0.5 − 2.5(+0−2=1) 16.7%0.5 / 3 0.7% −214 = 0 0 – Gull 3.1 64-bit 3041 +16−16 (+29) 14.5 − 17.5(+5−8=19) 45.3%14.5 / 32 0.5% +4 0 1 = = 1 = 0 = = = 0 = = = = = 1 0 0 0 = = = = = 0 0 1 = = 1 = – Nemorino 4.00 64-bit 3040 +17−17 (+28) 19.5 − 16.5(+10−7=19) 54.2%19.5 / 36 0.7% +50 = = = = 1 = 0 1 0 = 0 = = 1 = = = = 0 = 1 1 1 0 = = = 1 = 1 0 = = 1 1 0 – Arasan 20.4.1 64-bit 3038 +16−16 (+26) 16 − 16(+9−9=14) 50.0%16.0 / 32 1.3% +27 0 = 1 = 1 = = = 1 1 0 1 1 0 1 0 0 0 0 0 = = 1 = = 0 = = = 1 = = – Senpai 2.0 64-bit 3036 +12−12 (+24) 14.5 − 17.5(+5−8=19) 45.3%14.5 / 32 0.7% −3 0 1 = 0 1 = = = = = = = 0 0 = = = 1 = 0 1 = = = = 0 1 0 = = = 0 – ChessBrainVB 3.66 3036 +23−23 (+24) 2 − 2(+0−0=4) 50.0%2.0 / 4 4.5% +24 = = = = – SmarThink 1.98 64-bit 3026 +13−13 (+14) 17 − 19(+12−14=10) 47.2%17.0 / 36 9.1% −7 = = 0 0 0 1 1 1 0 0 1 1 0 1 0 = 0 1 0 = 1 = = 1 0 0 1 0 = = 1 1 0 0 = = – Arasan 20.5 64-bit 3025 +20−20 (+13) 3 − 1(+2−0=2) 75.0%3.0 / 4 15.3% +163 1 = = 1 – Xiphos 0.2 64-bit 3024 +18−18 (+12) 2.5 − 1.5(+2−1=1) 62.5%2.5 / 4 15.1% +94 1 0 = 1 – Chiron 2 64-bit 3016 +13−13 (+4) 20.5 − 19.5(+14−13=13) 51.3%20.5 / 40 35.1% +10 = 0 1 = 1 = 1 0 = 0 1 0 0 1 1 0 0 1 0 = = 1 = 0 = 0 = = = 1 = 1 1 1 1 = 0 0 0 1 – Pedone 1.7 64-bit 3014 +17−17 (+2) 2.5 − 1.5(+2−1=1) 62.5%2.5 / 4 42.4% +84 1 = 0 1 – Naum 4.6 64-bit 3013 +12−12 (+1) 23.5 − 16.5(+15−8=17) 58.8%23.5 / 40 45.3% +57 = 1 1 0 1 = = = 0 = 1 = = = = 0 1 0 1 = 1 1 1 = 1 1 0 1 0 = 1 1 = = 1 0 0 = = = – Ethereal 9.30 64-bit 3005 +25−26 (−7) 1 − 1(+1−1=0) 50.0%1.0 / 2 66.6% −7 0 1 – Vajolet2 2.5 64-bit 3002 +18−18 (−10) 2 − 2(+2−2=0) 50.0%2.0 / 4 78.6% −10 0 1 0 1 – Sting SF 9 64-bit 2999 +16−16 (−13) 16.5 − 15.5(+5−4=23) 51.6%16.5 / 32 85.4% −4 = 0 = = = 0 = = 1 = 0 1 = = 1 = = = = = = = = = 1 = = 0 = = 1 = – Defenchess 1.1f 64-bit 2998 +12−12 (−14) 18 − 18(+10−10=16) 50.0%18.0 / 36 91.2% −14 1 = = = 1 = = = 0 = = 1 0 0 1 1 0 = = 1 = 0 = 0 0 1 0 = = 0 0 1 = = 1 1 – Xiphos 0.1 64-bit 2987 +19−19 (−25) 19.5 − 12.5(+13−6=13) 60.9%19.5 / 32 97.5% +45 = 1 1 = 1 = 0 = 0 1 1 = 0 = = 1 1 1 1 1 = 1 1 = = 0 = = 0 0 = 1 – Rodent III 0.238 64-bit 2983 +15−15 (−29) 2 − 2(+1−1=2) 50.0%2.0 / 4 99.5% −29 = = 0 1 – Vajolet2 2.4 64-bit 2970 +21−21 (−42) 16.5 − 15.5(+7−6=19) 51.6%16.5 / 32 99.9% −31 = = 1 = = = 1 0 0 1 1 1 = = = = 0 = 0 = = 1 1 = = = = = 0 0 = = – Ethereal 9.00 64-bit 2969 +18−18 (−43) 17 − 15(+8−6=18) 53.1%17.0 / 32 100.0% −25 1 = = = = 0 0 1 1 = = = = 0 = = 1 1 1 0 1 = = = = 0 = 0 = = 1 = – Hakkapeliitta 3.0 64-bit 2955 +12−12 (−57) 20.5 − 11.5(+13−4=15) 64.1%20.5 / 32 100.0% +28 1 = 1 = = 0 0 = 1 1 = 1 = = = 0 = = 1 = = 1 1 1 1 = 1 0 1 1 = = – Wasp 2.6 64-bit 2948 +13−13 (−64) 21.5 − 10.5(+15−4=13) 67.2%21.5 / 32 100.0% +46 1 1 = = 1 1 1 1 1 0 = 1 = = 0 = = = 1 = 1 0 = = 0 = 1 1 1 = 1 1 – Bagatur 1.9 64-bit 2927 +23−23 (−85) 9 − 7(+4−2=10) 56.3%9.0 / 16 100.0% −48 = = = 1 1 = = = 1 = = = 0 1 = 0 – Bobcat 8.0 64-bit 2924 +13−13 (−88) 1.5 − 2.5(+1−2=1) 37.5%1.5 / 4 100.0% −170 0 = 1 0 – RubiChess 1.2.1 64-bit 2908 +19−19 (−104) 10.5 − 3.5(+9−2=3) 75.0%10.5 / 14 100.0% +80 0 = 1 1 0 1 = 1 1 1 1 1 1 = – Crafty 25.3 64-bit 2904 +28−28 (−108) 10.5 − 1.5(+9−0=3) 87.5%10.5 / 12 100.0% +176 1 1 1 1 1 1 = = 1 = 1 1 – Tucano 8.00 64-bit 2889 +25−25 (−123) 12.5 − 3.5(+10−1=5) 78.1%12.5 / 16 100.0% +70 1 = 1 1 1 = 1 = = 1 = 1 0 1 1 1 – Scorpio 2.8 64-bit 2886 +14−14 (−126) 22 − 10(+15−3=14) 68.8%22.0 / 32 100.0% −7 1 = 1 = 1 1 = = 1 = 1 1 1 1 0 = = = 1 0 = 1 = = 1 = = = 1 0 1 1\n\n### Rating changes by day",
null,
"### Rating changes with played games",
null,
"Created in 2005-2013 by CCRL team Last games added on January 25, 2020"
] |
[
null,
"http://www.computerchess.org.uk/ccrl/4040/rating-history-by-day-graphs/Sting_SF_9_9_64-bit.png",
null,
"http://www.computerchess.org.uk/ccrl/4040/rating-history-by-day-graphs-2/Sting_SF_9_9_64-bit.png",
null
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|
https://www.intechopen.com/books/hemodialysis/analysis-of-the-dialysis-dose-in-different-clinical-situations-a-simulation-based-approach
|
[
"Open access peer-reviewed chapter\n\n# Analysis of the Dialysis Dose in Different Clinical Situations: A Simulation-Based Approach\n\nBy Rodolfo Valtuille, Manuel Sztejnberg and Elmer. A. Fernandez\n\nSubmitted: May 2nd 2012Reviewed: September 18th 2012Published: February 27th 2013\n\nDOI: 10.5772/53529\n\nDownloaded: 1835\n\n## 1. Introduction\n\nEnd Stage Renal Disease (ESRD) is an important public health concern around the globe. It is associated with high morbidity and mortality being Hemodialysis (HD) the main applied therapy. \n\nA recent study (HEMO study) could not show any decrease in the morbidity and/or mortality associated with increases in the dose -expressed as equilibrated Kt/V (eqKt/V)- and/or the flow (comparing high versus low flux, where high flux is defined as a Kt/V of Beta 2 microglobulin (B2M) ≥ 20 ml/min) when utilizing the three-times-a-week (3-times/wk HD) schedule therapy. \n\nThis led to development of several HD schedules proposals based on the variation of the session time duration (TD) as well as on its weekly frequency (Fr). However, more frequent HD schedules require new indexes to measure the delivered dose. In this context, the Equivalent Renal Clearence (EKR) [Casino y López] and Standard Kt/V (stdKt/V) [Gotch] indexes have been proposed to quantify the dialysis dose for different HD frequency schedules.\n\nThe EKR concept equalizes the time-averaged concentration (TAC) of Urea (U) for different therapies which is then normalized by U distribution Volume. Gotch has proposed that the weekly dialysis dose (WDD) is better expressed as standardized kt-V (stdKt/V) when dialysis is more frequent than 3-times/wk. Standard Kt/V combines treatment dose and frequency allowing comparison of intermittent (HD, High flux HD, Hemofiltration, etc) and continuous (Continuous Ambulatory Peritoneal Dialysis) therapies; the formula is expressed as U generation rate (G) rate divided by the average peak concentration. \n\nEqKt/V is the true dialysis dose per session occurring when U rebound (R), which is related to compartments and flow disequilibrium produced during HD treatment, is completed 30-60 minutes after the end of the HD session.\n\nThe determination of eqKt/V requires the measurement or the “prediction” of the true Eq U because the value of sp (single pool)Kt/V - a dimensionless ratio which includes Clearence of dialyzer (K), duration of treatment (TD) and volume of total water of the patient (V) - is greater than the Kt/V achieved in the patient which is calculated using the immediate postHD blood U concentration.\n\nIn the last decade, several formulas were developed to predict eq Kt/V trying to avoid the extraction of an additional blood sample. The Daugirdas and Schneditz “rate formula” is the most popular and validated equation and it is based in the prediction of eqKt/V as a linear function of spKt/V and the rate of dialysis (K/V). \n\nAn alternative and robust formula, based in the double pool analysis by Smye, is the equation of Tattersall where he described a soluble time constant: the patient equilibration time (tp). \n\nThe majority of these formulas of prediction have been validated in the 3-times/wk HD schedules.\n\nNew formulas to predict eq Kt/V have been recently published. Examples include the eqKt/V formula based on observations of the HEMO study and two others developed by Leypoldt (based on blood sample analysis during hemofiltration and short and daily HD) .\n\nThe high accuracy of the extracellular U concentration evolution during and after (UR) an HD session by double pool U kinetic model has been verified in several studies. \n\nAccess and cardio-pulmonary recirculation can both influence the UR, but the effect occurs in the first minutes after the end of HD and is considered to be mild. \n\nSeveral factors other than clearance of U might play a role in morbidity and mortality of hemodialyzed patients.\n\nOne of them, recently revised, is the role of the “denominator” to normalize the Kt. The results derived from the HEMO study showed that Kt/V failed to explain the paradoxical outcomes related to size (underweight versus obese patients) and gender. This factor was considered in the Frequent Hemodialysis Network (FHN) study which is currently underway. The investigators included the body surface area (BSA) as a potential tool for a better normalization of Kt and to allow more appropriate comparison among different HD populations. \n\nSince 1980 the idea of emulating reality in a computer environment by simulation rapidly spread among biomedical researchers, being accepted as one of the most powerful tools both for understanding phenomenological aspects of a chosen physics or physiological complex and for predicting functional or operative conditions of technological systems. The main concept of this approach relies in numerically solving a mathematical model that governs a chosen physical system, whose the analytical solution is not known or potentially dangerous to reach for a specific application. In spite of many efforts spent in the past for formulating accurate and robust algorithms for solving mathematical models, the effectiveness of that approach heavily dependent on computational resources. This led to only recent widespread use of simulation strategy both scientific and medical problems .\n\nA variable volume double-compartment (VVDC) kinetic model can reflect the behavior of different molecules and can be used as a mirror to analyze the profile in vivo by taking blood samples during the HD procedure. \n\nIn this scenario, the computational simulation including all the variables which affect the dialysis procedure can be a safe and useful tool to mimic many treatment schemes to help improve our knowledge of the dialysis therapy. \n\nThe aim of this study is to utilize a variable volume double-compartment (VVDC) kinetic model to simulate:\n\n1. Several clinical situations that allow comparison between the true eqKt/V and all the developed predictors, including the effect of increasing the TD and Fr.\n\n2. Changes in Kt/V, EKR and stdKt/V related to changes in TD and Fr.\n\n3. Comparison between using V with BSA to normalize K.\n\nAdvertisement\n\n## 2. Materials and methods\n\n### 2.1. Simulation and analysis\n\nA variable volume double-compartment (VVDC) kinetic model has been implemented based on the existing models of the U concentration behaviour. The model is described in Figure 1 and the equations are as follows:\n\nd(VeCe)dt(t)=GKc(Ce(t)Ci(t))Ce(t)(Ke(t)+Kr+Kd)E1\nd(ViCi)dt(t)=Kc(Ce(t)Ci(t))E2\ndVdt(t)=α(t)E3",
null,
"Figure 1.Scheme of Variable-Volume Double Compartment dialysis kinetic model\n\nWhereas “V” is: solute distribution volume, “C”: solute concentration, “K”: clearance constant, “G”: solute generation, “c”: cellular, “e”: extracellular, “i”: intracellular, “r”: renal, “d”: dialyser, a: volume change velocity (this constant is positive between dialysis sessions and negative during them), “t”: time. Equations 1, 2 and 3 make a dependent differential equation system that can be numerically solved. Through these simulations, it is possible to obtain the time profile of intra and extracellular volumes and concentrations of the studied solutes (figure 2).\n\nBy defining a behaviour determined for several time intervals on certain variables, such as α and Kd, it is possible to simulate different dialysis schedules, regarding session duration times (TD) and time between dialysis sessions or dialysis frequency (Fr).",
null,
"Figure 2.(a) Simulation of a profile during HD and the rebound of the solute immediately after the end. (b) Simulation of the weekly HD profile showing the effect of increasing the TD with fixed Kd and Kc. (c) Urea dinamycs simulated with double or single pool.\n\n### 2.2. Simulated systems\n\n#### 2.2.1. Comparison between the true eq Kt/V and all the developed predictors\n\nThe simulations assumed that the subjects had a solute distribution volume of 580 ml/Kg and the intra and extracellular distribution relation is 2/3 and 1/3 of the total V. The extra-renal clearance constant (Ker) was considered invalid for the U.\n\nResidual renal clearance (Kr) was 0. 1ml/min in all the cases.\n\nDialysis schedules with a duration between 2 and 8 hours at 2-hour-intervals of 2 hour were simulated and the weekly frequency of treatment were 3 and 7 days/wk.\n\nThe simulations resulted in a time-dependent evolution of the molecule concentration under study (U) in each of the compartments, that is, the intracellular (Ci) and extracellular (Ce) compartments.\n\nWe analysed 1005 determinations of U pre HD, U posHD and eqU (60 minutes after the end of the simulated session). This determinations were obtained in the midweek of the 4th and 10th week of simulation\n\nThese determinations were product of the manipulation of six (6) variables-Table 1-\n\n Weight Kc(ml/min) Kd(ml/min) Uonset(mg%) UF(ml/session) UR% 60-120 400-1000 100-250 160 -240 500-4000 3.65-17.8\n\n### Table 1.\n\nRange of values of the different simulated variables.\n\nU G was 6. 25mg/min in all the simulations.\n\n#### 2.2.2. Formulas\n\nSimulated eqKt/V was compared with the previously described predictors with the next formulas :\n\nKt/V=Ln(UposUpre)E4\nKt/V=Ln(UeqUpre)E5\nKt/VTATTERSALL=Kt/V*[tt+35]E6\nKt/VDAUGIRDAS=Kt/V0.6*Kt/Vt+0.03E7\nKt/VHEMO=Kt/V0.39*Kt/VtE8\nKt/VLEYPOLDT1=0.924*Kt/V0.395*Kt/Vt+0.056E9\nKt/VLEYPOLDT2=0.915*Kt/V0.485*Kt/Vt+0.106E10\n\n### 2.3. Changes in Kt/V, EKR and stdKt/V related to changes in TD and Fr\n\nTypical 80-kg-patient with a residual renal clearance (Kr) of 0. 1ml/min and a weight gain a (interdialysis) and ultrafiltration (intradialysis) of 0. 65 ml/min was chosen to simulate the different therapeutic dialysis schedules.\n\nThe assumption was that this typical patient would have a solute distribution volume of 580 ml/Kg (46. 4 litres) and when the solute is U, the intra and extracellular distribution relation is 2/3 and 1/3 of the total V. The extrarenal clearance constant (Ker) was considered invalid for the U.\n\nDialysis schedules with a duration between 1 and 8 hours at intervals of 1 hour were simulated and the weekly frequency of treatment was changed from 3 to 7 days a week on each of them thus obtaining 28 different schemes.\n\nThe Fr applied to the simulations does not represent sessions uniformly distributed through the week; it was implemented according to the time tables used in the usual HD practice. For the 3-times/wk Fr, three sessions with an interval between the beginning of sessions of 48, 48 and 72 hours (that is, Monday, Wednesday and Friday) were performed. For the 4-times/wk sessions, the intervals are 24, 48, 24 and 72 hours. For the 5-and 6 -times/wk sessions, 4 and 5 intervals of 24 hours and the last one of 72 and 48 hours, respectively, are established. When the Fr is of 7-times/wk, the distribution is uniform.\n\nThe simulations resulted in a time-dependent evolution of the molecule concentration under study (Urea) in the intracellular (Ci) and extracellular (Ce) compartments.\n\nOver the U time profiles, the real Time Average Concentration (TAC) is calculated. Since the main objective was to evaluate which of the proposed indexes more accurately showed the dose changes caused by the scheme changes, the behaviour of the weekly Kt/V, EKR (Casino), std Kt/V (Gotch) and the rebound percentage (% rebound), were compared according the following formulas:\n\nKtV=j=1Nln(CePreCePost)jE11\nTAC=12Nj=1N(CePre+CePost)jE12\nEKR=GTACE13\nstdKtV=G1Nj=1N(CePre)jE14\n%R=100Nj=1N(CeqCePostCeq)jE15\n\n### 2.4. Hemodialysis simulation tool: HD-SIM\n\nThe simulations of hemodyalisis kinetics were performed through the utilization of a software specially developed for hemodyalisis simulation: HD-SIM. This software was developed on MATLAB (c) platform and consists of a calculation core and a graphical user interface (GUI).\n\nHD-SIM calculation core utilizes MATLAB ® (version 6. 5) simulation package SIMULINK® to support the VVDC kinetics model. Given the set of required parameters through the GUI, solute compartmental concentrations (Ce and Ci) and volumes (Ve and Vi) are calculated as functions of time. Concentration-time profiles are used for the calculation of different hemodyalisis quantity-quality estimators such as: TAC, EKR, Kt/V, and stdKt/V. The calculation core solver is used with: ode113 algorithm (Adams – variable step) that is recommended by MathWorks for narrow tolerances, automatic integration step, maximum step of 1 (1 hr), duration of 1680 (10 weeks), absolute tolerance of 10⁻⁷ (10⁻⁷ mg/ml) and relative tolerance of 10⁻⁷.\n\nHD-SIM GUI provides a friendly set of windows that allows inserting patient and dialyzer specific data into the simulation system that is required to feed the VVDC model, defining sets of TDs and Frs to evaluate a wide range of treatment schedules, and managing the outcome of the simulations from visualizing estimator values and concentration profiles to file-saving selected results. (figures 3, 4 and 5)",
null,
"Figure 3.Patient and simulation data displayed by HD-SIM",
null,
"Figure 4.Patient and simulation data displayed by HD-SIM",
null,
"Figure 5.HDSIM running the simulations.\n\nTable 2 shows the values at the the beginning of the simulation.\n\n Solute Ce onset (mg %) G (mg/min) Kc(ml/min) Kd(ml/min) Urea 230 6.25 600 250\n\n### Table 2.\n\nValues at the beginning of the simulation\n\n## 3. Statistical analysis\n\nAll values are expressed as mean±standard deviation (sd) or median (range) as appropriate. Correlation coefficients were determined using the Pearson method. For analysis of agreement between methods (for example simulated (sim) eqKtV versus EqKtV predictors) we used Bland Altman analysis. To compare sim eqKtV with predictors we also used analysis of error: mean error (sim eqKtV-predictor) and % mean error ( (sim eqKtV-predictor)/ sim eqKtV) x 100). We used MedCalc version 12. 3. 0(MedCalc Software,Mariakerke,Belgium) for the statistical analysis.\n\n## 4. Results\n\n### 4.1. Prediction of the eqKt/V\n\nThe eq KtV delivered in 1005 simulations was 0. 84±0. 47 with a median of 0. 78 and a range between 0. 10 and 2. 54, which represent the wide range of values commonly seen in current clinical practice. (Table 3)\n\n eqKt/V Tattersall Daugirdas HEMO Leypoldt 1 Leypoldt 2 Minimum 0.10 0.13 0.14 0.13 0.18 0.13 1st Quart 0.47 0.50 0.50 0.51 0.52 0.46 Mean 0.85 0.87 0.88 0.89 0.87 0.80 Median 0.78 0.80 0.82 0.82 0.81 0.75\n\n### Table 3.\n\nStatistical summary of Simulated and predicted eqKt/V values by different formulas. (1st Quart=first quartile)\n\n### 4.2. Behaviour of predictors\n\nAll predictors showed a high Pearson correlation coefficient (≥ 0. 99) with sim eqKt/V and among themselves.\n\nDaurgidas, Tattersall, HEMO and Leypoldt1 underestimated sim eqKt/V. Leypoldt2 was the only one to overestimate the sim eqKtV. (Tables 4 and 5)\n\n Daugirdas Tattersall HEMO Leypoldt1 Leypoldt2 Mean -0.0302 -0.0199 -0.0435 -0.0244 0.0428 SD 0.03680 0.03255 0.02959 0.05039 0.05670 Median -0.0350 -0.0241 -0.0459 -0.0300 0.0304 Minimum -0.101 -0.0836 -0.110 -0.110 -0.0454 Maximum 0.0783 0.0827 0.0721 0.170 0.259\n\n### Table 4.\n\nMean Error (ME) between sim eqKt/V and predictors\n\n Daugirdas Tattersall HEMO Leypoldt1 Leypoldt2 Mean 5.63 4.32 7.47 7.63 -3.18 SD 7.7 6.9 7.42 11.83 6.67 Median 4.65 3.23 5.89 4.60 -3.9 Minimum -2.14 -2.26 -1.95 -1.14 -2.82 Maximum 5.37 3.54 4.08 8.55 3.43\n\n### Table 5.\n\n% Error (% ME) between sim eqKt/V and predictors\n\nThe lower error of prediction expressed as ME or % ME was obtained with the Tattersall and the Daurgidas formula. Leypoldt1 and 2 showed the worst predictive performance.\n\nOne interesting point was the effect of increase TD of Fr it was used in unconventional schedules (different from 3-times/wk). Error was higher in schemes shorter than 4 hours and the increasing of Fr did not affect the prediction (Figures 6 and 7)",
null,
"Figure 6.Effect of the TD and increased Fr in the % error prediction of eqKt/V",
null,
"Figure 7.Effect of the TD and increased Fr in the % error prediction of eqKt/V\n\n### 4.3. Bland-Altman analysis\n\nA Bland-Altman analysis of agreement between gold standard (sim KtV) and eqKt/V predictors was performed. Tattersall and Daugirdas formulas showed the lower mean difference (±2sd): -0. 02 (+0. 04 -0. 08) and -0. 03 (+0. 04 -0. 1) respectively with a Gaussian distribution of error. Both Leypoldt formulas showed higher error with the increasing of the magnitude of eqKtV. HEMO study formula showed a higher mean difference than Tattersall and Daugirdas formulas with a lower 95% agreement interval (+0. 01-0. 1) (figure 8)",
null,
"Figure 8.Left side: Bland Altman plot comparing simulated eq Kt/V and predicted eq Kt/V by different predictors formulaes. Right side: Histogram of Error between simulated eq Kt/V and predicted eq Kt/V by different predictors formulas.\n\n### 4.4. Quantification of the Weekly Dialysis Dose (WDD)\n\nThe minimal dialysis dose recommended by the DOQI standards (Kt/V U/session = 1. 2) corresponded to EKR U =3. 17 ml/min and stdKt/V U = 2. 07 ml/min in a usual scheme of 3 days/4 hours (3d4hs) and the high dose equivalent similar to HEMO study (EqKt/V=1. 4) was 4. 28 ml/min and 2. 57 ml/min for stdKt/V in a schedule of 3 days 6 hours. Figure 9 shows the stdKt/V behaviour related to increase of TD and Fr as well as the equivalent values of minimal and high Kt/V.",
null,
"Figure 9.stdKt/V behaviour related to increase of TD and Fr as well as the equivalent values of minimal and high Kt/V.\n\nTable 6 shows tipical values of EKR, stdKt/V, wk Kt/V (weekly Kt/V) and Kt/V by session according changes in TD y Fr in a typical 80-kg-patient.\n\n Frequency time[h] EKR (ml/min) stdKt/V(ml/min) wk Kt/V(ml/min) KTV/Session 3 4 3.17 2.07 3.55 1.18 3 8 5.11 2.92 5.82 1.94 4 4 4.23 2.78 4.61 1.15 7 2 4.06 3.05 4.78 0.68 7 4 7.45 5 7.52 1.07 7 8 12.69 7.75 10.54 1.51\n\n### Table 6.\n\nEKR, stdKt/V, wkKt/V and Kt/V by session according changes in TD and Fr in a typical 80-kg-patient. (Ce onset=230;KD=250 ml/min;Kc=600ml/min.\n\nThe weekly Kt/V, EKR and std Kt/V showed a high correlation to express increasing of TD and Fr (weekly Kt/v-std Kt/V r= 0. 987 EKR-stdKt/V r=0. 9937) showing the weekly Kt/V (5. 68±2. 46) and the EKR (5. 55±3. 02) values to be higher than std Kt/V (3. 56±1. 76)\n\nThe behaviour proved different when the three indexes were separately analysed. When they are compared to quantify 3-times/wk and weekly schedules, the ekr and std Kt/V have a similar behaviour, the EKR tending to overestimate the WDD as the TD increases. (Figure 11) When the difference EKR-std Kt/V is showed in a graph (Figure 10) a high correlation of it (R2=0. 99) is verified, with a logarithmic increase of the Kt/V/session and is lower with the increase of Fr in a fixed TD. The weekly Kt/V has a behaviour similar to that of the EKR in the 3-times/wk schedules but clearly fails in the daily schedules, especially in the TD schedules >4 hours.\n\nWhen the Kt/V-session is analysed, the results match. The Kt/V/session increases as the TD increases when a certain number of sessions are fixed (Fr). When it is analysed for different Frs, the Kt/V/session only shows differences when duration is > 4 hours; however, if the Fr varies and the TD is fixed, instead we can observe that the Kt/V/session is not able to respond to the dose increases and tends to decrease as the WDD increases due to an increment of the Fr. (Figure 11)\n\nThe U rebound is complete one hour after the end of the HD session in all the simulations, decreasing as the TD increases.\n\nFigure 11 showed the effect of TD and Fr on different predictors of the WDD (wkKt/V, EKR and stdKt/V) as well the changes Kt/V-session.",
null,
"Figure 10.Difference (%) EKR-stdKtV related to Kt/V by session",
null,
"Figure 11.Effect of changes in increasing of TD and Fr on the behavior of WDD predictors (wkKt/V, stdKt/V, EKR) and Kt/V by session. (WDD=Weekly Dialysis Dose (ml/min)\n\n### 4.5. Comparison of V with BSA to normalize Kt/V\n\nIn the last four decades dialysis dose expressed as KtV has been widely used due to its low complexity and ability to predict to be a strong predictor or mortality in HD population. However, recent studies showed paradoxical outcomes related to sex and higher mortality in patients with high Kt/V and low Volume, leading to the proposal of a normalized volume using and the correction by a Volumen normalized by Body Surface Area (BSA). has been proposed. \n\nWe randomly simulated 1031 K*t with a range of between 14400 ml/min and 57600 ml/min and then Kt/V (using Watson formula for Volume) and Kt/V corrected by BSA (Dubois formula) were calculated and analysed\n\nKtV values delivered by simulation showed a mean of 1. 01, a median of 0. 99, a range between 0. 29-2. 44 and a standard deviation of 0. 40 The results of the allometrical correction of Volume Watson formula by BSA were 0. 084*V 0. 86 (female) r=0. 98 and 0. 1229*V 0. 73 (male) r=0. 99. (Figure 12)\n\nThe results after V normalized by BSA clearly changed between men and women and the overestimation in patients with lower volumes was corrected (Table 7 and figures 13 and 14)\n\n Sex f m Mean SD Mean SD Kt/V 1.158 0.4354 0.921 0.3415 Kt/Vcorr 1.862 0.6891 2.489 0.8909\n\n### Table 7.\n\nKt/V and Kt/V corrected by BSA (Dubois) according to sex.",
null,
"Figure 12.Allometric regression between Body Surface Area (Dubois) and Volume (Watson)",
null,
"Figure 13.Effect of changes in Volume and Sex on BSA-normalized Kt/V and Watson Kt/V\n\n## 5. Discussion\n\nIn this work we propose the simulation with a VVDC kinetic model as a useful and safe tool to investigate, learn and find out the numerous aspects of the HD treatment related to dialysis dose. Single pool models used by Gotch to developed the pharmaco- kinetic concept of Kt/V are simpler and also useful but it frequently leads to errors in showing the true behaviour of little known molecules or not yet validated treatments. VVDC kinetic model is used in current studies that analyze the influence of increasing TD and Fr in HD outcomes after the failure of HEMO study to demonstrate better results with high dose expressed as eqKtV. \n\nExponencial decay curves defined by WWDC to fit dialysis dose by session are actually used in several medical devices based on ionic dialysance or urea sensors. \n\nWe used WWDC based curve fitting and neural networks to predict dialysis dose from samples provided by an on-line urea monitor. \n\nThe main interpretation of the double compartment represent intra and extracellular fluid spaces, with diffusion of molecules between the spaces characterised by a mass transfer coefficient, Kc. This interpretation is based on the observation that Kc correlated with patient size. This model had been deeply developed by Smye and it had been the basis of the Tattersall formula. However, Scheneditz et al suggests that the two compartment based in different regional tissue flows (high and low blood flow) may describe urea distribution, and transport during dialysis, more accurately. This theorical approach also permited the development of a formula for dialysis dose that accounts for molecular rebound but only is based only on measurements of urea made during HD procedure. This formula has proved higher clinical usefulness: the Daurgirdas formula.\n\nIn this study we confirmed the robustness of the two widespread eqKtV predictors developed under the two different ways: Tattersall and Daugirdas formulas. They showed a high accuracy in the numerous simulated schedules. The lower error of Tattersall formula has been validated in clinical situations and could be explained in our study because it was developed under a theorical approach using a diffusion –based VVDC.\n\nFormula emerged from the blood U samples analysis of 1131 patients in the HEMO study showed as an interesting approach. It behaved with a higher error than Tattersall and Daurgirdas formulas but showing a very low bias in all the simulations.\n\nEq KtV was confirmed as the metric of dialysis session in the thrice a week schedule. Equivalent dose of stdKt/V for eqKt/V in schedules>3-times/wk may be easily calculated in a graphical fashion (Figure 9)\n\nThe main issue which justifies the fact that Kt/V U is considered the key of the adequacy of dialysis is that it is related to mortality. However, many studies have questioned the utility of Kt/V: mainly, scaling for the volume is a confounding factor since gender and body mass index directly affect morbidity and mortality in HD patients. \n\nIn our study the influence of the denominator to achieve a real dose independent of sex and volume showed similar results with others studies.\n\nVVDC proved particularly useful when we analysed the new proposed predictors of the WDD: EKR and standard Kt/V.\n\nStd KtV was confirmed as the best project to explain the different schedules. EKR was showed closely related with Kt/V and sensitive to changes in TD, overestimating the dose in daily HD schedules. VVDC allowed to graph different weight, dialyzer and patient clearences, etc.\n\nOther molecules such as B2M and phosphorus related to mortality and different behaviour with urea have not been simulated in this work but VVDC have been successfully used for both. B2M is a molecule of high molecular weight, with typical lower levels in plasma and lower distribution Volume fully explained by VVDC when we know completely their characteristics. On the contrary, Phosphorus shows a heterogeneous and complex behaviour that cannot be completely validated with a VVDC kinetic model.\n\nIn addition to U kinetics, clinicians must consider clinical indicators (in example extracellular volume control, blood pressure, anemia and cardiovascular status) and comorbidities (diabetes, ageing, undernutrition) when using frequent or prolonged dialysis no forgetting to provide the best possible clinical results and quality of life.\n\nAdvertisement\n\n## 6. Conclusions\n\nIn our experience, a VVDC kinetic model proved to be showed as a useful and safe tool to analyse different HD schedules and novels techniques before the clinical validation. The use of graphical interfaces to extrapolate the numerical results enhanced the VVDC simulation. Clinical practice and simulation interact in a permanent feedback. Std KtV was confirmed as the best project to explain the different schedules. Tattersall and Daugirdas showed highly accurate in the numerous simulated schedules.\n\n## Download for free\n\nchapter PDF\nCitations in RIS format\nCitations in bibtex format\n\n## More\n\n© 2013 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution 3.0 License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.\n\n## How to cite and reference\n\n### Cite this chapter Copy to clipboard\n\nRodolfo Valtuille, Manuel Sztejnberg and Elmer. A. Fernandez (February 27th 2013). Analysis of the Dialysis Dose in Different Clinical Situations: A Simulation-Based Approach, Hemodialysis, Hiromichi Suzuki, IntechOpen, DOI: 10.5772/53529. Available from:\n\n### chapter statistics\n\n1835total chapter downloads\n\n### More statistics for editors and authors\n\nLogin to your personal dashboard for more detailed statistics on your publications.\n\n### Related Content\n\n#### Hemodialysis\n\nEdited by Hiromichi Suzuki\n\nNext chapter\n\n#### Adsorption in Extracorporeal Blood Purification: How to Enhance Solutes Removal Beyond Diffusion and Convection\n\nBy Fabio Grandi, Piergiorgio Bolasco, Giuseppe Palladino, Luisa Sereni, Marialuisa Caiazzo, Mauro Atti and Paolo Maria Ghezzi\n\n#### Updates in Hemodialysis\n\nEdited by Hiromichi Suzuki\n\nFirst chapter\n\n#### Vascular Calcification in Patients with End-Stage Renal Disease\n\nBy Kosaku Nitta\n\nWe are IntechOpen, the world's leading publisher of Open Access books. Built by scientists, for scientists. Our readership spans scientists, professors, researchers, librarians, and students, as well as business professionals. 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https://davidcrellen.com/crvaxod/95416f-comparing-slopes-of-two-regression-lines-in-r
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"Why do most guitar amps have a preamp and a power amp section? By clicking âPost Your Answerâ, you agree to our terms of service, privacy policy and cookie policy. I can see a p value of the test that compares the 2 slopes and this shows that the two slopes are different. This module This module calculates power and sample size for testing whether two slopes from two groups are significantly different. I'd like to know whether there is a way to test the slopes for two or multiple independent datasets (populations) are equal in SPSS. Do we agree that the respondent with only 1 point representation may not make comments? In parliamentary democracy, how do Ministers compensate for their potential lack of relevant experience to run their own ministry? Ho: B 2 = B 3 The second contrast young vs. . Comparing Coefficients in Regression Analysis. R: Slope extraction using linear models Individual regression slopes can be extracted with only a few lines of R code and the most straightforward solution regression /dep weight /method = enter height. Regression model F test on different response variables? Test regression models. to test if both treatments have the … regression /dep weight /method = enter height. t = r/Sr = r (n-2)^1/2 / (1-r^2) ~ t (n--2) 2 Method of least sqare. What test should be used to compare several regression lines? exible approach for checking equal slopes and equal intercepts in ANCOVA-type models. Why is my 50-600V voltage tester able to detect 3V? Testing two trendlines for statistical significance. Accepted Answer: Oleg Komarov. I plot SBR v Age for each Sex using ggplot2, I can get the equation of each regression fit easy enough, However how do I test whether or not they are significantly different (which they are not). For example, setting R = 2.0 results in a Group 2 sample size that is double the sample size in Group 1 (e.g., N1 = 10 and N2 = 20, or N1 = 50 and N2 = 100). N2 = [R × N1], where the value [Y] is the next integer ≥ Y. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. To see this, let us focus on the interpretation of the regression coe cients. If R < 1, then N2 will be less than N1; if R … Is (1R,3aR,4S,6aS)‐1,4‐dibromo‐octahydropentalene chiral or achiral? There's no comparison with 1 so far. You'll Canadian Journal of … However, there is no test / get-out-of-jail-free card that will get you around that problem without gathering a new sample and running your study again. If not we can convert it to a comment to the question. 1 t test. Can warmongers be highly empathic and compassionated? On comparing regression lines with unequal slopes. ... For two independent groups, let (X 1j, Y 1j), ... the difference between the slopes, when there is complete heteroscedasticity. The slopes of the two regression lines (one for single-mated females and one for triple-mated females) are not significantly different (F 1, 36 =1.1, P=0.30). Is Bruce Schneier Applied Cryptography, Second ed. I made several simple linear regression models, with different X variables and the same sample size and Y variable. yes that is a good point. McArdle, B. to test if both treatments have the same intercept then test the trt coefficient to see if … Test a significant difference between two slope values. rev 2020.12.14.38164, The best answers are voted up and rise to the top, Cross Validated works best with JavaScript enabled, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site, Learn more about Stack Overflow the company, Learn more about hiring developers or posting ads with us. split file off. Testing whether there is an increase between two regression slopes in a time series, Comparing two regression coefficients from the same model, in R, Mixed model multiple comparisons for interaction between continuous and categorical predictor. I think the most appealing way would be to plot the regression lines for each species all on the same axes, maybe with error bars based on the standard errors. Edit: I noticed another question has been added to the body. 0. What is the extent of on-orbit refueling experience at the ISS? Zerbe GO, Archer PG, Banchero N, Lechner AJ. Figure 2 – t-test to compare slopes of regression lines Real Statistics Function : The following array function is provided by the Real Statistics Resource Pack. Values returned from the calculator include the probability value, the t-value for the significance test, and the degrees of freedom. Based on gung's answer you can also do an anova test using the following code (also guessing): Thanks for contributing an answer to Cross Validated! which spacecraft? Is there a single word to express someone feeling lonely in a relationship with his/ her partner? Yes Bill Huber I know what OP stands for. Why does my oak tree have clumps of leaves in the winter? Are cadavers normally embalmed with \"butt plugs\" before burial? It only takes a minute to sign up. If I understand the question, you can compare Pearson correlations with a Fisher transform, also called a \"Fisher's r-to-z\", as follows. If you fit separate models, this constraint goes away. 0 ⋮ Vote. (1988). They're definitely related, and a regression of the dataset gives me an R 2 of 0.95. document Comparing Regression Lines From Independent Samples . Tutorials in Quantitative Methods for Psychology 2013, Vol. I think an answer explaining the link is a good suggestion. Making statements based on opinion; back them up with references or personal experience. Comparing lethal dose ratios using probit regression with arbitrary slopes Chengfeng Lei and Xiulian Sun* Abstract Background: Evaluating the toxicity or effectiveness of two or more toxicants in a specific population often 50 LD Polo-Plus software, developed by Robertson et al. Are the vertical sections of the Ackermann function primitive recursive? How do I test for independence with non-exclusive categorical variables? @Macro, yes, but yours is mostly better (+1 earlier); you addressed all 3 questions which I missed on my first (not thorough) reading of the question. I agree with the previous suggestion. with the model that allows the effect of $P_i$ to be different for each species: $$E(L_i) = \\alpha_0 + \\alpha_1 S_2 + \\alpha_2 S_3 + \\alpha_4 P_i + \\alpha_5 P_iS_2 + \\alpha_6 P_i S_3$$. 2010s TV series about a cult of immortals. I The algorithm also provides a way to build regression models in studies where the primary interest is comparing the regression lines across groups rather than comparing groups after adjusting for a regression e ect. Suppose a researcher is interested in comparing regression lines between three treatments (r =3). I can also see the slope for M to be 0.9359... and the confidence intervals to include 1 [0.8713585, 1.0005241]. Assessing significance of slopes in regression models with interaction Posted on March 17, 2016 by Lionel Hertzog in R bloggers | 0 Comments [This article was first published on DataScience+ , and kindly contributed to R-bloggers ]. Your English is better than my <>. Note that if they are both independent and (for example) different species, then you would not be able to tell whether the difference you find is due to the differing species or the differing data sets, as they are perfectly confounded. split file off. If selected, a summary of this analysis will be presented on the results tab titled \"Are lines different?\" Apparently you have to set some dummy variables =0/1 … Similarly, the correlation for I. Virginica (r = 0.28) was significantly weaker (p = 0.02) than the one observed for I. This will allow you to test whether the intercepts differ. Use analysis of covariance (ancova) when you want to compare two or more regression lines to each other; ancova will tell you whether the regression lines are different from each other in either slope or intercept. In this work fundamental concepts on the use of the Student’s test were reviewed and Monte Carlo … The likelihoods can be extracted using the logLik function and the degrees of freedom for the test will be $4$ since you've deleted $4$ parameters to arrive at the submodel. For values of r between 0 and 1, there will be two regression lines that form an interior angle less than 90 degrees, as illustrated in the figure below. +1. The degrees of freedom for the test is then $6$. Using R: drawing several regression lines with ggplot2 Posted on June 2, 2013 by mrtnj in R bloggers | 0 Comments [This article was first published on There is grandeur in this view of life » R , and kindly contributed to R-bloggers ]. I was wondering if I can use estimate or contrast slopes of two years ( B1 vs B2) from regression lines, which are not titled in the data any comment on these commands : PROC REG; Model Y = X test b=the slope of model A ; ' You can compute it easily using the sum of squared residuals of each model. What is a simple, effective way to present these comparisons? Comparing two slopes - nonlinear regression with repeated measures 04 Apr 2014, 03:19 I'm unable to figure out which statistical procedure to use for comparing two slopes. The GLS estimators are MLEs and the first model is a submodel on the second, so you can use the likelihood ratio test here. I've found the link below showing methodology comparing … Code by PAC also works nicely. My contribution here is the part about confounding. The dummy variable suggestion is a good one, Welcome to our site, uoscar. For this, you'll need to stratify the data set and fit separate models since, the interaction-based model I suggested will constraint the residual variance to be the same in every group. If you have not already done so, download the zip file containing Data, R scripts, and other resources for these labs. In that case, you can still use the likelihood ratio test (the likelihood for the larger model is now calculated by summing the likelihoods from the three separate models). Versicolor.\". 2) (test statistic t. ( 1) test is a prametrictest used to find whether the means of diffrent groups differ. Troubleshooting. Examine residual plots for deviations from the assumptions of linear regression. (1 reply) Hi, I'm sort of new to regression, but I was wondering how one compares two regression slopes in R. Is it just a matter of calculating the slopes and then using the SD reported by R to test for a difference. The slopes of the regression lines, formed by the covariate and the outcome variable, should be the same for each group. Comparing the slopes of two independent regression lines when there is complete heteroscedasticity. It only takes a minute to sign up. Using Prism's linear regression Standardized coefs in regression with a categorical predictor: there's something wrong. The t-test of the interaction term will assess whether or not the slopes differ significantly. The plotted Hi, I want to compare the regression slopes of 3 data sets. For clarification, the difference between this solution and mine (see below), is that I test the equality of all coefficients (intercept + slope) whereas @gung test only equality in slope. Am J Physiol. If, @Macro Nice answer (+1)! The R2 was used to compare the good of fit among these models. How to repoduce the fitted values from a forecast::Arima in R by hand? The Y intercepts are significantly different (F 1, 36 =8.8, P =0.005); females that have mated three times have … What is a simple, effective way to present the comparison? What is the extent of on-orbit refueling experience at the ISS? The R code for your situation would be (I'm guessing): In R you can use anova for an analysis of covariance. Cross Validated is a question and answer site for people interested in statistics, machine learning, data analysis, data mining, and data visualization. 1. if you only want to test the variance, while leaving the main effects in, then the \"null\" model should be the model with the interactions I've written above. The p-value of x:group gives the probability for the two slopes to be different, and the … the GLM tool has a \"seperate slopes\" tool which is what I used to test the significance of seperate slopes. For example, setting R = 2.0 results in a Group 2 sample size that is double the sample size in Group 1 (e.g., N1 = 10 and N2 = 20, or N1 = 50 and N2 = 100). Why is my 50-600V voltage tester able to detect 3V? Comparing the slopes of two regression lines is an almost daily task in analytical laboratories. This ANCOVA model ts two regression lines, one for each tool type, but restricts the slopes of the regression lines to be identical. The first contrast compares the regression coefficients of the middle aged vs. senior. regression analysis is to test hypotheses about the slope and intercept of the regression equation. There is no problem with the fact that the data are independent. How to get confidence interval of difference or ratio of slopes? Is Bruce Schneier Applied Cryptography, Second ed. site design / logo © 2020 Stack Exchange Inc; user contributions licensed under cc by-sa. 1982 Mar;242(3):R178-80. For the ANCOVA model, 2 = slope of population regression lines for tool types A and B. and Is, Hi @Abe. Comparing Constants in Regression Analysis When the constants (or y intercepts) in two different regression equations are different, this indicates that the two regression lines are … When two slope coefficients are different, a one-unit change in a predictor is associated with different mean changes in the response. I am doing an assignment where I am comparing lodgepole pine and spruce trees to see which are more locally adapted. They are diffrent. i i To answer these questions with R code, use the following: 72 Easy methods for extracting individual regression slopes: Comparing SPSS, R, and Excel Roland Pfister, Katharina Schwarz, Robyn Carson, Markus On comparing regression lines with unequal slopes. i am doing this because i have 3 sets of data y1,y2, and y3, and i want to compare $S_1$ is the \"reference\" species - the regression line for that species is given by $\\alpha_0 + \\alpha_4 P_i$. Vote. How to compare 2 regression slopes with R? corresponding regression slopes (see the supplementary material). By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy. We can compare the regression coefficients of males with females to test the null hypothesis Ho: B f = B m , where B f is the regression coefficient for females, and B m is the regression coefficient for males. You would do best to test for a difference in slopes by including sex and a sex:Age interaction in a multiple regression analysis. Which fuels? 2. Other efficient ways to constrain the OMS output are explained in the SPSS Command Syntax Reference guide (IBM, 2010). Similarly, the correlation for I. Virginica (r = 0.28) was significantly weaker (p = 0.02) than the one observed for … Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. ing the slopes and intercepts of two probit regression lines and constructing their variance and covariance matrices. Given a legal chess position, is there an algorithm that gets a series of moves that lead to it? 3. Continue Reading. So, I'm adding an answer to that: How can I test the difference between residual variances? Plot of Fitted Model This Plot of Fitted Model pane shows the two regression lines: Line 1 2 Plot of Fitted Model Speed Scrap 100 140 180 220 260 300 340 140 240 340 440 540 There is a noticeable offset between the lines, with line #1 producing more scrap at all speeds. \"The structural relationship: regression in biology.\" up to date? Cross Validated is a question and answer site for people interested in statistics, machine learning, data analysis, data mining, and data visualization. ... 7. Could you turn this into an answer by adding an explanation? Remove left padding of line numbers in less, Get the first item in a sequence that matches a condition. From my way of thinking you both should get upvotes which is what I am doing. difference (or non-difference) between the species and their relationship to $P_i$ very apparent. It's an application of the Fisher test to test the equality of coefficients among two groups of individuals. @whuber The OP doesn't have enough reputation to make a comment. A Fisher's r-to-z comparison indicated that the Pearson correlation for I. Setosa (r = 0.28) was significantly lower (p = 0.02) than I. Versicolor (r = 0.55). Plot regression lines. Apparently you have to set some dummy variables =0/1 and regress against them to do this. How to view annotated powerpoint presentations in Ubuntu? Let $L_i$ be the sepal length and $P_i$ be the pedal width and $S_1, S_2, S_3$ be the dummy variables for the three species. up to date? which spacecraft? He compared two regression lines, which are the level of a blood biomarker in function of age in males and females. Can the VP technically take over the Senate by ignoring certain precedents? How can I test the difference between residual variances? \"We used linear regression to compare the relationship of Sepal Length to Petal Width for each Species. Include a dummy for species, let it interact with $P_i$, and see if this dummy is significant. Comparing slopes of linear regression lines: If there are three or more lines, how can I account for multiple comparisons? What kind of harm is Naomi concerned about for Ruth? N2 = [R × N1], where the value [Y] is the next integer ≥ Y. This would make the We will be typing in LMATRIX subcommands to pick off pairwise comparisons between the coefficients for GPA for each college. How can I test whether the regression slopes for different groups are equal? CompareCorrCoeff.pdf Comparing Correlation Coefficients, Slopes, and Intercepts Two Independent Samples H : 1 = 2 If you want to test the null hypothesis that the … The OP can always comment on their own question. Answer: Examine the ANOVA p-value from the interaction of Petal.Width by Species, then compare the slopes using lsmeans::lstrends, as follows. A simple analysis of the data given below would consist of making Method to compare variable coefficient in two regression models, stats.stackexchange.com/questions/55501/…. See my gist file to see how I compute the Chow test. If we use potentiometers as volume controls, don't they waste electric power? This of course assumes that the data are in one spreadsheet, there is only one x and one y column for the two regression lines and a grouping factor is used to slopes between the two lines. Fit lines - ANCOVA not enough 0.9359... and the confidence intervals include... Definitely related, and see if this dummy is significant regress against them to do this their. Odd functions that there is no interaction between the coefficients for GPA for each species stands for, use following! Assumption evaluates that there is complete heteroscedasticity suppose a researcher is interested in comparing regression lines are themselves significant... In less, get the first item in a relationship with his/ her partner by an object in. Comment on their own question M to be 0.9359... and the covariate first compares... we used linear regression He compared two regression slopes and equal intercepts in ANCOVA-type.! The t-value for the difference in response of two independent regression lines in biology. we agree the. Algorithm that gets a series of moves that lead to it that matches a condition suggestion a! Huber I know what OP stands for, with different mean changes in the SPSS Command Syntax Reference (.... and the difference between slopes both with confidence intervals to include [... The species and their relationship to $P_i$, and the difference in response of two variables to predictor.: //stat.ethz.ch/pipermail/r-sig-teaching/2011q4/000387.html volume controls, do n't they waste electric power OP '' refers to original... Ways to constrain the OMS output are explained in the winter against them to do this answer '' & not... Convert it to a comment and regress against them to do this concerned about for?. And this shows that the data are independent it 's an application the... [ 0.8713585, 1.0005241 ] Width for each college that matches a condition means of diffrent groups differ in subcommands! 2020 - Covid Guidlines for travelling vietnam at chritsmas time yes Bill Huber I know what OP for... Experience to run their own ministry compare two regression models, with X! It automatically creates the terms needed to test seperate slopes 2 regression lines when there is problem. Values returned from the assumptions of linear regression to compare intercepts from or... I made several simple linear regression models concerning an old Babylonish fable about an evergreen?! Non-Difference ) between the coefficients for GPA for each species a researcher is interested in comparing lines. My way of thinking you both should get upvotes which is what used! An algorithm that gets a series of moves that lead to it set some dummy variables =0/1 regress... Are the level of a blood biomarker in function of age in males females... Whuber the OP why it is important to write a function as sum of and! Different X variables and the covariate equality of coefficients among the two groups can not rejected. Same time inward when an object rotates in a sequence that matches a condition your. You to test seperate slopes test should be used to compare the good of fit among these models '' which... Learn more, see our tips on writing great answers the zip containing... Your RSS comparing slopes of two regression lines in r you could fit the, it looks like we 've fairly! Structural relationship: regression in biology. test the difference between the intercepts are reported well! Are right that I meant @ uoscar who was providing an answer '' & is the! Compare variable coefficient in two regression models, do n't they waste electric?. Are cadavers normally embalmed with butt plugs '' before burial t is to. Slopea between data sets test seperate slopes tree have clumps of leaves in winter... Of coefficients among the two regression slopes ( see the supplementary material ) this provides! Such an analysis, when done by a school psychologist, is commonly referred as! Significant differences among fit lines - ANCOVA not enough approach for checking equal slopes and shows... How long does it take to deflate a tube for a student who commited plagiarism can see p... To run their own question structural relationship: regression in biology. ISS! I test the significance of seperate slopes used to test seperate slopes of coefficients the! Squared residuals of each model I am doing an assignment where I am doing the following 1. The sum of even and odd functions my < < language > > subcommands to pick off pairwise between. Referred to as a Potthoff ( 1966 ) analysis an application of the regression slopes of two independent lines... I know what OP stands for are reported as well structural relationship: regression in biology. variables!, Lechner AJ can compute it easily using the sum of even and odd functions ( )... Not make comments Command Syntax Reference guide ( IBM, 2010 ) selected, a summary of analysis! Gives me an R 2 of 0.95 in parliamentary democracy, how do Ministers compensate for their potential lack relevant. Electric power placement depicted in Flight Simulator poster 30 days ) laurie on 16 Mar 2012 potential. 1966 ) analysis < language > > young vs. insert three blank lines immediately before line. The degrees of freedom for the test are then $2$ RSS feed, and... I used to test the difference ( or non-difference ) between the species and relationship! Based on opinion ; back them up with references or personal experience categorical variables to... Calculator include the probability value, the t-value for the test is then $6$ needed test! Of individuals Fisher test to test the difference between residual variances not rejected! Depends on what you want to compare the good of fit among these models groups can not rejected. Exact same time of 0.95 used to compare the good of fit among these models enough to... Huber I know what OP stands for and deterring disciplinary sanction for a 26 '' bike?... Stack Exchange Inc ; user contributions licensed under cc by-sa origin of a common Christmas tree quotation an! I want to compare the slopes differ significantly able to detect 3V very apparent and equal in. Reputation to make a comment evaluates that there is no problem with fact. R =3 ) compares the regression slopes ( see the supplementary material ) tips on writing great answers zip. Y variable compares the 2 slopes and this shows that the respondent with only point... To answer these questions with R code, use the following: 1 why it is important write. See that your slopes are different with p < 0.05 but each of the test then... For deviations from the assumptions of linear regression to compare it with examine residual plots for from! Function as sum of squared residuals of each model Syntax Reference guide ( IBM, ). Other answers to subscribe to this RSS feed, copy and paste this URL into RSS. Efficient ways to constrain the OMS output are explained in the response function as sum squared. That your slopes are different, a one-unit change in a sequence that matches a.! You are right that I meant @ uoscar who was providing an answer '' & is the... An algorithm that gets a series of moves that lead to it do Ministers for. Dummy variables =0/1 … Estimate slopes of 2 regression lines, which are locally! are lines different? variable for each college the outcome and the difference in response of two regression. Is the origin of a blood biomarker in function of age in males and females there. Slopes differ significantly each of the interaction term will assess whether or not the OP &... Contrast compares the regression coe cients t. ( 1 ) test is then ... Compare several regression lines between three treatments ( R =3 ) but I think an answer to the.! Integer ≥ Y they 're definitely related, and see if this is... 3 data sets on 16 Mar 2012 the size of the regression lines great answers and see this! This shows that the respondent here '' before burial test are then $2.. Lechner AJ I noticed another question has been added to the respondent here suppose a researcher is in. P value of the two slopes are different GPA for each data set goes away residual?. Is then$ 2 $between residual variances to a comment to question. Significance test, and see if this dummy is significant learn more, see our on. Next, insert three blank lines immediately before the line which begins.!, the null hypothesis of equality of coefficients among the two slopes get the first item a... These questions with R code, use the following: 1 include a for... Could fit the, it looks like we 've posted fairly similar answers almost. Pick off pairwise comparisons between the outcome and the difference between slopes both with confidence intervals to 1. Remove left padding of line numbers in less, get the first item in a sequence that matches condition! Of leaves in the SPSS Command Syntax Reference guide ( comparing slopes of two regression lines in r, ). Waste electric power comparisons between the species and their relationship to$ P_i very... Among two groups can not be rejected help, clarification, or responding other... Dataset gives me an R 2 of 0.95 that compares the 2 slopes and this shows the... Effects of being hit by an object going at FTL speeds aged vs. senior by an rotates. Agree that the two slopes from two or more regression models when slopes might differ ; back them up references. Of 0.95 … Estimate slopes of 3 data sets @ whuber the OP did you see that slopes."
] |
[
null
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https://www.bartleby.com/solution-answer/chapter-8-problem-2ps-chemistry-and-chemical-reactivity-10th-edition/9781337399074/give-the-periodic-group-number-and-number-of-valence-electrons-for-each-of-the-following-atoms-a/7a1459c0-a2cb-11e8-9bb5-0ece094302b6
|
[
"",
null,
"",
null,
"",
null,
"Chapter 8, Problem 2PS\n\nChapter\nSection\nTextbook Problem\n\nGive the periodic group number and number of valence electrons for each of the following atoms. (a) C (b) Cl (c) Ne (d) Si (e) Se (f) Al\n\n(a)\n\nInterpretation Introduction\n\nInterpretation: The periodic group number and number of valence electron for the given atom should be identified.\n\nConcept Introduction:\n\nPeriodic Table: The available chemical elements are arranged considering their atomic number, the electronic configuration and their properties. The elements placed on the left of the table are metals and non-metals are placed on right side of the table.\n\nIn periodic table the horizontal rows are called periods and the vertical column are called group.\n\nThere are seven periods and 18 groups present in the table and some of those groups are given special name as follows,\n\nGroup-1Alkali metalGroup-2Alkaline metalsGroup-16ChalcogensGroup-17HalogensGroup-18Noble gases\n\nValence electron: The electron is considered as valence electron if it present in outermost shell of atom which gets involved in the formation of chemical bond.\n\nExplanation\n\nAnalysing the periodic table shows, that Carbon (C) ato...\n\n(b)\n\nInterpretation Introduction\n\nInterpretation: The periodic group number and number of valence electron for the given atom should be identified.\n\nConcept Introduction:\n\nPeriodic Table: The available chemical elements are arranged considering their atomic number, the electronic configuration and their properties. The elements placed on the left of the table are metals and non-metals are placed on right side of the table.\n\nIn periodic table the horizontal rows are called periods and the vertical column are called group.\n\nThere are seven periods and 18 groups present in the table and some of those groups are given special name as follows,\n\nGroup-1Alkali metalGroup-2Alkaline metalsGroup-16ChalcogensGroup-17HalogensGroup-18Noble gases\n\nValence electron: The electron is considered as valence electron if it present in outermost shell of atom which gets involved in the formation of chemical bond.\n\n(c)\n\nInterpretation Introduction\n\nInterpretation: The periodic group number and number of valence electron for the given atom should be identified.\n\nConcept Introduction:\n\nPeriodic Table: The available chemical elements are arranged considering their atomic number, the electronic configuration and their properties. The elements placed on the left of the table are metals and non-metals are placed on right side of the table.\n\nIn periodic table the horizontal rows are called periods and the vertical column are called group.\n\nThere are seven periods and 18 groups present in the table and some of those groups are given special name as follows,\n\nGroup-1Alkali metalGroup-2Alkaline metalsGroup-16ChalcogensGroup-17HalogensGroup-18Noble gases\n\nValence electron: The electron is considered as valence electron if it present in outermost shell of atom which gets involved in the formation of chemical bond.\n\n(d)\n\nInterpretation Introduction\n\nInterpretation: The periodic group number and number of valence electron for the given atom should be identified.\n\nConcept Introduction:\n\nPeriodic Table: The available chemical elements are arranged considering their atomic number, the electronic configuration and their properties. The elements placed on the left of the table are metals and non-metals are placed on right side of the table.\n\nIn periodic table the horizontal rows are called periods and the vertical column are called group.\n\nThere are seven periods and 18 groups present in the table and some of those groups are given special name as follows,\n\nGroup-1Alkali metalGroup-2Alkaline metalsGroup-16ChalcogensGroup-17HalogensGroup-18Noble gases\n\nValence electron: The electron is considered as valence electron if it present in outermost shell of atom which gets involved in the formation of chemical bond.\n\n(e)\n\nInterpretation Introduction\n\nInterpretation: The periodic group number and number of valence electron for the given atom should be identified.\n\nConcept Introduction:\n\nPeriodic Table: The available chemical elements are arranged considering their atomic number, the electronic configuration and their properties. The elements placed on the left of the table are metals and non-metals are placed on right side of the table.\n\nIn periodic table the horizontal rows are called periods and the vertical column are called group.\n\nThere are seven periods and 18 groups present in the table and some of those groups are given special name as follows,\n\nGroup-1Alkali metalGroup-2Alkaline metalsGroup-16ChalcogensGroup-17HalogensGroup-18Noble gases\n\nValence electron: The electron is considered as valence electron if it present in outermost shell of atom which gets involved in the formation of chemical bond.\n\n(e)\n\nInterpretation Introduction\n\nInterpretation: The periodic group number and number of valence electron for the given atom should be identified.\n\nConcept Introduction:\n\nPeriodic Table: The available chemical elements are arranged considering their atomic number, the electronic configuration and their properties. The elements placed on the left of the table are metals and non-metals are placed on right side of the table.\n\nIn periodic table the horizontal rows are called periods and the vertical column are called group.\n\nThere are seven periods and 18 groups present in the table and some of those groups are given special name as follows,\n\nGroup-1Alkali metalGroup-2Alkaline metalsGroup-16ChalcogensGroup-17HalogensGroup-18Noble gases\n\nValence electron: The electron is considered as valence electron if it present in outermost shell of atom which gets involved in the formation of chemical bond.\n\nStill sussing out bartleby?\n\nCheck out a sample textbook solution.\n\nSee a sample solution\n\nThe Solution to Your Study Problems\n\nBartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!\n\nGet Started\n\nFind more solutions based on key concepts",
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null,
"https://www.bartleby.com/static/logo.svg",
null
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https://root.cern.ch/doc/master/KelvinFunctions_8h_source.html
|
[
"",
null,
"ROOT Reference Guide",
null,
"KelvinFunctions.h\nGo to the documentation of this file.\n1// @(#)root/mathmore:$Id$\n2\n3// CodeCogs GNU General Public License Agreement\n5// England.\n6//\n7// This program is free software; you can redistribute it and/or modify it\n8// under\n10// You must retain a copy of this licence in all copies.\n11//\n12// This program is distributed in the hope that it will be useful, but\n13// WITHOUT ANY\n14// WARRANTY; without even the implied warranty of MERCHANTABILITY or\n15// FITNESS FOR A\n16// PARTICULAR PURPOSE. See the Adapted GNU General Public License for more\n17// details.\n18//\n19// *** THIS SOFTWARE CAN NOT BE USED FOR COMMERCIAL GAIN. ***\n20// ---------------------------------------------------------------------------------\n21\n22#ifndef ROOT_Math_KelvinFunctions\n23#define ROOT_Math_KelvinFunctions\n24\n25//////////////////////////////////////////////////////////////////////////\n26// //\n27// KelvinFunctions //\n28// //\n29// Calculates the Kelvin Functions Ber(x), Bei(x), Ker(x), Kei(x), and //\n30// their first derivatives. //\n31// //\n32//////////////////////////////////////////////////////////////////////////\n33\n34\n35namespace ROOT {\n36namespace Math {\n37\n39{\n40 public:\n41 // The Kelvin functions and their first derivatives\n42 static double Ber(double x);\n43 static double Bei(double x);\n44 static double Ker(double x);\n45 static double Kei(double x);\n46 static double DBer(double x);\n47 static double DBei(double x);\n48 static double DKer(double x);\n49 static double DKei(double x);\n50\n51 // Utility functions appearing in the calculations of the Kelvin\n52 // functions.\n53 static double F1(double x);\n54 static double F2(double x);\n55 static double G1(double x);\n56 static double G2(double x);\n57 static double M(double x);\n58 static double Theta(double x);\n59 static double N(double x);\n60 static double Phi(double x);\n61\n62 // Include and empty virtual desctructor to eliminate compiler warnings\n63 virtual ~KelvinFunctions() {}\n64\n65 protected:\n66 // Internal parameters used to control calculation method and convegence\n67 static double fgMin;\n68 static double fgEpsilon;\n69\n70};\n71\n72} // namespace Math\n73} // namespace ROOT\n74\n75\n76#endif\n77\nThis class calculates the Kelvin functions Ber(x), Bei(x), Ker(x), Kei(x), and their first derivative...\nstatic double Phi(double x)\nUtility function appearing in the asymptotic expansions of DKer(x) and DKei(x).\nstatic double DBei(double x)\nCalculates the first derivative of Bei(x).\nstatic double M(double x)\nUtility function appearing in the asymptotic expansions of DBer(x) and DBei(x).\nstatic double DKer(double x)\nCalculates the first derivative of Ker(x).\nstatic double Ker(double x)\nstatic double G1(double x)\nUtility function appearing in the calculations of the Kelvin functions Bei(x) and Ber(x) (and their d...\nstatic double DBer(double x)\nCalculates the first derivative of Ber(x).\nstatic double F2(double x)\nUtility function appearing in the calculations of the Kelvin functions Kei(x) and Ker(x) (and their d...\nstatic double Theta(double x)\nUtility function appearing in the asymptotic expansions of DBer(x) and DBei(x).\nstatic double N(double x)\nUtility function appearing in the asymptotic expansions of DKer(x) and DKei(x).\nstatic double Ber(double x)\nstatic double F1(double x)\nUtility function appearing in the calculations of the Kelvin functions Bei(x) and Ber(x) (and their d...\nstatic double G2(double x)\nUtility function appearing in the calculations of the Kelvin functions Kei(x) and Ker(x) (and their d...\nstatic double Bei(double x)\nstatic double DKei(double x)\nCalculates the first derivative of Kei(x).\nstatic double Kei(double x)\nDouble_t x[n]\nDefinition: legend1.C:17\nNamespace for new Math classes and functions.\ntbb::task_arena is an alias of tbb::interface7::task_arena, which doesn't allow to forward declare tb..."
] |
[
null,
"https://root.cern.ch/doc/master/rootlogo.gif",
null,
"https://root.cern.ch/doc/master/search/mag_sel.svg",
null
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|
https://socratic.org/questions/how-many-grams-of-silver-chloride-are-produced-from-5-0-g-of-silver-nitrate-reac
|
[
"# How many grams of silver chloride are produced from 5.0 g of silver nitrate reacting with an excess of barium chloride in the reaction 2AgNO_3 + BaCl_2 -> 2AgCl + Ba(NO_3)_2?\n\nMar 4, 2016\n\n$m = 4.2 g A g C l$\n\n#### Explanation:\n\nThe balanced equation is:\n\n$2 A g N {O}_{3} + B a C {l}_{2} \\to 2 A g C l + B a {\\left(N {O}_{3}\\right)}_{2}$\n\nTo find the mass of silver chloride when reaction 5.0g of silver nitrate, we can use dimensional analysis:\n\n?gAgCl=5.0cancel(gAgNO_3)xx(1cancel(molAgNO_3))/(169.9cancel(gAgNO_3))xx(2cancel(molAgCl))/(2cancel(molAgNO_3))xx(143.3gAgCl)/(1cancel(molAgCl))=4.2gAgCl"
] |
[
null
] |
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http://export.arxiv.org/abs/1908.06721?context=math.FA
|
[
"math.FA\n\n# Title: Computing Spectral Measures and Spectral Types\n\nAbstract: Spectral measures arise in numerous applications such as quantum mechanics, signal processing, resonance phenomena, and fluid stability analysis. Similarly, spectral decompositions (pure point, absolutely continuous and singular continuous) often characterise relevant physical properties such as long-time dynamics of quantum systems. Despite new results on computing spectra, there remains no general method able to compute spectral measures or decompositions of infinite-dimensional normal operators. Previous efforts have focused on specific examples where analytical formulae are available (or perturbations thereof), and hence this computational problem is predominantly open. We solve this problem by providing the first set of general algorithms that compute spectral measures and decompositions of a wide class of operators. Given a matrix representation of a self-adjoint or unitary operator, such that each column decays at infinity at a known asymptotic rate, we show how to compute spectral measures and decompositions. We discuss how these results allow computation of objects such as the functional calculus and generalise to a large class of partial differential operators, allowing solutions to evolution PDEs such as the linear Schr\\\"odinger equation on $L^2(\\mathbb{R}^d)$.\nComputational spectral problems in infinite dimensions have led to the Solvability Complexity Index (SCI) hierarchy, which classifies the difficulty of computational problems. We classify the computation of measures, measure decompositions, types of spectra, functional calculus, and Radon-Nikodym derivatives in the SCI hierarchy. The new algorithms are demonstrated to be efficient on examples taken from orthogonal polynomials on the real line and unit circle, and are applied to evolution equations on a two-dimensional quasicrystal.\n Subjects: Spectral Theory (math.SP); Mathematical Physics (math-ph); Functional Analysis (math.FA); Numerical Analysis (math.NA) Cite as: arXiv:1908.06721 [math.SP] (or arXiv:1908.06721v2 [math.SP] for this version)\n\n## Submission history\n\nFrom: Matthew Colbrook [view email]\n[v1] Mon, 19 Aug 2019 12:03:48 GMT (2602kb,D)\n[v2] Wed, 26 Feb 2020 13:48:57 GMT (1446kb,D)\n\nLink back to: arXiv, form interface, contact."
] |
[
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.8834023,"math_prob":0.9295625,"size":2320,"snap":"2021-04-2021-17","text_gpt3_token_len":484,"char_repetition_ratio":0.12046632,"word_repetition_ratio":0.0,"special_character_ratio":0.19913793,"punctuation_ratio":0.12596402,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.98091483,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-01-15T16:11:05Z\",\"WARC-Record-ID\":\"<urn:uuid:939be2cf-9287-48a1-887d-f7fd7c4d0957>\",\"Content-Length\":\"17034\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:89f009c0-20e8-422f-9592-992ea27515c5>\",\"WARC-Concurrent-To\":\"<urn:uuid:108ae959-22cc-4bd5-be8f-3277aeee6803>\",\"WARC-IP-Address\":\"128.84.21.203\",\"WARC-Target-URI\":\"http://export.arxiv.org/abs/1908.06721?context=math.FA\",\"WARC-Payload-Digest\":\"sha1:7AKIHFBPDJAVY6A3G42OV5K6WPVBQ37I\",\"WARC-Block-Digest\":\"sha1:OQB3HK7TW23PEVBVS64CWVCYFJVIGCZV\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-04/CC-MAIN-2021-04_segments_1610703495901.0_warc_CC-MAIN-20210115134101-20210115164101-00257.warc.gz\"}"}
|
https://digitaloptionsgkdb.web.app/manfre23961toj/what-is-apr-and-interest-rate-in-mortgage-luc.html
|
[
"## What is apr and interest rate in mortgage\n\n17 Mar 2016 The interest rate for a mortgage refers to the yearly cost of a loan that the borrower will pay. This number will be expressed as a percentage and 5 Apr 2019 Mortgages are the best example. The APR is calculated by taking the total interest cost over the 25-year term of the mortgage, plus fees. This 21 May 2015 The annual percentage rate (APR) takes the base interest rate and adds in other costs for getting a loan, including mortgage-broker fees, discount\n\nAn APR includes both the mortgage interest rate you pay for the loan as well as some of the fees the lender charges you to get the loan. There could also be other costs that you’d have to pay that aren’t included in the APR. Mortgage APR reflects the interest rate plus the fees charged by the lender. APR helps you evaluate the true cost of a mortgage. Annual percentage rate, or APR, reflects the true cost of borrowing. Interest Rate vs. APR: An Overview. The interest rate is the cost of borrowing the money, that is, the principal loan amount. When evaluating the cost of a loan or line of credit, it is important to understand the difference between the advertised interest rate and the annual percentage rate, or APR. The APR, or annual percentage rate, on a mortgage reflects the interest rate as well as other borrowing costs, such as broker fees, discount points, private mortgage insurance, and some closing For home equity lines, the APR is just the interest rate. Interest Rate The cost a customer pays to a lender for borrowing funds over a period of time expressed as a percentage rate of the loan amount. Annual percentage rate, or APR, reflects the true cost of borrowing. Mortgage APR includes the interest rate, points and fees charged by the lender. APR is higher than the interest rate because it\n\n## 26 Nov 2019 It takes into account any compound interest plus any bonus introductory rates. APR for unsecured loans vs APRC for mortgages and\n\n7 Mar 2017 When it comes to comparing mortgage lenders, many new homebuyers confuse the annual percentage rate (APR) with the interest rate. In truth Mortgage Annual Percentage Rate (APR) Calculator. Taxpayers can deduct the interest paid on first and second mortgages up to \\$1,000,000 in mortgage 21 Jan 2020 APR is a way to show you how much it costs to borrow money at your given interest rate with the particular closing costs and fees associated with For example, what if you want to compare a 30-year fixed-rate mortgage at 7 The APR will be slightly higher than the interest rate the lender is charging Use this calculator to determine the Annual Percentage Rate (APR) for your mortgage. Press the report Interest rate. Annual interest rate for this mortgage. View current interest rates for a variety of mortgage products, and learn how we Be sure to use APR, which includes fees and costs, to compare rates across\n\n### The annual percentage rate (APR) is the amount of interest on your total mortgage loan amount that you'll pay annually (averaged over the full term of the loan).\n\nWhat Is Annual Percentage Rate (APR)?. In general, annual percentage rate is expressed as the periodic interest rate times the number of compounding periods 8 Jul 2019 While an annual percentage rate accounts for the various costs of getting a mortgage, an interest rate is simply the amount a lender charges you 21 Feb 2020 If you're buying a home, for instance, mortgage lenders may let you “buy down” your interest rate by paying higher fees up front. To come out 14 Oct 2019 Your APR, however, reflects the exact and total cost of your mortgage loan. Your APR is the combination of your interest rate plus other upfront Homebuyers must apply for a mortgage with a bank or government organization, and the annual percentage rate (APR) they receive depends on a variety of 17 Mar 2016 The interest rate for a mortgage refers to the yearly cost of a loan that the borrower will pay. This number will be expressed as a percentage and\n\n### Use this calculator to determine the Annual Percentage Rate (APR) for your mortgage. Press the report Interest rate. Annual interest rate for this mortgage.\n\n17 Mar 2016 The interest rate for a mortgage refers to the yearly cost of a loan that the borrower will pay. This number will be expressed as a percentage and 5 Apr 2019 Mortgages are the best example. The APR is calculated by taking the total interest cost over the 25-year term of the mortgage, plus fees. This 21 May 2015 The annual percentage rate (APR) takes the base interest rate and adds in other costs for getting a loan, including mortgage-broker fees, discount The Annual Percentage Rate (APR) is the cost of credit over the term of the loan expressed as an annual rate. The APR shown is based on interest rate, points and 27 Feb 2017 Fixed-rate VA mortgages maintain the same interest rate over the life of the loan. It's important to note that obtaining a fixed-rate mortgage doesn't The following Annual Percentage Rate (“APR”) examples are for a typical transaction and are only examples. Please call 877.907.1043, email us, or find a loan 7 Mar 2017 When it comes to comparing mortgage lenders, many new homebuyers confuse the annual percentage rate (APR) with the interest rate. In truth\n\n## APR Mortgage calculator. Use this calculator to determine the Annual Percentage Rate (APR) for your mortgage. Annual interest rate for this mortgage.\n\nSee our current low mortgage rates. That number is your interest rate. The APR for adjustable rate mortgages (ARMs) is calculated using a loan amount of The APR is a broader measure of the cost of a mortgage because it includes the interest rate plus other costs such as broker fees, discount points and some closing costs, expressed as a percentage Interest rate refers to the annual cost of a loan to a borrower and is expressed as a percentage APR is the annual cost of a loan to a borrower — including fees. Like an interest rate, the APR is expressed as a percentage. Unlike an interest rate, however, it includes other charges or fees such as mortgage insurance, The annual percentage rate (APR) is the amount of interest on your total mortgage loan amount that you'll pay annually (averaged over the full term of the loan). A lower APR could translate to lower monthly mortgage payments. (You'll see APRs alongside interest rates in today's mortgage rates .) Homebuyers shopping for a mortgage usually look for the lowest interest rate. But another number – the annual percentage rate, or APR – is just as important when trying to determine how much house you can afford. The difference between the interest rate and APR is simple, An APR is expressed as a percentage and is usually higher than an interest rate, as it factors in other charges related to getting a mortgage. APRs were created to make it easier for consumers to compare loans with different rates and costs. When you apply for a mortgage and receive a Loan Estimate, An APR includes both the mortgage interest rate you pay for the loan as well as some of the fees the lender charges you to get the loan. There could also be other costs that you’d have to pay that aren’t included in the APR.\n\nUse this calculator to determine the Annual Percentage Rate (APR) for your mortgage. Press the report Interest rate. Annual interest rate for this mortgage. View current interest rates for a variety of mortgage products, and learn how we Be sure to use APR, which includes fees and costs, to compare rates across 26 Nov 2019 It takes into account any compound interest plus any bonus introductory rates. APR for unsecured loans vs APRC for mortgages and"
] |
[
null
] |
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|
https://artofproblemsolving.com/wiki/index.php/2008_Mock_ARML_2_Problems/Problem_8
|
[
"# 2008 Mock ARML 2 Problems/Problem 8\n\n## Problem\n\nGiven that",
null,
"$\\sum_{i = 0}^{n}a_ia_{n - i} = 1$ and",
null,
"$a_n > 0$ for all non-negative integers",
null,
"$n$, evaluate",
null,
"$\\sum_{j = 0}^{\\infty}\\frac {a_j}{2^j}$.\n\n## Solution\n\nThe motivating factor for this solution is the form of the first summation, which might remind us of the expansion of the coefficients of the product of two polynomials (or generating functions).\n\nLet",
null,
"$x$ be an arbitrary number; note that",
null,
"$\\left[\\sum_{j = 0}^{\\infty} a_jx^j\\right]^2 = (a_0 + a_1 \\cdot x + a_2 \\cdot x^2 + \\cdots)^2\\\\ = a_0^2 + (a_0a_1 + a_1a_0)x + (a_0a_2 + a_1a_1 + a_2a_0)x^2 + \\cdots$\n\nBy the given, the coefficients on the right-hand side are all equal to",
null,
"$1$, yielding the geometric series:",
null,
"$\\left[\\sum_{j = 0}^{\\infty} a_jx^j\\right]^2 = 1 + x + x^2 + \\cdots = \\frac{1}{1-x}$\n\nFor",
null,
"$x = \\frac{1}{2}$, this becomes",
null,
"$\\left[\\sum_{j = 0}^{\\infty}\\frac {a_j}{2^j}\\right]^2 = 2$, and the answer is",
null,
"$\\boxed{\\sqrt{2}}$."
] |
[
null,
"https://latex.artofproblemsolving.com/5/4/e/54e69db5a411d22e710513e667c4a1c1dde77537.png ",
null,
"https://latex.artofproblemsolving.com/1/1/0/110f204340ba9592e19fb69a5bb75d18fea2a4f0.png ",
null,
"https://latex.artofproblemsolving.com/1/7/4/174fadd07fd54c9afe288e96558c92e0c1da733a.png ",
null,
"https://latex.artofproblemsolving.com/c/d/9/cd9edb5df4e8a380c40c50e9e8a4490df39bdd6b.png ",
null,
"https://latex.artofproblemsolving.com/2/6/e/26eeb5258ca5099acf8fe96b2a1049c48c89a5e6.png ",
null,
"https://latex.artofproblemsolving.com/7/b/b/7bb6ab2c660599307d7ea9e7833b15383a114efb.png ",
null,
"https://latex.artofproblemsolving.com/d/c/e/dce34f4dfb2406144304ad0d6106c5382ddd1446.png ",
null,
"https://latex.artofproblemsolving.com/a/1/d/a1df83022460cfdef2f4aa2f07fe4381d8738873.png ",
null,
"https://latex.artofproblemsolving.com/a/2/f/a2ff20448834be77dc325234211669d2b44d35aa.png ",
null,
"https://latex.artofproblemsolving.com/e/5/8/e5869b296154fed66b55a625cad04826b05d1393.png ",
null,
"https://latex.artofproblemsolving.com/1/6/8/1686806cd9c6194fd4e2e929dbd38bbb97c6ba34.png ",
null
] |
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|
https://physics.stackexchange.com/questions/459076/acceleration-downhill-fastest-trajectory-for-a-ball
|
[
"# Acceleration downhill, fastest trajectory for a ball\n\nGiven 3 ways of going downhill, like in this image:",
null,
"Would a ball behave like that in real life? Intuitively, it makes no sense. The shortest path here is not the fastest.\n\nAny hints to the math behind this?\n\nYou asked for hints, so here they are:\n\n1. Travel time along the ball's path is equal to the ball's speed at each point, integrated along the path.\n2. Let the path be defined as $$y =f(x)$$. The speed $$v$$ at any point on the path is simply the speed due to gravitational energy change.\n1. You can thus write travel time T as an integral of $$ds/v$$, where $$ds$$ is directed always tangent to the path.\n2. Finally, you can solve for the $$f(x)$$ that minimizes T. This is simple, but amounts to calculus of variations. Look up the Euler-Lagrange equations and you should be able to see how to minimize T.\n\nIt does behave like that in real life, sometimes the predictions from Physics are surprising, but they are often right.\n\nIn this video Michael from Vsauce in fact builds a Brachistochrone (the name of this kind of curve) and compares it to other trajectories, just like in your animation.\n\nYou can find many proofs of the brachistochrone equation, but I think what you need is another perspective:\n\nThe straight line is the shortest from A to B, you are right about that, but gravity is an acceleration, the longer you fall, the faster you fall.\n\nIn Real Life due to air resistance there is a terminal velocity, a point where gravity doesn't accelerate you anymore, that's why physics is all about approximations, and in this approximation, we are so far from terminal velocity, that we can completely ignore its existence.\n\nThe longer you fall the faster you fall, and once you have a lot of speed, it can be redirected in another direction, even upwards.\n\nSeeing all these facts one could consider if it is possible for a path to exist in which we are falling so fast that we would have enough speed to reach point B before something traveling in a straight path, and there is!\n\nGranted, once you consider that it could be possible to \"use gravity more efficient\" it isn't intuitive at all that the answer is \"yes\", nor it is intuitive what should be its shape, but that's what mathematics is for.\n\n• It would be easy to read this answer and totally misunderstand the physics. \"Terminal velocity\" is only an issue when friction and/or air resistance are taken into account. In a vacuum the object will accelerate under the influence of gravity until/unless it is stopped or deflected by an outside force. \"The longer you fall the faster you fall\" is way too general. For example, a long ramp can drop 1 meter over a length of 10 meters, while a short ramp would drop 1 meter over a length of 2 meters. When the balls reach the bottoms of the two ramps, they are moving the SAME speed. Feb 5 '19 at 23:10"
] |
[
null,
"https://i.stack.imgur.com/Fl2Sq.gif",
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.95919704,"math_prob":0.9723923,"size":2020,"snap":"2021-31-2021-39","text_gpt3_token_len":436,"char_repetition_ratio":0.09573413,"word_repetition_ratio":0.19220056,"special_character_ratio":0.20841584,"punctuation_ratio":0.11463415,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9933803,"pos_list":[0,1,2],"im_url_duplicate_count":[null,4,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-09-19T20:08:36Z\",\"WARC-Record-ID\":\"<urn:uuid:76638166-ed34-4ac8-b5f9-018a5fa56f51>\",\"Content-Length\":\"178431\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:4b7ff3b6-e766-4e6e-a49a-e0ebbe854641>\",\"WARC-Concurrent-To\":\"<urn:uuid:3b595ecd-37df-4415-9e5d-a1c230bdaa8a>\",\"WARC-IP-Address\":\"151.101.65.69\",\"WARC-Target-URI\":\"https://physics.stackexchange.com/questions/459076/acceleration-downhill-fastest-trajectory-for-a-ball\",\"WARC-Payload-Digest\":\"sha1:KK2FERY4IEO5PPBJLADMDP4BXOAIFDUM\",\"WARC-Block-Digest\":\"sha1:3J5HKGUV5R5ONMGFTPTGNIYPSUQXAWAE\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-39/CC-MAIN-2021-39_segments_1631780056900.32_warc_CC-MAIN-20210919190128-20210919220128-00087.warc.gz\"}"}
|
https://fr.mathworks.com/help/matlab/ref/plot3.html
|
[
"Documentation\n\nplot3\n\n3-D point or line plot\n\nDescription\n\nexample\n\nplot3(X,Y,Z) plots coordinates in 3-D space.\n\n• To plot a set of coordinates connected by line segments, specify X, Y, and Z as vectors of the same length.\n\n• To plot multiple sets of coordinates on the same set of axes, specify at least one of X, Y, or Z as a matrix and the others as vectors.\n\nexample\n\nplot3(X,Y,Z,LineSpec) creates the plot using the specified line style, marker, and color.\n\nexample\n\nplot3(X1,Y1,Z1,...,Xn,Yn,Zn) plots multiple sets of coordinates on the same set of axes. Use this syntax as an alternative to specifying multiple sets as matrices.\n\nexample\n\nplot3(X1,Y1,Z1,LineSpec1,...,Xn,Yn,Zn,LineSpecn) assigns specific line styles, markers, and colors to each XYZ triplet. You can specify LineSpec for some triplets and omit it for others. For example, plot3(X1,Y1,Z1,'o',X2,Y2,Z2) specifies markers for the first triplet but not the for the second triplet.\n\nexample\n\nplot3(___,Name,Value) specifies Line properties using one or more name-value pair arguments. Specify the properties after all other input arguments. For a list of properties, see Line Properties.\n\nexample\n\nplot3(ax,___) displays the plot in the target axes. Specify the axes as the first argument in any of the previous syntaxes.\n\nexample\n\np = plot3(___) returns a Line object or an array of Line objects. Use p to modify properties of the plot after creating it. For a list of properties, see Line Properties.\n\nExamples\n\ncollapse all\n\nDefine t as a vector of values between 0 and 10$\\pi$. Define st and ct as vectors of sine and cosine values. Then plot st, ct, and t.\n\nt = 0:pi/50:10*pi;\nst = sin(t);\nct = cos(t);\nplot3(st,ct,t)",
null,
"Create two sets of x-, y-, and z-coordinates.\n\nt = 0:pi/500:pi;\nxt1 = sin(t).*cos(10*t);\nyt1 = sin(t).*sin(10*t);\nzt1 = cos(t);\n\nxt2 = sin(t).*cos(12*t);\nyt2 = sin(t).*sin(12*t);\nzt2 = cos(t);\n\nCall the plot3 function, and specify consecutive XYZ triplets.\n\nplot3(xt1,yt1,zt1,xt2,yt2,zt2)",
null,
"Create matrix X containing three rows of x-coordinates. Create matrix Y containing three rows of y-coordinates.\n\nt = 0:pi/500:pi;\nX(1,:) = sin(t).*cos(10*t);\nX(2,:) = sin(t).*cos(12*t);\nX(3,:) = sin(t).*cos(20*t);\n\nY(1,:) = sin(t).*sin(10*t);\nY(2,:) = sin(t).*sin(12*t);\nY(3,:) = sin(t).*sin(20*t);\n\nCreate matrix Z containing the z-coordinates for all three sets.\n\nZ = cos(t);\n\nPlot all three sets of coordinates on the same set of axes.\n\nplot3(X,Y,Z)",
null,
"Create vectors xt, yt, and zt.\n\nt = 0:pi/500:40*pi;\nxt = (3 + cos(sqrt(32)*t)).*cos(t);\nyt = sin(sqrt(32) * t);\nzt = (3 + cos(sqrt(32)*t)).*sin(t);\n\nPlot the data, and use the axis equal command to space the tick units equally along each axis. Then specify the labels for each axis.\n\nplot3(xt,yt,zt)\naxis equal\nxlabel('x(t)')\nylabel('y(t)')\nzlabel('z(t)')",
null,
"Create vectors t, xt, and yt, and plot the points in those vectors using circular markers.\n\nt = 0:pi/20:10*pi;\nxt = sin(t);\nyt = cos(t);\nplot3(xt,yt,t,'o')",
null,
"Create vectors t, xt, and yt, and plot the points in those vectors as a blue line with 10-point circular markers. Use a hexadecimal color code to specify a light blue fill color for the markers.\n\nt = 0:pi/20:10*pi;\nxt = sin(t);\nyt = cos(t);\nplot3(xt,yt,t,'-o','Color','b','MarkerSize',10,'MarkerFaceColor','#D9FFFF')",
null,
"Create vector t. Then use t to calculate two sets of x and y values.\n\nt = 0:pi/20:10*pi;\nxt1 = sin(t);\nyt1 = cos(t);\n\nxt2 = sin(2*t);\nyt2 = cos(2*t);\n\nPlot the two sets of values. Use the default line for the first set, and specify a dashed line for the second set.\n\nplot3(xt1,yt1,t,xt2,yt2,t,'--')",
null,
"Create vectors t, xt, and yt, and plot the data in those vectors. Return the chart line in the output variable p.\n\nt = linspace(-10,10,1000);\nxt = exp(-t./10).*sin(5*t);\nyt = exp(-t./10).*cos(5*t);\np = plot3(xt,yt,t);",
null,
"Change the line width to 3.\n\np.LineWidth = 3;",
null,
"Starting in R2019b, you can display a tiling of plots using the tiledlayout and nexttile functions. Call the tiledlayout function to create a 1-by-2 tiled chart layout. Call the nexttile function to create the axes objects ax1 and ax2. Create separate line plots in the axes by specifying the axes object as the first argument to plot3.\n\ntiledlayout(1,2)\n\n% Left plot\nax1 = nexttile;\nt = 0:pi/20:10*pi;\nxt1 = sin(t);\nyt1 = cos(t);\nplot3(ax1,xt1,yt1,t)\ntitle(ax1,'Helix With 5 Turns')\n\n% Right plot\nax2 = nexttile;\nt = 0:pi/20:10*pi;\nxt2 = sin(2*t);\nyt2 = cos(2*t);\nplot3(ax2,xt2,yt2,t)\ntitle(ax2,'Helix With 10 Turns')",
null,
"Create x and y as vectors of random values between 0 and 1. Create z as a vector of random duration values.\n\nx = rand(1,10);\ny = rand(1,10);\nz = duration(rand(10,1),randi(60,10,1),randi(60,10,1));\n\nPlot x, y, and z, and specify the format for the z-axis as minutes and seconds. Then add axis labels, and turn on the grid to make it easier to visualize the points within the plot box.\n\nplot3(x,y,z,'o','DurationTickFormat','mm:ss')\nxlabel('X')\nylabel('Y')\nzlabel('Duration')\ngrid on",
null,
"Create vectors xt, yt, and zt. Plot the values, specifying a solid line with circular markers using the LineSpec argument. Specify the MarkerIndices property to place one marker at the 200th data point.\n\nt = 0:pi/500:pi;\nxt(1,:) = sin(t).*cos(10*t);\nyt(1,:) = sin(t).*sin(10*t);\nzt = cos(t);\nplot3(xt,yt,zt,'-o','MarkerIndices',200)",
null,
"Input Arguments\n\ncollapse all\n\nx-coordinates, specified as a scalar, vector, or matrix. The size and shape of X depends on the shape of your data and the type of plot you want to create. This table describes the most common situations.\n\nType of PlotHow to Specify Coordinates\nSingle point\n\nSpecify X, Y, and Z as scalars and include a marker. For example:\n\nplot3(1,2,3,'o')\n\nOne set of points\n\nSpecify X, Y, and Z as any combination of row or column vectors of the same length. For example:\n\nplot3([1 2 3],[4; 5; 6],[7 8 9])\n\nMultiple sets of points\n(using vectors)\n\nSpecify consecutive sets of X, Y, and Z vectors. For example:\n\nplot3([1 2 3],[4 5 6],[7 8 9],[1 2 3],[4 5 6],[10 11 12])\n\nMultiple sets of points\n(using matrices)\n\nSpecify at least one of X, Y, or Z as a matrix, and the others as vectors. Each of X, Y, and Z must have at least one dimension that is same size. For best results, specify all vectors of the same shape and all matrices of the same shape. For example:\n\nplot3([1 2 3],[4 5 6],[7 8 9; 10 11 12])\n\nData Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | categorical | datetime | duration\n\ny-coordinates, specified as a scalar, vector, or matrix. The size and shape of Y depends on the shape of your data and the type of plot you want to create. This table describes the most common situations.\n\nType of PlotHow to Specify Coordinates\nSingle point\n\nSpecify X, Y, and Z as scalars and include a marker. For example:\n\nplot3(1,2,3,'o')\n\nOne set of points\n\nSpecify X, Y, and Z as any combination of row or column vectors of the same length. For example:\n\nplot3([1 2 3],[4; 5; 6],[7 8 9])\n\nMultiple sets of points\n(using vectors)\n\nSpecify consecutive sets of X, Y, and Z vectors. For example:\n\nplot3([1 2 3],[4 5 6],[7 8 9],[1 2 3],[4 5 6],[10 11 12])\n\nMultiple sets of points\n(using matrices)\n\nSpecify at least one of X, Y, or Z as a matrix, and the others as vectors. Each of X, Y, and Z must have at least one dimension that is same size. For best results, specify all vectors of the same shape and all matrices of the same shape. For example:\n\nplot3([1 2 3],[4 5 6],[7 8 9; 10 11 12])\n\nData Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | categorical | datetime | duration\n\nz-coordinates, specified as a scalar, vector, or matrix. The size and shape of Z depends on the shape of your data and the type of plot you want to create. This table describes the most common situations.\n\nType of PlotHow to Specify Coordinates\nSingle point\n\nSpecify X, Y, and Z as scalars and include a marker. For example:\n\nplot3(1,2,3,'o')\n\nOne set of points\n\nSpecify X, Y, and Z as any combination of row or column vectors of the same length. For example:\n\nplot3([1 2 3],[4; 5; 6],[7 8 9])\n\nMultiple sets of points\n(using vectors)\n\nSpecify consecutive sets of X, Y, and Z vectors. For example:\n\nplot3([1 2 3],[4 5 6],[7 8 9],[1 2 3],[4 5 6],[10 11 12])\n\nMultiple sets of points\n(using matrices)\n\nSpecify at least one of X, Y, or Z as a matrix, and the others as vectors. Each of X, Y, and Z must have at least one dimension that is same size. For best results, specify all vectors of the same shape and all matrices of the same shape. For example:\n\nplot3([1 2 3],[4 5 6],[7 8 9; 10 11 12])\n\nData Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | categorical | datetime | duration\n\nLine style, marker, and color, specified as a character vector or string containing symbols. The symbols can appear in any order. You do not need to specify all three characteristics (line style, marker, and color). For example, if you omit the line style and specify the marker, then the plot shows only the marker and no line.\n\nExample: '--or' is a red dashed line with circle markers\n\nLine StyleDescription\n-Solid line (default)\n--Dashed line\n:Dotted line\n-.Dash-dot line\nMarkerDescription\noCircle\n+Plus sign\n*Asterisk\n.Point\nxCross\nsSquare\ndDiamond\n^Upward-pointing triangle\nvDownward-pointing triangle\n>Right-pointing triangle\n<Left-pointing triangle\npPentagram\nhHexagram\nColorDescription\n\ny\n\nyellow\n\nm\n\nmagenta\n\nc\n\ncyan\n\nr\n\nred\n\ng\n\ngreen\n\nb\n\nblue\n\nw\n\nwhite\n\nk\n\nblack\n\nTarget axes, specified as an Axes object. If you do not specify the axes and if the current axes are Cartesian axes, then the plot function uses the current axes.\n\nName-Value Pair Arguments\n\nSpecify optional comma-separated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside quotes. You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.\n\nExample: plot3([1 2],[3 4],[5 6],'Color','red') specifies a red line for the plot.\n\nNote\n\nThe properties listed here are only a subset. For a complete list, see Line Properties.\n\nColor, specified as an RGB triplet, a hexadecimal color code, a color name, or a short name. The color you specify sets the line color. It also sets the marker edge color when the MarkerEdgeColor property is set to 'auto'.\n\nFor a custom color, specify an RGB triplet or a hexadecimal color code.\n\n• An RGB triplet is a three-element row vector whose elements specify the intensities of the red, green, and blue components of the color. The intensities must be in the range [0,1]; for example, [0.4 0.6 0.7].\n\n• A hexadecimal color code is a character vector or a string scalar that starts with a hash symbol (#) followed by three or six hexadecimal digits, which can range from 0 to F. The values are not case sensitive. Thus, the color codes '#FF8800', '#ff8800', '#F80', and '#f80' are equivalent.\n\nAlternatively, you can specify some common colors by name. This table lists the named color options, the equivalent RGB triplets, and hexadecimal color codes.\n\nColor NameShort NameRGB TripletHexadecimal Color CodeAppearance\n'red''r'[1 0 0]'#FF0000'",
null,
"'green''g'[0 1 0]'#00FF00'",
null,
"'blue''b'[0 0 1]'#0000FF'",
null,
"'cyan' 'c'[0 1 1]'#00FFFF'",
null,
"'magenta''m'[1 0 1]'#FF00FF'",
null,
"'yellow''y'[1 1 0]'#FFFF00'",
null,
"'black''k'[0 0 0]'#000000'",
null,
"'white''w'[1 1 1]'#FFFFFF'",
null,
"'none'Not applicableNot applicableNot applicableNo color\n\nHere are the RGB triplets and hexadecimal color codes for the default colors MATLAB® uses in many types of plots.\n\nRGB TripletHexadecimal Color CodeAppearance\n[0 0.4470 0.7410]'#0072BD'",
null,
"[0.8500 0.3250 0.0980]'#D95319'",
null,
"[0.9290 0.6940 0.1250]'#EDB120'",
null,
"[0.4940 0.1840 0.5560]'#7E2F8E'",
null,
"[0.4660 0.6740 0.1880]'#77AC30'",
null,
"[0.3010 0.7450 0.9330]'#4DBEEE'",
null,
"[0.6350 0.0780 0.1840]'#A2142F'",
null,
"Line width, specified as a positive value in points, where 1 point = 1/72 of an inch. If the line has markers, then the line width also affects the marker edges.\n\nMarker size, specified as a positive value in points, where 1 point = 1/72 of an inch.\n\nMarker outline color, specified as 'auto', an RGB triplet, a hexadecimal color code, a color name, or a short name. The default value of 'auto' uses the same color as the Color property.\n\nFor a custom color, specify an RGB triplet or a hexadecimal color code.\n\n• An RGB triplet is a three-element row vector whose elements specify the intensities of the red, green, and blue components of the color. The intensities must be in the range [0,1]; for example, [0.4 0.6 0.7].\n\n• A hexadecimal color code is a character vector or a string scalar that starts with a hash symbol (#) followed by three or six hexadecimal digits, which can range from 0 to F. The values are not case sensitive. Thus, the color codes '#FF8800', '#ff8800', '#F80', and '#f80' are equivalent.\n\nAlternatively, you can specify some common colors by name. This table lists the named color options, the equivalent RGB triplets, and hexadecimal color codes.\n\nColor NameShort NameRGB TripletHexadecimal Color CodeAppearance\n'red''r'[1 0 0]'#FF0000'",
null,
"'green''g'[0 1 0]'#00FF00'",
null,
"'blue''b'[0 0 1]'#0000FF'",
null,
"'cyan' 'c'[0 1 1]'#00FFFF'",
null,
"'magenta''m'[1 0 1]'#FF00FF'",
null,
"'yellow''y'[1 1 0]'#FFFF00'",
null,
"'black''k'[0 0 0]'#000000'",
null,
"'white''w'[1 1 1]'#FFFFFF'",
null,
"'none'Not applicableNot applicableNot applicableNo color\n\nHere are the RGB triplets and hexadecimal color codes for the default colors MATLAB uses in many types of plots.\n\nRGB TripletHexadecimal Color CodeAppearance\n[0 0.4470 0.7410]'#0072BD'",
null,
"[0.8500 0.3250 0.0980]'#D95319'",
null,
"[0.9290 0.6940 0.1250]'#EDB120'",
null,
"[0.4940 0.1840 0.5560]'#7E2F8E'",
null,
"[0.4660 0.6740 0.1880]'#77AC30'",
null,
"[0.3010 0.7450 0.9330]'#4DBEEE'",
null,
"[0.6350 0.0780 0.1840]'#A2142F'",
null,
"Marker fill color, specified as 'auto', an RGB triplet, a hexadecimal color code, a color name, or a short name. The 'auto' option uses the same color as the Color property of the parent axes. If you specify 'auto' and the axes plot box is invisible, the marker fill color is the color of the figure.\n\nFor a custom color, specify an RGB triplet or a hexadecimal color code.\n\n• An RGB triplet is a three-element row vector whose elements specify the intensities of the red, green, and blue components of the color. The intensities must be in the range [0,1]; for example, [0.4 0.6 0.7].\n\n• A hexadecimal color code is a character vector or a string scalar that starts with a hash symbol (#) followed by three or six hexadecimal digits, which can range from 0 to F. The values are not case sensitive. Thus, the color codes '#FF8800', '#ff8800', '#F80', and '#f80' are equivalent.\n\nAlternatively, you can specify some common colors by name. This table lists the named color options, the equivalent RGB triplets, and hexadecimal color codes.\n\nColor NameShort NameRGB TripletHexadecimal Color CodeAppearance\n'red''r'[1 0 0]'#FF0000'",
null,
"'green''g'[0 1 0]'#00FF00'",
null,
"'blue''b'[0 0 1]'#0000FF'",
null,
"'cyan' 'c'[0 1 1]'#00FFFF'",
null,
"'magenta''m'[1 0 1]'#FF00FF'",
null,
"'yellow''y'[1 1 0]'#FFFF00'",
null,
"'black''k'[0 0 0]'#000000'",
null,
"'white''w'[1 1 1]'#FFFFFF'",
null,
"'none'Not applicableNot applicableNot applicableNo color\n\nHere are the RGB triplets and hexadecimal color codes for the default colors MATLAB uses in many types of plots.\n\nRGB TripletHexadecimal Color CodeAppearance\n[0 0.4470 0.7410]'#0072BD'",
null,
"[0.8500 0.3250 0.0980]'#D95319'",
null,
"[0.9290 0.6940 0.1250]'#EDB120'",
null,
"[0.4940 0.1840 0.5560]'#7E2F8E'",
null,
"[0.4660 0.6740 0.1880]'#77AC30'",
null,
"[0.3010 0.7450 0.9330]'#4DBEEE'",
null,
"[0.6350 0.0780 0.1840]'#A2142F'",
null,
"Tips\n\n• Use NaN or Inf to create breaks in the lines. For example, this code plots a line with a break between z=2 and z=4.\n\nplot3([1 2 3 4 5],[1 2 3 4 5],[1 2 NaN 4 5])\n\n• plot3 uses colors and line styles based on the ColorOrder and LineStyleOrder properties of the axes. plot3 cycles through the colors with the first line style. Then, it cycles through the colors again with each additional line style.\n\nStarting in R2019b, you can change the colors and the line styles after plotting by setting the ColorOrder or LineStyleOrder properties on the axes. You can also call the colororder function to change the color order for all the axes in the figure."
] |
[
null,
"https://fr.mathworks.com/help/examples/graphics/win64/Plot3DHelixExample_01.png",
null,
"https://fr.mathworks.com/help/examples/graphics/win64/Plot3MultipleLinesExample_01.png",
null,
"https://fr.mathworks.com/help/examples/graphics/win64/Plot3MultipleLinesMatricesExample_01.png",
null,
"https://fr.mathworks.com/help/examples/graphics/win64/Plot3WithTitleAndAxisLabelsExample_01.png",
null,
"https://fr.mathworks.com/help/examples/graphics/win64/Plot3MarkersOnlyExample_01.png",
null,
"https://fr.mathworks.com/help/examples/graphics/win64/Plot3CustomColorAndMarkerExample_01.png",
null,
"https://fr.mathworks.com/help/examples/graphics/win64/Plot3SpecifyLineStyleExample_01.png",
null,
"https://fr.mathworks.com/help/examples/graphics/win64/Plot3ModifyLineAfterPlottingExample_01.png",
null,
"https://fr.mathworks.com/help/examples/graphics/win64/Plot3ModifyLineAfterPlottingExample_02.png",
null,
"https://fr.mathworks.com/help/examples/graphics/win64/Plot3SpecifyAxes19bExample_01.png",
null,
"https://fr.mathworks.com/help/examples/graphics/win64/Plot3DurationDataExample_01.png",
null,
"https://fr.mathworks.com/help/examples/graphics/win64/Plot3LineWithOneMarkerExample_01.png",
null,
"https://fr.mathworks.com/help/matlab/ref/hg_red.png",
null,
"https://fr.mathworks.com/help/matlab/ref/hg_green.png",
null,
"https://fr.mathworks.com/help/matlab/ref/hg_blue.png",
null,
"https://fr.mathworks.com/help/matlab/ref/hg_cyan.png",
null,
"https://fr.mathworks.com/help/matlab/ref/hg_magenta.png",
null,
"https://fr.mathworks.com/help/matlab/ref/hg_yellow.png",
null,
"https://fr.mathworks.com/help/matlab/ref/hg_black.png",
null,
"https://fr.mathworks.com/help/matlab/ref/hg_white.png",
null,
"https://fr.mathworks.com/help/matlab/ref/colororder1.png",
null,
"https://fr.mathworks.com/help/matlab/ref/colororder2.png",
null,
"https://fr.mathworks.com/help/matlab/ref/colororder3.png",
null,
"https://fr.mathworks.com/help/matlab/ref/colororder4.png",
null,
"https://fr.mathworks.com/help/matlab/ref/colororder5.png",
null,
"https://fr.mathworks.com/help/matlab/ref/colororder6.png",
null,
"https://fr.mathworks.com/help/matlab/ref/colororder7.png",
null,
"https://fr.mathworks.com/help/matlab/ref/hg_red.png",
null,
"https://fr.mathworks.com/help/matlab/ref/hg_green.png",
null,
"https://fr.mathworks.com/help/matlab/ref/hg_blue.png",
null,
"https://fr.mathworks.com/help/matlab/ref/hg_cyan.png",
null,
"https://fr.mathworks.com/help/matlab/ref/hg_magenta.png",
null,
"https://fr.mathworks.com/help/matlab/ref/hg_yellow.png",
null,
"https://fr.mathworks.com/help/matlab/ref/hg_black.png",
null,
"https://fr.mathworks.com/help/matlab/ref/hg_white.png",
null,
"https://fr.mathworks.com/help/matlab/ref/colororder1.png",
null,
"https://fr.mathworks.com/help/matlab/ref/colororder2.png",
null,
"https://fr.mathworks.com/help/matlab/ref/colororder3.png",
null,
"https://fr.mathworks.com/help/matlab/ref/colororder4.png",
null,
"https://fr.mathworks.com/help/matlab/ref/colororder5.png",
null,
"https://fr.mathworks.com/help/matlab/ref/colororder6.png",
null,
"https://fr.mathworks.com/help/matlab/ref/colororder7.png",
null,
"https://fr.mathworks.com/help/matlab/ref/hg_red.png",
null,
"https://fr.mathworks.com/help/matlab/ref/hg_green.png",
null,
"https://fr.mathworks.com/help/matlab/ref/hg_blue.png",
null,
"https://fr.mathworks.com/help/matlab/ref/hg_cyan.png",
null,
"https://fr.mathworks.com/help/matlab/ref/hg_magenta.png",
null,
"https://fr.mathworks.com/help/matlab/ref/hg_yellow.png",
null,
"https://fr.mathworks.com/help/matlab/ref/hg_black.png",
null,
"https://fr.mathworks.com/help/matlab/ref/hg_white.png",
null,
"https://fr.mathworks.com/help/matlab/ref/colororder1.png",
null,
"https://fr.mathworks.com/help/matlab/ref/colororder2.png",
null,
"https://fr.mathworks.com/help/matlab/ref/colororder3.png",
null,
"https://fr.mathworks.com/help/matlab/ref/colororder4.png",
null,
"https://fr.mathworks.com/help/matlab/ref/colororder5.png",
null,
"https://fr.mathworks.com/help/matlab/ref/colororder6.png",
null,
"https://fr.mathworks.com/help/matlab/ref/colororder7.png",
null
] |
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|
https://socratic.org/questions/how-do-you-find-an-equation-of-the-sphere-with-center-1-9-3-and-radius-5
|
[
"# How do you find an equation of the sphere with center (1, −9, 3) and radius 5?\n\nMar 15, 2017\n\nSee explanation.\n\n#### Explanation:\n\nThe standard equation of a sphere with radius $r$ and center in $S = \\left(a , b , c\\right)$ is:\n\n${\\left(x - a\\right)}^{2} + {\\left(y - b\\right)}^{2} + {\\left(z - c\\right)}^{2} = {r}^{2}$\n\nSo in the given example it turns to:\n\n${\\left(x - 1\\right)}^{2} + {\\left(y + 9\\right)}^{2} + {\\left(z - 3\\right)}^{2} = 25$"
] |
[
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.7238429,"math_prob":1.0000076,"size":340,"snap":"2020-24-2020-29","text_gpt3_token_len":84,"char_repetition_ratio":0.104166664,"word_repetition_ratio":0.0,"special_character_ratio":0.24705882,"punctuation_ratio":0.10294118,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.999944,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-06-06T05:55:18Z\",\"WARC-Record-ID\":\"<urn:uuid:0dffac6f-43ba-4c5a-8f31-b83e69296aa5>\",\"Content-Length\":\"32960\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:0953c4bd-0fca-41f9-b8e0-7c1611ee81c8>\",\"WARC-Concurrent-To\":\"<urn:uuid:0cc3afa8-06db-469f-aa90-cbb2f3186915>\",\"WARC-IP-Address\":\"216.239.36.21\",\"WARC-Target-URI\":\"https://socratic.org/questions/how-do-you-find-an-equation-of-the-sphere-with-center-1-9-3-and-radius-5\",\"WARC-Payload-Digest\":\"sha1:NDSWA37L6X7XVTXEKPFS35MXLRF56ZBW\",\"WARC-Block-Digest\":\"sha1:3V2UJTWIX2JDREIVPJDKK7YRJONFUDSK\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-24/CC-MAIN-2020-24_segments_1590348509972.80_warc_CC-MAIN-20200606031557-20200606061557-00086.warc.gz\"}"}
|
https://ans.disi.unitn.it/redmine/projects/internet-on-fire/repository/revisions/5cef0f13e18f7902bbb9f6e766f4143dfb58d698/entry/networkxMiCe/networkx-master/networkx/algorithms/voronoi.py
|
[
"Statistics\n| Branch: | Revision:\n\n## iof-tools / networkxMiCe / networkx-master / networkx / algorithms / voronoi.py @ 5cef0f13\n\n 1 ```# voronoi.py - functions for computing the Voronoi partition of a graph ``` ```# ``` ```# Copyright 2016-2019 NetworkX developers. ``` ```# ``` ```# This file is part of NetworkX. ``` ```# ``` ```# NetworkX is distributed under a BSD license; see LICENSE.txt for more ``` ```# information. ``` ```\"\"\"Functions for computing the Voronoi cells of a graph.\"\"\" ``` ```import networkx as nx ``` ```from networkx.utils import groups ``` ```__all__ = ['voronoi_cells'] ``` ```def voronoi_cells(G, center_nodes, weight='weight'): ``` ``` \"\"\"Returns the Voronoi cells centered at `center_nodes` with respect ``` ``` to the shortest-path distance metric. ``` ``` ``` ``` If *C* is a set of nodes in the graph and *c* is an element of *C*, ``` ``` the *Voronoi cell* centered at a node *c* is the set of all nodes ``` ``` *v* that are closer to *c* than to any other center node in *C* with ``` ``` respect to the shortest-path distance metric. _ ``` ``` ``` ``` For directed graphs, this will compute the \"outward\" Voronoi cells, ``` ``` as defined in _, in which distance is measured from the center ``` ``` nodes to the target node. For the \"inward\" Voronoi cells, use the ``` ``` :meth:`DiGraph.reverse` method to reverse the orientation of the ``` ``` edges before invoking this function on the directed graph. ``` ``` ``` ``` Parameters ``` ``` ---------- ``` ``` G : NetworkX graph ``` ``` ``` ``` center_nodes : set ``` ``` A nonempty set of nodes in the graph `G` that represent the ``` ``` center of the Voronoi cells. ``` ``` ``` ``` weight : string or function ``` ``` The edge attribute (or an arbitrary function) representing the ``` ``` weight of an edge. This keyword argument is as described in the ``` ``` documentation for :func:`~networkx.multi_source_dijkstra_path`, ``` ``` for example. ``` ``` ``` ``` Returns ``` ``` ------- ``` ``` dictionary ``` ``` A mapping from center node to set of all nodes in the graph ``` ``` closer to that center node than to any other center node. The ``` ``` keys of the dictionary are the element of `center_nodes`, and ``` ``` the values of the dictionary form a partition of the nodes of ``` ``` `G`. ``` ``` ``` ``` Examples ``` ``` -------- ``` ``` To get only the partition of the graph induced by the Voronoi cells, ``` ``` take the collection of all values in the returned dictionary:: ``` ``` ``` ``` >>> G = nx.path_graph(6) ``` ``` >>> center_nodes = {0, 3} ``` ``` >>> cells = nx.voronoi_cells(G, center_nodes) ``` ``` >>> partition = set(map(frozenset, cells.values())) ``` ``` >>> sorted(map(sorted, partition)) ``` ``` [[0, 1], [2, 3, 4, 5]] ``` ``` ``` ``` Raises ``` ``` ------ ``` ``` ValueError ``` ``` If `center_nodes` is empty. ``` ``` ``` ``` References ``` ``` ---------- ``` ``` .. Erwig, Martin. (2000), ``` ``` \"The graph Voronoi diagram with applications.\" ``` ``` *Networks*, 36: 156--163. ``` ``` 3.0.CO;2-L> ``` ``` ``` ``` \"\"\" ``` ``` # Determine the shortest paths from any one of the center nodes to ``` ``` # every node in the graph. ``` ``` # ``` ``` # This raises `ValueError` if `center_nodes` is an empty set. ``` ``` paths = nx.multi_source_dijkstra_path(G, center_nodes, weight=weight) ``` ``` # Determine the center node from which the shortest path originates. ``` ``` nearest = {v: p for v, p in paths.items()} ``` ``` # Get the mapping from center node to all nodes closer to it than to ``` ``` # any other center node. ``` ``` cells = groups(nearest) ``` ``` # We collect all unreachable nodes under a special key, if there are any. ``` ``` unreachable = set(G) - set(nearest) ``` ``` if unreachable: ``` ``` cells['unreachable'] = unreachable ``` ``` return cells ```"
] |
[
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.68162376,"math_prob":0.7292562,"size":3710,"snap":"2021-43-2021-49","text_gpt3_token_len":1110,"char_repetition_ratio":0.13491635,"word_repetition_ratio":0.014771049,"special_character_ratio":0.39110512,"punctuation_ratio":0.12592593,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9931691,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-12-07T00:46:07Z\",\"WARC-Record-ID\":\"<urn:uuid:4accbf14-1e47-4cbb-9a12-ec967800b1fa>\",\"Content-Length\":\"34456\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:76419b9b-445c-43a6-86db-989cff8b2d56>\",\"WARC-Concurrent-To\":\"<urn:uuid:99e9c7c0-cef4-4146-b765-6e81eeffc8d5>\",\"WARC-IP-Address\":\"193.205.194.89\",\"WARC-Target-URI\":\"https://ans.disi.unitn.it/redmine/projects/internet-on-fire/repository/revisions/5cef0f13e18f7902bbb9f6e766f4143dfb58d698/entry/networkxMiCe/networkx-master/networkx/algorithms/voronoi.py\",\"WARC-Payload-Digest\":\"sha1:QDA2Z2BN3NOSUZXZ4EHNBOA6LEHLAXG2\",\"WARC-Block-Digest\":\"sha1:GODJFZNYHOKZM7Z3F7K7F64OZWV67TNZ\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-49/CC-MAIN-2021-49_segments_1637964363327.64_warc_CC-MAIN-20211206224536-20211207014536-00010.warc.gz\"}"}
|
https://keras.io/examples/vision/cutmix/
|
[
"» Code examples / Computer Vision / CutMix data augmentation for image classification\n\n# CutMix data augmentation for image classification\n\nAuthor: Sayan Nath\nDate created: 2021/06/08\nDescription: Data augmentation with CutMix for image classification on CIFAR-10.",
null,
"View in Colab",
null,
"GitHub source\n\n## Introduction\n\nCutMix is a data augmentation technique that addresses the issue of information loss and inefficiency present in regional dropout strategies. Instead of removing pixels and filling them with black or grey pixels or Gaussian noise, you replace the removed regions with a patch from another image, while the ground truth labels are mixed proportionally to the number of pixels of combined images. CutMix was proposed in CutMix: Regularization Strategy to Train Strong Classifiers with Localizable Features (Yun et al., 2019)\n\nIt's implemented via the following formulas:",
null,
"where `M` is the binary mask which indicates the cutout and the fill-in regions from the two randomly drawn images and `λ` (in `[0, 1]`) is drawn from a `Beta(α, α)` distribution\n\nThe coordinates of bounding boxes are:",
null,
"which indicates the cutout and fill-in regions in case of the images. The bounding box sampling is represented by:",
null,
"where `rx, ry` are randomly drawn from a uniform distribution with upper bound.\n\n## Setup\n\n``````import numpy as np\nimport pandas as pd\nimport matplotlib.pyplot as plt\nimport tensorflow as tf\nfrom tensorflow import keras\n\nnp.random.seed(42)\ntf.random.set_seed(42)\n``````\n\nIn this example, we will use the CIFAR-10 image classification dataset.\n\n``````(x_train, y_train), (x_test, y_test) = tf.keras.datasets.cifar10.load_data()\ny_train = tf.keras.utils.to_categorical(y_train, num_classes=10)\ny_test = tf.keras.utils.to_categorical(y_test, num_classes=10)\n\nprint(x_train.shape)\nprint(y_train.shape)\nprint(x_test.shape)\nprint(y_test.shape)\n\nclass_names = [\n\"Airplane\",\n\"Automobile\",\n\"Bird\",\n\"Cat\",\n\"Deer\",\n\"Dog\",\n\"Frog\",\n\"Horse\",\n\"Ship\",\n\"Truck\",\n]\n``````\n``````(50000, 32, 32, 3)\n(50000, 10)\n(10000, 32, 32, 3)\n(10000, 10)\n``````\n\n## Define hyperparameters\n\n``````AUTO = tf.data.AUTOTUNE\nBATCH_SIZE = 32\nIMG_SIZE = 32\n``````\n\n## Define the image preprocessing function\n\n``````def preprocess_image(image, label):\nimage = tf.image.resize(image, (IMG_SIZE, IMG_SIZE))\nimage = tf.image.convert_image_dtype(image, tf.float32) / 255.0\nreturn image, label\n``````\n\n## Convert the data into TensorFlow `Dataset` objects\n\n``````train_ds_one = (\ntf.data.Dataset.from_tensor_slices((x_train, y_train))\n.shuffle(1024)\n.map(preprocess_image, num_parallel_calls=AUTO)\n)\ntrain_ds_two = (\ntf.data.Dataset.from_tensor_slices((x_train, y_train))\n.shuffle(1024)\n.map(preprocess_image, num_parallel_calls=AUTO)\n)\n\ntrain_ds_simple = tf.data.Dataset.from_tensor_slices((x_train, y_train))\n\ntest_ds = tf.data.Dataset.from_tensor_slices((x_test, y_test))\n\ntrain_ds_simple = (\ntrain_ds_simple.map(preprocess_image, num_parallel_calls=AUTO)\n.batch(BATCH_SIZE)\n.prefetch(AUTO)\n)\n\n# Combine two shuffled datasets from the same training data.\ntrain_ds = tf.data.Dataset.zip((train_ds_one, train_ds_two))\n\ntest_ds = (\ntest_ds.map(preprocess_image, num_parallel_calls=AUTO)\n.batch(BATCH_SIZE)\n.prefetch(AUTO)\n)\n``````\n\n## Define the CutMix data augmentation function\n\nThe CutMix function takes two `image` and `label` pairs to perform the augmentation. It samples `λ(l)` from the Beta distribution and returns a bounding box from `get_box` function. We then crop the second image (`image2`) and pad this image in the final padded image at the same location.\n\n``````def sample_beta_distribution(size, concentration_0=0.2, concentration_1=0.2):\ngamma_1_sample = tf.random.gamma(shape=[size], alpha=concentration_1)\ngamma_2_sample = tf.random.gamma(shape=[size], alpha=concentration_0)\nreturn gamma_1_sample / (gamma_1_sample + gamma_2_sample)\n\n@tf.function\ndef get_box(lambda_value):\ncut_rat = tf.math.sqrt(1.0 - lambda_value)\n\ncut_w = IMG_SIZE * cut_rat # rw\ncut_w = tf.cast(cut_w, tf.int32)\n\ncut_h = IMG_SIZE * cut_rat # rh\ncut_h = tf.cast(cut_h, tf.int32)\n\ncut_x = tf.random.uniform((1,), minval=0, maxval=IMG_SIZE, dtype=tf.int32) # rx\ncut_y = tf.random.uniform((1,), minval=0, maxval=IMG_SIZE, dtype=tf.int32) # ry\n\nboundaryx1 = tf.clip_by_value(cut_x - cut_w // 2, 0, IMG_SIZE)\nboundaryy1 = tf.clip_by_value(cut_y - cut_h // 2, 0, IMG_SIZE)\nbbx2 = tf.clip_by_value(cut_x + cut_w // 2, 0, IMG_SIZE)\nbby2 = tf.clip_by_value(cut_y + cut_h // 2, 0, IMG_SIZE)\n\ntarget_h = bby2 - boundaryy1\nif target_h == 0:\ntarget_h += 1\n\ntarget_w = bbx2 - boundaryx1\nif target_w == 0:\ntarget_w += 1\n\nreturn boundaryx1, boundaryy1, target_h, target_w\n\n@tf.function\ndef cutmix(train_ds_one, train_ds_two):\n(image1, label1), (image2, label2) = train_ds_one, train_ds_two\n\nalpha = [0.25]\nbeta = [0.25]\n\n# Get a sample from the Beta distribution\nlambda_value = sample_beta_distribution(1, alpha, beta)\n\n# Define Lambda\nlambda_value = lambda_value\n\n# Get the bounding box offsets, heights and widths\nboundaryx1, boundaryy1, target_h, target_w = get_box(lambda_value)\n\n# Get a patch from the second image (`image2`)\ncrop2 = tf.image.crop_to_bounding_box(\nimage2, boundaryy1, boundaryx1, target_h, target_w\n)\n# Pad the `image2` patch (`crop2`) with the same offset\ncrop2, boundaryy1, boundaryx1, IMG_SIZE, IMG_SIZE\n)\n# Get a patch from the first image (`image1`)\ncrop1 = tf.image.crop_to_bounding_box(\nimage1, boundaryy1, boundaryx1, target_h, target_w\n)\n# Pad the `image1` patch (`crop1`) with the same offset\ncrop1, boundaryy1, boundaryx1, IMG_SIZE, IMG_SIZE\n)\n\n# Modify the first image by subtracting the patch from `image1`\n# (before applying the `image2` patch)\nimage1 = image1 - img1\n# Add the modified `image1` and `image2` together to get the CutMix image\nimage = image1 + image2\n\n# Adjust Lambda in accordance to the pixel ration\nlambda_value = 1 - (target_w * target_h) / (IMG_SIZE * IMG_SIZE)\nlambda_value = tf.cast(lambda_value, tf.float32)\n\n# Combine the labels of both images\nlabel = lambda_value * label1 + (1 - lambda_value) * label2\nreturn image, label\n``````\n\nNote: we are combining two images to create a single one.\n\n## Visualize the new dataset after applying the CutMix augmentation\n\n``````# Create the new dataset using our `cutmix` utility\ntrain_ds_cmu = (\ntrain_ds.shuffle(1024)\n.map(cutmix, num_parallel_calls=AUTO)\n.batch(BATCH_SIZE)\n.prefetch(AUTO)\n)\n\n# Let's preview 9 samples from the dataset\nimage_batch, label_batch = next(iter(train_ds_cmu))\nplt.figure(figsize=(10, 10))\nfor i in range(9):\nax = plt.subplot(3, 3, i + 1)\nplt.title(class_names[np.argmax(label_batch[i])])\nplt.imshow(image_batch[i])\nplt.axis(\"off\")\n``````",
null,
"## Define a ResNet-20 model\n\n``````def resnet_layer(\ninputs,\nnum_filters=16,\nkernel_size=3,\nstrides=1,\nactivation=\"relu\",\nbatch_normalization=True,\nconv_first=True,\n):\nconv = keras.layers.Conv2D(\nnum_filters,\nkernel_size=kernel_size,\nstrides=strides,\nkernel_initializer=\"he_normal\",\nkernel_regularizer=keras.regularizers.l2(1e-4),\n)\nx = inputs\nif conv_first:\nx = conv(x)\nif batch_normalization:\nx = keras.layers.BatchNormalization()(x)\nif activation is not None:\nx = keras.layers.Activation(activation)(x)\nelse:\nif batch_normalization:\nx = keras.layers.BatchNormalization()(x)\nif activation is not None:\nx = keras.layers.Activation(activation)(x)\nx = conv(x)\nreturn x\n\ndef resnet_v20(input_shape, depth, num_classes=10):\nif (depth - 2) % 6 != 0:\nraise ValueError(\"depth should be 6n+2 (eg 20, 32, 44 in [a])\")\n# Start model definition.\nnum_filters = 16\nnum_res_blocks = int((depth - 2) / 6)\n\ninputs = keras.layers.Input(shape=input_shape)\nx = resnet_layer(inputs=inputs)\n# Instantiate the stack of residual units\nfor stack in range(3):\nfor res_block in range(num_res_blocks):\nstrides = 1\nif stack > 0 and res_block == 0: # first layer but not first stack\nstrides = 2 # downsample\ny = resnet_layer(inputs=x, num_filters=num_filters, strides=strides)\ny = resnet_layer(inputs=y, num_filters=num_filters, activation=None)\nif stack > 0 and res_block == 0: # first layer but not first stack\n# linear projection residual shortcut connection to match\n# changed dims\nx = resnet_layer(\ninputs=x,\nnum_filters=num_filters,\nkernel_size=1,\nstrides=strides,\nactivation=None,\nbatch_normalization=False,\n)\nx = keras.layers.Activation(\"relu\")(x)\nnum_filters *= 2\n\n# v1 does not use BN after last shortcut connection-ReLU\nx = keras.layers.AveragePooling2D(pool_size=8)(x)\ny = keras.layers.Flatten()(x)\noutputs = keras.layers.Dense(\nnum_classes, activation=\"softmax\", kernel_initializer=\"he_normal\"\n)(y)\n\n# Instantiate model.\nmodel = keras.models.Model(inputs=inputs, outputs=outputs)\nreturn model\n\ndef training_model():\nreturn resnet_v20((32, 32, 3), 20)\n\ninitial_model = training_model()\ninitial_model.save_weights(\"initial_weights.h5\")\n``````\n\n## Train the model with the dataset augmented by CutMix\n\n``````model = training_model()\n\nmodel.fit(train_ds_cmu, validation_data=test_ds, epochs=15)\n\ntest_loss, test_accuracy = model.evaluate(test_ds)\nprint(\"Test accuracy: {:.2f}%\".format(test_accuracy * 100))\n``````\n``````Epoch 1/15\n1563/1563 [==============================] - 62s 24ms/step - loss: 1.9216 - accuracy: 0.4090 - val_loss: 1.9737 - val_accuracy: 0.4061\nEpoch 2/15\n1563/1563 [==============================] - 37s 24ms/step - loss: 1.6549 - accuracy: 0.5325 - val_loss: 1.5033 - val_accuracy: 0.5061\nEpoch 3/15\n1563/1563 [==============================] - 38s 24ms/step - loss: 1.5536 - accuracy: 0.5840 - val_loss: 1.2913 - val_accuracy: 0.6112\nEpoch 4/15\n1563/1563 [==============================] - 38s 24ms/step - loss: 1.4988 - accuracy: 0.6097 - val_loss: 1.0587 - val_accuracy: 0.7033\nEpoch 5/15\n1563/1563 [==============================] - 38s 24ms/step - loss: 1.4531 - accuracy: 0.6291 - val_loss: 1.0681 - val_accuracy: 0.6841\nEpoch 6/15\n1563/1563 [==============================] - 37s 24ms/step - loss: 1.4173 - accuracy: 0.6464 - val_loss: 1.0265 - val_accuracy: 0.7085\nEpoch 7/15\n1563/1563 [==============================] - 37s 24ms/step - loss: 1.3932 - accuracy: 0.6572 - val_loss: 0.9540 - val_accuracy: 0.7331\nEpoch 8/15\n1563/1563 [==============================] - 37s 24ms/step - loss: 1.3736 - accuracy: 0.6680 - val_loss: 0.9877 - val_accuracy: 0.7240\nEpoch 9/15\n1563/1563 [==============================] - 38s 24ms/step - loss: 1.3575 - accuracy: 0.6782 - val_loss: 0.8944 - val_accuracy: 0.7570\nEpoch 10/15\n1563/1563 [==============================] - 38s 24ms/step - loss: 1.3398 - accuracy: 0.6886 - val_loss: 0.8598 - val_accuracy: 0.7649\nEpoch 11/15\n1563/1563 [==============================] - 38s 24ms/step - loss: 1.3277 - accuracy: 0.6939 - val_loss: 0.9032 - val_accuracy: 0.7603\nEpoch 12/15\n1563/1563 [==============================] - 38s 24ms/step - loss: 1.3131 - accuracy: 0.6964 - val_loss: 0.7934 - val_accuracy: 0.7926\nEpoch 13/15\n1563/1563 [==============================] - 37s 24ms/step - loss: 1.3050 - accuracy: 0.7029 - val_loss: 0.8737 - val_accuracy: 0.7552\nEpoch 14/15\n1563/1563 [==============================] - 37s 24ms/step - loss: 1.2987 - accuracy: 0.7099 - val_loss: 0.8409 - val_accuracy: 0.7766\nEpoch 15/15\n1563/1563 [==============================] - 37s 24ms/step - loss: 1.2953 - accuracy: 0.7099 - val_loss: 0.7850 - val_accuracy: 0.8014\n313/313 [==============================] - 3s 9ms/step - loss: 0.7850 - accuracy: 0.8014\nTest accuracy: 80.14%\n``````\n\n## Train the model using the original non-augmented dataset\n\n``````model = training_model()\nmodel.fit(train_ds_simple, validation_data=test_ds, epochs=15)\n\ntest_loss, test_accuracy = model.evaluate(test_ds)\nprint(\"Test accuracy: {:.2f}%\".format(test_accuracy * 100))\n``````\n``````Epoch 1/15\n1563/1563 [==============================] - 38s 23ms/step - loss: 1.4864 - accuracy: 0.5173 - val_loss: 1.3694 - val_accuracy: 0.5708\nEpoch 2/15\n1563/1563 [==============================] - 36s 23ms/step - loss: 1.0682 - accuracy: 0.6779 - val_loss: 1.1424 - val_accuracy: 0.6686\nEpoch 3/15\n1563/1563 [==============================] - 36s 23ms/step - loss: 0.8955 - accuracy: 0.7449 - val_loss: 1.0555 - val_accuracy: 0.7007\nEpoch 4/15\n1563/1563 [==============================] - 36s 23ms/step - loss: 0.7890 - accuracy: 0.7878 - val_loss: 1.0575 - val_accuracy: 0.7079\nEpoch 5/15\n1563/1563 [==============================] - 36s 23ms/step - loss: 0.7107 - accuracy: 0.8175 - val_loss: 1.1395 - val_accuracy: 0.7062\nEpoch 6/15\n1563/1563 [==============================] - 36s 23ms/step - loss: 0.6524 - accuracy: 0.8397 - val_loss: 1.1716 - val_accuracy: 0.7042\nEpoch 7/15\n1563/1563 [==============================] - 36s 23ms/step - loss: 0.6098 - accuracy: 0.8594 - val_loss: 1.4120 - val_accuracy: 0.6786\nEpoch 8/15\n1563/1563 [==============================] - 36s 23ms/step - loss: 0.5715 - accuracy: 0.8765 - val_loss: 1.3159 - val_accuracy: 0.7011\nEpoch 9/15\n1563/1563 [==============================] - 36s 23ms/step - loss: 0.5477 - accuracy: 0.8872 - val_loss: 1.2873 - val_accuracy: 0.7182\nEpoch 10/15\n1563/1563 [==============================] - 36s 23ms/step - loss: 0.5233 - accuracy: 0.8988 - val_loss: 1.4118 - val_accuracy: 0.6964\nEpoch 11/15\n1563/1563 [==============================] - 36s 23ms/step - loss: 0.5165 - accuracy: 0.9045 - val_loss: 1.3741 - val_accuracy: 0.7230\nEpoch 12/15\n1563/1563 [==============================] - 36s 23ms/step - loss: 0.5008 - accuracy: 0.9124 - val_loss: 1.3984 - val_accuracy: 0.7181\nEpoch 13/15\n1563/1563 [==============================] - 36s 23ms/step - loss: 0.4896 - accuracy: 0.9190 - val_loss: 1.3642 - val_accuracy: 0.7209\nEpoch 14/15\n1563/1563 [==============================] - 36s 23ms/step - loss: 0.4845 - accuracy: 0.9231 - val_loss: 1.5469 - val_accuracy: 0.6992\nEpoch 15/15\n1563/1563 [==============================] - 36s 23ms/step - loss: 0.4749 - accuracy: 0.9294 - val_loss: 1.4034 - val_accuracy: 0.7362\n313/313 [==============================] - 3s 9ms/step - loss: 1.4034 - accuracy: 0.7362\nTest accuracy: 73.62%\n``````\n\nIn this example, we trained our model for 15 epochs. In our experiment, the model with CutMix achieves a better accuracy on the CIFAR-10 dataset (80.36% in our experiment) compared to the model that doesn't use the augmentation (72.70%). You may notice it takes less time to train the model with the CutMix augmentation.\n\nYou can experiment further with the CutMix technique by following the original paper."
] |
[
null,
"https://colab.research.google.com/img/colab_favicon.ico",
null,
"https://github.com/favicon.ico",
null,
"https://i.imgur.com/cGvd13V.png",
null,
"https://i.imgur.com/eNisep4.png",
null,
"https://i.imgur.com/Snph9aj.png",
null,
"https://keras.io/img/examples/vision/cutmix/cutmix_16_0.png",
null
] |
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|
https://www.gradesaver.com/textbooks/science/chemistry/chemistry-molecular-science-5th-edition/chapter-14-acids-and-bases-questions-for-review-and-thought-topical-questions-page-652c/65
|
[
"## Chemistry: The Molecular Science (5th Edition)\n\n$pH = 5.118$\n1. Drawing the equilibrium (ICE) table, we get these concentrations at equilibrium:** The image is in the end of this answer. -$[H_3O^+] = [Conj. Base] = x$ -$[Boric Acid] = [Boric Acid]_{initial} - x = 0.1 - x$ For approximation, we consider: $[Boric Acid] = 0.1M$ 2. Now, use the Ka value and equation to find the 'x' value. $Ka = \\frac{[H_3O^+][Conj. Base]}{ [Boric Acid]}$ $Ka = 5.8 \\times 10^{- 10}= \\frac{x * x}{ 0.1}$ $Ka = 5.8 \\times 10^{- 10}= \\frac{x^2}{ 0.1}$ $5.8 \\times 10^{- 11} = x^2$ $x = 7.616 \\times 10^{- 6}$ Percent ionization: $\\frac{ 7.616 \\times 10^{- 6}}{ 0.1} \\times 100\\% = 0.007616\\%$ %ionization < 5% : Right approximation. Therefore: $[H_3O^+] = [Conj. Base] = x = 7.616 \\times 10^{- 6}M$ And, since 'x' has a very small value (compared to the initial concentration): $[Boric Acid] \\approx 0.1M$ 3. Calculate the pH Value $pH = -log[H_3O^+]$ $pH = -log( 7.616 \\times 10^{- 6})$ $pH = 5.118$",
null,
""
] |
[
null,
"https://gradesaver.s3.amazonaws.com/uploads/solution/b97bf72f-f4f1-4320-af57-02bba33f36a1/steps_image/small_1532014740.png",
null
] |
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|
https://www.geeksforgeeks.org/implementation-linkedlist-javascript/?ref=lbp
|
[
"# Implementation of LinkedList in Javascript\n\nIn this article, we will be implementing LinkedList data structure in Javascript. LinkedList is the dynamic data structure, as we can add or remove elements at ease, and it can even grow as needed. Just like arrays, linked lists store elements sequentially, but don’t store the elements contiguously like an array.\nNow, Lets see an example of a Linked List Node:\n\n `// User defined class node ` `class` `Node { ` ` ``// constructor ` ` ``constructor(element) ` ` ``{ ` ` ``this``.element = element; ` ` ``this``.next = ``null` ` ``} ` `} `\n\nAs in the above code we define a class Node having two properties: element and next. Element holds the data of a node while next holds the pointer to the next node, which is initialized to the null value.\nNow, lets see an implementation of Linked List class:\n\n `// linkedlist class ` `class` `LinkedList { ` ` ``constructor() ` ` ``{ ` ` ``this``.head = ``null``; ` ` ``this``.size = ``0``; ` ` ``} ` ` ` ` ``// functions to be implemented ` ` ``// add(element) ` ` ``// insertAt(element, location) ` ` ``// removeFrom(location) ` ` ``// removeElement(element) ` ` ` ` ``// Helper Methods ` ` ``// isEmpty ` ` ``// size_Of_List ` ` ``// PrintList ` `} `\n\nThe above example shows a Linked List class with a constructor and list of methods to be implemented. Linked List class has two properties: i.e. head and size, where head stores the first node of a List, and size indicates the number of nodes in a list.\nLet’s implement each of these functions:\n\n1. add(element) – It adds an element at the end of list.\n\n `// adds an element at the end ` `// of list ` `add(element) ` `{ ` ` ``// creates a new node ` ` ``var node = ``new` `Node(element); ` ` ` ` ``// to store current node ` ` ``var current; ` ` ` ` ``// if list is Empty add the ` ` ``// element and make it head ` ` ``if` `(``this``.head == ``null``) ` ` ``this``.head = node; ` ` ``else` `{ ` ` ``current = ``this``.head; ` ` ` ` ``// iterate to the end of the ` ` ``// list ` ` ``while` `(current.next) { ` ` ``current = current.next; ` ` ``} ` ` ` ` ``// add node ` ` ``current.next = node; ` ` ``} ` ` ``this``.size++; ` `} `\n\nIn the order to add an element at the end of the list we consider the following :\n\n• If the list is empty then add an element and it will be head\n• If the list is not empty then iterate to the end of the list and add an element at the end of the list\n\ncurrent is used to iterate through the list after every iteration we update it to be the next of the current node. If next is null(the last element of a list contains null in the next) then we add the element to the list.\n\n2. insertAt(element, index) – It inserts an element at the given index in a list.\n\n `// insert element at the position index ` `// of the list ` `insertAt(element, index) ` `{ ` ` ``if` `(index > ``0` `&& index > ``this``.size) ` ` ``return` `false``; ` ` ``else` `{ ` ` ``// creates a new node ` ` ``var node = ``new` `Node(element); ` ` ``var curr, prev; ` ` ` ` ``curr = ``this``.head; ` ` ` ` ``// add the element to the ` ` ``// first index ` ` ``if` `(index == ``0``) { ` ` ``node.next = ``this``.head; ` ` ``this``.head = node; ` ` ``} ``else` `{ ` ` ``curr = ``this``.head; ` ` ``var it = ``0``; ` ` ` ` ``// iterate over the list to find ` ` ``// the position to insert ` ` ``while` `(it < index) { ` ` ``it++; ` ` ``prev = curr; ` ` ``curr = curr.next; ` ` ``} ` ` ` ` ``// adding an element ` ` ``node.next = curr; ` ` ``prev.next = node; ` ` ``} ` ` ``this``.size++; ` ` ``} ` `} `\n\nIn order to add an element at the end of the list we consider three conditions as follows:\n\n• if the index is zero we add an element at the front of the list and make it head\n• If the index is the last position of the list we append the element at the end of the list\n• if the index is inbetween 0 or size – 1 we iterate over to the index and add an element at that index\n\nIn the above method prev holds the previous of current node.\n\n3. removeFrom(index) – It removes and returns an element from the list from the specified index\n\n `// removes an element from the ` `// specified location ` `removeFrom(index) ` `{ ` ` ``if` `(index > ``0` `&& index > ``this``.size) ` ` ``return` `-``1``; ` ` ``else` `{ ` ` ``var curr, prev, it = ``0``; ` ` ``curr = ``this``.head; ` ` ``prev = curr; ` ` ` ` ``// deleting first element ` ` ``if` `(index == = ``0``) { ` ` ``this``.head = curr.next; ` ` ``} ``else` `{ ` ` ``// iterate over the list to the ` ` ``// position to removce an element ` ` ``while` `(it < index) { ` ` ``it++; ` ` ``prev = curr; ` ` ``curr = curr.next; ` ` ``} ` ` ` ` ``// remove the element ` ` ``prev.next = curr.next; ` ` ``} ` ` ``this``.size--; ` ` ` ` ``// return the remove element ` ` ``return` `curr.element; ` ` ``} ` `} `\n\nIn order to remove an element from the list we consider three condition:\n\n• If the index is 0 then we remove head and make next node head of the list\n• if the index is size – 1 then we remove the last element form the list and make prev the last element\n• if its in between 0 to size – 1 we remove the element by using prev and current node\n4. removeElement(element) – This method removes element from the list. It returns the removed element, or if its not found it returns -1.\n\n `// removes a given element from the ` `// list ` `removeElement(element) ` `{ ` ` ``var current = ``this``.head; ` ` ``var prev = ``null``; ` ` ` ` ``// iterate over the list ` ` ``while` `(current != ``null``) { ` ` ``// comparing element with current ` ` ``// element if found then remove the ` ` ``// and return true ` ` ``if` `(current.element == = element) { ` ` ``if` `(prev == ``null``) { ` ` ``this``.head = current.next; ` ` ``} ``else` `{ ` ` ``prev.next = current.next; ` ` ``} ` ` ``this``.size--; ` ` ``return` `current.element; ` ` ``} ` ` ``prev = current; ` ` ``current = current.next; ` ` ``} ` ` ``return` `-``1``; ` `} `\n\nThe above method is just a modification of removeFrom(index), as it searches for an element and removes it, rather than removing from a specified location\n\nHelper Methods\n\nLets declare some helper methods which are useful while working with LinkedList.\n\n1. indexOf(element) – it returns the index of a given element, if the element is in the list.\n\n `// finds the index of element ` `indexOf(element) ` `{ ` ` ``var count = ``0``; ` ` ``var current = ``this``.head; ` ` ` ` ``// iterae over the list ` ` ``while` `(current != ``null``) { ` ` ``// compare each element of the list ` ` ``// with given element ` ` ``if` `(current.element == = element) ` ` ``return` `count; ` ` ``count++; ` ` ``current = current.next; ` ` ``} ` ` ` ` ``// not found ` ` ``return` `-``1``; ` `} `\n\nIn this method, we iterate over the list to find the index of an element. If it is not present in the list it returns -1 instead.\n\n2. isEmpty() – it returns true if the list is empty.\n\n `// checks the list for empty ` `isEmpty() ` `{ ` ` ``return` `this``.size == ``0``; ` `} `\n\nIn this method we check for the size property of the LinkedList class, and if its zero then the list is empty.\n\n3. size_of_list() – It returns the size of list\n\n `// gives the size of the list ` `size_of_list() ` `{ ` ` ``console.log(``this``.size); ` `} `\n\n4. printList() – It prints the contents of the list.\n\n `// prints the list items ` `printList() ` `{ ` ` ``var curr = ``this``.head; ` ` ``var str = ``\"\"``; ` ` ``while` `(curr) { ` ` ``str += curr.element + ``\" \"``; ` ` ``curr = curr.next; ` ` ``} ` ` ``console.log(str); ` `} `\n\nIn this method, we iterate over the entire list and concatenate the elements of each node and print it.\n\nNote: Different helper methods can be declared in the LinkedList class as required.\n\nImplementation\n\nNow lets use the LinkedList class and its different methods described above.\n\n `// creating an object for the ` `// Linkedlist class ` `var ll = ``new` `LinkedList(); ` ` ` `// testing isEmpty on an empty list ` `// returns true ` `console.log(ll.isEmpty()); ` ` ` `// adding element to the list ` `ll.add(``10``); ` ` ` `// prints 10 ` `ll.printList(); ` ` ` `// returns 1 ` `console.log(ll.size_of_list()); ` ` ` `// adding more elements to the list ` `ll.add(``20``); ` `ll.add(``30``); ` `ll.add(``40``); ` `ll.add(``50``); ` ` ` `// returns 10 20 30 40 50 ` `ll.printList(); ` ` ` `// prints 50 from the list ` `console.log(``\"is element removed ?\"` `+ ll.removeElement(``50``)); ` ` ` `// prints 10 20 30 40 ` `ll.printList(); ` ` ` `// returns 3 ` `console.log(``\"Index of 40 \"` `+ ll.indexOf(``40``)); ` ` ` `// insert 60 at second position ` `// ll contains 10 20 60 30 40 ` `ll.insertAt(``60``, ``2``); ` ` ` `ll.printList(); ` ` ` `// returns false ` `console.log(``\"is List Empty ? \"` `+ ll.isEmpty()); ` ` ` `// remove 3rd element from the list ` `console.log(ll.removeFrom(``3``)); ` ` ` `// prints 10 20 60 40 ` `ll.printList(); `\n\nThis article is contributed by Sumit Ghosh. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.",
null,
"My Personal Notes arrow_drop_up\n\nArticle Tags :\n\n6\n\nPlease write to us at contribute@geeksforgeeks.org to report any issue with the above content."
] |
[
null,
"https://media.geeksforgeeks.org/wp-content/cdn-uploads/20200604102104/GFG-FSRNL-Article-2.png",
null
] |
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|
https://essayheroes.us/it6010-mathematics-for-computing/
|
[
"## IT6010 – Mathematics for Computing\n\nQ1) Design a Knapsack public key cryptosystem, using this system, encrypt the plaintext “BHP”. Show the details of the design process (give the selected values with explanation why selected them) and encryption process. Include in your answer Octave codes used. Use the ASCII or Unicode code to convert the plaintext characters to numbers. Finally, show how to decrypt the obtained cipher values to get the plaintext character back. (LOs 2,4) [6 Marks]\n\nQ2) Answer each of the following:\n\n• Explain why the security of the Monoalphabetic ciphers is easy to compromise?\n• Define the “hashing”, then explain why hashing is used creating a digital signature.\n• Distinguish between the Stream Cipher System and Block Cipher Systems, name one example for each system. (LO 4) [3 Marks]\n\nQ3) Affine Cipher is an example of a Monoalphabetic substitution cipher. The encryption process is substantially mathematical done by using the following formula:\n\nC = (P ∗ ?1 + ?2) mod 26.\n\nWhere k1, k2 are two integers representing the key (selected randomly), C is the ciphertext value, and P is the plaintext value. Where C and P integers with values between 0 and 25.\n\n• Write an Octave programme to implement this system, run your programme using the Plaintext: “the quick brown fox jumped over the lazy dog”. Show the obtained ciphertext with the selected values of the keys k1 & k2. [4 Marks]\n• Given that the plaintext “s” mapped to ciphertext “W”, plaintext “x” mapped to ciphertext “Z” when encrypted with Affine Cipher. Determine, mathematically, the values for the two keys K1 and K2. [4 Marks]\n\n(LOs 2,4) [8 Marks]\n\nQ4) Given the following cipher text which has been ciphered with Mixed Alphabet Monoalphabetic Cipher:\n\nUZQSOVUOHXMOPVGPOZPEVSGZWSZOPFPESXUDBMET SXAIZVUEPHZHMDZSHZOWSFPAPPDTSVPQUZWYMXUZU HSXEPYEPOPDZSZUFPOMBZWPFUPZHMDJUDTMOHMQ\n\nBy using statistical method to exploit the weaknesses in this cipher, you can conclude that there are two plain text letters that correspond two letters in the above ciphertext. Give these letters justifying your conclusion in detail.\n\n(LO1) [ 3 Marks]"
] |
[
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.80403167,"math_prob":0.8134164,"size":2115,"snap":"2023-40-2023-50","text_gpt3_token_len":529,"char_repetition_ratio":0.12648034,"word_repetition_ratio":0.0,"special_character_ratio":0.21607564,"punctuation_ratio":0.10743801,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9860347,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-12-01T23:09:39Z\",\"WARC-Record-ID\":\"<urn:uuid:8434babb-d1f8-458b-b4df-aebb27d6633c>\",\"Content-Length\":\"98481\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:87e3798f-ec1e-4689-a9b7-09e67ee73446>\",\"WARC-Concurrent-To\":\"<urn:uuid:6c62d1e9-e2e8-497c-bebd-d82f9033604e>\",\"WARC-IP-Address\":\"198.54.120.245\",\"WARC-Target-URI\":\"https://essayheroes.us/it6010-mathematics-for-computing/\",\"WARC-Payload-Digest\":\"sha1:23VJUWQVWGXFQ7HDD5D5GPOUOGKERMWS\",\"WARC-Block-Digest\":\"sha1:KHBCMANXWLP2OWLJIGLMON72Z5OTLBVO\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-50/CC-MAIN-2023-50_segments_1700679100308.37_warc_CC-MAIN-20231201215122-20231202005122-00123.warc.gz\"}"}
|
https://math.stackexchange.com/questions/4124511/why-does-the-dual-space-consisting-of-unitary-equivalence-classes-of-irreducible
|
[
"# Why does the dual space consisting of unitary equivalence classes of irreducible representations of compact $G$ not form a group?\n\nI am trying to understand unitary representations of compact groups $$G$$. Equip the class of all unitary irreducible representations of $$G$$ with the usual equivalence relation, unitary equivalence. We define the dual space as the set of equivalence classes with respect to this relation. The dual space cannot ever form a group. I would like to check that my reasoning as to why this is true is correct. This is my reasoning:\n\nWe can try to equip this set with binary operation $$[\\pi][\\pi']:=[\\pi\\cdot\\pi']$$ where $$(\\pi\\cdot\\pi')(x)=\\pi(x)\\cdot\\pi'(x)$$. Then this operation is pointwise multiplication of irreducible representations (which are just group homomorphisms). $$\\textbf{But}$$, irreducible representations of compact groups are finite dimensional therefore can be expressed as square matrices, e.g.\n\n$$\\pi(x)=n\\times n$$ matrix, $$\\pi'(x)=m\\times m$$ matrix. Then pointwise multiplication (and indeed regular matrix multiplication) cannot be defined unless $$n=m$$. However, in general the dual space will have representations of different dimensions - thus we cannot define a sensible binary operation on them.\n\nThis is in contrast with the $$\\textit{dual group}$$ for Abelian locally compact groups, because irreducibles are just continuous homomorphisms into $$\\mathbb{C}$$ and can therefore be equipped with pointwise multiplication to give group structure.\n\n$$\\textbf{One question}$$ comes to mind for me: how do we know there are no other binary operations we might come up with, that would give the dual space a group structure?\n\n• Even if all the irreducible representations of a compact group you considered did have a fixed dimension $n$, there is no reason the operation you mentioned be well defined.\n– D_S\nMay 2, 2021 at 17:00\n\nYou ask a soft question, and the answer seems to be \"No one has ever come up with one.\" What operations can you do to two irreducible representations $$\\pi$$ and $$\\pi'$$ to get another irreducible representation? I can think of none that would produce a group structure."
] |
[
null
] |
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|
https://groupprops.subwiki.org/w/index.php?title=Automorphism_group_of_alternating_group:A6&direction=next&oldid=49834
|
[
"# Automorphism group of alternating group:A6\n\nView a complete list of particular groups (this is a very huge list!)[SHOW MORE]\n\n## Definition\n\nThis group is defined in the following equivalent ways:\n\n1. It is the automorphism group of alternating group:A6.\n2. It is the automorphism group of symmetric group:S6.\n3. It is the projective semilinear group of degree two over the field of nine elements, i.e., it is the group",
null,
"$P\\Gamma L(2,9)$.\n\nNote that for any",
null,
"$n \\ne 2,3,6$, the automorphism group of the alternating group",
null,
"$A_n$ is precisely the symmetric group",
null,
"$S_n$, which is a complete group. The case",
null,
"$n = 2$ is uninteresting. For",
null,
"$n = 3$, the automorphism group of",
null,
"$A_n$ is",
null,
"$C_2$, the cyclic group of order 2. The case",
null,
"$n = 6$ is the only case where the automorphism group of the alternating group is strictly bigger than the symmetric group. Similarly, it is the only case where the automorphism group of the symmetric group is strictly bigger than the symmetric group. Further information: symmetric groups on finite sets are complete\n\n## Arithmetic functions\n\nWant to compare and contrast arithmetic function values with other groups of the same order? Check out groups of order 1440#Arithmetic functions\n\n### Basic arithmetic functions\n\nFunction Value Similar groups Explanation for function value\norder (number of elements, equivalently, cardinality or size of underlying set) 1440 groups with same order As",
null,
"$\\operatorname{Aut}(A_6)$:",
null,
"$|\\operatorname{Inn}(A_6)||\\operatorname{Out}(A_6)| = (360)(4) = 1440$\nAs",
null,
"$\\operatorname{Aut}(S_6)$:",
null,
"$|\\operatorname{Inn}(S_6)||\\operatorname{Out}(S_6)| = (720)(2) = 1440$\nAs",
null,
"$P\\Gamma L(2,q), q = p^r, q = 9, p = 3, r = 2$:",
null,
"$r(q^3 - q) = 2(9^3 - 9) = 1440$\n\n### Arithmetic functions of a counting nature\n\nFunction Value Similar groups Explanation for function value\nnumber of conjugacy classes 13 groups with same order and number of conjugacy classes | groups with same number of conjugacy classes As",
null,
"$P\\Gamma L(2,p^2), p = 3$ (odd):",
null,
"$(p^2 + 3p + 8)/2 = (3^2 + 3 \\cdot 3 + 8)/2 = 13$ (more here)\n\n## GAP implementation\n\n### Group ID\n\nThis finite group has order 1440 and has ID 5841 among the groups of order 1440 in GAP's SmallGroup library. For context, there are 5,958 groups of order 1440. It can thus be defined using GAP's SmallGroup function as:\n\nSmallGroup(1440,5841)\n\nFor instance, we can use the following assignment in GAP to create the group and name it",
null,
"$G$:\n\ngap> G := SmallGroup(1440,5841);\n\nConversely, to check whether a given group",
null,
"$G$ is in fact the group we want, we can use GAP's IdGroup function:\n\nIdGroup(G) = [1440,5841]\n\nor just do:\n\nIdGroup(G)\n\nto have GAP output the group ID, that we can then compare to what we want.\n\n### Other descriptions\n\nDescription Functions used\nAutomorphismGroup(AlternatingGroup(6)) AutomorphismGroup, AlternatingGroup\nAutomorphismGroup(SymmetricGroup(6)) AutomorphismGroup, SymmetricGroup"
] |
[
null,
"https://groupprops.subwiki.org/w/images/math/4/2/8/4289361dd67fc8c4df0a95603ad68220.png ",
null,
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https://en.wikibooks.org/wiki/Fractals/Iterations_in_the_complex_plane/Mandelbrot_set_interior
|
[
"# Fractals/Iterations in the complex plane/Mandelbrot set interior\n\nThis book shows how to code different algorithms for drawing parameter plane (Mandelbrot set) for complex quadratic polynomial.\n\nOne can find different types of points / sets on parameter plane.\n\n# Interior of Mandelbrot set - hyperbolic components\n\n## The Lyapunov exponent\n\nMath equation :\n\n$\\lambda _{f}(z_{0})=\\lim _{n\\rightarrow \\infty }{\\frac {1}{n}}\\sum _{i=0}^{n-1}\\left(\\ln \\left|f'(z_{i})\\right|\\right)$",
null,
"where:\n\n$f'(x)={\\frac {d}{dz}}f_{c}(z)=2z$",
null,
"means first derivative of f with respect to z\n\n• image and description by janthor\n• image by Anders Sandberg\n\n## absolute value of the orbit\n\n# Hypercomputing the Mandelbrot Set? by Petrus H. Potgieter February 1, 2008\nn=1000; # For an nxn grid\nm=50; # Number of iterations\nc=meshgrid(linspace(-2,2,n))\\ # Set up grid\n+i*meshgrid(linspace(2,-2,n))’;\nx=zeros(n,n); # Initial value on grid\nfor i=1:m\nx=x.^2+c; # Iterate the mapping\nendfor\nimagesc(min(abs(x),2.1)) # Plot monochrome, absolute\n# value of 2.1 is escape\n\n\n### internal level sets\n\nColor of point:\n\n• is proportional to the value of z is at final iteration.\n• shows internal level sets of periodic attractors.\n\n### bof60\n\nImage of bof60 in on page 60 in the book \"the Beauty Of Fractals\".Description of the method described on page 63 of bof. It is used only for interior points of the Mandelbrot set.\n\nColor of point is proportional to:\n\n• the smallest distance of its orbit from origin\n• the smallest value z gets during iteration\n• illuminating the closest approach the iterates of the origin (critical point) make to the origin inside the set\n• \"Each pixel of each particular video frame represents a particular complex number c = a + ib. For each sequential frame n, the magnitude of z(c,n) := z(c, n-1)^2 + c is displayed as a grayscale intensity value at each of these points c: larger magnitude points are whiter, smaller magnitudes are darker. As n rises from 1 to 256, points outside the Mandelbrot Set quickly saturate to pure white, while points within the Mandelbrot Set oscillate through the darker intensities.\" Brian Gawalt\n\nLevel sets of distance are sets of points with the same distance\n\nif (Iteration==IterationMax)\n/* interior of Mandelbrot set = color is proportional to modulus of last iteration */\nelse { /* exterior of Mandelbrot set = black */\ncolor=0;\ncolor=0;\ncolor=0;\n}\n\n• fragment of code : fractint.cfrm from Gnofract4d\nbof60 {\ninit:\nfloat mag_of_closest_point = 1e100\nloop:\nfloat zmag = |z|\nif zmag < mag_of_closest_point\nmag_of_closest_point = zmag\nendif\nfinal:\n#index = sqrt(mag_of_closest_point) * 75.0/256.0\n}\n\n\n## Period of hyperbolic components\n\nPeriod of hyperbolic component of Mandelbrot set is a period of limit set of critical orbit.\n\nAlgorithms for computing period:\n\n• direct period detection from iterations of critical point z = 0.0 on dynamical plane\n• \"quick and dirty\" algorithm : check if $abs(z_{n})",
null,
"then colour c-point with colour n. Here n is a period of attracting orbit and eps is a radius of circle around attracting point = precision of numerical computations\n• \"methods based on interval arithmetic when implemented properly are capable of finding all period-n cycles for considerable large n.\" (ZBIGNIEW GALIAS )\n• Floyd's cycle-finding algorithm\n• the spider algorithm\n• atom domain, BOF61\n• Period detection\n\n## internal coordinate and multiplier map\n\nThe algorithm by Claude Heiland-Allen:\n\n• check c\n• When c is outside the Mandelbrot set\n• give up now\n• or use external coordinate\n• when c is not outside (inside or on the boundary) : For each period p, starting from 1 and increasing:\n• Find periodic point z0 such that fp(z0,c)=z0 using Newton's method in one complex variable\n• Find b by evaluating first derivative with respect to z of fp at z0\n• If |b|≤1 then return b, otherwise continue with the next p\n\n### computing\n\nFor periods:\n\n• 1 to 3 explicit equations can be used\n• >3 it must be find using numerical methods\n\n#### period 1\n\n c+(w/2)^2-w/2=0;\n\n\nand solve it for w\n\n(%i1) eq1:c+(w/2)^2-w/2=0;\n2\nw w\n(%o1) -- - - + c = 0\n4 2\n(%i2) solve(eq1,w);\n(%o2) [w = 1 - sqrt(1 - 4 c), w = sqrt(1 - 4 c) + 1]\n(%i3) s:solve(eq1,w);\n(%o3) [w = 1 - sqrt(1 - 4 c), w = sqrt(1 - 4 c) + 1]\n(%i4) s:map(rhs,s);\n(%o4) [1 - sqrt(1 - 4 c), sqrt(1 - 4 c) + 1]\n\n\nso\n\n w = w(c) = 1.0 - csqrt(1.0-4.0*c)\n\n\n#### period 2\n\n w = 4.0*c + 4;\n\n\n#### period 3\n\n $c^{3}+2c^{2}-(w/8-1)c+(w/8-1)^{2}=0$",
null,
"It can be solved using Maxima CAS:\n\n(%i1) e1:c^3 + 2*c^2 - (w/8-1)*c + (w/8-1)^2 = 0;\n\n3 2 w w 2\n(%o1) c + 2 c + (1 - -) c + (- - 1) = 0\n8 8\n(%i2) solve(e1,w);\n(%o2) [w = (- 4 sqrt((- 4 c) - 7) c) + 4 c + 8, w = 4 sqrt((- 4 c) - 7) c + 4 c + 8]\n\n\n#### numerical approximation\n\ncomplex double AproximateMultiplierMap(complex double c, int period, double eps2, double er2)\n{\ncomplex double z; // variable z\ncomplex double zp ; // periodic point\ncomplex double zcr = 0.0; // critical point\ncomplex double d = 1;\n\nint p;\n\n// first find periodic point\nzp = GivePeriodic( c, zcr, period, eps2, er2); // Find periodic point z0 such that Fp(z0,c)=z0 using Newton's method in one complex variable\n\n// Find w by evaluating first derivative with respect to z of Fp at z0\nif ( cabs2(zp)<er2) {\n\nz = zp;\nfor (p=0; p < period; p++){\nd = 2*z*d; /* first derivative with respect to z */\nz = z*z +c ; /* complex quadratic polynomial */\n\n}}\nelse d= 10000; //\n\nreturn d;\n}\n\n\n### Internal angle\n\nMethod by Renato Fonseca : \"a point c in the set is given a hue equal to argument\n\n$arg(z_{n_{max}})=arctan{\\frac {Im(z_{n_{max}})}{Re(z_{n_{max}})}}$",
null,
"(scaled appropriatly so that we end up with a number in the range 0 - 255). The number z_nmax is the last one calculated in the z's sequence.\"\n\n#### Fractint\n\nFractint : Color Parameters : INSIDE=ATAN\n\ncolors by determining the angle in degrees the last iterated value has with respect to the real axis, and using the absolute value. This feature should be used with periodicity=0\n\n### Internal rays\n\nWhen $radius\\,$",
null,
"varies and $angle\\,$",
null,
"is constant then $c\\,$",
null,
"goes along internal ray. It is used as a path inside Mandelbrot set.\n\n\ndouble complex Give_c(double t, double r, int p)\n{\n/*\ninput:\nInternalAngleInTurns = t in range [0,1]\np = period\n\noutput = c = complex point of 2D parameter plane\n*/\n\ncomplex double w = 0.0;\ncomplex double c = 0.0;\n\nt = t*2*M_PI; // from turns to radians\n// point of unit circle\nw = r* cexp(I*t);\n\n// map circle to component\nswitch (p){\n\ncase 1: c = (2.0*w - w*w)/4.0; break;\ncase 2: c = (w -4.0)/ 4.0; break;\n\n}\nreturn c;\n}\n\n\n/* find c in component of Mandelbrot set\nuses complex type so #include <complex.h> and -lm\nuses code by Wolf Jung from program Mandel\nsee function mndlbrot::bifurcate from mandelbrot.cpp\nhttp://www.mndynamics.com/indexp.html\n\n*/\ndouble complex GiveC(double InternalAngleInTurns, double InternalRadius, unsigned int period)\n{\n//0 <= InternalRay<= 1\n//0 <= InternalAngleInTurns <=1\ndouble t = InternalAngleInTurns *2*M_PI; // from turns to radians\ndouble Cx, Cy; /* C = Cx+Cy*i */\nswitch ( period ) {\ncase 1: // main cardioid\nbreak;\ncase 2: // only one component\nCx = InternalRadius * 0.25*cos(t) - 1.0;\nbreak;\n// for each period there are 2^(period-1) roots.\ndefault: // safe values\nCx = 0.0;\nCy = 0.0;\nbreak; }\n\nreturn Cx+ Cy*I;\n}\n\n// draws points to memmory array data\nint DrawInternalRay(double InternalAngleInTurns, unsigned int period, int iMax, unsigned char data[])\n{\n\ncomplex double c;\nint i; // number of point to draw\n\nfor(i=0;i<=iMax;++i){\nDrawPoint(c,data);\n}\n\nreturn 0;\n}\n\n\nExample: internal ray of angle = 1/6 of main cardioid.\n\nInternal angle:\n\n$angle=1/6\\,$",
null,
"$0\\leq radius\\leq 1\\,$",
null,
"Point of internal radius of unit circle:\n\n$w=radius*e^{i*angle}\\,$",
null,
"Map point $w$",
null,
"to parameter plane:\n\n$c={\\frac {w}{2}}-{\\frac {w^{2}}{4}}\\,$",
null,
"For $epsilon=0\\,$",
null,
"this is equation for main cardioid.\n\n### Internal curve\n\nWhen $radius\\,$",
null,
"is constant varies and $angle\\,$",
null,
"varies then $c\\,$",
null,
"goes along internal curve.\n\n/* find c in component of Mandelbrot set\nuses complex type so #include <complex.h> and -lm\nuses code by Wolf Jung from program Mandel\nsee function mndlbrot::bifurcate from mandelbrot.cpp\nhttp://www.mndynamics.com/indexp.html\n*/\ndouble complex GiveC(double InternalAngleInTurns, double InternalRadius, unsigned int period)\n{\n//0 <= InternalRay<= 1\n//0 <= InternalAngleInTurns <=1\ndouble t = InternalAngleInTurns *2*M_PI; // from turns to radians\ndouble Cx, Cy; /* C = Cx+Cy*i */\nswitch ( period ) {\ncase 1: // main cardioid\nbreak;\ncase 2: // only one component\nCx = InternalRadius * 0.25*cos(t) - 1.0;\nbreak;\n// for each period there are 2^(period-1) roots.\ndefault: // safe values\nCx = 0.0;\nCy = 0.0;\nbreak;\n}\n\nreturn Cx+ Cy*I;\n}\n\n// draws points to memory array data\nint DrawInternalCurve(double InternalRadius , unsigned int period, int iMax, unsigned char data[])\n{\ncomplex double c;\ndouble InternalAngle; // in turns = from 0.0 to 1.0\ndouble AngleStep;\nint i;\n// int iMax =100;\n\nAngleStep = 1.0/iMax;\n\nfor (i=0; i<=iMax; ++i) {\nInternalAngle = i * AngleStep;"
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|
https://books.google.co.ve/books?id=NepJAAAAMAAJ&pg=PA6&focus=viewport&vq=%22A+diameter+of+a+circle+is+a+straight+line+drawn+through+the+centre,+and+terminated+both+ways+by+the+circumference.%22&dq=related:ISBN8474916712&lr=&output=html_text
|
[
"Im�genes de p�ginas PDF EPUB\n .flow { margin: 0; font-size: 1em; } .flow .pagebreak { page-break-before: always; } .flow p { text-align: left; text-indent: 0; margin-top: 0; margin-bottom: 0.5em; } .flow .gstxt_sup { font-size: 75%; position: relative; bottom: 0.5em; } .flow .gstxt_sub { font-size: 75%; position: relative; top: 0.3em; } .flow .gstxt_hlt { background-color: yellow; } .flow div.gtxt_inset_box { padding: 0.5em 0.5em 0.5em 0.5em; margin: 1em 1em 1em 1em; border: 1px black solid; } .flow div.gtxt_footnote { padding: 0 0.5em 0 0.5em; border: 1px black dotted; } .flow .gstxt_underline { text-decoration: underline; } .flow .gtxt_heading { text-align: center; margin-bottom: 1em; font-size: 150%; font-weight: bold; font-variant: small-caps; } .flow .gtxt_h1_heading { text-align: center; font-size: 120%; font-weight: bold; } .flow .gtxt_h2_heading { font-size: 110%; font-weight: bold; } .flow .gtxt_h3_heading { font-weight: bold; } .flow .gtxt_lineated { margin-left: 2em; margin-top: 1em; margin-bottom: 1em; white-space: pre-wrap; } .flow .gtxt_lineated_code { margin-left: 2em; margin-top: 1em; margin-bottom: 1em; white-space: pre-wrap; font-family: monospace; } .flow .gtxt_quote { margin-left: 2em; margin-right: 2em; margin-top: 1em; margin-bottom: 1em; } .flow .gtxt_list_entry { margin-left: 2ex; text-indent: -2ex; } .flow .gimg_graphic { margin-top: 1em; margin-bottom: 1em; } .flow .gimg_table { margin-top: 1em; margin-bottom: 1em; } .flow { font-family: serif; } .flow span,p { font-family: inherit; } .flow-top-div {font-size:83%;} One of the alterations made with this view, respects the Doctrine of Proportion, the method of treating which, as it is laid down in the fifth of Euclid, has great advantages accompanied with considerable defects; of which, however, it must be observed, that the advantages are essential, and the defects only accidental. To explain the nature of the former requires a more minute examination than is suited to this place, and must therefore be reserved for the Notes; but, in the mean time, it may be remarked, that no definition, except that of Euclid, has ever been given, from which the properties of proportionals can be deduced by reasonings, which, at the same time that they are perfectly rigorous, are also simple and direct. As to the defects, the prolixness and obscurity that have so often been complained of in the fifth Book, they seem to arise chiefly from the nature of the language employed, which being no other than that of ordinary discourse, cannot express, without much tediousness and circumlocution, the relations of mathematical quantities, when taken in their utmost generality, and when no assistance can be received from diagrams. As it is plain that the concise language of Algebra is directly calculated to remedy this inconvenience, I have endeavoured to introduce it here, in a very simple form however, and without changing the nature of the reasoning, or departing in any thing from the rigour of geometrical demonstration. By this means, the steps of the reasoning which were before far separated, are brought near to one another, and the force of the whole is so clearly and directly perceived, that I am persuaded no more difficulty will be found in understanding the propositions of the fifth Book than those of any other of the Elements. In the second Book, also, some algebraic signs have been introduced, for the sake of representing more readily the addition and subtraction of the rectangles on which the demonstrations depend. The use of such symbolical writing, in translating from an original, where no symbols are used, cannot, I think, be regarded as an unwarrantable liberty : for, if by that means the translation is not made into English, it is made into that universal language so much sought after in all the sciences, but destined, it would seem, to be enjoyed only by the mathematical. The alterations above mentioned are the most material that have been attempted on the books of Euclid. There are, however, a few others, which, though less considerable, it is hoped may in some degree facilitate the study of the Elements. Such are those made on the definitions in the first Book, and particularly on that of a straight line. A new axiom is also introduced in the room of the 12th, for the purpose of demonstrating more easily some of the properties of parallel lines. In the third Book, the remarks concerning the angles made by a straight line, and the circumference of a circle, are left out, as tending to perplex one who has advanced no farther than the elements of the science. Some propositions also have been added; but for a fuller detail concerning these changes, I must refer to the Notes, in which several of the more difficult, or more interesting subjects of Elementary Geometry are treated at considerable length. COLLEGE OF EDINBURGH, Dec. 1, 1813. ELEMENTS OF G E O ME TRY. BOOK I. THE PRINCIPLES. EXPLANATION OF TERMS AND SIGNS. mag i. Geometry is a science which has for its object the measurement of nitudes. Magnitudes may be considered under three dimensions,-length, breadth, height or thickness. 2. In Geometry there are several general terms or principles ; such as, Definitions, Propositions, Axioms, Theorems, Problems, Lemmas, Scho liums, Corollaries, &c. 3. A Definition is the explication of any term or word in a science, show ing the sense and meaning in which the term is employed. Every definition ought to be clear, and expressed in words that are common and perfectly well understood. 4. An Axiom, or Maxim, is a self-evident proposition, requiring no formal demonstration to prove the truth of it; but is received and assented to as soon as mentioned. Such as, the whole of any thing is greater than a part of it; or, the whole is equal to all its parts taken together; or, two quantities that are each of them equal to a third quantity, are equal to each other. 5. A Theorem is a demonstrative proposition ; in which some property is asserted, and the truth of it required to be proved. Thus, when it is said that the sum of the three angles of any plane tri angle is equal to two right angles, this is called a Theorem; and the method of collecting the several arguments and proofs, and laying them together in proper order, by means of which the truth of the proposition becomes evident, is called a Demonstration. 6. A Direct Demonstration is that which concludes with the direct and cer tain proof of the proposition in hand. It is also called Positive or Affirmative, and sometimes an Ostensive De monstration, because it is most satisfactory to the mind. 7. An Indirect or Negative Demonstration is that which shows a proposition to be true, by proving that some absurdity would necessarily follow if the proposition advanced were false. This is sometimes called Reductio ad Absurdum ; because it shows the absurdity and falsehood of all suppositions contrary to that contained in the proposition. 8. A Problern is a proposition or a question proposed, which requires a 80 lution. As, to draw one line perpendicular to another ; or to divide a line into two equal parts. 9. Solution of a problem is the resolution or answer given to it. A Numerical or Numeral solution, is the answer given in numbers. A Geometrical solution, is the answer given by the principles of Geome try. And a Mechanical solution, is one obtained by trials. 10. A Lemma is a preparatory proposition, laid down in order to shorten the demonstration of the main proposition which follows it. 11. A Corollary, or Consectary, is a consequence drawn immediately from some proposition or other premises. 12. A Scholium is a remark or observation made on some foregoing propo sition or premises. 13. An Hypothesis is a supposition assumed to be true, in order to argue from, or to found upon it the reasoning and demonstration of some pro position. 14. A Postulate, or Petition, is something required to be done, which is so easy and evident that no person will hesitate to allow it. 15. Method is the art of disposing a train of arguments in a proper order, to investigate the truth or falsity of a proposition, or to demonstrate it to others when it has been found out. This is either Analytical or Syn thetical. 16. Analysis, or the Analytic method, is the art or mode of finding out the truth of a proposition, by first supposing the thing to be done, and then reasoning step by step, till we arrive at some known truth. This is also called the Method of Invention, or Resolution ; and is that which is com monly used in Algebra. 17. Synthesis, or the Synthetic Method, is the searching out truth, by first laying down simple principles, and pursuing the consequences flowing from them till we arrive at the conclusion. This is also called the Me thod of Composition ; and is that which is commonly used in Geometry. 18. The sign = (or two parallel lines), is the sign of equality ; thus, A=B, implies that the quantity denoted by A is equal to the quantity denoted by B, and is read A equal to B. 19. To signify that A is greater than B, the expression A 7B is used. And to signify that A is less than B, the expression AB is used. 20. The sign of Addition is an erect cross; thus A+B implies the sum of A and B, and is called A plus B. 21. Subtraction is denoted by a single line; as A-B, which is read A minus B; A-B represents their difference, or the part of A remaining, when a part equal to B has been taken away from it. In like manner, A-B+C, or A+C—B, signifies that A and C are to be added together, and that B is to be subtracted from their sum. 22. Multiplication is expressed by an oblique cross, by a point, or by simple apposition: thus, XB, A . B, or AB, signifies that the quantity denoted by A is to be multiplied by the quantity denoted hy B. The expression AB should not be employed when there is any danger of confounding it with that of the line AB, the distance between the points A and B. The multiplication of numbers cannot be expressed by simple apposition. 23. When any quantities are enclosed in a parenthesis, or have a line drawn over them, they are considered as one quantity with respect to other symbols: thus, the expression AX(B+C—D), or AXB+C—D, represents the product of A by the quantity, B+C—D. In like manner, (A+B)X(A—B+C), indicates the product of A+B by the quantity AB+c. 24. The Co-efficient of a quantity is the number prefixed to it: thus, 2AB signifies that the line AB is to be taken 2 times; JAB signifies the half of the line AB. 25. Division, or the ratio of one quantity to another, is usually denoted by placing one of the two quantities over the other, in the form of a fraction : A thus, signifies the ratio or quotient arising from the division of the B quantity A by B. In fact, this is division indicated. 26. The Square, Cube, &c. of a quantity, are expressed by placing a small figure at the right hand of the quantity: thus, the square of the line AB is denoted by AB, the cube of the line AB is designated by AB3 ; and so on. 27. The Roots of quantities are expressed by means of the radical sign V, with the proper index annexed ; thus, the square root of 5 is indicated V5; V(AXB) means the square root of the product of A and B, or the mean proportional between them. The roots of quantities are sometimes expressed by means of fractional indices : thus, the cube root of AXBXC may be expressed by VAXBXC, or (AXB XC)), and SO on. 28. Numbers in a parenthesis, such as (15. 1.), refers back to the number of the proposition and the Book in which it has been announced or demonstrated. The expression (15. 1.) denotes the fifteenth proposition, first book, and so on. In like manner, (3. Ax.) designates the third axiom; (2. Post.) the second postulate; (Def. 3.) the third definition, and so on. 29. The word, therefore, or hence, frequently occurs. To express either of these words, the sign .. is generally used. 30. If the quotients of two pairs of numbers, or quantities, are equal, the A С quantities are said to be proportional: thus, if B ; then, A is to B as C to D. And the abbreviations of the proportion is, A:B::C:D; it is sometimes written A: B=C: D.",
null,
"DEFINITIONS. 66 1. “A Point is that which has position, but not magnitude*.” (See Notes.) 2. A line is length without breadth. “ COROLLARY. The extremities of a line are points; and the intersections “ of one line with another are also points.” 3. :-“If two lines are such that they cannot coincide in any two points, with “out coinciding altogether, each of them is called a straight line. “Cor. Hence two straight lines cannot inclose a space. Neither can two 6 straight lines have a common segment; that is, they cannot coincide “ in part, without coinciding altogether.” 4. A superficies is that which has only length and breadth. • Cor. The extremities of a superficies are lines; and the intersections of one superficies with another are also lines.” 5. A plane superficies is that in which any two points being taken, the straight line between them lies wholly in that superficies. 6. A plane rectilineal angle is the inclination of two straight lines to one another, which meet together, but are not in the same straight line. D B N. B. \"When several angles are at one point B, any one of them is expressed by three letters, of which the letter that is at the vertex of the angle, that is, at the point in which the straight lines that contain the angle meet one another, is put between the other two letters, and one of these 'two is somewhere upon one of those straight lines, and the other upon the other line: Thus the angle which is contained by the straight lines, AB, CB, is named the angle ABC, or CBA; that which is contained by AB, * The definitions marked with inverted commas are different from those of Euclid. « AnteriorContinuar »"
] |
[
null,
"https://books.google.co.ve/books/content",
null
] |
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|
https://www.programiz.com/cpp-programming/library-function/cwchar/wcrtomb
|
[
"",
null,
"# C++ wcrtomb()\n\nThe wcrtomb() function in C++ converts a wide character to its narrow multibyte representation.\n\nThe wcrtomb() is defined in <cwchar> header file.\n\n## wcrtomb() prototype\n\n`size_t wcrtomb( char* s, wchar_t wc, mbstate_t* ps );`\n\nThe wcrtomb() function converts the wide character represented by wc to a narrow multibyte character and is stored in the address pointed to by s.\n\n• If s is not a null pointer, the wcrtomb() function determines the maximum number of bytes required to store the multibyte representation of wc and stores it in the memory location pointed to by s. A maximum of MB_CUR_MAX bytes can be written. The value of ps is updated as required.\n• If s is a null pointer, the call is equivalent to `wcrtomb(buf, L'\\0', ps)` for some internal buffer buf.\n• If `wc == L'\\0'`, a null byte is stored.\n\n## wcrtomb() Parameters\n\n• s: Pointer to the multibyte character array to store the result.\n• wc: Wide character to convert.\n• ps: Pointer to the conversion state used when interpreting the multibyte string\n\n## wcrtomb() Return value\n\n• On success, the wcrtomb() function returns the number of bytes written to the character array whose first element is pointed to by s.\n• On failure (i.e. wc is not a valid wide character), it returns -1, errno is set to EILSEQ and leaves *ps in unspecified state.\n\n## Example: How wcrtomb() function works?\n\n``````#include <cwchar>\n#include <clocale>\n#include <iostream>\nusing namespace std;\n\nint main()\n{\nsetlocale(LC_ALL, \"en_US.utf8\");\n\nwchar_t str[] = L\"u\\u00c6\\u00f5\\u01b5\";\nchar s;\nint retVal;\n\nmbstate_t ps = mbstate_t();\nfor (int i=0; i<wcslen(str); i++)\n{\nretVal = wcrtomb(s, str[i], &ps);\nif (retVal!=-1)\ncout << \"Size of \" << s << \" is \" << retVal << \" bytes\" << endl;\nelse\ncout << \"Invalid wide character\" << endl;\n}\n\nreturn 0;\n}``````\n\nWhen you run the program, the output will be:\n\n```Size of u is 1 bytes\nSize of Æ is 2 bytes\nSize of õ is 2 bytes\nSize of Ƶ is 2 bytes```"
] |
[
null,
"https://www.facebook.com/tr",
null
] |
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|
https://www.geeksforgeeks.org/c-program-to-compare-two-strings-using-operator-overloading/?ref=rp
|
[
"Given two strings, how to check if the two strings are equal or not, using Operator Overloading.\n\nExamples:\n\n```Input: ABCD, XYZ\nOutput: ABCD is not equal to XYZ\nABCD is greater than XYZ\n\nInput: Geeks, Geeks\nOutput: Geeks is equal to Geeks\n```\n\n## Recommended: Please try your approach on {IDE} first, before moving on to the solution.\n\n• Declare a class with a string variable and operator function ‘==’, ‘<=' and '>=’ that accepts an instance of the class and compares it’s variable with the string variable of the current instance.\n• Create two instances of the class and initialize their class variables with the two input strings respectively.\n• Now, use the overloaded operator(==, <= and >=) function to compare the class variable of the two instances.\n\nBelow is the implementation of the above approach:\n\n `// C++ program to compare two Strings ` `// using Operator Overloading ` ` ` `#include ` `#include ` `#include ` ` ` `using` `namespace` `std; ` ` ` `// Class to implement operator overloading ` `// function for concatenating the strings ` `class` `CompareString { ` ` ` `public``: ` ` ``// Classes object of string ` ` ``char` `str; ` ` ` ` ``// Parametrized Constructor ` ` ``CompareString(``char` `str1[]) ` ` ``{ ` ` ``// Initialize the string to class object ` ` ``strcpy``(``this``->str, str1); ` ` ``} ` ` ` ` ``// Overloading '==' under a function ` ` ``// which returns integer 1/true ` ` ``// if left operand string ` ` ``// and right operand string are equal. ` ` ``//(else return 0/false) ` ` ``int` `operator==(CompareString s2) ` ` ``{ ` ` ``if` `(``strcmp``(str, s2.str) == 0) ` ` ``return` `1; ` ` ``else` ` ``return` `0; ` ` ``} ` ` ` ` ``// Overloading '<=' under a function ` ` ``// which returns integer 1/true ` ` ``// if left operand string is smaller than ` ` ``// or equal to the right operand string. ` ` ``// (else return 0/false) ` ` ``int` `operator<=(CompareString s3) ` ` ``{ ` ` ``if` `(``strlen``(str) <= ``strlen``(s3.str)) ` ` ``return` `1; ` ` ``else` ` ``return` `0; ` ` ``} ` ` ` ` ``// Overloading '>=' under a function ` ` ``// which returns integer 1/true ` ` ``// if left operand string is larger than ` ` ``// or equal to the right operand string. ` ` ``//(else return 0/false) ` ` ``int` `operator>=(CompareString s3) ` ` ``{ ` ` ``if` `(``strlen``(str) >= ``strlen``(s3.str)) ` ` ``return` `1; ` ` ``else` ` ``return` `0; ` ` ``} ` `}; ` ` ` `void` `compare(CompareString s1, CompareString s2) ` `{ ` ` ` ` ``if` `(s1 == s2) ` ` ``cout << s1.str << ``\" is equal to \"` ` ``<< s2.str << endl; ` ` ``else` `{ ` ` ``cout << s1.str << ``\" is not equal to \"` ` ``<< s2.str << endl; ` ` ``if` `(s1 >= s2) ` ` ``cout << s1.str << ``\" is greater than \"` ` ``<< s2.str << endl; ` ` ``else` ` ``cout << s2.str << ``\" is greater than \"` ` ``<< s1.str << endl; ` ` ``} ` `} ` ` ` `// Testcase1 ` `void` `testcase1() ` `{ ` ` ``// Declaring two strings ` ` ``char` `str1[] = ``\"Geeks\"``; ` ` ``char` `str2[] = ``\"ForGeeks\"``; ` ` ` ` ``// Declaring and initializing the class ` ` ``// with above two strings ` ` ``CompareString s1(str1); ` ` ``CompareString s2(str2); ` ` ` ` ``cout << ``\"Comparing \\\"\"` `<< s1.str << ``\"\\\" and \\\"\"` ` ``<< s2.str << ``\"\\\"\"` `<< endl; ` ` ` ` ``compare(s1, s2); ` `} ` ` ` `// Testcase2 ` `void` `testcase2() ` `{ ` ` ``// Declaring two strings ` ` ``char` `str1[] = ``\"Geeks\"``; ` ` ``char` `str2[] = ``\"Geeks\"``; ` ` ` ` ``// Declaring and initializing the class ` ` ``// with above two strings ` ` ``CompareString s1(str1); ` ` ``CompareString s2(str2); ` ` ` ` ``cout << ``\"\\n\\nComparing \\\"\"` `<< s1.str << ``\"\\\" and \\\"\"` ` ``<< s2.str << ``\"\\\"\"` `<< endl; ` ` ` ` ``compare(s1, s2); ` `} ` ` ` `// Driver code ` `int` `main() ` `{ ` ` ``testcase1(); ` ` ``testcase2(); ` ` ` ` ``return` `0; ` `} `\n\nOutput:\n\n```Comparing \"Geeks\" and \"ForGeeks\"\nGeeks is not equal to ForGeeks\nForGeeks is greater than Geeks\n\nComparing \"Geeks\" and \"Geeks\"\nGeeks is equal to Geeks\n```\n\nRated as one of the most sought after skills in the industry, own the basics of coding with our C++ STL Course and master the very concepts by intense problem-solving.\n\nMy Personal Notes arrow_drop_up",
null,
"Silent achiever\n\nIf you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.\n\nPlease Improve this article if you find anything incorrect by clicking on the \"Improve Article\" button below.\n\nArticle Tags :\nPractice Tags :\n\n2\n\nPlease write to us at contribute@geeksforgeeks.org to report any issue with the above content."
] |
[
null,
"https://media.geeksforgeeks.org/auth/profile/t3jec6pwyda7l67c7n7g",
null
] |
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|
https://metanumbers.com/25044
|
[
"## 25044\n\n25,044 (twenty-five thousand forty-four) is an even five-digits composite number following 25043 and preceding 25045. In scientific notation, it is written as 2.5044 × 104. The sum of its digits is 15. It has a total of 4 prime factors and 12 positive divisors. There are 8,344 positive integers (up to 25044) that are relatively prime to 25044.\n\n## Basic properties\n\n• Is Prime? No\n• Number parity Even\n• Number length 5\n• Sum of Digits 15\n• Digital Root 6\n\n## Name\n\nShort name 25 thousand 44 twenty-five thousand forty-four\n\n## Notation\n\nScientific notation 2.5044 × 104 25.044 × 103\n\n## Prime Factorization of 25044\n\nPrime Factorization 22 × 3 × 2087\n\nComposite number\nDistinct Factors Total Factors Radical ω(n) 3 Total number of distinct prime factors Ω(n) 4 Total number of prime factors rad(n) 12522 Product of the distinct prime numbers λ(n) 1 Returns the parity of Ω(n), such that λ(n) = (-1)Ω(n) μ(n) 0 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\n\nThe prime factorization of 25,044 is 22 × 3 × 2087. Since it has a total of 4 prime factors, 25,044 is a composite number.\n\n## Divisors of 25044\n\n1, 2, 3, 4, 6, 12, 2087, 4174, 6261, 8348, 12522, 25044\n\n12 divisors\n\n Even divisors 8 4 2 2\nTotal Divisors Sum of Divisors Aliquot Sum τ(n) 12 Total number of the positive divisors of n σ(n) 58464 Sum of all the positive divisors of n s(n) 33420 Sum of the proper positive divisors of n A(n) 4872 Returns the sum of divisors (σ(n)) divided by the total number of divisors (τ(n)) G(n) 158.253 Returns the nth root of the product of n divisors H(n) 5.14039 Returns the total number of divisors (τ(n)) divided by the sum of the reciprocal of each divisors\n\nThe number 25,044 can be divided by 12 positive divisors (out of which 8 are even, and 4 are odd). The sum of these divisors (counting 25,044) is 58,464, the average is 4,872.\n\n## Other Arithmetic Functions (n = 25044)\n\n1 φ(n) n\nEuler Totient Carmichael Lambda Prime Pi φ(n) 8344 Total number of positive integers not greater than n that are coprime to n λ(n) 2086 Smallest positive number such that aλ(n) ≡ 1 (mod n) for all a coprime to n π(n) ≈ 2767 Total number of primes less than or equal to n r2(n) 0 The number of ways n can be represented as the sum of 2 squares\n\nThere are 8,344 positive integers (less than 25,044) that are coprime with 25,044. And there are approximately 2,767 prime numbers less than or equal to 25,044.\n\n## Divisibility of 25044\n\n m n mod m 2 3 4 5 6 7 8 9 0 0 0 4 0 5 4 6\n\nThe number 25,044 is divisible by 2, 3, 4 and 6.\n\n## Classification of 25044\n\n• Arithmetic\n• Refactorable\n• Abundant\n\n### Expressible via specific sums\n\n• Polite\n• Non-hypotenuse\n\n## Base conversion (25044)\n\nBase System Value\n2 Binary 110000111010100\n3 Ternary 1021100120\n4 Quaternary 12013110\n5 Quinary 1300134\n6 Senary 311540\n8 Octal 60724\n10 Decimal 25044\n12 Duodecimal 125b0\n16 Hexadecimal 61d4\n20 Vigesimal 32c4\n36 Base36 jbo\n\n## Basic calculations (n = 25044)\n\n### Multiplication\n\nn×i\n n×2 50088 75132 100176 125220\n\n### Division\n\nni\n n⁄2 12522 8348 6261 5008.8\n\n### Exponentiation\n\nni\n n2 627201936 15707645285184 393382268522148096 9851865532868676916224\n\n### Nth Root\n\ni√n\n 2√n 158.253 29.2573 12.5799 7.58125\n\n## 25044 as geometric shapes\n\n### Circle\n\nRadius = n\n Diameter 50088 157356 1.97041e+09\n\n### Sphere\n\nRadius = n\n Volume 6.5796e+13 7.88165e+09 157356\n\n### Square\n\nLength = n\n Perimeter 100176 6.27202e+08 35417.6\n\n### Cube\n\nLength = n\n Surface area 3.76321e+09 1.57076e+13 43377.5\n\n### Equilateral Triangle\n\nLength = n\n Perimeter 75132 2.71586e+08 21688.7\n\n### Triangular Pyramid\n\nLength = n\n Surface area 1.08635e+09 1.85116e+12 20448.3\n\n## Cryptographic Hash Functions\n\nmd5 bcea8e33f6a05964bdf4ac26c1aa89cf 2c8243060a2ca1b942644533edda1612f37fcac4 bd3ac55a278691ea54c89400db9895904ff48d5773feec2911963bb000cfa4f6 98ec1db6c8e0f4e1a2bc038088b879e2908ba73f5436e067b58741026f294c9a50eeab18b10b8cb954357bb6af38cce7f6b7a906d83abeab833bf5cfe93c50ab a25a7cfea1945b29cf1e708a65d9b61062649b20"
] |
[
null
] |
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|
https://learn.careers360.com/ncert/question-how-much-momentum-will-a-dumb-bell-of-mass-10-kg-transfer-to-the-floor-if-it-falls-from-a-height-of-80-cm-take-its-downward-acceleration-to-be-10-m-s-raise-to-power-minus-2/
|
[
"# Q 18. How much momentum will a dumb-bell of mass 10 kg transfer to the floor if it falls from a height of 80 cm? Take its downward acceleration to be 10 m s-2 .\n\nD Devendra Khairwa\n\nFor calculating momentum, we need the final velocity of the bell.\n\nBy equation of motion we can write :\n\nor\n\nor\n\nThus the momentum is :\n\nor\n\nExams\nArticles\nQuestions"
] |
[
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.8544262,"math_prob":0.94625837,"size":456,"snap":"2020-10-2020-16","text_gpt3_token_len":114,"char_repetition_ratio":0.14159292,"word_repetition_ratio":0.5168539,"special_character_ratio":0.25,"punctuation_ratio":0.10891089,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.98568875,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-04-04T02:46:16Z\",\"WARC-Record-ID\":\"<urn:uuid:eae374a4-ba4a-489a-a444-13f89f1a3605>\",\"Content-Length\":\"762121\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:65b86f8d-0952-416d-9433-66378f25b7e3>\",\"WARC-Concurrent-To\":\"<urn:uuid:c0446b44-8701-4d43-a187-743ad37e595d>\",\"WARC-IP-Address\":\"13.126.158.197\",\"WARC-Target-URI\":\"https://learn.careers360.com/ncert/question-how-much-momentum-will-a-dumb-bell-of-mass-10-kg-transfer-to-the-floor-if-it-falls-from-a-height-of-80-cm-take-its-downward-acceleration-to-be-10-m-s-raise-to-power-minus-2/\",\"WARC-Payload-Digest\":\"sha1:XLM6YDJCACRTQ4T2KZ3DMKOL5C6XEAXH\",\"WARC-Block-Digest\":\"sha1:IYL62ARGSJPNQXACY36RFRLEW4JHG25R\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-16/CC-MAIN-2020-16_segments_1585370519111.47_warc_CC-MAIN-20200404011558-20200404041558-00097.warc.gz\"}"}
|
https://vole.wtf/kilobytes-gambit/
|
[
"# The Kilobyte’s Gambit\n\nCan you beat 1024 bytes of JavaScript?\n\nNext\n\n• You play as white. Click on a piece, then click where to move.\n• Supports castling, en passant & pawn promotion (to queen only).\n• It won’t announce victory/defeat, only prevent any further moves.\n• The entire ‘brain’ of the chess engine fits into 1024 bytes (only 3 times the length of this help text), including setting up the board & validating moves.\n\nAdapted from code by Oscar Toledo G. and graphics by Pinot with their kind permission\n\nNEW: Want to use this in a Twitch stream? Click here to add grid labels & a 1 minute timer\n\n(NB: if puzzled by a pawn move, please check for en passant before reporting a bug)\n\n## How It Works\n\n(NB: if puzzled by a pawn move, please check for en passant before reporting a bug)\n\nHere’s all of the chess engine’s code, it’s a modified version of the 1.25K game on Oscar Toledo G.’s site, where you’ll find all his award-winning tiny chess programs and an ebook explaining how they work.\n\n`for(B=y=u=b=0,x=10,z=15,I=[],l=[];l[B]=(\"ustvrtsuqqqqqqqq\"+\"yyyyyyyy}{|~z|{}@G@TSb~?A6J57IKJT576,+-48HLSUmgukgg OJNMLK IDHGFE\").charCodeAt(B)-64,B++<120;I[B-1]=B%x?B/x%x<2|B%x<2?7:B/x&4?0:l[u++]:7);X=(c,h,e,S,s)=>{c^=8;for(var T,o,L,E,D,O=20,G,N=-1e8,n,g,d=S&&X(c,0)>1e4,C,R,A,K=78-h<<9,a=c?x:-x;++O<99;)if((o=I[T=O])&&(G=o&z^c)<7){A=G--&2?8:4;C=9-o&z?l[61+G]:49;do{R=I[T+=l[C]];g=D=G|T+a-e?0:e;if(!R&&(G||A<3||g)||(1+R&z^c)>9&&G|A>2){if(!(2-R&7))return K;for(E=n=G|I[T-a]-7?o&z:6^c;E;E=!E&&!d&&!(g=T,D=T<O?g-3:g+2,I[D]<z|I[D+O-T]|I[T+=T-O])){L=(R&&l[R&7|32]*2-h-G)+(G?0:n-o&z?110:(D&&14)+(A<2)+1);if(S>h||1<S&S==h&&L>2|d){I[T]=n,I[g]=I[D],I[O]=D?I[D]=0:0;L-=X(c,h+1,E=G|A>1?0:T,S,L-N);if(!(h||S-1|B-O|T-b|L<-1e4))return W(I,B=b,c,y=E);E=1-G|A<7|D|!S|R|o<z||X(c,0)>1e4;I[O]=o;I[T]=R;I[D]=I[g];D?I[g]=G?0:9^c:0}if(L>N||!h&L==N&&Math.random()<.5)if(N=L,S>1)if(h?s-L<0:(B=O,b=T,0))return N}}}while(!R&G>2||(T=O,G|A>2|z<o&!R&&++C*--A))}return-K+768<N|d&&N};Y=(V)=>{X(8,0,y,V);X(8,0,y,1)};Z=(U)=>{b=U;I[b]&8?W(I,B=b):X(0,0,y,1)}`\n\nIncluded above are setting up the board and pieces, checking your moves are legal, and deciding how to respond. It doesn’t flag up checkmate/stalemate though, you’ll have to work that out for yourself.\n\nLooking 4 steps ahead, a points system considers factors such as the value of pieces, the strength of areas of the board, and speed of capture/victory. It calls an external function to update the display, and the display code calls functions to trigger moves.\n\nGraphics were adapted from Pinot W. Ichwandardi’s thread imagining The Queen’s Gambit as an MS-DOS game. You can discover more of his work on Twitter and Instagram.\n\nYou can also follow Oscar Toledo G. on Twitter to find out about his boot sector and retro games.\n\nHuge thanks to Pinot and Oscar for letting VOLE.wtf reuse their work."
] |
[
null
] |
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|
https://worksheetpic101.z21.web.core.windows.net/3s-multiplication-facts-worksheet.html
|
[
"# 3s Multiplication Facts Worksheet\n\nMultiplication Facts Worksheets we have 9 Images about Multiplication Facts Worksheets like Multiplying by Facts 3, 4 and 6 (Other Factor 1 to 12) (A), Dividing by 3 with Quotients from 1 to 9 (A) and also Dividing by 3 with Quotients from 1 to 9 (A). Read more:\n\n## Multiplication Facts Worksheets",
null,
"www.mathworksheets4kids.com\n\nmultiplication facts fact number horizontal worksheets worksheet single printable factors mathworksheets4kids\n\n## Multiplication Facts – Nine Worksheets / FREE Printable Worksheets",
null,
"www.worksheetfun.com\n\nmultiplication facts worksheets worksheet worksheetfun printable math table times drill\n\n## Multiplication Test - 3s And 4s By Allyssa Copeland | TpT",
null,
"www.teacherspayteachers.com\n\nmultiplication 4s 3s test\n\n## Multiplication Facts Practice Worksheets-Distance Learning Packet 2nd Grade",
null,
"www.teacherspayteachers.com\n\npacket fluency basic\n\n## Dividing By 3 With Quotients From 1 To 9 (A)",
null,
"www.math-drills.com\n\nmath dividing worksheet division facts quotients worksheets drills practice\n\n## Multiplication Basic Facts 0 To 12 | FreeEducationalResources.com",
null,
"www.freeeducationalresources.com\n\nmultiplication facts 4s number 5s basic\n\n## Multiplication Facts (3s) Flashcards",
null,
"www.twocreativeteachers.com\n\nfacts multiplication 3s flashcards 10s maths\n\n## 36 Horizontal Multiplication Facts Questions -- 7 By 0-9 (A)",
null,
"www.math-drills.com\n\nmultiplication math facts worksheet questions horizontal worksheets drills open\n\n## Multiplying By Facts 3, 4 And 6 (Other Factor 1 To 12) (A)",
null,
"www.math-drills.com\n\nfacts multiplying multiplication math drills factor\n\nMultiplication facts practice worksheets-distance learning packet 2nd grade. Facts multiplying multiplication math drills factor. Multiplying by facts 3, 4 and 6 (other factor 1 to 12) (a)"
] |
[
null,
"http://www.mathworksheets4kids.com/multiplication/facts/single-number-horizontal-large.png",
null,
"http://www.worksheetfun.com/wp-content/uploads/2013/03/multiplication-drill23.png",
null,
"https://ecdn.teacherspayteachers.com/thumbitem/Multiplication-Test-3s-and-4s-1500875971/original-570179-1.jpg",
null,
"https://ecdn.teacherspayteachers.com/thumbitem/50-OFF-on-Multiplications-Facts-Practice-and-Review-2847580-1588610487/original-2847580-3.jpg",
null,
"https://www.math-drills.com/division/images/division_facts_0303_0109_0_001_pin.jpg",
null,
"https://imgs.freeeducationalresources.com/freeeducationresources/pdfbookmultiplication9prev2smallc.jpg",
null,
"http://www.twocreativeteachers.com/uploads/3/0/2/1/30212753/s721203654691744814_p273_i1_w576.png",
null,
"https://www.math-drills.com/multiplication/images/mult07h36_001_pin.jpg",
null,
"https://www.math-drills.com/multiplication/images/multiplication_facts_346_0112_001_pin.jpg",
null
] |
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|
https://mathradical.com/calculator-with-radical/rational-equations/prentice-hall-algebra-1.html
|
[
"Algebra Tutorials!",
null,
"Home",
null,
"Exponents and Radicals",
null,
"Division of Radicals",
null,
"Exponents and Radicals",
null,
"RADICALS & RATIONAL EXPONENTS",
null,
"Radicals and Rational Exponents",
null,
"Radical Equations",
null,
"Solving Radical Equations",
null,
"Roots and Radicals",
null,
"RADICAL EQUATION",
null,
"Simplifying Radical Expressions",
null,
"Radical Expressions",
null,
"Solving Radical Equations",
null,
"Solving Radical Equations",
null,
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null,
"Exponents and Radicals",
null,
"Roots;Rational Exponents;Radical Equations",
null,
"Solving and graphing radical equations",
null,
"Solving Radical Equations",
null,
"Radicals and Rational Exponents",
null,
"exponential_and_radical_properties",
null,
"Roots, Radicals, and Root Functions",
null,
"Multiplication of Radicals",
null,
"Solving Radical Equations",
null,
"Radical Expressions and Equations",
null,
"SOLVING RADICAL EQUATIONS",
null,
"Equations Containing Radicals and Complex Numbers",
null,
"Square Roots and Radicals",
null,
"Solving Radical Equations in One Variable Algebraically",
null,
"Polynomials and Radicals",
null,
"Roots,Radicals,and Fractional Exponents",
null,
"Adding, Subtracting, and Multiplying Radical Expressions",
null,
"Square Formula and Powers with Radicals",
null,
"Simplifying Radicals",
null,
"Exponents and Radicals Practice",
null,
"Solving Radical Equations",
null,
"Solving Radical Equations",
null,
"Solving Radical Equations",
null,
"Lecture-Radical Expressions",
null,
"Radical Functions\nTry the Free Math Solver or Scroll down to Tutorials!\n\n Depdendent Variable\n\n Number of equations to solve: 23456789\n Equ. #1:\n Equ. #2:\n\n Equ. #3:\n\n Equ. #4:\n\n Equ. #5:\n\n Equ. #6:\n\n Equ. #7:\n\n Equ. #8:\n\n Equ. #9:\n\n Solve for:\n\n Dependent Variable\n\n Number of inequalities to solve: 23456789\n Ineq. #1:\n Ineq. #2:\n\n Ineq. #3:\n\n Ineq. #4:\n\n Ineq. #5:\n\n Ineq. #6:\n\n Ineq. #7:\n\n Ineq. #8:\n\n Ineq. #9:\n\n Solve for:\n\n Please use this form if you would like to have this math solver on your website, free of charge. Name: Email: Your Website: Msg:\n\nprentice hall algebra 1 workbook answer key\nRelated topics:\nequation roots+matlab | glencoe/mcgraw-hill algebra 1 answers | free worksheets solving equations | formula for square root | common factors lesson plans | radical in fraction with exponent | free 6th grade algebra sites | mixed numbers as decimal | algebra learning freeware | how to find the common factor of three numbers | free sats maths papers | math quiz substitution\n\nAuthor Message\nruvbelsaun",
null,
"Registered: 02.04.2003\nFrom:",
null,
"Posted: Sunday 31st of Dec 07:40 1. Hello Guys Can someone out there assist me? My algebra teacher gave us prentice hall algebra 1 workbook answer key assignment today. Normally I am good at mixed numbers but somehow I am just stuck on this one assignment. I have to turn it in by this weekend but it looks like I will not be able to complete it in time. So I thought of coming online to find help. I will really be thankful if someone can help me work this (topicKwds) out in time.\nnxu",
null,
"Registered: 25.10.2006\nFrom: Siberia, Russian Federation",
null,
"Posted: Sunday 31st of Dec 17:45 Algebrator is a real treasure that can help you with Pre Algebra. Since I was imperfect in Pre Algebra, one of my class tutors recommended me to try the Algebrator and based on his advice, I looked for it online, purchased it and began using it. It was just remarkable . If you sincerely follow each and every lesson offered there on Basic Math, you would surely master the fundamentals of radical expressions and like denominators within hours.\nJrobhic",
null,
"Registered: 09.08.2002\nFrom: Chattanooga, TN",
null,
"Posted: Monday 01st of Jan 11:02 Algebrator really helps you out in prentice hall algebra 1 workbook answer key. I have researched every Math software on the net. It is very easy to use . You just enter your problem and it will produce a complete step-by-step report of the solution. This helped me much with geometry, radical inequalities and function domain. It helps you understand algebra better. I was tired of paying a fortune to Maths Tutors who could not give me the required time and attention. It is a inexpensive tool which could change your entire attitude towards math. Using Algebrator would be a pleasure. Take it.\nmatohkid204",
null,
"Registered: 08.01.2004\nFrom:",
null,
"Posted: Tuesday 02nd of Jan 09:34 Sounds exactly like what I am looking for . Where can I get hold of it?\nDouble_J",
null,
"Registered: 25.11.2004\nFrom: Netherlands",
null,
"Posted: Wednesday 03rd of Jan 07:43 Try to look for it here : https://mathradical.com/lecture-radical-expressions.html. Give it a go because Algebrator has a unconditional money back guarantee, Happy to help.\nMibxrus",
null,
"Registered: 19.10.2002",
null,
"Posted: Thursday 04th of Jan 19:51 least common denominator, quadratic formula and side-side-side similarity were a nightmare for me until I found Algebrator, which is really the best math program that I have ever come across. I have used it through several algebra classes – Algebra 1, Pre Algebra and Remedial Algebra. Just typing in the algebra problem and clicking on Solve, Algebrator generates step-by-step solution to the problem, and my math homework would be ready. I truly recommend the program."
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|
https://cyberretaliatorsolutions.com/2021/05/16/ibm-spss-modeler-foundations-v18-2-spvc-0e069g-spvc/
|
[
"### IBM SPSS Modeler Foundations (V18.2) SPVC – 0E069G SPVC\n\nDetails\n\nCourse Code: 0E069G\n\nBrand: DS&BA – SPSS\n\nCategory: Analytics\n\nSkill Level: Basic\n\nDuration: 16.00H\n\nModality: SPVC\n\nAudience\n\n• Data scientists\n• Business analysts\n• Clients who are new to IBM SPSS Modeler or want to find out more about using it\n\nPrerequisites\n\n• Knowledge of your business requirements\n\nShort Summary\n\nThis course teaches how to use IBM SPSS Modeler 18.2.\n\nOverview\n\nContains PDF course guide, as well as a lab environment where students can work through demonstrations and exercises at their own pace.\n\nThis course provides the foundations of using IBM SPSS Modeler and introduces the participant to data science. The principles and practice of data science are illustrated using the CRISP-DM methodology. The course provides training in the basics of how to import, explore, and prepare data with IBM SPSS Modeler v18.2, and introduces the student to modeling.\n\nIf you are enrolling in a Self Paced Virtual Classroom or Web Based Training course, before you enroll, please review the Self-Paced Virtual Classes and Web-Based Training Classes on our Terms and Conditions page, as well as the system requirements, to ensure that your system meets the minimum requirements for this course. http://www.ibm.com/training/terms\n\nTopic\n\nIntroduction to IBM SPSS Modeler\n• Introduction to data science\n• Describe the CRISP-DM methodology\n• Introduction to IBM SPSS Modeler\n• Build models and apply them to new data\n\nCollect initial data\n• Describe field storage\n• D\nescribe field measurement level\n• Import from various data formats\n• Export to various data formats\n\nUnderstand the data\n• Audit the data\n• Check for invalid values\n• Take action for invalid values\n• Define blanks\n\nSet the unit of analysis\n• Remove duplicates\n• Aggregate data\n• Transform nominal fields into flags\n• Restructure data\n\nIntegrate data\n• Append datasets\n• Merge datasets\n• Sample records\n\nTransform fields\n• Use the Control Language for Expression Manipulation\n• Derive fields\n• Reclassify fields\n• Bin fields\n\nFurther field transformations\n• Use functions\n• Replace field values\n• Transform distributions\n\nExamine relationships\n• Examine the relationship between two categorical fields\n• Examine the relationship between a categorical and continuous field\n• Examine the relationship between two continuous fields\n\nIntroduction to modeling\n• Describe modeling objectives\n• Create supervised models\n• Create segmentation models\n\nImprove efficiency\n• Use database scalability by SQL pushback\n• Process outliers and missing values with the Data Audit node\n• Use the Set Globals node\n• Use parameters\n• Use looping and conditional execution\n\nObjectives\n\nIntroduction to IBM SPSS Modeler\n• Introduction to data science\n• Describe the CRISP-DM methodology\n• Introduction to IBM SPSS Modeler\n• Build models and apply them to new data\n\nCollect initial data\n• Describe field storage\n• Describe field measurement level\n• Import from various data formats\n• Export to various data formats\n\nUnderstand the data\n• Audit the data\n• Check for invalid values\n• Take action for invalid values\n• Define blanks\n\nSet the unit of analysis\n• Remove duplicates\n• Aggregate data\n• Transform nominal fields into flags\n• Restructure data\n\nIntegrate data\n• Append datasets\n• Merge datasets\n• Sample records\n\nTransform fields\n• Use the Control Language for Expression Manipulation\n• Derive fields\n• Reclassify fields\n• Bin fields\n\nFurther field transformations\n• Use functions\n• Replace field values\n• Transform distributions\n\nExamine relationships\n• Examine the relationship between two categorical fields\n• Examine the relationship between a categorical and continuous field\n• Examine the relationship between two continuous fields\n\nIntroduction to modeling\n• Describe modeling objectives\n• Create supervised models\n• Create segmentation models\n\nImprove efficiency\n• Use database scalability by SQL pushback\n• Process outliers and missing values with the Data Audit node\n• Use the Set Globals node\n• Use parameters\n• Use looping and conditional execution\n\nTags :",
null,
"Call Now +27 72 266 2599"
] |
[
null,
"data:image/svg+xml;base64,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",
null
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|
http://www.numbersaplenty.com/3655808
|
[
"Search a number\nBaseRepresentation\nbin1101111100100010000000\n320212201211022\n431330202000\n51413441213\n6210205012\n743034222\noct15744200\n96781738\n103655808\n112077732\n121283768\n139b0000\n146b2412\n154c3308\nhex37c880\n\n3655808 has 40 divisors (see below), whose sum is σ = 7889955. Its totient is φ = 1687296.\n\nThe previous prime is 3655807. The next prime is 3655831. The reversal of 3655808 is 8085563.\n\nMultipling 3655808 by its product of nonzero digits (28800), we get a square (105287270400 = 3244802).\n\nIt is a powerful number, because all its prime factors have an exponent greater than 1 and also an Achilles number because it is not a perfect power.\n\nIt can be written as a sum of positive squares in 3 ways, for example, as 64 + 3655744 = 8^2 + 1912^2 .\n\nIt is an ABA number since it can be written as A⋅BA, here for A=2, B=1352.\n\nIt is a Duffinian number.\n\nIt is not an unprimeable number, because it can be changed into a prime (3655807) by changing a digit.\n\nIt is a polite number, since it can be written in 4 ways as a sum of consecutive naturals, for example, 281210 + ... + 281222.\n\nAlmost surely, 23655808 is an apocalyptic number.\n\nIt is an amenable number.\n\nIt is a practical number, because each smaller number is the sum of distinct divisors of 3655808\n\n3655808 is an abundant number, since it is smaller than the sum of its proper divisors (4234147).\n\nIt is a pseudoperfect number, because it is the sum of a subset of its proper divisors.\n\n3655808 is an frugal number, since it uses more digits than its factorization.\n\n3655808 is an odious number, because the sum of its binary digits is odd.\n\nThe sum of its prime factors is 66 (or 15 counting only the distinct ones).\n\nThe product of its (nonzero) digits is 28800, while the sum is 35.\n\nThe square root of 3655808 is about 1912.0167363284. The cubic root of 3655808 is about 154.0497955572.\n\nThe spelling of 3655808 in words is \"three million, six hundred fifty-five thousand, eight hundred eight\"."
] |
[
null
] |
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|
https://gis.stackexchange.com/questions/159106/integrate-elevation-and-euclidean-distance-in-arcgis-for-desktop
|
[
"# integrate elevation and Euclidean distance in ArcGIS for Desktop?\n\nI have a number sequential GPS locations from marked animals - usually 4 to 5 locations per day for 1.5 years - and am trying to delineate seasons based on elevation and distance.\n\nFrom low elevations in winter, animals generally move to higher elevations in summer. The seasonal movements span x, y and z dimensions. I can calculate the Euclidean distance between two points (or seasonal ranges) to account for change in x and y, and also calculate the change in elevation to account or z. However, I am wondering if there is a way to integrate Euclidean distance traveled and change in elevation.\n\nThe hope is to calculate a single term that accounts for both change elevation and Euclidean distance between seasons.\n\nHow can I do this in ArcGIS for Desktop?\n\n• Why would you not just calculate the Eucidean distance in all 3 dimensions (converting the elevation to the same unit as needed)? It's the same formula, just with the extra squared delta added in. – Evil Genius Aug 20 '15 at 18:40\n• Careful, do not use the Euclidean distance formula on latitude and longitude coordinates. You will need to convert those coordinates into projected X/Ys first. (UTM, State plane, etc) – Mintx Aug 20 '15 at 20:29\n• Why settle for a single term? A pragmatic way to put your question might be \"what is gained by keeping the distance and elevation terms separate in my model\"? That is answered by comparing the model with both terms to any model in which they are combined. A good start to combining them, therefore, would be to fit the full model with both terms (along with any other factors you have available). The estimated coefficients of distance and elevation will give a good starting estimates for the relative weights in the reduced model you seek. – whuber Aug 21 '15 at 13:45\n\nConvert points to individual lines using Points to Line (Data Management). Place points along the line at regular interval. To do so you might use linear referencing, alternatively search this site, something will pop-up.",
null,
"Calculate distance for each point along the line (Chainage in below table) . Search this site, let me know if fail, I’ll post script or field calculator solution. Sample your elevation model to assign Z values to points. Scale Chainage and Z fields using relevant ranges, so that values are in range (0.00…1.00):",
null,
"Export this table and use add XY data (lScaled, zScaled) to convert table to points. Remove prj file if any from output points. Convert points to individual line using Points to Line (Data Management).\n\nPlay with smooth line to reveal your seasons:",
null,
"It is likely your seasons boundaries are somewhere on steepest parts\n\n• The GIS technique exhibited here is good. However, the impression of boundaries in the plot strongly depends on the (arbitrary) choice of relative scaling of the distance and elevation. This approach to the analysis therefore just hides the difficulty rather than solves it. – whuber Aug 21 '15 at 13:47\n• Single term here is vertical gradient with aim to find 'spring' and 'autumn' points. For 1.5 years of observation the line shown gives the answer, I'd say spring is at point (0.2,0.4) . Next step is to average this reading for ind.head curve. I am assuming these animals aren't leaving on rock face, thus to analyze longsection of their travel we need to exagerate y-axis. Very common approach, in fact I never saw longsection of real terrain with equal scale factor for both axis. – FelixIP Aug 21 '15 at 22:03\n• Perhaps 1.5 long axis is more apprpriate here. Will it make scaling less arbitrary? Variablle normalization it is – FelixIP Aug 21 '15 at 22:29"
] |
[
null,
"https://i.stack.imgur.com/7VSoq.jpg",
null,
"https://i.stack.imgur.com/HwdrG.png",
null,
"https://i.stack.imgur.com/hrP7P.png",
null
] |
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|
https://www.sarthaks.com/8621/reaction-between-n2-and-o2-takes-place-as-follows
|
[
"# Reaction between N2 and O2 takes place as follows:\n\n+1 vote\n122 views\n\nReaction between N2 and O2 takes place as follows:",
null,
"If a mixture of 0.482 mol of N2 and 0.933 mol of O2 is placed in a 10 L reaction vessel and allowed to form N2O at a temperature for which Kc = 2.0 × 10–37, determine the composition of equilibrium mixture.\n\n+1 vote\nby (127k points)\nselected by\n\nLet the concentration of N2O at equilibrium be x.\n\nThe given reaction is:",
null,
"Therefore, at equilibrium, in the 10 L vessel:",
null,
"The value of equilibrium constant i.e. Kc = 2.0 × 10–37 is very small. Therefore, the amount of N2 and O2 reacted is also very small. Thus, x can be neglected from the expressions of molar concentrations of N2 and O2. Then,",
null,
""
] |
[
null,
"https://www.sarthaks.com/",
null,
"https://www.sarthaks.com/",
null,
"https://www.sarthaks.com/",
null,
"https://www.sarthaks.com/",
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{"ft_lang_label":"__label__en","ft_lang_prob":0.9322884,"math_prob":0.9933855,"size":343,"snap":"2020-45-2020-50","text_gpt3_token_len":91,"char_repetition_ratio":0.12979351,"word_repetition_ratio":0.0,"special_character_ratio":0.2682216,"punctuation_ratio":0.17948718,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99407405,"pos_list":[0,1,2,3,4,5,6,7,8],"im_url_duplicate_count":[null,null,null,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-12-01T07:51:02Z\",\"WARC-Record-ID\":\"<urn:uuid:71f5f766-88f2-4626-b218-0d9f121f880a>\",\"Content-Length\":\"53081\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:e2c191b5-7708-48da-b434-193f2af51c38>\",\"WARC-Concurrent-To\":\"<urn:uuid:229ab960-33eb-4778-ba37-b42a4968a410>\",\"WARC-IP-Address\":\"104.26.7.26\",\"WARC-Target-URI\":\"https://www.sarthaks.com/8621/reaction-between-n2-and-o2-takes-place-as-follows\",\"WARC-Payload-Digest\":\"sha1:OBHMWAR4MRY4TIUUBXW3ZLSLOIAV6HMJ\",\"WARC-Block-Digest\":\"sha1:COHFSIHJPBJMHCRLDC3B3SCKWKNUW7JQ\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-50/CC-MAIN-2020-50_segments_1606141672314.55_warc_CC-MAIN-20201201074047-20201201104047-00516.warc.gz\"}"}
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https://socratic.org/questions/58724fe2b72cff609237f6cb
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[
"Question 7f6cb\n\nFeb 21, 2017\n\nI'd go for no reaction, but I suspect that the answer is 4. dissociation.\n\nExplanation:\n\nPotassium chloride, $\\text{KCl}$, and sodium hydroxide, $\\text{NaOH}$, are both soluble ionic compounds, so you can expect them to exist as ions in aqueous solution.\n\n${\\text{KCl\"_ ((aq)) -> \"K\"_ ((aq))^(+) + \"Cl}}_{\\left(a q\\right)}^{-}$\n\n${\\text{NaOH\"_ ((aq)) -> \"Na\"_ ((aq))^(+) + \"OH}}_{\\left(a q\\right)}^{-}$\n\nNow, the problem with mixing these two solutions is that the products are soluble ionic compounds as well, which means that the ions will continue to exist as ions in the resulting solution.\n\nThat is the case because all ionic compounds that contain group 1 elements (sodium, $\\text{Na}$, and potassium, $\\text{K}$, in your case) are soluble in water.\n\nSodium chloride, $\\text{NaCl}$, and potassium hydroxide, $\\text{KOH}$, are soluble in aqueous solution, so they will not be formed by this reaction.\n\nIn other words, no reaction will take place when you mix these two solutions.\n\n${\\text{K\"_ ((aq))^(+) + \"Cl\"_ ((aq))^(-) + \"Na\"_ ((aq))^(+) + \"OH\"_ ((aq))^(-) -> \"Na\"_ ((aq))^(+) + \"Cl\"_ ((aq))^(-) + \"K\"_ ((aq))^(+) + \"OH}}_{\\left(a q\\right)}^{-}$\n\nNotice that all the ions are present on both sides of the chemical equation, which tells you that no reaction is taking place, i.e. they are all spectator ions.\n\n\"KCl\"_ ((aq)) + \"NaOH\"_ ((aq)) -> color(red)(\"N. R.\")#\n\nHere $\\textcolor{red}{\\text{N. R.}}$ stands for no reaction.\n\nThat said, you can say that the two compounds dissociate completely when dissolved in water, so maybe the answer could be 4. dissociation.\n\nIf that's the case, then the question could have been worded better. Each compound dissociates in its own aqueous solution, so you can't really say that the two dissociate because the react with each other."
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[
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{"ft_lang_label":"__label__en","ft_lang_prob":0.89906234,"math_prob":0.99838275,"size":1387,"snap":"2019-43-2019-47","text_gpt3_token_len":381,"char_repetition_ratio":0.17570499,"word_repetition_ratio":0.00896861,"special_character_ratio":0.32876712,"punctuation_ratio":0.107279696,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99933434,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-10-17T20:11:36Z\",\"WARC-Record-ID\":\"<urn:uuid:7ccd7cf0-3557-404c-a8b6-ad19378f81e3>\",\"Content-Length\":\"37580\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:c709d134-d815-4a68-9698-7a2b60a898a4>\",\"WARC-Concurrent-To\":\"<urn:uuid:f0412eef-34e1-49ee-bb48-4f7b6af62169>\",\"WARC-IP-Address\":\"54.221.217.175\",\"WARC-Target-URI\":\"https://socratic.org/questions/58724fe2b72cff609237f6cb\",\"WARC-Payload-Digest\":\"sha1:NGDM4MZJ6KKPRAXU6RC2VD2GDDUMIC6R\",\"WARC-Block-Digest\":\"sha1:LIMFPPGUYOB3V63PI4XGB2JIBXXPSZK7\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-43/CC-MAIN-2019-43_segments_1570986676227.57_warc_CC-MAIN-20191017200101-20191017223601-00556.warc.gz\"}"}
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https://gmplib.org/list-archives/gmp-devel/2012-March/002306.html
|
[
"# ABS_CAST\n\nNiels Möller nisse at lysator.liu.se\nTue Mar 27 12:05:35 CEST 2012\n\n```I had a look at the ABS_CAST macro introduced a while ago,\n\n#define ABS_CAST(T,x) ((x) >= 0 ? (T)(x) : -((T)((x) + 1) - 1))\n\nAs I understand it, the point is that, e.g.,\n\nint x;\nunsigned absx;\n...\nabsx = ABS_CAST (unsigned, x);\n\nshould give the right result for x = INT_MIN (where plain ABS would give\nthe result INT_MIN). And be more portable than the simpler definition\n\n#define ABS_CAST(T, x) ((T) ABS(x))\n\nBut the current definition seems strange. When x < 0, it will cast the\nnegative value to an unsigned type (which I suspect is not portable\naccording to the C89 spec (maybe it's more well defined in C99?)), and\nI'm not sure what is gained by the extra +1 and -1 when doing that. I'd\n\n#define ABS_CAST(T,x) ((x) >= 0 ? (T)(x) : (((T)(-((x) + 1))) + 1))\n\nThen in the case x < 0, first add 1, and note that both (x+1) and -(x+1)\nalways fit in a signed int. Then negate, cast the resulting\n*non-negative* number to unsigned, and then an unsigned add of 1 to get\nthe correct absolute value.\n\nAm I misunderstanding anything here?\n\nRegards,\n/Niels\n\n--\nNiels Möller. PGP-encrypted email is preferred. Keyid C0B98E26.\nInternet email is subject to wholesale government surveillance.\n\n```"
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[
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https://mathoverflow.net/questions/37792/a-possible-generalization-of-the-homotopy-groups
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[
"# A possible generalization of the homotopy groups.\n\nThe homotopy groups $\\pi_{n}(X)$ arise from considering equivalence classes of based maps from the $n$-sphere $S^{n}$ to the space $X$. As is well known, these maps can be composed, giving arise to a group operation. The resulting group contains a great deal of information about the given space. My question is: is there any extra information about a space that can be discovered by considering equivalence classes of based maps from the $n$-tori $T^{n}=S^{1}\\times S^{1}\\times \\cdots \\times S^{1}$. In the case of $T^{2}$, it would seem that since any path $S^{1}\\to X$ can be \"thickened\" to create a path $T^{2}\\to X$ if $X$ is three-dimensional, the group arising from based paths $T^{2}\\to X$ would contain $\\pi_{1}(X)$. Perhaps more generally, can useful information be gained by examining equivalence classes of based maps from some arbitrary space $Y$ to a given space $X$.\n\n• Well, if you examine homotopy classes of based maps from all based spaces Y at once, then you get enough information to characterize the space X up to homotopy equivalence, by the Yoneda lemma in the homotopy category. (-: Sep 5 '10 at 17:25\n• There's something similar to this that I thought of once: given any two spaces $X$ and $Y$, the set of homotopy classes of maps $X \\times I \\to Y$ sending all $(x, 0)$ and $(0,x)$ to a fixed base point form a group. If $X = I^{n-1}$, I believe the result contains, at least in some cases, all the homotopy groups $\\pi_1$ through $\\pi_n$. But given how hard the latter are to compute, I doubt that this construction is all that useful. [But if it is, I am not in a position to know.] Sep 5 '10 at 20:39\n• Mike- isn't this true even if we restricted to based maps for all based <i>co-Moore</i> spaces at once to X? Or am I completely off-base? Sep 5 '10 at 21:53\n• arxiv.org/abs/math/9904026 Groups of Flagged Homotopies and Higher Gauge Theory Valery V.Dolotin - there is some generalization of the homotopy groups. Feb 16 '13 at 14:33\n\nThere's always information to be got. But in this case:\n\n• Based homotopy classes of maps $T^2\\to X$ don't form a group! To define a natural function $\\mu\\colon [T,X]_*\\times [T,X]_*\\to [T,X]_*$, you need a map $c\\colon T\\to T\\vee T$ (where $\\vee$ is one point union). And if you want $\\mu$ to be unital, associative, etc., you'll want $c$ to be counital, coassociative, etc. For $T=T^n$ with $n\\geq2$, there is no $c$ that is counital. (The usual way to see this is to think about the cohomology $H^*T$ with its cup-product structure.)\n\n• The inclusion $S^1\\vee S^1\\to T^2$ gives a map $$r\\colon [T^2,X]_* \\to [S^1\\vee S^1,X]_*\\approx \\pi_1X\\times \\pi_1X.$$ The image of this map will be pairs $(a,b)$ of elements in $\\pi_1X$ which commute: $ab=ba$. It won't usually be injective; so there might be something interesting to think about the in preimages $r^{-1}(a,b)$.\n\nBack in the 1940's, Ralph Fox defined something called the torus homotopy group. For a based space $(Y,y_0)$ and natural number $r$, the $r$-dimensional torus homotopy group $\\tau_r(Y,y_0)$ is just the fundamental group of the mapping space ${\\rm map}(T^{r-1},Y)$, based at the constant map (where $T^{r-1}$ is of course a torus).\n\nThe group $\\tau_r(Y,y_0)$ contains isomorphic copies of $\\pi_n(Y,y_0)$ for all $n\\leq r$. Also, Whitehead products become commutators in the torus homotopy group. By passing to the limit over $r$ one obtains the (infinite) torus homotopy group $\\tau(Y, y_0)$, which contains all of the homotopy information of $Y$ in one place!\n\nUnfortunately for Fox, the idea doesn't seem to have caught on (although I hear he had a few others which did). MathSciNet only turns up 11 papers containing the phrase \"torus homotopy groups\" (although the most recent is from 2007).\n\nYour problem is that $T^n$ is not in general a co-Moore space. Therefore Eckmann-Hilton duality breaks down, as the dual spaces no longer form a spectrum, and there would be no (co)homology theory dual to such a \"homotopy theory\". Thus, a theory of homotopy classes of pointed maps from $T^n$ to $X$ would be much less interesting than a theory of homotopy classes of pointed maps from $S^n$ to $X$.\n\nOn the other hand, the study of homotopy classes of pointed maps from a co-Moore space other than $S^n$ to $X$ does lead to useful theories of homotopy with coefficients. I believe these classify $X$ up to homotopy equivalence.\n\nI was told by Brian Griffiths that Fox was hoping to obtain a generalisation of the van Kampen theorem and so continue work of J.H.C Whitehead on adding relations to homotopy groups (see his 1941 paper with that title).\n\nHowever if one frees oneself from the base point fixation one might be led to consider Loday's cat$^n$-group of a based $(n+1)$-ad, $X_*=(X;X_1, \\ldots, X_n)$; let $\\Phi X_*$ be the space of maps $I^n \\to X$ which take the faces of the $n$-cube $I^n$ in direction $i$ into $X_i$ and the vertices to the base point. Then $\\Phi$ has compositions $+_i$ in direction $i$ which form a lax $n$-fold groupoid. However the group $\\Pi X_*= \\pi_1(\\Phi, x)$, where $x$ is the constant map at the base point $x$, inherits these compositions to become a cat$^n$-group, i.e. a strict $n$-fold groupoid internal to the category of groups (the proof is non trivial).\n\nThere is a Higher Homotopy van Kampen Theorem for this functor $\\Pi$ which enables some new nonabelian calculations in homotopy theory (see our paper in Topology 26 (1987) 311-334).\n\nSo a key step is to move from spaces with base point to certain structured spaces.\n\nComment Feb 16, 2013: The workers in algebraic topology near the beginning of the 20th century were looking for higher dimensional versions of the fundamental group, since they knew that the nonabelian fundamental group was useful in problems of analysis and geometry. In 1932, Cech submitted a paper on Higher Homotopy Groups to the ICM at Zurich, but Alexandroff and Hopf quickly proved the groups were abelian for $n >1$ and on these grounds persuaded Cech to withdraw his paper, so that only a small paragraph appeared in the Proceedings. It is reported that Hurewicz attended that conference. In due course, the idea of higher versions of the fundamental group came to be seen as a mirage.\n\nOne explanation of the abelian nature of the higher homotopy groups is that group objects in the category of groups are abelian groups, as a result of the interchange law, also called the Eckmann-Hilton argument. However group objects in the category of groupoids are equivalent to crossed modules, and so are in some sense \"more nonabelian\" than groups. Crossed modules were first defined by J.H.C. Whitehead, 1946, in relation to second relative homotopy groups. This leads to the possibility, now realised, of \"higher homotopy groupoids\", Higher Homotopy Seifert-van Kampen Theorems, and the notions of higher dimensional group theory.\n\nSee this presentation for more background."
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https://fastdatascience.com/why-do-we-need-explainable-ai-video/
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[
"## What is explainable AI?\n\nExplainable AI, or XAI, is a set of methods and techniques that allow us to understand how a machine learning model works and why it makes the decisions it does. Without XAI, a machine learning model might be a “black box”, where even the developers cannot understand it they arrived at a certain decision.\n\n## Examples of how explainable AI can work\n\nExplainable AI techniques can vary. In the case of simple machine learning models like linear regression (formula y = mx + c), it’s easy to understand why a model has made a certain decision because there are only two parameters, the gradient m and the intercept c.\n\nHowever, for more complex machine learning models, such as deep learning models, convolutional neural networks, and so on, we could have many millions of parameters inside the model and it becomes increasingly harder to understand the decisions made.\n\n## Explainable AI for very complex models\n\nExplainable AI techniques in the case of extremely complex models normally consist of introducing small variations, or perturbations, into the input to the model, and observing the changes in the model’s output. For example, if a computer vision model is 87% confident that an image is a cat, and changing one pixel reduces the confidence to 85%, we can conclude that the pixel contained an element of ‘cattiness’ from the point of view of the model. By doing this across the image, we can get a very accurate map of which parts of the image are most cat-like to the model.\n\nThe beauty of XAI is that we don’t need to have any understanding of the model architecture to perform this analysis.\n\nThere are several well-known frameworks for XAI, the most widely used in Python currently being LIME."
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[
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https://thejediwife.com/makeup/you-asked-how-many-moles-are-in-18-0-grams-of-h2o.html
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[
"# You asked: How many moles are in 18 0 grams of H2O?\n\nContents\n\nThis is stated: the molar mass of water is 18.02 g/mol. Notice that the molar mass and the formula mass are numerically the same.\n\n## How many moles are in 18.0 grams of H2O?\n\nAs the molecular mass of the water is 18gram/ per mole. Mole = weight in grams / molecular mass — 1000/18 = 55.5 mole.\n\n## How many moles of water are in 1.8 grams of water?\n\nNow, 1.8g of H2O=1.818=0.1 mol H2O.\n\n## How many moles are in 1 mole of H2O?\n\nA mole (mol) is the amount of a substance that contains 6.02 × 10 23 representative particles of that substance. The mole is the SI unit for amount of a substance. Just like the dozen and the gross, it is a name that stands for a number. There are therefore 6.02 × 10 23 water molecules in a mole of water molecules.\n\n## How many moles of O are in H2O?\n\nThere is one moles of oxygen atoms per mole of water (given by the formula H2O).\n\n## How many grams are in H2O?\n\nThe average mass of one H2O molecule is 18.02 amu. The number of atoms is an exact number, the number of mole is an exact number; they do not affect the number of significant figures. The average mass of one mole of H2O is 18.02 grams.\n\n## How many water molecules are present in 18 moles of water?\n\nIt can be obtained by dividing the given mass (18 g) by molecular mass of water (18 g). – Thus 18 g of water will contain one mole of water, that is 6.023×1023 molecules. – In the second option it’s given that the number of moles is 18. Therefore 18 mole of water will contain 18×6.023×1023 number of molecules.\n\n## How many moles are present in 18 ml of water?\n\nThus, the mass of the water is 18g. This is the same as the molecular mass of water. Now we can calculate the moles of water present using the below formula. So, the number of moles of water will be [dfrac{{18}}{{18}} = 1] mole.\n\n## How many moles of water are present in 1.00 L of the liquid density of water is 1.00 g ml?\n\nIt just so happens that at standard temperature and pressure, the density of water is 1g per mL. A liter of water is 1000g of water. To get the number of moles per liter of water, we divide the mass of 1L of water (1000g) by the mass of a mole of water (18g / mole). 1000 / 18 = moles.\n\nTHIS IS EXCITING: Frequent question: Why am I getting acne on my arms and back?\n\n## How many grams are in 3 moles of water?\n\nWhat is the mass of 3 moles of water? – Quora. One mole of any substance. =Gram Atomic weight or gram molecular weight of that substance. Three mole of water weighs=18*3=54 Gram.\n\n## How many moles of H2 are in water?\n\nThere are two hydrogen atoms in a water molecule, so there are two moles of hydrogen atoms in a mole of water.\n\n## How many moles of H2O are in 1l?\n\nThe density of water is 1g/cc, so if you do dimensional analysis, you can find that in 1 L of water, there is 55.56 mol.\n\n## How many atoms are there in 18 gram of water?\n\nThe chemical formula of water is H2O, in water two mole of hydrogen is present and one mole of oxygen is present. So, in a single molecule of water, two mole of hydrogen are present. 18 g of water will contain ⇒1×12.046×1023=12.046×1023 atoms of hydrogen.\n\n## How many oxygen atoms are in 18 grams of water?\n\n– As in one mole of water there are6.022×1023 molecules, that’s how the mole was defined. – And as the chemical formula for water is H2O, and one mole of water corresponds to one mole of oxygen atoms. Hence, there will be 6.022×1023 oxygen atoms in one mole, or we can say 18 g of water.\n\n## How many atoms are in H2O?\n\nAtoms join together to form molecules. A water molecule has three atoms: two hydrogen (H) atoms and one oxygen (O) atom. That’s why water is sometimes referred to as H2O.\n\nTHIS IS EXCITING: What is aloe vera peel good for?"
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null
] |
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|
https://www.qalaxia.com/questions/Prove-that-three-times-the-square-of-any-side-of
|
[
"",
null,
"Krishna\n0\n\nStep 1: According to the given data built an imaginary diagram",
null,
"ABC be equilateral triangle.\n\nAD be perpendicular bisector from A on to BC.\n\nSo BD = DC = \\frac{1}{2} BC\n\nStep 2: Apply the Pythagoras theorem to an right angle triangle in equilateral.\n\nEXAMPLE: Consider ADC is a right angle triangle.\n\nSo, AC^2 = AD^2 + DC^2\n\nAC^2 = AD^2 + (\\frac{1}{2} BC)^2\n\nIt is an equilateral triangle so AB = BC = AC\n\nAC^2 = AD^2 + (\\frac{1}{2} AC)^2"
] |
[
null,
"https://d3648m43e37g8z.cloudfront.net/o72ob1cnnte20haf0hsrriib7agw8uprq765mp1519993736668.jpeg",
null,
"https://www.qalaxia.com/questions/o3jhxtl7rvxl7621atd7qhkk0av48x1e5ew1r7b31545506549578.png",
null
] |
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|
https://www.bartleby.com/solution-answer/chapter-45-problem-19e-calculus-mindtap-course-list-8th-edition/9781285740621/evaluate-the-indefinite-integral-x21x33x4dx/a030c631-9406-11e9-8385-02ee952b546e
|
[
"",
null,
"",
null,
"",
null,
"Chapter 4.5, Problem 19E\n\nChapter\nSection\nTextbook Problem\n\n# Evaluate the indefinite integral. ∫ ( x 2 + 1 ) ( x 3 + 3 x ) 4 d x\n\nTo determine\n\nTo evaluate:\n\nThe indefinite integral x2+1x3+3x4 dx\n\nExplanation\n\n1) Concept:\n\ni) The substitution rule\n\nIf u=g(x) is a differentiable function whose range is an interval I and f is continuous on I, then f(gx)g'xdx=f(u)du.\n\nii) Indefinite integral\n\nxn dx=xn+1n+1+C (n-1)\n\n2) Given:\n\nx2+1x3+3x4 dx\n\n3) Calculation:\n\nHere, use the substitution method because the differential of the function x3+3x is 3x2+3dx\n\nSubstitute u=x3+3x.\n\nDifferentiate u=x3+3x with respect to x.\n\ndu=3x2+3dx\n\nFactoring out 3 common,\n\ndu=3x2+1dx\n\nAs x2+1dx is a part of the integration, solving for x2+1dx by dividing both side by 3\n\n### Still sussing out bartleby?\n\nCheck out a sample textbook solution.\n\nSee a sample solution\n\n#### The Solution to Your Study Problems\n\nBartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!\n\nGet Started\n\n#### Find more solutions based on key concepts",
null,
""
] |
[
null,
"https://www.bartleby.com/static/search-icon-white.svg",
null,
"https://www.bartleby.com/static/close-grey.svg",
null,
"https://www.bartleby.com/static/solution-list.svg",
null,
"https://www.bartleby.com/static/logo.svg",
null
] |
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|
http://hltd.org/lib/initial_value_problem.htm
|
[
"# initial value problem\n\nInitial Value Problem\nIVP\n\nA differential equation or partial differential equation accompanied by conditions for the value of the function and possibly its derivatives at one particular point in the domain.\n\n Differential Equation y\" + y = sin x Initial Value Problem (IVP) y\" + y = sin x, y(0) = 1, y'(0) = – 2 Boundary Value Problem (BVP) y\" + y = sin x, y(0) = 1, y(1) = – 2"
] |
[
null
] |
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|
https://xscode.com/zziz/kalman-filter
|
[
"### kalman-filter\n\n#### by zziz",
null,
"Kalman Filter implementation in Python using Numpy only in 30 lines.\n\n149 Stars 44 Forks Last release: Not found 4 Commits 0 Releases\n\nAvailable items",
null,
"#### No Items, yet!\n\nThe developer of this repository has not created any items for sale yet. Need a bug fixed? Help with integration? A different license? Create a request here:\n\nImplementation of Kalman filter in 30 lines using Numpy. All notations are same as in Kalman Filter Wikipedia Page.\n\nIt is a generic implementation of Kalman Filter, should work for any system, provided system dynamics matrices are set up properly. Included example is the prediction of position, velocity and acceleration based on position measurements. Synthetic data is generated for the purpose of illustration.\n\nRunning:\n\n`python kalman-filter.py`\n```import numpy as np\n\nclass KalmanFilter(object):\ndef init(self, F = None, B = None, H = None, Q = None, R = None, P = None, x0 = None):\n``` if(F is None or H is None):\nraise ValueError(\"Set proper system dynamics.\")\n\nself.n = F.shape\nself.m = H.shape\n\nself.F = F\nself.H = H\nself.B = 0 if B is None else B\nself.Q = np.eye(self.n) if Q is None else Q\nself.R = np.eye(self.n) if R is None else R\nself.P = np.eye(self.n) if P is None else P\nself.x = np.zeros((self.n, 1)) if x0 is None else x0\n\ndef predict(self, u = 0):\nself.x = np.dot(self.F, self.x) + np.dot(self.B, u)\nself.P = np.dot(np.dot(self.F, self.P), self.F.T) + self.Q\nreturn self.x\n\ndef update(self, z):\ny = z - np.dot(self.H, self.x)\nS = self.R + np.dot(self.H, np.dot(self.P, self.H.T))\nK = np.dot(np.dot(self.P, self.H.T), np.linalg.inv(S))\nself.x = self.x + np.dot(K, y)\nI = np.eye(self.n)\nself.P = np.dot(np.dot(I - np.dot(K, self.H), self.P),\n(I - np.dot(K, self.H)).T) + np.dot(np.dot(K, self.R), K.T)```\ndef example():\ndt = 1.0/60\nF = np.array([[1, dt, 0], [0, 1, dt], [0, 0, 1]])\nH = np.array([1, 0, 0]).reshape(1, 3)\nQ = np.array([[0.05, 0.05, 0.0], [0.05, 0.05, 0.0], [0.0, 0.0, 0.0]])\nR = np.array([0.5]).reshape(1, 1)\n```x = np.linspace(-10, 10, 100)\nmeasurements = - (x**2 + 2*x - 2) + np.random.normal(0, 2, 100)\n\nkf = KalmanFilter(F = F, H = H, Q = Q, R = R)\npredictions = []\n\nfor z in measurements:\npredictions.append(np.dot(H, kf.predict()))\nkf.update(z)\n\nimport matplotlib.pyplot as plt\nplt.plot(range(len(measurements)), measurements, label = 'Measurements')\nplt.plot(range(len(predictions)), np.array(predictions), label = 'Kalman Filter Prediction')\nplt.legend()\nplt.show()```\nif name == 'main':\nexample()\n```\n\n#### Output",
null,
""
] |
[
null,
"https://avatars1.githubusercontent.com/u/2147644",
null,
"https://xscode.com/zziz/kalman-filter",
null,
"https://github.com/zziz/kalman-filter/raw/master/asset/Figure_1.png",
null
] |
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|
https://jp.maplesoft.com/support/help/addons/view.aspx?path=GraphTheory%2FSpecialGraphs%2FMeredithGraph
|
[
"",
null,
"MeredithGraph - Maple Help\n\nGraphTheory[SpecialGraphs]\n\n MeredithGraph\n construct Meredith graph",
null,
"Calling Sequence MeredithGraph()",
null,
"Description\n\n • The MeredithGraph command creates the Meredith graph.\n • The Meredith graph is a 4-regular distance-transitive graph with 70 vertices and 140 edges.",
null,
"Examples\n\n > $\\mathrm{with}\\left(\\mathrm{GraphTheory}\\right):$\n > $\\mathrm{with}\\left(\\mathrm{SpecialGraphs}\\right):$\n > $G≔\\mathrm{MeredithGraph}\\left(\\right)$\n ${G}{≔}{\\mathrm{Graph 1: an undirected graph with 70 vertices and 140 edge\\left(s\\right)}}$ (1)\n > $\\mathrm{IsRegular}\\left(G\\right)$\n ${\\mathrm{true}}$ (2)\n > $\\mathrm{ChromaticNumber}\\left(G\\right)$\n ${3}$ (3)",
null,
"References\n\n \"Meredith graph\", Wikipedia. http://en.wikipedia.org/wiki/Meredith_graph",
null,
"Compatibility\n\n • The GraphTheory[SpecialGraphs][MeredithGraph] command was introduced in Maple 2020."
] |
[
null,
"https://bat.bing.com/action/0",
null,
"https://jp.maplesoft.com/support/help/addons/arrow_down.gif",
null,
"https://jp.maplesoft.com/support/help/addons/arrow_down.gif",
null,
"https://jp.maplesoft.com/support/help/addons/arrow_down.gif",
null,
"https://jp.maplesoft.com/support/help/addons/arrow_down.gif",
null,
"https://jp.maplesoft.com/support/help/addons/arrow_down.gif",
null
] |
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|
https://math.paperswithcode.com/paper/the-inverse-problem-for-the-dirichlet-to
|
[
"## The Inverse Problem for the Dirichlet-to-Neumann map on Lorentzian manifolds\n\n27 Sep 2016 · Stefanov Plamen, Yang Yang ·\n\nWe consider the Dirichlet-to-Neumann map \\$\\Lambda\\$ on a cylinder-like Lorentzian manifold related to the wave equation related to the metric \\$g\\$, a magnetic field \\$A\\$ and a potential \\$q\\$. We show that we can recover the jet of \\$g,A,q\\$ on the boundary from \\$\\Lambda\\$ up to a gauge transformation in a stable way... We also show that \\$\\Lambda\\$ recovers the following three invariants in a stable way: the lens relation of \\$g\\$, and the light ray transforms of \\$A\\$ and \\$q\\$. Moreover, \\$\\Lambda\\$ is an FIO away from the diagonal with a canonical relation given by the lens relation. We present applications for recovery of \\$A\\$ and \\$q\\$ in a logarithmically stable way in the Minkowski case, and uniqueness with partial data. read more\n\nPDF Abstract\n\n# Code Add Remove Mark official\n\nNo code implementations yet. Submit your code now\n\nAnalysis of PDEs"
] |
[
null
] |
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|
https://tex.stackexchange.com/questions/483128/is-the-space-after-the-differential-d-operator-canonical-when-using-a-times-font
|
[
"# Is the space after the differential d operator canonical when using a Times font?\n\nI have this simple code,\n\n\\documentclass[12pt]{book}\n\\usepackage{mathtools}\n\\usepackage{newtxtext}\n\\usepackage[lite]{mtpro2}\n\\begin{document}\n$d\\bar{p}$ and $dt$.\n\\end{document}\n\n\nwith this output,",
null,
"I think it's a canonical space is due to the presence of the \\bar{...} command? Sometimes to bring it back I insert a negative space \\! to bring the p to the left near the d.\n\nThis little adjustment must always be done or I should create a particular macro. Which one could be always using the same command \\bar? It gets a bit complicated for me in my book to change the original command \\bar{...}. Thank you.\n\nUsing Steven Segletes' suggestion of \\ooalign{$d\\bar{#1}$\\cr$d#1$}, one can see if the problem is universal across \\bar. If the superposition produces a \"thick\" second letter, the kerning is not correct. (using newtxmath as Steven does not have mtpro2)\n\nUnfortunately, that proves not to be the case, as some cases seem kerned correctly and others not:\n\n\\documentclass[12pt]{book}\n\\usepackage{mathtools}\n\\usepackage{newtxtext}\n\\newcommand\\testkern{%\n\\ooalign{$d\\bar{#1}$\\cr$d#1$}}\n\\textwidth 1in\n\\begin{document}\n\\noindent\\testkern{a}\n\\testkern{b}\n\\testkern{c}\n\\testkern{d}\n\\testkern{e}\n\\testkern{f}\n\\testkern{g}\n\\testkern{h}\n\\testkern{i}\n\\testkern{j}\n\\testkern{k}\n\\testkern{l}\n\\testkern{m}\n\\testkern{n}\n\\testkern{o}\n\\testkern{p}\n\\testkern{q}\n\\testkern{r}\n\\testkern{s}\n\\testkern{t}\n\\testkern{u}\n\\testkern{v}\n\\testkern{w}\n\\testkern{x}\n\\testkern{y}\n\\testkern{z}\n\\end{document}",
null,
"Applying a universal -1mu kern to \\bar\n\n\\newcommand\\xbar{\\mkern-1mu\\bar}\n\\newcommand\\testkern{%\n\\ooalign{$d\\xbar{#1}$\\cr$d#1$}}\n\n\ntherefore, may fix some letter combinations, but will inevitably break others:",
null,
"• Without mtpro2, the space does not manifest. However, it does show, when, instead of mtpro2, one uses newtxmath. Apr 4, 2019 at 10:18\n• If the problem is universal with \\bar in that font, you could always do \\let\\svbar\\bar\\renewcommand\\bar{\\mkern-1mu\\svbar} Apr 4, 2019 at 10:24\n• Yes, if the two superimposed p's are \"thick\", that means the kerning is different between the two cases. If the superimposed p's look like one, then the kerning is correct. Apr 4, 2019 at 10:26\n• I removed some offtopic comments. (the conversation seemed to be finished anyway). Thanks. Apr 7, 2019 at 15:01\n• @Sebastiano -- The present \"title\" of thiis question doesn't make much sense to me. Would you be willing to change it to the following: Is the space after the differential d operator canonical when using a Times font? Aug 3, 2020 at 19:23\n\nA proposal to renew the command of \\bar as follows:\n\n\\let\\svbar\\bar\n\\renewcommand\\bar{%\n#1\\ThisStyle{\\setbox0=\\hbox{$\\SavedStyle#1$}\\kern-\\wd0}\\svbar{\\,\\phantom{#1}}\\!}\n\n\nThis will guarantee proper kerning of the letter, as it is set first thing without the \\bar. Then, I kern backward across the letter, and apply the \\bar to a variant of the letter's \\phantom. In this case, the variant is a shifted \\phantom, which is then unshifted following the \\bar, so as not to introduce any stray space.\n\nTherefore, if there are residual kerning issues, they will be with the placement of the superimposed bar, relative to the underlying properly kerned letter.\n\nThe MWE uses the \\ooalign test given in the question to judge the quality of the \\bar macro, using letter boldness as an indicator for bad kerning. As you can see, there are no thick/boldened letters signifying a kern mismatch. Therefore, with this approach, one must merely judge if the placement of the bar relative to the letter is suitable or not.\n\nWhile all examples are shown relative to the letter \"d\", the method, in fact, will perform similarly, regardless of the preceding letter.\n\nEDITED to work across math styles.\n\n\\documentclass[12pt]{book}\n\\usepackage{mathtools}\n\\usepackage{newtxtext}\n\\usepackage{scalerel}\n\\let\\svbar\\bar\n\\renewcommand\\bar{%\n#1\\ThisStyle{\\setbox0=\\hbox{$\\SavedStyle#1$}\\kern-\\wd0}\\svbar{\\,\\phantom{#1}}\\!}\n\\newcommand\\testkern[]{%\n\\ooalign{$#1 d\\bar{#2}$\\cr$#1 d#2$}}\n\\textwidth 1in\n\\begin{document}\n\\noindent\\testkern{a} \\testkern{b} \\testkern{c} \\testkern{d}\n\\testkern{e} \\testkern{f} \\testkern{g} \\testkern{h} \\testkern{i}\n\\testkern{j} \\testkern{k} \\testkern{l} \\testkern{m} \\testkern{n}\n\\testkern{o} \\testkern{p} \\testkern{q} \\testkern{r} \\testkern{s}\n\\testkern{t} \\testkern{u} \\testkern{v} \\testkern{w} \\testkern{x}\n\\testkern{y} \\testkern{z}\n\n\\noindent\\testkern[\\scriptstyle]{a} \\testkern[\\scriptstyle]{b}\n\\testkern[\\scriptstyle]{c} \\testkern[\\scriptstyle]{d}\n\\testkern[\\scriptstyle]{e} \\testkern[\\scriptstyle]{f}\n\\testkern[\\scriptstyle]{g} \\testkern[\\scriptstyle]{h}\n\\testkern[\\scriptstyle]{i} \\testkern[\\scriptstyle]{j}\n\\testkern[\\scriptstyle]{k} \\testkern[\\scriptstyle]{l}\n\\testkern[\\scriptstyle]{m} \\testkern[\\scriptstyle]{n}\n\\testkern[\\scriptstyle]{o} \\testkern[\\scriptstyle]{p}\n\\testkern[\\scriptstyle]{q} \\testkern[\\scriptstyle]{r}\n\\testkern[\\scriptstyle]{s} \\testkern[\\scriptstyle]{t}\n\\testkern[\\scriptstyle]{u} \\testkern[\\scriptstyle]{v}\n\\testkern[\\scriptstyle]{w} \\testkern[\\scriptstyle]{x}\n\\testkern[\\scriptstyle]{y} \\testkern[\\scriptstyle]{z}\n\n\\noindent$2 d\\bar{p}^2\\ne2d p^2$\n\\end{document}",
null,
"• My always thanks from my first question I asked two and a half years ago :-) Apr 4, 2019 at 11:21\n• @Sebastiano It has been my pleasure to assist you. Apr 4, 2019 at 11:26\n• Steven I can't get a green check mark. I'm sorry. The two answers are both beautiful. Apr 4, 2019 at 19:53\n• @Sebastiano No problem. Sometimes, a question without a checkmark brings more eyes, from those thinking it is still unanswered. Apr 4, 2019 at 19:54\n• I really appreciate the answers. When I can't choose, they are rare for me, it's because I can't penalize one user over another. Apr 4, 2019 at 19:55\n\nIf I compile\n\n\\documentclass[12pt]{book}\n\\usepackage{mathtools}\n\\usepackage{newtxtext}\n\\usepackage[lite]{mtpro2}\n\\begin{document}\n\n$d\\bar{p}$\n\n$dp$\n\n\\showoutput\n\n\\end{document}\n\n\nI get, for the two formulas\n\n....\\mathon\n....\\LMP1/mtt/m/it/12 d\n....\\kern1.43999\n....\\vbox(7.88399+2.568)x7.98\n.....\\hbox(7.88399+0.0)x0.0, shifted 3.312\n......\\LMP2/mtt/m/n/12 N\n.....\\kern-5.484\n.....\\hbox(5.484+2.568)x7.98\n......\\LMP1/mtt/m/it/12 p\n....\\mathoff\n\n....\\mathon\n....\\LMP1/mtt/m/it/12 d\n....\\kern1.43999\n....\\kern-2.40001\n....\\LMP1/mtt/m/it/12 p\n....\\kern0.48\n....\\mathoff\n\n\nAfter removing the call to mtpro2, I get\n\n....\\mathon\n....\\OML/cmm/m/it/12 d\n....\\vbox(6.77774+2.33331)x5.89717\n.....\\hbox(6.77774+0.0)x0.0, shifted 0.99028\n......\\OT1/cmr/m/n/12 ^^V\n.....\\kern-5.16667\n.....\\hbox(5.16667+2.33331)x5.89717\n......\\OML/cmm/m/it/12 p\n....\\mathoff\n\n....\\mathon\n....\\OML/cmm/m/it/12 d\n....\\OML/cmm/m/it/12 p\n....\\mathoff\n\n\nThe obvious difference is that d in the font \\LMP1/mtt/m/it/12 (pointing to mt2mit at 12pt) has an italic correction, which isn't present in the \\OML/cmm/m/it/12 font (pointing to cmsy10 at 12pt).\n\nIndeed, if I do tftopl mt2mit, I get\n\n(CHARACTER C d\n(CHARWD R 0.551)\n(CHARHT R 0.717)\n(CHARIC R 0.12)\n(COMMENT\n(KRN O 0 R -0.06)\n[...]\n(KRN C p R -0.2)\n[...]\n(KRN C t R -0.04)\n[...]\n(KRN O 263 R -0.02)\n)\n)\n\n\nand with tftopl cmsy10 I get\n\n(CHARACTER O 100\n(CHARWD R 0.611113)\n(CHARHT R 0.694445)\n)\n\n\nAs you can see, there is also a kerning pair with p or t, which moves in the character when there is no accent, but this is not possible when the next item is an Acc atom.\n\nYou can manually compute the appropriate kerning.\n\n\\documentclass[12pt]{book}\n\\usepackage{mathtools}\n\\usepackage{newtxtext}\n\\usepackage[lite]{mtpro2}\n\n\\newcommand{\\dwithbar}{%\nd\\computedaccentkern{#1}\\bar{#1}%\n}\n\\makeatletter\n\\newcommand{\\computedaccentkern}{%\n\\mathpalette\\computedaccentkern@{#1}%\n}\n\\newcommand{\\computedaccentkern@}{%\n\\begingroup\n\\sbox\\z@{$\\m@th#1d#2$}\n\\sbox\\tw@{$\\m@th#1d{\\kern0pt#2}$}%\n\\kern\\dimexpr\\wd\\z@-\\wd\\tw@\\relax\n\\endgroup\n}\n\\makeatother\n\n\\begin{document}\n\n$d\\bar{p}$ $d\\bar{p}$\n\n$\\dwithbar{p}$ $\\dwithbar{p}$\n\n$dp$ $dp$\n\n$d\\bar{t}$ $d\\bar{t}$\n\n$\\dwithbar{t}$ $\\dwithbar{t}$\n\n$dt$ $dt$\n\n\\end{document}\n\n\nYou can define similarly for other accents, say \\dot:\n\n\\newcommand{\\dwithdot}{%\nd\\computedaccentkern{#1}\\dot{#1}%\n}\n\n\nor a generic\n\n\\newcommand{\\dwithacc}{%\nd\\computedaccentkern{#2}#1{#2}%\n}\n\n\nto be called like \\dwithacc\\bar{p} or \\dwithacc\\dot{p}.",
null,
"• Shocking :-) I dare say amazed. I don't understand almost anything (\\mathon...\\mathoff :-) where they come from, CHARACTER etc...) but I can imagine that it's a problem with encoding the different incompatible fonts that I'm using. Apr 4, 2019 at 11:20\n• @Sebastiano The first part is the analysis of what TeX internally does with the input, in terms of boxes and glue. Then I looked at the metrics for the fonts, finding the correspondence with what we saw in the boxes and glue representation. Apr 4, 2019 at 11:21\n• Do i understand your solution correctly that it specifically addresses kerns following the letter \"d\", or is it universal for any letter combinations? Apr 4, 2019 at 11:57\n• @StevenB.Segletes It's specifically for d, but could be modified quite easily for other pairs. Apr 4, 2019 at 12:02\n• @egreg Doesn't know who to vote for the two questions to. If I don't, it's because they're both beautiful. Apr 4, 2019 at 19:52\n\nThis is more of a comment, but requires an example.\n\nThe problem described does not occur with Computer Modern, and the reason is the difference in the metrics in the .tfm file: the \"d\" in the alphabet used for math does not have an italic correction. This is by design, since \"d\" is most often used by Knuth for the differential operator; if he uses it as a variable, he would add a thin space following the \"d\" if needed.\n\nHere is the example used in the question, set with Computer Modern.\n\n\\documentclass[12pt]{article}\n\\usepackage{amsmath}\n\\begin{document}\nThe differential $d$ as set using Computer Modern: \\qquad\n$d\\bar{p}$ and $dt$.\n\\end{document}",
null,
"In short, the space that is inserted (differently with and without diacritics on the letter following the \"d\") is the result of metrics for the \"d\" not being defined in the same manner used in Computer Modern. (This is not a problem when an upright \"d\" is used for the differential function.)\n\n• Thank you very much for your precious answer and contribute. Aug 3, 2020 at 18:52\n\nThis could be an intermediate solution, without macro, using diffcoeff package (I remember that derivative package - see pag. 29 - does not include the differential symbol as shown in this image) with the option ISO to have upright differential symbol.",
null,
"In this case it is possible to observe that a bit of horizontal spacing has decreased.",
null,
"\\documentclass[a4paper,12pt]{article}\n\\usepackage[lite]{mtpro2}\n\\usepackage{derivative}\n\\usepackage[ISO]{diffcoeff}\n\\begin{document}\n\\begin{equation}\n\nFor those who would like to compile the code and they haven't installed \\usepackage[lite]{mtpro2} to replace it with \\usepackage{newtxmath}. The only difference is the length of the \\bar above the letter."
] |
[
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"https://i.stack.imgur.com/4HOYB.png",
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"https://i.stack.imgur.com/ahgmZ.jpg",
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"https://i.stack.imgur.com/jDQIA.jpg",
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"https://i.stack.imgur.com/EpTp1.jpg",
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"https://i.stack.imgur.com/tWdEw.png",
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"https://i.stack.imgur.com/tVNYy.png",
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"https://i.stack.imgur.com/UIg4e.png",
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"https://i.stack.imgur.com/QoCpV.png",
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] |
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https://www.taxaj.com/home-loan-emi-calculator
|
[
"## Home Loan EMI Calculator\n\nGiven the high price of real estate in India, purchasing a house can be a challenging task without an external source of finance. An increasing number of prospective home buyers are opting for this type of credit to fund their house purchase. It is no surprise that housing credit grew by over 16% in FY18.\n\nThe primary responsibility of a potential borrower is to have an exact estimate of the EMI amount they are liable to pay. One can take advantage of a home loan EMI calculator to arrive at the precise number.\n\n# HOME LOAN EMI Calculator\n\nRs.\n\n%\n\nYr\n\nEMI Amount:\n\nEquated Monthly Instalment or EMI is a fixed amount that a borrower must pay back to the lender every month till their tenure ends.\n\nCalculating the EMI and its components can be a cumbersome exercise for first-time financers. A home loan EMI calculator India can do these complex calculations in no time, and save you from the trouble of doing it manually.\n\n• Manually performing such complicated home loan EMI calculations can be both time-consuming and inaccurate. A home loan monthly EMI calculator saves the valuable time of prospective home buyers.\n• It gives you an accurate estimate, which is pivotal for financial planning. There is no probability of any inaccuracies or ambiguity.\n• The EMI calculation procedure for each type of loan is different. For example, home loan EMI calculation is different from personal loan EMI. The housing loan EMI calculator is specific only for home loans.\n• The online calculator is free for unlimited use. You can check the EMI for various loan amounts and determine which amount suits your financial situation.\n\n### The formula to determine home loan EMI amount\n\nAll online calculators use a specific home loan EMI calculator formula to arrive at the exact EMI amount, which is –\n\nE = [P x R x (1+R) ^N] / [(1+R) ^N-1]\n\n E EMI amount P Principal amount R Rate of interest N Loan tenure\n\nhome loan EMI calculator online can help you find the exact amount without fail.\n\nFor example, assume that a person avails a home loan worth Rs. 1 Crore for a tenure of 15 years at an agreed-upon interest rate of 12%. So, according to the formula –\n\nE = [1, 00, 00,000 x 12 x (1+12) ^ 15] / [)1+12) ^ 20-1]\n\nhome loan EMI calculator India will instantly help you compute the exact result, which in this case should be Rs. 1, 10,108.\n\nNow, each loan EMI has two components – a principal component and an interest component. At the beginning of the tenure, the interest component is high, and the principal part is relatively low. The equation changes with every passing month, as the total interest to be paid reduces faster. So, with every EMI paid, the interest component decreases while the principal component increases.\n\n#### How to use TAXAJ online home loan EMI calculator?\n\nTAXAJ is one of the leading financial resources providers. The housing loan EMI calculator India available here is very easy to use.\n\nAll you have to do is enter the loan amount, interest rate and the loan tenure in years.\n\nThe exact EMI value will be calculated and displayed within seconds.\n\n#### Advantages of using TAXAJ calculator\n\nThere are numerous advantages of using the calculator available at this website.\n\n1. It’s easy to use. All you have to do is insert a few necessary details, and the calculator will do the rest.\n2. It’s free for everyone. You don’t even have to register to the website.\n3. There is no limit on the number of times you can use it. So, you can quickly check the EMI for different home loan amounts.\n\nAs a debt category, the home loans corpus is expected to grow faster in the coming years. An online bank EMI calculator for a home loan is the go-to tool for all prospective debtors."
] |
[
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.9301768,"math_prob":0.9500926,"size":3713,"snap":"2023-40-2023-50","text_gpt3_token_len":841,"char_repetition_ratio":0.17120518,"word_repetition_ratio":0.025954198,"special_character_ratio":0.22030702,"punctuation_ratio":0.08864266,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.95547956,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-10-02T02:23:24Z\",\"WARC-Record-ID\":\"<urn:uuid:6ddc6c23-d879-4038-9deb-14c637aecf13>\",\"Content-Length\":\"183322\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:52811911-fc5e-4452-b98d-6977f3ce9135>\",\"WARC-Concurrent-To\":\"<urn:uuid:7f67eae4-a4bf-48fa-9d9f-9ffc1f5e6092>\",\"WARC-IP-Address\":\"169.148.148.139\",\"WARC-Target-URI\":\"https://www.taxaj.com/home-loan-emi-calculator\",\"WARC-Payload-Digest\":\"sha1:U62RN3MDAYA6YS7FNDW6NPIVPDW6FQF4\",\"WARC-Block-Digest\":\"sha1:YNATRJ36AL3NKC6NV4HPO25HKB3EVQAF\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-40/CC-MAIN-2023-40_segments_1695233510942.97_warc_CC-MAIN-20231002001302-20231002031302-00064.warc.gz\"}"}
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https://stat.ethz.ch/pipermail/r-sig-meta-analysis/2018-September/001114.html
|
[
"# [R-meta] Inflated confidence intervals\n\nViechtbauer, Wolfgang (SP) wolfg@ng@viechtb@uer @ending from m@@@trichtuniver@ity@nl\nTue Sep 18 19:14:42 CEST 2018\n\n```Please always cc the mailing list.\n\nI don't know what you mean by 'trivariate mean' or 'adjusted mean' (adjusted for what?). If you want the average of the three outcomes, then it would be:\n\nintrcpt + 1/3 * MeasurementHDL + 1/3 * MeasurementTC\n\nso in this case:\n\n-0.2376 + 1/3 * 0.1982 + 1/3 * -0.0148 = -0.1764667\n\nwhich you can also get with: predict(resMV, newmods = c(1/3, 1/3)).\n\nI don't know what you mean by 'Univariate model'. A model that does not distinguish between the three outcomes? Why would this model give an estimate that is equal to the intercept of the model whose output you showed?\n\nBest,\nWolfgang\n\n-----Original Message-----\nFrom: Wasim Iqbal (UG) [mailto:W.Iqbal using newcastle.ac.uk]\nSent: Sunday, 16 September, 2018 17:18\nTo: Viechtbauer, Wolfgang (SP)\nSubject: Re: Inflated confidence intervals\n\nSorry the difference for both HDL and LDL from the intercept would be....-0.0541. -0.0394 would be just for HDL\n\nWasim\n________________________________________\nFrom: Wasim Iqbal (UG)\nSent: 16 September 2018 16:13:16\nTo: Viechtbauer, Wolfgang (SP)\nSubject: Re: Inflated confidence intervals\n\nSorry I am getting easily confused. Essentially, if you were to work out the trivariate mean (or adjusted mean) for this model would this be the difference of both HDL and LDL from the intercept (i.e. -0.0394)? Therefore, if I was to show this in a table with the univariate model this would be:\n\nUnivariate model: -0.2376\nTrivariate model : -0.0394\n\nI assumed that we must add the intercept to the slopes of HDL and LDL to get the overall adjusted mean? However, now having second thoughts based on what you said (and my textbooks) by adding the intercept ( i.e. -0.2376+0.1982+-0.0148) I am actually including the intercept again when it was already included? (silly me).\n\nThank you for clarifying. Its the simple things that catch me!\n\nKind regards\nWasim\n________________________________________\nFrom: Viechtbauer, Wolfgang (SP) <wolfgang.viechtbauer using maastrichtuniversity.nl>\nSent: 16 September 2018 14:30:01\nTo: Wasim Iqbal (UG)\nCc: r-sig-meta-analysis using r-project.org; Gavin Stewart; Chris Seal\nSubject: RE: Inflated confidence intervals\n\nI apparently haven't had enough coffee today, so first a correction on my part:\n\npredict(resMV, newmods = c(1,0)) gives the estimated (average) outcome for HDL (i.e., -0.2376 + 0.1982 = -0.0394). The coefficient for HDL (i.e., 0.1982) is already the difference between HDL and LDL.\n\nBut you seem to be after something different. Apparently, you want to add the intecept and the two coefficients together, so: -0.2376 + 0.1982 + -0.0148 =~ -0.0541, which indeed you would obtain with predict(resMV, newmods = c(1,1)). But what is the meaning of this?\n\nIf you want a marginal mean, that is, the average of the three outcomes, then you would want:\n\nintercept + 1/3 * HDL + 1/3 * TC\n\n(assuming the intercept corresponds to LDL, as in the output you showed), which you would get with predict(resMV, newmods = c(1/3,1/3)). But maybe I am still misunderstanding.\n\nBest,\nWolfgang\n```\n\nMore information about the R-sig-meta-analysis mailing list"
] |
[
null
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https://lettuce.io/core/release/api/io/lettuce/core/api/reactive/RedisGeoReactiveCommands.html
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[
"Skip navigation links\nLettuce\nio.lettuce.core.api.reactive\n\n## Interface RedisGeoReactiveCommands<K,V>\n\n• ### Method Summary\n\nAll Methods\nModifier and Type Method and Description\n`Mono<Long>` ```geoadd(K key, double longitude, double latitude, V member)```\nSingle geo add.\n`Mono<Long>` ```geoadd(K key, double longitude, double latitude, V member, GeoAddArgs args)```\nSingle geo add.\n`Mono<Long>` ```geoadd(K key, GeoAddArgs args, GeoValue<V>... values)```\nMulti geo add.\n`Mono<Long>` ```geoadd(K key, GeoAddArgs args, Object... lngLatMember)```\nMulti geo add.\n`Mono<Long>` ```geoadd(K key, GeoValue<V>... values)```\nMulti geo add.\n`Mono<Long>` ```geoadd(K key, Object... lngLatMember)```\nMulti geo add.\n`Mono<Double>` ```geodist(K key, V from, V to, GeoArgs.Unit unit)```\nRetrieve distance between points `from` and `to`.\n`Flux<Value<String>>` ```geohash(K key, V... members)```\nRetrieve Geohash strings representing the position of one or more elements in a sorted set value representing a geospatial index.\n`Flux<Value<GeoCoordinates>>` ```geopos(K key, V... members)```\nGet geo coordinates for the `members`.\n`Flux<V>` ```georadius(K key, double longitude, double latitude, double distance, GeoArgs.Unit unit)```\nRetrieve members selected by distance with the center of `longitude` and `latitude`.\n`Flux<GeoWithin<V>>` ```georadius(K key, double longitude, double latitude, double distance, GeoArgs.Unit unit, GeoArgs geoArgs)```\nRetrieve members selected by distance with the center of `longitude` and `latitude`.\n`Mono<Long>` ```georadius(K key, double longitude, double latitude, double distance, GeoArgs.Unit unit, GeoRadiusStoreArgs<K> geoRadiusStoreArgs)```\nPerform a `georadius(Object, double, double, double, GeoArgs.Unit, GeoArgs)` query and store the results in a sorted set.\n`Flux<V>` ```georadiusbymember(K key, V member, double distance, GeoArgs.Unit unit)```\nRetrieve members selected by distance with the center of `member`.\n`Flux<GeoWithin<V>>` ```georadiusbymember(K key, V member, double distance, GeoArgs.Unit unit, GeoArgs geoArgs)```\nRetrieve members selected by distance with the center of `member`.\n`Mono<Long>` ```georadiusbymember(K key, V member, double distance, GeoArgs.Unit unit, GeoRadiusStoreArgs<K> geoRadiusStoreArgs)```\nPerform a `georadiusbymember(Object, Object, double, GeoArgs.Unit, GeoArgs)` query and store the results in a sorted set.\n`Flux<V>` ```geosearch(K key, GeoSearch.GeoRef<K> reference, GeoSearch.GeoPredicate predicate)```\nRetrieve members selected by distance with the center of `reference` the search `predicate`.\n`Flux<GeoWithin<V>>` ```geosearch(K key, GeoSearch.GeoRef<K> reference, GeoSearch.GeoPredicate predicate, GeoArgs geoArgs)```\nRetrieve members selected by distance with the center of `reference` the search `predicate`.\n`Mono<Long>` ```geosearchstore(K destination, K key, GeoSearch.GeoRef<K> reference, GeoSearch.GeoPredicate predicate, GeoArgs geoArgs, boolean storeDist)```\nPerform a `geosearch(Object, GeoSearch.GeoRef, GeoSearch.GeoPredicate, GeoArgs)` query and store the results in a sorted set.\n• ### Method Detail\n\n• #### geoadd\n\n```Mono<Long> geoadd(K key,\ndouble longitude,\ndouble latitude,\nV member)```\nSingle geo add.\nParameters:\n`key` - the key of the geo set.\n`longitude` - the longitude coordinate according to WGS84.\n`latitude` - the latitude coordinate according to WGS84.\n`member` - the member to add.\nReturns:\nLong integer-reply the number of elements that were added to the set.\n• #### geoadd\n\n```Mono<Long> geoadd(K key,\ndouble longitude,\ndouble latitude,\nV member,\nGeoAddArgs args)```\nSingle geo add.\nParameters:\n`key` - the key of the geo set.\n`longitude` - the longitude coordinate according to WGS84.\n`latitude` - the latitude coordinate according to WGS84.\n`member` - the member to add.\n`args` - additional arguments.\nReturns:\nLong integer-reply the number of elements that were added to the set.\nSince:\n6.1\n• #### geoadd\n\n```Mono<Long> geoadd(K key,\nObject... lngLatMember)```\nMulti geo add.\nParameters:\n`key` - the key of the geo set.\n`lngLatMember` - triplets of double longitude, double latitude and V member.\nReturns:\nLong integer-reply the number of elements that were added to the set.\n• #### geoadd\n\n```Mono<Long> geoadd(K key,\nGeoValue<V>... values)```\nMulti geo add.\nParameters:\n`key` - the key of the geo set.\n`values` - `GeoValue` values to add.\nReturns:\nLong integer-reply the number of elements that were added to the set.\nSince:\n6.1\n• #### geoadd\n\n```Mono<Long> geoadd(K key,\nGeoAddArgs args,\nObject... lngLatMember)```\nMulti geo add.\nParameters:\n`key` - the key of the geo set.\n`args` - additional arguments.\n`lngLatMember` - triplets of double longitude, double latitude and V member.\nReturns:\nLong integer-reply the number of elements that were added to the set.\nSince:\n6.1\n• #### geoadd\n\n```Mono<Long> geoadd(K key,\nGeoAddArgs args,\nGeoValue<V>... values)```\nMulti geo add.\nParameters:\n`key` - the key of the geo set.\n`args` - additional arguments.\n`values` - `GeoValue` values to add.\nReturns:\nLong integer-reply the number of elements that were added to the set.\nSince:\n6.1\n• #### geodist\n\n```Mono<Double> geodist(K key,\nV from,\nV to,\nGeoArgs.Unit unit)```\nRetrieve distance between points `from` and `to`. If one or more elements are missing `null` is returned. Default in meters by, otherwise according to `unit`\nParameters:\n`key` - the key of the geo set.\n`from` - from member.\n`to` - to member.\n`unit` - distance unit.\nReturns:\ndistance between points `from` and `to`. If one or more elements are missing `null` is returned.\n• #### geohash\n\n```Flux<Value<String>> geohash(K key,\nV... members)```\nRetrieve Geohash strings representing the position of one or more elements in a sorted set value representing a geospatial index.\nParameters:\n`key` - the key of the geo set.\n`members` - the members.\nReturns:\nbulk reply Geohash strings in the order of `members`. Returns `null` if a member is not found.\n• #### geopos\n\n```Flux<Value<GeoCoordinates>> geopos(K key,\nV... members)```\nGet geo coordinates for the `members`.\nParameters:\n`key` - the key of the geo set.\n`members` - the members.\nReturns:\na list of `GeoCoordinates`s representing the x,y position of each element specified in the arguments. For missing elements `null` is returned.\n• #### georadius\n\n```Flux<V> georadius(K key,\ndouble longitude,\ndouble latitude,\ndouble distance,\nGeoArgs.Unit unit)```\nRetrieve members selected by distance with the center of `longitude` and `latitude`.\nParameters:\n`key` - the key of the geo set.\n`longitude` - the longitude coordinate according to WGS84.\n`latitude` - the latitude coordinate according to WGS84.\n`distance` - radius distance.\n`unit` - distance unit.\nReturns:\nbulk reply.\n• #### georadius\n\n```Flux<GeoWithin<V>> georadius(K key,\ndouble longitude,\ndouble latitude,\ndouble distance,\nGeoArgs.Unit unit,\nGeoArgs geoArgs)```\nRetrieve members selected by distance with the center of `longitude` and `latitude`.\nParameters:\n`key` - the key of the geo set.\n`longitude` - the longitude coordinate according to WGS84.\n`latitude` - the latitude coordinate according to WGS84.\n`distance` - radius distance.\n`unit` - distance unit.\n`geoArgs` - args to control the result.\nReturns:\nnested multi-bulk reply. The `GeoWithin` contains only fields which were requested by `GeoArgs`.\n• #### georadius\n\n```Mono<Long> georadius(K key,\ndouble longitude,\ndouble latitude,\ndouble distance,\nGeoArgs.Unit unit,\nGeoRadiusStoreArgs<K> geoRadiusStoreArgs)```\nPerform a `georadius(Object, double, double, double, GeoArgs.Unit, GeoArgs)` query and store the results in a sorted set.\nParameters:\n`key` - the key of the geo set.\n`longitude` - the longitude coordinate according to WGS84.\n`latitude` - the latitude coordinate according to WGS84.\n`distance` - radius distance.\n`unit` - distance unit.\n`geoRadiusStoreArgs` - args to store either the resulting elements with their distance or the resulting elements with their locations a sorted set.\nReturns:\nLong integer-reply the number of elements in the result.\n• #### georadiusbymember\n\n```Flux<V> georadiusbymember(K key,\nV member,\ndouble distance,\nGeoArgs.Unit unit)```\nRetrieve members selected by distance with the center of `member`. The member itself is always contained in the results.\nParameters:\n`key` - the key of the geo set.\n`member` - reference member.\n`distance` - radius distance.\n`unit` - distance unit.\nReturns:\nset of members.\n• #### georadiusbymember\n\n```Flux<GeoWithin<V>> georadiusbymember(K key,\nV member,\ndouble distance,\nGeoArgs.Unit unit,\nGeoArgs geoArgs)```\nRetrieve members selected by distance with the center of `member`. The member itself is always contained in the results.\nParameters:\n`key` - the key of the geo set.\n`member` - reference member.\n`distance` - radius distance.\n`unit` - distance unit.\n`geoArgs` - args to control the result.\nReturns:\nnested multi-bulk reply. The `GeoWithin` contains only fields which were requested by `GeoArgs`.\n• #### georadiusbymember\n\n```Mono<Long> georadiusbymember(K key,\nV member,\ndouble distance,\nGeoArgs.Unit unit,\nGeoRadiusStoreArgs<K> geoRadiusStoreArgs)```\nPerform a `georadiusbymember(Object, Object, double, GeoArgs.Unit, GeoArgs)` query and store the results in a sorted set.\nParameters:\n`key` - the key of the geo set.\n`member` - reference member.\n`distance` - radius distance.\n`unit` - distance unit.\n`geoRadiusStoreArgs` - args to store either the resulting elements with their distance or the resulting elements with their locations a sorted set.\nReturns:\nLong integer-reply the number of elements in the result.\n• #### geosearch\n\n```Flux<V> geosearch(K key,\nGeoSearch.GeoRef<K> reference,\nGeoSearch.GeoPredicate predicate)```\nRetrieve members selected by distance with the center of `reference` the search `predicate`. Use `GeoSearch` to create reference and predicate objects.\nParameters:\n`key` - the key of the geo set.\n`reference` - the reference member or longitude/latitude coordinates.\n`predicate` - the bounding box or radius to search in.\nReturns:\nbulk reply.\nSince:\n6.1\n• #### geosearch\n\n```Flux<GeoWithin<V>> geosearch(K key,\nGeoSearch.GeoRef<K> reference,\nGeoSearch.GeoPredicate predicate,\nGeoArgs geoArgs)```\nRetrieve members selected by distance with the center of `reference` the search `predicate`. Use `GeoSearch` to create reference and predicate objects.\nParameters:\n`key` - the key of the geo set.\n`reference` - the reference member or longitude/latitude coordinates.\n`predicate` - the bounding box or radius to search in.\n`geoArgs` - args to control the result.\nReturns:\nnested multi-bulk reply. The `GeoWithin` contains only fields which were requested by `GeoArgs`.\nSince:\n6.1\n• #### geosearchstore\n\n```Mono<Long> geosearchstore(K destination,\nK key,\nGeoSearch.GeoRef<K> reference,\nGeoSearch.GeoPredicate predicate,\nGeoArgs geoArgs,\nboolean storeDist)```\nPerform a `geosearch(Object, GeoSearch.GeoRef, GeoSearch.GeoPredicate, GeoArgs)` query and store the results in a sorted set.\nParameters:\n`destination` - the destination where to store results.\n`key` - the key of the geo set.\n`reference` - the reference member or longitude/latitude coordinates.\n`predicate` - the bounding box or radius to search in.\n`geoArgs` - args to control the result.\n`storeDist` - stores the items in a sorted set populated with their distance from the center of the circle or box, as a floating-point number, in the same unit specified for that shape.\nReturns:\nLong integer-reply the number of elements in the result.\nSince:\n6.1\nSkip navigation links\nLettuce\n\nCopyright © 2021 lettuce.io. All rights reserved."
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[
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https://answers.everydaycalculation.com/multiply-fractions/1-24-times-49-10
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[
"Solutions by everydaycalculation.com\n\n## Multiply 1/24 with 49/10\n\n1st number: 1/24, 2nd number: 4 9/10\n\nThis multiplication involving fractions can also be rephrased as \"What is 1/24 of 4 9/10?\"\n\n1/24 × 49/10 is 49/240.\n\n#### Steps for multiplying fractions\n\n1. Simply multiply the numerators and denominators separately:\n2. 1/24 × 49/10 = 1 × 49/24 × 10 = 49/240\n\nMathStep (Works offline)",
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"Download our mobile app and learn to work with fractions in your own time:"
] |
[
null,
"https://answers.everydaycalculation.com/mathstep-app-icon.png",
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https://bamdevmishra.in/codes/rsvrg/
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[
"## Bamdev Mishra\n\n### Riemannian stochastic variance reduced gradient algorithm on manifolds\n\n#### Authors\n\nH. Kasai, H. Sato, and B. Mishra\n\n#### Abstract\n\nStochastic variance reduction algorithms have recently become popular for minimizing the average of a large, but finite, number of loss functions. In this paper, we propose a novel Riemannian extension of the Euclidean stochastic variance reduced gradient algorithm (R-SVRG) to a compact manifold search space. To this end, we show the developments on the Grassmann manifold. The key challenges of averaging, addition, and subtraction of multiple gradients are addressed with notions like logarithm mapping and parallel translation of vectors on the Grassmann manifold. We present a global convergence analysis of the proposed algorithm with a decay step-size and a local convergence rate analysis under a fixed step-size with some natural assumptions. The proposed algorithm is applied on a number of problems on the Grassmann manifold like principal components analysis, low-rank matrix completion, and the Karcher mean computation. In all these cases, the proposed algorithm outperforms the standard Riemannian stochastic gradient descent algorithm."
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http://www.mathsatsharp.co.za/topics/numbers-operations-and-relationships/fractions-and-decimals
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[
"# Category Archives: Fractions and Decimals\n\n## Worksheet 26: Term 1 Revision Grade 9\n\nThis grade 9 maths worksheet covers all work studied in grade 9 in the first term according to the CAPS curriculum. Questions and sections include the number system, prime factors, simplifying common fraction and decimal expressions, converting between decimals, fractions and percentages, exponents, scientific notation, patterns, functions and relationships, substitution, algebraic expressions and solving algebraic […]\n\n## Worksheet 4: Decimal Fractions\n\nThis grade 9 mathematics worksheet contains work on Decimal fractions as covered in the first term of the CAPS curriculum. Questions include: changing between equivalent forms of common fractions, percentages and decimal fractions, simplifying sums using BODMAS and squares, cubes, square-roots and cube-roots, rounding off to a specified number of decimal places and story sums. […]\n\n## Worksheet 29: Term 3 Revision\n\nThis grade 8 mathematics worksheet includes revision on all work covered in the third term according to South Africa’s CAPS syllabus. Topics include – common fractions, decimal fractions, Pythagoras, area and perimeter of 2D shapes, surface area and volume of 3D objects and data handling. Download here: Worksheet 29: Term 3 Revision Worksheet 29 Memorandum: […]\n\n## Worksheet 14: Decimal Fractions\n\nThis worksheet tests all the decimal fraction decimal fractions skills grade 8’s following the CAPS curriculum should know at the end of term 3. It includes comparing decimals and fractions, rounding off to 1 and 2 decimal places, doing calculations including squaring, cubing, square-rooting and cube-rooting decimals, converting between decimals, fractions and percentages, working out […]\n\n## Worksheet 13: Common Fractions\n\nThis mathematics worksheet covers all the basics for common fractions that grade 8 students following the CAPS curriculum should be able to do at the end of the third term. It includes converting between mixed number and improper fractions, equivalent fractions, converting between fractions, decimals and percentages, doing sums with fractions including squaring, cubing and […]\n\n## Worksheet 3: Common Fractions\n\nThis grade 9 CAPS mathematics worksheet revises the skills necessary for common fractions. Sums include using BEDMAS to simplify expressions, converting between mixed number fractions and improper fractions, finding equivalent fractions (an important skill for algebraic fractions), converting between common fractions, decimals and percentages, and being able to use these skills in context (the dreaded […]"
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https://www.audiolabs-erlangen.de/resources/MIR/FMP/C2/C2_STFT-FreqGridDensity.html
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[
"",
null,
"# STFT: Frequency Grid Density\n\nComputing a discrete STFT introduces a frequency grid which resolution depends on the signal's sampling rate and the STFT window size, see Section 2.1.4 of [Müller, FMP, Springer 2015]. In this notebook, we discuss how to make the frequency grid denser by suitably padding the windowed sections in the STFT computation. Often, one loosely says that this procedure increases the frequency resolution. This, however, is not true in a qualitative sense as we explain below.\n\n## DFT Frequency Grid¶\n\nLet $x\\in \\mathbb{R}^N$ be discrete signal of length $N\\in\\mathbb{N}$ with samples $x(0), x(1), \\ldots, x(N-1)$. Given the sampling rate $F_\\mathrm{s}$, we assume that $x$ is obtained by sampling a continues-time signal $f:\\mathbb{R}\\to\\mathbb{R}$. Then, the discrete Fourier transform (DFT) $X := \\mathrm{DFT}_N \\cdot x$ can be interpreted as an approximation of the continuous Fourier transform $\\hat{f}$ for certain frequencies (see Equation (2.132) of [Müller, FMP, Springer 2015]):\n\n$$X(k) := \\sum_{n=0}^{N-1} x(n) \\exp(-2 \\pi i k n / N) \\approx {F_\\mathrm{s}} \\cdot \\hat{f} \\left(k \\cdot \\frac{F_\\mathrm{s}}{N}\\right)$$\n\nfor $k\\in[0:N-1]$. Thus, the index $k$ of $X(k)$ corresponds to the physical frequency\n\n\\begin{equation} F_\\mathrm{coef}^N(k) := \\frac{k\\cdot F_\\mathrm{s}}{N} \\end{equation}\n\ngiven in Hertz. In other words, the discrete Fourier transform introduces a linear frequency grid of resolution $F_\\mathrm{s}/N$, which depends on the size $N$ of the $\\mathrm{DFT}_N$. To increase the density of the frequency grid, one idea is to increase the size of the DFT by artificially appending zeros to the signal. To this end, let $L\\in\\mathbb{N}$ with $L\\geq N$. Then, we apply zero padding to the right of the signal $x$ obtaining the signal $\\tilde{x}\\in \\mathbb{R}^L$:\n\n\\begin{equation} \\tilde{x}(n) :=\\left\\{\\begin{array}{ll} x(n) ,& \\,\\,\\mbox{for}\\,\\, n \\in[0:N-1],\\\\ 0, & \\,\\,\\mbox{for}\\,\\, n \\in[N:L-1]. \\end{array}\\right. \\end{equation}\n\nApplying a $\\mathrm{DFT}_L$, we obtain:\n\n$$\\tilde{X}(k) = \\mathrm{DFT}_L \\cdot \\tilde{x} = \\sum_{n=0}^{L-1} \\tilde{x}(n) \\exp(-2 \\pi i k n / L) = \\sum_{n=0}^{N-1} x(n) \\exp(-2 \\pi i k n / L) \\approx {F_\\mathrm{s}} \\cdot \\hat{f} \\left(k \\cdot \\frac{F_\\mathrm{s}}{L}\\right)$$\n\nfor $k\\in[0:L-1]$. The coefficient $\\tilde{X}(k)$ now corresponds to the physical frequency\n\n\\begin{equation} F_\\mathrm{coef}^L(k) := \\frac{k\\cdot F_\\mathrm{s}}{L}, \\end{equation}\n\nthus introducing a linear frequency resolution of $F_\\mathrm{s}/L$. For example, if $L=2N$, the frequency grid resolution is increased by a factor of $2$. In other words, the longer DFT results in more frequency bins that are more closely spaced. However, note that this trick does not improve the approximation quality of the DFT (note that the number of summands in the Riemann approximation is still $N$). Only, the linear sampling of the frequency axis is refined when using $L\\geq N$ and zero padding. The following example compares $\\mathrm{DFT}_N \\cdot x$ with $\\mathrm{DFT}_L \\cdot \\tilde{x}$.\n\nIn :\nimport numpy as np\nfrom matplotlib import pyplot as plt\nimport librosa\n%matplotlib inline\n\nFs = 32\nduration = 2\nfreq1 = 5\nfreq2 = 15\nN = int(duration * Fs)\nt = np.arange(N) / Fs\nt1 = t[:N//2]\nt2 = t[N//2:]\n\nx1 = 1.0 * np.sin(2 * np.pi * freq1 * t1)\nx2 = 0.7 * np.sin(2 * np.pi * freq2 * t2)\nx = np.concatenate((x1, x2))\n\nplt.figure(figsize=(8, 2))\n\nax1 = plt.subplot(1, 2, 1)\nplt.plot(x, c='k')\nplt.title('Orginal signal ($N$=%d)' % N)\nplt.xlabel('Time (samples)')\nplt.xlim([0, N - 1])\nplt.subplot(1, 2, 2)\nY = np.abs(np.fft.fft(x)) / Fs\nplt.plot(Y, c='k')\nplt.title('Magnitude DFT of original signal ($N$=%d)' % N)\nplt.xlabel('Frequency (bins)')\nplt.xlim([0, N - 1])\nplt.tight_layout()\n\nL = 2 * N\npad_len = L - N\nt_tilde = np.concatenate((t, np.arange(len(x), len(x) + pad_len) / Fs))\nx_tilde = np.concatenate((x, np.zeros(pad_len)))\n\nplt.figure(figsize=(8, 2))\nax1 = plt.subplot(1, 2, 1)\nplt.plot(x_tilde, c='k')\nplt.title('Padded signal ($L$=%d)' % L)\nplt.xlabel('Time (samples)')\nplt.xlim([0, L - 1])\nplt.subplot(1, 2, 2)\nY_tilde = np.abs(np.fft.fft(x_tilde)) / Fs\nplt.plot(Y_tilde, c='k')\nplt.title('Magnitude DFT of padded signal ($L$=%d)' % L)\nplt.xlabel('Frequency (bins)')\nplt.xlim([0, L - 1])\n\nplt.tight_layout()",
null,
"",
null,
"The next code example implements a function for computing the DFT with increased frequency grid resolution, where all parameters are interpreted in a physical way (in terms of seconds and Hertz).\n\nIn :\ndef compute_plot_DFT_extended(t, x, Fs, L):\nN = len(x)\npad_len = L - N\nt_tilde = np.concatenate((t, np.arange(len(x), len(x) + pad_len) / Fs))\nx_tilde = np.concatenate((x, np.zeros(pad_len)))\nY = np.abs(np.fft.fft(x_tilde)) / Fs\nY = Y[:L//2]\nfreq = np.arange(L//2)*Fs/L\n# freq = np.fft.fftfreq(L, d=1/Fs)\n# freq = freq[:L//2]\nplt.figure(figsize=(12, 2))\n\nax1 = plt.subplot(1, 3, 1)\nplt.plot(t_tilde, x_tilde, c='k')\nplt.title('Signal ($N$=%d)' % N)\nplt.xlabel('Time (seconds)')\nplt.xlim([t, t[-1]])\n\nax2 = plt.subplot(1, 3, 2)\nplt.plot(t_tilde, x_tilde, c='k')\nplt.title('Padded signal (of size $L$=%d)' % L)\nplt.xlabel('Time (seconds)')\nplt.xlim([t_tilde, t_tilde[-1]])\n\nax3 = plt.subplot(1, 3, 3)\nplt.plot(freq, Y, c='k')\nplt.title('Magnitude DFT of padded signal ($L$=%d)' % L)\nplt.xlabel('Frequency (Hz)')\nplt.xlim([freq, freq[-1]])\nplt.tight_layout()\n\nreturn ax1, ax2, ax3\n\nN = len(x)\n\nL = N\nax1, ax2, ax3 = compute_plot_DFT_extended(t, x, Fs, L)\n\nL = 2 * N\nax1, ax2, ax3 = compute_plot_DFT_extended(t, x, Fs, L)\n\nL = 4 * N\nax1, ax2, ax3 = compute_plot_DFT_extended(t, x, Fs, L)",
null,
"",
null,
"",
null,
"## STFT with Increased Frequency Grid Resolution¶\n\nWe now show how the same zero-padding strategy can be used to increase the frequency grid resolution of an STFT. The librosa function librosa.stft implements this idea by means of the two parameters n_fft (corresponding to $L$) and win_length (corresponding to $N$). Care has to be taken when converting the parameters to the physical domain. Our example is the note C4 played by a violin (with vibrato).\n\nIn :\nimport os\nimport IPython.display as ipd\n\nfn_wav = os.path.join('..', 'data', 'C2', 'FMP_C2_F05c_C4_violin.wav')\n\nFs = 11025\nx, Fs = librosa.load(fn_wav, sr=Fs)\nipd.display(ipd.Audio(x, rate=Fs))\n\nt_wav = np.arange(0, x.shape) * 1 / Fs\nplt.figure(figsize=(5, 1.5))\nplt.plot(t_wav, x, c='gray')\nplt.xlim([t_wav, t_wav[-1]])\nplt.xlabel('Time (seconds)')\nplt.tight_layout()",
null,
"We now compute an STFT with zero-padding. In the visualization, the axis are shown in terms of time frames and frequency bins.\n\nIn :\ndef compute_stft(x, Fs, N, H, L=N, pad_mode='constant', center=True):\nX = librosa.stft(x, n_fft=L, hop_length=H, win_length=N,\nY = np.log(1 + 100 * np.abs(X) ** 2)\nF_coef = librosa.fft_frequencies(sr=Fs, n_fft=L)\nT_coef = librosa.frames_to_time(np.arange(X.shape), sr=Fs, hop_length=H)\nreturn Y, F_coef, T_coef\n\ndef plot_compute_spectrogram(x, Fs, N, H, L, color='gray_r'):\nY, F_coef, T_coef = compute_stft(x, Fs, N, H, L)\nplt.imshow(Y, cmap=color, aspect='auto', origin='lower')\nplt.xlabel('Time (frames)')\nplt.ylabel('Frequency (bins)')\nplt.title('L=%d' % L)\nplt.colorbar()\n\nN = 256\nH = 64\ncolor = 'gray_r'\nplt.figure(figsize=(10, 4))\n\nL = N\nplt.subplot(1,3,1)\nplot_compute_spectrogram(x, Fs, N, H, L)\n\nL = 2 * N\nplt.subplot(1,3,2)\nplot_compute_spectrogram(x, Fs, N, H, L)\n\nL = 4 * N\nplt.subplot(1,3,3)\nplot_compute_spectrogram(x, Fs, N, H, L)\n\nplt.tight_layout()",
null,
"Next, we repeat the same computation, where the axis are now converted to show physical units specified in seconds and Hertz. Furthermore, we zoom into the time-frequency plane to highlight the effect of having a denser frequency grid density.\n\nIn :\ndef plot_compute_spectrogram_physical(x, Fs, N, H, L, xlim, ylim, color='gray_r'):\nY, F_coef, T_coef = compute_stft(x, Fs, N, H, L)\nextent=[T_coef, T_coef[-1], F_coef, F_coef[-1]]\nplt.imshow(Y, cmap=color, aspect='auto', origin='lower', extent=extent)\nplt.xlabel('Time (seconds)')\nplt.ylabel('Frequency (Hz)')\nplt.title('L=%d' % L)\nplt.ylim(ylim)\nplt.xlim(xlim)\nplt.colorbar()\n\nxlim_sec = [2, 3]\nylim_hz = [2000, 3000]\n\nplt.figure(figsize=(10, 4))\n\nL = N\nplt.subplot(1,3,1)\nplot_compute_spectrogram_physical(x, Fs, N, H, L, xlim=xlim_sec, ylim=ylim_hz)\n\nL = 2 * N\nplt.subplot(1,3,2)\nplot_compute_spectrogram_physical(x, Fs, N, H, L, xlim=xlim_sec, ylim=ylim_hz)\n\nL = 4 * N\nplt.subplot(1,3,3)\nplot_compute_spectrogram_physical(x, Fs, N, H, L, xlim=xlim_sec, ylim=ylim_hz)\n\nplt.tight_layout()",
null,
"## Further Notes¶\n\nAcknowledgment: This notebook was created by Meinard Müller."
] |
[
null,
"https://www.audiolabs-erlangen.de/resources/MIR/FMP/data/C2_nav.png",
null,
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 ",
null,
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 ",
null,
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 ",
null,
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 ",
null,
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 ",
null,
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 ",
null,
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 ",
null,
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null
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http://hieudt.info/division-practice-worksheets-3rd-grade/
|
[
"division practice worksheets grade awesome of wor.\n\nworksheet relating multiplication printable worksheets for grade drills advanced math 3 and division word problems practice sheets 3rd workshe.\n\nformidable division worksheets grade no remainders with best long images on of n.\n\ngrade long division practice worksheets for all download and free language arts library print on 3rd gr.\n\nlong division practice worksheets grade collection of pra.\n\npractice math medium to large size of multiplication facts worksheets understanding fact family grade and division pr.\n\ngrade division coloring sheets pages worksheets multiplication printable 3 fun mystery pi 3rd and practice third.\n\nmedium to large size of basic division worksheets practice grade long 3rd multiplication and divisio.\n\nfree printable division worksheets luxury 8 multiplication and for grade elegant best in math long single digit with remainder sheet skills practice 3rd.\n\nworksheet long division practice worksheets grade math teacher teaching 3rd multiplication and printable free library download print.\n\nmath facts practice worksheets also multiplication best of telling time clock to f.\n\nfraction number stories worksheets grade division practice equivalent fractions den 3rd.\n\nthird grade test practice multiplication division 3rd and worksheets math worksheet.\n\ngrade math multiplication coloring worksheets more and division word problems multiple step problem printable for 3rd w.\n\nbasic division worksheets practice fa fact worksheet medium printable grade long free to di.\n\nbasic division worksheets free for grade reading comprehension 3rd multiplication and practice best school math.\n\nfree multiplication worksheets grade 3 math practice printable new third line for and division 3rd.\n\nlong division practice worksheets grade worksheet and no remainder 4 or 2 digit divisor divi.\n\nworksheets proofreading grade practice high school for division 3rd multiplication and wor.\n\nprintable division worksheets grade long practice free to for 1 3rd multiplication and practi.\n\nthird grade net a how to write paper top argumentative essay editing service commutative property of o.\n\ndivision practice worksheets grade 3rd multiplication and.\n\nfree math worksheets grade division vertical subtraction facts to questions a worksheet 3rd multiplication.\n\nlong division practice worksheets de common for 3rd grade multiplication and fo.\n\ndivision worksheets printable for teachers grade practice 4 3rd multiplication and colle.\n\nmultiplication practice worksheets grade delighted and division coloring gallery 3rd.\n\ndivision worksheets grade practice s 3rd multiplication and home math sheets triple.\n\nbasic math facts worksheets third grade practice and division awesome 3rd multiplication ma.\n\nns third grade multiplication and n worksheets word long worksheet for activities practice coloring.\n\nworksheets grade math multiplication and division word printable picture for 3 problems 3rd multip.\n\nnice multiplication and division coloring worksheets roll multiply dice games make practicing facts fun use this one over a grade free 3rd.\n\nfree third grade math worksheets multiplication problems and division word wor.\n\ndivision practice ksheets grade multiplication and printable 3rd worksheets w.\n\npractice worksheets for long division grade multiplication and 3rd printable practi.\n\nbasic division fact worksheets of third grade 3rd multiplication and practice.\n\ngrade division worksheets prepossessing free math about long practice library multiplication and printable."
] |
[
null
] |
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|
https://www.scivision.dev/matlab-package-import/
|
[
"## Matlab package import like Python\n\nMatlab users can share code projects as toolboxes and/or packages. Matlab packages work for Matlab ≥ R2008a as well as GNU Octave. Matlab toolboxes work for Matlab ≥ R2016a and not GNU Octave. The packages format brings benefits to toolboxes as well.\n\nMatlab namespaces: a key issue with Matlab vs. Python arise from that Matlab users often add many paths for their project. If any function names clash, there can be unexpected behavior as it’s not immediately clear which function is being used without further investigation of path ordering. As in Python and other languages, there is considerable benefit for using a package format where the function names are specified in their namespace.\n\naddpath example: Matlab package format. Suppose project directory structure:\n\n``````myproj\nutils\nmem1.m\nconversion\ndeg1.m\nsys\ndisk1.m``````\n\nTo use these functions, the end users do:\n\n``addpath(genpath('myproj'))``\n\nThis is where the namespace can have clashes, and with large projects it’s not clear where a function is without further introspection.\n\npackage example: make this project a Matlab / Octave package by changing the subdirectories containing .m files to start with a “+” plus symbol:\n\n``````myproj\n+utils\nmem1.m\n+conversion\ndeg1.m\n+sys\ndisk1.m``````\n\nThe end users simply:\n\n``addpath('myproj')``\n\naccess specific functions like:\n\n``myproj.utils.mem1(arg1)``\n\nThen multiple subdirectories can have the same function name without clashing in the Matlab namespace. Suppose the function “mem1” is used frequently in another function. To avoid typing the fully resolved function name each time, use the import statement:\n\n``````function myfunc()\n\nimport myproj.utils.mem1\n\nmem1(arg1)\n\nmem1(arg2)``````\n\nPrivate functions: Matlab packages can have private functions that are only accessible from functions in that level of the namespace. Continuing the example from above, if we added function:\n\n``````myproj\n+utils\nprivate\nmysecret.m``````\n\nthen only functions under +utils/ can see and use mysecret.m function. mysecret() is used directly, without `import` since it’s only visible to functions at that directory level.\n\nMatlab .mltbx toolboxes became available in R2016a. The Matlab-proprietary toolbox format also allows end users to create their own packages containing code, examples and even graphical Apps. In effect .mltbx provides metadata and adds the package to the bottom of Matlab path upon installation. The installation directory is under (system specific)/MathWorks/MATLAB Add-Ons/Toolboxes/packageName. Whether or not the project uses .mltbx, the namespace of the project is kept cleaner by using a Matlab package layout."
] |
[
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|
https://cs.stackexchange.com/questions/3563/nlog-n-and-n-log-n-against-polynomial-running-time/3569
|
[
"# n*log n and n/log n against polynomial running time\n\nI understand that $\\Theta(n)$ is faster than $\\Theta(n\\log n)$ and slower than $\\Theta(n/\\log n)$. What is difficult for me to understand is how to actually compare $\\Theta(n \\log n)$ and $\\Theta(n/\\log n)$ with $\\Theta(n^f)$ where $0 < f < 1$.\n\nFor example, how do we decide $\\Theta(n/\\log n)$ vs. $\\Theta(n^{2/3})$ or $\\Theta(n^{1/3})$\n\nI would like to have some directions towards proceeding in such cases. Thank you.\n\nIf you just draw a couple of graphs, you'll be in good shape. Wolfram Alpha is a great resource for these kinds of investigations:",
null,
"",
null,
"Generated by this link. Note that in the graph, log(x) is the natural logarithm, which is the reason the one graph's equation looks a little funny.\n\n$\\log n$ is the inverse of $2^n$. Just as $2^n$ grows faster than any polynomial $n^k$ regardless of how large a finite $k$ is, $\\log n$ will grow slower than any polynomial functions $n^k$ regardless of how small a nonzero, positive $k$ is.\n\n$n / \\log n$ vs $n^k$, for $k < 1$ is identical to: $n / \\log n$ vs $n / n^{1-k}$\n\nas $n^{1-k} > \\log n$ for large $n$, $n / \\log n > n^k$ for $k < 1$ and large $n$.\n\nFor many algorithms, it sometimes happens that the constants are different, causing one or another is faster or slower for smaller data sizes, and are not as well-ordered by algorithmic complexity.\n\nHaving said that, if we only consider the super-large data sizes, ie. which one eventually wins, then O(n^f) is faster than O(n/log n) for 0 < f < 1.\n\nA large part of algorithmic complexity is to determine which algorithm is eventually faster, thus knowing that O(n^f) is faster than O(n/log n) for 0 < f < 1, is often enough.\n\nA general rule is that multiplying (or dividing) by log n will eventually be negligible compared to multiplying (or dividing) by n^f for any f > 0.\n\nTo show this more clearly, let us consider what happens as n increases.\n\n n n / log n n^(1/2)\n2 n/ 1 ?\n4 n/ 2 n/ 2\n8 n/ 3 ?\n16 n/ 4 n/ 4\n64 n/ 6 n/ 8\n256 n/ 8 n/16\n1024 n/10 n/32\n\n\nNotice which decreases more rapidly? It is the n^f column.\n\nEven if f was closer to 1, the n^f column will just start slower, but as n doubles, the rate of change of the denominator speeds up, whereas the denominator of the n/log n column appears to change at a constant rate.\n\nLet us plot a particular case on a graph",
null,
"",
null,
"Source: Wolfram Alpha\n\nI selected O(n^k) such that k is quite close to 1 (at 0.9). I also selected the constants so that initially O(n^k) is slower. However, notice that it eventually \"wins\" in the end, and takes less time than O(n/log n).\n\n• what about n/log n – mihsathe Sep 8 '12 at 3:42\n• That was a bit of a typo, that's what I meant in the beginning. Anyways, I added a more appropriate graph that shows n^k eventually being faster, even if constants are selected such that it is initially slower. – ronalchn Sep 8 '12 at 4:06\n\nJust think of $n^f$ as $\\dfrac{n}{n^{1-f}}$. So for your example, $n^{2/3}=n/n^{1/3}$. Then it is easy to compare the growth of\n\n$$\\frac{n}{\\log n} \\quad \\text{vs.} \\quad \\frac{n}{n^{1-f}}.$$\n\nRemember that $\\log n$ grows asymptotically slower than any $n^\\varepsilon$, for every $\\varepsilon>0$.\n\nWhen comparing running times, it always helpful to compare them by using big values of n. For me, this helps build intuition about which function is slower\n\nIn your case think of n = 10^10 and a = .5\n\nO(n/logn) = O(10^10/10) = O(10^9)\nO(n^1/2) = O(10^10^.5) = O(10^5)\n\n\nHence, O(n^a) is faster than O(n/logn), when 0 < a < 1 I have used just one value, however, you can use multiple values to build intuition about the function\n\n• Don't write O(10^9), but the main point about trying some numbers to build intuition is right. – Steve Jessop Sep 8 '12 at 4:19\n• Fail. This is not correct. You substituted a single n constant, which may be biased. If I chose different constants, I could make any algorithm look better. Big O notation is used to establish trends in what will be faster in the long term. To do this, you have to be able to show that it is faster for large n, even if it is slower when n is smaller. – ronalchn Sep 8 '12 at 4:20\n• Thanks. Added multiple values part and to consider bigger numbers – Himanshu Jindal Sep 8 '12 at 4:25\n• It should be noted that just because f(a) > g(a) for some constant a, does not necessarily imply that O(f(x)) > O(g(x)). This is useful to build intuition, but is insufficient to compose a rigorous proof. In order to show that this relationship holds, you must show this to be true for ALL large n, not just one large n. Likewise, you must show it to be true for all polynomials of positive degree < 1. – user1512185 Sep 8 '12 at 4:26\n\nLet $f \\prec g$ denote \"f grows asymptotically slower than g\", then you can use the following easy rule for polylogarithmic? functions:\n\n$$n^{\\alpha_1}(\\log n)^{\\alpha_2}(\\log \\log n)^{\\alpha_3} \\prec n^{\\beta_1}(\\log n)^{\\beta_2}(\\log \\log n)^{\\beta_3} \\Longleftrightarrow (\\alpha_1, \\alpha_2, \\alpha_3) < (\\beta_1, \\beta_2, \\beta_3)$$\n\nThe order relation between the tuples is lexicographic. I.e. $(2, 10) < (3, 5)$ and $(2, 10) > (2, 5)$\n\n$\\mathcal{O}(n/\\log n) \\Rightarrow (1, -1, 0)$\n$\\mathcal{O}(n^{2/3}) \\Rightarrow (2/3, 0, 0)$\n$\\mathcal{O}(n^{1/3}) \\Rightarrow (1/3, 0, 0)$\n$$(1/3, 0, 0) < (2/3, 0, 0) < (1, -1, 0)\\\\ \\Rightarrow \\mathcal{O}(n^{1/3}) \\prec \\mathcal{O}(n^{2/3}) \\prec \\mathcal{O}(n/\\log n)$$"
] |
[
null,
"https://i.stack.imgur.com/fdtNZ.gif",
null,
"https://i.stack.imgur.com/7Tqb8.gif",
null,
"https://i.stack.imgur.com/xdqzn.gif",
null,
"https://i.stack.imgur.com/bKEmp.gif",
null
] |
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http://catalarem.tk/special-relativity-equation-sheet-for-heat.html
|
[
"Special relativity equation sheet for heat\n\nSpecial equation\n\nSpecial relativity equation sheet for heat\n\n1) holds for a system total energy E, where the constant c is the speed of light, a momentum of magnitude p, , equation having intrinsic rest mass m 0, such as a particle , macroscopic body sheet assuming the special relativity case of sheet flat spacetime. thin sheet of iron and sheet then heated the combination at 1220 K for for an hour. We are going sheet to give several forms of the heat equation for reference purposes, but we will only be really solving one of them. special An equation sheet would be. is the amount of heat energy is the specific heat, is the mass, is the change in temperature. Heat Engine R 4/ 11. Fluids Heat, Waves, Optics Relativity. Show transcribed image textpoints) Is the heat equation compatible with the special relativity?\n\n67 × 10− 11Nm2/ kg2 special h= 6. ( Hint: one of the cardinal properties in special relativity is that no information sheet can propagate faster than the speed of light in the vacuum. Special Relativity. Process of elimination is not a terribly good strategy. However, it violates one important principle of the Einstein’ s special theory of equation relativity i. A heat series of videos covering the heat GCSE Physics syllabus for AQA OCR and Edexcel. The heat treatment.\n\nThe Dirac sea model which was used to predict the existence of antimatter is closely related to the energy- momentum equation. Special relativity equation sheet for heat. APIpe calculates the minimum internal diameter wall thickness for a pipeline transporting special hydrocarbon fluids according relativity to the recommended practice ( 14E § 18) issued by the offshore industry' s most prominent authority: the API. 05 × 10− 34Js Units: 1N= kgm/ s2 1J. Also note that the term containing relaxation time when eliminated, the equation becomes the basic heat conduction equation of Fourier' s law. APIpe calculates the performance criteria for liquids gases a combination of the two ( 2- phase fluid). Conservation of sheet energy for relativity finite systems is valid in such for physical theories as special relativity and quantum theory ( including QED) in the flat space- time. GCSE sheet exams are taken in the UK ( and elsewhere) by students usually aged 15/ 16. Special RelativityWe have covered a lot! Sunlight is a bunch of high- energy special photons coming from one direction, which involves relatively little entropy. The equation for temperature change given applied heat is. The theory of relativity refers to two special different elements of the same theory: general relativity and special relativity. You may have noticed a negative sign in the equation above. A little later that energy sheet is re- radiated from the Earth as heat which is the same amount energy spread relativity over substantially more photons sheet involves a lot more entropy heat ( relatively).\nAccording to the principle of equivalence from general relativity. Einstein' s Theory of Special Relativity; Static Electricity. Einstein' s theory of relativity is a famous theory, but it' s little understood. 626 × 10− 34Js ¯ h = 1. PHYSICS 113: Contemporary Physics – Final Exam Formula Sheet sheet Not every equation here will actually be needed on the heat exam some may be needed more than once.\n\nTo illustrate the use of the above equation, let' s calculate the rate of heat transfer on a cold day. PHYSICS 113: Contemporary Physics – Final Exam Formula Sheet d~ p F~ net = dt For a single timestep: Not every equation here will actually be needed on the exam some may be needed more than once. Relativity is the dependence of sheet various physical phenomena on relative motion of the observer and the observed objects. Since most springs would never stretch anything close to a meter other units like the newton per centimeter [ N/ cm] newton per millimeter [ N/ mm] are also common. Participate special in expert discussion on special and general relativity topics. the velocity of light in vacuum is the greatest known speed and has a finite value special of 2.\n\nWith the discovery of special relativity by Henri Poincaré Albert Einstein energy was proposed to be one component of an energy- momentum 4- for vector. 998 x 10^ 8 m/ s. The first partial differential equation that we’ ll be looking at once we get started with sheet solving will be the heat equation, which governs sheet the for temperature distribution in an object. Pipe Flow Calculator ( API RP 14E criteria). Special relativity equation sheet for heat. PHYSICS 1250 SYLLABUS/ ASSIGNMENT SHEET Spring 1. Physical Constants: c= 3 × 108m/ s G= 6.\n\nSpecial sheet\n\nSpecial Relativity S. a single A4 page just to special relativity stuff on my cheat sheet. the ones that aren' t on the formula sheet). AVAILABLE BOOKS Click here to order any book THE GREATEST STANDING ERRORS IN PHYSICS.\n\nspecial relativity equation sheet for heat\n\nby Miles Mathis Painting Experiment with an Air Pump by Joseph Wright of Derby, 1768, National Gallery, London email me at com go to my art site. Diffusion is one of the fundamental processes by which material moves."
] |
[
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.89162576,"math_prob":0.9867607,"size":5045,"snap":"2019-43-2019-47","text_gpt3_token_len":1102,"char_repetition_ratio":0.16643523,"word_repetition_ratio":0.04,"special_character_ratio":0.21308225,"punctuation_ratio":0.08961748,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99232966,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-10-23T04:41:59Z\",\"WARC-Record-ID\":\"<urn:uuid:1c6feb94-09df-4e86-b1f5-a9057b34ccee>\",\"Content-Length\":\"9953\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:5a4b8f4d-c86d-4054-acc0-545518f11209>\",\"WARC-Concurrent-To\":\"<urn:uuid:c6aa083a-3d6c-44f8-a2fd-cd615b18838d>\",\"WARC-IP-Address\":\"104.28.12.190\",\"WARC-Target-URI\":\"http://catalarem.tk/special-relativity-equation-sheet-for-heat.html\",\"WARC-Payload-Digest\":\"sha1:ZLDCLTCSST7RWMBXQAYVPRFIJJDWFVAF\",\"WARC-Block-Digest\":\"sha1:24O4GAI4O6D5M5HTMCTTI56ACGXLRDAG\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-43/CC-MAIN-2019-43_segments_1570987829458.93_warc_CC-MAIN-20191023043257-20191023070757-00391.warc.gz\"}"}
|
https://www.numpyninja.com/post/5-must-know-python-tools
|
[
"top of page",
null,
"Search\n\n# 5 Must know Python tools!\n\nPython is a strong, flexible, and user-friendly programming language. It's straightforward to read, learn and write. Compared to other prominent languages like C/C++ and Java, you require fewer lines of code to accomplish the same purpose.\n\nHere I have compiled a list of 5 Must know Python tools that will help you in your development/data science journey.",
null,
"Let’s Begin!\n\n1. Iterating over Range Objects:\n\nLet's get into the basics and understand the Range() function and how it works.\n\nRange() function returns a sequence of numbers. The most important use of range functions is to iterate through a sequence of numbers using loops etc.",
null,
"Here the range function returns the sequence of numbers from 0 to 4.\n\nRange(5) simply means to Range(0,5,1)\n\n0 – Refers to the start of the sequence. By default 0 will be the start of the sequence.\n\n5 – Refers to the end of the sequence. Range always includes the first element of the sequence and excludes the end of the sequence. Hence 5 was not included in the Output.\n\n1 – Refers to the step size. By default, 1 will be the step size.\n\nHere is another example of iterating over range objects. “i” is the loop variable or iterator variable and range(11) is iterable. Iterable is any object which can be iterated over, and this also refers to the number of iterations that we desire. In this example, we are iterating over the range of numbers from 0 to 10 and identifying whether the number is even or odd.\n\nfor i in range(11):\n\nif i%2 == 0:\n\nprint(str(i) + \" This is a Even number\")\n\nelse:\n\nprint(str(i) + \" This is a Odd number\")\n\nThe output of the above code looks like this.\n\nLet's see how python produced this Output. range(11) will produce an output sequence 0,1,2,3,4,5,6,7,8,9,10",
null,
"First Iteration:\n\nIterator variable i = 0\n\nIn the next line of code, it checks for a condition i%2 == 0. This means that, if the modulus of i is equal to 0 then i is an even number else it's an odd number.\n\nSecond Iteration:\n\nIterator variable i = 1\n\nIn the next line of code, it checks for a condition i%2 == 0. This means that, if the modulus of i is equal to 0 then i is an even number else it's an odd number. Here the condition is False and prints \"This is an odd number\".\n\nIteration continues until it reaches the end i=10.\n\n2. Nested For loops:\n\nNested loops are one of the best ways to loop a loop. This logic exists in all programming languages. Here we can discuss how nested For loop works in python. If a loop exists within the body of another loop then it is called a Nested loop. Nested loops can be used if we want to execute the inner loop multiple times. The outer loop will control the number of iterations that the inner loop will undergo.\n\nfor i in range(2):\n\nfor j in range(5):\n\nprint([i,j])\n\nWe need to understand the below points to understand how nested FOR loops work.\n\n1. In this example, the outer loop can be taken as an i loop and the inner loop as a j loop\n\n2. i loop will have 2 iterations. i.e one iteration for 0 and one iteration for 1 as range(2) will produce 0,1.\n\n3. During the first iteration of i loop, i.e for i = 0, inner loop j will be triggered and a sequence of numbers 0 to 4 will be generated.\n\n4. For the next iteration of i loop, i.e for i= 1 inner loop j will be triggered again and a sequence of numbers from 0 to 4 will be generated.\n\nIn simple words, all combinations of i and j have been produced as a result using the nested loops.",
null,
"The output of the above code would look like this.\n\n3. Triple Nested Loops:\n\nTriple nested loops also work in the same way as above whereas here there are 3 loops.\n\nprofit = [1000,1200,1500,1100]\n\nfor i in ['Product A','Product B']:\n\nfor j in profit:\n\nfor k in time_horizon:\n\nprint([i,j,j*k])\n\nLet's understand how this works.\n\nIn the above example, We have two products, Product A and Product B. We have stored the Expected Profit of products A and B in a list called \"Profit\". Let's see how we can calculate the expected profit monthly, quarterly, and annually for products A & B.\n\nFor achieving this in Code, Stored the time horizon into a tuple called \"time_horizon\"\n\ntime_horizon = (1,3,12)\n\nWe are trying to multiply the j * k (profit * time horizon) to calculate the expected profit of monthly, quarterly, and annual expected profit of products A & B.",
null,
"The output of the code would look like this. We need to understand the below points to know how triple nested loops work.\n\n1. We are using 3 loops i, j, k. The number of elements in the output depends on the number of elements in each loop.\n\n2. During the first iteration, i loop (for product A), j loop will be triggered (the first element in j is 1000) and k loop will be triggered and calculates j * k. ( i.e 1000*1 , 1000 * 3, 1000*12, 1200 * 1, 1200 * 3, 1200 * 12 and so on)\n\nInteresting Isn't it?\n\n4. List Comprehension:\n\nList comprehension is the most widely used feature in Python. List comprehension is used as an alternative to the regular FOR loops. The main advantage of list comprehension is, it requires very fewer lines of code to achieve the same results as using FOR loops with a lengthier code.\n\nLet’s dig deeper to understand how list comprehension works.",
null,
"The above example shows the comparison between the traditional For loops and list comprehension. In the traditional For loop, we created an empty list called list1, and we wrote a For loop iterating over the range of 0 to 9 sequence and multiplying each element in a sequence into 2, and appending the calculated values as elements into the empty list “List1”. The same is achieved using List comprehension in a single line of code.\n\nHere is another example:",
null,
"We can also include if conditions in the list comprehension like below. Where we calculated the raise to the power of 3 for all the odd numbers between 0 to 9.",
null,
"5. Lambda Functions:",
null,
"Lambda functions are also called anonymous functions.\n\nFeatures of Lambda functions are\n\n1. Can have one or many parameters but can contain a single expression only.\n\n2. Allows you to write just one line of code to include a simple functionality in a more complex expression.",
null,
"The above example shows the comparison between traditional functions and lambda functions. Lambda functions allow you to have the expression and arguments in the same line of code, unlike traditional functions.\n\nWhen to Use Lambda functions:\n\n1. When the function is expected to be available in your code only for short period.\n\n2. When a function is being conceded as an argument for a superior function in respect of the order of the function. So this is a scenario where one function picks another function as an argument of it.\n\nConclusion:\n\nThese are the 5 tools in python that can be extremely helpful when coding. It’s very important to understand the basics and learn how to iterate over the different objects/sequence of a programming language to code in a better-optimized way. We cannot completely avoid the traditional approach. That being said, there are certain cases where you can use the alternative approach. Thanks for reading!"
] |
[
null,
"https://static.wixstatic.com/media/72f31a_9040cbf645be44b1b46628b907af9144~mv2.jpg/v1/fill/w_980,h_522,al_c,q_85,usm_0.66_1.00_0.01,enc_auto/72f31a_9040cbf645be44b1b46628b907af9144~mv2.jpg",
null,
"https://static.wixstatic.com/media/01b473_8d50ea27b9114ba18d2869c8c53c0dee~mv2.jpg/v1/fill/w_980,h_735,al_c,q_85,usm_0.66_1.00_0.01,enc_auto/01b473_8d50ea27b9114ba18d2869c8c53c0dee~mv2.jpg",
null,
"https://static.wixstatic.com/media/01b473_9630c353daca48d19cff40ea56a6350c~mv2.png/v1/fill/w_457,h_380,al_c,q_85,enc_auto/01b473_9630c353daca48d19cff40ea56a6350c~mv2.png",
null,
"https://static.wixstatic.com/media/01b473_c90ab3b759bd4b04b14ca75f7db6182b~mv2.png/v1/fill/w_467,h_320,al_c,q_85,enc_auto/01b473_c90ab3b759bd4b04b14ca75f7db6182b~mv2.png",
null,
"https://static.wixstatic.com/media/01b473_fc5a5138217048eabb18813294ca8352~mv2.png/v1/fill/w_506,h_381,al_c,q_85,enc_auto/01b473_fc5a5138217048eabb18813294ca8352~mv2.png",
null,
"https://static.wixstatic.com/media/01b473_0b6aeb5b533a4f3b915f72524854a702~mv2.png/v1/fill/w_478,h_558,al_c,q_85,enc_auto/01b473_0b6aeb5b533a4f3b915f72524854a702~mv2.png",
null,
"https://static.wixstatic.com/media/01b473_b7bce399050d43b193173ddb82185122~mv2.png/v1/fill/w_503,h_389,al_c,q_85,enc_auto/01b473_b7bce399050d43b193173ddb82185122~mv2.png",
null,
"https://static.wixstatic.com/media/01b473_a6095858cac54ba1bd3d00f95fba3577~mv2.png/v1/fill/w_536,h_331,al_c,q_85,enc_auto/01b473_a6095858cac54ba1bd3d00f95fba3577~mv2.png",
null,
"https://static.wixstatic.com/media/01b473_6025f79229534e57907aa265e83353ec~mv2.png/v1/fill/w_615,h_153,al_c,q_85,enc_auto/01b473_6025f79229534e57907aa265e83353ec~mv2.png",
null,
"https://static.wixstatic.com/media/01b473_ccb9f8202f854030be4b5f3c6216ed8e~mv2.jpg/v1/fill/w_980,h_735,al_c,q_85,usm_0.66_1.00_0.01,enc_auto/01b473_ccb9f8202f854030be4b5f3c6216ed8e~mv2.jpg",
null,
"https://static.wixstatic.com/media/01b473_26dfa279b6be406fbd4308e80e6ddb37~mv2.png/v1/fill/w_660,h_500,al_c,q_85,enc_auto/01b473_26dfa279b6be406fbd4308e80e6ddb37~mv2.png",
null
] |
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|
https://whatisconvert.com/24-cubic-meters-in-cubic-feet
|
[
"# What is 24 Cubic Meters in Cubic Feet?\n\n## Convert 24 Cubic Meters to Cubic Feet\n\nTo calculate 24 Cubic Meters to the corresponding value in Cubic Feet, multiply the quantity in Cubic Meters by 35.314666572208 (conversion factor). In this case we should multiply 24 Cubic Meters by 35.314666572208 to get the equivalent result in Cubic Feet:\n\n24 Cubic Meters x 35.314666572208 = 847.55199773298 Cubic Feet\n\n24 Cubic Meters is equivalent to 847.55199773298 Cubic Feet.\n\n## How to convert from Cubic Meters to Cubic Feet\n\nThe conversion factor from Cubic Meters to Cubic Feet is 35.314666572208. To find out how many Cubic Meters in Cubic Feet, multiply by the conversion factor or use the Volume converter above. Twenty-four Cubic Meters is equivalent to eight hundred forty-seven point five five two Cubic Feet.",
null,
"## Definition of Cubic Meter\n\nThe cubic meter (also written \"cubic metre\", symbol: m3) is the SI derived unit of volume. It is defined as the volume of a cube with edges one meter in length. Another name, not widely used any more, is the kilolitre. It is sometimes abbreviated to cu m, m3, M3, m^3, m**3, CBM, cbm.\n\n## Definition of Cubic Foot\n\nThe cubic foot is a unit of volume, which is commonly used in the United States and the United Kingdom. It is defined as the volume of a cube with sides of one foot (0.3048 m) in length. Cubic feet = length x width x height. There is no universally agreed symbol but lots of abbreviations are used, such as ft³, foot³, feet/-3, etc. CCF is for 100 cubic feet.\n\n### Using the Cubic Meters to Cubic Feet converter you can get answers to questions like the following:\n\n• How many Cubic Feet are in 24 Cubic Meters?\n• 24 Cubic Meters is equal to how many Cubic Feet?\n• How to convert 24 Cubic Meters to Cubic Feet?\n• How many is 24 Cubic Meters in Cubic Feet?\n• What is 24 Cubic Meters in Cubic Feet?\n• How much is 24 Cubic Meters in Cubic Feet?\n• How many ft3 are in 24 m3?\n• 24 m3 is equal to how many ft3?\n• How to convert 24 m3 to ft3?\n• How many is 24 m3 in ft3?\n• What is 24 m3 in ft3?\n• How much is 24 m3 in ft3?"
] |
[
null,
"https://whatisconvert.com/images/24-cubic-meters-in-cubic-feet",
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.87500256,"math_prob":0.96290284,"size":2021,"snap":"2020-10-2020-16","text_gpt3_token_len":576,"char_repetition_ratio":0.22161627,"word_repetition_ratio":0.13793103,"special_character_ratio":0.30034637,"punctuation_ratio":0.12064965,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9916167,"pos_list":[0,1,2],"im_url_duplicate_count":[null,2,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-02-25T19:29:12Z\",\"WARC-Record-ID\":\"<urn:uuid:c3ba45ba-a641-49e8-b3cc-cc550fc499b2>\",\"Content-Length\":\"27787\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:5c8ec9ff-eb47-4e2e-8ead-c976db7d36e2>\",\"WARC-Concurrent-To\":\"<urn:uuid:7a778cd7-7b23-4bc8-967d-412648480f29>\",\"WARC-IP-Address\":\"104.31.70.53\",\"WARC-Target-URI\":\"https://whatisconvert.com/24-cubic-meters-in-cubic-feet\",\"WARC-Payload-Digest\":\"sha1:QRWMWERL5OVZCZIQROU4QHXITYZPJMO4\",\"WARC-Block-Digest\":\"sha1:VOW5P4TIJQLWUYA3QYPGY2HVIERGFLQ5\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-10/CC-MAIN-2020-10_segments_1581875146127.10_warc_CC-MAIN-20200225172036-20200225202036-00205.warc.gz\"}"}
|
https://www.seomxl.com/zxwz/33619.html
|
[
"# 软件介绍\n\n[软件1]：R （Version 4.1.2）\n\n[软件2]：RStudio（Version 1.4.1106）\n\n[数据]：后台回复：气泡图数据，即可获得示例数据\n\n# 教程讲解\n\n1.加载需要的R包\n\n``library(openxlsx)library(tidyverse)``\n\n2.数据介绍，就是一般的GO富集分析结果，每一列代表一种类型的数据\n\n• Category包括三个变量，分别是BP，CC，MF，接触过组学的同学都懂\n• GOID就是GO术语的ID\n• 其他列看第一列就明白意思了",
null,
"3.读取数据\n\n``data <- read.xlsx(\"GO_气泡图.xlsx\")``\n\n4.使用ggplot2进行作图\n\n• 将Category映射到shape，用不同的形状表示不同的生物过程\n• 将Count映射到size，更加明显看到节点的大小\n``ggplot(data,aes(Count,Description, shape=Category, colour=padj, size=Count))+ geom_point()``",
null,
"5.进一步的对图形进行美化\n\n• 使用windowsFonts函数提取系统字体\n• data\\$Description 这个函数的命名，完全是因为，在绘图过程中，y坐标上的术语按照字母顺序排列了，而我们需要让他按照原始文件的顺序排列\n• 可能你么有发现，图上的Description与数据中的顺序刚好相反，因此使用scale_y_discrete()来进行调节\n• guides()函数是用来调整图例的，这里的意思就是将Category放在第一\n``data\\$Description <- factor(data\\$Description,levels = unique(data\\$Description))windowsFonts(A=windowsFont(\"Times New Roman\"))ggplot(data,aes(Count,Description, shape=Category, colour=padj, size=Count))+ geom_point()+ theme(text = element_text(family = \"A\",size=15,face = \"bold\"))+ scale_color_gradient(low = \"blue\",high=\"red\")+ scale_y_discrete(limits=rev(data\\$Description))+ guides(shape=guide_legend(order = 1))``",
null,
"6.你也可以给他加一个分面\n\n``ggplot(data,aes(Count,Description, shape=Category, colour=padj, size=Count))+ geom_point()+ theme(text = element_text(family = \"A\",size=15,face = \"bold\"))+ scale_color_gradient(low = \"blue\",high=\"red\")+ scale_y_discrete(limits=rev(data\\$Description))+ guides(shape=guide_legend(order = 1))+ facet_grid(.~Category)``",
null,
"6.高级版气泡图，赶紧来学习一下吧！"
] |
[
null,
"https://p3.toutiaoimg.com/origin/tos-cn-i-qvj2lq49k0/6d479c8918664accb0dd24387ff17ca4",
null,
"https://p3.toutiaoimg.com/origin/tos-cn-i-qvj2lq49k0/6fa7541431b545598424a2942d572ac5",
null,
"https://p3.toutiaoimg.com/origin/tos-cn-i-qvj2lq49k0/cb85fc57d4d24d3eb0f999bb5cbe3bf9",
null,
"https://p3.toutiaoimg.com/origin/tos-cn-i-qvj2lq49k0/1aa9cdc9f59842609f3bbc248e8c0569",
null
] |
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|
https://codeforces.com/blog/entry/72146
|
[
"### bigintegers's blog\n\nBy bigintegers, history, 6 weeks ago,",
null,
",",
null,
"This is a problem on an algorithms final that I'm studying for.\n\nYou are tryng to get from City A to City for the cheapest cost. Your company will pay for exactly one flight between two cities (from a list of flights), but aside from that, you need to drive from the rest of the trip. Given a matrix $C[x, y]$ that represents the money needed to drive from city $x$ to city $y$, and a Boolean matrix $F[x, y]$, which is TRUE if there's a flight from $x$ to $y$ and FALSE otherwise, find an algorithm that finds the minimum amount of money you have to pay to get form $A$ to $B$.\n\nThis is a problem from a previous final that I am studying with. Apparently the full credit solution was something that runs in $\\mathcal{O}(V^2)$ time, but the only solution that I can think of is to run Dijkstra's $n^2$ times (bruteforce). Can someone please help me study? We haven't covered anything super advanced (this is an intro algorithms class).",
null,
"",
null,
"Comments (5)\n » 6 weeks ago, # | ← Rev. 5 → Dijkstra's gives you the shortest path from one node to all others. Define:Si — the shortest path (driving only) from A to i Ti — the shortest path (driving only) from i to B The Si values you can compute in O(n2) with a single Dijkstra's. The Ti values you can compute with a single Dijkstra's as well, by inverting the graph and running a Dijkstra's from B.Now for every edge between a pair of nodes U-V that has a flight allowed, just consider SU+TV and take the minimum of all.\n » 6 weeks ago, # | ← Rev. 4 → If I understood the problem correctly, run Dijkstra from the city where you need to finish, determining the costs of paths to all other cities from it. Do the same from the starting city to all other cities. It is going to take $O(V^2)$ (two Dijkstras).Now that you have two arrays, the first one, $s[]$, denoting the respective costs of paths to all cities from the starting point, and the second one — from the finishing, $f[]$, just bruteforce all ordered pairs of cities $(i, j)$, between which flight is available, and take the minimum sum of $s[i] + f[j]$ — this will be the answer.\n » Dijkstra's gives you the shortest path from one node to all others. Define:$S_i$ — the shortest path (driving only) from $A$ to $i$$T_i$ — the shortest path (driving only) from $i$ to $B$The $S_i$ values you can compute in $O(n^2)$ with a single Dijkstra's. The $T_i$ values you can compute with a single Dijkstra's as well, by inverting the graph and running a Dijkstra's from $B$.Now for every edge between a pair of nodes $U$-$V$ that has a flight allowed, just consider $S_U + T_V$ and take the minimum of all.\n » Almost the same problem (uses same idea) if you wish to implement it: https://cses.fi/problemset/task/1195\n » 6 weeks ago, # | ← Rev. 2 → Another alternative to the given solutions is to create extra nodes. Represent each city $u$ with two nodes $u_1$ and $u_0$, a node where you haven't used the flight and another where you have. Then, for each road between any two nodes u and v, two edges $u_1 - v_1$ and $u_0 - v_0$ should exists. Planes from $u$ to $v$ go instead from $u_1$ to $v_0$. To cover the possibility of not using planes, remember to add an edge between $B_1$ and $B_0$ of cost $0$. The answer is given as the minimum distance between $A_1$ and $B_0$.Also, this approach can be easily transformed to deal with cases where you can take $2$ or more planes."
] |
[
null,
"https://sta.codeforces.com/s/70391/images/flags/24/gb.png",
null,
"https://sta.codeforces.com/s/70391/images/icons/paperclip-16x16.png",
null,
"https://sta.codeforces.com/s/70391/images/blog/tags.png",
null,
"https://sta.codeforces.com/s/70391/images/icons/comments-48x48.png",
null
] |
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|
https://codereview.stackexchange.com/questions/195049/solving-the-burst-balloon-problem-using-dynamic-programming
|
[
"Solving the Burst Balloon problem using Dynamic Programming\n\nContinuing where I left off previously to solve the problem described here, I've now solved the same using dynamic programming (following Tikhon Jelvis blog on DP).\n\nTo refresh, the challenge is to find a sequence in which to burst a row of balloons that will earn the maximum number of coins. Each time balloon $i$ is burst, we earn $C_{i-1} \\cdot C_i \\cdot C_{i+1}$ coins, then balloons $i-1$ and $i+1$ become adjacent to each other.\n\nimport qualified Data.Array as Array\n\nburstDP :: [Int] -> Int\nburstDP l = go 1 len\nwhere\ngo left right | left <= right = maximum [ds Array.! (left, k-1)\n+ ds Array.! (k+1, right)\n+ b (left-1)*b k*b (right+1) | k <- [left..right]]\n| otherwise = 0\nlen = length l\nds = Array.listArray bounds\n[go m n | (m, n) <- Array.range bounds]\nbounds = ((0,0), (len+1, len+1))\nl' = Array.listArray (0, len-1) l\nb i = if i == 0 || i == len+1 then 1 else l' Array.! (i-1)\n\nI'm looking for:\n\n1. Correctness\n2. Program structure\n4. Any other higher order functions that can be used\n5. Other optimizations that can be done\n• This code isn't complete. What's Array? – Zeta May 24 '18 at 17:36\n• @Zeta Data.Array imported from the array package – user3169543 May 25 '18 at 16:55\n\nYour use of Array for memoization can be extracted into array-memoize.\n\nIf one can stop instead of having negative balloons decrease score, go can be condensed into one case.\n\nimport Data.Function.ArrayMemoize (arrayMemoFix)\nimport Data.Array ((!), listArray)\n\nburstDP :: [Int] -> Int\nburstDP l = arrayMemoFix ((0,0), (len+1, len+1)) go (1, len) where\ngo ds (left, right) = maximum $0 : [ds (left, k-1) + ds (k+1, right) + b (left-1)*b k*b (right+1) | k <- [left..right]] b = (!)$ listArray (0, len+1) (1 : l ++ )\nlen = length l\n\nIf you don't care too much about performance, we can also memoize directly on the balloon list:\n\nburstDP :: [Int] -> Int\nburstDP = memoFix3 go 1 1 where go ds l r b = maximum\n[ ds left l x + ds right x r + l*x*r\n| (left, x:right) <- zip (inits b) (tails b)\n]"
] |
[
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.7972524,"math_prob":0.99465877,"size":1107,"snap":"2019-43-2019-47","text_gpt3_token_len":345,"char_repetition_ratio":0.098821394,"word_repetition_ratio":0.0,"special_character_ratio":0.34146342,"punctuation_ratio":0.1336207,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99824846,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-10-23T14:32:47Z\",\"WARC-Record-ID\":\"<urn:uuid:10db7cc5-c8d3-44ac-9726-04bf98ec6721>\",\"Content-Length\":\"146366\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:e243087d-6f43-4bfa-927b-66f3fd927eeb>\",\"WARC-Concurrent-To\":\"<urn:uuid:d44d6dfb-1cc6-4b12-a48b-4e01d745fb2b>\",\"WARC-IP-Address\":\"151.101.65.69\",\"WARC-Target-URI\":\"https://codereview.stackexchange.com/questions/195049/solving-the-burst-balloon-problem-using-dynamic-programming\",\"WARC-Payload-Digest\":\"sha1:7D5UA7W3ZZMCEF4KHNZIP4HPXSQIC2TK\",\"WARC-Block-Digest\":\"sha1:RJ45T5QRAXM724HS3GEIGNTJWYJ2QCCH\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-43/CC-MAIN-2019-43_segments_1570987833766.94_warc_CC-MAIN-20191023122219-20191023145719-00449.warc.gz\"}"}
|
https://studyres.com/doc/8081013/13800000000-years-ago-the-first-sky
|
[
"# Download 13800000000 Years Ago The First Sky\n\nDocument related concepts\n\nFermi paradox wikipedia, lookup\n\nDrake equation wikipedia, lookup\n\nInternational Ultraviolet Explorer wikipedia, lookup\n\nAstrophotography wikipedia, lookup\n\nGalaxy Zoo wikipedia, lookup\n\nUrsa Major wikipedia, lookup\n\nUniverse wikipedia, lookup\n\nShape of the universe wikipedia, lookup\n\nHistory of supernova observation wikipedia, lookup\n\nModified Newtonian dynamics wikipedia, lookup\n\nHubble's law wikipedia, lookup\n\nHubble Deep Field wikipedia, lookup\n\nWilkinson Microwave Anisotropy Probe wikipedia, lookup\n\nStar formation wikipedia, lookup\n\nBig Bang wikipedia, lookup\n\nUltimate fate of the universe wikipedia, lookup\n\nExpansion of the universe wikipedia, lookup\n\nFlatness problem wikipedia, lookup\n\nObservable universe wikipedia, lookup\n\nDark energy wikipedia, lookup\n\nFine-tuned Universe wikipedia, lookup\n\nObservational astronomy wikipedia, lookup\n\nCosmic microwave background wikipedia, lookup\n\nTimeline of astronomy wikipedia, lookup\n\nNon-standard cosmology wikipedia, lookup\n\nPhysical cosmology wikipedia, lookup\n\nTranscript\n```OUR UNIVERSE : AN\nEXPANDING MYSTERY\nSupratik Pal\nIndian Statistical Institute, Kolkata\nMeeeeeee…..\nNight Sky\nFrom New York\nBeyond Naked Eye: Telescopes\nRadio Telescope:\nProud to be an Indian\nEye in the Sky: Hubble Space Telescope\nSupernova Anisotropy Probe\nWilkinson Microwave Anisotropy Probe\nHappy Birthday to our Universe: 13800000000 Years Ago\nThe First Sky\nA Star is Born\nBrighter than Stars : Nebulae\nOur\nGalaxy\nMilky Way\nCloud made of Hydrogen in our Galaxy\nEven what we can not see also exists\nOur Galaxy is one among Millions\nHow far are They ?\nOur\nGalaxy\nNearest\nGalaxy\n4 Light Years\n= (300000 km/sec) X (4X365X24X60X60 sec)\n= 40000000000000 kilo-meters !!!\nTo See the Unseen: Lens in the Sky\nTo See the Unseen: Collision in the Sky\nDeath of a Star: Supernova Explosion\nWhat do they tell us ?\nAge of the Universe = 13800000000 Years\nSize of our Universe = 13800000000 Light Years\n= 100000000000000000000000 kilo-meters !!!\nWhy are they so important ?\nUniverse is expanding at accelerated rate\nHuge Energy Still Unknown\nCosmic Microwave Background Radiation\nThe Cosmic Constituents: As of Now\nScientific\nQueries\nWhat?\nWhy?\nHow?\nAnd miles to go\nDark energy or cosmological constant?\nWhat is dark energy?\nWhy is cosmological constant so small?\nWhat is dark matter?\nWho governs fast expansion at the beginning?\nHow were stars, galaxies etc formed?\nGravitational waves: yes or no?\nHow to match precise observational data?\nHow to discriminate a model from others?\nMany more…..\nWant to make it a career?\nBasic level …..\nMathematical Methods\nClassical Mechanics\nQuantum Mechanics\nElectrodynamics\nAdvanced level …..\nGeneral Relativity\nQuantum Field Theory\nParticle Physics\nComputer Programming\n```"
] |
[
null
] |
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|
https://prepinsta.com/sapient-nitro/aptitude/divisibility/quiz-1/
|
[
"# Quiz – 1\n\nQuestion 1",
null,
"Time: 00:00:00\nX is a 5 digit number when we subtract the sum of the digits form X, it becomes divisible by _____",
null,
"5\n\n5\n\n1\n\n1\n\n6\n\n6\n\n9,3\n\n9,3\n\nNone of these\n\nNone of these\n\nOnce you attempt the question then PrepInsta explanation will be displayed.\n\nStart\n\nQuestion 2",
null,
"Time: 00:00:00\nA and B are two cars travelling to a destination which is 360 kilometres away. A takes 4 hours to reach the destination. How much time will it take B to reach the destination if the speeds of A and B are in the ratio 9: 12?",
null,
"2.5 hrs\n\n2.5 hrs\n\n4.5 hrs\n\n4.5 hrs\n\n3 hrs\n\n3 hrs\n\n3.5 hrs\n\n3.5 hrs\n\nOnce you attempt the question then PrepInsta explanation will be displayed.\n\nStart\n\nQuestion 3",
null,
"Time: 00:00:00\nThe average of three numbers is 77.The first number is twice the second and the second number is twice the third. Find the first number?",
null,
"33\n\n33\n\n66\n\n66\n\n77\n\n77\n\n132\n\n132\n\nOnce you attempt the question then PrepInsta explanation will be displayed.\n\nStart\n\nQuestion 4",
null,
"Time: 00:00:00\nDustin is driving his car at speed of 50 kilometres per hour. He going to Texas which is located 345 kilometres from his starting point.How long will it take him to reach Texas?",
null,
"70\n\n70\n\n71\n\n71\n\n72\n\n72\n\n6.9\n\n6.9\n\nOnce you attempt the question then PrepInsta explanation will be displayed.\n\nStart\n\nQuestion 5",
null,
"Time: 00:00:00\nHow many number of two-digit positive integer < than 100, which are not divisible by 2, 3 and 5 is",
null,
"23\n\n23\n\n25\n\n25\n\n24\n\n24\n\n26\n\n26\n\nOnce you attempt the question then PrepInsta explanation will be displayed.\n\nStart\n\nQuestion 6",
null,
"Time: 00:00:00\nIf the number 7x86038 is exactly divisible by 11, then the smallest whole number in place of x?",
null,
"1\n\n1\n\n3\n\n3\n\n2\n\n2\n\n4\n\n4\n\nOnce you attempt the question then PrepInsta explanation will be displayed.\n\nStart\n\nQuestion 7",
null,
"Time: 00:00:00\nA and B are two number when divided by 7 leaves a remainder 3 and 5. What will be the remainder when A-B is divided by 7 ?",
null,
"1\n\n1\n\n2\n\n2\n\n5\n\n5\n\n4\n\n4\n\nOnce you attempt the question then PrepInsta explanation will be displayed.\n\nStart\n\nQuestion 8",
null,
"Time: 00:00:00\nThe sum of three consecutive natural numbers each divisible by 3 is 72. What is the largest among them?",
null,
"x-21\n\nx-21\n\nx+27\n\nx+27\n\nx+30\n\nx+30\n\nx+7\n\nx+7\n\nOnce you attempt the question then PrepInsta explanation will be displayed.\n\nStart\n\nQuestion 9",
null,
"Time: 00:00:00\nWhen the integer n is divided by 8, the remainder is 3. What is the remainder if 6n is divided by 8?",
null,
"4\n\n4\n\n1\n\n1\n\n2\n\n2\n\n3\n\n3\n\nOnce you attempt the question then PrepInsta explanation will be displayed.\n\nStart\n\nQuestion 10",
null,
"Time: 00:00:00\n3/7 of the oranges grown are too sour to eat out 3,80,205 oranges that are grown on a farm. The owner has to sell the eatable Orange. How many Oranges can the farm owner sell?",
null,
"1,62,945\n\n1,62,945\n\n2,17,260\n\n2,17,260\n\n3,25,890\n\n3,25,890\n\n4,34,520\n\n4,34,520\n\nOnce you attempt the question then PrepInsta explanation will be displayed.\n\nStart\n\n[\"0\",\"40\",\"60\",\"80\",\"100\"]\n[\"Need more practice! \\r\\n \\r\\n \\r\\n\",\"Keep trying! \\r\\n \\r\\n \\r\\n\",\"Not bad! \\r\\n \\r\\n \\r\\n\",\"Good work! \\r\\n \\r\\n \\r\\n\",\"Perfect! \\r\\n \\r\\n \\r\\n\"]\n\nCompleted\n\n0/0\n\nAccuracy\n\n0%"
] |
[
null,
"data:image/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==",
null,
"data:image/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==",
null,
"data:image/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==",
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null,
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null,
"data:image/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==",
null,
"data:image/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==",
null,
"data:image/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==",
null,
"data:image/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==",
null,
"data:image/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==",
null,
"data:image/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==",
null,
"data:image/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==",
null,
"data:image/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==",
null,
"data:image/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==",
null,
"data:image/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==",
null,
"data:image/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==",
null,
"data:image/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==",
null,
"data:image/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==",
null,
"data:image/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==",
null
] |
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|
https://support.klipfolio.com/hc/en-us/community/posts/360025757473-Calculate-growth-rate
|
[
"Hi All,\n\nI found it super weird that there is not even a single thread on the growth rate calculation - or maybe I am a bad researcher.\n\nLet's assume I have a datetime and id col. I plot two graphs which show count per day and count per month. What formula should I use to calculate a growth rate? I assume there should something like offset.\n\nRegards,\n\nEka"
] |
[
null
] |
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|
https://www.gradesaver.com/textbooks/math/other-math/thinking-mathematically-6th-edition/chapter-5-number-theory-and-the-real-number-system-5-4-the-irrational-numbers-exercise-set-5-4-page-296/59
|
[
"## Thinking Mathematically (6th Edition)\n\n$3\\sqrt7$\nRationalize the denominator by multiplying $\\sqrt7$ to both the numerator and the denominator: $=\\dfrac{21\\sqrt7}{\\sqrt7(\\sqrt7)} \\\\=\\dfrac{21\\sqrt7}{7} \\\\=3\\sqrt7$"
] |
[
null
] |
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|
https://www.hackmath.net/en/math-problem/18093
|
[
"# Cuboid and ratio\n\nFind the dimensions of a cuboid having a volume of 810 cm3 if the lengths of its edges coming from the same vertex are in ratio 2: 3: 5\n\na = 6 cm\nb = 9 cm\nc = 15 cm\n\n### Step-by-step explanation:",
null,
"Did you find an error or inaccuracy? Feel free to write us. Thank you!\n\nTips for related online calculators\nCheck out our ratio calculator.\nDo you have a linear equation or system of equations and looking for its solution? Or do you have a quadratic equation?"
] |
[
null,
"https://www.hackmath.net/img/93/cuboid_2.jpg",
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.89106596,"math_prob":0.99289274,"size":3765,"snap":"2022-27-2022-33","text_gpt3_token_len":1012,"char_repetition_ratio":0.20818931,"word_repetition_ratio":0.14804845,"special_character_ratio":0.26640105,"punctuation_ratio":0.117359415,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9894414,"pos_list":[0,1,2],"im_url_duplicate_count":[null,4,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-08-07T18:39:22Z\",\"WARC-Record-ID\":\"<urn:uuid:b9c2d734-691d-41cf-84c4-0242c543b75d>\",\"Content-Length\":\"26079\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:1ad16c7c-cd9d-498d-838b-36df9ae9db22>\",\"WARC-Concurrent-To\":\"<urn:uuid:a49c3ba8-4f19-4260-8713-649b34e10766>\",\"WARC-IP-Address\":\"172.67.134.123\",\"WARC-Target-URI\":\"https://www.hackmath.net/en/math-problem/18093\",\"WARC-Payload-Digest\":\"sha1:BDQGMPC645BG3RKJOK4UOONXIMGBVM24\",\"WARC-Block-Digest\":\"sha1:GVC3ECABBX2MVQOJ5YTRQUL2JSJPEHPG\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-33/CC-MAIN-2022-33_segments_1659882570692.22_warc_CC-MAIN-20220807181008-20220807211008-00324.warc.gz\"}"}
|
https://data.jrc.ec.europa.eu/dataset?tags=elcd&tags=heat+and+steam&contributor_name_string=Pennington%2C+David
|
[
"## 82 datasets found\n\nContributors: Pennington, David Keywords: elcd heat and steam\n\nA detailed heat plant model was used, which combines measured emissions taken from national statistics plus calculated values for not measured emissions of e.g. simple organics...\nA detailed heat plant model was used, which combines measured emissions taken from national statistics plus calculated values for not measured emissions of e.g. simple organics...\nA detailed heat plant model was used, which combines measured emissions taken from national statistics plus calculated values for not measured emissions of e.g. simple organics...\nA detailed heat plant model was used, which combines measured emissions taken from national statistics plus calculated values for not measured emissions of e.g. simple organics...\nA detailed heat plant model was used, which combines measured emissions taken from national statistics plus calculated values for not measured emissions of e.g. simple organics...\nA detailed heat plant model was used, which combines measured emissions taken from national statistics plus calculated values for not measured emissions of e.g. simple organics...\nA detailed heat plant model was used, which combines measured emissions taken from national statistics plus calculated values for not measured emissions of e.g. simple organics...\nA detailed heat plant model was used, which combines measured emissions taken from national statistics plus calculated values for not measured emissions of e.g. simple organics...\nA detailed heat plant model was used, which combines measured emissions taken from national statistics plus calculated values for not measured emissions of e.g. simple organics...\nA detailed heat plant model was used, which combines measured emissions taken from national statistics plus calculated values for not measured emissions of e.g. simple organics...\nA detailed heat plant model was used, which combines measured emissions taken from national statistics plus calculated values for not measured emissions of e.g. simple organics...\nA detailed heat plant model was used, which combines measured emissions taken from national statistics plus calculated values for not measured emissions of e.g. simple organics...\nA detailed heat plant model was used, which combines measured emissions taken from national statistics plus calculated values for not measured emissions of e.g. simple organics...\nA detailed heat plant model was used, which combines measured emissions taken from national statistics plus calculated values for not measured emissions of e.g. simple organics...\nA detailed heat plant model was used, which combines measured emissions taken from national statistics plus calculated values for not measured emissions of e.g. simple organics...\nA detailed heat plant model was used, which combines measured emissions taken from national statistics plus calculated values for not measured emissions of e.g. simple organics...\nA detailed heat plant model was used, which combines measured emissions taken from national statistics plus calculated values for not measured emissions of e.g. simple organics...\nA detailed heat plant model was used, which combines measured emissions taken from national statistics plus calculated values for not measured emissions of e.g. simple organics...\nA detailed heat plant model was used, which combines measured emissions taken from national statistics plus calculated values for not measured emissions of e.g. simple organics...\nA detailed heat plant model was used, which combines measured emissions taken from national statistics plus calculated values for not measured emissions of e.g. simple organics..."
] |
[
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.94384664,"math_prob":0.9561223,"size":3639,"snap":"2019-51-2020-05","text_gpt3_token_len":640,"char_repetition_ratio":0.13204952,"word_repetition_ratio":1.0,"special_character_ratio":0.18658972,"punctuation_ratio":0.18181819,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.98487127,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-01-29T00:40:37Z\",\"WARC-Record-ID\":\"<urn:uuid:e435c89e-1420-425a-aa05-fa6d3c401251>\",\"Content-Length\":\"102603\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:63c7b2ad-870e-4153-802a-4e9ad0e55604>\",\"WARC-Concurrent-To\":\"<urn:uuid:e401088a-970f-48e6-8774-73efd84bbba6>\",\"WARC-IP-Address\":\"139.191.229.20\",\"WARC-Target-URI\":\"https://data.jrc.ec.europa.eu/dataset?tags=elcd&tags=heat+and+steam&contributor_name_string=Pennington%2C+David\",\"WARC-Payload-Digest\":\"sha1:PWMD3SYRUR4RGDYVGRWDH6ZG4ABXWQEW\",\"WARC-Block-Digest\":\"sha1:7QS53QSDJOAA3A3NXKROSURT4BWITBPL\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-05/CC-MAIN-2020-05_segments_1579251783342.96_warc_CC-MAIN-20200128215526-20200129005526-00483.warc.gz\"}"}
|
https://artofproblemsolving.com/wiki/index.php/2005_CEMC_Gauss_(Grade_7)_Problems/Problem_13
|
[
"# 2005 CEMC Gauss (Grade 7) Problems/Problem 13\n\n## Problem\n\nIn the diagram, the length of",
null,
"$DC$ is twice the length of",
null,
"$BD$. What is the area of the triangle",
null,
"$ABC$?",
null,
"$\\text{(A)}\\ 24 \\qquad \\text{(B)}\\ 72 \\qquad \\text{(C)}\\ 12 \\qquad \\text{(D)}\\ 18 \\qquad \\text{(E)}\\ 36$",
null,
"$[asy] draw((0,0)--(-3,0)--(0,4)--cycle); draw((0,0)--(6,0)--(0,4)--cycle); label(\"3\",(-1.5,0),N); label(\"4\",(0,2),E); label(\"A\",(0,4),N); label(\"B\",(-3,0),S); label(\"C\",(6,0),S); label(\"D\",(0,0),S); draw((0,0.4)--(0.4,0.4)--(0.4,0)); [/asy]$\n\n## Solution\n\nSince",
null,
"$BD = 3$ and",
null,
"$DC$ is twice the length of",
null,
"$BD$, then",
null,
"$DC = 6$. Therefore, triangle",
null,
"$ABC$ has a base of length",
null,
"$9$ and a height of length",
null,
"$4$. Therefore, the area of triangle",
null,
"$ABC$ is",
null,
"$\\frac{1}{2}bh = \\frac{1}{2}(9)(4) = \\frac{1}{2}(36) = 18$. Therefore, the correct answer is",
null,
"$D$"
] |
[
null,
"https://latex.artofproblemsolving.com/2/7/e/27e525b776c49bbe7d0ae66cfc7ab8f58f40624e.png ",
null,
"https://latex.artofproblemsolving.com/8/9/f/89fff82bb65d0215e49c8c91cb7c553da52205e2.png ",
null,
"https://latex.artofproblemsolving.com/e/2/a/e2a559986ed5a0ffc5654bd367c29dfc92913c36.png ",
null,
"https://latex.artofproblemsolving.com/3/9/d/39d11e585229b84aa3fd108d5613d7d47bb550b6.png ",
null,
"https://latex.artofproblemsolving.com/4/3/3/43330d5778a7805f72e4c2b774d2b4f1316a93db.png ",
null,
"https://latex.artofproblemsolving.com/f/d/5/fd5828647f7d2a8d60ff73bb0e6686110093d922.png ",
null,
"https://latex.artofproblemsolving.com/2/7/e/27e525b776c49bbe7d0ae66cfc7ab8f58f40624e.png ",
null,
"https://latex.artofproblemsolving.com/8/9/f/89fff82bb65d0215e49c8c91cb7c553da52205e2.png ",
null,
"https://latex.artofproblemsolving.com/4/7/7/4772bd4c79b2b1b15acfc88d61cda5e9b88617c9.png ",
null,
"https://latex.artofproblemsolving.com/e/2/a/e2a559986ed5a0ffc5654bd367c29dfc92913c36.png ",
null,
"https://latex.artofproblemsolving.com/b/f/2/bf2c9074b396e3af0dea52d792660eea1c77f10f.png ",
null,
"https://latex.artofproblemsolving.com/c/7/c/c7cab1a05e1e0c1d51a6a219d96577a16b7abf9d.png ",
null,
"https://latex.artofproblemsolving.com/e/2/a/e2a559986ed5a0ffc5654bd367c29dfc92913c36.png ",
null,
"https://latex.artofproblemsolving.com/e/7/5/e75e4abfc59b4a75a4c22cbe2c0d99b8525168e2.png ",
null,
"https://latex.artofproblemsolving.com/9/f/f/9ffb448918db29f2a72f8f87f421b3b3cad18f95.png ",
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.60151964,"math_prob":1.000009,"size":587,"snap":"2023-40-2023-50","text_gpt3_token_len":208,"char_repetition_ratio":0.14236706,"word_repetition_ratio":0.014925373,"special_character_ratio":0.4173765,"punctuation_ratio":0.08547009,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9999962,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30],"im_url_duplicate_count":[null,null,null,null,null,null,null,7,null,7,null,null,null,null,null,null,null,4,null,null,null,null,null,null,null,null,null,3,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-09-21T08:02:39Z\",\"WARC-Record-ID\":\"<urn:uuid:39309e87-d73e-4177-acbc-0c10a4088341>\",\"Content-Length\":\"39491\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:8f9a3190-6fb8-4570-a045-bebcd8c8c1e1>\",\"WARC-Concurrent-To\":\"<urn:uuid:0a58a482-a936-4747-a2a2-8bd47de942f3>\",\"WARC-IP-Address\":\"172.67.69.208\",\"WARC-Target-URI\":\"https://artofproblemsolving.com/wiki/index.php/2005_CEMC_Gauss_(Grade_7)_Problems/Problem_13\",\"WARC-Payload-Digest\":\"sha1:5C45U35M4DV5UOLJUX6FI3NOKTWFYS7W\",\"WARC-Block-Digest\":\"sha1:A4PLB367KJ26JHQJYZGK7IMZMTWTJTAN\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-40/CC-MAIN-2023-40_segments_1695233505362.29_warc_CC-MAIN-20230921073711-20230921103711-00536.warc.gz\"}"}
|
https://mitiq.readthedocs.io/en/stable/guide/executors.html
|
[
"# Executors#\n\nError mitigation methods can involve running many circuits. The `mitiq.Executor` class is a tool for efficiently running many circuits and storing the results.\n\n```from mitiq import Executor, Observable, PauliString, QPROGRAM, QuantumResult\n```\n\n## The input function#\n\nTo instantiate an `Executor`, provide a function which either:\n\n1. Inputs a `mitiq.QPROGRAM` and outputs a `mitiq.QuantumResult`.\n\n2. Inputs a sequence of `mitiq.QPROGRAM`s and outputs a sequence of `mitiq.QuantumResult`s.\n\nThe function must be annotated to tell Mitiq which type of `QuantumResult` it returns. Functions with no annotations are assumed to return `float`s.\n\nA `QPROGRAM` is “something which a quantum computer inputs” and a `QuantumResult` is “something which a quantum computer outputs.” The latter is canonically a bitstring for real quantum hardware, but can be other objects for testing, e.g. a density matrix.\n\n```print(QPROGRAM)\n```\n```typing.Union[cirq.circuits.circuit.Circuit, pyquil.quil.Program, qiskit.circuit.quantumcircuit.QuantumCircuit, braket.circuits.circuit.Circuit, pennylane.tape.tape.QuantumTape]\n```\n```print(QuantumResult)\n```\n```typing.Union[float, mitiq.typing.MeasurementResult, numpy.ndarray]\n```\n\n## Creating an `Executor`#\n\nThe function `mitiq_cirq.compute_density_matrix` inputs a Cirq circuit and returns a density matrix as an `np.ndarray`.\n\n```import inspect\n\nfrom mitiq.interface import mitiq_cirq\n\nprint(inspect.getfullargspec(mitiq_cirq.compute_density_matrix).annotations[\"return\"])\n```\n```numpy.ndarray[typing.Any, numpy.dtype[numpy.complex64]]\n```\n\nWe can instantiate an `Executor` with it as follows.\n\n```executor = Executor(mitiq_cirq.compute_density_matrix)\n```\n\n## Running circuits#\n\nWhen first created, the executor hasn’t been called yet and has no executed circuits and no computed results in memory.\n\n```print(\"Calls to executor:\", executor.calls_to_executor)\nprint(\"\\nExecuted circuits:\\n\", *executor.executed_circuits, sep=\"\\n\")\nprint(\"\\nQuantum results:\\n\", *executor.quantum_results, sep=\"\\n\")\n```\n```Calls to executor: 0\n\nExecuted circuits:\n\nQuantum results:\n```\n\nTo run a circuit of sequence of circuits, use the `Executor.evaluate` method.\n\n```import cirq\n\nq = cirq.LineQubit(0)\ncircuit = cirq.Circuit(cirq.H.on(q))\n\nobs = Observable(PauliString(\"Z\"))\n\nresults = executor.evaluate(circuit, obs)\nprint(\"Results:\", results)\n```\n```Results: [0.010000020265579224]\n```\n\nThe `executor` has now been called and has results in memory. Note that `mitiq_cirq.compute_density_matrix` simulates the circuit with noise by default, so the resulting state (density matrix) is noisy.\n\n```print(\"Calls to executor:\", executor.calls_to_executor)\nprint(\"\\nExecuted circuits:\\n\", *executor.executed_circuits, sep=\"\\n\")\nprint(\"\\nQuantum results:\\n\", *executor.quantum_results, sep=\"\\n\")\n```\n```Calls to executor: 1\n\nExecuted circuits:\n\n0: ───H───\n\nQuantum results:\n\n[[0.505 +0.j 0.49749368+0.j]\n[0.49749368+0.j 0.49499997+0.j]]\n```\n\nThe interface for running a sequence of circuits is the same.\n\n```circuits = [cirq.Circuit(pauli.on(q)) for pauli in (cirq.X, cirq.Y, cirq.Z)]\n\nresults = executor.evaluate(circuits, obs)\nprint(\"Results:\", results)\n```\n```Results: [-0.9800000190734863, -0.9800000190734863, 1.0]\n```\n\nIn addition to the results of running these circuits we have the full history.\n\n```print(\"Calls to executor:\", executor.calls_to_executor)\nprint(\"\\nExecuted circuits:\\n\", *executor.executed_circuits, sep=\"\\n\")\nprint(\"\\nQuantum results:\\n\", *executor.quantum_results, sep=\"\\n\")\n```\n```Calls to executor: 4\n\nExecuted circuits:\n\n0: ───H───\n0: ───X───\n0: ───Y───\n0: ───Z───\n\nQuantum results:\n\n[[0.505 +0.j 0.49749368+0.j]\n[0.49749368+0.j 0.49499997+0.j]]\n[[0.01+0.j 0. +0.j]\n[0. +0.j 0.99+0.j]]\n[[0.01+0.j 0. +0.j]\n[0. +0.j 0.99+0.j]]\n[[1.+0.j 0.+0.j]\n[0.+0.j 0.+0.j]]\n```\n\n### Batched execution#\n\nNotice in the above output that the executor has been called once for each circuit it has executed. This is because `mitiq_cirq.compute_density_matrix` inputs one circuit and outputs one `QuantumResult`.\n\nSeveral quantum computing services allow running a sequence, or “batch,” of circuits at once. This is important for error mitigation when running many circuits to speed up the computation.\n\nTo define a batched executor, annotate it with `Sequence[T]`, `List[T]`, `Tuple[T]`, or `Iterable[T]` where `T` is a `QuantumResult`. Here is an example:\n\n```from typing import List\n\nimport numpy as np\n\ndef batch_compute_density_matrix(circuits: List[cirq.Circuit]) -> List[np.ndarray]:\nreturn [mitiq_cirq.compute_density_matrix(circuit) for circuit in circuits]\n\nbatched_executor = Executor(batch_compute_density_matrix, max_batch_size=10)\n```\n\nYou can check if Mitiq detected the ability to batch as follows.\n\n```batched_executor.can_batch\n```\n```True\n```\n\nNow when running a batch of circuits, the executor will be called as few times as possible.\n\n```circuits = [cirq.Circuit(pauli.on(q)) for pauli in (cirq.X, cirq.Y, cirq.Z)]\n\nresults = batched_executor.evaluate(circuits, obs)\n\nprint(\"Results:\", results)\nprint(\"\\nCalls to executor:\", batched_executor.calls_to_executor)\nprint(\"\\nExecuted circuits:\\n\", *batched_executor.executed_circuits, sep=\"\\n\")\nprint(\"\\nQuantum results:\\n\", *batched_executor.quantum_results, sep=\"\\n\")\n```\n```Results: [-0.9800000190734863, -0.9800000190734863, 1.0]\n\nCalls to executor: 1\n\nExecuted circuits:\n\n0: ───X───\n0: ───Y───\n0: ───Z───\n\nQuantum results:\n\n[[0.01+0.j 0. +0.j]\n[0. +0.j 0.99+0.j]]\n[[0.01+0.j 0. +0.j]\n[0. +0.j 0.99+0.j]]\n[[1.+0.j 0.+0.j]\n[0.+0.j 0.+0.j]]\n```\n\n## Using `Executor`s in error mitigation techniques#\n\nYou can provide a function or an `Executor` to the `executor` argument of error mitigation techniques, but providing an `Executor` is strongly recommended for seeing the history of results.\n\n```from mitiq import zne\n```\n```batched_executor = Executor(batch_compute_density_matrix, max_batch_size=10)\n\nzne_value = zne.execute_with_zne(\ncirq.Circuit(cirq.H.on(q) for _ in range(6)),\nexecutor=batched_executor,\nobservable=obs\n)\nprint(f\"ZNE value: {zne_value :g}\")\n```\n```ZNE value: 0.999972\n```\n```print(\"Calls to executor:\", batched_executor.calls_to_executor)\nprint(\"\\nExecuted circuits:\\n\", *batched_executor.executed_circuits, sep=\"\\n\")\nprint(\"\\nQuantum results:\\n\", *batched_executor.quantum_results, sep=\"\\n\")\n```\n```Calls to executor: 1\n\nExecuted circuits:\n\n0: ───H───H───H───H───H───H───\n0: ───H───H───H───H───H───H───H───H───H───H───H───H───\n0: ───H───H───H───H───H───H───H───H───H───H───H───H───H───H───H───H───H───H───\n\nQuantum results:\n\n[[0.992667 +0.j 0.01470262+0.j]\n[0.01470265+0.j 0.00733284+0.j]]\n[[0.98565817+0.j 0.0287549 +0.j]\n[0.02875516+0.j 0.01434151+0.j]]\n[[0.97895914+0.j 0.0421859 +0.j]\n[0.04218622+0.j 0.02104016+0.j]]\n```\n\n## Defining an `Executor` that returns measurement outcomes (bitstrings)#\n\nIn the previous examples we have shown executors that return the density matrix of the final state. This is possible only for classical simulations. The typical result of a real quantum computation is instead a list of bitstrings corresponding to the (“0” or “1”) outcomes obtained when measuring each qubit in the computational basis. In Mitiq this type of quantum backend is captured by an `Executor` that returns a `MeasurementResult` object.\n\nFor example, here is an example of a Cirq executor function that returns raw measurement outcomes:\n\n```from mitiq import MeasurementResult\n\ndef noisy_sampler(circuit, noise_level=0.1, shots=1000) -> MeasurementResult:\ncircuit_to_run = circuit.with_noise(cirq.depolarize(noise_level))\nsimulator = cirq.DensityMatrixSimulator()\nresult = simulator.run(circuit_to_run, repetitions=shots)\nbitstrings = np.column_stack(list(result.measurements.values()))\nqubit_indices = tuple(\nint(q[2:-1]) # Extract index from \"q(index)\" string\nfor k in result.measurements.keys()\nfor q in k.split(\",\")\n)\nreturn MeasurementResult(bitstrings, qubit_indices)\n```\n```# Circuit with measurements to test the noisy_sampler function\ncircuit_with_measurements = circuit.copy()\ncircuit_with_measurements.append(cirq.measure(*circuit.all_qubits()))\n\nprint(\"Circuit to execute:\", circuit_with_measurements)\nnoisy_sampler(circuit_with_measurements)\n```\n```Circuit to execute:\n```\n``` 0: ───H───M───\n```\n```MeasurementResult: {'nqubits': 1, 'qubit_indices': (0,), 'shots': 1000, 'counts': {'0': 492, '1': 508}}\n```\n\nThe rest of the Mitiq workflow is the same as in the case of a density matrix executor. For example:\n\n```executor = Executor(noisy_sampler)\nobs = Observable(PauliString(\"X\"))\nresults = executor.evaluate(circuit, obs)\n\nprint(\"Results:\", results)\nprint(\"Calls to executor:\", executor.calls_to_executor)\nprint(\"\\nExecuted circuits:\\n\", *executor.executed_circuits, sep=\"\\n\")\nprint(\"\\nQuantum results:\\n\", *executor.quantum_results, sep=\"\\n\")\n```\n```Results: [(0.756+0j)]\nCalls to executor: 1\n\nExecuted circuits:\n\n0: ───H───Y^-0.5───M───\n\nQuantum results:\n\nMeasurementResult: {'nqubits': 1, 'qubit_indices': (0,), 'shots': 1000, 'counts': {'0': 878, '1': 122}}\n```"
] |
[
null
] |
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|
https://mathematica.stackexchange.com/questions/196961/solving-and-plotting-an-ode-in-polar-coordinates
|
[
"# Solving and plotting an ODE in polar coordinates\n\nI'm super new to Mathematica, but it's the software used at my school, and I'm really trying to get better at it. While I'm new to Mathematica, I'm not new to other STEM topics and am doing some research on spinning black holes. I'm doing a presentation in a few weeks and am trying to put together some animations of some plots.\n\nOne I'm working on involves integrating and plotting the equation:\n\n$$\\dfrac{dr}{d\\phi} = \\dfrac{(r - M)^2}{r}\\sqrt{\\dfrac{ r^3}{2M^3} + \\dfrac{r}{2M}}$$\n\nThe result should look something like the attached image,",
null,
"If anyone could offer me any assistance, I'd really appreciate it.\n\n• As a first step, I would write r as an explicit function of phi (e.g. replace every r with r[phi]). Then find an expression for the derivative r'[phi]. This would give a differential equation, that you might solve analytically with DSolve or numerically with NDSolve. Putting M=1 to normalise your coordinates would probably help. Apr 24, 2019 at 20:32\n• For an inflection point $r^2+2 r{'2}= r r^{''}$ holds good. $r^{'}=\\frac{dr}{d\\phi};$ For constant $M, r_{inflection\\, point} /M \\approx 2$ Differentiate and verify. The original equation does not tally dimensionally.. so it could be in error Apr 24, 2019 at 21:10\n• Maybe this GitHub repository is useful to you: github.com/anderote/kerr-solutions (clone it and the open the notebooks from the repository) Apr 24, 2019 at 21:52\n• Thank you so much for the responses! @Mikado, isn't the equation itself already a derivative of r with respect to phi? Apr 24, 2019 at 22:02\n• Welcome to Mathematica.SE, Nathan! I suggest the following: 1) Take the tour and check the faqs. 2) When you see good questions and answers, vote them up by clicking the gray triangles, because the credibility of the system is based on the reputation gained by users sharing their knowledge. Also, please remember to accept the answer, if any, that solves your problem, by clicking the checkmark sign! 3) As you receive help, try to give it too, by answering questions in your area of expertise. Apr 25, 2019 at 11:44\n\nTo get a plot like the one you show, I have to correct a sign error in your equation. After doing so, the equation is easily solved with NDSolveValue. Like so.\n\nrF =\nNDSolveValue[\n{r'[ϕ] == -(r[ϕ] - 1)^2/r[ϕ]/Sqrt Sqrt[r[ϕ]^3 + r[ϕ]], r == 100},\nr, {ϕ, 0, 8 π}]\n\nPolarPlot[rF[ϕ], {ϕ, 0, 8 π}, PlotRange -> {{-2, 8}, {-1.5, 1.5}}]",
null,
"### Update\n\nThe following is added to address concerns raised by the OP in a comment to this answer.\n\nMathematica is has so much stuff in it that it is indeed hard for beginners to find there way around the app. The documentation is quite extensive and there really is a lot of introductory material in it, but again, there is so much of it that it hard for beginners to use it.\n\nI recommend that you begin your further exploration of Mathematica by following this link (or its equivalent in the built-in Documentation Center).\n\nNow let's look into how Manipulate can be used to make a demonstration of a particle moving along the spiral shown in the polar plot. The main point is add an Epilog option to the plot which will draw the moving point.\n\nManipulate[\nPolarPlot[rF[ϕ], {ϕ, 0, 1080 °},\nEpilog -> {Red, AbsolutePointSize, Point[rF[Φ °] {Cos[Φ °], Sin[Φ °]}]},\nPlotRange -> {{-2, 6}, {-1.5, 1.6}},\nPerformanceGoal -> \"Quality\",\nImageSize -> Medium],\n{{Φ, 5, \"ϕ (deg)\"}, 5, 1080, 5, Appearance -> {\"Large\", \"Labeled\"}}]",
null,
"### Notes\n\n• I have an engineering background, so I like to see polar plots read out in degrees. If I didn't have this prejudice, the demo code could be made a little simpler. If you have a scientific mind, you can simplify the code by removing all references to degrees.\n• What looks like a simple slider controling the position of red point is actually an animator control. If you click on the plus ( + ) button at its right end, it will reveal a full set of animation controls. You should also click on the plus button at the top-right of the demonstration panel and see what it reveals.\n• The Point graphics primitive in the Epilog specification must be in expressed in Cartesion coordinates. Hence, Point[rF[Φ °] {Cos[Φ °], Sin[Φ °]}]\n• The PerformanceGoal option is given to keep the spiral from being distorted when the slider is moving.\n• Ahhh! Thank you so much! I hate to be a bother, but is there any way you could explain to me what you did there? I'm sure it's probably so simple to someone who's somewhat familiar with this program, but I just can't seem to find a good place to start learning. I've looked at so many videos online and it just seems like none of them have much to do with what I'm trying to do. Out of all the people I've talked to, all the professors, the fellow students, you've been the first person to be able to tackle this so quickly. Any resources you know of I should be checking out? Thanks again! Apr 25, 2019 at 1:06\n• And a follow-up question, any chance you could coach me on how to get a point to follow along that path? I know I need to use the manipulate command (or at least I think I do), but I'm not sure how to specify the point's \"location\". Apr 25, 2019 at 1:13\n• @NathanJune. I have updated my answer to address the issues you raise in your comments. Also, since you seem to find my answer useful, please consider accepting it. You can do that by clicking on the check mark that appears on the left of the answer below the down arrow. Apr 25, 2019 at 5:02\n\nPutting\n\n$$u= \\frac{r}{2M,}$$\n\nwe get a long analytic WA solution involving three types of Elliptic Integrals. A numeric solution can be attempted with NDSolve."
] |
[
null,
"https://i.stack.imgur.com/sMs4V.jpg",
null,
"https://i.stack.imgur.com/daKoD.png",
null,
"https://i.stack.imgur.com/rVZur.png",
null
] |
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https://math.stackexchange.com/questions/14625/how-can-a-structure-have-infinite-length-and-infinite-surface-area-but-have-fin/14633
|
[
"# How can a structure have infinite length and infinite surface area, but have finite volume?\n\nConsider the curve $\\frac{1}{x}$ where $x \\geq 1$. Rotate this curve around the x-axis.\n\nOne Dimension - Clearly this structure is infinitely long.\n\nTwo Dimensions - Surface Area = $2\\pi\\int_∞^1\\frac{1}{x}dx = 2\\pi(\\ln ∞ - \\ln 1) = ∞$\n\nThree Dimensions - Volume = $\\pi\\int_∞^1{x}^{-2}dx = \\pi(-\\frac{1}{∞} + \\frac{1}{1}) = \\pi$\n\nSo this structure has infinite length and infinite surface area. However it has finite volume, which just does not make sense.\n\nEven more interesting, the \"walls\" of this structure are infinitely thin. Since the volume is finite, we could fill this structure with a finite amount of paint. To fill the structure the paint would need to cover the complete surface area of the inside of this structure. Since the \"walls\" are infinitely thin, why would a finite amount of paint not be able to cover the outside of the \"walls\" too?\n\n• The infinite is often counterintuitive. You cannot actually fill it with paint, though: Planck would get in your way (eventually, the horn is thinner than atoms). Dec 17, 2010 at 3:04\n• This is known as Gabriel's Horn: mathworld.wolfram.com/GabrielsHorn.html Dec 17, 2010 at 3:12\n• Related, I suppose: en.wikipedia.org/wiki/Banach%E2%80%93Tarski_paradox Dec 17, 2010 at 3:14\n• A simpler $2$-dim example: one obtains finite area and infinite perimeter by appending the rectangles $\\rm R_n$ of height $\\rm 1/2^n$ and width $1,$ for all $\\rm\\ i\\in \\mathbb N$ Dec 17, 2010 at 3:35\n• Does the existence of infinitely long regions of the plane with finite area, such as the area under $y = exp(-x)$ in the first quadrant, involve any sort of paradox? The finite volume of rotation described by pacman is similarly an instance of how a finite value can be the limit of an infinite series. Dec 17, 2010 at 4:22\n\nIt seems you already have made sense of this whole thing from a mathematical point of view (it has infinite surface area and finite volume -- there's no contradiction here). The paradox is that infinity, at times, does not match well with our day-to-day experiences.\n\nHere's a related example (and hopefully a little bit easier to picture): Take a unit square. Cut it in half vertically down the middle -- forming two pieces. The area clearly remains the same, but the total perimeter (counting both pieces) has increased by 2. Keep cutting the right-most piece vertically down the middle forever. The area remains unchanged throughout, whereas the perimeter is $4+\\lim_{n \\rightarrow \\infty} \\sum_{i=1}^n 2=\\infty$.",
null,
"Now, if you wanted to make it look more like a horn, you could move the pieces around, for example:",
null,
"which still has area 1 and perimeter infinity. If you wanted to make it have volume 1 and surface area infinity, replace \"square\" with \"cube\".\n\n• The same concept is contained in the Dirac delta function. It has infinite height & perimeter but always has area equal to 1. Dec 17, 2010 at 12:45\n\nAs for the physics, Gabriel's horn is in no meaningful sense a physically realistic object. One way to summarize the lesson here is that the assumption that very thin objects have zero thickness is only reasonable if this causes a reasonable amount of error in one's computations, but in the construction of Gabriel's horn the thickness of the membrane comes to dominate the computation and it is no sense reasonable to ignore this error. Any time a mathematical model fails to accurately reflect reality one should question the assumptions that go into building that model, and to the extent that this is a mathematical model of anything, the assumption that thickness is negligible is the one that should be thrown out. If you try to repeat the construction of Gabriel's horn with a fixed finite thickness you will, of course, find that the resulting object has infinite volume.\n\nThe answer to the paint question is as follows:\n\nTo define terms, let's say you are rotating about the $x$ axis and the volume is between the surface and the $y-z$ plane. If we take a small (but finite) patch of the $y-z$ plane of $\\Delta A$ area then the area above it is roughly $\\Delta A$ as $\\sqrt{y^2 + z^2} \\rightarrow \\infty$ and the volume is roughly $\\frac{\\Delta A}{\\sqrt{y^2 + z^2}}$. So as we move away from the $x$ axis, the trapped volume goes to zero but the surface area does not.\n\nNow back to the paint analogy. It takes infinite paint because a fixed volume of paint covers a fixed surface area (i.e. one gallon / 400 sq.ft.). This is true even as $\\sqrt{y^2 + z^2} \\rightarrow \\infty$, so we find ourselves having to paint a surface area equivalent to the $y-z$ plane. Now if we tried to fill the volume with the paint, we are no longer required to cover at a given rate of 1 gal. / 400 sq.ft. In other words our film thickness is $\\frac{1}{\\sqrt{y^2 + z^2}}$ which tends to zero.\n\nSo in summary, your assumption regarding the walls being infinitely thin is true, but you relate volume and surface area using the metaphor of paint. Paint always has a finite spread rate no matter how thin the film. This film does not get thinner as we move away from the $x$ axis. The volume between the curve and the $y-z$ plane however does.\n\nLet $f:]0,+\\infty[ \\to [0,+\\infty[$ a measurable function, $N\\in \\mathbb{N}$, $x\\in \\mathbb{R}^N$ and $t\\in \\mathbb{R}$. Consider the set:\n\n$$E_f:=\\{ (x,t)\\in \\mathbb{R}^{N+1}:\\ |x|\\leq |f(t)|\\}$$\n\nwhich is the body of revolution generated by $f$ with respect to the $t$ axis in $\\mathbb{R}^{N+1}$. Using cylindrical coordinates, one finds for the Lebesgue measure $\\mathcal{L}^{N+1}(E_f)$ the following expression:\n\n$$\\mathcal{L}^{N+1} (E_f)=\\omega_N \\int_0^{+\\infty} f^N (t)\\ \\text{d} t\\; ,$$\n\nwhere $\\omega_N$ is the volume of the unit ball in $\\mathbb{R}^N$ (i.e. $\\omega_N:=\\pi^{\\frac{N}{2}}/ \\Gamma (\\frac{N}{2} +1)$), hence $\\mathcal{L}^{N+1}(E_f)=\\omega_N \\| f\\|_{L^N}^N$ and $\\mathcal{L}^{N+1} (E_f)$ is finite iff $f\\in L^N(]0,+\\infty[)$.\n\nOn the other hand, if $f$ is also Lipschitz continuous, it is easy to compute the surface area (or De Giorgi perimeter) $\\mathcal{P} (E_f)$ of $E_f$: using cylindrical coordinates one finds:\n\n$$\\mathcal{P} (E_f)=N\\omega_N \\int_0^{+\\infty} f^{N-1}(t)\\ \\sqrt{1+|f^\\prime (t)|^2} \\text{d} t\\; ,$$\n\nthus:\n\n$$N\\omega_N \\| f\\|_{L^{N-1}}^{N-1} \\leq \\mathcal{P} (E_f) \\leq N\\omega_N\\sqrt{1+\\| f^\\prime \\|_{L^\\infty}^2}\\ \\| f\\|_{L^{N-1}}^{N-1}$$\n\nand $\\mathcal{P} (E_f)$ is finite iff $\\| f\\|_{L^{N-1}}^{N-1}$ does.\n\nLet $\\mathcal{S} (E_f)$ be the measure of the sections of $E_f$ obtained cutting the set with any hyperplane $\\Pi:=\\{ (x,t)|\\ \\langle a,x\\rangle =0\\}$ ($|a|=1$) containing the axis of revolution; then:\n\n$$\\mathcal{S} (E_f) =\\omega_{N-1} \\int_{0}^{+\\infty} f^{N-1}(t)\\ \\text{d} t\\; ,$$\n\nand also $\\mathcal{S} (E_f)$ is finite iff $f\\in L^{N-1} (E_f)$.\n\nSince $f$ is defined in the interval $[0,+\\infty[$, one in general doesn't have $f\\in L^{N}\\Rightarrow f\\in L^{N-1}$ not even if $f$ is Lipschitz (e.g., $f(x):=\\chi_{[0,1[}(x)+x^{1-N}\\chi_{[1,+\\infty[} (x)$ is $L^N$ but not $L^{N-1}$): thus in general it is always possible to pick a Lipschitz function $f$ such that $\\mathcal{L}^{N+1} (E_f)$ is finite and $\\mathcal{P} (E_f)$, $\\mathcal{S} (E_f)$ are not.\n\nN.B.: Instead of the De Giorgi perimeter, one can use the Hausdorff measure $\\mathcal{H}^{N}$ or the Minkowski content $\\mathcal{M}$ as well: in fact there is equality among $\\mathcal{P} (E_f)$, $\\mathcal{H}^{N} (E_f)$ and $\\mathcal{M} (E_f)$ because the boundary $\\partial E_f$ is sufficiently regular when $f$ is Lipschitz.\n\nI found this explanation illuminating. It's from Jerome Keisler's Elementary Calculus.\n\nSuppose you have a clay cylinder with radius 1 and length 1. Its cross-sectional area is $\\pi$, so its total volume is $\\pi$. The surface area, not counting the ends, is $2\\pi$.\n\nNow roll the cylinder with your hands so that it is only half as thick as it was. Its radius is now $\\frac12$, so its cross-sectional area is only $\\frac14\\pi$. The volume must remain the same, so the cylinder's length is now $4$, and its surface area, again not counting the ends, has doubled, to $4\\pi$.\n\nYou can repeat this process, rolling it into a snake with radius $\\frac14$. Its length then increases to $16$, and its surface area doubles again to $8\\pi$.\n\nAt each step as you roll the cylinder into a thinner and thinner snake, the volume always remains constant, but the surface area increases without bound. A snake with a radius of $r$ has a length of $\\frac1{r^2}$ and a surface area of $\\frac{2\\pi}r$, both of which go to infinity as $r$ goes to zero. None of this should seem surprising.\n\nNow instead of rolling the whole snake, just roll the right-hand half of the snake at each step. The volume is still constant, as it must be, and the surface area still goes to infinity. The shape you get is quite similar to Gabriel's horn."
] |
[
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"https://i.stack.imgur.com/s22uq.png",
null,
"https://i.stack.imgur.com/2CgVv.png",
null
] |
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https://forum.aspose.com/t/populate-dropdown-from-datatable-c-in-excel/182931
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[
"# Populate dropdown from datatable c# in Excel\n\nHi Team,\n\nI am trying to populate dropdown in Excel cell from datatable c#. Datatable has one column.\nDo you have some example for this task?\n\nThank you,\npa\n\nYou may create drop down list / Combobox control using Aspose.Cells APIs, for reference kindly check:\n\nFor setting the contents of the dropdown from a database/datasource, you can import data from database to some Worksheet cells and set this data as a data source range for the Combobox control, kindly check how to import data to worksheet from different data sources:\nImport Data into Worksheet\n\n``````OleDbConnection con = new OleDbConnection(\"provider=microsoft.jet.oledb.4.0;data source=d:\\\\test\\\\Northwind.mdb\");\ncon.Open();\nOleDbCommand cmd = new OleDbCommand(\"Select CustomerID from Customers\", con);\nda.SelectCommand = cmd;\nDataSet ds = new DataSet();\nda.Fill(ds, \"Customers\");\n\nWorkbook wb = new Workbook();\nsheet2.Name = \"Customers\";\n//Import the datatable\nsheet2.Cells.ImportDataTable(ds.Tables[\"Customers\"], false, 0, 0);\n//Get the first default worksheet.\nWorksheet sheet = wb.Worksheets;\n//Get the worksheet cells collection.\nCells cells = sheet.Cells;\n//Input a value.\ncells[\"B3\"].PutValue(\"Customers:\");\n//Set it bold.\nAspose.Cells.Style stl = wb.CreateStyle();\nstl.Font.IsBold = true;\ncells[\"B3\"].SetStyle(stl);\n\nComboBox comboBox = sheet.Shapes.AddComboBox(2, 0, 2, 0, 22, 100);\nint maxrow = sheet2.Cells.MaxDataRow;\nstring maxcellname = CellsHelper.CellIndexToName(maxrow, 0);\n//Set the input range.\ncomboBox.InputRange = \"Customers!A1:\" + maxcellname;\n//Set no. of list lines displayed in the combo box's\n//list portion.\ncomboBox.DropDownLines = 5;\n//Set the combo box with 3-D shading.\n//AutoFit Columns;\nsheet.AutoFitColumns();\n//To hide Customers sheet (Sheet2);\n//wb.Worksheets.IsVisible = false;\n//Saves the file.\nwb.Save(@\"d:\\test\\tst_dataobtained.xls\");``````\n\nHi,\nI did your example. I can see combobox with populated data.\nHow can I read selected value from this box when I upload this file?\nSelected value not showing in the cell (it is showing in combobox).\n\nRK\n\nYou may please use formula using INDEX() to display value from a combo box. Please try the following sample code and share your feedback.\n\n``````// Instantiating a \"Products\" DataTable object\nDataTable dataTable = new DataTable(\"Customers\");\n\n// Adding columns to the DataTable object\n\nfor (int i = 0; i < 10; i++)\n{\n// Creating an empty row in the DataTable object\nDataRow dr = dataTable.NewRow();\n\n// Adding data to the row\ndr = string.Format(\"Customer {0}\", i + 1);\n\n// Adding filled row to the DataTable object\n}\n\nWorkbook wb = new Workbook();\nsheet2.Name = \"Customers\";\n//Import the datatable\nsheet2.Cells.ImportDataTable(dataTable, false, 0, 0);\n//Get the first default worksheet.\nWorksheet sheet = wb.Worksheets;\n//Get the worksheet cells collection.\nCells cells = sheet.Cells;\n//Input a value.\ncells[\"B3\"].PutValue(\"Customers:\");\n//Set it bold.\nAspose.Cells.Style stl = wb.CreateStyle();\nstl.Font.IsBold = true;\ncells[\"B3\"].SetStyle(stl);\n\nComboBox comboBox = sheet.Shapes.AddComboBox(2, 0, 2, 0, 22, 100);\nint maxrow = sheet2.Cells.MaxDataRow;\nstring maxcellname = CellsHelper.CellIndexToName(maxrow, 0);\n//Set the input range.\ncomboBox.InputRange = \"Customers!A1:\" + maxcellname;\n//Set no. of list lines displayed in the combo box's\n//list portion.\ncomboBox.DropDownLines = 5;\n//Set the combo box with 3-D shading.\n//AutoFit Columns;\nsheet.AutoFitColumns();\n\nsheet.Cells[\"B6\"].Formula = @\"=INDEX(Customers!\\$A\\$1:\\$A\\$10,Sheet1!B4)\";\n//To hide Customers sheet (Sheet2);\n//wb.Worksheets.IsVisible = false;\n//Saves the file.\nwb.Save(@\"tst_dataobtained.xlsx\");``````\n\nHi,\n\nDo you have sample without creating combobox, but do this with Data Validation?\n\nThank you,\nRK\n\nYou may please try following sample code. If it does not fulfill your requirements, please create a required file using Excel and share with us. We will assist you to create similar file using Aspose.Cells.\n\n``````// Create a workbook object.\nWorkbook workbook = new Workbook();\n\n// Get the first worksheet.\nWorksheet worksheet1 = workbook.Worksheets;\n\n// Add a new worksheet and access it.\nWorksheet worksheet2 = workbook.Worksheets[i];\n\n// Create a range in the second worksheet.\nAspose.Cells.Range range = worksheet2.Cells.CreateRange(\"E1\", \"E4\");\n\n// Name the range.\nrange.Name = \"MyRange\";\n\n// Fill different cells with data in the range.\nrange[0, 0].PutValue(\"Blue\");\nrange[1, 0].PutValue(\"Red\");\nrange[2, 0].PutValue(\"Green\");\nrange[3, 0].PutValue(\"Yellow\");\n\n// Get the validations collection.\nValidationCollection validations = worksheet1.Validations;\n\n// Create Cell Area\nCellArea ca = new CellArea();\nca.StartRow = 0;\nca.EndRow = 0;\nca.StartColumn = 0;\nca.EndColumn = 0;\n\n// Create a new validation to the validations list.\n\n// Set the validation type.\nvalidation.Type = Aspose.Cells.ValidationType.List;\n\n// Set the operator.\nvalidation.Operator = OperatorType.None;\n\n// Set the in cell drop down.\nvalidation.InCellDropDown = true;\n\n// Set the formula1.\nvalidation.Formula1 = \"=MyRange\";\n\n// Enable it to show error.\nvalidation.ShowError = true;\n\n// Set the alert type severity level.\n\n// Set the error title.\nvalidation.ErrorTitle = \"Error\";\n\n// Set the error message.\nvalidation.ErrorMessage = \"Please select a color from the list\";\n\n// Specify the validation area.\nCellArea area;\narea.StartRow = 0;\narea.EndRow = 4;\narea.StartColumn = 0;\narea.EndColumn = 0;\n\n// Save the Excel file.\nworkbook.Save(\"output.out.xlsx\");``````\n\nPlease show how program this list in cell C4.\nData in the Sheet2\n\nIn the Sheet2 can be more than 300 rows.\n\nThank you,\nRKTest Data Validation List .zip (6.4 KB)\n\nThanks for the template file.\n\nI think you should find some time to see and understand the code segments shared by Ahsan Iqbal. Anyways, I have written the following sample code to accomplish your task. I have used your template file as an input file and added List data validation type to C4 cell in the first worksheet based on the underlying data in the second sheet.\ne.g\nSample code:\n\n``````// Create a workbook object.\nWorkbook workbook = new Workbook(\"e:\\\\test2\\\\Test Data Validation List .xlsx\");\n\n// Get the first worksheet.\nWorksheet worksheet1 = workbook.Worksheets;\n\n// Get the second sheet.\nWorksheet worksheet2 = workbook.Worksheets;\n\n// Create a range in the first worksheet.\nAspose.Cells.Range range = worksheet2.Cells.CreateRange(\"A1\", \"A5\");\n\n// Name the range.\nrange.Name = \"MyRange\";\n\n// Get the validations collection.\nValidationCollection validations = worksheet1.Validations;\n\n// Create Cell Area\nCellArea ca = new CellArea();\nca.StartRow = 3;\nca.EndRow = 3;\nca.StartColumn = 2;\nca.EndColumn = 2;\n\n// Create a new validation to the validations list.\n\n// Set the validation type.\nvalidation.Type = Aspose.Cells.ValidationType.List;\n\n// Set the operator.\nvalidation.Operator = OperatorType.None;\n\n// Set the in cell drop down.\nvalidation.InCellDropDown = true;\n\n// Set the formula1 using named range.\n//validation.Formula1 = \"=MyRange\";\n\n//Or\n// Alternatively, you may set the formula1 directly.\nvalidation.Formula1 = \"=Sheet2!A1:A5\";\n\n// Enable it to show error.\nvalidation.ShowError = true;\n\n// Set the alert type severity level.\n\n// Set the error title.\nvalidation.ErrorTitle = \"Error\";\n\n// Set the error message.\nvalidation.ErrorMessage = \"Please select a name from the list\";\n\n// Save the Excel file.\nworkbook.Save(\"e:\\\\test2\\\\out1.xlsx\");\n``````\n\nHope, this helps a bit.\n\nIt is works for me.\n\nThank you very much.\nRK\n\nGood to know that your issue is sorted out by the suggested code segment. Feel free to contact us any time if you need further help or have some other issue or queries, we will be happy to assist you soon."
] |
[
null
] |
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|
https://brilliant.org/practice/geometry-warmups-level-3-challenges/?subtopic=geometric-measurement&chapter=fun-geometry-quizzes
|
[
"",
null,
"Geometry\n\n# Geometry Warmups: Level 3 Challenges",
null,
"In the figure above, we have a square and a circle inside a larger square.\n\nFind the radius of the circle, to 3 decimal places.",
null,
"Find the area (in $$\\text{cm}^2$$) of the shaded green square in the blue isosceles right triangle, whose legs have length 6 cm.\n\n$\\tan6^{\\circ} \\times \\tan42^{\\circ} \\times \\tan66^{\\circ} \\times \\tan78^{\\circ}=\\, ?$",
null,
"The 5 circles have the same size. If the side of the large square is 1, what is the radius of each circle (to 3 decimal places)?",
null,
"Three balls are placed inside a cone such that each ball is in contact with the edge of the cone and the next ball. If the radii of the balls are 20 cm, 12 cm, and $$r$$ cm from top to bottom, what is the value of $$r$$?\n\n×"
] |
[
null,
"https://ds055uzetaobb.cloudfront.net/brioche/chapter/Geometry%20Warmups-lMhtoW.png",
null,
"https://ds055uzetaobb.cloudfront.net/brioche/solvable/c51154c5a1.a07994ea00.WQ1Ak2.png",
null,
"https://brilliant-staff-media.s3-us-west-2.amazonaws.com/tiffany-wang/IuMBtklwlt.png",
null,
"https://ds055uzetaobb.cloudfront.net/brioche/uploads/c7pnzH4R3H-23535.svg",
null,
"https://ds055uzetaobb.cloudfront.net/brioche/solvable/2f74a2ffda.1ce8aaa0e4.7au7hi.png",
null
] |
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|
https://export.arxiv.org/abs/0809.0767
|
[
"math.AC\n\n# Title: A note on k[z]-automorphisms in two variables\n\nAbstract: We prove that for a polynomial $f\\in k[x,y,z]$ equivalent are: (1)$f$ is a $k[z]$-coordinate of $k[z][x,y]$, and (2) $k[x,y,z]/(f)\\cong k^{}$ and $f(x,y,a)$ is a coordinate in $k[x,y]$ for some $a\\in k$. This solves a special case of the Abhyankar-Sathaye conjecture. As a consequence we see that a coordinate $f\\in k[x,y,z]$ which is also a $k(z)$-coordinate, is a $k[z]$-coordinate. We discuss a method for constructing automorphisms of $k[x,y,z]$, and observe that the Nagata automorphism occurs naturally as the first non-trivial automorphism obtained by this method - essentially linking Nagata with a non-tame $R$-automorphism of $R[x]$, where $R=k[z]/(z^2)$.\n Comments: 8 pages Subjects: Commutative Algebra (math.AC); Algebraic Geometry (math.AG) MSC classes: 14R10, 13B25, 14J50 Cite as: arXiv:0809.0767 [math.AC] (or arXiv:0809.0767v1 [math.AC] for this version)\n\n## Submission history\n\nFrom: Stefan Maubach [view email]\n[v1] Thu, 4 Sep 2008 08:16:40 GMT (8kb)\n\nLink back to: arXiv, form interface, contact."
] |
[
null
] |
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|
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