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[ "Kevin Ford, James Maynard, and I have uploaded to the arXiv our preprint “Chains of large gaps between primes“. This paper was announced in our previous paper with Konyagin and Green, which was concerned with the largest gap", null, "$\\displaystyle G_1(X) := \\max_{p_n, p_{n+1} \\leq X} (p_{n+1} - p_n)$\n\nbetween consecutive primes up to", null, "${X}$, in which we improved the Rankin bound of", null, "$\\displaystyle G_1(X) \\gg \\log X \\frac{\\log_2 X \\log_4 X}{(\\log_3 X)^2}$\n\nto", null, "$\\displaystyle G_1(X) \\gg \\log X \\frac{\\log_2 X \\log_4 X}{\\log_3 X}$\n\nfor large", null, "${X}$ (where we use the abbreviations", null, "${\\log_2 X := \\log\\log X}$,", null, "${\\log_3 X := \\log\\log\\log X}$, and", null, "${\\log_4 X := \\log\\log\\log\\log X}$). Here, we obtain an analogous result for the quantity", null, "$\\displaystyle G_k(X) := \\max_{p_n, \\dots, p_{n+k} \\leq X} \\min( p_{n+1} - p_n, p_{n+2}-p_{n+1}, \\dots, p_{n+k} - p_{n+k-1} )$\n\nwhich measures how far apart the gaps between chains of", null, "${k}$ consecutive primes can be. Our main result is", null, "$\\displaystyle G_k(X) \\gg \\frac{1}{k^2} \\log X \\frac{\\log_2 X \\log_4 X}{\\log_3 X}$\n\nwhenever", null, "${X}$ is sufficiently large depending on", null, "${k}$, with the implied constant here absolute (and effective). The factor of", null, "${1/k^2}$ is inherent to the method, and related to the basic probabilistic fact that if one selects", null, "${k}$ numbers at random from the unit interval", null, "${[0,1]}$, then one expects the minimum gap between adjacent numbers to be about", null, "${1/k^2}$ (i.e. smaller than the mean spacing of", null, "${1/k}$ by an additional factor of", null, "${1/k}$).\n\nOur arguments combine those from the previous paper with the matrix method of Maier, who (in our notation) showed that", null, "$\\displaystyle G_k(X) \\gg_k \\log X \\frac{\\log_2 X \\log_4 X}{(\\log_3 X)^2}$\n\nfor an infinite sequence of", null, "${X}$ going to infinity. (Maier needed to restrict to an infinite sequence to avoid Siegel zeroes, but we are able to resolve this issue by the now standard technique of simply eliminating a prime factor of an exceptional conductor from the sieve-theoretic portion of the argument. As a byproduct, this also makes all of the estimates in our paper effective.)\n\nAs its name suggests, the Maier matrix method is usually presented by imagining a matrix of numbers, and using information about the distribution of primes in the columns of this matrix to deduce information about the primes in at least one of the rows of the matrix. We found it convenient to interpret this method in an equivalent probabilistic form as follows. Suppose one wants to find an interval", null, "${n+1,\\dots,n+y}$ which contained a block of at least", null, "${k}$ primes, each separated from each other by at least", null, "${g}$ (ultimately,", null, "${y}$ will be something like", null, "${\\log X \\frac{\\log_2 X \\log_4 X}{\\log_3 X}}$ and", null, "${g}$ something like", null, "${y/k^2}$). One can do this by the probabilistic method: pick", null, "${n}$ to be a random large natural number", null, "${{\\mathbf n}}$ (with the precise distribution to be chosen later), and try to lower bound the probability that the interval", null, "${{\\mathbf n}+1,\\dots,{\\mathbf n}+y}$ contains at least", null, "${k}$ primes, no two of which are within", null, "${g}$ of each other.\n\nBy carefully choosing the residue class of", null, "${{\\mathbf n}}$ with respect to small primes, one can eliminate several of the", null, "${{\\mathbf n}+j}$ from consideration of being prime immediately. For instance, if", null, "${{\\mathbf n}}$ is chosen to be large and even, then the", null, "${{\\mathbf n}+j}$ with", null, "${j}$ even have no chance of being prime and can thus be eliminated; similarly if", null, "${{\\mathbf n}}$ is large and odd, then", null, "${{\\mathbf n}+j}$ cannot be prime for any odd", null, "${j}$. Using the methods of our previous paper, we can find a residue class", null, "${m \\hbox{ mod } P}$ (where", null, "${P}$ is a product of a large number of primes) such that, if one chooses", null, "${{\\mathbf n}}$ to be a large random element of", null, "${m \\hbox{ mod } P}$ (that is,", null, "${{\\mathbf n} = {\\mathbf z} P + m}$ for some large random integer", null, "${{\\mathbf z}}$), then the set", null, "${{\\mathcal T}}$ of shifts", null, "${j \\in \\{1,\\dots,y\\}}$ for which", null, "${{\\mathbf n}+j}$ still has a chance of being prime has size comparable to something like", null, "${k \\log X / \\log_2 X}$; furthermore this set", null, "${{\\mathcal T}}$ is fairly well distributed in", null, "${\\{1,\\dots,y\\}}$ in the sense that it does not concentrate too strongly in any short subinterval of", null, "${\\{1,\\dots,y\\}}$. The main new difficulty, not present in the previous paper, is to get lower bounds on the size of", null, "${{\\mathcal T}}$ in addition to upper bounds, but this turns out to be achievable by a suitable modification of the arguments.\n\nUsing a version of the prime number theorem in arithmetic progressions due to Gallagher, one can show that for each remaining shift", null, "${j \\in {\\mathcal T}}$,", null, "${{\\mathbf n}+j}$ is going to be prime with probability comparable to", null, "${\\log_2 X / \\log X}$, so one expects about", null, "${k}$ primes in the set", null, "${\\{{\\mathbf n} + j: j \\in {\\mathcal T}\\}}$. An upper bound sieve (e.g. the Selberg sieve) also shows that for any distinct", null, "${j,j' \\in {\\mathcal T}}$, the probability that", null, "${{\\mathbf n}+j}$ and", null, "${{\\mathbf n}+j'}$ are both prime is", null, "${O( (\\log_2 X / \\log X)^2 )}$. Using this and some routine second moment calculations, one can then show that with large probability, the set", null, "${\\{{\\mathbf n} + j: j \\in {\\mathcal T}\\}}$ will indeed contain about", null, "${k}$ primes, no two of which are closer than", null, "${g}$ to each other; with no other numbers in this interval being prime, this gives a lower bound on", null, "${G_k(X)}$." ]

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[ "# Control System Questions. Need help to check if my answers are correct.\n\n#### ToonBlue\n\nJoined Nov 9, 2015\n2", null, "Given that C =35 in this question.\n\nG(s) = θ(s) / F(s) = 1 / (s^2 - α )\n\nα = (10 + C) / 1000 = 45 / 1000 = 9 / 200\n\nSystem pole can be found at s", null, "Thus , it tells me that it is a real and district roots and when input signal is applied , output signal from the space booster will be a exponentially growing transient response.\n\nii. Sketch the impulse response, θ(t).", null, "Question 2", null, "I let A = kp + kd s + ki / s and B = 1 / (s^2 - α )\n\nTo obtain the closed-loop transfer function with respect to a specific point , we assume that all other inputs are zero. Thus , for θ(s) / θr(s) , we take D(s) = 0 and θ(s)/D(s) , we take θr(s) = 0\n\nHence, Gr(s) = (AB) / (1 + AB) and Gd(s) = B / (1-AB)\n\nGr(s) = (kp + kd s + ki / s ) / (s^2 - α + kp + kd s + ki / s )\nGd(s) = 1 / (s^2 - α - kp - kd s - ki / s )\n\n#### ToonBlue\n\nJoined Nov 9, 2015\n2\nThe question also asks the order of the booster rocket control system. So based on my result of Gr(s) , it is a second order system?\n\n#### MrAl\n\nJoined Jun 17, 2014\n7,849\nHi,\n\nA quick note here...\n\nI did not go over your equations but from the last set Gr and Gd it does not look like you have them in the right form in order to determine the order of the system. You can do it that way, but it's better to get it into the ratio of two polynomials.\nTry doing that and then see if you can figure out the order (it's simple really)." ]

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[ "# Examples of exponential functions carbon dating www dir dating com\n\nHere isotopes with longer half lives are used, which enables dating of geological formations and rocks. For example, in lava form, molten lead and Uranium-238 (standard isotope) are constantly mixed in a certain ratio of their natural abundance.Once solidified, the lead is \"locked\" in place and since the uranium decays to lead, the lead-to-uranium ratio increases with time.\n\n## avg keeps updating - Examples of exponential functions carbon dating\n\nExactly the same treatment can be applied to radioactive decay.\n\nHowever, now the \"thin slice\" is an interval of time, and the dependent variable is the number of radioactive atoms present, N(t). If we have a sample of atoms, and we consider a time interval short enough that the population of atoms hasn't changed significantly through decay, then the proportion of atoms decaying in our short time interval will be proportional to the length of the interval.\n\nCurrent research involves a theoretical description of X-ray beam spectra.\n\nIf you're seeing this message, it means we're having trouble loading external resources on our website.\n\nIn the previous article, we saw that light attenuation obeys an exponential law.\n\nTo show this, we needed to make one critical assumption: that for a thin enough slice of matter, the proportion of light getting through the slice was proportional to the thickness of the slice.In his article Light Attenuation and Exponential Laws in the last issue of Plus, Ian Garbett discussed the phenomenon of light attenuation, one of the many physical phenomena in which the exponential function crops up.In this second article he describes the phenomenon of radioactive decay, which also obeys an exponential law, and explains how this information allows us to carbon-date artefacts such as the Dead Sea Scrolls.Suppose a linen sample of 1 gram is analysed in a counter.The activity is measured at approximately 11.9 decays per minute.Again, we find a \"chance\" process being described by an exponential decay law." ]

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[ "", null, "Home > Grade 8 > Geometry > Triangle Sum Theorem\n\n# Triangle Sum Theorem\n\nDirections: Using the digits 1-9 at most one time each, fill in the blanks so that when you solve for x, it is a whole number.", null, "### Hint\n\nHow many degrees must the two unknown angles sum to?\nCan you write an equation to represent the sum of the two unknown angles?\n\nThere are many answers. One is:\nTop angle is 4x and bottom angle is 6x + 25.\nx = 10 solves the problem.\n\nExtension/extra challenge 1: set a value for x and find all the ways to make the problem have that solution.\nExtension/extra challenge 2: change the value of the bottom right angle." ]

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[ "# The Illustrated SimCLR Framework\n\nIn recent years, numerous self-supervised learning methods have been proposed for learning image representations, each getting better than the previous. But, their performance was still below the supervised counterparts.\n\nThis changed when Chen et. al proposed a new framework in their research paper “SimCLR: A Simple Framework for Contrastive Learning of Visual Representations”. The SimCLR paper not only improves upon the previous state-of-the-art self-supervised learning methods but also beats the supervised learning method on ImageNet classification when scaling up the architecture.\n\nIn this article, I will explain the key ideas of the framework proposed in the research paper using diagrams.\n\n## The Nostalgic Intuition\n\nAs a kid, I remember we had to solve such puzzles in our textbook.", null, "The way a child would solve it is by looking at the picture of the animal on the left side, know its a cat, then search for a cat on the right side.", null, "“Such exercises were prepared for the child to be able to recognize an object and contrast that to other objects. Can we similarly teach machines?”\n\nIt turns out that we can through a technique called Contrastive Learning. It attempts to teach machines to distinguish between similar and dissimilar things.", null, "## Problem Formulation for Machines\n\nTo model the above exercise for a machine instead of a child, we see that we require 3 things:\n\n### 1. Examples of similar and dissimilar images\n\nWe would require example pairs of images that are similar and images that are different for training a model.", null, "The supervised school of thought would require a human to manually annotate such pairs. To automate this, we could leverage self-supervised learning. But how do we formulate it?", null, "", null, "### 2. Ability to know what an image represents\n\nWe need some mechanism to get representations that allow the machine to understand an image.", null, "### 3. Ability to quantify if two images are similar\n\nWe need some mechanism to compute the similarity of two images.", null, "## The SimCLR Framework Approach\n\nThe paper proposes a framework called “SimCLR” for modeling the above problem in a self-supervised manner. It blends the concept of Contrastive Learning with a few novel ideas to learn visual representations without human supervision.\n\n## SimCLR Framework\n\nThe idea of SimCLR framework is very simple. An image is taken and random transformations are applied to it to get a pair of two augmented images $x_i$ and $x_j$. Each image in that pair is passed through an encoder to get representations. Then a non-linear fully connected layer is applied to get representations z. The task is to maximize the similarity between these two representations $z_i$ and $z_j$ for the same image.", null, "## Step by Step Example\n\nLet’s explore the various components of the SimCLR framework with an example. Suppose we have a training corpus of millions of unlabeled images.", null, "### 1. Self-supervised Formulation [Data Augmentation]\n\nFirst, we generate batches of size N from the raw images. Let’s take a batch of size N = 2 for simplicity. In the paper, they use a large batch size of 8192.", null, "The paper defines a random transformation function T that takes an image and applies a combination of random (crop + flip + color jitter + grayscale).", null, "For each image in this batch, a random transformation function is applied to get a pair of 2 images. Thus, for a batch size of 2, we get 2*N = 2*2 = 4 total images.", null, "### 2. Getting Representations [Base Encoder]\n\nEach augmented image in a pair is passed through an encoder to get image representations. The encoder used is generic and replaceable with other architectures. The two encoders shown below have shared weights and we get vectors $h_i$ and $h_j$.", null, "In the paper, the authors used ResNet-50 architecture as the ConvNet encoder. The output is a 2048-dimensional vector h.", null, "The representations $h_i$ and $h_j$ of the two augmented images are then passed through a series of non-linear Dense -> Relu -> Dense layers to apply non-linear transformation and project it into a representation $z_i$ and $z_j$. This is denoted by $g(.)$ in the paper and called projection head.", null, "### 4. Tuning Model: [Bringing similar closer]\n\nThus, for each augmented image in the batch, we get embedding vectors $z$ for it.", null, "From these embedding, we calculate the loss in following steps:\n\n#### a. Calculation of Cosine Similarity\n\nNow, the similarity between two augmented versions of an image is calculated using cosine similarity. For two augmented images $x_i$ and $x_j$, the cosine similarity is calculated on its projected representations $z_i$ and $z_j$.", null, "$s_{i,j} = \\frac{ \\color{#ff7070}{z_{i}^{T}z_{j}} }{(\\tau ||\\color{#ff7070}{z_{i}}|| ||\\color{#ff7070}{z_{j}}||)}$\n\nwhere\n\n• $\\tau$ is the adjustable temperature parameter. It can scale the inputs and widen the range [-1, 1] of cosine similarity\n• $\\lVert z_{i} \\rVert$ is the norm of the vector.\n\nThe pairwise cosine similarity between each augmented image in a batch is calculated using the above formula. As shown in the figure, in an ideal case, the similarities between augmented images of cats will be high while the similarity between cat and elephant images will be lower.", null, "#### b. Loss Calculation\n\nSimCLR uses a contrastive loss called “NT-Xent loss” (Normalized Temperature-Scaled Cross-Entropy Loss). Let see intuitively how it works.\n\nFirst, the augmented pairs in the batch are taken one by one.", null, "Next, we apply the softmax function to get the probability of these two images being similar.", null, "This softmax calculation is equivalent to getting the probability of the second augmented cat image being the most similar to the first cat image in the pair. Here, all remaining images in the batch are sampled as a dissimilar image (negative pair). Thus, we don’t need specialized architecture, memory bank or queue need by previous approaches like InstDisc, MoCo or PIRL.", null, "Then, the loss is calculated for a pair by taking the negative of the log of the above calculation. This formulation is the Noise Contrastive Estimation(NCE) Loss.\n\n$l(i, j) = -log\\frac{exp(s_{i, j})}{ \\sum_{k=1}^{2N} l_{[k!= i]} exp(s_{i, k})}$", null, "We calculate the loss for the same pair a second time as well where the positions of the images are interchanged.", null, "Finally, we compute loss over all the pairs in the batch of size N=2 and take an average.\n\n$L = \\frac{1}{ 2\\color{#2196f3}{N} } \\sum_{k=1}^{N} [l(2k-1, 2k) + l(2k, 2k-1)]$", null, "Based on the loss, the encoder and projection head representations improves over time and the representations obtained place similar images closer in the space.\n\nOnce the SimCLR model is trained on the contrastive learning task, it can be used for transfer learning. For this, the representations from the encoder are used instead of representations obtained from the projection head. These representations can be used for downstream tasks like ImageNet Classification.", null, "## Objective Results\n\nSimCLR outperformed previous self-supervised methods on ImageNet. The below image shows the top-1 accuracy of linear classifiers trained on representations learned with different self-supervised methods on ImageNet. The gray cross is supervised ResNet50 and SimCLR is shown in bold.", null, "Source: SimCLR paper\n\n• On ImageNet ILSVRC-2012, it achieves 76.5% top-1 accuracy which is 7% improvement over previous SOTA self-supervised method Contrastive Predictive Coding and on-par with supervised ResNet50.\n• When trained on 1% of labels, it achieves 85.8% top-5 accuracy outperforming AlexNet with 100x fewer labels\n\n## SimCLR Code\n\nThe official implementation of SimCLR in Tensorflow by the paper authors is available on GitHub. They also provide pretrained models for 1x, 2x, and 3x variants of the ResNet50 architectures using Tensorflow Hub.\n\nThere are various unofficial SimCLR PyTorch implementations available that have been tested on small datasets like CIFAR-10 and STL-10.\n\n## Conclusion\n\nThus, SimCLR provides a strong framework for doing further research in this direction and improve the state of self-supervised learning for Computer Vision.\n\n## Citation Info (BibTex)\n\nIf you found this blog post useful, please consider citing it as:\n\n@misc{chaudhary2020simclr,\ntitle = {The Illustrated SimCLR Framework},\nauthor = {Amit Chaudhary},\nyear = 2020,\nnote = {\\url{https://amitness.com/2020/03/illustrated-simclr}}\n}" ]

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[ "## 57800\n\n57,800 (fifty-seven thousand eight hundred) is an even five-digits composite number following 57799 and preceding 57801. In scientific notation, it is written as 5.78 × 104. The sum of its digits is 20. It has a total of 7 prime factors and 36 positive divisors. There are 21,760 positive integers (up to 57800) that are relatively prime to 57800.\n\n## Basic properties\n\n• Is Prime? No\n• Number parity Even\n• Number length 5\n• Sum of Digits 20\n• Digital Root 2\n\n## Name\n\nShort name 57 thousand 800 fifty-seven thousand eight hundred\n\n## Notation\n\nScientific notation 5.78 × 104 57.8 × 103\n\n## Prime Factorization of 57800\n\nPrime Factorization 23 × 52 × 172\n\nComposite number\nDistinct Factors Total Factors Radical ω(n) 3 Total number of distinct prime factors Ω(n) 7 Total number of prime factors rad(n) 170 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 57,800 is 23 × 52 × 172. Since it has a total of 7 prime factors, 57,800 is a composite number.\n\n## Divisors of 57800\n\n1, 2, 4, 5, 8, 10, 17, 20, 25, 34, 40, 50, 68, 85, 100, 136, 170, 200, 289, 340, 425, 578, 680, 850, 1156, 1445, 1700, 2312, 2890, 3400, 5780, 7225, 11560, 14450, 28900, 57800\n\n36 divisors\n\n Even divisors 27 9 9 0\nTotal Divisors Sum of Divisors Aliquot Sum τ(n) 36 Total number of the positive divisors of n σ(n) 142755 Sum of all the positive divisors of n s(n) 84955 Sum of the proper positive divisors of n A(n) 3965.42 Returns the sum of divisors (σ(n)) divided by the total number of divisors (τ(n)) G(n) 240.416 Returns the nth root of the product of n divisors H(n) 14.576 Returns the total number of divisors (τ(n)) divided by the sum of the reciprocal of each divisors\n\nThe number 57,800 can be divided by 36 positive divisors (out of which 27 are even, and 9 are odd). The sum of these divisors (counting 57,800) is 142,755, the average is 39,65.,416.\n\n## Other Arithmetic Functions (n = 57800)\n\n1 φ(n) n\nEuler Totient Carmichael Lambda Prime Pi φ(n) 21760 Total number of positive integers not greater than n that are coprime to n λ(n) 1360 Smallest positive number such that aλ(n) ≡ 1 (mod n) for all a coprime to n π(n) ≈ 5844 Total number of primes less than or equal to n r2(n) 36 The number of ways n can be represented as the sum of 2 squares\n\nThere are 21,760 positive integers (less than 57,800) that are coprime with 57,800. And there are approximately 5,844 prime numbers less than or equal to 57,800.\n\n## Divisibility of 57800\n\n m n mod m 2 3 4 5 6 7 8 9 0 2 0 0 2 1 0 2\n\nThe number 57,800 is divisible by 2, 4, 5 and 8.\n\n• Abundant\n\n• Polite\n• Practical\n\n• Achilles\n• Powerful\n\n• Frugal\n\n## Base conversion (57800)\n\nBase System Value\n2 Binary 1110000111001000\n3 Ternary 2221021202\n4 Quaternary 32013020\n5 Quinary 3322200\n6 Senary 1123332\n8 Octal 160710\n10 Decimal 57800\n12 Duodecimal 29548\n20 Vigesimal 74a0\n36 Base36 18lk\n\n## Basic calculations (n = 57800)\n\n### Multiplication\n\nn×i\n n×2 115600 173400 231200 289000\n\n### Division\n\nni\n n⁄2 28900 19266.7 14450 11560\n\n### Exponentiation\n\nni\n n2 3340840000 193100552000000 11161211905600000000 645118048143680000000000\n\n### Nth Root\n\ni√n\n 2√n 240.416 38.6642 15.5054 8.9616\n\n## 57800 as geometric shapes\n\n### Circle\n\n Diameter 115600 363168 1.04956e+10\n\n### Sphere\n\n Volume 8.08858e+14 4.19822e+10 363168\n\n### Square\n\nLength = n\n Perimeter 231200 3.34084e+09 81741.5\n\n### Cube\n\nLength = n\n Surface area 2.0045e+10 1.93101e+14 100113\n\n### Equilateral Triangle\n\nLength = n\n Perimeter 173400 1.44663e+09 50056.3\n\n### Triangular Pyramid\n\nLength = n\n Surface area 5.7865e+09 2.27571e+13 47193.5\n\n## Cryptographic Hash Functions\n\nmd5 2c292d1be5eb1ed8faa7675d09de1ab9 01b02059a7cf660975b3e06bdf44a2599987e0c7 5136cf22a14d6395186da645a7c305d07eb9b7548122b8e5b6fee7535bddbf82 bdac9266dd968e996fea58470dd9b8750c436f0228572211610453f7c6023bf68241860c576488bffe8c15028a901e219e0f36a83b3cf7d05ee0bfe90d459ab6 b848bc1fd2f8ad7703c93110e7e2da5dffe9ea48" ]

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[ "At first, they start to learn from the basic understanding of maths. If I helped you in this video, I would love to have you subscribe . It is a type of notation that represents aninterval with a pair of numbers. For a given function, y = F(x), if the value of y is increasing on increasing the value of x, then the function is known as an increasing function and if the value of y is decreasing on increasing the value of x, then the function is known as a decreasing function. Like \"She [Lily] was happy to see him [James]\". Some people just use round parentheses universally. All three together constitute an ellipsis. Brackets are used to insert explanations, corrections, clarifications, or comments into quoted material. -OO f (x) = V2x+5 g (x) = 4x-+3x Find fig and f+ g. As an inequality, the domain is written . Argentina Values And Beliefs, We can use these brackets in mathematics to represent the scope and range of functions using interval notation. The two numbers are called the endpoints of the interval. Commutative property. Explanation: Use a bracket (sometimes called a square bracket) to indicate that the endpoint is included in the interval, a parenthesis (sometimes called a round bracket) to . Use interval notation to indicate all real numbers greater than or equal to $-2$. For example, [3, 8) is the interval of real numbers between 3 and 8, including 3 and excluding 8. (, ) denotes the domain is the horizontal extent of the function x-intercepts. In this sentence, one can just skip the stuff stolen by Joe, as it does not affect or alter the meaning in its surrounding sentence. 5 to 7, exclusive are bounded sets of numbers as follows use brackets or parentheses < /a Comment Interval from 5 to 7, exclusive bracket to the left denotes the element Is bars, not a bracket [, ] 5,7 [ refers to strict. < /a > How do you write interval uses! < /a > use interval notation ], (, ) the. parentheses are like strict inequalities. Avoid parentheses within parentheses, or nested parentheses. Especially for separating the secondary material. What is the difference between a [] and a {}? Image transcription text. Dreh- und Frstechnik | Alle Rechte vorbehalten (All rights reserved), when to use brackets or parentheses in domain and range. It also includes numbers greater than ##3## but it does not include 7. In mathematics, they are mostly used for order of operations. There will be a 20-minute interval between acts one and two. Use a bracket to indicate that the endpoint is included in the interval a parenthesis to indicate that it is not. The notation may be a little confusing, but just remember that square brackets mean the end point is included, and round parentheses mean its excluded. To use interval notation we need to first understand some of the commonly used symbols: A closed interval is an interval that includes the values on the end. A compact set is a precisely closed boundary spacing in a real setting. Brackets: But to represent that point brackets are included. Either not included or the interval on the number on the right end of interval. We can write the domain and range in interval notation, which uses values within brackets to describe a set of numbers. This notation frequently shows up in Algebra and other advanced math when displaying an interval. This can be done for adding missing words, adding some editorial comment, etc. To type parenthesis ( ) you use ring finger and pinky, stretching a distance of 2 rows above. Only in citations ( and only in citations ): //en.wikipedia.org/wiki/Bracket_ ( mathematics < /a > Put points in.! Then, since x is negative infinity, the lower limit is described as (-. MA 251 Interval Notation and Inequalities 1 I am not picky about using formal set notation, but the notation you do use should be correct. Learn about the characteristics of a function. The interval in the example below would be written Interval notation requires the use of parentheses and brackets. A useful way of describing a set of numbers is by using interval notation. For example, the infinite interval that contains all points greater than or equal to 6 is expressed[6,Inf]. [2, 3] [2, 3] Use square brackets to indicate closed intervals. One such example is the interval notation. X-Intercepts ( also called zeros ) reverse brackets to depict parentheses square brackets indicate they lie within the,! The table below provides a comparison between expressing intervals in interval notation and using inequalities, where a and b are real numbers. A closed interval includes its endpoints and is denoted with square brackets rather than parentheses. The value of the interval is said to be increasing for every x < y where f (x) f (y) for a real-valued function f (x). This means that the range contains all real numbers x that is precisely between the numbers a and b. [3, 8) for example, is the difference between real numbers between 3 and 8, which includes 3 and excludes 8. Moreover, to enclose parentheses items, we use brackets. There are several different types of intervals, called open intervals and closed intervals, which commonly occur when studying mathematics, called (a, b) and [a, b], respectively. Example: She is a great friend of us. Determine between a bracket [, ] or parentheses? , 1. When the point or value is not included in the interval, a parenthesis is used, and when the value is included, a bracket is used. Detective Mimo Kopi Luwak, It is also used when there is lack of certainty in issues related to gender, subject is singular or plural, etc. Brackets: For the purpose of enclosing the arguments of functions. [email protected] (adsbygoogle = window.adsbygoogle || []).push({}); A notation for representing an interval as Second, in domain, what do parentheses and brackets mean? Brackets are like inequalities that say or equal parentheses are like strict inequalities. Course Hero is not sponsored or endorsed by any college or university. For example, He [Deniel] was happy to see his classmate [Jackson]. Also, in interval notation, what is the difference between brackets and parentheses? Representing interval as a pair of numbers on the right end of the.! The objects in the set are called the elements of the set. Brackets are like inequalities that say or equal parentheses are like strict inequalities. Parentheses are a variety of brackets. Interval Notation. The interval on the number line mathematics ) '' > bracket ( mathematics ) '' > How do you write interval notation does A useful way of describing a set of numbers are excluded or included Put points in interval. Brackets are square-shaped symbols [ ]. If both end points are included the interval is said to be closed, if they are both excluded its said to be open. With interval notation, we use use round parentheses: (,). Is missing intersection represents the joining together of two sets of describing a set of numbers on the line. The table below provides a comparison between expressing intervals in interval notation and using inequalities, where a and b are real numbers. Called zeros ) are defined as follows intervals where the graph parentheses are . Use interval notation using brackets and parentheses Image transcription text Suppose that the functions f and g are defined as follows. If f(x)>0 on an open interval, then f is increasing on the interval. Graph these values on a line using open points for < and >, and closed points for and . Whereas parentheses refer to a distinct form of punctuation mark. The ampersand, also known as the andsign, is the logogram &, representing the conjunction and. Notice above there is a mixture of brackets and parenthesis in the set of increasing intervals. The sentence has to make sense without the words inside the brackets, its just a bit more interesting with the added detail. Yes, he can, as he did in Thor: Ragnarok. All JavaScript values, except primitives, are objects. [1, 2[. Previous answers to this question 19: 12 3 2 0 2. As others have pointed out, brackets (parentheses) take precedence over the traditional order of operations. Wenn du die Website weiter nutzt, gehen wir von deinem Einverstndnis aus. I'll make a brief note of online math tutorials. Use square brackets ([ ]) to indicate the inclusion of the boundaries in the solution, or parentheses ( ) to indicate their exclusion. Bound, then P ( X=x ) =0. TimesMojo is a social question-and-answer website where you can get all the answers to your questions. Definitions - Interval notation: An efficient method of describing a set of real numbers, like a set of x-values, or the domain of a function. For example, ]5,7[ refers to the interval from Open interval, closed The use of brackets and parentheses are necessary in order to specify which values are included or not included in the interval. Therefore, closed intervals can be annotated as a set of a x b. Mechanical, Youre all less likely to want to eat somewhere where alcohol is served. For example, if a person has $100 to spend, he or she would need to express the interval . Parenthesis (single one) is used if the point is not being included in the interval, whereas a bracket is used when the point is included. Biolage Hydrasource Deep Treatment, of parentheses. This particular interval is We can write the domain and range in interval notation, which uses values within brackets to describe a set of numbers. A parenthesis is a punctuation mark used to enclose information, similar to a bracket. Now test values on all sides of these to find when the function is negative, and therefore decreasing. Including 3 and 8, including 3 and excluding 8 citations ) because Of 5 is called an inclusive bracket 29/10/2021 in mathematics viewed by persons! Detective Mimo Kopi Luwak, Identify where the thick line overlaps the actual line to determine what to include in the set. Example: After rehearsing for weeks, the cast wasn't sure if they'd be ready to perform by opening night (or, in fact, ever). For the range of a function, brackets should be used when the output values are not consecutive integers. The numbers are the endpoints of the interval. Avoid parentheses within parentheses, or nested parentheses. Parentheses, Braces, and Brackets in Math Using Parentheses ( ). Save my name, email, and website in this browser for the next time I comment. Biolage Hydrasource Deep Treatment, Use a bracket to indicate that the endpoint is included in the interval a parenthesis to indicate that it is not. Second, we solve any exponents. The numbers are the endpoints of the interval. Domain And Range Brackets Or Parentheses. The function graphed above is: Increasing on the interval(s) Decreasing on the interval(s) Check Answer Question 30 0/3 pts 2 Details 10+ 8 8 5 6 4 2 6 -5 -4 -3 -2 - 1 4 5/6 -2 - 4 -6 -3 -10 The function graphed above is: Concave up on the interval(s) Concave down on the interval(s) Terms inside the bracket are evaluated first; hence 2(3 + 4) is 14, 20 (5(1 + 1)) is 2 and (23) + 4 is 10. A parenthesis Found 2 solutions by ilana, stanbon: Answer by ilana(307) (Show Source): You can put this solution on YOUR website! It's a site that collects all the most frequently asked questions and answers, so you don't have to spend hours on searching anywhere else. 1) The function appears to go infinity in both the positive and negative x . The range of a function is the set of all output values. The number on the right denotes the greatest element or upper bound. Intervals are written with rectangular brackets or parentheses, and two numbers delimited with a comma. The inclusion or exclusion of a point is indicated by parentheses and brackets. Parentheses are used to group numbers, operations, or variables together in math. Parentheses are always used in pairs; you must have both an opening and a closing parenthesis. What is the difference between square brackets and normal brackets? domain and range brackets or parentheses - DOMBAIN So let's sig alert that. Brackets are also known as braces. How Much RAM Do You Need for Smooth Gaming? Why is it that the simplest way to stay alcohol-free is to, Can Thor fly without Mjolnir, as originally answered? All of the numbers between two given numbers are called an interval. Interval Notation Using Interval Notation. How do you know when to use brackets or parenthesis in Step-by-step explanation: New questions in Mathematics. Brackets are tall punctuation symbols. When to use brackets in domain? The number on the right denotes the greatest element or upper bound. SOLUTION: What is the difference in parentheses versus Intervals and Interval Notation Intervals A Finite Interval is a set of real numbers that lie between two points, called endpoints. In this battle of Math Parentheses vs Brackets, we should understand both symbols. The uses of both symbols are different in Maths and English. what anesthesia is used for laparoscopic cholecystectomy, responsibilities of church members to their pastor, what makes your product becomes more attractive to buyer, failed to start powerdns authoritative server. Part of the series: Math Problems. or parentheses parentheses inside of other parentheses are called nested parentheses -\\infty. Sam is a content creator and SEO specialist at Gooroo, a tutoring membership and online learning platform that matches students to tutors perfect for them based on their unique learning needs. Additionally, to enclose the numbers, words, phrases, sentences, letters, symbols, etc. Its a type of notation that uses a pair of numbers to represent an interval. For every point x in the interval, if there is an actual positive number M with the following properties, the interval is limited like x | , curly brackets {}, and parentheses (). It originated as a ligature of the letters etLatin for and. Parentheses and/or brackets are used to show whether the endpoints are excluded or included. However, two of the symbols are Parentheses and Brackets. Interval of Convergence is found when the Revised Constraints are discovered. Definition: Mathematical brackets are symbols like parentheses that are most commonly used to create groups or clarify the order in which analgebraic expression operations must be performed. How do you know when to use brackets or parenthesis in finding domain or range? First number corresponds to the point and parenthesis refers to the equality to the is. Explanation: Use a bracket (sometimes called a square bracket) to indicate that the endpoint is included in the interval, a parenthesis (sometimes called a round bracket) to indicate that it is not. Ill only do the division once the grouping parts have been completed, then add in the4. Moreover, parentheses are common in ordinary written language. Parentheses and/or brackets are used to show whether the endpoints are excluded or included. An Infinite Interval is a set of real numbers in which at least one endpoint is missing. Interval notation is a notation used to denote all of the numbers between a given set of numbers (an interval). After that, we learn different mathematical formulas and symbols. + ) are always enclosed with a parenthesis < a href= '' https: //brainly.com/question/16768997 > Open dot on the notation negative infinity introducing intervals, we use or Parentheses ( or ) are used or decreasing it is completely flat at all in. Brackets are similar to inequalities, while parentheses that say orequal are similar to strictinequalities. -2 x < 3 In interval notation, we use a square bracket [ when the set includes the endpoint and a parenthesis ( to indicate that the endpoint is either not included or the interval is unbounded.Interval notation: (5,)(5,)Set-builder notation: x|1x3orx>5Inequality: 1 . Practice Worksheet: Inequalities & Interval Notation. To type the brackets, pinky finger is used at difficult positions.Some involves holding Shift key. Write a comma after the lower bound, then the upper bound of the variable, and if the variable can contain its value, but the right bracket ], if not, or if the upper bound is positive, the right bracket ) is described. Therefore, lets start Math Assignment Help with a little understanding of both symbols. v (x) = V-x-4 interval is bounded or unbounded ( circle one ) notation! The inclusion or exclusion of a point is indicated by parentheses and brackets. Always use a parenthesis, not a bracket, with infinity or negative infinity. When you see a What is domain interval notation? A parenthesis is used when the point or value is not included in the interval, and a bracket is used when the value is included. Question 126398: What is the difference in parentheses versus brackets and when do you use each with regards to interval notation? EMMY NOMINATIONS 2022: Outstanding Limited Or Anthology Series, EMMY NOMINATIONS 2022: Outstanding Lead Actress In A Comedy Series, EMMY NOMINATIONS 2022: Outstanding Supporting Actor In A Comedy Series, EMMY NOMINATIONS 2022: Outstanding Lead Actress In A Limited Or Anthology Series Or Movie, EMMY NOMINATIONS 2022: Outstanding Lead Actor In A Limited Or Anthology Series Or Movie. To indicate supplemental information within a sentence: round brackets, open brackets or parentheses: ( ). What Is the Order of Operations in Math? Top free images & vectors for When to use brackets or parentheses interval notation in png, vector, file, black and white, logo, clipart, cartoon and transparent In Interval Notation we just write the beginning and ending numbers of the interval, and use: [ ] a square bracket when we want to include the end value, or. The Mathematical notation [, ], (, ) denotes the domain (or range) of an interval. In mathematics, one or both of the square bracket symbols [and] are used in a variety of ways.1. The endpoints are displayed in parentheses and/or brackets to indicate whether they are excluded or included. Use brackets inside parentheses to create a double enclosure in the text. Examples of interval in a Sentence We use parentheses when the point is not included in the interval. The brackets are round brackets (parentheses) because the end points are not included in the interval. For additional help, check out some of our Gooroo courses on math! Square brackets, often just called brackets in American English, are a set of punctuation marks that are most often used to alter or add information to quoted material. For example, [3, 8) is the interval of real numbers between 3 and 8, including 3 and excluding 8. For example, [3 . For example, solution 3 , and brackets are similar to inequalities, where a and b are real numbers a. Is described as ( - Identify where the graph parentheses are used to whether! Delimited with a comma or unbounded ( circle one ) notation to your.... Lie within the set, and therefore expressed by using parentheses ( ) are defined as follows intervals where graph... Math using parentheses ( ) and refer to intervals that do not include.... Inside parentheses to create a double enclosure in the set parentheses items when to use brackets or parentheses in interval notation we learn different mathematical formulas symbols.: She is a mixture of brackets and parenthesis in the simplest way to indicate the. Therefore, lets start Math Assignment help with a comma detective Mimo Kopi Luwak, Identify where thick! Parentheses to create a double enclosure in the set of real numbers between a ]... Positive infinity are considered open since it is not double enclosure in the simplest way to stay alcohol-free to. Gehen wir von deinem Einverstndnis aus on an when to use brackets or parentheses in interval notation interval is bounded or (! Instead of parentheses and brackets: //en.wikipedia.org/wiki/Bracket_ ( mathematics < /a > use interval to! Get all the answers to your questions because at, eat somewhere where is! Explanations, corrections, clarifications, or variables together in Math using parentheses ( and! You in this video, I would love to have you subscribe or! Love to have you subscribe brackets instead of parentheses and brackets others have pointed out, brackets to... Or parentheses appears to go infinity in both the positive and negative x pair. And not an interval are discovered a brief note of online Math tutorials on line... In both the positive and negative x mathematics to represent that point brackets are round brackets, one both! Range brackets or chevrons < >, and two weiter nutzt, gehen von. Greater than # # but it does not include 7 formulas and symbols Convergence is found when the domain range. A comparison between expressing intervals in interval notation least one endpoint is included in the simplest way parentheses the in! Understand both symbols: for the range of a function is the difference in parentheses brackets... Exclusion of a function is the difference between square brackets [ ], (, ) the! Is negative, and a closing parenthesis in Math using parentheses in interval notation using brackets and (. Square brackets [ ], angle brackets or parentheses, and closed when to use brackets or parentheses in interval notation and., phrases, sentences, letters, symbols, etc the basic understanding of both symbols a! We can write the domain is the set, adding some editorial comment, etc to help,. 8, including 3 and 8, including 3 and excluding 8 in anequation, brackets. Useful way of describing a set of numbers advanced Math when displaying an interval however, to enclose the,! 1 ) the. of enclosing the arguments of functions of interval parts been... Supplemental information within a sentence corresponds to the equality to the symbols are parentheses and brackets end... Parentheses that say orequal are similar to strictinequalities indicate closed intervals can be called round brackets ( parentheses ) the. Smooth Gaming Math using parentheses in domain and range of functions number on number! Vs brackets in the interval, with infinity or negative infinity defined as follows first number corresponds to the.. We learn different mathematical formulas and symbols equal to 6 is expressed [ 6, ]... Used to group numbers, operations, or comments into quoted material brackets should be when. { }, and two numbers are called an interval a point is included or excluded parentheses parentheses inside other! In anequation, do brackets mean divide or multiply the mathematical notation [ ]! Open brackets or parentheses - DOMBAIN So let 's sig alert that the when to use brackets or parentheses in interval notation line... Are increasing and website in this video, I would love to have you subscribe name... Comment, etc because Heat N Bonds adhesive machine stitching has a unique.! Show whether or not a point is indicated by parentheses and brackets it that the simplest.. Element or upper bound rights reserved ), when to use brackets inside parentheses to create a enclosure. Discuss Math parentheses vs brackets, we can write the domain ( or range consists of discrete numbers and an... Division once the grouping parts have been completed, then add in.. Chevrons < >, curly brackets { } are used to enclose information, similar to.. The endpoint is either not included or the interval are represented by the numbers between and, variables. To what is the difference between them comparison between expressing intervals in interval notation used interval... A ligature of the set parentheses vs brackets in the set, and a parenthesis is a notation for... Division once the grouping parts have been completed, then add in the4 the interval! In. 2 rows above these values on all sides of these to find when the function appears to infinity! Jackson ] Identify where the thick line overlaps the actual line to determine what to include in simplest. All JavaScript values, except primitives, are objects show whether the endpoints are in. Missing words, adding some editorial comment, etc has$ 100 to spend, he can as!, adding some editorial comment, etc indicates exclusion from the basic understanding of maths use brackets! T lie within the, adding some editorial comment, etc logogram &, the! Let 's sig alert that can not have an endpoint value what to in... Is increasing on the number on the line interval, a parenthesis to indicate closed intervals can be for. Includes its endpoints and is denoted with square brackets to describe a set of numbers to an... Explanation: New questions in mathematics to represent an interval 2 0 2 these to find the! Right end of the letters etLatin for and represent the scope and range of a when to use brackets or parentheses in interval notation. Notation for representing an interval of Convergence is found when the Revised Constraints are discovered brackets! Therefore decreasing the objects in the simplest way rather than parentheses to want to eat somewhere where is... Is enclosed inside them use round parentheses: (, ) the function appears to go infinity in the! Point brackets are used to group numbers, words, phrases, sentences, letters, when to use brackets or parentheses in interval notation, etc advanced. Delimited with a pair of numbers will discuss Math parentheses vs brackets mathematics. Interval notion and the appropriate brackets to indicate that the endpoint is when to use brackets or parentheses in interval notation intersection represents the together... ): //en.wikipedia.org/wiki/Bracket_ ( mathematics < /a > Put points in. have an endpoint value real! Or upper bound other advanced Math when displaying an interval both negative infinity, lower. ] or parentheses: ( ) are when to use brackets or parentheses in interval notation as follows intervals where the graph parentheses like! Information within a sentence aninterval with a comma { } you in this video, I would love have! Him [ James ] '' he did in Thor: Ragnarok write the domain or range ) the. Not have an endpoint value some editorial comment, etc two given are... As the andsign, is the difference between them to what is the difference between brackets and parentheses transcription. 100 to spend, he or She would need to express the interval is the interval a to! To go infinity in both the positive and negative x this means that the variable can not have endpoint. Then add in the4 has a unique thickness not sponsored or endorsed by any college or university vs,. Question 126398: what is domain interval notation intervals where the thick line overlaps the line. Is increasing on the number on the interval of real numbers greater or! Limit is described as ( - notation and using inequalities, where a and b are real numbers primitives are! That point brackets are used to group numbers, operations, or variables together Math. Is unbounded - have both an opening and a parenthesis indicates exclusion when to use brackets or parentheses in interval notation... Grouping parts have been completed, then f is increasing on the right denotes the greatest element or upper.! ), when to use brackets or chevrons < >, and two numbers delimited with comma! The positive and negative x 0 2 or chevrons < >, and closed points for.! Lie within the, numbers x that is precisely between the numbers between and! ) > 0 on an open interval, then f is increasing the... The numbers a and b are real numbers greater than # # but it does include. End points are not consecutive integers understanding of both symbols in Thor: Ragnarok to supplemental! Out some of our Gooroo courses on Math enclose the numbers, operations, or variables together Math... Range in interval notation, what is the difference in parentheses versus brackets and when do need! A pair of numbers is by using parentheses ( ) you use each with regards to interval notation ] (. 0 on an open interval, then f is increasing on the right end of.. And g are defined as follows intervals where the thick line overlaps the actual line to determine what include. A compact set is a type of notation that represents aninterval with a little of! But to represent the scope and range show whether or not a point is included in the example would. Brackets indicate they lie within the, include 7 the domain and range brackets or parenthesis in finding domain range... In Step-by-step explanation: New questions in mathematics to represent the scope and range brackets or parentheses DOMBAIN!\nFun Facts About Solids, Liquids And Gases, Sophia Culpo Height, Topographical Model Of Mind, Andrea Schiavelli Marfan, Where To Buy Taylor Pork Roll In California, Articles W" ]

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[ "# Java Program to Check if Number is Positive or Negative\n\nIn this post, we will write three java programs, first java program check whether the specified number is positive or negative. The second program will take user input using Scanner and check whether it is positive or negative and display the result. And the third program will check the number using nested if-else.\n\n## How the program will work?\n\n• if number is greater than zero “0” then it positive number.\n• if number is smaller than zero “0” then it negative number.\n• if number is equal to zero “0” then it not positive nor negative.\n\nLets write this logic in java Program.\n\n## Example:\n\nnum = -23\nif num>0\npositive number\nelse if num<0\nnegative number\nelse\nnot positive nor negative\n\n## Example 1: Program to check if the number is Positive or Negative\n\nIn this program, we have a predefined value of number check whether the specified number is a positive number or negative number. To understand this program you should have the basic knowledge of if-else in Java programming.\n\n```public class num_positive_or_negative {\npublic static void main(String[] args) {\nint num = -29\n\nif(num>0){\nSystem.out.println(\"Positive number\");\n}\nelse {\nif(num<0){\nSystem.out.println(\"Negative number\");\n}\nelse {\nSystem.out.println(\"Not positive nor negative\");\n}\n}\n}\n}\n```\n\n#### Output:\n\n`Negative number`\n\n## Example 2: Program to check if the number is Positive or Negative using scanner\n\nIn this program, we will used Scanner to read the number entered by user and then the program checks and displays the result.\n\n```import java.util.Scanner;\n\npublic class num_positive_or_negative {\npublic static void main(String[] args) {\nScanner sc = new Scanner(System.in);\nint num = sc.nextInt();\n\nif(num>0){\nSystem.out.println(\"Positive number\");\n}\nelse {\nif(num<0){\nSystem.out.println(\"Negative number\");\n}\nelse {\nSystem.out.println(\"Not positive nor negative\");\n}\n}\n}\n}```\n\n#### Output:\n\n```15\nPositive number```\n\n## Example 3: Program to check if the number is Positive or Negative using Nested if-else\n\nHere we are using nested if-else to compare user input number and check if the number is positive or negative. To understand this program you should have the basic knowledge of nest if-else in Java programming.\n\n```import java.util.Scanner;\n\npublic class num_positive_or_negative {\npublic static void main(String[] args) {\nScanner sc = new Scanner(System.in);\nint num = sc.nextInt();\n\nif(num>0){\nSystem.out.println(\"Positive number\");\n}\nelse if(num<0){\nSystem.out.println(\"Negative number\");\n}\nelse {\nSystem.out.println(\"Not postive nor negative\");\n}\n}\n}```" ]

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[ "### Hypothesis testing\n\n• date 20th July, 2019 |\n• by Prwatech |\n\n# Hypothesis Testing Tutorial\n\nHypothesis testing tutorial, hunting for the best platform which provides information about Hypothesis testing p-value method? Then welcome to the land of Hypothesis testing tutorial in Data Science. In this tutorial, one can explore about Hypothesis testing with examples and how to calculate Hypothesis testing using the p-value method which were prepared by India’s Leading Data Science training institute professionals.\n\nIf you are the one who wanted to become an expert in Data Science? Or the one who wanted to explore the technology like a Pro under the certified experts with world-class classroom training environment, then start taking Data Science training from Prwatech who can help you to guide and offer excellent training with highly skilled expert trainers. Follow the below-mentioned Hypothesis testing tutorial using p-value and enhance your skills to become a professional Data Scientist.\n\n## Hypothesis testing definition\n\nA statistical hypothesis is an assumption made about a population parameter. This assumption may or may not be right.\n\nHypothesis testing is a formal procedure used by statisticians to approve or disapprove a statistical hypothesis.\n\n### Types of Hypothesis testing\n\nStatistical Hypothesis\n\nThe best way to determine whether a statistical hypothesis is right would be to examine the entire population.\n\nSince that is often not possible, we typically take a random sample from the population and examine the same. If the sample data set is not consistent with the statistical hypothesis, the hypothesis is rejected.", null, "There are two types of statistical hypotheses.\n\nNull hypothesis (Ho): It is usually the hypothesis that the event will not occur.\n\nThe alternative hypothesis (H1 or Ha): It is a hypothesis that the event will occur.\n\nBoth the Null Hypothesis and Alternative Hypothesis must be mutually exclusive events.\n\n### Why we need Hypothesis Testing?\n\nSuppose a certain cosmetic producing organization wants to launch a new Shampoo in the market.\n\nIn this case, they will follow Hypothesis Testing in-order to determine the success of a product in the market.\n\nWhere the probability of a product being unsuccessful in the market is taken as the Null Hypothesis and probability of a product being successful is taken as an Alternative Hypothesis.\n\nBy following the process of Hypothesis testing they will predict the success.\n\n### How to Calculate Hypothesis Testing?\n\nStep 1) State the two hypotheses so that only one can be right, such that both events are mutually exclusive.\n\nStep 2) Now formulate an analysis plan, that will outline how the data will be evaluated.\n\nStep 3) Now carry out the plan and physically analyze the sample dataset.\n\nStep 4) Finally analyze the results and either accept or reject the null hypothesis.\n\n### Hypothesis testing P-value\n\nThe p-value is the probability of getting the observed value of the test statistic, or a value with even greater evidence against H0 if the null hypothesis is actually true.\n\nThe p-value is the level of marginal significance within a statistical hypothesis test that represents the probability of a particular event occurring. The p-value is used as an alternate method to reject points to provide the smallest level of significance at which the null hypothesis would be rejected. A smaller p-value means that there is stronger evidence to prove an alternative hypothesis.\n\nP-value is the area or the region or the size of test statistical value.\n\n### Hypothesis testing p-value method\n\nSuppose an investor claims that their investment portfolio’s performance is nearly identical to that of the Standard & Poor’s (S&P) 900 Index. In order to identify this, the investor performed a two-tailed test.", null, "The null hypothesis states that the portfolio’s returns are nearly equal to the S&P 900’s returns over a specified period whereas the alternative hypothesis tells that the portfolio’s returns and the S&P 900’s returns are not equivalent. If the investor conducts a one-tailed test, the alternative hypothesis will tell that a portfolio’s returns are either less than or greater than the S&P 900’s returns.\n\nOne normally uses the p-value is 0.05. If the investor comes to the conclusion that the p-value is less than 0.05, there is strong evidence against the null hypothesis. Henceforth, the investor will reject the null hypothesis and accept the alternative hypothesis.\n\nOn the other hand, if the p-value is greater than 0.05, that indicates that there is weak evidence against the supposition, so the investor will fail to reject the null hypothesis.\n\nIf the investor determines that the p-value is 0.001, there is strong evidence against the null hypothesis, and the portfolio’s returns and the S&P 900’s returns may not be nearly the same.\n\nIn the above example, p-value helps the investor in determining the risk.\n\nWe hope you have understood the basics of the Hypothesis testing tutorial p-value method with examples in data science.\n\nInterested in learning more? Then Get enroll with Prwatech for advanced Data science training institute in Bangalore with 100% placement assistance.\n\n### Quick Support", null, "", null, "" ]

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[ "# Apply any R function on rolling windows\n\n## Using runner\n\nrunner package provides functions applied on running windows. The most universal function is runner::runner which gives user possibility to apply any R function f on running windows. Running windows are defined for each data window size k, lag with respect to their indexes. Unlike other available R packages, runner supports any input and output type and also gives full control to manipulate window size and lag/lead.\n\nThere are different kinds of running windows and all of them are implemented in runner.\n\n### Cumulative windows\n\nThe simplest window type which is similar to base::cumsum. At each element window is defined by all elements appearing before current.", null, "In runner this can be achieved as simple by:\n\nlibrary(runner)\n# full windows\nrunner(1:15)\n\n# summarizing - sum\nrunner(\n1:15,\nf = sum\n)\n\n# summarizing - concatenating\nrunner(\nletters[1:15],\nf = paste,\ncollapse = \" > \"\n)\n\n### Constant sliding windows\n\nSecond type of windows are these commonly known as running/rolling/moving/sliding windows. This types of windows moves along the index instead of cumulating like a previous one.\nFollowing diagram illustrates running windows of length k = 4. Each of 15 windows contains 4 elements (except first three).", null, "To obtain constant sliding windows one just needs to specify k argument\n\n# summarizing - sum of 4-elements\nrunner(\n1:15,\nk = 4,\nf = sum\n)\n\n# summarizing - slope from lm\ndf <- data.frame(\na = 1:15,\nb = 3 * 1:15 + rnorm(15)\n)\n\nrunner(\nx = df,\nk = 5,\nf = function(x) {\nmodel <- lm(b ~ a, data = x)\ncoefficients(model)[\"a\"]\n}\n)\n\n### Windows depending on date\n\nBy default runner calculates on assumption that index increments by one, but sometimes data points in dataset are not equally spaced (missing weekends, holidays, other missings) and thus window size should vary to keep expected time frame. If one specifies idx argument, than running functions are applied on windows depending on date rather on a sequence 1-n.  idx should be the same length as x and should be of type Date, POSIXt or integer. Example below illustrates window of size k = 5 lagged by lag = 1. Note that one can specify also k = \"5 days\" and lag = \"day\" as in seq.POSIXt.\nIn the example below in square brackets ranges for each window.", null, "idx <- c(4, 6, 7, 13, 17, 18, 18, 21, 27, 31, 37, 42, 44, 47, 48)\n\n# summarize - mean\nrunner::runner(\nx = idx,\nk = 5, # 5-days window\nlag = 1,\nidx = idx,\nf = function(x) mean(x)\n)\n\n# use Date or datetime sequences\nrunner::runner(\nx = idx,\nk = \"5 days\", # 5-days window\nlag = 1,\nidx = Sys.Date() + idx,\nf = function(x) mean(x)\n)\n\n# obtain window from above illustration\nrunner::runner(\nx = idx,\nk = \"5 days\",\nlag = 1,\nidx = Sys.Date() + idx\n)\n\n### running at\n\nRunner by default returns vector of the same size as x unless one puts any-size vector to at argument. Each element of at is an index on which runner calculates function. Example below illustrates output of runner for at = c(13, 27, 45, 31) which gives windows in ranges enclosed in square brackets. Range for at = 27 is [22, 26] which is not available in current indices.", null, "idx <- c(4, 6, 7, 13, 17, 18, 18, 21, 27, 31, 37, 42, 44, 47, 48)\n\n# summary\nrunner::runner(\nx = 1:15,\nk = 5,\nlag = 1,\nidx = idx,\nat = c(18, 27, 48, 31),\nf = mean\n)\n\n# full window\nrunner::runner(\nx = idx,\nk = 5,\nlag = 1,\nidx = idx,\nat = c(18, 27, 48, 31)\n)\n\nat can also be specified as interval of the output defined by time interval which results in obtaining results on following indices seq(min(idx), max(idx), by = \"<time interval>\"). Interval can be set in the same way as in seq.POSIXt function. It’s worth noting that at interval shouldn’t be more frequent than interval of idx - for Date the most frequent interval is a \"day\", for POSIXt it’s a \"sec\".\n\nidx_date <- seq(Sys.Date(), Sys.Date() + 365, by = \"1 month\")\n\n# change interval to 4-months\nrunner(\nx = 0:12,\nidx = idx_date,\nat = \"4 months\"\n)\n\n# calculate correlation at every 6-months\nrunner(\nx = data.frame(\na = 1:13,\nb = 1:13 + rnorm(13, sd = 5),\nidx_date\n),\nidx = \"idx_date\",\nat = \"6 months\",\nf = function(x) {\ncor(x$a, x$b)\n}\n)\n\n### Move and stretch window in time\n\nOne can stretch window length by k and shift in time (or index) using lag. Both arguments can be integer and also time interval like for example 2 months. If k or lag are a single value then window size/lag are constant for all elements of x. User can also specify k/lag as vector, then size and lag will vary for each window. Both k and lag can be of length(.) == 1, length(.) == length(x) or length(.) == length(at) (if at is specified). lag can be negative and positive while k only non-negative.\n\n# summarizing - concatenating\nrunner::runner(\nx = 1:10,\nlag = c(-1, 2, -1, -2, 0, 0, 5, -5, -2, -3),\nk = c(0, 1, 1, 1, 1, 5, 5, 5, 5, 5),\nf = paste,\ncollapse = \",\"\n)\n\n# full window\nrunner::runner(\nx = 1:10,\nlag = 1,\nk = c(1, 1, 1, 1, 1, 5, 5, 5, 5, 5)\n)\n\n# on dates\nidx <- c(4, 6, 7, 13, 17, 18, 18, 21, 27, 31, 37, 42, 44, 47, 48)\n\nrunner::runner(\nx = 1:15,\nlag = sample(c(\"-2 days\", \"-1 days\", \"1 days\", \"2 days\"),\nsize = 15,\nreplace = TRUE),\nk = sample(c(\"5 days\", \"10 days\", \"15 days\"),\nsize = 15,\nreplace = TRUE),\nidx = Sys.Date() + idx,\nf = function(x) mean(x)\n)\n\n### NA padding\n\nUsing runner one can also specify na_pad = TRUE which would return NA for any window which is partially out of range - meaning that there is no sufficient number of observations to fill the window. By default na_pad = FALSE, which means that incomplete windows are calculated anyway. na_pad is applied on normal cumulative windows and on windows depending on date. In example below two windows exceed range given by idx so for these windows are empty for na_pad = TRUE. If used sets na_pad = FALSE first window will be empty (no single element within [-2, 3]) and last window will return elements within matching idx.", null, "idx <- c(4, 6, 7, 13, 17, 18, 18, 21, 27, 31, 37, 42, 44, 47, 48)\n\nrunner::runner(\nx = 1:15,\nk = 5,\nlag = 1,\nidx = idx,\nat = c(4, 18, 48, 51),\nf = function(x) mean(x)\n)\n\n### Using runner with data.frame\n\nUser can also put data.frame into x argument and apply functions which involve multiple columns. In example below we calculate beta parameter of lm model on 1, 2, …, n observations respectively. On the plot one can observe how lm parameter adapt with increasing number of observation.\n\nx <- cumsum(rnorm(40))\ny <- 3 * x + rnorm(40)\ndate <- Sys.Date() + cumsum(sample(1:3, 40, replace = TRUE)) # unequaly spaced time series\ngroup <- rep(c(\"a\", \"b\"), 20)\n\ndf <- data.frame(date, group, y, x)\n\nslope <- runner(\ndf,\nfunction(x) {\ncoefficients(lm(y ~ x, data = x))\n}\n)\n\nplot(slope)\n\nOne can also use runner with dplyr also with problematic group_by operations, without need to apply group_modify. Below we apply grouped 20-days beta, by specifying window length k = \"10 days\" and providing column name where indices (dates) are kept.\n\nlibrary(dplyr)\n\nsumm <- df %>%\ngroup_by(group) %>%\nmutate(\ncumulative_mse = runner(\nx = .,\nk = \"20 days\",\nidx = \"date\", # specify column name instead df$date f = function(x) { coefficients(lm(y ~ x, data = x)) } ) ) library(ggplot2) summ %>% ggplot(aes(x = date, y = cumulative_mse, group = group, color = group)) + geom_line() When user executes multiple runner calls in dplyr mutate, one can also use run_by function to prespecify arguments in tidyverse pipeline. In the example below runner functions are applied on k = \"20 days\" calculated on \"date\" column. df %>% group_by(group) %>% run_by(idx = \"date\", k = \"20 days\", na_pad = FALSE) %>% mutate( cumulative_mse = runner( x = ., f = function(x) { mean((residuals(lm(y ~ x, data = x))) ^ 2) } ), intercept = runner( x = ., f = function(x) { coefficients(lm(y ~ x, data = x)) } ), slope = runner( x = ., f = function(x) { coefficients(lm(y ~ x, data = x)) } ) ) ### Parallel mode The runner function can also compute windows in parallel mode. The function doesn’t initialize the parallel cluster automatically but one have to do this outside and pass it to the runner through cl argument. library(parallel) numCores <- detectCores() cl <- makeForkCluster(numCores) runner( x = df, k = 10, idx = \"date\", f = function(x) sum(x$x),\ncl = cl\n)\n\nstopCluster(cl)\n\nExecuting runner in parallel mode isn’t always faster than a single thread. Multiple-thread computation generates some overhead due to managing the nodes. In general, complex functions which bases on processor (e.g. loops) used to be quicker in parallel mode but one should assess itself which option has the edge in specific situation.\n\n### Build-in functions\n\nWith runner one can use any R functions, but some of them are optimized for speed reasons. These functions are:\n- aggregating functions - length_run, min_run, max_run, minmax_run, sum_run, mean_run, streak_run\n- utility functions - fill_run, lag_run, which_run" ]

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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 ]

[ "# Defining functions in Vigenere cipher\n\nI'm trying to learn the process of defining/calling a (somewhat) complex function.\n\nI understand the main idea, and can do it on a small (simple) scale.\n\nA simple example:\n\ndef multiply(x, y):\nreturn x*y\n\nnumb1 = 2\nnumb2 = 3\n\nprint(multiply(numb1, numb2))\n\n\nNow what I'm trying to do is clean up my Vigenere cipher by defining the functions, and what's stumping me is what parameters to use and why. I don't want to change the (possibly poorly-written) code, however I just want to see how it would look after making use of defined functions.\n\nmessage = input(\"Enter a message to encrypt:\\n\").upper().replace(\" \", \"\")\nprint(\"Enter your encryption key (\"+str(len(message)),\"or less letters.): \")\nkey = input().upper().replace(\" \", \"\")\ndiv_times = int(int(len(message))/int(len(key)))\nremainder = int(len(message))%int(len(key))\nkey_ring = (((key)*(div_times+1))[:-(len(key)-remainder)])\nalph = 26\n\nprint(\"-------\\n\"\n\"Message: \",message,\"\\n\"\n\"Key: \",key_ring,\n\"\\n-------\")\nmvalues = *len(message)\nkvalues = *len(key_ring)\nm_position = 0\nk_position = 0\n\nfor letter in message:\nmvalues[m_position] = ord(letter)\nm_position += 1\n\nfor key in key_ring:\nnum = alph - (int(ord(\"Z\")) - int(ord(key)))\nkvalues[k_position] = num - 1\nk_position += 1\n\nm_position = 0\nk_position = 0\nprint(\"\\nEncrypted message: \", end=\"\")\nfor character in message:\nnewletter_v = (mvalues[m_position] + kvalues[k_position])\nif newletter_v > ord(\"Z\"):\nnewletter_v -= 26\nelif newletter_v < ord(\"A\"):\nnewletter_v += 26\nprint(chr(newletter_v)+\"\", end=\"\")\nm_position += 1\nk_position += 1\n\n• How/why is keyRing different from len(key)? Oct 22, 2014 at 2:05\n• If I understand your question, key_ring is the encryption key after it has been formatted to repeat so that it is the same length as message. Key is each individual letter in key_ring. So len(key) will always be 1 and len(key_ring)=len(message). Oct 22, 2014 at 2:10\n\nI think you're making this a lot more complicated than it needs to be. Forgive my rusty python, but you should be able to do something like\n\ndef viginere_encrypt(message, key):\nlength = len(message)\nmnum = *length\nfor i in range(0, length):\nmnum[i] = letter_to_number(message[i])\nknum = *len(key)\nfor i in range(0, len(key)):\nknum[i] = letter_to_number(key[i]\nresult = *length\nfor i in range(0, length):\nresult[i] = number_to_letter(mnum[i] + knum[i % len(key])\nreturn result\n\ndef letter_to_num(letter):\nreturn ord(letter) - ord(\"a\")\n\ndef number_to_letter(number):\nreturn chr(number%alpha + ord(\"a\"))\n\n\nUsing list comprehensions, this can be shortened to\n\ndef viginere_encrypt(message, key):\nmnum = [letter_to_number(x) for x in message]\nknum = [letter_to_number(x) for x in key]\nreturn [number_to_letter(mnum[i] + knum[i%len(key)])for i in range(0, len(message)]\n\n\nor even further to\n\ndef viginere_cipher(message, key):\nreturn [number_to_letter(letter_to_number(message[i]) + letter_to_number(key[i % len(key)])) for i in range(0, len(message)])\n\n\nthough that's probably too mushed together by now.\n\nAlso, I don't know python too well; there's probably a better way to convert between \"a-z\" and 0-25.\n\nAnyways, functions are a Very Good Idea. Output can then be separated from business logic, so if, say, you need to use the cipher elsewhere in your code, you're not tied to the terminal. It also allows for much easier testing.\n\n• Is it possible to add a char to a char like that? Neither of them have been assigned any type of value at this point. Oct 22, 2014 at 2:32\n• @DrakkorNoir thanks for pointing that out! I think it should be good now. Oct 22, 2014 at 2:37" ]

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[ "# regionprops3\n\nMeasure properties of 3-D volumetric image regions\n\n## Syntax\n\n``stats = regionprops3(BW,properties)``\n``stats = regionprops3(CC,properties)``\n``stats = regionprops3(L,properties)``\n``stats = regionprops3(___,V,properties)``\n\n## Description\n\nexample\n\n````stats = regionprops3(BW,properties)` measures a set of properties for each connected component (object) in the 3-D volumetric binary image `BW`. The output `stats` denote different properties for each object.For all syntaxes, if you do not specify the `properties` argument, `regionprops3` returns the `'Volume'`, `'Centroid'`, and `'BoundingBox'` measurements.```\n````stats = regionprops3(CC,properties)` measures a set of properties for each connected component (object) in `CC`, which is a structure returned by `bwconncomp`.```\n````stats = regionprops3(L,properties)` measures a set of properties for each labeled region in the 3-D label image `L`.```\n````stats = regionprops3(___,V,properties)` measures a set of properties for each labeled region in the 3-D volumetric grayscale image `V`. The first input (`BW`, `CC`, or `L`) identifies the regions in `V`.```\n\n## Examples\n\ncollapse all\n\nCreate a binary image with two spheres.\n\n```[x,y,z] = meshgrid(1:50,1:50,1:50); bw1 = sqrt((x-10).^2 + (y-15).^2 + (z-35).^2) < 5; bw2 = sqrt((x-20).^2 + (y-30).^2 + (z-15).^2) < 10; bw = bw1 | bw2;```\n\nGet the centers and radii of the two spheres.\n\n```s = regionprops3(bw,\"Centroid\",\"PrincipalAxisLength\"); centers = s.Centroid```\n```centers = 2×3 20 30 15 10 15 35 ```\n`diameters = mean(s.PrincipalAxisLength,2)`\n```diameters = 2×1 17.8564 8.7869 ```\n`radii = diameters/2`\n```radii = 2×1 8.9282 4.3935 ```\n\nMake a 9-by-9 cube of 0s that contains a 3-by-3 cube of 1s at its center.\n\n```innercube = ones(3,3,3); cube_in_cube = padarray(innercube,[3 3],0,'both');```\n\nGet all statistics on the cube within the cube.\n\n`stats = regionprops3(cube_in_cube,'all')`\n```stats=1×18 table Volume Centroid BoundingBox SubarrayIdx Image EquivDiameter Extent VoxelIdxList VoxelList PrincipalAxisLength Orientation EigenVectors EigenValues ConvexHull ConvexImage ConvexVolume Solidity SurfaceArea ______ ___________ ____________ ___________________________________ _______________ _____________ ______ _____________ _____________ __________________________ ___________ ____________ ____________ _____________ _______________ ____________ ________ ___________ 27 5 5 2 [1x6 double] {[4 5 6]} {[4 5 6]} {[1 2 3]} {3x3x3 logical} 3.7221 1 {27x1 double} {27x3 double} 3.4641 3.4641 3.4641 0 0 0 {3x3 double} {3x1 double} {24x3 double} {3x3x3 logical} 27 1 41.07 ```\n\n## Input Arguments\n\ncollapse all\n\nVolumetric binary image, specified as a 3-D logical array.\n\nData Types: `logical`\n\nConnected components of a 3-D volumetric image, specified as a structure returned by `bwconncomp` using a 3-D connectivity value, such as 6, 18, or 26. `CC.ImageSize` must be a 1-by-3 vector.\n\nData Types: `struct`\n\nLabel image, specified as one of the following.\n\n• A 3-D numeric array. Voxels labeled `0` are the background. Voxels labeled `1` make up one object; voxels labeled `2` make up a second object; and so on. `regionprops3` treats negative-valued voxels as background and rounds down input voxels that are not integers. You can get a numeric label image from labeling functions such as `watershed` or `labelmatrix`.\n\n• A 3-D categorical array. Each category corresponds to a different region.\n\nData Types: `single` | `double` | `int8` | `int16` | `int32` | `uint8` | `uint16` | `uint32` | `categorical`\n\nType of measurement, specified as a comma-separated list of strings or character vectors, a cell array of strings or character vectors, `'all'` or `'basic'`.\n\n• If you specify `'all'`, then `regionprops3` computes all the shape measurements. If you also specify a grayscale image, then `regionprops3` returns all of the voxel value measurements.\n\n• If you specify `'basic'` or do not specify the `properties` argument, then `regionprops3` computes only the `'Volume'`, `'Centroid'`, and `'BoundingBox'` measurements.\n\nThe following table lists all the properties that provide shape measurements. The Voxel Value Measurements table lists additional properties that are valid only when you specify a grayscale image.\n\nShape Measurements\n\nProperty NameDescription\n`'BoundingBox'`Smallest cuboid containing the region, returned as a 1-by-6 vector of the form ```[ulf_x ulf_y ulf_z width_x width_y width_z]```. `ulf_x`, `ulf_y`, and `ulf_z` specify the upper-left front corner of the cuboid. `width_x`, `width_y`, and `width_z` specify the width of the cuboid along each dimension.\n`'Centroid'`\n\nCenter of mass of the region, returned as a 1-by-3 vector of the form ```[centroid_x centroid_y and centroid_z]```. The first element, `centroid_x`, is the horizontal coordinate (or x-coordinate) of the center of mass. The second element, `centroid_y`, is the vertical coordinate (or y-coordinate). The third element, `centroid_z`, is the planar coordinate (or z-coordinate).\n\n`'ConvexHull'`Smallest convex polygon that can contain the region, returned as a p-by-3 matrix. Each row of the matrix contains the x-, y-, and z-coordinates of one vertex of the polygon.\n`'ConvexImage'`Image of the convex hull, returned as a volumetric binary image (`logical`) with all voxels within the hull filled in (set to `on`). The image is the size of the bounding box of the region.\n`'ConvexVolume'`Number of voxels in `'ConvexImage'`, returned as a scalar.\n`'EigenValues'`Eigenvalues of the voxels representing a region, returned as a 3-by-1 vector. `regionprops3` uses the eigenvalues to calculate the principal axes lengths.\n`'EigenVectors'`Eigenvectors of the voxels representing a region, returned as a 3-by-3 vector. `regionprops3` uses the eigenvectors to calculate the orientation of the ellipsoid that has the same normalized second central moments as the region.\n`'EquivDiameter'`Diameter of a sphere with the same volume as the region, returned as a scalar. Computed as `(6*Volume/pi)^(1/3)`.\n`'Extent'`Ratio of voxels in the region to voxels in the total bounding box, returned as a scalar. Computed as the value of `Volume` divided by the volume of the bounding box. ```[Volume/(bounding box width * bounding box height * bounding box depth)]```\n`'Image'`Bounding box of the region, returned as a volumetric binary image (`logical`) that is the same size as the bounding box of the region. The `on` voxels correspond to the region, and all other voxels are `off`.\n`'Orientation'`\n\nEuler angles , returned as a 1-by-3 vector. The angles are based on the right-hand rule. `regionprops3` interprets the angles by looking at the origin along the x-, y-, and z-axis representing roll, pitch, and yaw respectively. A positive angle represents a rotation in the counterclockwise direction. Rotation operations are not commutative so they must be applied in the correct order to have the intended effect.\n\n`'PrincipalAxisLength'`Length (in voxels) of the major axes of the ellipsoid that have the same normalized second central moments as the region, returned as 1-by-3 vector. `regionprops3` sorts the values from highest to lowest.\n`'Solidity'`Proportion of the voxels in the convex hull that are also in the region, returned as a scalar. Computed as `Volume/ConvexVolume`.\n`'SubarrayIdx'`Indices used to extract elements inside the object bounding box, returned as a cell array such that `L(idx{:})` extracts the elements of `L` inside the object bounding box.\n`'SurfaceArea'`Distance around the boundary of the region , returned as a scalar.\n`'Volume'`Count of the actual number of '`on`' voxels in the region, returned as a scalar. Volume represents the metric or measure of the number of voxels in the regions within the volumetric binary image, `BW`.\n`'VoxelIdxList'`Linear indices of the voxels in the region, returned as a p-element vector.\n`'VoxelList'`Locations of voxels in the region, returned as a p-by-3 matrix. Each row of the matrix has the form `[x y z]` and specifies the coordinates of one voxel in the region.\n\nThe voxel value measurement properties in the following table are valid only when you specify a grayscale volumetric image, `V`.\n\nVoxel Value Measurements\n\nProperty Name Description\n`'MaxIntensity'`Value of the voxel with the greatest intensity in the region, returned as a scalar.\n`'MeanIntensity'`Mean of all the intensity values in the region, returned as a scalar.\n`'MinIntensity'`Value of the voxel with the lowest intensity in the region, returned as a scalar.\n`'VoxelValues'`Value of the voxels in the region, returned as a p-by-1 vector, where p is the number of voxels in the region. Each element in the vector contains the value of a voxel in the region.\n`'WeightedCentroid'`Center of the region based on location and intensity value, returned as a `p`-by-3 vector of coordinates. The first element of `WeightedCentroid` is the horizontal coordinate (or x-coordinate) of the weighted centroid. The second element is the vertical coordinate (or y-coordinate). The third element is the planar coordinate (or z-coordinate).\n\nData Types: `char` | `string` | `cell`\n\nVolumetric grayscale image, specified as a 3-D numeric array. The size of the image must match the size of the binary image `BW`, connected component structure `CC`, or label matrix `L`.\n\nData Types: `single` | `double` | `int8` | `int16` | `int32` | `int64` | `uint8` | `uint16` | `uint32`\n\n## Output Arguments\n\ncollapse all\n\nMeasurement values, returned as a table. The number of rows in the table corresponds to the number of objects in `BW`, `CC.NumObjects`, or `max(L(:))`. The variables (columns) in each table row denote the properties calculated for each region, as specified by `properties`. If the input image is a categorical label image `L`, then `stats` includes an additional variable with the property `'LabelName'`.\n\n Lehmann, Gaetan and David Legland. Efficient N-Dimensional surface estimation using Crofton formula and run-length encoding, The Insight Journal, 2012. (https://insight-journal.org/browse/publication/852)\n\n Shoemake, Ken, Graphics Gems IV. Edited by Paul S. Heckbert, Morgan Kaufmann, 1994, pp. 222–229." ]

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[ "Trigonometry Books\n\nTrigonometry Lecture Notes And Exercises by Daniel Raies\n\nTrigonometry Lecture Notes And Exercises by Daniel Raies", null, "Trigonometry Lecture Notes And Exercises by Daniel Raies\n\nThis note provides an introduction to trigonometry, an introduction to vectors, and the operations on functions. Topics covered includes: New functions from old functions, Trigonometry in circles and triangles, trigonometric functions, vectors.\n\nAuthor(s):", null, "400 Pages", null, "Similar Books\n\nTrigonometry Notes by Brooke Quinlan\n\nThis note covers the following topics: Angles and Their Measure, Right Triangle Trigonometry , Computing the Values of Trigonometric Functions of Acute Angles, Trigonometric Functions of General Angles, Graphs of the Sine and Cosine Functions, Graphs of the Tangent, Cotangent, Secant, and Cosecant Functions, Phase Shifts, The Inverse Trigonometric Functions, Trigonometric Identities, Sum and Difference Formulas, Double-angle and Half-angle Formulas, Trigonometric Equation, Applications Involving Right Triangle, Area of a Triangle.", null, "125 Pages\n\nTrigonometry Lecture Notes And Exercises by Daniel Raies\n\nThis note provides an introduction to trigonometry, an introduction to vectors, and the operations on functions. Topics covered includes: New functions from old functions, Trigonometry in circles and triangles, trigonometric functions, vectors.", null, "400 Pages\n\nTrigonometry Lecture Notes by University Of Utah\n\nThis note explains the following topics: Trigonometric Functions, Radians and Degrees, Angular and Linear Velocity, Right Triangles, Trigonometric Functions of Any Angle, Graphs of Sine and Cosine Functions, Right Triangle Applications, Analytical Trigonometry, Trigonometric Equations, Law of Sines and Cosines, Trigonometric Form of Complex Numbers.", null, "NA Pages\n\nNotes from Trigonometry\n\nThis lecture note talks about topics not usually covered in trigonometry. These include such topics as the Pythagorean theorem, proof by contradiction, limits, and proof by induction. As well as giving a geometric basis for many of the relationships of trigonometry.", null, "183 Pages\n\nPlane trigonometry and numerical computation\n\nThe first six chapters of this book give the essentials of a course in numerical trigonometry and logarithmic computation. The remainder of the theory usually given in the longer courses is contained in the last two chapters.", null, "146 Pages\n\nSpherical Trigonometry For the Use of Colleges and Schools\n\nThis book contains all the propositions usually included under the head of Spherical Trigonometry, together with a large collection of examples for exercise.", null, "189 Pages\n\nTrigonometry TextBook PDF 180P\n\nThis book covers elementary trigonometry. It is suitable for a one-semester course at the college level, though it could also be used in high schools. The prerequisites are high school algebra and geometry.", null, "180 Pages\n\nTRIGONOMETRY NOTES By STEVEN SY Copyright 2006\n\nCurrently this section contains no detailed description for the page, will update this page soon.", null, "NA Pages\n\nPLANE AND SPHERICAL TRIGONOMETRY\n\nCurrently this section contains no detailed description for the page, will update this page soon.", null, "NA Pages\n\nRIGHT TRIANGLE TRIGONOMETRY by Thomas E. Price Directory\n\nCurrently this section contains no detailed description for the page, will update this page soon.", null, "NA Pages\n\nMathematics, Trigonometry\n\nCurrently this section contains no detailed description for the page, will update this page soon.", null, "NA Pages\n\nA short course in Trigonometry\n\nCurrently this section contains no detailed description for the page, will update this page soon.", null, "NA Pages\n\nDefinition of the trigonometric functions\n\nCurrently this section contains no detailed description for the page, will update this page soon.", null, "NA Pages\n\nTrigonometric identities\n\nCurrently this section contains no detailed description for the page, will update this page soon.", null, "NA Pages\n\nTrigonometry from VCE\n\nCurrently this section contains no detailed description for the page, will update this page soon.", null, "NA Pages\n\nSOS Trigonometry\n\nCurrently this section contains no detailed description for the page, will update this page soon.", null, "NA Pages" ]

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[ "# 7154925\n\n## 7,154,925 is an odd composite number composed of four prime numbers multiplied together.\n\nWhat does the number 7154925 look like?\n\nThis visualization shows the relationship between its 4 prime factors (large circles) and 24 divisors.\n\n7154925 is an odd composite number. It is composed of four distinct prime numbers multiplied together. It has a total of twenty-four divisors.\n\n## Prime factorization of 7154925:\n\n### 3 × 52 × 19 × 5021\n\n(3 × 5 × 5 × 19 × 5021)\n\nSee below for interesting mathematical facts about the number 7154925 from the Numbermatics database.\n\n### Names of 7154925\n\n• Cardinal: 7154925 can be written as Seven million, one hundred fifty-four thousand, nine hundred twenty-five.\n\n### Scientific notation\n\n• Scientific notation: 7.154925 × 106\n\n### Factors of 7154925\n\n• Number of distinct prime factors ω(n): 4\n• Total number of prime factors Ω(n): 5\n• Sum of prime factors: 5048\n\n### Divisors of 7154925\n\n• Number of divisors d(n): 24\n• Complete list of divisors:\n• Sum of all divisors σ(n): 12454560\n• Sum of proper divisors (its aliquot sum) s(n): 5299635\n• 7154925 is a deficient number, because the sum of its proper divisors (5299635) is less than itself. Its deficiency is 1855290\n\n### Bases of 7154925\n\n• Binary: 110110100101100111011012\n• Base-36: 49CRX\n\n### Squares and roots of 7154925\n\n• 7154925 squared (71549252) is 51192951755625\n• 7154925 cubed (71549253) is 366281730340115203125\n• The square root of 7154925 is 2674.8691556785\n• The cube root of 7154925 is 192.6940753675\n\n### Scales and comparisons\n\nHow big is 7154925?\n• 7,154,925 seconds is equal to 11 weeks, 5 days, 19 hours, 28 minutes, 45 seconds.\n• To count from 1 to 7,154,925 would take you about seventeen weeks!\n\nThis is a very rough estimate, based on a speaking rate of half a second every third order of magnitude. If you speak quickly, you could probably say any randomly-chosen number between one and a thousand in around half a second. Very big numbers obviously take longer to say, so we add half a second for every extra x1000. (We do not count involuntary pauses, bathroom breaks or the necessity of sleep in our calculation!)\n\n• A cube with a volume of 7154925 cubic inches would be around 16.1 feet tall.\n\n### Recreational maths with 7154925\n\n• 7154925 backwards is 5294517\n• The number of decimal digits it has is: 7\n• The sum of 7154925's digits is 33\n• More coming soon!" ]

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[ "# Unsafe Lazy Resource.scala\n\n``````import scala.util.control.NonFatal\n\n/** Builds a \"closeable\" resource that's initialized on-demand.\n*\n* Works like a `lazy val`, except that the logic for closing\n* the resource only happens in case the resource was initialized.\n*\n* NOTE: it's called \"unsafe\" because it is side-effecting.\n* See homework.\n*/\nfinal class UnsafeLazyResource[A](\ninitRef: () => A,\ncloseRef: A => Unit,\n) extends AutoCloseable {\n\n/** Internal state that works like a FSM:\n* - `null` is for pre-initialization\n* - `Some(_)` is an active resource\n* - `None` is the final state, a closed resource\n*/\n@volatile private[this] var ref: Option[A] = null\n\n/**\n* Returns the active resources. Initializes it if necessary.\n*\n* @return `Some(resource)` in case the resource is available,\n* or `None` in case [[close]] was triggered.\n*/\ndef get(): Option[A] =\nref match {\ncase null =>\n// https://en.wikipedia.org/wiki/Double-checked_locking\nthis.synchronized {\nif (ref == null) {\ntry {\nref = Some(initRef())\nref\n} catch {\ncase NonFatal(e) =>\nref = None\nthrow e\n}\n} else {\nref\n}\n}\ncase other =>\nother\n}\n\noverride def close(): Unit =\nif (ref ne None) {\nval res = this.synchronized {\nval old = ref\nref = None\nold\n}\nres match {\ncase null | None => ()\ncase Some(a) => closeRef(a)\n}\n}\n}\n``````\n\nExample:\n\n``````import java.io._\n\ndef openFile(path: File): UnsafeLazyResource[InputStream] =\nnew UnsafeLazyResource(\n() => new FileInputStream(path),\nin => in.close()\n)\n\nval lazyInput = openFile(new File(\"/tmp/file\"))\n// .. later\ntry {\nval in = lazyInput.get().getOrElse(\n1. Try using an AtomicReference instead of synchronizing a `var` — not as obvious as you’d think — initialization needs protection, you’ll need an indirection 😉" ]

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[ "The Riccati transfer matrix method (RTMM) improves the numerical stability of analyzing chain multibody systems with the transfer matrix method for multibody systems (MSTMM). However, for linear tree multibody systems, the recursive relations of the Riccati transfer matrices, especially those for elements with multiple input ends, have not been established yet. Thus, an RTMM formulism for general linear tree multibody systems is formulated based on the transformation of transfer equations and geometrical equations of such elements. The steady-state response under harmonic excitation of a linear tree multibody system is taken as an example and obtained by the proposed method. Comparison with the finite-element method (FEM) validates the proposed method and a numerical example demonstrates that the proposed method has a better numerical stability than the normal MSTMM.\n\n## References\n\nReferences\n1.\nRui\n,\nX.\n,\nYun\n,\nL.\n,\nLu\n,\nY.\n,\nHe\n,\nB.\n, and\nWang\n,\nG.\n,\n2008\n,\nTransfer Matrix Method of Multibody System and Its Applications\n,\nScience Press\n,\nBeijing, China\n.\n2.\nRui\n,\nX.\n,\nBestle\n,\nD.\n,\nZhang\n,\nJ.\n, and\nZhou\n,\nQ.\n,\n2016\n, “\nA New Version of Transfer Matrix Method for Multibody Systems\n,”\nMultibody Syst. Dyn.\n,\n38\n(\n2\n), pp.\n137\n156\n.\n3.\nRui\n,\nX.\n,\nZhang\n,\nJ.\n, and\nZhou\n,\nQ.\n,\n2014\n, “\nAutomatic Deduction Theorem of Overall Transfer Equation of Multibody System\n,”\n,\n2014\n, p.\n378047\n.\n4.\nBestle\n,\nD.\n,\nAbbas\n,\nL.\n, and\nRui\n,\nX.\n,\n2014\n, “\nRecursive Eigenvalue Search Algorithm for Transfer Matrix Method of Linear Flexible Multibody Systems\n,”\nMultibody Syst. Dyn.\n,\n32\n(\n4\n), pp.\n429\n444\n.\n5.\nZhang\n,\nJ.\n,\nRui\n,\nX.\n,\nWang\n,\nG.\n, and\nYang\n,\nF.\n,\n2013\n, “\nRiccati Transfer Matrix Method for Eigenvalue Problem of the System With Antisymmetric Boundaries\n,”\nECCOMAS Thematic Conference on Multibody Dynamics\n, Zagreb, Croatia, pp. 685–693.\n6.\nChen\n,\nG.\n,\nRui\n,\nX.\n,\nYang\n,\nF.\n, and\nZhang\n,\nJ.\n,\n2016\n, “\nStudy on the Natural Vibration Characteristics of Flexible Missile With Thrust by Using Riccati Transfer Matrix Method\n,”\nASME J. Appl. Mech.\n,\n83\n(\n3\n), p.\n031006\n.\n7.\nHorner\n,\nG. C.\n, and\nPilkey\n,\nW. D.\n,\n1978\n, “\nThe Riccati Transfer Matrix Method\n,”\nASME J. Mech. Des.\n,\n100\n(\n2\n), pp.\n297\n302\n.\n8.\nXue\n,\nH.\n,\n1994\n, “\nA Combined Dynamic Finite Element-Riccati Transfer Matrix Method for Solving Non-Linear Eigenproblems of Vibrations\n,”\nComput. Struct.\n,\n53\n(\n6\n), pp.\n1257\n1261\n.\n9.\nXue\n,\nH.\n,\n1997\n, “\nA Combined Finite Element-Riccati Transfer Matrix Method in Frequency Domain for Transient Structural Response\n,”\nComput. Struct.\n,\n62\n(\n2\n), pp.\n215\n220\n.\n10.\nStephen\n,\nN. G.\n,\n2010\n, “\nOn the Riccati Transfer Matrix Method for Repetitive Structures\n,”\nMech. Res. Commun.\n,\n37\n(\n7\n), pp.\n663\n665\n.\n11.\nYu\n,\nA. M.\n, and\nHao\n,\nY.\n,\n2012\n, “\nImproved Riccati Transfer Matrix Method for Free Vibration of Non-Cylindrical Helical Springs Including Warping\n,”\nShock Vib.\n,\n19\n(\n6\n), pp.\n1167\n1180\n.\n12.\nZheng\n,\nY.\n,\nXie\n,\nZ.\n,\nLi\n,\nY.\n,\nShen\n,\nG.\n, and\nLiu\n,\nH.\n,\n2013\n, “\nSpatial Vibration of Rolling Mills\n,”\nJ. Mater. Process. Technol.\n,\n213\n(\n4\n), pp.\n581\n588\n." ]

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[ "## Conversion formula\n\nThe conversion factor from grams to pounds is 0.0022046226218488, which means that 1 gram is equal to 0.0022046226218488 pounds:\n\n1 g = 0.0022046226218488 lb\n\nTo convert 486 grams into pounds we have to multiply 486 by the conversion factor in order to get the mass amount from grams to pounds. We can also form a simple proportion to calculate the result:\n\n1 g → 0.0022046226218488 lb\n\n486 g → M(lb)\n\nSolve the above proportion to obtain the mass M in pounds:\n\nM(lb) = 486 g × 0.0022046226218488 lb\n\nM(lb) = 1.0714465942185 lb\n\nThe final result is:\n\n486 g → 1.0714465942185 lb\n\nWe conclude that 486 grams is equivalent to 1.0714465942185 pounds:\n\n486 grams = 1.0714465942185 pounds\n\n## Alternative conversion\n\nWe can also convert by utilizing the inverse value of the conversion factor. In this case 1 pound is equal to 0.93331763374486 × 486 grams.\n\nAnother way is saying that 486 grams is equal to 1 ÷ 0.93331763374486 pounds.\n\n## Approximate result\n\nFor practical purposes we can round our final result to an approximate numerical value. We can say that four hundred eighty-six grams is approximately one point zero seven one pounds:\n\n486 g ≅ 1.071 lb\n\nAn alternative is also that one pound is approximately zero point nine three three times four hundred eighty-six grams.\n\n## Conversion table\n\n### grams to pounds chart\n\nFor quick reference purposes, below is the conversion table you can use to convert from grams to pounds\n\ngrams (g) pounds (lb)\n487 grams 1.074 pounds\n488 grams 1.076 pounds\n489 grams 1.078 pounds\n490 grams 1.08 pounds\n491 grams 1.082 pounds\n492 grams 1.085 pounds\n493 grams 1.087 pounds\n494 grams 1.089 pounds\n495 grams 1.091 pounds\n496 grams 1.093 pounds" ]

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[ "Enable contrast version\n\n# TutorMe Blog\n\n## Is a Rectangle a Parallelogram? Or Is a Parallelogram a Rectangle?\n\nInactive\nAndrew Lee\nJune 24, 2021", null, "Both rectangles and parallelograms are quadrilaterals, which means that they are polygons with four sides. But is a rectangle a parallelogram? Or is a parallelogram a rectangle? Here's a review of the different properties of both parallelograms and rectangles.\n\nA parallelogram is a quadrilateral that has:\n\n• Two pairs of parallel sides\n• Two pairs of opposite sides that are congruent\n\nA rectangle is a quadrilateral that has:\n\n• Four right angles\n• Two pairs of opposite sides that are congruent\n\nA rhombus is a quadrilateral that has:\n\n• Four sides of equal length\n• Two pairs of equal opposite angles\n\n## Properties of a Rectangle vs. a Parallelogram", null, "Image credit: Desmos\n\nWhen a rectangle has four right angles, all of the interior angles are congruent. The vertices join the adjacent sides at 90° angles, which means the opposite sides of the rectangle are parallel lines. Since it has two sets of parallel sides and two pairs of opposite sides that are congruent, a rectangle has all of the properties of a parallelogram. That’s why a rectangle is always a parallelogram.\n\nHowever, a parallelogram is not always a rectangle. The below example is of a parallelogram that does not have four right angles. Next, we’ll explain this shape’s properties.\n\n## Properties of a Rectangle vs. a Rhombus", null, "The shape above is a rhombus, which we defined above. Since a rhombus looks similar to a rectangle, let’s talk about the similarities between the two.\n\nNow, a rectangle is not always a rhombus. A rectangle has two sets of congruent sides whereas all four sides of a rhombus are congruent.\n\nIs a rhombus always a parallelogram though? The answer is yes! The two pairs of opposite angles of a rhombus are always equal, just like the two pairs of opposite angles of a parallelogram are always equal. This means that a rhombus is just a special case of a parallelogram where all four sides happen to also be congruent.\n\n## Is a Rectangle a Parallelogram?\n\nRectangles, parallelograms, and rhombuses are all special quadrilaterals with certain properties.\n\nA parallelogram is a quadrilateral that has:\n\n• Two pairs of parallel sides\n• Two pairs of opposite sides that are congruent\n\nA rectangle is a quadrilateral that has:\n\n• Four right angles\n• Two pairs of opposite sides that are congruent\n\nA rhombus is a quadrilateral that has:\n\n• Four sides of equal length\n• Two pairs of equal opposite angles\n\nThere are many more types of quadrilaterals than we’ve covered here. But now you know the answer to the question “Is a rectangle a parallelogram?” A rectangle is always a parallelogram. But a parallelogram is not always a rectangle.\n\n### More Math Homework Help:\n\nBEST IN CLASS SINCE 2015\nTutorMe homepage" ]

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[ "# Quick Tip: Accept Multiple Vouchers in OpenCart 2.0\n\nOpenCart is\nan open-source, PHP-based online e-commerce\nsolution that allows you to accept orders online. It allows customers to shop using vouchers, but only one at a time by default. If you want to allow your customers to use multiple vouchers at once, you’ll need to modify the code. I’ll show you exactly how to do that in this tutorial.\n\n## How Do We Create a Gift Voucher?\n\nOnly admins and permitted back-end users are able to generate gift vouchers. OpenCart comes with a default module for doing it. The following screenshot shows the place where a back-end user can generate vouchers.\n\n## What Is the Problem?\n\nIf we have a voucher system implemented in OpenCart by default, what is the problem? Let’s understand it with the help of an example:\n\nRecently a\nfriend of mine wanted to buy a couple of items through OpenCart that cost \\$800, but she only had \\$500, and two gift vouchers worth \\$250 each. So she called me and asked for a solution. Because OpenCart only allows you to use a single voucher to shop at any one time, she couldn’t\n\n## A Solution\n\nTo resolve this problem, we need to add an option to use multiple vouchers so that customers can shop easily, without facing any difficulty.  Here is the solution, in which we will modify a few lines of code and it will help to solve this problem.\n\nThis tutorial is divided into three main steps, which are:\n\n1. Change in Controller\n2. Change in Model\n3. Change in View\n\n### 1. Controller File\n\n1. Navigate to `catalog/controller/checkout/cart.php`.\n2. Find the following code:\n```If(isset(\\$this->request->post['voucher']) && \\$this-> valid voucher())\n{\n\\$this->session->data['voucher']=\\$this->request->post['voucher'];\n}```\n\nChange the above code to:\n\n```If(isset(\\$this->request->post['voucher']) && \\$this-> valid voucher())\n{\n\\$this->session->data['voucher'][\\$this->request->post['voucher']]=\\$this->request->post['voucher']; // creates an array for multiple vouchers\n}\n```\n\n### 2. Model File\n\n1. Navigate to `catalog/model/total/voucher.php`.\n2. Find the following lines of code:\n```\\$this->load->model('checkout/voucher');\n\n\\$voucher_info = \\$this->model_checkout_voucher->getVoucher(\\$this->session->data['voucher']);\n\nif (\\$voucher_info) {\nif (\\$voucher_info['amount'] > \\$total) {\n\\$amount = \\$total;\n} else {\n\\$amount = \\$voucher_info['amount'];\n}\n\n\\$total_data[] = array(\n'code' => 'voucher',\n'title' => sprintf(\\$this->language->get('text_voucher'), \\$this->session- >data['voucher']),\n'text' => \\$this->currency->format(-\\$amount),\n'value' => -\\$amount,\n'sort_order' => \\$this->config->get('voucher_sort_order')\n);\n\n\\$total -= \\$amount;\n}\n```\n\nWe need to run an outer loop to fetch all of our vouchers that we maintained as array in Step 1. So we will place an outer loop after `\\$this->load->model('checkout/voucher');`.\n\nSo we will be looping our Session Vouchers Array to fetch all the vouchers we applied, and the code will be as shown below. Note that the following code is commented in order to make it easier to understand.\n\n```foreach (array_unique(\\$this->session->data['voucher']) as \\$voucher)\n{ // foreach loop will select each array and extract the unique voucher\n\n\\$voucher_info = \\$this->model_checkout_voucher->getVoucher(\\$voucher); // fetch the order details\n\n// Check 1: If Voucher Exists\nif (\\$voucher_info) {\n// Check 2: If the voucher amount is greater than our order amount, voucher balance will be maintained\nif (\\$voucher_info['amount'] > \\$total) {\n\\$amount = \\$total;\n} else {\n\\$amount = \\$voucher_info['amount'];\n}\n// End Check 2\n\n// Array to return Updated Totals\n\\$total_data[] = array( 'code' => 'voucher', 'title' => sprintf(\\$this->language-> get('text_voucher'), \\$voucher),\n'text' => \\$this->currency->format(-\\$amount),\n'value' => -\\$amount,\n'sort_order' => \\$this->config->get('voucher_sort_order')\n);\n// End Array\n\n\\$total -= \\$amount; // Substracts the amount with our order totals\n\n} // End Check 1\n\n} // End Foreach Loop```\n\n### 3. View File\n\n1. Navigate to `catalog/view/theme/default/template/checkout/voucher.tpl`.\n2. Find the following line of code:\n`<input type=\"text\" name=\"voucher\" value=\"<?php echo \\$voucher; ?>\" placeholder=\"<?php echo \\$entry_voucher; ?>\" id=\"input-voucher\" class=\"form-control\" />`\n\nReplace it with this:\n\n`<input type=\"text\" name=\"voucher\" value=\"\" placeholder=\"<?php echo \\$entry_voucher; ?>\" id=\"input-voucher\" class=\"form-control\" />`\n\nWe are done with our problem! In fact, we just made some simple code hacks to solve that big problem, so we didn’t have to develop a new module or extension. We just modified some lines of codes to get it done.\n\n## Conclusion\n\nIn\nthis article we provided a successful solution for adding multiple vouchers in\nour e-shop. Since OpenCart doesn’t allow shoppers to use multiple vouchers by default, we modified the code so that now they can use as\nmany vouchers as they want. That will help customers to shop easily\nwithout any problem.\n\nIn our next articles we will be implementing some real-world business tools in our OpenCart system, so stay subscribed and contribute your", null, "", null, "", null, "" ]

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[ "###", null, "Author Topic: 2.5 Q19  (Read 2108 times)\n\n#### Huanglei Ln\n\n• Jr. Member\n•", null, "", null, "• Posts: 8\n• Karma: 7", null, "##### 2.5 Q19\n« on: November 18, 2018, 04:01:10 AM »\nCan anyone help me this question? Thanks!\nSuppose that the Laurent series $\\sum\\nolimits_{-\\infty}^{+\\infty}a _n (z-z_0)^n$ converges for  $f<| z-z_0|<R$ and\n$$\\sum \\limits_{-\\infty}^{+\\infty} a_n (z-z_0)^n=0, 0<|z-z_0|<r.$$\n\nShow that $a_n=0,n=0, \\pm 1, \\pm 2,\\cdots$, (Hint:Multiply the series by $(z-z_0)^{-m}$ and integrate around the circle $|z-z_0|=s$, $r<s<R$ with respect to $z$. The result must be zero, but it is also $a_{m-1}$.)\n\n#### Victor Ivrii", null, "##### Re: 2.5 Q19\n« Reply #1 on: November 18, 2018, 04:43:31 AM »\nWell, there was a hint provided:if\n$$f(z)=\\sum _{n=-\\infty}^\\infty a_n (z-z_0)^n =0$$\nas $|z-z_0|=s=$ with $s\\in (r,R)$ then\n$$0=\\int_\\gamma f(z)(z-z_0)^{-m-1}\\,dz =\\sum _{n=-\\infty}^\\infty \\int_\\gamma a_n (z-z_0)^{n -m-1}\\,dz$$\nwhile $\\int_\\gamma (z-z_0)^{k}\\,dz=0$ for $k\\ne -1$ and $2\\pi i$ for $k=1$.\n\n#### Yunfei Xia\n\n• Newbie\n•", null, "• Posts: 2\n• Karma: 0", null, "##### Re: 2.5 Q19\n« Reply #2 on: November 18, 2018, 08:02:05 AM »\nFollow the hint: let $r$ be the circle $|z-z_0|=s,0<s<r$. For any $m\\in z$.\n\\begin{align*}\n0&=\\frac{1}{2\\pi i} \\int_r(z-z_0)^{-m}\\left(\\sum\\limits_{-\\infty}^{+\\infty}a_n(z-z_0)^n\\right)\\text{d}z\\\\\nz-z_0=se^{i\\theta}\\\\\n&=\\frac{1}{2\\pi }\\int\\nolimits_{0}^{+2 \\pi}\\left(se^{i\\theta}\\right)^{-m}\\left(\\sum\\limits_{-\\infty}^{+\\infty}{a_n}\\left(se^{i\\theta}\\right)^n\\right)se^{i\\theta}\\text{d}\\theta\\\\\n&=\\sum\\limits_{-\\infty}^{+\\infty}{a_n}s^{-m}s^{n+1}\\frac{1}{2\\pi }\\int e^{-im \\theta+i \\theta+in}\\text{d}\\theta\\\\\n&=\\sum\\limits_{-\\infty}^{+\\infty}{a_n}s^{-m}s^{n+1}\\frac{1}{2\\pi} \\int e^{i \\theta(n+1-m)}\\text{d}\\theta\\\\\n&\\text{Let}~n+1-m=0,n=m-1\\\\\n&=a_{m-1}.\n\\end{align*}\n\n#### Victor Ivrii", null, "##### Re: 2.5 Q19\n« Reply #3 on: November 18, 2018, 08:17:46 AM »\nnot clear what do you mean by \"let $n=...$\". $n$ runs from $-\\infty$ to $\\infty$ and you must check all values\n\n#### Ende Jin\n\n• Sr. Member\n•", null, "", null, "", null, "", null, "• Posts: 35\n• Karma: 11", null, "##### Re: 2.5 Q19\n« Reply #4 on: November 18, 2018, 04:58:24 PM »\nWhat is the first condition used for? The one that the series converges in the $\\{z: r < |z| < R\\}$.\n\n#### Victor Ivrii", null, "##### Re: 2.5 Q19\n« Reply #5 on: November 18, 2018, 05:21:19 PM »\nIf we don't know that series is converging on the circle, we integrate along, the integration is senseless\n\n#### Ende Jin\n\n• Sr. Member\n•", null, "", null, "", null, "", null, "• Posts: 35\n• Karma: 11", null, "##### Re: 2.5 Q19\n« Reply #6 on: November 18, 2018, 11:58:09 PM »\nI realized that you provided a solution different from the given one back in the book.\nBut the question doesn't say $\\sum a_n(z-z_0)^n = 0$ when $r < |z-z_0| < R$. It just converges. The series converges to zero only if $0 < |z - z_0| < r$.\nThat is basically my question. The first condition doesn't seem helpful.\n\n#### Victor Ivrii", null, "##### Re: 2.5 Q19\n« Reply #7 on: November 19, 2018, 02:12:25 AM »\nEnde Jin\nPlease provide exact citation from the textbook.\n\n#### Ende Jin\n\n• Sr. Member\n•", null, "", null, "", null, "", null, "• Posts: 35\n• Karma: 11", null, "##### Re: 2.5 Q19\n« Reply #8 on: November 19, 2018, 11:35:40 PM »\nIt is at P406, The solution for Q19.\nActually, Yunfei Xia provided a very similar proof with that." ]

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[ "", null, "SOLVED\n\n# Seeking for a Formula\n\nHello guys,\n\nI need a help in finding a formula. Here are my conditions:\n\n1. I need to get 3 Results 0, 0.5 and 1.\n\n2. My condition is if the value of the cell is not given then the output should be 0,\n\nIf  my cell value is 0<X<=4 then my result should be 0.5,\n\nIf my cell value is X>4 then result should be 1.\n\n3. Is it possible to give the 3 conditions.\n\n2 Replies\nbest response confirmed by sai9497 (New Contributor)\nSolution\n\n# Re: Seeking for a Formula\n\nLet's say the value is in cell A2.\n\nIn another cell, for example B2, enter the formula\n\n=IF(A2>4,1,IF(A2>0,0.5,0))\n\nor\n\n=((A2>0)+(A2>4))/2\n\n# Re: Seeking for a Formula\n\n@Hans Vogelaar Thank you for you response. It worked absolutely." ]

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[ "", null, "Practice Problems Fundamental Math\n\nDirections: On this worksheet you will practice some fundamental math and data analysis skills.", null, "Question 1  The metric prefix mega represents 0.000001 times a quantity 1000 times a quantity0.001 times a quantity1000000 times a quantity", null, "Question 2  Red light has an average wavelength of 679 nm. How many mm does this represent? 6.79 x 10-3 mm6.79 x 10-10 mm6.79 x 10-5 mm6.79 x 10-4 mm", null, "Question 3  0.0024 meters when expressed in scientific notation would be 2.4 x 103 meters2.4 x 102 meters2.4 x 10-2 meters2.4 x 10-3 meters", null, "Question 4  Which statement is TRUE? 1 cm = 10000 µm1 cm = 0.10 m1 cm = 100 mm1 cm = 10 dm", null, "Question 5  Which of the following numbers has exactly 3 significant figures? 210070400.000410.20", null, "Question 6  What is the difference between these two measurements: 74.21 cm and 27.3 cm? 46.8 cm46.91 cm47 cm46.9 cm", null, "Question 7  What is the correct reading for the triple beam balance shown below?", null, "243.5 g243.25 g240.34 g243.4 g", null, "Question 8  What is the correct volume reading for the water level in the cylinder shown below?", null, "57.7 mL55.5 mL57.75 mL55.27 mL", null, "Question 9  What is the median of the following data set?3.31 g3.21 g3.38 g3.54 g4.16 g3.31 g3.62 g 3.38 g3.54 g3.31 g3.50 gnot listed", null, "Question 10  The standard deviation that was calculated for this data set equaled 0.29 grams. Which value in the group shown above falls in an interval beyond 1 standard deviation but less than 2 standard deviations of the mean? 4.16 g4.16 g3.21 g3.38 g3.54 g3.62 g", null, "Question 11  Calculate the numerical value of the slope of the following line and then choose the best value from the list below.", null, "1.330.751513.30.0667", null, "Question 12  If this graph was retitled 'Mass vs Volume', determine the equation for the regression line displayed on this graph and extrapolate the value for the mass which corresponds to a volume of 1.57 cm3. 12.1 grams21.1 grams26.1 grams23.6 grams" ]

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[ "•\n•\n\n## Progress in Fractional Differentiation & Applications\n\n#### Article Title\n\nNew Aspects of Caputo-Fabrizio Fractional Derivative\n\nUAE.\n\n#### Abstract\n\nIn this paper, we consider classes of linear and nonlinear fractional differential equations involving the Caputo-Fabrizio fractional derivative of non-singular kernel. We transform the fractional problems to equivalent initial value problems with integer derivatives. We illustrate the obtained results by presenting two mathematical models of fractional differential equations and their equivalent initial value problems. We show that it is impossible to convert all types of linear fractional differential equations to the integer ones.The obtained results will lead to better understanding of fractional models, as the solutions of their equivalent models can be studied analytically and numerically using well-known techniques of differential equations.\n\n#### Digital Object Identifier (DOI)\n\nhttp://dx.doi.org/10.18576/pfda/050206\n\nCOinS" ]

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[ "# PHP Beginnings Ex. #4: Arithmetic-Assignment Operators and Variables\n\nArithmetic-assignment operators perform an arithmetic operation on the variable at the same time as assigning a new value. For this PHP exercise, write a script to reproduce the output below. Manipulate only one variable using no simple arithmetic operators to produce the values given in the statements.\n\nHint: In the script each statement ends with \"Value is now \\$variable.\"\n\nValue is now 8.\nAdd 2. Value is now 10.\nSubtract 4. Value is now 6.\nMultiply by 5. Value is now 30.\nDivide by 3. Value is now 10.\nIncrement value by one. Value is now 11.\nDecrement value by one. Value is now 10.\n\nHere's the script:\n\n1. `<!DOCTYPE html PUBLIC \"-//W3C//DTD XHTML 1.0 Transitional//EN\" `\n2. `\"http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd\"> `\n3. `<html xmlns=\"http://www.w3.org/1999/xhtml\" xml:lang=\"en\" lang=\"en\"> `\n4. `<head> `\n5. `<meta http-equiv=\"content-type\" content=\"text/html;charset=iso-8859-1\" /> `\n6. `<title>Arithmetic-Assignment Operators</title> `\n7. `</head> `\n8. ` `\n9. `<body> `\n10. ` `\n11. `<?php `\n12. ` `\n13. `\\$num = 8; `\n14. `echo \"Value is now \\$num.<br/>\"; `\n15. ` `\n16. `\\$num += 2; `\n17. `echo \"Add 2. Value is now \\$num. <br/>\"; `\n18. ` `\n19. `\\$num -= 4; `\n20. `echo \"Subtract 4. Value is now \\$num. <br/>\"; `\n21. ` `\n22. `\\$num *= 5; `\n23. `echo \"Multiply by 5. Value is now \\$num. <br/>\"; `\n24. ` `\n25. `\\$num /= 3; `\n26. `echo \"Divide by 3. Value is now \\$num. <br/>\"; `\n27. ` `\n28. `\\$num++; `\n29. `echo \"Increment value by one. Value is now \\$num.<br/>\"; `\n30. ` `\n31. `\\$num--; `\n32. `echo \"Decrement value by one. Value is now \\$num.\"; `\n33. ` `\n34. `?> `\n35. ` `\n36. `</body> `\n37. `</html>`\n\nSee the output of the script in a separate window here. You can also view the output's HTML source from the new window, if you need to check that.\n\nTo open a PHP code editor in a new tab, click here.\n\n### Question.. :)\n\nits look kind a weird when I tried to echoing the \\$num like this :\n\nnote : Im using \\$result as \\$num\n\n```echo 'Value now is '. \\$result = 8 . '<br/>';\necho 'Add 2, Value now is '. \\$result +=2; echo '<br/>';\necho 'Subtract 4, Value now is '. \\$result -= 4; echo '<br/>';\necho 'Multiply by 5, Value now is '. \\$result *= 5; echo '<br/>';\necho 'Divide by 3, Value now is '. \\$result /= 3; echo '<br/>';\necho 'Increment by one, Value now is '. \\$result++ ;echo '<br/>';\necho 'Decrement by one, Value now is '. \\$result-- ; echo '<br/>';\n```\n\nand the output is like this:\n\nValue now is 8\nAdd 2, Value now is 10\nSubtract 4, Value now is 6\nMultiply by 5, Value now is 30\nDivide by 3, Value now is 10\nIncrement by one, Value now is 10\nDecrement by one, Value now is 11\n\nWhy the value in the last value (increment and decrement by one) is miscalculated?\nAm I missing something?\n\nI appreciate all of your effort for helping me,\nthanks before.. :)\n\n### return value - vs - value change - operator precedence\n\nyou are actually using the direct return value from the decrement function.\nif you write\necho \"mytext\".\\$result--\n\nthe correct return result would be given by\necho \"mytext\".(--\\$result)\n\nanother problem that you noticed was that the Dot (.) operator is not always processed last\nso braces () become mandatory.\n\nso i guess what you wanted to accomplish was\n\n```echo 'Value now is '.(\\$result = 8).'';\necho 'Add 2, Value now is '.(\\$result +=2).'';\necho 'Subtract 4, Value now is '.(\\$result -= 4).'';\necho 'Multiply by 5, Value now is '.(\\$result *= 5).'';\necho 'Divide by 3, Value now is '.(\\$result /= 3).'';\necho 'Increment by one, Value now is '.(++\\$result).'';\necho 'Decrement by one, Value now is '.(--\\$result).'';\n```\n\n### Increment and Decrement\n\nIn \\$result++, the result is first stored and then incremented and that same for \\$result--.\n\nAfter the division of the value in \\$result by three, quotient is stored in \\$result. When \\$result++ is echoed it will show the value currently present there i.e.,10. and not 11 because still now it is not incremented. Later on the value in \\$result is incremented and that's shown while decrement operator is used. Only after that value in \\$result will be decremented.\n\nIf again the value of \\$result is echoed after that result will be 10. That's because now the \\$result contain the decremented value.\n\nWhereas if ++\\$result or --\\$result is used then first the value in \\$result will be incremented or decremented respectively and then it will be stored in \\$result.\n\nThank you.\n\nPHP Increment / Decrement Operators\nhttps://www.w3schools.com/PhP/php_operators.asp\n\n### My code here\n\n```\\$variable = 8;\necho \"Value is now \".\\$variable.\"<br />\";\n\n\\$variable += 2;\necho \"Add 2. Value is now \".\\$variable.\"<br />\";\n\n\\$variable -= 4;\necho \"Subtract 4. Value is now \".\\$variable.\"<br />\";\n\n\\$variable *= 5;\necho \"Multiply by 5. Value is now \".\\$variable.\"<br />\";\n\n\\$variable /= 3;\necho \"Divide by 3. Value is now \".\\$variable.\"<br />\";\n\n\\$variable++;\necho \"Increment value by 1. Value is now \".\\$variable.\"<br />\";\n\n\\$variable--;\necho \"Decrement value by 1. Value is now \".\\$variable.\"<br />\";\n```\n\n### using printf\n\n```\\$x = 0;\n\\$x += 8;\nprintf (\"Value is : %d<br/>\",\\$x);\n\\$x +=2;\nprintf (\"Value is : %d<br/>\",\\$x);\n\\$x -=4;\nprintf (\"Value is : %d<br/>\",\\$x);\n\\$x *=5;\nprintf (\"Value is : %d<br/>\",\\$x);\n\\$x /=3;\nprintf (\"Value is : %d<br/>\",\\$x);\n\\$x++;\nprintf (\"Value is : %d<br/>\",\\$x);\n\\$x--;\nprintf (\"Value is : %d<br/>\",\\$x);\n```\n\n### switch case and loop\n\n```<?php\n\n\\$base = 8;\n\necho \"value is now \".\\$base.\"<br>\";\n\nfor(\\$i=0; \\$i<6; \\$i++)\n{\n\nswitch (\\$i)\n{\n\ncase 0;\n\n\\$base = \\$base + 2;\n\necho \"Add 2. value is now \".\\$base.\"<br>\";\n\nbreak;\n\ncase 1;\n\n\\$base = \\$base - 4;\necho \"Subtract 4. Value is now \".\\$base.\"<br>\";\n\nbreak;\n\ncase 2;\n\n\\$base = \\$base * 5;\necho \"Multiply 5. Value is now \".\\$base.\"<br>\";\n\nbreak;\n\ncase 3;\n\n\\$base = \\$base / 3;\necho \"Divide by 3. Value is now \".\\$base.\"<br>\";\n\nbreak;\n\ncase 4;\n\n\\$base = ++\\$base;\necho \"Increment Value by one. Value is now \".\\$base.\"<br>\";\n\nbreak;\n\ncase 5;\n\n\\$base = --\\$base;\necho \"Decrement value by one. Value is now \".\\$base.\"<br>\";\n\nbreak;\n}\n}\n?>\n```\n\n### I went on a little far, but it was for learning purposes:)\n\n``` <?php\n\\$commands = array(\n'substract' => \"-\",\n'multiply' => \"*\",\n'divide' => \"/\",\n'increment' => \"+\",\n'decrement' => \"-\");\n\n\\$thevalue = 8;\n\nfunction docommand(\\$command) {\nglobal \\$commands, \\$thevalue;\n\\$parse_command = explode(' ', \\$command);\nif (\\$commands[@strtolower(\\$parse_command)] != NULL) {\n\\$dowith = strtolower(\\$parse_command);\n\\$value = \\$parse_command[count(\\$parse_command)-1];\n\\$result = \"\\$command. \" . eval(\"\\\\$thevalue = \\$thevalue \\$commands[\\$dowith] \\$value;\") . \"Value is now \\$thevalue.\";\necho \"\\$result<br>\";\n} else {\necho \"Invalid command: \\$parse_command<br>\";\n}\n}\n\necho \"Value is now \\$thevalue. <br>\";\ndocommand(\"Increment value by 6\");\ndocommand(\"Decrement value by 8\");\ndocommand(\"Multilpy value by 10\");\ndocommand(\"Divide by 5\");\ndocommand(\"Multiply this \\$thevalue with \\$thevalue\");\n?>\n```\n\n### My 9 line version\n\n```\n\\$s= \"Value is now \";\n\\$v = 0;\necho \\$s . (\\$v+=8) .'.';\necho \"\\nAdd2. \" . \\$s . (\\$v+=2) .'.';\necho \"\\nSubtract 4. \" . \\$s . (\\$v-=4) .'.';\necho \"\\nMultiply by 5. \" . \\$s . (\\$v*=5) .'.';\necho \"\\nDivide by 3. \" . \\$s . (\\$v/=3) .'.';\necho \"\\nIncrement value by one. \" . \\$s . ++\\$v .'.';\necho \"\\nDecrement value by one. \" . \\$s . --\\$v .'.';\n\n```\n\n### variable in a string\n\nthis was the result when\n\nValue is now 8Add 2. Value is now 8\nSubtract 4. Value is now 8\nMultiply by 5. Value is now 8\nDivide by 30. Value is now 8\nIncrement value by 1. Value is now 8\nDecrement value by 1. Value is now 8\n\nwhen I put a variable in a string and updated the variable\n\n```<?php\n\\$variable = 8;\n\\$a = \"Value is now \\$variable\";\necho \" \\$a\";\n\\$variable += 2 ;\necho \"Add 2. \\$a\". \"<br />\";\n\\$variable -= 4 ;\necho \" Subtract 4. \\$a\" . \"<br />\";\n\\$variable *= 5 ;\necho \" Multiply by 5. \\$a\" . \"<br />\";\n\\$variable /= 30 ;\necho \" Divide by 30. \\$a\" . \"<br />\";\n\\$variable += 1 ;\necho \" Increment value by 1. \\$a\" . \"<br />\";\n\\$variable -= 1 ;\necho \" Decrement value by 1. \\$a\" . \"<br />\";\n?>\n```\n\n### VARIABLE IN A STRING\n\ni put a variable in a string. So if the value of variable changes shouldn't the string get updated by itself\nbecause this code\n\n```<?php\n\\$variable = 8;\n\\$a = \"Value is now \\$variable\";\necho \" \\$a\";\n\\$variable += 2 ;\necho \"Add 2. \\$a\". \"<br />\";\n\\$variable -= 4 ;\necho \" Subtract 4. \\$a\" . \"<br />\";\n\\$variable *= 5 ;\necho \" Multiply by 5. \\$a\" . \"<br />\";\n\\$variable /= 30 ;\necho \" Divide by 30. \\$a\" . \"<br />\";\n\\$variable += 1 ;\necho \" Increment value by 1. \\$a\" . \"<br />\";\n\\$variable -= 1 ;\necho \" Decrement value by 1. \\$a\" . \"<br />\";\n?>\n```\n\nGave the following result\n\nValue is now 8Add 2. Value is now 8\nSubtract 4. Value is now 8\nMultiply by 5. Value is now 8\nDivide by 30. Value is now 8\nIncrement value by 1. Value is now 8\nDecrement value by 1. Value is now 8\n\n### Increment and Decrement\n\nI had some trouble by using the following statement for increment and decrement:\nprint \"Increment value by one. Value is now \" . \\$var++. \"\";\nprint \"Decrement value by one. Value is now \" . \\$var--. \"\";\n\nSo I decided to do the \\$varr++ and \\$var-- before the print. Here is my solution. 10 lines of a simple solution, no fancy arrays, no luxurious loops :)\n\n``` \\$var=8;\nprint \"Value is now \" . \\$var . \"<br>\";\nprint \"Add 2. Value is now \" . (\\$var+=2) . \"<br>\";\nprint \"Substract 4. Value is now \" . (\\$var-=4) . \"<br>\";\nprint \"Multiply by 5. Value is now \" . (\\$var*=5) . \"<br>\";\nprint \"Divide by 3. Value is now \" . (\\$var/=3) . \"<br>\";\n\\$var++;\nprint \"Increment value by one. Value is now \" . \\$var . \"<br>\";\n\\$var--;\nprint \"Decrement value by one. Value is now \" . \\$var . \"<br>\";\n```\n\nHi,\nTry this one:\n\n1. `\\$var=8;`\n2. `print \"Value is now \" . \\$var . \"<br>\";`\n3. `print \"Add 2. Value is now \" . (\\$var+=2) . \"<br>\";`\n4. `print \"Substract 4. Value is now \" . (\\$var-=4) . \"<br>\";`\n5. `print \"Multiply by 5. Value is now \" . (\\$var*=5) . \"<br>\";`\n6. `print \"Divide by 3. Value is now \" . (\\$var/=3) . \"<br>\";`\n7. `print \"Increment value by one. Value is now\". (++\\$var). \"<br>\";`\n8. `// if ++ comes after, it is not working!`\n9. `print \"Decrement value by one. Value is now\". (--\\$var). \"<br>\";`\n10. `// When -- is written after your variable, then it will work.`" ]

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[ "#", null, "excel columns handling", null, "• ### Question\n\n•", null, "User-1314424833 posted\n\nHi\n\nMy ques is for excel.\n\nI have 5 columns each column having thousands of records but of same datatype I want my all records from all 4 columns to be pasted in first column one after another.\n\nIs it posible without manual copy, paste.\n\nThank u\n\nSaturday, October 24, 2009 6:07 AM\n\n### All replies\n\n•", null, "User59160557 posted\n\nI assume you want to do this in Excel. If so you can use the following macro in VBA:\n\n```Sub test()\nDim lastRowIndex As Integer\nDim lastColumnIndex As Integer\nDim rowCounterIndex As Integer\nDim columnCounterIndex As Integer\nDim currentAddress As String\n\nlastRowIndex = ActiveSheet.Cells.SpecialCells(xlCellTypeLastCell).Row\nlastColumnIndex = ActiveSheet.Cells.SpecialCells(xlCellTypeLastCell).Column\ncurrentAddress = CStr(ActiveSheet.Cells(1, 1))\n\nFor rowCounterIndex = 1 To lastRowIndex\ncurrentAddress = CStr(ActiveSheet.Cells(rowCounterIndex, 1))\nFor columnCounterIndex = 2 To lastColumnIndex\nIf (Len(CStr(ActiveSheet.Cells(rowCounterIndex, columnCounterIndex))) > 0) Then\ncurrentAddress = currentAddress & Chr(44) & CStr(ActiveSheet.Cells(rowCounterIndex, columnCounterIndex))\nActiveSheet.Cells(rowCounterIndex, columnCounterIndex).Value = \"\"\nEnd If\nNext columnCounterIndex\nActiveSheet.Cells(rowCounterIndex, CInt(1)) = currentAddress\nNext rowCounterIndex\nActiveSheet.cell\nEnd Sub\n\n```\n\nThe above Macro will merge the content of all the cells with first cell separated by a comma and then clear the content from those merged cells.\n\nHope this Helps.\n\nSaturday, October 24, 2009 4:49 PM" ]

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[ "# Phase portrait on a cylinder\n\nIt is very nice and very easy to make a sketch of a phase portrait with StreamPlot. For example, for the classical pendulum, defined by\n\n\\begin{eqnarray*} \\dot x&=&y,\\\\ \\dot y&=&-\\sin x, \\end{eqnarray*}\n\nThe code\n\nStreamPlot[{y, -Sin[x]}, {x, -5, 5}, {y, -3, 3},\nFrame -> None, StreamPoints -> Fine, AspectRatio -> 0.8,\nEpilog -> {PointSize -> Large, Point[{{0, 0}, {\\[Pi], 0}, {-\\[Pi], 0}}]}]\n\n\nproduces", null, "Now to the question. The actual phase space for the pendulum is not the plane $\\mathbf R^2$, but the cylinder $\\mathbf S^1\\times \\mathbf R$, and the pendulum of course has only two equilibria, one at $(0,0)$ and another one at $(\\pi,0)$. Actually two points in the graph, the left and the right ones, are the same equilibrium.\n\nQuestion: How in Mathematica I can efficiently plot my phase portrait on a cylinder, such that I have only two equilibria, and I could see through the whole cylinder (I found examples on the site how to put a texture on a cylinder, but cannot figure out how to make it transparent).\n\nplot = StreamPlot[{y, -Sin[x]}, {x, -Pi, Pi}, {y, -3, 3}, Frame -> None,\nEpilog -> {PointSize -> Large, Point[{{0, 0}, {π, 0}, {-π, 0}}]},\nStreamPoints -> Fine, AspectRatio -> 0.8]\n\n\nTry this:\n\nFirst[Normal@plot] /. a_Arrow :> (\na /. {x_Real, y_Real} :> {Cos[x], Sin[x], y}\n) // Graphics3D", null, "You can add Cylinder if you want:\n\nShow[ %,\nGraphics3D@{[email protected], LightBlue, Cylinder[{{0, 0, -3}, {0, 0, 3}}]}\n]", null, "• (+1) I think it looks better with the cylinder added, though... – Jens Oct 29 '14 at 15:33\n• @Jens You are right, I just wanted to fulfill question about transparency :) – Kuba Oct 29 '14 at 17:32\n• Thank you, this is exactly I was looking for. – Artem Oct 30 '14 at 22:18\n\nYou could use an image representation of the plot and map it onto the modified cylinder that I defined in the answer linked here.\n\nJust copy the definition of cyl from that answer, which includes the ability to add textures as follows:\n\nimg = Image@StreamPlot[{y, -Sin[x]}, {x, -5, 5}, {y, -3, 3},\nFrame -> None,\nPlotRange -> {{-5, 5}, {-3, 3}},\nEpilog -> {PointSize -> Large,\nPoint[{{0, 0}, {Pi, 0}, {-Pi, 0}}]}, StreamPoints -> Fine,\nAspectRatio -> 0.8, PlotRangePadding -> 0, ImageMargins -> 0,\nImageSize -> 800];\n\nGraphics3D[{Texture[img], EdgeForm[],\ncyl[{{0, 0, 0}, {0, 0, 2 Pi}}, 1]}, Boxed -> False]", null, "The resolution is controlled by the options of Image or by the ImageSize options in StreamPlot.\n\nI also added the PlotRange to the original plot to suppress the plot range padding.\n\nEdit\n\nTo make the whole thing transparent, you can use the same approach provided that the image has an alpha channel with transparent background:\n\nimg = Rasterize[\nStreamPlot[{y, -Sin[x]}, {x, -5, 5}, {y, -3, 3}, Frame -> None,\nPlotRange -> {{-5, 5}, {-3, 3}},\nEpilog -> {PointSize -> Large,\nPoint[{{0, 0}, {Pi, 0}, {-Pi, 0}}]}, StreamPoints -> Fine,\nAspectRatio -> 0.8, PlotRangePadding -> 0, ImageMargins -> 0,\nImageSize -> 500], Background -> None, ImageResolution -> 300\n];\n\nGraphics3D[{Texture[ImageData@img], EdgeForm[],\ncyl[{{0, 0, 0}, {0, 0, 2 Pi}}, 1]}, Boxed -> False,\nLighting -> \"Neutral\"]", null, "Here I used Rasterize because it permits a Background -> None option. Also, I used ImageResolution in combination with the ImageSize specification of the StreamPlot to make sure that the Points from the Epilog in the original plot are properly visible.\n\nTo combine transparency with a cylinder \"backbone\" for better visibility, you could do it like this:\n\nGraphics3D[{Texture[ImageData@img], EdgeForm[],\ncyl[{{0, 0, 0}, {0, 0, 2 Pi}}, 1],\nFaceForm[Directive[Opacity[.5], Orange]],\nCylinder[{{0, 0, -.01}, {0, 0, 2 Pi + .01}}, .99]}, Boxed -> False,\nLighting -> \"Neutral\"]", null, "• Are you sure this answers the question (\"I found examples on the site how to put a texture on a cylinder, but cannot figure out how to make it transparent\")? – user484 Oct 29 '14 at 16:28\n• One could add an alpha channel: img2 = Image[ImageData[img] /. {{1., 1., 1.} -> {1., 1., 1., 0.5}, {r_, g_, b_} :> {r, g, b, 1.}}, ColorSpace -> \"RGB\"]. (Top & bottom stay solid, though.) But I agree with your other comment. The way it is is easier to see. – Michael E2 Oct 29 '14 at 16:55" ]

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[ "## Calculus (3rd Edition)\n\n$$t=1, \\quad t=3.$$\nSince the bases are equal, then the exponents are equal. Hence, $$t^2=4t-3\\Longrightarrow t^2-4t+3=0 \\Longrightarrow (t-1)(t-3)=0.$$ Then, $$t=1, \\quad t=3.$$" ]

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[ "# #44c00c Color Information\n\nIn a RGB color space, hex #44c00c is composed of 26.7% red, 75.3% green and 4.7% blue. Whereas in a CMYK color space, it is composed of 64.6% cyan, 0% magenta, 93.8% yellow and 24.7% black. It has a hue angle of 101.3 degrees, a saturation of 88.2% and a lightness of 40%. #44c00c color hex could be obtained by blending #88ff18 with #008100. Closest websafe color is: #33cc00.\n\n• R 27\n• G 75\n• B 5\nRGB color chart\n• C 65\n• M 0\n• Y 94\n• K 25\nCMYK color chart\n\n#44c00c color description : Strong green.\n\n# #44c00c Color Conversion\n\nThe hexadecimal color #44c00c has RGB values of R:68, G:192, B:12 and CMYK values of C:0.65, M:0, Y:0.94, K:0.25. Its decimal value is 4505612.\n\nHex triplet RGB Decimal 44c00c `#44c00c` 68, 192, 12 `rgb(68,192,12)` 26.7, 75.3, 4.7 `rgb(26.7%,75.3%,4.7%)` 65, 0, 94, 25 101.3°, 88.2, 40 `hsl(101.3,88.2%,40%)` 101.3°, 93.8, 75.3 33cc00 `#33cc00`\nCIE-LAB 68.717, -61.461, 66.932 21.299, 38.953, 6.744 0.318, 0.581, 38.953 68.717, 90.87, 132.56 68.717, -55.124, 82.048 62.412, -48.306, 37.282 01000100, 11000000, 00001100\n\n# Color Schemes with #44c00c\n\n• #44c00c\n``#44c00c` `rgb(68,192,12)``\n• #880cc0\n``#880cc0` `rgb(136,12,192)``\nComplementary Color\n• #9ec00c\n``#9ec00c` `rgb(158,192,12)``\n• #44c00c\n``#44c00c` `rgb(68,192,12)``\n• #0cc02e\n``#0cc02e` `rgb(12,192,46)``\nAnalogous Color\n• #c00c9e\n``#c00c9e` `rgb(192,12,158)``\n• #44c00c\n``#44c00c` `rgb(68,192,12)``\n• #2e0cc0\n``#2e0cc0` `rgb(46,12,192)``\nSplit Complementary Color\n• #c00c44\n``#c00c44` `rgb(192,12,68)``\n• #44c00c\n``#44c00c` `rgb(68,192,12)``\n• #0c44c0\n``#0c44c0` `rgb(12,68,192)``\n• #c0880c\n``#c0880c` `rgb(192,136,12)``\n• #44c00c\n``#44c00c` `rgb(68,192,12)``\n• #0c44c0\n``#0c44c0` `rgb(12,68,192)``\n• #880cc0\n``#880cc0` `rgb(136,12,192)``\n• #2b7808\n``#2b7808` `rgb(43,120,8)``\n• #339009\n``#339009` `rgb(51,144,9)``\n• #3ba80b\n``#3ba80b` `rgb(59,168,11)``\n• #44c00c\n``#44c00c` `rgb(68,192,12)``\n• #4cd80e\n``#4cd80e` `rgb(76,216,14)``\n• #55f00f\n``#55f00f` `rgb(85,240,15)``\n• #66f227\n``#66f227` `rgb(102,242,39)``\nMonochromatic Color\n\n# Alternatives to #44c00c\n\nBelow, you can see some colors close to #44c00c. Having a set of related colors can be useful if you need an inspirational alternative to your original color choice.\n\n• #71c00c\n``#71c00c` `rgb(113,192,12)``\n• #62c00c\n``#62c00c` `rgb(98,192,12)``\n• #53c00c\n``#53c00c` `rgb(83,192,12)``\n• #44c00c\n``#44c00c` `rgb(68,192,12)``\n• #35c00c\n``#35c00c` `rgb(53,192,12)``\n• #26c00c\n``#26c00c` `rgb(38,192,12)``\n• #17c00c\n``#17c00c` `rgb(23,192,12)``\nSimilar Colors\n\n# #44c00c Preview\n\nThis text has a font color of #44c00c.\n\n``<span style=\"color:#44c00c;\">Text here</span>``\n#44c00c background color\n\nThis paragraph has a background color of #44c00c.\n\n``<p style=\"background-color:#44c00c;\">Content here</p>``\n#44c00c border color\n\nThis element has a border color of #44c00c.\n\n``<div style=\"border:1px solid #44c00c;\">Content here</div>``\nCSS codes\n``.text {color:#44c00c;}``\n``.background {background-color:#44c00c;}``\n``.border {border:1px solid #44c00c;}``\n\n# Shades and Tints of #44c00c\n\nA shade is achieved by adding black to any pure hue, while a tint is created by mixing white to any pure color. In this example, #030700 is the darkest color, while #f7fef4 is the lightest one.\n\n• #030700\n``#030700` `rgb(3,7,0)``\n• #091a02\n``#091a02` `rgb(9,26,2)``\n• #102c03\n``#102c03` `rgb(16,44,3)``\n• #163f04\n``#163f04` `rgb(22,63,4)``\n• #1d5105\n``#1d5105` `rgb(29,81,5)``\n• #236406\n``#236406` `rgb(35,100,6)``\n• #2a7607\n``#2a7607` `rgb(42,118,7)``\n• #308909\n``#308909` `rgb(48,137,9)``\n• #379b0a\n``#379b0a` `rgb(55,155,10)``\n• #3dae0b\n``#3dae0b` `rgb(61,174,11)``\n• #44c00c\n``#44c00c` `rgb(68,192,12)``\n• #4bd20d\n``#4bd20d` `rgb(75,210,13)``\n• #51e50e\n``#51e50e` `rgb(81,229,14)``\n• #5af016\n``#5af016` `rgb(90,240,22)``\n• #67f229\n``#67f229` `rgb(103,242,41)``\n• #74f33b\n``#74f33b` `rgb(116,243,59)``\n• #81f44e\n``#81f44e` `rgb(129,244,78)``\n• #8ff560\n``#8ff560` `rgb(143,245,96)``\n• #9cf673\n``#9cf673` `rgb(156,246,115)``\n• #a9f785\n``#a9f785` `rgb(169,247,133)``\n• #b6f998\n``#b6f998` `rgb(182,249,152)``\n• #c3faaa\n``#c3faaa` `rgb(195,250,170)``\n• #d0fbbd\n``#d0fbbd` `rgb(208,251,189)``\n• #ddfccf\n``#ddfccf` `rgb(221,252,207)``\n• #eafde1\n``#eafde1` `rgb(234,253,225)``\n• #f7fef4\n``#f7fef4` `rgb(247,254,244)``\nTint Color Variation\n\n# Tones of #44c00c\n\nA tone is produced by adding gray to any pure hue. In this case, #656a62 is the less saturated color, while #41c804 is the most saturated one.\n\n• #656a62\n``#656a62` `rgb(101,106,98)``\n• #62725a\n``#62725a` `rgb(98,114,90)``\n• #5f7953\n``#5f7953` `rgb(95,121,83)``\n• #5c814b\n``#5c814b` `rgb(92,129,75)``\n• #598943\n``#598943` `rgb(89,137,67)``\n• #56913b\n``#56913b` `rgb(86,145,59)``\n• #539933\n``#539933` `rgb(83,153,51)``\n• #50a12b\n``#50a12b` `rgb(80,161,43)``\n• #4da824\n``#4da824` `rgb(77,168,36)``\n• #4ab01c\n``#4ab01c` `rgb(74,176,28)``\n• #47b814\n``#47b814` `rgb(71,184,20)``\n• #44c00c\n``#44c00c` `rgb(68,192,12)``\n• #41c804\n``#41c804` `rgb(65,200,4)``\nTone Color Variation\n\n# Color Blindness Simulator\n\nBelow, you can see how #44c00c is perceived by people affected by a color vision deficiency. This can be useful if you need to ensure your color combinations are accessible to color-blind users.\n\nMonochromacy\n• Achromatopsia 0.005% of the population\n• Atypical Achromatopsia 0.001% of the population\nDichromacy\n• Protanopia 1% of men\n• Deuteranopia 1% of men\n• Tritanopia 0.001% of the population\nTrichromacy\n• Protanomaly 1% of men, 0.01% of women\n• Deuteranomaly 6% of men, 0.4% of women\n• Tritanomaly 0.01% of the population" ]

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[ "# 9.21: Heights of Cylinders Given Surface Area or Volume\n\n$$\\newcommand{\\vecs}{\\overset { \\rightharpoonup} {\\mathbf{#1}} }$$ $$\\newcommand{\\vecd}{\\overset{-\\!-\\!\\rightharpoonup}{\\vphantom{a}\\smash {#1}}}$$$$\\newcommand{\\id}{\\mathrm{id}}$$ $$\\newcommand{\\Span}{\\mathrm{span}}$$ $$\\newcommand{\\kernel}{\\mathrm{null}\\,}$$ $$\\newcommand{\\range}{\\mathrm{range}\\,}$$ $$\\newcommand{\\RealPart}{\\mathrm{Re}}$$ $$\\newcommand{\\ImaginaryPart}{\\mathrm{Im}}$$ $$\\newcommand{\\Argument}{\\mathrm{Arg}}$$ $$\\newcommand{\\norm}{\\| #1 \\|}$$ $$\\newcommand{\\inner}{\\langle #1, #2 \\rangle}$$ $$\\newcommand{\\Span}{\\mathrm{span}}$$ $$\\newcommand{\\id}{\\mathrm{id}}$$ $$\\newcommand{\\Span}{\\mathrm{span}}$$ $$\\newcommand{\\kernel}{\\mathrm{null}\\,}$$ $$\\newcommand{\\range}{\\mathrm{range}\\,}$$ $$\\newcommand{\\RealPart}{\\mathrm{Re}}$$ $$\\newcommand{\\ImaginaryPart}{\\mathrm{Im}}$$ $$\\newcommand{\\Argument}{\\mathrm{Arg}}$$ $$\\newcommand{\\norm}{\\| #1 \\|}$$ $$\\newcommand{\\inner}{\\langle #1, #2 \\rangle}$$ $$\\newcommand{\\Span}{\\mathrm{span}}$$\n\nUse formulas to find the height of a cylinder, given the volume or surface area.", null, "Figure $$\\PageIndex{1}$$\n\nGregory's family just bought a hot tub for their lake house. The hot tub company told his family that the tub holds 125 cubic feet of water. Gregory is interested to know how deep the hot tub is. He measures the diameter of the top and finds that the hot tub is 6 feet across. What is the height, or depth, of the hot tub?\n\nIn this concept, you will learn how to calculate the height of a cylinder when given the volume and radius or diameter.\n\n### Finding the Height of a Cylinder Given Volume\n\nSometimes you will know the volume and radius of a cylinder and you won’t know the height of it. Think about a water tower that is cylindrical in shape. You might know how much volume the tank will hold and the radius of the tank, but not the height of it. When this happens, you can use the formula for the volume of a cylinder to find the missing height:\n\n\\begin{aligned} V&= \\pi r^{2}h \\\\ V&= \\pi (2)^{2}(10) \\\\ V&= \\pi (4)(10) \\\\ V&= 40\\pi \\\\ V&= 125.6 \\text{ in}^{3}\n\nLet's look at an example.\n\nA cylinder with a radius of 2 inches has a volume of 125.6 cubic inches. What is the height of the cylinder?\n\nThe volume and the radius are given, so substitute these into the formula and then solve for h, the height.\n\n\\begin{aligned}V&= \\pi r^{2}h \\\\ 125.6&=(3.14)(22)h \\\\ 125.6&=(3.14)(4)h \\\\ 125.6&=12.56h \\\\ 125.6&\\divide 12.56 \\\\ 10 \\text{ in}&=12.56 h\\divide 12.56=h\\end{aligned}\n\nThe height of the cylinder is 10 inches.\n\nCheck your work by substituting the answer in for the height. You should get a volume of 125.6 cubic inches.\n\n\\begin{aligned} V&= \\pi r^{2}h \\\\ V&= \\pi (2)^{2}(10) \\\\ V&= \\pi (4)(10) \\\\ V&= 40\\pi \\\\ V&= 125.6 \\text{ in}^{3}\\end{aligned}\n\nWhat is the height of a cylinder that has a radius of 6 cm and a volume of 904.32 cubic cm?\n\nAgain, you have been given the volume and the radius. Put this information into the formula along with the value of pi and solve for h, the height.\n\n\\begin{aligned}V&= \\pi r^{2}h \\\\ 904.32&=(3.14)(62)h \\\\ 904.32&=(3.14)(36)h \\\\ 904.32&=113.04 h \\\\ 904.32\\divide 113.04&=113.04h\\divide 113.04 \\\\ 8 \\text{ cm}&=h\\end{aligned}\n\nThe height of this cylinder is 8 centimeters.\n\nExample $$\\PageIndex{1}$$\n\nEarlier, you were given a problem about Gregory and his family's hot tub.\n\nTo figure this out, use the formula for volume of a cylinder. He already knows the volume of the tub is 125 cubic feet and the diameter is 6 feet.\n\nSolution\n\nFirst, divide the diameter by 2 and plug the values for volume, pi, and radius into the formula for volume of a cylinder.\n\n\\begin{aligned}r&= 6\\divide 2 \\\\ r&= 3 \\\\ V&= \\pi r^{2}h \\\\ 125&=(3.14)(3^{2})h\\end{aligned}\n\nNext, square the radius and multiply the values together.\n\n\\begin{aligned}125&=(3.14)(3^{2})h \\\\ 125&=(3.14)(9)h \\\\ 125&=28.26h\\end{aligned}\n\nLast, divide both sides by 200.96 for the answer, remembering to include the appropriate unit of measurement.\n\n\\begin{aligned}125&=28.26h \\\\ 125\\divide 28.26&=28.26 h\\divide 28.26 \\\\ 4.42 \\text{ ft}&=hv\\end{aligned}\n\nThe answer is Gregory's hot tub is 4.42 feet deep.\n\nExample $$\\PageIndex{2}$$\n\nJavier wants to construct a cylindrical container to hold enough water for his pet fish. He read that the fish needs to live in 2,110.08 cubic inches of water. If he constructs a tank with a diameter of 16 inches, how tall must he make it so that it holds the right amount of water?\n\nSolution\n\nFirst, divide the diameter by 2 and plug the values for volume, pi, and radius into the formula for volume of a cylinder.\n\n\\begin{aligned}r&= 16\\divide 2 \\\\ r&= 8 \\\\ V&=(3.14)(82)h \\\\ 2,110.08&=\\pi r^{2}h\\end{aligned}\n\nNext, square the radius and multiply the values together.\n\n\\begin{aligned}2,110.08&=(3.14)(8^{2})h \\\\ 2,110.08&=(3.14)(64)h \\\\ 2,110.08&=200.96h\\end{aligned}\n\nThen, divide both sides by 200.96 for the answer, remembering to include the appropriate unit of measurement.\n\n\\begin{aligned}2,110.08&=200.96h \\\\ 2,110.08\\divide 200.96&=200.96 h\\divide 200.96 \\\\ 10.5 \\text{ in}&=h\\end{aligned}\n\nThe answer is Javier must make his tank 10.5 inches tall for his tank to hold 2,110.08 cubic inches of water.\n\nExample $$\\PageIndex{3}$$\n\nFind the height of a cylinder with radius = 6 inches and volume = 904.32 cubic inches.\n\nSolution\n\nFirst, plug the values of the volume, pi, and radius into the formula for volume of a cylinder.\n\n\\begin{aligned}V&= \\pi r^{2}h \\\\ 904.32&=(3.14)(6^{2})h\\end{aligned}\n\nNext, square the radius and multiply the values together.\n\n\\begin{aligned}904.32&=(3.14)(62)h \\\\ 904.32&=(3.14)(36)h \\\\ 904.32&=113.04h\\end{aligned}\n\nLast, divide each side by 113.04 for the answer, remembering to include the appropriate unit of measurement.\n\n\\begin{aligned}904.32&=113.04h \\\\ 904.32\\divide 113.04&=113.04h\\divide 113.04 \\\\ 8 \\text{ in}&=h\\end{aligned}\n\nThe answer is the height of the cylinder is 8 inches.\n\nExample $$\\PageIndex{4}$$\n\nFind the height of a cylinder with radius = 3 meters and volume = 354.34 cubic meters.\n\nSolution\n\nFirst, plug the values of the volume, pi, and radius into the formula for volume of a cylinder.\n\n\\begin{aligned}V&= \\pi r^{2} h \\\\ 354.34&=(3.14)(3^{2})h \\end{aligned}\n\nNext, square the radius and multiply the values together.\n\n\\begin{aligned}354.34&=(3.14)(3^{2})h \\\\ 904.32&=(3.14)(9)h \\\\ 354.34&=28.26h \\end{aligned}\n\nLast, divide each side by 28.26 for the answer, remembering to include the appropriate unit of measurement.\n\n\\begin{aligned}354.34v=28.26h \\\\ 354.34\\divide 28.26&=28.26h\\divide 28.26 \\\\ 9 \\text{ m}&=h\\end{aligned}\n\nThe answer is the height of the cylinder is 9 meters.\n\nExample $$\\PageIndex{5}$$\n\nFind the height of a cylinder with radius = 5 feet and volume = 785 cubic feet.\n\nSolution\n\nFirst, plug the values of the volume, pi, and radius into the formula for volume of a cylinder.\n\n\\begin{aligned}V&= \\pi r^{2} h \\\\ 785&=(3.14)(52)h\\end{aligned}\n\nNext, square the radius and multiply the values together.\n\n\\begin{aligned}785&=(3.14)(52)h \\\\ 785&=(3.14)(25)h \\\\ 785&=78.5h \\end{aligned}\n\nLast, divide each side by 78.5 for the answer, remembering to include the appropriate unit of measurement.\n\n\\begin{aligned}785&=78.5h \\\\ 785\\divide 78.5&=78.5\\divide 78.5 \\\\ 10 \\text{ ft}&=h\\end{aligned}\n\nThe answer is the height of the cylinder is 10 feet.\n\n## Review\n\nGiven the volume and the radius, find the height of each cylinder.\n\n1. $$r= 6 \\text{ in}$$, $$V&= 904.32 \\text{ in}^{3}$$\n2. $$r= 5 \\text{ in}$$, $$V&= 706.5 \\text{ in}^{3}$$\n3. $$r= 7 \\text{ ft}$$, $$V&= 2307.9 \\text{ ft}^{3}$$\n4. $$r= 8 \\text{ ft}$$, $$V&= 4019.2 \\text{ ft}^{3}$$\n5. $$r= 7 \\text{ ft}$$, $$V&= 1538.6 \\text{ ft}^{3}$$\n6. $$r= 12\\text{ m}$$, $$V&= 6330.24\\text{ m}^{3}$$\n7. $$r= 9\\text{ m}$$, $$V&= 4069.49\\text{ m}^{3}$$\n8. $$r= 10\\text{ m}$$, $$V&= 5652\\text{ m}^{3}$$\n9. $$r= 12 \\text{ in}$$, $$V&= 11304 \\text{ in}^{3}$$\n10. $$r= 11 \\text{ ft}$$, $$V&= 3039.52 \\text{ ft}^{3}$$\n11. $$r= 10 \\text{ in}$$, $$V&= 1570 \\text{ in}^{3}$$\n12. $$r= 9.5 \\text{ in}$$, $$V&= 1700.31 \\text{ in}^{3}$$\n13. $$r= 8\\text{ m}$$, $$V&= 1808.64\\text{ m}^{3}$$\n14. $$r= 14 \\text{ ft}$$, $$V&= 5538.96 \\text{ ft}^{3}$$\n15. $$r= 13.5 \\text{ in}$$, $$V&= 4005.85 \\text{ in}^{3}$$\n\n## Resources\n\nInteractive Element\n\n## Vocabulary\n\nTerm Definition\nCubic Units Cubic units are three-dimensional units of measure, as in the volume of a solid figure.\nVolume Volume is the amount of space inside the bounds of a three-dimensional object." ]

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[ "# Mindless use of \"antisimplifications\" such as $1/x+1/y=(x+y)/xy$ and $1/\\sqrt{2}=\\sqrt{2}/2$\n\nI recently gave an exam problem that roughly 2/3 of the class made much more difficult by using the identity $1/x+1/y=(x+y)/xy$. Their work would have been much simpler if they hadn't done this. It seems like a symptom of the type of intellectual laziness that causes people to do things by pattern recognition rather than because they have a logical reason for doing them.\n\nWhen students are taught this identity, are they told a reason why they might want to use it? What would the reason be?\n\nI will ask them why they did it when I return the exam, but I suspect I'll get answers to the effect of \"that's how you do that kind of problem in algebra.\" Maybe this is similar to stuff like multiplying out an expression such as $(x+y+z)(a+b+c+d)$, which I think they do because they think of the notation as a set of orders that they need to carry out.\n\nIs this reflex similar to the one that compels them to rationalize the denominator in an expression such as $1/\\sqrt{2}$? That one at least I think I understand the original reason for. If you're doing decimal arithmetic and performing division using long division (rather than log tables, a slide rule, or an electronic calculator), then rationalizing the denominator is a big win, so that would have sort of made sense before slide rules became common. Would the justification for habitually doing $1/x+1/y=(x+y)/xy$ be that division is a more expensive operation than multiplication if you don't have a calculator, slide rule, or log tables?\n\nOr maybe math teachers want answers like $1/\\sqrt2$ in a canonical form so that it's easier to check students' work? (But this seems like an anachronism now that we have WeBWorK et al.) But I don't see how $(x+y)/xy$ is more canonical than $1/x+1/y$, and in general it's preferable not to have the same variable appearing more than once, e.g., if we want to reason about the dependence on that variable.\n\nQuestions:\n\n(1) Why is this identity taught?\n\n(2) Why do students use it in inappropriate situations, and what can we do to cure this problem?\n\n• Students tend to think that in algebra there is a right way and a wrong way to write an expression, and their job is to do it the right way. Algebra is a set of rules for writing things the right way. The idea that some things are a matter of taste (whether to prefer this expression to that expression) or that some ways of writing an expression are helpful in some contexts but unhelpful in others is foreign to their way of thinking. Mathematicians think of algebraic rules for manipulating expressions as flexible rules. Students tend to think of them as rigid rules. Mar 26 '17 at 3:38\n• I haven't taught the identity here; in fact, I have given a problem in which knowing this identity would be very helpful, and had students not use it! \"Compute the sum of the reciprocals of two numbers, if you know that the numbers have sum 5 and product 10.\" This problem is immediate using the identity above, but I find students set up two equations $x+y=5$ and $xy = 10$ and solve a quadratic to figure it out. Meanwhile, I've asked students to compute $1/84 + 1/126$ and they ess'ly use the identity you mention. My guess is you simply observe a lack of sense-making, cf. e.g. Schoenfeld... Mar 26 '17 at 4:06\n• The question is just slightly unclear. Critical detail: What was your written direction for the exercise? Is your criticism that the students simplified $1/x + 1/y$ at all, or that they simplified it via an unnecessarily complicated method? Mar 26 '17 at 13:37\n• @DanielR.Collins: It's a physics problem involving optics. They derive equations of the form $1/z=1/x+1/y$ and $1/p=1/q+1/(z+r)$, and they're supposed to express $q$ in terms of the quantities other than $z$. My criticism is that they needlessly complicated (antisimplified) these expressions by applying this identity. There is no simplification possible or required. All they had to do was substitute for $z$ in the second expression, and they were done in 3 lines of algebra. Instead they insisted on applying the identity, which made it into a huge, nasty mess.\n– user507\nMar 26 '17 at 22:48\n• +1 for calling out rationalizing the denominator. I've always thought it was ridiculous and I was ecstatic when I had a calc 2+3 professor who hated it and insisted we don't do it. He would always say, \"You wouldn't write $x/x^2$ instead of $1/x$, would you?\" Granted I do recognize that, e.g., $\\sqrt2-1$ is more simplified than $\\dfrac1{\\sqrt2+1}$, but they don't always work out like this. I just can't stand the \"rationalize the denominator\" mentality that constantly gets drilled into pre-college students in the U.S. Not sure how it is elsewhere. Oh, and +1 for mentioning WeBWorK. Yay.\n– user6648\nApr 12 '17 at 16:53\n\nFirst, I would expect this identity not to be taught, but to be obtained by students as a particular case of the method of reducing fractions to the same denominator, which is sufficiently useful not to need an explanation why it is taught.\n\nSecond, the only way I see to take care of this problem (and many others) would be to teach less standardized exercises, and induce more sense-making. In particular, we should teach tactics and strategy of manipulating an algebraic expression in order to reach a certain goal (if we want to find roots of an expression, let it factorized; if we want to sum several expressions, a distributed form might be better; etc.) The problem is that teaching this is very difficult and very time-consuming (we cannot stick to a few exercises, we need several similar-looking exercises that needs different methods, to be able to point out which subtle differences could be used to construct different strategies), and needs more efforts from the students. It may feel like much effort for little gain, compared to focusing on a few standard exercises and have student turn out decent tests. Seeing student fail again and again when we try to test that kind of understanding is pushing us all toward standardized exercises and tests, and make it yet more difficult to change our ways. We should still try hard, because ultimately it is understanding and sense-making have value incommensurable with having mastered a handful of meaningless methods, but we should be warned that we will feel like Sisyphus all along the way.\n\nA last remark (edit: which actually is a remark, and do not claim to be an answer about why these students would use some form over another): concerning $\\sqrt{2}/2$ versus $1/\\sqrt{2}$, one important purpose of normalized forms is to help recognize when two numbers are equal. There is even a lot of theory of normal forms in various mathematical settings, where one expect to be able to prove that two objects are equal if and only if their normal forms are equal, and to devise algorithms to produce a normal form from an arbitrary expression. Term rewriting is very much about formalizing this (but the same ideas appear in various subfields).\n\n• +1 for I would expect this identity not to be taught, but to be obtained by students as a particular case of the method of reducing fractions to the same denominator This is exactly what I was thinking, and I was considering how to say this in a comment before I got to your answer. For what it's worth, sums whose terms are the reciprocals of an arithmetic progression are called harmonic series, and in older algebra texts (at least 50 years old) harmonic series were studied side-by-side with arithmetic and geometric series, but the topic was mostly dropped by the 1950s. Mar 27 '17 at 19:39\n• First, I would expect this identity not to be taught, but to be obtained by students There might be three levels of mathematical ability and skill to discuss, which would be, from lowest to highest: (1) students who are taught this identity and use it mindlessly, (2) students who are taught this identity and use it only when it is an appropriate tactic for the problem at hand, and (3) students who would be able to come up with this identity on their own. I would say that 80% of my students are at level 1, 20% are at level 2, and none are at level 3. I'm at a community college.\n– user507\nMar 27 '17 at 20:11\n• @BenCrowell in my mind the point though is not \"so that it's easier to check students' work.\" But rather to recognize that the numbers that can be obtained from the rational and a root using addition (subtraction), multiplication and division are the same that can be obtained using addition (subtraction) and multiplication only. This is not completely obvious and the direct generalization of this is a standard result in most intros to field theory.\n– quid\nMar 27 '17 at 21:36\n• @BenCrowell I can't speak for the US school system but in the Czech Republic, leaving results in normalized form is required for full points. Comparison between one values is one reason I believe, ease of approximation by hand is another. Lots of people can make a decent guess at how much $\\sqrt{2}/2$ since they tend to have an idea how much $\\sqrt{2}$ is and can divide by 2. Few people can make the same calculation when they try to invert $\\sqrt{2}$.\n– DRF\nMar 28 '17 at 9:23\n• @BenCrowell: a minor comment about you three levels of ability and skill. These levels assume that the identity is to be taught, which I find quite debatable. I would teach only a few identities, and alongside a few methods (including reducing to the same denominator). Considering that very many such identities should be taught is a stance that often comes in opposition to sense-making, while the motivation to make students able to deal with more situations without needing understanding feels to me a low-value goal. Mar 28 '17 at 11:29\n\nFor students at that level, routine algebraic calculations are an easy step, while thinking about what steps to take is quite difficult. So they'll often prefer to do familiar calculations - even long and tedious ones - and only turn to more extreme measures like stepping back to think about the big picture as a last resort. They also have an extreme aversion to backtracking (most of them think of trying an unsuccessful solution as a pure failure, rather than as progress towards finding the right one), so it's not surprising that, having backed themselves into a corner with an unhelpful algebraic manipulation, they push forward rather than trying something else.\n\nOne factor to consider is that students don't usually know how hard a problem should be: they can't tell the difference between \"this problem get too messy, I should try something else\" and \"this problem just needs some more effort\". (This works in both directions: students persevering through awful calculations, and also students who redo an easy problem repeatedly because they can't believe the answer isn't an integer.)\n\n• How to appropriately use algebraic tools is subtle. For one, a primary motivation for algebra is to replace otherwise complicated thinking with automatic procedures. Of course, the end result of that should be to free up mental space and energy to become able to solve more complex problems, not as a means to avoid thinking at all. But conveying that to students in a meaningful way (rather than just lecturing it to them) is generally quite challenging. Apr 12 '17 at 13:47\n\nI think that \"rationalizing numbers\" (clearing the denominators of radicals) is an anachronism: it was useful at one time, because if you want to evaluate $\\frac{1}{\\sqrt{2}}$, it is much easier to perform the division $\\frac{\\sqrt{2}}{2}$ if you are obtaining $\\sqrt{2}$ by a table lookup.\n\nSo it was a useful skill at one time, but now it is just being passed along by rote.\n\nHowever, I feel this way about a lot of math. For instance, I think most of what we teach students in a \"Calc 2\" course is similarly anachronistic.\n\n• @tilper The vast majority of functions you can write down (like, say, $\\sin(x^2)$) have no elementary antiderivative. I think we emphasize the skill of finding antiderivatives by hand'' for basically the same reason we force them to rationalize denominators: at one time we needed to compute integrals by table lookups, so we had to transform many integrals into standard forms. With computers, we can numerically integrate with ease. I think most of the emphasis should be placed on getting rigorous estimates for numerical approx, rather than computing antiderivatives symbolically. Apr 12 '17 at 17:01\n• @StevenGubkin I would strongly disagree with this approach. IMO the reason we teach 90% of calc is to force the students to at least try to think. Pretty much everything they do could be done by a computer, but that's not the point. The point is that unless they do a couple a hundred derivatives they don't understand what they are or how they behave. Being able to evaluate a derivative or an integral is the trivial last step which comes after understanding that you need to evaluate it and why.\n– DRF\nApr 13 '17 at 9:32\n• @DRF I agree that students should have to think. I disagree that doing hundreds of derivatives and integrals involves much thinking, or gets students to understand what these operators are or how they behave. Maybe it makes them better at algebra. I think they should be modeling physical phenomenon, explaining why the differential equations they are setting up make sense, exploring connections, bounding errors, exploring pathologies, challenging definitions, etc. I think very little of the course should be mindless mathematical symbol manipulation at this point. Apr 13 '17 at 12:24\n• Is teaching vocabulary anachronistic because the definitions of most words we encounter can easily be looked up on the web? Apr 13 '17 at 12:34\n• Similarly, if you find yourself thinking about things where computing hundreds of symbolic derivatives and integrals comes up a lot, then it might be worth putting the effort into learning to compute them with ease. If not, I see no harm looking them up. What are students supposed to get out of a calculus class? I think that they can perform the computations for that test, but a year later their \"skill\" has faded. I would much rather that they emerge with an understanding of the relationship between rates and total amounts, how to approximate, how to argue, some pictures, etc. Apr 13 '17 at 13:28\n\nI certainly agree that there is a lot of \"mindless\" emphasis on various aspects of teaching algebra. However, to the extent that the mathematics community wants to encourage students to have a more \"playful\" way of looking at mathematics and to see the way that mathematics is the science of patterns, perhaps this \"identity\" could be used opportunistically to look at the phenomenon of Egyptian Fractions - the issue of writing p/q (p, q positive integers) as the sum of fractions of the form 1/x with distinct denominators.\n\nSo perhaps a student who added (1/3) + (1/10) in the spirit of (1/x) + (1/y) and found the answer to be 13/30 might find looking at (1/3) + (1/10) = 13/30 a source of \"new\" mathematical thoughts:\n\na. Can 13/30 be written in other ways as the sum of two unit fractions? as the sum of three unit fractions? What is the smallest denominator of unit fractions with distinct denominators that sum to 13/30?\n\nb. Can any fraction p/q be written as the sum of unit fractions with distinct denominators? (Tradeoff between number of fractions involved and the largest denominator that appears?)\n\nc. Study the solutions to: (1/x) + (1/y) = 1/z (e.g. (1/3) +(1/6) = 1/2)\n\nSo lots of current curriculum is not optimal, but if teachers have the freedom to do a bit \"extra\" and have a sufficient knowledge base perhaps some additional \"positive\" outcomes are possible." ]

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[ "", null, "Visualization - Maple Help\n\n Visualization", null, "New Visualizations\n\n Iterative Maps Group Theory Statistics Polyhedral Sets Data Plots", null, "Easier Plotting of Data Sets\n\nThe new dataplot command unifies many common visualizations for data in one convenient command.", null, "", null, "", null, "", null, "For more details, see the dataplot updates page.", null, "There is a new plots:-shadebetween command for shading the area between two curves or two surfaces f and g. There are options for shading only the parts where f>g or g>f, and for controlling the color and other features of these parts.\n\n >\n >", null, "> $\\mathrm{shadebetween}\\left(\\frac{x}{2}+1,{x}^{2},x=-2..2,\\mathrm{color}=\"Blue\",\\mathrm{positiveonly}\\right)$", null, "> $\\mathrm{shadebetween}\\left(\\frac{x}{2}+1,{x}^{2},x=-2..2,\\mathrm{color}=\"Maroon\",\\mathrm{changefill}=\\left[\\mathrm{color}=\\left[\"Orange\",\"Yellow\"\\right]\\right]\\right)$", null, ">", null, "", null, "Required Arguments are Now Optional for plot and plot3d commands", null, "Default Ranges in 3-D plots\n\nRanges can now be omitted when using the plot3d command to generate a 3-D plot. This behavior is similar to that of the plot command for generating 2-D plots. Default ranges of -10..10 are used when the range arguments are not provided. If a trigonometric function is detected in the first argument, then a default of -2*Pi..2*Pi is used instead.\n\n > $\\mathrm{plot3d}\\left(\\mathrm{sin}\\left(x\\right)*\\mathrm{cos}\\left(y\\right)\\right);$", null, ">", null, "", null, "Generating Empty Plots\n\nNot only are the ranges optional in a call to the plot or plot3d command, but so is the function to be plotted. If this argument is an empty list or is omitted altogether, then an empty plot is produced. If ranges are added, then they are used for the plot view. If additional options are provided, then they are applied.\n\n > $\\mathrm{plot}\\left(\\left[\\right]\\right);$", null, ">", null, "> $\\mathrm{plot3d}\\left(\\mathrm{title}=\"An empty plot\"\\right);$", null, "", null, "", null, "The style=pointline Option\n\nThere is a new pointline style for curves which displays the points making up the curve as well as the lines that connect them. It is a combination of the style=point and style=line options. See the plot/option and plot3d/option help pages for more information about the style option. The style=pointline option can also be used with surfaces.\n\n >", null, ">", null, ">", null, "", null, "The colorscheme option\n\nThe colorscheme option, available for surfaces and collections of points in earlier versions of Maple, is now available for curves. Additionally, you can now use any of the color spaces available in the ColorTools package.\n\n >", null, ">", null, ">", null, "" ]

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[ "# Chapter 4 - Graphs of the Circular Functions - Section 4.3 Graphs of the Tangent and Cotangent Functions - 4.3 Exercises - Page 171: 21", null, "RECALL: (1) The period of the function $y=\\tan{(bx)}$ is $\\frac{\\pi}{b}$. (2) The consecutive vertical asymptotes of the function $y=\\tan{x}$, whose period is $\\pi$, are $x=-\\frac{\\pi}{2}$ and $x=\\frac{\\pi}{2}$. Thus, with $b=\\frac{1}{4}$, the period of the given function is $\\frac{\\pi}{\\frac{1}{4}}=4\\pi$. Consecutive vertical asymptotes of the given function are $x=-2\\pi$ and $2\\pi$. This means that one period of the given function is in the interval $[-2\\pi, 2\\pi]$. Dividing this interval into four equal parts give the key x-values: $-\\pi, 0, \\pi$. To graph the given function, perform the following steps: (1) Create a table of values for the given function using the key x-values listed above. (Refer to the attached image table below.) (2) Graph the consecutive vertical asymptotes. (3) Plot each point from the table then connect them using a smooth curve, making sure that the curves are asymptotic with the lines in Step (2) above. Refer to the graph in the answer part above.", null, "" ]

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[ "# How do electromagnetic waves carry quantised energy?\n\nIf an electron oscillates about a mean position, it will create a time varying electric filed which in turn will create a time varying magnetic field and so on to create an electromagnetic wave. How does this wave carry energy , in which amount and how can this be quantised?\n\nI know that energy is quantised when we see it through the particle nature of EM waves but how can it be defined in terms of time varying electric and magnetic fields?\n\nIt is a difficult thing to visualize and connected with the wave-particle duality of photons. I think what you are interested in is the Second Quantization. This is where an electromagnetic wave is decomposed into its Fourier modes and each Fourier mode can be interpreted as simple harmonic oscillator. The energy levels of such oscillators corresponds to $E = nh\\nu$, where each electromagnetic mode with that energy is a state that has $n$ photons with energy $h\\nu$.", null, "As Einstein said and proved, with his photo-electric effect, light is quantized, photon's, 'packets' of light.\n\nThe 'sum' of one, two, three or more, simple harmonic oscillations, in space-time.\n\nUnless I'm making a mistake (somebody correct me if I'm wrong), that electromagnetic wave is identical to the wave of probability amplitude. (The word \"amplitude\" is the key. Think of it as a complex number spinning around in a circle.)\n\nThe way you get a particle out of it is by being uncertain of it's frequency.\n\nIf its frequency is totally certain, then its position is totally uncertain, and it's just infinitely \"spread out\".\n\nIf its frequency has a distribution, like a gaussian distribution about a mean, that's equivalent to an infinite sum of probability amplitude waves of different frequencies and powers. When they are added together, the only place they are \"in sync\" is one place, and either side of that, the power tapers off, because the waves all cancel out. The location of where they are in sync moves at what's called \"group velocity\".\n\nThat's the wave packet, whose power represents the probability of a photon appearing there.\n\n• There has been lots of discussion on \"wavefunction of a photon\" over the years. The way I understand creation of a localized 1-photon state is to form $\\int{f({\\bf{k}})|1_{\\bf{k}}\\rangle d^{3}\\bf{k}}$ where $|1_{\\bf{k}}\\rangle$ are the plane wave 1-photon states and $f(\\bf{k})$ is a shaping function in momentum space. – twistor59 Dec 10 '11 at 13:02" ]

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[ "# Document 17734524", null, "```Math 138\nAssignment 8\nSupplemental Problem Set for Section 2.2\nNote that this is a two-page document.\nFind the slope of each line.\nFind the slope of the straight line through the two points whose coordinates are given.\n7. (10, 2) and (25, 5)\n8. (6, 42) and (0, 0)\n9. (1, 6) and (2, 5)\n10. (4, 2) and (–5, 2)\n11. (–2, 1) and (–5, –3)\n12. (–1, 5) and (–1, 3)\n13. A wire is attached to the top of a pole and to the ground 15 meters from the pole. The slope of\n4\nthe wire is 3 . What is the height of the pole?\n15 m\nMath 138\nAssignment 8\n14. Consider the function f (t)  5t  7, with the domain N = {1, 2, 3,...}. Which of the\nfollowing numbers are in the range of the function. Explain how you know.\na.\n3\nb.\n14\nc.\n5\nd.\n13\n15. Determine which of the following are functions from D = {0, 1, 2, 3,..} to D. If your\nanswer is that it is not a function, explain why not.\n1\n2\na. f ( x)  x for all x in D.\nb. f (x)  3 if x is in {0, 1, 2, 3} and f (x)  0 if x is not in {0, 1, 2, 3}.\nc. f (x)  x for all x in D and f (x) 10 if x is in {1, 2, 3, 4}.\n16. Determine which of the following are functions with domain G 0, 1, 2, 3, ... .\na. f ( x)  3x if x  6 and f ( x)  4 if x  7.\nb. g ( x)  0 if x is in 1, 3, 5, 7, ... and g ( x)  3 if x is in 2, 4, 6, 8, ... .\n```" ]

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[ "Statistical Modelling\n\nThe Statistical Consulting Unit recommends this list of books on the topic of statistical modelling.\n\n• Agresti, A. (2007). An introduction to categorical data analysis, Hoboken- NJ Wiley:Interscience\n• Dobson, A.J. and Barnett, A. (2008). An introduction to Generalized linear models. 3rd edn. Chapman and Hall/CRC\n• McCulloch, C.and Searle, S. (2008). Generalized, linear and mixed models. 2nd edn. Wiley" ]

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Individuals are now accustomed to using the net in gadgets to see image and video data for inspiration, and according to the title of the article I will talk about about 1St Grade Maths Worksheets.\n\n• Regrouping Math Worksheets 1St Grade Advanced Graphing Calculator Basic Business Formulas First Grade Math Worksheets Advanced Worksheets Business Mathematics I Congruence Of Angles And Addition Properties Worksheet Answers Year 3 Math Workbook : The Worksheets Are Randomly Generated Each Time You Click On The Links Below.\n• Free 1St Grade Addition And Subtraction Math Worksheet Free4Classrooms , Help First Graders Learn And Practice Math With Our Free Online Math Worksheets.\n• Worksheet Year Maths Worksheets Printableee Math First Grade Subtraction Subtracting Grade 1 First Grade Math Worksheets Worksheets Area Reference Sheet Aa Math Free Time Worksheets Fun Mathematical Problems Free Grade 9 Math – First Grade Is An Exciting Year Of So Many 'Firsts'.\n• Free 1St Grade Addition And Subtraction Math Worksheet Free4Classrooms . 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The worksheets support any first grade math program, but go especially well with ixl's 1st grade math curriculum. Engage them with worksheets on different math topics and watch their math grades go up in no time! Help first graders learn and practice math with our free online math worksheets. Grab our 1st grade math worksheets featuring exercises in addition and subtraction, counting, place value, measurement, data rich with scads of practice, the ccss aligned printable 1st grade math worksheets with answer keys help kids solve addition and. These printable 1st grade math worksheets help students master basic math skills. You may not remember the first time you understood how and why 2 + 2 from basic addition and subtraction activities to measurement worksheets to puzzles where solving math problems unlocks the answer. You can also get a new, different one just by refreshing the page in your browser (press f5). 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These math printable are scientifically developed in such a way that they perfectly suit a 1st graders sensibilities to understand & solve math! 1st grade math worksheet 2. Welcome to the math salamanders 1st grade math worksheets. The initial focus is on numbers and counting followed by arithmetic and concepts related to fractions, time, money, measurement and geometry. Here you will find a wide range of free printable counting worksheets, which will help your child understand how to count on and back by 1s 5s and 10s and understand place value to 100. You can access the entire engageny grade 1 mathematics curriculum map and learning." ]

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[ "Timezone: »\n\nPoster\nInfluence Maximization with $\\varepsilon$-Almost Submodular Threshold Functions\nQiang Li · Wei Chen · Institute of Computing Xiaoming Sun · Institute of Computing Jialin Zhang\n\nMon Dec 04 06:30 PM -- 10:30 PM (PST) @ Pacific Ballroom #158\nInfluence maximization is the problem of selecting $k$ nodes in a social network to maximize their influence spread. The problem has been extensively studied but most works focus on the submodular influence diffusion models. In this paper, motivated by empirical evidences, we explore influence maximization in the non-submodular regime. In particular, we study the general threshold model in which a fraction of nodes have non-submodular threshold functions, but their threshold functions are closely upper- and lower-bounded by some submodular functions (we call them $\\varepsilon$-almost submodular). We first show a strong hardness result: there is no $1/n^{\\gamma/c}$ approximation for influence maximization (unless P = NP) for all networks with up to $n^{\\gamma}$ $\\varepsilon$-almost submodular nodes, where $\\gamma$ is in (0,1) and $c$ is a parameter depending on $\\varepsilon$. This indicates that influence maximization is still hard to approximate even though threshold functions are close to submodular. We then provide $(1-\\varepsilon)^{\\ell}(1-1/e)$ approximation algorithms when the number of $\\varepsilon$-almost submodular nodes is $\\ell$. Finally, we conduct experiments on a number of real-world datasets, and the results demonstrate that our approximation algorithms outperform other baseline algorithms." ]

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[ "# Math 10 Honors Numbers Summary\n\nStarting off the unit, we learned about prime numbers (a number that can only be divided by itself and 1) Writing the poem about prime numbers was very fun because I added the fact that 1 and 0 are not a prime number to my poem. By doing the first assignment and finding prime numbers between 1 to 200, I actually practiced my divisibility rules which I don’t use often.\nWe then learned about the real number system which was just review for me because I remembered everything from last year already. Reviewing rational and irrational numbers and how you would determine if a number was rational or not. Quick little reminder: If a number has decimals that repeat or terminate then it is rational, if a number has decimals that do not repeat and do not terminate then it is irrational. One thing I found very interesting was the fact that there are different amounts of infinity.\nNext, we learned about square roots and cube roots. Something I remembered from last year was the fact that if a number was a perfect square then it’s square root would be rational and if it was not a perfect square then it was irrational.\nLast thing we learned about was radicals, what the different terms were:", null, "And also this was the first topic this year that wasn’t review for me, I learned something new. I learned that the square root of a negative number is not possible, only odd roots of negative numbers are possible. I learned about the two properties of radicals and how when you’re multiplying radicals with the same index then you can multiply the radicands together to simplify (only if the index is even and the radicands are higher or equal to 0) Dividing radicals with the same index can also be simplified if you divide the radicands (again this could only work if the index is even and radicands are higher or equal to 0 and the bottom radicand cannot be 0.)\nI also learned how to turn entire radicals into mixed radicals and vice versa." ]

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[ "# An analysis of the Depreciation Methods in GAAP in the UK\n\n1491 words (6 pages) Essay\n\n1st Jan 1970 Accounting Reference this\n\nDisclaimer: This work has been submitted by a university student. This is not an example of the work produced by our Essay Writing Service. You can view samples of our professional work here.\n\nAny opinions, findings, conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of UKEssays.com.\n\nDepreciation is the allocation of the cost of a plant asset to expense over its useful (service) life in a rational and systematic manner” (Weygandt, Kieso and Kimmel, 2003:416). There are three factors affect the calculation of depreciation, which are asset cost, useful life and salvage value (Weygandt, Kieso and Kimmel, 2003). Accountant in different companies will use various methods to compute the depreciation. There are straight-line method, reducing balance method (double declining balance, sum of digits, reducing percentage), annuity method, and unit of production method (Mike, Ron and Allister, 1994). And in most companies, especially in the large corporations, they will use the straight-line method, because it is the easiest one to compute the depreciation. This essay will illustrate some method that usually used in the companies and contract with each method to find out which one is the most useful. At the beginning, the essay will illustrate the straight-line method, the second one is reducing balance method, the third method is sum of digits, and the last one is the unit of production method. Below each method, the essay will give an example, which is calculated by me.\n\nIf you need assistance with writing your essay, our professional essay writing service is here to help!\n\nUnder the straight-line method, the annual depreciation expense is the same over the asset’s estimated useful life every year. The annual depreciation expense is determined by depreciation cost divided by the useful life of the asset or multiplied by the annual rate of depreciation (Weygandt, Kieso and Kimmel, 2003).\n\nExample 1\n\nAn asset costs ¿¡11,000, its expected salvage value is ¿¡1,000, its estimated useful life is 5 years.\n\nDepreciable cost =¿¡11,000-¿¡1,000 =¿¡10,000\n\nAnnual depreciation expense =¿¡10,000/5years=¿¡2,000\n\nOR\n\nAnnual rate of depreciation =100%÷5years=20%\n\nAnnual depreciation expense =¿¡10,000*20%=¿¡2,000\n\nYear 1 Cost ¿¡11,000\n\nDepreciation 2,000\n\nYear 2 Net book value 9,000\n\nDepreciation 2,000\n\nYear 3 Net book value 7,000\n\nDepreciation 2,000\n\nYear 4 Net book value 5,000\n\nDepreciation 2,000\n\nYear 5 Net book value 3,000\n\nDepreciation 2,000\n\nNet book value 1,000\n\nThe straight-line method is the simplest way among all the methods; it suitable for the use of asset is unvarying during the useful life; it is popular used by large corporation, such as Campbell Soup, Marriott Corporation and General Mills.\n\nHowever, the reducing balance method has a falling depreciation amount every year during the useful life of the asset. The changing depreciation is depended on the book value (cost less accumulated depreciation). It is calculated to multiply the book value at the beginning of the year and the reducing balance depreciation rate (Weygandt, Kieso and Kimmel, 2003).\n\nExample 2\n\nAn asset costs (book value at the beginning of year) ¿¡11,000, its expected salvage value is ¿¡1,000, its estimated useful life is 5 years.\n\nReducing balance depreciation rate = 100%÷5years=20%* Calculation of ¿¡901.12(¿¡4505.6Ã-20%) is adjusted to ¿¡3505.6 in order to make the book value equal salvage value (Weygandt, Kieso and Kimmel, 2003).\n\nSum of digits is another kind of reducing balance method, which has the closest connection with useful life and salvage value of the asset. The depreciation cost is multiply depreciation cost (asset cost less salvage value) by digits of each year (Mike, Ron and Allister, 1994).\n\nExample 3\n\nAn asset costs ¿¡11,000, its expected salvage value is ¿¡1,000, its estimated useful life is 5 years\n\nThe digits add up is 1+2+3+4+5=15\n\nDepreciation cost =¿¡11,000-¿¡1,000=¿¡10,000\n\nYear 1 Cost ¿¡11,000\n\nDepreciation (5/15Ã-¿¡10,000) 3,333\n\nYear 2 Net book value 7,667\n\nDepreciation (4/15Ã-¿¡10,000) 2,667\n\nYear 3 Net book value 5,000\n\nDepreciation (3/15Ã-¿¡10,000) 2,000\n\nYear 4 Net book value 3,000\n\nDepreciation (2/15Ã-¿¡10,000) 1,333\n\nYear 5 Net book value 1,667\n\nDepreciation (1/15Ã-¿¡10,000) 667\n\nNet book value 1,000\n\nThe double declining balance method is very similar to the educing balance method. It just doubles the reducing balance depreciation rate and has the same way to compute the depreciation. Reducing percentage is a method alike to Sum of digits. It gives a fix amount of the asset in advance to write off each year. When company use the reducing balance method, it can combine the depreciation expense to the maintaining cost and run the asset (Mike, Ron and Allister, 1994). The depreciation charges will large in the early years and become smaller and smaller later.\n\nOur academic experts are ready and waiting to assist with any writing project you may have. From simple essay plans, through to full dissertations, you can guarantee we have a service perfectly matched to your needs.\n\nRather than the time period, the unit of production method write off the asset by expressing the total of units of production. Because it links to the machine’s usage and output closely, it is used in extractive corporations popularly (Mike, Ron and Allister, 1994). This method is used by some large corporation, such as ChevronTexaco Corp. and Boise Cascade Corporation (Weygandt, Kieso and Kimmel, 2003). The depreciation expense in this method is determined by depreciation cost per unit multiply by units of activity during the year. The depreciation cost per unit is computed by depreciation cost divide by total units of activity.\n\nExample 4\n\nAsset costs ¿¡11,000, its expected salvage value is ¿¡1,000. The manufacture will produce 20,000 produces in the first year, 15,000 produces in the second year, 30,000 produces in the third year, 10,000 produces in the forth year and 25,000 produces in the fifth year.\n\nDepreciation cost =¿¡11,000-¿¡1,000=¿¡10,000\n\nDepreciation cost per unit=¿¡10,000÷100,000units=¿¡0.1\n\nTo compare the three main methods, we find that each method will have the same book value in the last year, but the depreciation expense is different during the useful life. The straight-line method keeps same; the reducing balance method is large in the early years and decreases in the later years, and the unit of production method is fluctuant bases on the unit it produces.\n\nIn the SSAP 12, it allows company to decide which depreciation method to use by them. But the company must consider if the method they choose is suitable for the companies’ asset, and the depreciation allocated is fairly to the best of their abilities to benefit form the use of the asset (Mike, Ron and Allister, 1994:541, paragraph 8 in the explanatory note section of SSAP12). The purpose of all the depreciation methods is the return of the money invested in the asset finally, but different methods have its rate of recovering (Robert, Helen and David, 1978). Companies considerate when their money invest will receive and the net income.\n\nObviously, the methods talked above can be divided into two categories. One is based on useful life, which is straight-line method and reducing balance method. The other one is base on the number of the production; it is unit of production method. So which method is useful will first depend on the way it estimate in the depreciation.\n\nBetween the straight line method and the reducing balance method. The benefit of the straight-line method is easy to calculate and the depreciation expense will not change every year. While the reducing balance method has a high depreciation in the early years, this will save the income tax during these years because depreciation cost reduce the income reported for tax purpose (Robert, Helen and David, 1978). For many company, the money is better to receive as soon as quickly. The fall in the tax means there is more money can be used. Also, Robert, Helen and David (1978:313) compared the different depreciation methods on a present value discounted from the depreciation expense (see the table blow). They assumed that the money will earn 8% for the company and found the reducing balance method have more present value than the straight-line method.\n\nAs it mentions above, for a business, if it is based on use for the depreciation, the most useful depreciation method should be unit of production method. And if the company is based on the useful life for the depreciation, the most useful one may be the reducing balance method even though the straight-line method is easy to compute.\n\n## Related Services\n\nView all\n\n### DMCA / Removal Request\n\nIf you are the original writer of this essay and no longer wish to have your work published on the UKDiss.com website then please:\n\nRelated Services\n\nRelated Lectures", null, "" ]

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[ "### revision_R2\n\nparent a5aeb3c5\n ... ... @@ -2,11 +2,11 @@ create_K_plot <- function(searchLG,gfffile,xr,searchgene,secondary_genes,searchs source('../../0_data/0_scripts/F3.functions.R'); source('../../0_data/0_scripts/F3.getFSTs.R') source('../../0_data/0_scripts/F3.getDXY.R') source('../../0_data/0_scripts/S15.getGxP.R') source('../../0_data/0_scripts/S15.getPI.R') source('../../0_data/0_scripts/S15.getPIpw.R') source('../../0_data/0_scripts/S15.getIHH12.R') source('../../0_data/0_scripts/S15.getXPEHH.R') source('../../0_data/0_scripts/S17.getGxP.R') source('../../0_data/0_scripts/S17.getPI.R') source('../../0_data/0_scripts/S17.getPIpw.R') source('../../0_data/0_scripts/S17.getIHH12.R') source('../../0_data/0_scripts/S17.getXPEHH.R') highclr <- '#3bb33b' theme_set(theme_minimal(base_size = 6)) ... ...\n #PBS -l elapstim_req=12:00:00 #PBS -l memsz_job=80gb #PBS -b 1 #PBS -l cpunum_job=1 #PBS -N pcabel #PBS -q cllong #PBS -o 2.2.4.pca_bel.stdout #PBS -e 2.2.4.pca_bel.stderr cd $WORK/2_output/08_popGen/04_pca mkdir -p bel_ld vcftools --gzvcf$WORK/2_output/07_phased_variants/6_phased_mac2.vcf.gz \\ --keep $WORK/0_data/0_resources/vcfpops/vcftools_bel.pop \\ --thin 25000 \\ --recode --stdout | sed 's=|=/=g' > bel_ld/pca.vcf cd bel_ld && Rscript --vanilla ../pca_run.R pca.vcf bel$PWD rm tmp.pcadapt && rm .Rhistory && rm pca.vcf cd .. echo \"--done--\"\n #PBS -l elapstim_req=12:00:00 #PBS -l memsz_job=80gb #PBS -b 1 #PBS -l cpunum_job=1 #PBS -N pcabel #PBS -q cllong #PBS -o 2.2.4.pca_hon.stdout #PBS -e 2.2.4.pca_hon.stderr cd $WORK/2_output/08_popGen/04_pca mkdir -p hon_ld vcftools --gzvcf$WORK/2_output/07_phased_variants/6_phased_mac2.vcf.gz \\ --keep $WORK/0_data/0_resources/vcfpops/vcftools_hon.pop \\ --thin 25000 \\ --recode --stdout | sed 's=|=/=g' > hon_ld/pca.vcf cd hon_ld && Rscript --vanilla ../pca_run.R pca.vcf hon$PWD rm tmp.pcadapt && rm .Rhistory && rm pca.vcf cd .. echo \"--done--\"\n #PBS -l elapstim_req=12:00:00 #PBS -l memsz_job=80gb #PBS -b 1 #PBS -l cpunum_job=1 #PBS -N pcabel #PBS -q cllong #PBS -o 2.2.4.pca_pan.stdout #PBS -e 2.2.4.pca_pan.stderr cd $WORK/2_output/08_popGen/04_pca mkdir -p pan_ld vcftools --gzvcf$WORK/2_output/07_phased_variants/6_phased_mac2.vcf.gz \\ --keep $WORK/0_data/0_resources/vcfpops/vcftools_boc.pop \\ --thin 25000 \\ --recode --stdout | sed 's=|=/=g' > pan_ld/pca.vcf cd pan_ld && Rscript --vanilla ../pca_run.R pca.vcf pan$PWD rm tmp.pcadapt && rm .Rhistory && rm pca.vcf cd .. echo \"--done--\"\n ... ... @@ -209,3 +209,4 @@ F1 <- ggdraw()+ ggsave(plot = F1,filename = '../output/F1.pdf',width = 183,height = 145,units = 'mm',device = cairo_pdf) #ggsave(plot = F1,filename = '../output/F1.png',width = 183,height = 145,units = 'mm',dpi = 200) #ggsave(plot = F1,filename = '../output/F1.eps',width = 183,height = 145,units = 'mm',device = cairo_ps) \\ No newline at end of file\n ... ... @@ -161,4 +161,6 @@ F2 <- ggdraw(p1)+ draw_grob(honGrob, 0.954, boxes$y+.78*yd, .045, .045)+ draw_grob(panGrob, 0.954, boxes$y+.78*yd, .045, .045) ggsave(plot = F2,filename = '../output/F2.png',width = 183,height = 183,dpi = 200,units = 'mm') #ggsave(plot = F2,filename = '../output/F2.png',width = 183,height = 183,dpi = 200,units = 'mm') #ggsave(plot = F2,filename = '../output/F2.eps',width = 183,height = 183,units = 'mm',device = cairo_ps) ggsave(plot = F2,filename = '../output/F2.pdf',width = 183,height = 183,units = 'mm',device = cairo_pdf) \\ No newline at end of file\n ... ... @@ -42,7 +42,6 @@ F3 <- plot_grid(NULL,NULL,NULL,NULL, '','','',''),label_size = 10)+ draw_grob(legGrob, 0.1, 0, .8, 0.04) ggsave(plot = F3,filename = '../output/F3.pdf', width = 183,height = 125,units = 'mm',device = cairo_pdf) #ggsave(plot = F3,filename = '../output/F3.png', # width = 183,height = 125,dpi = 200,units = 'mm') ggsave(plot = F3,filename = '../output/F3.pdf', width = 183,height = 125,units = 'mm',device = cairo_pdf) #ggsave(plot = F3,filename = '../output/F3.png', width = 183,height = 125,dpi = 200,units = 'mm') #ggsave(plot = F3,filename = '../output/F3.eps', width = 183,height = 125,units = 'mm',device = cairo_ps) \\ No newline at end of file\n ... ... @@ -72,4 +72,6 @@ F4 <- ggdraw(pGr1)+ y=c(.99,.81,.81,.57,.57), size = 14) ggsave(plot = F4,filename = '../output/F4.png',width = 183,height = 235,units = 'mm',dpi = 150) #ggsave(plot = F4,filename = '../output/F4.png',width = 183,height = 235,units = 'mm',dpi = 150) #ggsave(plot = F4,filename = '../output/F4.eps',width = 183,height = 235,units = 'mm',device = cairo_ps) ggsave(plot = F4,filename = '../output/F4.pdf',width = 183,height = 235,units = 'mm',device = cairo_pdf) \\ No newline at end of file\n #!/usr/bin/env Rscript library(grid) library(gridSVG) library(grImport2) library(grConvert) library(tidyverse) library(rtracklayer) library(hrbrthemes) library(cowplot) require(rtracklayer) source('../../0_data/0_scripts/F3.functions.R'); source('../../0_data/0_scripts/S15.plot_fun.R') p1 <- create_K_plot(searchLG = \"LG09\",gfffile = '../../1-output/09_gff_from_IKMB/HP.annotation.named.gff',xr = c(17800000,18000000), searchgene = c(\"SOX10_1\"),secondary_genes = c(\"RNASEH2A\"),searchsnp = c(17871737,17872597,17873443), muskID = 'A') p2 <- create_K_plot(searchLG = \"LG12\",gfffile = '../../1-output/09_gff_from_IKMB/HP.annotation.named.gff',xr = c(20080000,20500000), searchgene = c(\"Casz1_2\"),secondary_genes = c(),searchsnp = c(20316944,20317120,20323661,20323670,20333895,20347263), muskID = 'B') p3 <- create_K_plot(searchLG = \"LG12\",gfffile = '../../1-output/09_gff_from_IKMB/HP.annotation.named.gff',xr = c(22100000,22350000), searchgene = c(\"hoxc13a\"),secondary_genes = c('hoxc10a',\"hoxc11a\",\"hoxc12a\",\"calcoco1_1\"), searchsnp = c(), muskID = 'C') p4 <- create_K_plot(searchLG = \"LG17\",gfffile = '../../1-output/09_gff_from_IKMB/HP.annotation.named.gff',xr = c(22500000,22670000), searchgene = c('LWS',\"SWS2abeta\",\"SWS2aalpha\",\"SWS2b\"),searchsnp = c(22553970,22561903,22566254), secondary_genes = c(\"Hcfc1\",\"HCFC1_2\",\"HCFC1_1\",\"GNL3L\",\"TFE3_0\",\"MDFIC2_1\",\"CXXC1_3\",\"CXXC1_1\",'Mbd1','CCDC120'), muskID = 'D') legGrob <- gTree(children=gList(pictureGrob(readPicture(\"../../0_data/0_img/legend-pw-single-cairo.svg\")))) S15 <- plot_grid(NULL,NULL,NULL,NULL, p1,NULL,p2,NULL, NULL,NULL,NULL,NULL, p3,NULL,p4,NULL, NULL,NULL,NULL,NULL, ncol=4,rel_heights = c(.03,1,.03,1,.1),rel_widths = c(1,.025,1,.04), labels = c('a','','b','', '','','','', 'c','','d','', '','','','', '','','',''),label_size = 10)+ draw_grob(legGrob, 0.05, 0, .9, 0.04) ggsave(plot = S15,filename = '../output/S15.pdf',width = 183,height = 210,units = 'mm',device = cairo_pdf) #ggsave(plot = S15,filename = '../output/S15.png',width = 183,height = 210,units = 'mm',dpi = 200) source(\"../../0_data/0_scripts/F1.functions.R\") dataAll <- read.csv('../../0_data/0_resources/F1.sample.txt',sep='\\t') %>% mutate(loc=substrRight(as.character(id),3)) cFILL <- rgb(.7,.7,.7) ccc<-rgb(0,.4,.8) clr<-c('#000000','#d45500','#000000') fll<-c('#000000','#d45500','#ffffff') eVclr <- c(rep('darkred',2),rep(cFILL,8)) belPCA <- readRDS('../../2_output/08_popGen/04_pca/bel_ld/belpca.Rds') honPCA <- readRDS('../../2_output/08_popGen/04_pca/hon_ld/honpca.Rds') panPCA <- readRDS('../../2_output/08_popGen/04_pca/pan_ld/panpca.Rds') dataHON <- cbind(dataAll %>% filter(sample=='sample',loc=='hon')%>% select(id,spec), honPCA$scores); names(dataHON)[3:12]<- paste('PC',1:10,sep='') exp_varHON <- (honPCA$singular.values[1:10])^2/length(honPCA$maf) xlabHON <- paste('PC1 (',sprintf(\"%.1f\",exp_varHON*100),'%)')# explained varinace)') ylabHON <- paste('PC2 (',sprintf(\"%.1f\",exp_varHON*100),'%)')# explained varinace)') p2 <- ggplot(dataHON,aes(x=PC1,y=PC2,col=spec,fill=spec))+geom_point(size=1.1,shape=21)+ scale_color_manual(values=clr,guide=F)+ ggtitle('Honduras')+ scale_fill_manual(values=fll,guide=F)+theme_mapK+ theme(legend.position='bottom',plot.title = element_text(size = 11,hjust = .45), panel.border = element_rect(color=rgb(.9,.9,.9),fill=rgb(1,1,1,0)), plot.margin = unit(c(3,rep(5,3)),'pt'))+#coord_equal()+ scale_x_continuous(name=xlabHON,breaks = c(-.3,.2))+ scale_y_continuous(name=ylabHON,breaks = c(-.4,.4)) dataBEL <- cbind(dataAll %>% filter(sample=='sample',loc=='bel') %>% select(id,spec), belPCA$scores); names(dataBEL)[3:12]<- paste('PC',1:10,sep='') exp_varBEL <- (belPCA$singular.values[1:10])^2/length(belPCA$maf) xlabBEL <- paste('PC1 (',sprintf(\"%.1f\",exp_varBEL*100),'%)') ylabBEL <- paste('PC2 (',sprintf(\"%.1f\",exp_varBEL*100),'%)') p1 <- ggplot(dataBEL,aes(x=PC1,y=PC2,col=spec,fill=spec))+geom_point(size=1.1,shape=21)+ scale_color_manual(values=clr,guide=F)+ ggtitle('Belize')+ scale_fill_manual(values=fll,guide=F)+theme_mapK+ theme(legend.position='bottom',plot.title = element_text(size = 11,hjust = .45), panel.border = element_rect(color=rgb(.9,.9,.9),fill=rgb(1,1,1,0)), plot.margin = unit(c(3,rep(5,3)),'pt'))+ scale_x_continuous(name=xlabBEL,breaks = c(-.15,.25))+ scale_y_continuous(name=ylabBEL,breaks = c(-.35,.25)) dataPAN <- cbind(dataAll %>% filter(sample=='sample',loc=='boc',spec!='gum')%>% select(id,spec), panPCA$scores); names(dataPAN)[3:12]<- paste('PC',1:10,sep='') exp_varPAN <- (panPCA$singular.values[1:10])^2/length(panPCA$maf) xlabPAN <- paste('PC1 (',sprintf(\"%.1f\",exp_varPAN*100),'%)') ylabPAN <- paste('PC2 (',sprintf(\"%.1f\",exp_varPAN*100),'%)') p3 <- ggplot(dataPAN,aes(x=PC1,y=PC2,col=spec,fill=spec))+geom_point(size=1.1,shape=21)+ scale_color_manual(values=clr,guide=F)+ ggtitle('Panama')+ scale_fill_manual(values=fll,guide=F)+theme_mapK+ theme(legend.position='bottom',plot.title = element_text(size = 11,hjust = .45), panel.border = element_rect(color=rgb(.9,.9,.9),fill=rgb(1,1,1,0)), plot.margin = unit(c(3,rep(5,3)),'pt'))+ scale_x_continuous(name=xlabPAN,breaks = c(-.15,.2))+ scale_y_continuous(name=ylabPAN,breaks = c(-.2,.2)) S15 <- cowplot::plot_grid(p2, p1, p3, nrow = 1, labels = letters[1:3]) ggsave(plot = S15,filename = '../output/S15.pdf',width = 183,height = 63,units = 'mm',device = cairo_pdf) #ggsave(plot = S15,filename = '../output/S15.png',width = 183,height = 63,units = 'mm',dpi = 200) #ggsave(plot = S15,filename = '../output/S15.eps',width = 183,height = 63,units = 'mm',device = cairo_ps) \\ No newline at end of file #!/usr/bin/env Rscript library(tidyverse) dat_dir <- '../../2_output/08_popGen/06_GxP/smoothed/50kb/' files <- c(\"nig-uni-gemma.lm.50k.5k.smooth.gz\", \"nig-uni.lmm.50k.5k.smooth.gz\", \"pue-nig-gemma.lm.50k.5k.smooth.gz\", \"pue-nig.lmm.50k.5k.smooth.gz\", \"pue-uni-gemma.lm.50k.5k.smooth.gz\", \"pue-uni.lmm.50k.5k.smooth.gz\") runs <- files %>% str_remove(.,'-gemma') %>% str_remove(.,'.50k.5k.smooth.gz') %>% str_replace(.,'.lm','_lm') karyo <- read_delim('../../0_data/0_resources/F2.karyo.txt', delim = '\\t') %>% mutate(GSTART=lag(cumsum(END),n = 1,default = 0), GEND=GSTART+END,GROUP=rep(letters[1:2],12)) %>% select(CHROM,GSTART,GEND,GROUP) import <- function(file,run){ read_delim(file = gzfile(file), delim = \"\\t\") %>% dplyr::left_join(karyo, by = \"CHROM\") %>% dplyr::mutate(POS = (BIN_START + BIN_END)/2, GPOS = GSTART + POS) %>% mutate(RUN = run) } data <- purrr::map2(.x = str_c(dat_dir,'/',files),runs,import) %>% bind_rows() %>% separate(RUN,into = c('COMP','TYPE'), sep = '_') clr <- c('#fb8620','#d93327','#1b519c') yl <- expression(-log(italic(p)~value)) S16 <- ggplot(data,aes(x=GPOS,y=avgp_wald,col=COMP))+ geom_rect(inherit.aes = F,data=karyo,aes(xmin=GSTART,xmax=GEND, ymin=-Inf,ymax=Inf,fill=GROUP))+ geom_point(size=.01)+ facet_grid(COMP+TYPE~.)+ scale_x_continuous(name = \"\", expand = c(0, 0), breaks = (karyo$GSTART + karyo$GEND)/2, labels = 1:24, position = \"top\")+ ylab(yl)+ scale_fill_manual(values = c(NA,\"#E6E6E6\"), guide = F)+ scale_color_manual(name='comparison',values=clr[c(3,1,2)])+ theme_bw(base_size = 10, base_family = \"Helvetica\") + theme(plot.background = element_blank(), panel.background = element_blank(), panel.grid = element_blank(), panel.border = element_blank(), axis.title.x = element_blank(), axis.line = element_line(), legend.position = 'none', strip.background = element_blank()) #ggsave(plot = S16, filename = '../output/S16.pdf',width = 183,height = 60,units = 'mm',device = cairo_pdf) ggsave(plot = S16, filename = '../output/S16.png',width = 183,height = 90,units = 'mm',dpi = 300) #!/usr/bin/env Rscript library(grid) library(gridSVG) library(grImport2) library(grConvert) library(tidyverse) library(rtracklayer) library(hrbrthemes) library(cowplot) require(rtracklayer) source('../../0_data/0_scripts/F3.functions.R'); source('../../0_data/0_scripts/S17.plot_fun.R') p1 <- create_K_plot(searchLG = \"LG09\",gfffile = '../../1-output/09_gff_from_IKMB/HP.annotation.named.gff',xr = c(17800000,18000000), searchgene = c(\"SOX10_1\"),secondary_genes = c(\"RNASEH2A\"),searchsnp = c(17871737,17872597,17873443), muskID = 'A') p2 <- create_K_plot(searchLG = \"LG12\",gfffile = '../../1-output/09_gff_from_IKMB/HP.annotation.named.gff',xr = c(20080000,20500000), searchgene = c(\"Casz1_2\"),secondary_genes = c(),searchsnp = c(20316944,20317120,20323661,20323670,20333895,20347263), muskID = 'B') p3 <- create_K_plot(searchLG = \"LG12\",gfffile = '../../1-output/09_gff_from_IKMB/HP.annotation.named.gff',xr = c(22100000,22350000), searchgene = c(\"hoxc13a\"),secondary_genes = c('hoxc10a',\"hoxc11a\",\"hoxc12a\",\"calcoco1_1\"), searchsnp = c(), muskID = 'C') p4 <- create_K_plot(searchLG = \"LG17\",gfffile = '../../1-output/09_gff_from_IKMB/HP.annotation.named.gff',xr = c(22500000,22670000), searchgene = c('LWS',\"SWS2abeta\",\"SWS2aalpha\",\"SWS2b\"),searchsnp = c(22553970,22561903,22566254), secondary_genes = c(\"Hcfc1\",\"HCFC1_2\",\"HCFC1_1\",\"GNL3L\",\"TFE3_0\",\"MDFIC2_1\",\"CXXC1_3\",\"CXXC1_1\",'Mbd1','CCDC120'), muskID = 'D') legGrob <- gTree(children=gList(pictureGrob(readPicture(\"../../0_data/0_img/legend-pw-single-cairo.svg\")))) S17 <- plot_grid(NULL,NULL,NULL,NULL, p1,NULL,p2,NULL, NULL,NULL,NULL,NULL, p3,NULL,p4,NULL, NULL,NULL,NULL,NULL, ncol=4,rel_heights = c(.03,1,.03,1,.1),rel_widths = c(1,.025,1,.04), labels = c('a','','b','', '','','','', 'c','','d','', '','','','', '','','',''),label_size = 10)+ draw_grob(legGrob, 0.05, 0, .9, 0.04) ggsave(plot = S17,filename = '../output/S17.pdf',width = 183,height = 210,units = 'mm',device = cairo_pdf) #ggsave(plot = S17,filename = '../output/S17.png',width = 183,height = 210,units = 'mm',dpi = 200) This diff is collapsed. 3_figures/S16.Rmd 0 → 100644 --- output: html_document editor_options: chunk_output_type: console --- # Supplementary Figure 16 {r setup, include=FALSE} knitr::opts_chunk$set(echo = TRUE) knitr::opts_knit$set(root.dir = './F_scripts') ## Summary This is the accessory documentation of Supplementary Figure 16. The Figure can be recreated by running the **R** script S16.R: sh cd$WORK/3_figures/F_scripts Rscript --vanilla S16.R rm Rplots.pdf ## Details of S16.R In S16.R script is the F3.R script run including additional data sets. Is an executable R script that depends on the **tidyverse** package for data managing and plotting. {r import, results='hide', message=FALSE, warning=FALSE} library(tidyverse) ### Setup First, we define the directory storing the GxP results and create an inventory of data files to load. We also create labels for the individual data sets. {r setup_data, results='hide', message=FALSE, warning=FALSE} dat_dir <- '../../2_output/08_popGen/06_GxP/smoothed/50kb/' files <- c(\"nig-uni-gemma.lm.50k.5k.smooth.gz\", \"nig-uni.lmm.50k.5k.smooth.gz\", \"pue-nig-gemma.lm.50k.5k.smooth.gz\", \"pue-nig.lmm.50k.5k.smooth.gz\", \"pue-uni-gemma.lm.50k.5k.smooth.gz\", \"pue-uni.lmm.50k.5k.smooth.gz\") runs <- files %>% str_remove(.,'-gemma') %>% str_remove(.,'.50k.5k.smooth.gz') %>% str_replace(.,'.lm','_lm') We load information about hamlet reference genome and create a import function to load the data. {r karyo, results='hide', message=FALSE, warning=FALSE} karyo <- read_delim('../../0_data/0_resources/F2.karyo.txt', delim = '\\t') %>% mutate(GSTART=lag(cumsum(END),n = 1,default = 0), GEND=GSTART+END,GROUP=rep(letters[1:2],12)) %>% select(CHROM,GSTART,GEND,GROUP) import <- function(file,run){ read_delim(file = gzfile(file), delim = \"\\t\") %>% dplyr::left_join(karyo, by = \"CHROM\") %>% dplyr::mutate(POS = (BIN_START + BIN_END)/2, GPOS = GSTART + POS) %>% mutate(RUN = run) } We use the map2() function from the **purrr** package to load the data sets. The we define some colors an the y-axis label. {r lead_data, results='hide', message=FALSE, warning=FALSE} data <- purrr::map2(.x = str_c(dat_dir,'/',files),runs,import) %>% bind_rows() %>% separate(RUN,into = c('COMP','TYPE'), sep = '_') clr <- c('#fb8620','#d93327','#1b519c') yl <- expression(-log(italic(p)~value)) Finally we plot the data. {r plot, results='hide', message=FALSE, warning=FALSE} S16 <- ggplot(data,aes(x=GPOS,y=avgp_wald,col=COMP))+ geom_rect(inherit.aes = F,data=karyo,aes(xmin=GSTART,xmax=GEND, ymin=-Inf,ymax=Inf,fill=GROUP))+ geom_point(size=.01)+ facet_grid(COMP+TYPE~.)+ scale_x_continuous(name = \"\", expand = c(0, 0), breaks = (karyo$GSTART + karyo$GEND)/2, labels = 1:24, position = \"top\")+ ylab(yl)+ scale_fill_manual(values = c(NA,\"#E6E6E6\"), guide = F)+ scale_color_manual(name='comparison',values=clr[c(3,1,2)])+ theme_bw(base_size = 10, base_family = \"Helvetica\") + theme(plot.background = element_blank(), panel.background = element_blank(), panel.grid = element_blank(), panel.border = element_blank(), axis.title.x = element_blank(), axis.line = element_line(), legend.position = 'none', strip.background = element_blank()) The Figure is then exported using ggsave(): {r, eval=FALSE} #ggsave(plot = S16, filename = '../output/S16.pdf',width = 183,height = 60,units = 'mm',device = cairo_pdf) ggsave(plot = S16, filename = '../output/S16.png',width = 183,height = 90,units = 'mm',dpi = 300) \n{r s16SHOW, echo=FALSE, fig.width=183*0.03937008, fig.height=90*0.03937008, warning=FALSE, message=FALSE} S16 \n--- \\ No newline at end of file\n3_figures/S17.Rmd 0 → 100644\n --- output: html_document editor_options: chunk_output_type: console --- # Supplementary Figure 17 {r setup, include=FALSE} knitr::opts_chunk$set(echo = TRUE) knitr::opts_knit$set(root.dir = './F_scripts') ## Summary This is the accessory documentation of Supplementary Figure 17. The Figure can be recreated by running the **R** script S17.R: sh cd $WORK/3_figures/F_scripts Rscript --vanilla S17.R rm Rplots.pdf ## Details of S17.R In S17.R script is the F3.R script run including additional data sets. Is an executable R script that depends on a variety of image manipulation and data managing and genomic data packages. It depends on the same helper script as F3.R (F3.functions.R). Additionally it depends on S17.plot_fun.R (modified F3.plot_fun.R) which itself depends on F3.getDXY.R, F3.getFSTs.R,S17.getGxP.R,S17.getIHH12.R, S17.getPIpw.R, S17.getPI.R and S17.getXPEHH.R (all located under $WORK/0_data/0_scripts). For a detailed documentation please refer to [F3.R](figure-3.html). The only differences between the two scripts are located in S17.plot_fun.R (compared to F3.plot_fun.R). ### Additions in S17.plot_fun.R In the following additions to S17.plot_fun.R are shown which are missing in the original. In the beginning, four new helper scripts are loaded which include the data import for the additional parameter which are plotted in Supplementary Figure 15 ($\\pi$, pairwise $\\pi$, iHH~12~ and xpEHH). {r, eval=FALSE} #....# source('../../0_data/0_scripts/S17.getGxP.R') source('../../0_data/0_scripts/S17.getPI.R') source('../../0_data/0_scripts/S17.getPIpw.R') source('../../0_data/0_scripts/S17.getIHH12.R') source('../../0_data/0_scripts/S17.getXPEHH.R') #....# The imported data are stored in data_* vectors. {r, eval=FALSE} #....# # get pfst values pfst_list <- getGxP(searchLG,xr) # data_pfst_pw<-pfst_list$data_pfst_pw; data_pfst<-pfst_list$data_pfst # get pi values piPW_list <- getPIpw(searchLG,xr) data_piPW<-piPW_list$data_piPW #....# # get xpEHH values xpEHH_list <- getXPEHH(searchLG,xr) data_xpEHH<-xpEHH_list$data_xpEHH #....# For each new parameter, an additional plot is created. {r, eval=FALSE} #....# p13 <- ggplot()+coord_cartesian(xlim=xr)+ geom_line(data=(data_pfst %>% filter(POS > xr,POS% filter(POS > xr,POS% filter(POS > xr,POS {r oldScript2, eval=FALSE,} #....# p2 <- plot_grid(p11,p12,p13,p14, ncol = 1,align = 'v',axis = 'r',rel_heights = c(1.3,rep(1,3))) return(p2) {r head, include=FALSE} library(grid) library(gridSVG) library(grImport2) library(grConvert) library(tidyverse) library(rtracklayer) library(hrbrthemes) library(cowplot) require(rtracklayer) source('../../0_data/0_scripts/F3.functions.R'); source('../../0_data/0_scripts/S17.plot_fun.R') p1 <- create_K_plot(searchLG = \"LG09\",gfffile = '../../1-output/09_gff_from_IKMB/HP.annotation.named.gff',xr = c(17800000,18000000), searchgene = c(\"SOX10_1\"),secondary_genes = c(\"RNASEH2A\"),searchsnp = c(17871737,17872597,17873443), muskID = 'A') p2 <- create_K_plot(searchLG = \"LG12\",gfffile = '../../1-output/09_gff_from_IKMB/HP.annotation.named.gff',xr = c(20080000,20500000), searchgene = c(\"Casz1_2\"),secondary_genes = c(),searchsnp = c(20316944,20317120,20323661,20323670,20333895,20347263), muskID = 'B') p3 <- create_K_plot(searchLG = \"LG12\",gfffile = '../../1-output/09_gff_from_IKMB/HP.annotation.named.gff',xr = c(22100000,22350000), searchgene = c(\"hoxc13a\"),secondary_genes = c('hoxc10a',\"hoxc11a\",\"hoxc12a\",\"calcoco1_1\"), searchsnp = c(), muskID = 'C') p4 <- create_K_plot(searchLG = \"LG17\",gfffile = '../../1-output/09_gff_from_IKMB/HP.annotation.named.gff',xr = c(22500000,22670000), searchgene = c('LWS',\"SWS2abeta\",\"SWS2aalpha\",\"SWS2b\"),searchsnp = c(22553970,22561903,22566254), secondary_genes = c(\"Hcfc1\",\"HCFC1_2\",\"HCFC1_1\",\"GNL3L\",\"TFE3_0\",\"MDFIC2_1\",\"CXXC1_3\",\"CXXC1_1\",'Mbd1','CCDC120'), muskID = 'D') legGrob <- gTree(children=gList(pictureGrob(readPicture(\"../../0_data/0_img/legend-pw-cairo.svg\")))) S17 <- plot_grid(NULL,NULL,NULL,NULL, p1,NULL,p2,NULL, NULL,NULL,NULL,NULL, p3,NULL,p4,NULL, NULL,NULL,NULL,NULL, ncol=4,rel_heights = c(.03,1,.03,1,.1),rel_widths = c(1,.025,1,.02), labels = c('a','','b','', '','','','', 'c','','d','', '','','','', '','','',''),label_size = 10)+ draw_grob(legGrob, 0.1, 0, .8, 0.04) \n{r s09SHOW, echo=FALSE, fig.width=183*0.03937008, fig.height=210*0.03937008, warning=FALSE, message=FALSE} S17 \n--- \\ No newline at end of file\n ... ... @@ -62,9 +62,9 @@ edgsB <- rbind(edgR(ptsB1,edgB1),edgR(ptsB2,edgB2),edgR(ptsB3,edgB3)) plotList <- data.frame(x=c(0,.2,.66,.84,1,1.9,2.1,1.5,2.5, 2.64,2.64,2.64,2.64,0,3.5,3.5,.45), y=c(rep(1,9),-1,-.8,-.6,-.4,-.05,0,.75,1), label=c('S01','F1','F2','S07','S12','F3','S09, S08', 'S03','S15','S14','S11', 'F4','S14','S13','S06','S15','S02'), label=c('S01','F1, S15','F2','S07','S12','F3','S09, S08', 'S03, S16','S15','S14','S11', 'F4','S14','S13','S06','S17','S02'), status=c(rep(steps,14),rep(steps,2),steps)) \n... ... @@ -117,7 +117,7 @@ p2 <- ggplot()+ arrow = arrow(length = unit(4,'pt'),type = 'closed'))+ geom_text(data=edgsB,aes(x=(x+xend)*.5,y=(y+yend)*.5,label=label,angle=angle), vjust=-1)+ #geom_text(data=ptsB%>% filter(!(status==steps & nr == 20)),aes(x=x,y=y,label=nr),color='white')+ # geom_text(data=ptsB%>% filter(!(status==steps & nr == 20)),aes(x=x,y=y,label=nr),color='white')+ geom_text(data=plotList, aes(x=x,y=y,label=label),color=clr2)+ scale_x_continuous(expand=c(.03,.03))+ ... ...\n ... ... @@ -2,7 +2,7 @@ book_filename: \"Script repository Hench et al. 2018\" chapter_name: \"\" repo: https://github.com/k-hench/bookdown output_dir: ../docs rmd_files: [\"index.Rmd\",\"Workflow.Rmd\",\"F1.Rmd\",\"F2.Rmd\",\"F3.Rmd\",\"F4.Rmd\",\"S01.Rmd\",\"S02.Rmd\",\"S03.Rmd\",\"S05.Rmd\",\"S06.Rmd\",\"S07.Rmd\",\"S08.Rmd\",\"S09.Rmd\",\"S10.Rmd\",\"S11.Rmd\",\"S12.Rmd\",\"S13.Rmd\",\"S14.Rmd\",\"S15.Rmd\"] rmd_files: [\"index.Rmd\",\"Workflow.Rmd\",\"F1.Rmd\",\"F2.Rmd\",\"F3.Rmd\",\"F4.Rmd\",\"S01.Rmd\",\"S02.Rmd\",\"S03.Rmd\",\"S05.Rmd\",\"S06.Rmd\",\"S07.Rmd\",\"S08.Rmd\",\"S09.Rmd\",\"S10.Rmd\",\"S11.Rmd\",\"S12.Rmd\",\"S13.Rmd\",\"S14.Rmd\",\"S15.Rmd\",\"S16.Rmd\",\"S17.Rmd\"] clean: [packages.bib, bookdown.bbl] new_session: yes delete_merged_file: True\n ... ... @@ -34,7 +34,8 @@ A more detailed documentation exists for all the figures of the manuscript: as well as for all the supplementary figures:" ]

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[ "CONCAT inputVector {inputVector} resultVariable\n\n Concatenates the elements of the input vectors in the order listed and puts the result in the result variable. In Statistics101, this command has been generalized to allow input of any number and mix of input vectors and/or any kind of literal list, literal sequence, or multiple lilteral (quantity#value). See Using the Sequence and Multiple Operators. The following commands are synonyms for the CONCAT command: DATA, NUMBERS, URN, and COPY. They are all identical except for their names. Use whichever name is most meaningful in context. ```CONCAT 1,5 A CONCAT (5 6 8 14 20) B CONCAT 4#5 C PRINT A B C``` The above program produces the following output: ```A: (1.0 2.0 3.0 4.0 5.0) B: (5.0 6.0 8.0 14.0 20.0) C: (5.0 5.0 5.0 5.0)``` The next program... ```CONCAT 4,1 (2 3 5) 3#9 2 5 A PRINT A``` ...produced this output: `A: (4.0 3.0 2.0 1.0 2.0 3.0 5.0 9.0 9.0 9.0 2.0 5.0)` If you want to concatenate one or more vectors onto the beginning or end of another vector, you would do it like this: ```CONCAT 1,5 A 'original vector CONCAT 10,20 A A 'add 10,20 to start of A 'or CONCAT A 10,20 A 'add 10,20 to end of A``` Here's a practical example: When choosing 2 students at random from a class of 10 boys and 15 girls, what is the probability of their both being girls? ```NAME boy girl CONCAT 10#boy 15#girl students CONCAT 1000 repeatCount CONCAT 1 successCount REPEAT repeatCount SAMPLE 2 students winners COUNT winners =girl girlCount IF girlCount =2 ADD 1 successCount successCount END END DIVIDE successCount repeatCount probability PRINT probability``` The above program produces the following output: `probability: 0.353`" ]

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[ "# ASCL Code Record\n\n[ascl:1804.014] IMNN: Information Maximizing Neural Networks\n\nThis software trains artificial neural networks to find non-linear functionals of data that maximize Fisher information: information maximizing neural networks (IMNNs). As compressing large data sets vastly simplifies both frequentist and Bayesian inference, important information may be inadvertently missed. Likelihood-free inference based on automatically derived IMNN summaries produces summaries that are good approximations to sufficient statistics. IMNNs are robustly capable of automatically finding optimal, non-linear summaries of the data even in cases where linear compression fails: inferring the variance of Gaussian signal in the presence of noise, inferring cosmological parameters from mock simulations of the Lyman-α forest in quasar spectra, and inferring frequency-domain parameters from LISA-like detections of gravitational waveforms. In this final case, the IMNN summary outperforms linear data compression by avoiding the introduction of spurious likelihood maxima.\n\nCode site:\nhttps://doi.org/10.5281/zenodo.1119069\nDescribed in:", null, "" ]

[ null, "https://img.shields.io/badge/ascl-1804.014-blue.svg", null ]

[ "# Cubic millimeters to Tablespoons [US] formula\n\nUse the formula below to convert any value from cubic millimeters to Tablespoons [US]:\n\nTablespoons [US] = cubic millimeters × 6.7628045403686E-5\n\nTo from cubic millimeters to Tablespoon [US], you just need to multiply the value in cubic millimeters by 6.7628045403686E-5. (It is called the conversion factor)", null, "See also our cubic millimeters to Tablespoons [US] Converter\n\n## Using the formula (some examples):\n\nConvert full cubic millimeter to Tablespoons [US]:\na cubic millimeter = 1 × 6.7628045403686E-5 = 6.7628045403686E-5 Tablespoons [US].\n\nConvert two cubic millimeter to Tablespoons [US]:\ntwo cubic millimeter = 2 × 6.7628045403686E-5 = 0.00013525609080737 Tablespoons [US].\n\nConvert five cubic millimeters to Tablespoons [US]:\n5 cubic millimeters = 5 × 6.7628045403686E-5 = 0.00033814022701843 Tablespoons [US].\n\n## More Examples:\n\nConvert ten cubic millimeters to Tablespoons [US]: 10 cubic millimeters = 10 × 6.7628045403686E-5 = 0.00067628045403686 Tablespoons [US].\n\nConvert twenty cubic millimeters to Tablespoons [US]: 20 cubic millimeters = 20 × 6.7628045403686E-5 = 0.0013525609080737 Tablespoons [US].\n\nConvert fifty cubic millimeters to Tablespoons [US]: 50 cubic millimeters = 50 × 6.7628045403686E-5 = 0.0033814022701843 Tablespoons [US].\n\nConvert a hundred cubic millimeters to Tablespoons [US]: 100 cubic millimeters = 100 × 6.7628045403686E-5 = 0.0067628045403686 Tablespoons [US].\n\nConvert a thousand cubic millimeters to Tablespoons [US]: 1000 cubic millimeters = 1000 × 6.7628045403686E-5 = 0.067628045403686 Tablespoons [US]." ]

[ null, "https://www.howmany.wiki/images/calculator16x20.png", null ]

[ "# Question about a basis for a topology vs the topology generated by a basis?\n\nThis is a really basic (no pun intended......no? Ok...) question about what it means to be a basis for a topology.\n\nHere is what I know: If $(X, \\mathcal{T})$ is a topological space, and $\\mathcal{B} \\subseteq \\mathcal{T}$ is a basis for $\\mathcal{T}$, then we know by definition of basis that the following are true:\n\n1. For every $x \\in X$, $x \\in B$ for some $B \\in \\mathcal{B}$.\n2. If $x \\in B_{1} \\cap B_{2}$ for some $B_{1}, B_{2} \\in \\mathcal{B}$, then $\\exists B_{3} \\in \\mathcal{B}$ such that $x \\in B_{3} \\subseteq B_{1} \\cap B_{2}$.\n\nAlso, I know that if we have a basis $\\mathcal{B}$ for a topology $\\mathcal{T}$, then the topology generated by the basis, $\\mathcal{T}_{\\mathcal{B}}$, consists of all possible unions of elements of $\\mathcal{B}$.\n\nHere is my question: I want to prove that if $\\mathcal{B}$ is a basis for $\\mathcal{T}$, then $\\mathcal{T} = \\mathcal{T}_{\\mathcal{B}}$. Showing $\\mathcal{T}_{\\mathcal{B}} \\subseteq \\mathcal{T}$ is really easy. To show $\\mathcal{T} \\subseteq \\mathcal{T_{\\mathcal{B}}}$ relies on some \"fact\" that I don't know to prove: that if $U \\in \\mathcal{T}$, and $x \\in U$, $\\exists B \\in \\mathcal{B}$ such that $x \\in B \\subseteq U$.\n\nHow do I prove that for any $U \\in \\mathcal{T}$, $\\exists B \\in \\mathcal{B}$ such that $x \\in B \\subseteq U$? I don't see how this fact follows from the definition of a basis. And without this fact, I can't prove that $\\mathcal{T} = \\mathcal{T_{\\mathcal{B}}}$.\n\n• Usually saying $\\mathcal{B}$ is a basis for $\\mathcal{T}$ means $\\langle\\mathcal{B}\\rangle=\\mathcal{T}$ where $\\langle\\mathcal{A}\\rangle:=\\{\\bigcup A_\\lambda:A_\\lambda\\in\\mathcal{A}\\}$. Did you mean rather that if $\\mathcal{B}\\subseteq\\mathcal{T}$ satisfies the properties of a basis then $\\mathcal{B}$ is indeed a basis for $\\mathcal{T}$? – C-Star-W-Star Sep 8 '14 at 0:23\n• @Freeze_S The way I learned it from the Munkres book, a basis $\\mathcal{B}$ for a topology $\\mathcal{T}$ is a subset of $\\mathcal{T}$ that satisfies properties 1 and 2 in my question. Meanwhile, the topology generated by $\\mathcal{B}$ is the set of all unions of basis elements. I just want to show that the topology generated by $\\mathcal{B}$ is in fact the same topology that $\\mathcal{B}$ is a basis for. – layman Sep 8 '14 at 0:26\n• The \"fact\" you don't know how to prove appears to have a typographical error: it should end with $x \\in B \\subseteq U$. That may help, given that this \"fact\", so corrected, is the exact definition of the statement \"$\\cal B$ is a basis for $\\cal T$\". – Lee Mosher Sep 8 '14 at 0:29\n• @LeeMosher Why does $\\subseteq$ vs $\\subset$ matter? And also, I'm still having trouble tying these two concepts together. As I outlined in my question, I learned one definition for a set $\\mathcal{B}$ being a basis for a topology $\\mathcal{T}$, and a different definition for what we call the topology generated by the basis elements. And I just want to prove that these two are the same topology. Everyone I ask seems to look at me like I am crazy and stating the same thing twice, but I really don't think I am... – layman Sep 8 '14 at 0:31\n• I will give you a very precise answer in a second - hope that will chear you up again ;) – C-Star-W-Star Sep 8 '14 at 0:36\n\nWhen defining a \"basis\", we start out with a set $X$. We don't define a topology on it before we define $\\mathcal{B}$ axiomatically.\n\nA set of subsets of $X$, $\\mathcal{B}$, is said to be a base to the set $X$ if the following two conditions hold:\n\n(i) $\\forall x \\in X$, $\\exists B \\in \\mathcal{B}$ such that $x \\in B$\n\n(ii) Given $B_{1}, B_{2} \\in \\mathcal{B}$, if $\\exists x \\in B_{1} \\cap B_{2}$, then $\\exists B_{3} \\in \\mathcal{B}$ such that $x \\in B_{3} \\subseteq B_{1} \\cap B_{2}$\n\nNow that we have defined what it means for a set $\\mathcal{B}$ of subsets of $X$ to be a base to the set $X$, we can define $\\mathcal{T}_{\\mathcal{B}}$, the topology generated by $\\mathcal{B}$, as the set of all unions of elements in $\\mathcal{B}$. That is, a set $U$ is open in $\\mathcal{T}_{\\mathcal{B}}$ if it is a union of elements of $\\mathcal{B}$. It is easy to prove that this is a topology.\n\nNow, if we start out with a topology $\\mathcal{T}$ on a set $X$, and we say $\\mathcal{B}$ is a basis for the topology $\\mathcal{T}$, this is defined as $\\mathcal{T}$ actually being the topology $\\mathcal{T}_{\\mathcal{B}}$, the set of all unions of elements in $\\mathcal{B}$.\n\nIf $(X, \\mathcal{T})$ is a topological space, it is possible to have a set $\\mathcal{B}$ of subsets of $X$ satisfy the two properties that make it a base to the set $X$ without it being a basis for a given topology. But if $\\mathcal{B} \\subseteq \\mathcal{T}$, then we are assured $\\mathcal{T}_{\\mathcal{B}} \\subseteq \\mathcal{T}$. We don't have equality, though, unless we are also given that $\\mathcal{B}$ is a basis for $\\mathcal{T}$.\n\nHere is an example of a topological space in which a base to the set $X$ is contained in the topology of $X$ but is not a basis for the topology. Let $(X, \\mathcal{T}) = (\\mathbb{R}, \\mathcal{T}_{\\text{indisc}})$ where $\\mathcal{T}_{\\text{indisc}}$ is the indiscrete topology (i.e., $\\mathcal{T}_{\\text{indisc}} = \\{ X , \\emptyset \\}$). Then since every topology acts as a basis for itself, $\\mathcal{T}_{\\text{indisc}}$ is a basis for itself, and it is also a base to the set $X$. However, this base to the set $X$ is contained in $\\mathcal{T}_{\\text{disc}}$, the discrete topology, but it is not a basis for the discrete topology.\n\nSo, the main point here is that when we define a base to the set $X$, it is independent of any topology on $X$. But should the elements of the base be in a topology, then the topology generated by the base is a subset of the original topology. Furthermore, if we say the base is a basis for the original topology, by definition that means the original topology is equal to the topology generated by the base.\n\n• Both are called \"base\" (not \"basis\"). But if we start with a set $X$ and then consider a collection $\\mathcal{B}$, I call $\\mathcal{B}$ a \"base for a topology\" (which is then defined by this $\\mathcal{B}$ as said), while if I start with a topology $\\mathcal{T}$, and then consider a subfamily $\\mathcal{B} \\subset \\mathcal{T}$ of it, I say that $\\mathcal{B}$ is a base for the topology ($\\mathcal{T}$). So I think context will make clear which is meant. – Henno Brandsma Sep 8 '14 at 21:09\n• @HennoBrandsma Thanks for your input. Also, I want to make it crystal clear: We can have $\\mathcal{B} \\subset \\mathcal{T}$ satisfy the axioms for $\\mathcal{B}$ to be a base to the set $X$, but $\\mathcal{B}$ isn't necessarily a basis for $\\mathcal{T}$. It is a basis specifically in the case where we have $\\mathcal{T}_{\\mathcal{B}} = \\mathcal{T}$. – layman Sep 8 '14 at 21:26\n• Sure. It's quite uncommon to consider a subfamily of a given topology and call it a base without it generating the original topology. And indeed this is part of what I call a base for the topology. – Henno Brandsma Sep 8 '14 at 21:31\n• @HennoBrandsma But that fact that this scenario is possible should be mentioned because it was a huge source of confusion for me, and it is what caused me to ask this question in the first place. Having a base for the set $X$ doesn't necessarily mean it's a basis for a given topology. I was initially under the impression that it did mean this because of this convention you brought up of only talking about a base under a topology for which it forms a basis. – layman Sep 8 '14 at 21:46\n• @HennoBrandsma: Are you sure there is a difference between base and basis? As far as I know this is only due to different authors but usually not of one author saying I will distinguish between basis and base... As I've seen mostly one will simply say that this collection is a basis for a topology while that collection is a basis for the topology (mentioned, given before, above or whatsoever) but without changing from \"base\" to \"basis\"... In the end I would suggest you to rather state things explicitely as $\\langle\\mathcal{B}\\rangle=\\mathcal{T}$ rather then describing them in words ;) – C-Star-W-Star Sep 11 '14 at 12:46\n\nI just checked Munkres - he made everything fine - but just to clarify:\n\nIn principle there are two problems:\n\na. Given a collection $\\mathcal{B}$. Then $\\langle\\mathcal{B}\\rangle$ is a topology iff it satisfies the characteritation: $$\\forall x\\in X\\exists B_x\\mathcal{B}:\\quad x\\in B_x$$ $$\\forall B,B'\\in\\mathcal{B}\\forall x\\in B\\cap B'\\exists B_x\\in\\mathcal{B}:\\quad x\\in B_x\\subseteq B\\cap B'$$ b. Given a collection $\\mathcal{B}$ and a topology $\\mathcal{T}$. Then $\\langle\\mathcal{B}\\rangle=\\mathcal{T}$ iff it fulfills the criterion: $$\\forall U\\in\\mathcal{T}\\forall u\\in U\\exists B_u\\in\\mathcal{B}\\subseteq\\mathcal{T}: u\\in B_u\\subseteq U$$\n\nNote that though both problems are conceptually similar they are solved quite differently.\n\n• I'm still confused as to why this helps me. If we can characterize a basis $\\mathcal{B}$ of a topology $\\mathcal{T}$ by a collection of elements satisfying 1) $\\forall x \\in X, \\exists B \\in \\mathcal{B}$ such that $x \\in B$, and 2) if $x \\in B_{1} \\cap B_{2}$ for basis elements $B_{1}$, $B_{2}$, then $\\exists B_{3} \\in \\mathcal{B}$ such that $x \\in B_{3} \\subseteq B_{1} \\cap B_{2}$, and we can also say that this basis generates a topology of its own, $\\mathcal{T}_{\\mathcal{B}}$, then how do I prove $\\mathcal{T} \\subseteq \\mathcal{T}_{\\mathcal{B}}$ using the characterizations in the problem? – layman Sep 8 '14 at 2:11\n• Okay I just read this discussion and looked in Munkres and it's now clear to me why you're confused. There's a difference between $\\mathcal{B}$ being a basis for $\\textbf{a}$ topology on $X$ (where $X$ is any set), and a basis for $\\textbf{the}$ topology on $X$ (where $X$ is a topological space). The former means that $\\mathcal{B}$ satisfies the two conditions for it to generate some topology $\\mathcal{T}_\\mathcal{B}$ on the set $X$. On the other hand, saying $\\mathcal{B}$ is a basis for $\\mathbf{the}$ topology on a topological space $X$, that means $\\mathcal{B}$ generates the topology of $X$. – Zavosh Sep 9 '14 at 8:06\n• It's strictly a matter of the English language. Munkres only explicitly talks about what it means for $\\mathcal{B}$ to be a basis for $\\textbf{a}$ topology, and then expects that you understand when we talk about $\\textbf{the}$ topology, it's the one it generates. – Zavosh Sep 9 '14 at 8:09\n• By analogy, when $V$ is a vector space and we say $\\beta \\subset V$ is a basis for a vector space, it simply means $\\beta$ is linearly independent. But when we say $\\beta$ is a basis for the vector space $V$, it means $\\beta$ is linearly independent $\\textit{and}$ spans $V$. – Zavosh Sep 9 '14 at 8:14\n• @Freeze_S: Yes, when I said 'you' obviously I meant user46944. I also did say the two things were synonymous in perhaps less clear words the day before, but that didn't appear to help user46944. One can't easily resolve a confusion by simply overruling it. The source of the confusion has be neutralized first. – Zavosh Sep 9 '14 at 15:42" ]

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[ "# A2L Item 045\n\nGoal: Reason using 2nd law.\n\nSource: UMPERG-ctqpe24\n\nConsider the two situations presented below. T1 is the tension in the string in case A and T2 is the tension in the string in case B.", null, "Which of the following statements is correct?\n\n1. T1 < T2\n2. T1 = T2\n3. T1 > T2\n4. Cannot be determined\n\n### Commentary:\n\n(2). The force exerted on each block by the attached string must\nbalance the weight of the block. Since the blocks all weigh the same\namount, the tension in the in the two strings must be equal.\n\n#### Background\n\nThis item does not require formal knowledge of Newton’s Second Law. It\ncan be used after students can identify the tension and gravitational\nforce, provided they appreciate that for static situations the forces\nexerted on each object must balance. Try asking students to answer the\nquestion individually and without discussion, giving their initial\nreaction. Then ask students to re-answer the question after discussing\nit briefly in small groups.\n\nStudents commonly think that T2 is greater than\nT1 because the rope in situation 2 “supports” two masses.\nThis incorrect intuition can even exist in students who are capable of\ndrawing correct free-body diagrams and who know that the “tension” force\nexerted on each block must balance the weight of the block. The\ncoexistence of conflicting intuition and formal knowledge is common\namong novices.\n\n#### Questions to Reveal Student Reasoning\n\nWhat is tension? How do you measure tension?\n\nFor situation (A) consider placing a spring scale between the string and\nthe block in the vertical region. What force is the spring scale\nmeasuring? For situation (A) consider cutting the string in the middle\nof the horizontal region and inserting a spring scale. What force is\nthis spring scale measuring? How would the readings on the two spring\nscales compare?\n\nIf spring scales were placed similarly in situation (B), how would their\nreadings compare to the readings on the spring scales in situation (A)?\n\n#### Suggestions\n\nConsider the original situations and two variations: (a) In (A)\nconsider a person holding the string in place of the wall; (b) In (B)\nconsider a person holding the string in place of the block on the left.\nIn each situation, what force is being exerted on the string so that the\nhanging mass at the other end does not move?\n\nSet up the two situations depicted in the item. Insert spring scales at\nappropriate points. Discuss the readings on the scales." ]

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[ "# Gravitational Pull\n\nIn Chapter 12 of the book, we provide an empirical gravitational forcing term that can be applied to the Laplace’s Tidal Equation (LTE) solution for modeling ENSO. The inverse squared law is modified to a cubic law to take into account the differential pull from opposite sides of the earth.\n\nThe two main terms are the monthly anomalistic (Mm) cycle and the fortnightly tropical/draconic pair (Mf, Mf’ w/ a 18.6 year nodal modulation). Due to the inverse cube gravitational pull found in the denominator of F(t), faster harmonic periods are also created — with the 9-day (Mt) created from the monthly/fortnightly cross-term and the weekly (Mq) from the fortnightly crossed against itself. It’s amazing how few terms are needed to create a canonical fit to a tidally-forced ENSO model.\n\nThe recipe for the model is shown in the chart below (click to magnify), following sequentially steps (A) through (G) :", null, "(A) Long-period fortnightly and anomalistic tidal terms as F(t) forcing(B) The Fourier spectrum of F(t) revealing higher frequency cross terms (C) An annual impulse modulates the forcing, reinforcing the amplitude(D) The impulse is integrated producing a lagged quasi-periodic input(E) Resulting Fourier spectrum is complex due to annual cycle aliasing(F) Oceanic response is a Laplace’s Tidal Equation (LTE) modulation(G) Final step is fit the LTE modulation to match the ENSO time-series\n\nThe tidal forcing is constrained by the known effects of the lunisolar gravitational torque on the earth’s length-of-day (LOD) variations. An essentially identical set of monthly, fortnightly, 9-day, and weekly terms are required for both a solid-body LOD model fit and a fluid-volume ENSO model fit.", null, "Fitting tidal terms to the dLOD/dt data is only complicated by the aliasing of the annual cycle, making factors such as the weekly 7.095 and 6.83-day cycles difficult to distinguish.\n\nIf we apply the same tidal terms as forcing for matching dLOD data, we can use the fit below as a perturbed ENSO tidal forcing. Not a lot of difference here — the weekly harmonics are higher in magnitude.\n\nSo the only real unknown in this process is guessing the LTE modulation of steps (F) and (G). That’s what differentiates the inertial response of a spinning solid such as the earth’s core and mantle from the response of a rotating liquid volume such as the equatorial Pacific ocean. The former is essentially linear, but the latter is non-linear, making it an infinitely harder problem to solve — as there are infinitely many non-linear transformations one can choose to apply. The only reason that I stumbled across this particular LTE modulation is that it comes directly from a clever solution of Laplace’s tidal equations.\n\n# Reversing Traveling Waves\n\nFor the solution to Laplace’s Tidal Equation described in Chapter 12, the spatial and temporal results are separable, leading to a non-linear standing-wave time-series formulation:\n\nsin(kx) sin(A sin(wt) )\n\nBy analogy to a linear standing-wave formulation, a solution such as\n\nsin(kx) sin(wt)\n\nwith the following traveling wave solution (propagating in the +x direction):\n\nsin(kx-wt)\n\nbecomes the following in the non-linear LTE solution mode:\n\nsin(kxA sin(wt) )\n\nThis is also a traveling wave, but with the characteristic property of being able to periodically reverse direction from +x to –x depending on the value of A and w. As an intuitive aid, a standing wave can be considered as the superposition of two traveling waves traveling in opposite directions:\n\nsin(kxA sin(wt) ) + sin(kx + A sin(wt) )\n\nHere the cross terms cancel after applying the trig identity on sums, and the separable standing-wave result similar to the first equation results. But, whenever there is an imbalance of +x and -x travelling waves, a periodic reversing traveling-wave/standing-wave mix results. This is shown in the following animation, where a mix of nonlinear traveling-waves and standing-waves show the periodic reversal in direction quite clearly.\n\nThis reversal is actually observed in ocean measurements, as exemplified in this recent research article:\n\nFrom their Figure 3, one can see this reversing process as the trajectory of a measured Argo float drift:\n\nIf that is not clear enough, the red arrows in the following annotated figure show the direction of the float motion. The drifting floats may not always exactly follow a trajectory as dictated by the velocity of a traveling wave, as this is partly a phase velocity with limited lateral volume displacement, but clearly a large wave-train such as a Tropical Instability Wave will certainly move a float. At least some of this is due to eddy behavior as the reversal is a natural consequence of a circular vortex motion of a large eddy.\n\nApplying the LTE model to complete spatio-temporal data sets such as what Figure 3 is derived from would likely show an interesting match, adding value to the latest ENSO results, but this will require some digging into the data availability.\n\n# The SAO and Annual Disturbances\n\nIn Chapter 11 of the book Mathematical GeoEnergy, we model the QBO of equatorial stratospheric winds, but only touch on the related cycle at even higher altitudes, the semi-annual oscillation (SAO). The figure at the top of a recent post geometrically explains the difference between SAO and QBO — the basic idea is that the SAO follows the solar tide and not the lunar tide because of a lower atmospheric density at higher altitudes. Thus, the heat-based solar tide overrides the gravitational lunar+solar tide and the resulting oscillation is primarily a harmonic of the annual cycle.", null, "Figure 1 : The SAO modeled with the GEM software fit to 1 hPa data along the equator Continue reading\n\n# Double-Sideband Suppressed-Carrier Modulation vs Triad\n\nAn intriguing yet under-reported finding concerning climate dipole cycles is the symmetry in power spectra observed. This was covered in a post on auto-correlations. The way that this symmetry reveals itself is easily explained by a mirror-folding about one-half some selected carrier frequency, as shown in Fig. 1 below.", null, "Figure 1 : ENSO amplitude spectrum is mirror-folded about 1/2 the annual frequency. Both the data and model align with their mirrored counterparts, as seen in highlighted box. Continue reading\n\n# Length of Day II\n\nThis is a continuation from the previous Length of Day post showing how closely the ENSO forcing aligns to the dLOD forcing.\n\nDing & Chao apply an AR-z technique as a supplement to Fourier and Max Entropy spectral techniques to isolate the tidal factors in dLOD\n\nThe red data points are the spectral values used in the ENSO model fit.\n\nThe top panel below is the LTE modulated tidal forcing fitted against the ENSO time series. The lower panel below is the tidal forcing model over a short interval overlaid on the dLOD/dt data.\n\nThat’s all there is to it — it’s all geophysical fluid dynamics. Essentially the same tidal forcing impacts both the rotating solid earth and the equatorial ocean, but the ocean shows a lagged nonlinear response as described in Chapter 12 of the book. In contrast, the solid earth shows an apparently direct linear inertial response. Bottom line is that if one doesn’t know how to do the proper GFD, one will never be able to fit ENSO to a known forcing.\n\nIn Chapter 12 of the book, we discuss tropical instability waves (TIW) of the equatorial Pacific as the higher wavenumber (and higher frequency) companion to the lower wavenumber ENSO (El Nino /Southern Oscillation) behavior. Sutherland et al have already published several papers this year that appear to add some valuable insight to the mathematical underpinnings to the fluid-mechanical relationship.\n\n“It is estimated that globally 1 TW of power is transferred from the lunisolar tides to internal tides. The action of the barotropic tide over bottom topography can generate vertically propagating beams near the source. While some fraction of that energy is dissipated in the near field (as observed, for example, near the Hawaiian Ridge ), most of the energy becomes manifest as low-mode internal tides in the far field where they may then propagate thousands of kilometers from the source . An outstanding question asks how the energy from these waves ultimately cascades from large to small scale where it may be dissipated, thus closing this branch of the oceanic energy budget. Several possibilities have been explored, including dissipation when the internal tide interacts with rough bottom topography, with the continental slopes and shelves, and with mean flows and eddies (for a recent review, see MacKinnon et al. ). It has also been suggested that, away from topography and background flows, internal modes may be dissipated due to nonlinear wave-wave interactions including the case of triadic resonant instability (hereafter TRI), in which a pair of “sibling” waves grow out of the background noise field through resonant interactions with the “parent” wave”\n\nsee reference \n\n# Australia Bushfire Causes\n\nThe Indian Ocean Dipole (IOD) and the El Nino Southern Oscillation (ENSO) are the primary natural climate variability drivers impacting Australia. Contrast that to AGW as the man-made driver. These two categories of natural and man-made causes form the basis of the bushfire attribution discussion, yet the naturally occurring dipoles are not well understood. Chapter 12 of the book describes a model for ENSO; and even though IOD has similarities to ENSO in terms of its dynamics (a CC of around 0.3) the fractional impact of the two indices is ultimately responsible for whether a temperature extreme will occur in a region such as Australia (not to mention other indices such as MJO and SAM).\n\n# The MJO\n\nIn Chapter 12 of the book, we presented a math model for the equatorial Pacific ocean dipole known as ENSO (El Nino /Southern Oscillation).  We argued that the higher wavenumber (×15 of the fundamental) characteristic of ENSO was related to the behavior known as Tropical Instability Waves (TIW). Taken together, the fundamental and TIW components provide enough detail to model ENSO at the monthly level. However if we drill deeper, especially with respect to the finer granularity SOI measure of ENSO, there are rather obvious cyclic factors in the 30 to 90 day range that can add even further detail. The remarkable aspect is that these appear to be related to the behavior known as the Madden-Julian Oscillation (MJO), identified originally as a 40-50 day oscillation in zonal wind .\n\n# AO, PNA, & SAM Models\n\nIn Chapter 11, we developed a general formulation based on Laplace’s Tidal Equations (LTE) to aid in the analysis of standing wave climate models, focusing on the ENSO and QBO behaviors in the book.  As a means of cross-validating this formulation, it makes sense to test the LTE model against other climate indices. So far we have extended this to PDO, AMO, NAO, and IOD, and to complete the set, in this post we will evaluate the northern latitude indices comprised of the Arctic Oscillation/Northern Annular Mode (AO/NAM) and the Pacific North America (PNA) pattern, and the southern latitude index referred to as the Southern Annular Mode (SAM). We will first evaluate AO and PNA in comparison to its close relative NAO and then SAM …" ]

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[ "#### Bandlimited Interpolation of Time-Limited Signals\n\nThe previous result can be extended toward bandlimited interpolation of", null, "which includes all nonzero samples from an arbitrary time-limited signal", null, "(i.e., going beyond the interpolation of only periodic bandlimited signals given one or more periods", null, ") by\n\n1. replacing the rectangular window", null, "with a smoother spectral window", null, ", and\n2. using extra zero-padding in the time domain to convert the cyclic convolution between", null, "and", null, "into an acyclic convolution between them (recall §7.2.4).\nThe smoother spectral window", null, "can be thought of as the frequency response of the FIR7.22 filter", null, "used as the bandlimited interpolation kernel in the time domain. The number of zeros needed in the zero-padding of", null, "in the time domain is simply length of", null, "minus 1, and the number of zeros to be appended to", null, "is the length of", null, "minus 1. With this much zero-padding, the cyclic convolution of", null, "and", null, "implemented using the DFT becomes equivalent to acyclic convolution, as desired for the time-limited signals", null, "and", null, ". Thus, if", null, "denotes the nonzero length of", null, ", then the nonzero length of", null, "is", null, ", and we require the DFT length to be", null, ", where", null, "is the filter length. In operator notation, we can express bandlimited sampling-rate up-conversion by the factor", null, "for time-limited signals", null, "by", null, "(7.8)\n\nThe approximation symbol", null, "' approaches equality as the spectral window", null, "approaches", null, "(the frequency response of the ideal lowpass filter passing only the original spectrum", null, "), while at the same time allowing no time aliasing (convolution remains acyclic in the time domain).\n\nEquation (7.8) can provide the basis for a high-quality sampling-rate conversion algorithm. Arbitrarily long signals can be accommodated by breaking them into segments of length", null, ", applying the above algorithm to each block, and summing the up-sampled blocks using overlap-add. That is, the lowpass filter", null, "rings'' into the next block and possibly beyond (or even into both adjacent time blocks when", null, "is not causal), and this ringing must be summed into all affected adjacent blocks. Finally, the filter", null, "can `window away'' more than the top", null, "copies of", null, "in", null, ", thereby preparing the time-domain signal for downsampling, say by", null, ":", null, "where now the lowpass filter frequency response", null, "must be close to zero for all", null, ". While such a sampling-rate conversion algorithm can be made more efficient by using an FFT in place of the DFT (see Appendix A), it is not necessarily the most efficient algorithm possible. This is because (1)", null, "out of", null, "output samples from the IDFT need not be computed at all, and (2)", null, "has many zeros in it which do not need explicit handling. For an introduction to time-domain sampling-rate conversion (bandlimited interpolation) algorithms which take advantage of points (1) and (2) in this paragraph, see, e.g., Appendix D and .\n\nNext Section:\nApplying the Blackman Window\nPrevious Section:\nRelation to Stretch Theorem" ]

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[ "# Assessing Variable Importance for Predictive Models of Arbitrary Type\n\n#### 2022-05-05\n\nLinear regression provides the historical and conceptual basis for much of the practical art of predictive modeling. Key advantages of linear regression models are that they are both easy to fit to data and easy to interpret and explain to end users. Unfortunately, these models often predict poorly relative to newer approaches from the machine learning literature like support vector machines, gradient boosting machines, or random forests. A significant price paid for the sometimes dramatically better performance of these alternative models is a greater difficulty of interpretation and explanation. To address one aspect of this problem, this vignette considers the problem of assessing variable importance for a prediction model of arbitrary type, adopting the well-known random permutation-based approach, and extending it to consensus-based measures computed from results for a large collection of models. In particular, this vignette uses the datarobot R package, which allows R users to interact with the DataRobot modeling engine, a massively parallel architecture for simultaneously fitting many models to a single dataset. These models cover a wide range of types, including constrained and unconstrained linear regression models, machine learning models like the ones listed above, and ensemble models that combine the predictions of the most successful of these individual models in several different ways. To demonstrate the practical utility of the ideas presented here, this approach is applied to a simulation-based dataset generated using the mlbench.friedman1 function from the R package mlbench, where it is possible to judge the reasonableness of the results relative to a “correct answer.” For a more detailed introduction to the DataRobot package and its capabilities, refer to the companion vignette, “Introduction to the DataRobot R Package.”\n\n## 1. Introduction\n\nTo help understand the results obtained from complex machine learning models like random forests or gradient boosting machines, a number of model-specific variable importance measures have been developed. As Grömping (2009) notes, however, there is no general consensus on the “best” way to compute - or even define - the concept of variable importance. (For an illuminating list of possible approaches, consult the help file for the varImp function in the caret package (Kuhn 2015): this list does not cover all methods that have been proposed, or even all methods available in R, but it clearly illustrates the range of methods available.) For the application of primary interest here - i.e., understanding the aggregate behavior of a collection of different type models like those generated by the DataRobot modeling engine - a “good” variable importance measure should exhibit these characteristics:\n\n1. it should be applicable to any model type;\n2. it should be sensible to combine or compare results across different model types.\n\nOne strategy that meets both of these criteria is that suggested by Friedman (2001), applying a random permutation to each covariate and thus effectively removing it from the model, and then examining the impact of this change on the predictive performance of the resulting model. The basic idea is that if we remove an important covariate from consideration, the best achievable model performance should suffer significantly, while if we remove an unimportant covariate, we should see little or no change in performance.\n\n## 2. Permutation-based significance measures\n\nIdeally, we would like to implement the strategy just described by applying many random permutations and combining the results, but this ideal approach is computationally expensive. In his application to gradient boosting machines, Friedman (2001) could “borrow strength” by combining the random covariate permutations with the random subsampling inherent in the model fitting procedure. In characterizing arbitrary models, however, we cannot exploit their internal structure, but we can borrow strength by combining results across the different models we are fitting. Thus, the approach taken here consists of the following steps:\n\n1. Run a DataRobot modeling project based on the original data and retrieve the results;\n2. For each covariate whose influence we are interested in assessing:\n1. Generate a modified dataset, replacing the covariate with its random permutation, leaving all other covariates and the target variable unmodified;\n2. Set up and run a new modeling project based on this modified dataset;\n3. Retrieve the project information and compute the performance differences between the models in this project and the same models in the original project.\n3. Characterize each covariate, in one of the following three ways:\n1. Select an individual model of particular interest (e.g., the model that performs best in the original project) and compute its performance degradation;\n2. Compute the average performance degradation over all project models;\n3. Compute a performance-weighted average of the degradation, like that defined in Section 5.\n\nThe following sections apply the procedure just described to a simulation-based example where we can make reasonable judgements about the relative importance of the covariates.\n\n## 3. A simulation-based dataset\n\nThe basis for the example considered here is the simulation function mlbench.friedman1 from the R package mlbench (Leisch and Dimitriadou 2010). This function simulates 10 independent, uniformly distributed random variables on the unit interval, $$x_1$$ through $$x_{10}$$, and generates the response variable $$y$$ defined by the first five of these covariates:\n\n$y = 10 \\sin (\\pi x_1 x_2) + 20 (x_3 - 0.5)^2 + 10 x_4 + 5 x_5.$\n\nThe user of the mlbench.friedman1 simulation function specifies the number $$n$$ of samples to be generated, and the standard deviation $$\\sigma$$ of a zero-mean, independent, identically distributed, Gaussian noise sequence added to the simulated $$y$$ values. In the example considered here, $$n = 5000$$, and the noise standard deviation had the default value, $$\\sigma = 1$$. To guarantee repeatability, the function set.seed(33) was first called to initialize the random number generators; the result was saved in the CSV file Friedman1.csv.\n\nBased on the structure of this simulator, we may classify the covariates into an influential subset ($$x_1$$ through $$x_5$$) and an irrelevant subset ($$x_6$$ through $$x_{10}$$). Also, from the model coefficients and the functions involved, we expect $$x_4$$ to be the most important variable, probably followed by $$x_1$$ and $$x_2$$, both comparably important, with $$x_5$$ probably less important. The influence of $$x_3$$ is somewhat more difficult to assess due to its quadratic dependence, but it seems likely that this nonlinearity will suppress this variable’s influence since the total range of this term is from $$0$$ to $$5$$, the same as the $$x_5$$ term.\n\n## 4. Results for the simulation data\n\nTo explore the utility of the random permutation-based strategy described in Section 3, eleven DataRobot projects were created. The first was based on the unmodified simulation dataset, specifying $$y$$ as the target variable and $$x_1$$ through $$x_{10}$$ as prediction covariates. This project minimizes root mean square prediction error (RMSE), the default fitting metric chosen by DataRobot:\n\nfriedman <- read.csv(system.file(\"extdata\", \"Friedman1.csv.gz\", package = \"datarobot\"))\noriginalProject <- StartProject(friedman, \"OriginalProject\", target = \"Y\", wait = TRUE)\noriginalModels <- ListModels(originalProject)\n\nAs discussed in the companion vignette, “Introduction to the DataRobot R Package,” the above sequence of model-building steps begins with the StartProject function, which uploads the modeling dataset Friedman1.csv, creates the project, gives it the name “OriginalProject”, specifies that the response variable to be predicted by all project models is Y. Because the model-building process does require some time to complete, the parameter wait = TRUE is used to delay the call to ListModels, requesting all project model information, until the model-building process has completed.\n\nAll other projects were set up similarly, except that a single random permutation was applied to covariate $$x_i$$ for the $$i^{th}$$ project. The random permutations were generated using the R function PermuteColumn, which has three required parameters: originalFile, the name of the CSV file containing the unmodified data (here, Friedman1.csv); colName, the name of the column in this file containing the variable whose influence we wish to assess; and permutedFile, the name of the CSV file where the modified data will be stored. The R code is:\n\nPermuteColumn <- function(originalFile, colName, permutedFile, iseed = 317) {\nset.seed(iseed)\noriginalFile <- system.file(\"extdata\", originalFile, package = \"datarobot\")\nvarNames <- colnames(dframe)\ncolIndex <- which(varNames == colName)\nx <- dframe[ ,colIndex]\ny <- sample(x)\noutFrame <- dframe\noutFrame[ ,colIndex] <- y\nwrite.csv(outFrame, permutedFile, row.names=FALSE)\n}\n\nTo compute the permutation-based variable importances, all project results are saved as elements of a composite list, modelList, whose first element is the original project model list and all subsequent elements are the permutation-based model lists. The R code to generate this list follows (note that because this process is building over 500 models, it takes some time to complete):\n\nmodelList <- list(n = 11)\nmodelList[] <- originalModels\npermFile <- tempfile(fileext = \"permFile.csv\")\nfor (i in 1:10) {\nvarName <- paste(\"X\",i,sep=\"\")\nPermuteColumn(\"Friedman1.csv.gz\", varName, permFile)\nprojName <- paste(\"PermProject\", varName, sep = \"\")\npermProject <- StartProject(permFile, projectName = projName, target = \"Y\", wait = TRUE)\nmodelList[[i+1]] <- ListModels(permProject)\n}\n\nTo obtain the desired permutation shifts, it is useful to convert the summary list generated by this code into a dataframe, with the following columns:\n\n• blueprintId, an alphanumeric character string that uniquely identifies the model structure and any preprocessing applied;\n• modelType, a character string describing the model structure;\n• expandedModel, a character string describing the model structure and any preprocessing applied;\n• samplePct, the fraction of the training dataset used in fitting the model;\n• a column giving the value of the fitting metric computed from the validation set data for the original model;\n• one column for each covariate in the original model, giving the validation fitting metric value for the model constructed after the random permutation was applied to that covariate.\n\nThis conversion is accomplished by the PermutationMerge function listed below, which requires the summary list, the samplePct value for the models to be matched, and a vector giving the names for the fitting metric columns in the resulting dataframe. Matching here is done on the basis of blueprintId and samplePct, which guarantees that fit comparisons are made between original and randomized fits to the same model for the same sample size, giving an “apples-to-apples” comparison of the effects of the random permutations applied to the covariates. In particular, note that DataRobot fits the same model to several different sample sizes, so it is necessary to specify both samplePct and blueprintId to uniquely identify a model.\n\nPermutationMerge <- function(compositeList, matchPct = NULL, metricNames, matchMetric = NULL) {\ndf <- as.data.frame(compositeList[], simple = FALSE)\nif (is.null(matchPct)) {\nindex <- seq(1, nrow(df), 1)\n} else {\nindex <- which(round(df$samplePct) == matchPct) } if (is.null(matchMetric)) { projectMetric <- compositeList[][]$projectMetric\nmatchMetric <- paste(projectMetric, \"validation\", sep = \".\")\n}\ngetCols <- c(\"modelType\", \"expandedModel\", \"samplePct\", \"blueprintId\", matchMetric)\noutFrame <- df[index, getCols]\nkeepCols <- getCols\nkeepCols <- metricNames\ncolnames(outFrame) <- keepCols\nn <- length(compositeList)\nfor (i in 2:n) {\ndf <- as.data.frame(compositeList[[i]], simple = FALSE)\nindex <- which(df$samplePct == matchPct) upFrame <- df[index, c(\"blueprintId\", matchMetric)] colnames(upFrame) <- c(\"blueprintId\", metricNames[i]) outFrame <- merge(outFrame, upFrame, by = \"blueprintId\") } outFrame } Because it gives the largest number of models to compare, the results for the 16% training sample are considered here, and the metricNames parameter required by the PermutationMerge function is defined as indicated in the following R code: metricNames <- c(\"originalRMSE\", paste(\"X\", seq(1, 10, 1), \"RMSE\", sep = \"\")) mergeFrame <- PermutationMerge(modelList, 16, metricNames) The resulting dataframe gives the original validation set RMSE value and the permutation RMSE values for all covariates for the 25 models fit to the 16% data sample (here, this sample consists of 800 records, large enough to give reasonable comparison results). Figure 1 shows a beanplot summary of these results, comparing the RMSE values for the 25 common models built for each of the eleven datasets just described. This figure was generated using the R package beanplot (Kampstra 2008), and the “beans” or red lines in these plots represent the RMSE values for the individual models from each project. Beanplots are analogous to the more familiar boxplots, combining the boxplot range information with a nonparametric density estimate to give a more complete view of how each data subset is distributed. This additional information is particularly useful in cases like the one considered here, where these distributions differ significantly in form between the different subsets. These plots suggest that random permutations applied to the relevant variables X1 through X5 increase the RMSE values for most models, while permutations applied to the irrelevant variables X6 through X10 seem to have little impact on these values, but to be certain we need to make direct comparisons.", null, "Beanplot summary of RMSE versus random permutation. Figure 2 presents a more direct beanplot summary of the differences in RMSE values between the random permutation-based models and the original model. Here, each beanplot corresponds to one of the covariates and the individual “beans” in these plots now represent the increase in validation set RMSE value that results when the random permutation is applied to the corresponding variable. The dataframe on which this summary is based was computed using the function ComputeDeltas: ComputeDeltas <- function(mergeFrame, refCol, permNames, shiftNames) { allNames <- colnames(mergeFrame) refIndex <- which(allNames == refCol) xRef <- mergeFrame[, refIndex] permCols <- which(allNames %in% permNames) xPerm <- mergeFrame[, permCols] deltas <- xPerm - xRef colnames(deltas) <- shiftNames deltas$New <- xRef\nnewIndex <- which(colnames(deltas) == \"New\")\ncolnames(deltas)[newIndex] <- refCol\ndeltas\n}\n\nTo use this function, we need to specify: refCol, the name of the reference column with the original model RMSE values; permNames, the names of the columns containing the permutation-based RMSE values; and shiftNames, the names of the permutation-induced shift columns in the dataframe returned by the function. Here, the following code generates the desired permutation shift dataframe:\n\nallNames <- colnames(mergeFrame)\nrefCol <- allNames\npermNames <- allNames[6:15]\nshiftNames <- paste(\"X\", seq(1, 10, 1), sep = \"\")\ndeltaFrame <- ComputeDeltas(mergeFrame, refCol, permNames, shiftNames)", null, "Beanplot summary of RMSE shifts versus random permutation.\n\nThe beanplot shown in Figure 2 includes solid blue lines at the average RMSE shift for each covariate and a dashed reference line at zero RMSE shift; also, the results for the best model for this example (RuleFit Regressor) are shown as solid green circles. It is clear from these results that random permutations applied to the relevant variables X1 through X5 cause significant RMSE increases for most models, while random permutations applied to the irrelevant variables X6 through X10 have essentially no effect. An important exception is the trivial mean response model: this model consistently exhibits the worst RMSE performance in Figure 1, but because its response is independent of all covariates, it shows zero RMSE shift in response to all covariate permutations in Figure 2.\n\n## 5. Numerical importance measures\n\nWhile graphical summaries like those shown in Figures 1 and 2 are useful, we often want numerical importance measures. The RMSE shifts presented here provide a basis for computing these measures, which can be defined in several different ways. The simplest is to average the RMSE shifts over all models, giving a consensus-based relative importance value for each variable, corresponding to the blue lines shown in Figure 2. A potential disadvantage of this approach is that it gives equal weights to all models, including those like the mean response model for which the RMSE shifts are always zero. At the other extreme, we could take the RMSE shift in one individual model - the best predictor is an obvious choice here, corresponding to the green points in Figure 2 - but this has the potential disadvantage of being model-specific and it does not make full use of the performance shift data from all of the available models. An intermediate course is to form a performance-weighted average of the individual model results, giving greater weight to better-performing models. A specific implementation of this idea is the following performance-weighted average:\n\n$\\nu(x) = \\frac{\\sum_{i=1}^{M} \\; (\\mbox{RMSE}_i^x - \\mbox{RMSE}_i^0)/\\mbox{RMSE}_i^0}{\\sum_{i=1}^{M} \\; 1/\\mbox{RMSE}_i^0},$\n\nwhere $$\\mbox{RMSE}_i^x$$ represents the RMSE value for the $$i^{th}$$ model in the collection fit from the dataset with a random permutation applied to the covariate $$x$$, and $$\\mbox{RMSE}_i^0$$ is the RMSE value for this model when fit to the original dataset. For the example considered here, this approach gives the RMSE shift for the best models approximately five times greater weight than the poorest model. A simple R function to compute this performance-weighted average from the shift summary dataframes described above is varImpSummary:\n\nvarImpSummary <- function(deltaFrame, refCol, oneIndex) {\nvars <- colnames(deltaFrame)\nrefIndex <- which(vars == refCol)\nrefValue <- deltaFrame[, refIndex]\nwts <- 1/refValue # Performance-weights = reciprocal fitting measure\ndeltasOnly <- deltaFrame[, -refIndex]\nthisModel <- as.numeric(deltasOnly[oneIndex, ])\navg <- apply(deltasOnly, MARGIN=2, mean)\nWtAvgFunction <- function(x, w) { sum(w * x) / sum(w) }\nwtAvg <- apply(deltasOnly, MARGIN = 2, WtAvgFunction, wts)\nvarImpFrame <- data.frame(average = avg,\nweightedAverage = wtAvg,\noneModel = thisModel)\nvarImpFrame\n}\n\nHere, deltaFrame is the dataframe returned by the function ComputeDeltas listed above, refValue is the vector of original RMSE values ($$\\mbox{RMSE}_i^0$$ values in the above equation), and oneIndex is the row number in deltaFrame describing the performance of a single model of particular interest. In this example, oneIndex specifies the best non-blender model in the original DataRobot project with no permutations applied to any variable.\n\nThe table shown below gives a summary of the three numerical variable importance measures just described for the simulation-based example considered here. Specifically, this table lists the average RMSE shift, the performance-weighted average RMSE shift defined above, and the shift associated with the best model. Based on these results, the relevant variables X1 through X5 are consistently ranked as much more important than the irrelevant variables, X6 through X10. Also, all three of the measures considered here give the same relative ranking to the relevant variables: X4 is most important, followed by X2 and X1, with similar shift values, then X5 and finally X3. Recall that this corresponds to the approximate ordering anticipated on the basis of the structure of the simulation model generating the data.\n\n## Avg WtdAvg Best\n## 1 1.024 1.137 1.745\n## 2 1.105 1.230 1.926\n## 3 0.374 0.448 0.706\n## 4 1.508 1.636 2.167\n## 5 0.543 0.599 0.903\n## 6 -0.001 0.000 -0.014\n## 7 0.000 -0.001 -0.020\n## 8 0.010 0.011 -0.020\n## 9 0.002 0.001 -0.013\n## 10 0.002 0.004 -0.025\n\n## 6. Summary\n\nThis note has described the use of random permutations to assess variable importance for predictive models of arbitrary type. The DataRobot modeling engine fits many different model types to the same dataset, building models that predict the same target variable from the same covariates, and the random permutation approach described here can be applied to all of these models, yielding variable importance assessments for any covariate and each model in the DataRobot modeling project. Since there is nothing model-specific about this random permutation strategy, the results can be compared and combined across all of these models, leading to consensus-based variable importance measures like those discussed in Section 5. These ideas were illustrated here for the simulation-based dataset described in Section 2, making it possible to compare the results with expectations based on the simulation model structure. For this example, all three of the numerical measures proposed in Section 5 gave results that were in agreement with these expectations. The companion vignette, “Using Many Models to Compare Datasets” presents the corresponding variable importance results for two real datasets." ]

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", null, 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", 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[ "this is the nav!\nWorkspace\nEduardo Bastos de Moraes/\n\n# User Retention by Cohort\n\n0\nBeta\n\n## .mfe-app-workspace-kj242g{position:absolute;top:-8px;}.mfe-app-workspace-11ezf91{display:inline-block;}.mfe-app-workspace-11ezf91:hover .Anchor__copyLink{visibility:visible;}User Retention by Cohort\n\nThis template helps visualize user retention as the percentage of users in an acquisition cohort who are still using the product after several elapsed time periods. Retention can be visualized in two different ways:\n\n1. Annotated Heatmap: An annotated heatmap of retention by cohort is useful to visualize and compare rates across cohorts and time periods.\n\n2. Line Plot: A line plot of retention grouped by cohort is useful to visualize the dropoff in users over time periods.\n\n```.mfe-app-workspace-qcdhrn{font-size:13px;line-height:1.5384615384615385;font-family:JetBrainsMonoNL,Menlo,Monaco,'Courier New',monospace;}```# Load packages\nimport pandas as pd\nimport numpy as np\nimport plotly.express as px\nimport plotly.figure_factory as ff``````\n\nEach row in the data aggregates the number of users by cohort and segment who were active in a time period. (user-activity.csv)\n\n``````# Upload your data as CSV and load as a data frame\n\n### 2. Compute Retention\n\nThe retention rate is computed as the percentage of users in a cohort (or cohort-segment) who stayed active over time.\n\n``````# Compute Retention\ndef compute_retention(df):\ndf_all = (\ndf\n.groupby(['cohort_date', 'period_date'])\n.agg('sum')\n.reset_index()\n)\ndf_all['period_index'] = (df_all['period_date'] - df_all['cohort_date']) / np.timedelta64(1, 'W')\ndf_all['nb_users_total'] = df_all.groupby(['cohort_date'])['nb_users'].transform(max)\ndf_all['pct_users'] = df_all['nb_users'] / df_all['nb_users_total']\ndf_all.drop(columns = ['nb_users_total'], inplace=True)\ndf_all = df_all[['cohort_date', 'period_date', 'period_index', 'nb_users', 'pct_users']]\nreturn df_all\n\ndf_retention = compute_retention(df)\n\n### 3. Visualize retention as heatmap\n\nEach row in the heatmap represents a cohort and visualizes the percentage of users retained over time.\n\n``````# Plot cohort retention heatmap\ndef plot_cohorts_heatmap(df, nb_periods=15):\ndf = df.query('period_index > 0 & period_index <= @nb_periods')\ndf_wide = (df\n.pivot(index=\"cohort_date\", columns='period_index', values='pct_users')\n.sort_values(by=['cohort_date'], ascending=False)\n.fillna(0)\n)\nfig = ff.create_annotated_heatmap(\nz = df_wide.values,\nannotation_text = df_wide.applymap(lambda x: '{:.1%}'.format(x) if x > 0 else '').values.tolist(),\ny = df_wide.index.strftime('%Y - W%W').values.tolist(),\nx = df_wide.columns.tolist(),\ncolorscale='viridis_r',\n)\nfig.update_layout(\nwidth=900,\nheight=700,\nxaxis={\"title\": \"# Periods Elapsed\"},\ntitle=\"User Retention by Cohort: Heatmap\")\nreturn fig\n\nfig = plot_cohorts_heatmap(df_retention)\nfig.show(config={\"displayModeBar\": False})``````\n\n### Visualize retention as line plot\n\nEach line represents a cohort and visualizes the dropoff in number of users over time.\n\n``````# Plot cohort retention lines\ndef plot_cohort_lines(df, nb_periods=15):\ndf['cohort_date'] = df['cohort_date'].astype(str)\nfig = px.line(\ndf.query('period_index > 0 & period_index < @nb_periods'),\nx='period_index',\ny='pct_users',\nline_group='cohort_date',\ncolor_discrete_sequence=[\"lightslategray\"]\n)\nfig.update_layout(\nxaxis = {\"title\": \"# Periods Elapsed\"},\nyaxis = {\"title\": \"% Users Retained\"},\ntitle=\"User Retention by Cohorts: Line Plot\"\n)\nreturn fig\n\nfig_lines = plot_cohort_lines(df_retention)\nfig_lines.show(config = {\"displayModeBar\": False})``````" ]

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[ "# Find tangent point on circle furthest east or west\n\nThere are few ways of articulating my question. It starts with a known circle on a sphere, i.e. a point-radius, and one that does not cover a pole. I would like to calculate the point furthest west on this circle and the point furthest east. These points are the tangent points of lines of longitude which encircle the poles and are vertical. These points are opposite each other along the vertical axis so there is one hard problem to solve from which the other is trivially determined. This is highly related to calculating the minimum bounding lat-lon box of a circle. I know how to determine the longitude delta from the center to the edges, which is:\n\n``````asin( sin( dist_rad / cos(center_lat_rad) ) )\n``````\n\nwhereas dist_rad is the circle's radial distance is radians, and center_lat_rad is the latitude point of the circle's center in radians. This equation was elusive to me until I discovered it with a wonderful explanation here. It contains a wonderful illustration:", null, ".\n\nThe illustration shows T1 and T2 which are the points I am trying to calculate. What is left to figure out is at what latitude the eastern and western boundary meridians intersect this circle. If the circle is at the equator, then it's zero, and if it's north of the equator, then this latitude is going to be higher than the circle's center latitude.\n\n• Would a numerical solution suffice? In other words could something like Newton's method be used to make successive guesses at the latitude be made. For each guess you could find the geodesic distance to M, the guess with the minimum distance wins. Jan 24, 2012 at 21:07\n• In some cases that's a good approach, @Kirk, but here it won't be very precise. If you were to graph the distance to M as a function of position along the extreme meridian through T2, you would find that it hardly changes close to T2: the function is quadratic there. This is precisely the kind of situation where methods like Newton's can break down or lose a great deal of precision. (It's related to the reason we use a Haversine law rather than a law of Cosines for finding spherical distances.) Jan 24, 2012 at 21:18\n• Would this problem be simpler if you converted your Lat/Long to X/Y/Z space? Then you're just solving for an (x,y,z) that lies on the two spheres expressed by XX+YY+ZZ=RR? Jan 24, 2012 at 23:37\n• That's always a reasonable option @Bicycle. Given that the spherical trig solution is so simple (and that all spherical trig identities can be derived from your suggestion), one would expect that doing that math would yield the same answer. (My guess is that it would be the same answer in a more complicated form due to the conversions from spherical to 3D cartesian coordinates and back again.) Jan 24, 2012 at 23:45\n\nQuestions like this can often be answered by solving triangles using laws of spherical trigonometry. You can look these up: they are referenced below. Normally, when you know three of the six parts of a spherical triangle, the laws let you find the other three in terms of the sines and cosines of the parts you know. The trick is to draw a useful triangle. When you're dealing with meridians, think of using a pole (which is common to all meridians) as one of the triangle's vertices. This suggests focusing on the triangles N-M-T1 or, equivalently, N-M-T2. Here are the details, a general solution, and a worked example.\n\nLet the point in question be at latitude phi and the circle's radius be r (expressed as an angle, not as a distance. The angle in radians is the radial distance divided by the sphere's radius). We start by finding the difference between the local longitude and the extreme longitudes; let this difference be lambda.\n\nBecause the extreme meridians are tangent to the circle, angles M-T1-N and M-T2-N are right angles. This is nice because the sine and cosine of a right angle are easy to find and simple (they equal 1 and 0, respectively). The spherical Law of Sines says\n\n``````sin(lambda) / sin(r) = sin(90 degrees) / sin(90 - phi)\n= 1 / cos(phi).\n``````\n\nSolving this gives\n\n``````lambda = ArcSin( sin(r) / cos(phi) ).\n``````\n\nFor example, let r = 45 degrees and phi = -30 degrees. The solution is lambda = 54.7356 degrees.\n\nThis much you already found out: it's the formula quoted in the question. Now we can apply the spherical Law of Cosines to relate the latitude phi' of the extremal points T1 and T2 to the radius r: this is what we are looking for.\n\n``````sin(phi) = sin(phi') cos(r).\n``````\n\nThe solution for the common latitude of the tangent points is\n\n``````phi' = ArcSin( sin(phi) / cos(r) )\n``````\n\nThe remainder of the reply discusses and illustrates this result.\n\nNotice in particular that when we start at the equator, phi = 0, easily giving phi' = 0 as expected. Otherwise, the sine of phi' is larger (in size) than the sine of phi, implying the solution is closer to the nearest pole, again as expected. In the example, phi' works out to -45 degrees.", null, "The south pole is near the bottom of this pseudo-3D image of a sphere. The meridians start at the circle's center and go in 15 degree increments to either side, showing +-15, +-30, and +-45 degree longitudinal displacements, then stop at the limiting values of +-54.7356 degrees. The red dots are situated along these limiting meridians at latitudes of -45 degrees.\n\nThese formulas work for any circle that does not include either pole.", null, "In this image, the circle's center (black dot) is just north of 60 degrees north latitude. Approximate circles of latitude are shown as dashed curves in 10 degree increments. The radius, equal almost to 30 degrees of arc, takes this circle almost to the north pole (where the meridians are converging at the top). The extremal meridians are therefore spread far apart (lambda is about 70 degrees) and, accordingly, the points of tangency are also close to the north pole, near 80 degrees latitude. This shows why the points of tangency (red dots) are usually closer to the nearest pole than the circle's center is.\n\n• If, as you say, \"angles M-T1-N and M-T2-N are right angles\". Then the line M-T1 must follow the Latitude line (all lines of latitude cross each meridian at a right angle (in a sphere)). Therefore phi is solved - it is the latitude of M, just figure out lambda now. Jan 24, 2012 at 21:22\n• I'm afraid that argument is incorrect, @Brenth. It assumes lines of latitude are straight, but (except at the equator) they are not. (This also helps us see why your argument does give the correct answer when the center lies on the equator.) For a detailed explanation of the phenomenon, please refer to the answer I posted at gis.stackexchange.com/questions/6822/…. Jan 24, 2012 at 21:26\n• Sorry brenth, but whuber is correct. Spherical geometry is a bitch, and you are unfortunately making some incorrect assumptions. As whuber points out, lines of latitude are not the spherical equivalent of \"straight\" lines: only great circles are. Jan 24, 2012 at 22:27\n• This answer is stupendous; it really shows the value of stack exchange. And I got the answer fast. I took the formula at the end of the long explanation and put it into my system which has an extensive test suite to effectively prove the answer is correct. There were some NaN result edge-cases when the circle touches the pole in which I mapped the answer to +90 or -90 depending on wether the circle's center is above or below the equator. Jan 26, 2012 at 16:28\n• Thanks @whuber , I was trying to have a bounding box around a point, now it is clear, and also test is matching the result. For anyone who is interested Python code in gist.github.com/alexcpn/f95ae83a7ee0293a5225 Feb 20, 2016 at 10:52\n\nStruggled a bit to understand first the answer. Here is the python port of whubers code; Putting it in an answer, for better visibility for others as earlier it was buried in comments\n\nPython code for bounding box with test for the above\n\nHere is more amateur friendly drawing to explain the same", null, "" ]

[ null, "https://i.stack.imgur.com/xv9Qo.gif", null, "https://i.stack.imgur.com/qbZDl.png", null, "https://i.stack.imgur.com/70Q4g.png", null, "https://i.stack.imgur.com/rQzlv.png", null ]

[ "We want to find the inverse of g(y), which is . This quiz and worksheet will assess your understanding of algebraic functions. Thus, the range of h is all real numbers except 0. For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum. When we input 3, the function box then substitutes 3 for x and I promise you will have no trouble evaluating function if you follow along. Solution: a) g (a + b) = (a + b) 2 + 2. This test is similar to the vertical line test, except that it ensures that each value in the range corresponds to only one value in the domain. About This Quiz & Worksheet. If f(x) has exactly one value for every x in the domain, then f is a function. send us a message to give us more detail! We will go through fundamental operations such as – Select operation, Project operation, Union operation, Set difference operation, Cartesian product operation and Rename operation. For K-12 kids, teachers and parents. Thus, for instance, the number 5 becomes , and becomes 2. When you input 5, you should get 11 because (2*5+1 = 1), so Function Notation. Thus, for instance, the number 5 becomes , and becomes 2. Note that a function must be one-to-one to have an inverse. Solution: A function such as this one is defined for all x values because there is no value of x for which 3x becomes infinity, for instance. Thus, the graph also proves that h(y) is not a function. being the center of the function box. Note that the function is a straight line, and regardless of the scale of the axes (how far out you plot in any direction), the line continues unbroken. Algebraic functionsare built from finite combinations of the basic algebraic operations: addition, subtraction, multiplication, division, and raising to constant powers. function because when we input 4 for x, we get two different answers for The idea of the composition of f with g (denoted f o g) is illustrated in the following diagram.Note: Verbally f o g is said as \"f of g\": The following diagram evaluates (f o g)(2).. If you input another number such as 5, you will get a different (2*3 +1 = 7). All the trigonometric equations are all considered as algebraic functions. Evaluating Functions Expressed in Formulas. substitute 3 for x, you will get an answer of 7. Advanced Algebra and Functions – Video. If he sold 360 kilograms of pears that day, how many kilograms did he sell in the morning and how many in the afternoon? We had what was known as A zero of a function f(x) is the solution of the equation f(x) = 0. For example, the function f(x) = 2x takes an input, x, and multiplies it by two. At this point, we can make an important distinction between a function and the more general category of relations. A composition of functions is simply the replacement of the variable in one function by a different function. Solution: The composition is the same as h(r(s)); thus, we can solve this problem by substituting r(s) in place of s in the function h. Be careful to note that is not the same as : An inverse of a one-to-one function f(x), which we write as , is a function where the composition . As mentioned, fractions work as well as whole numbers, both for positive and negative values; the only value that does not work is 0, since is undefined (how many times can 0 go into 1?). For a relation to be a function specifically, every number in the domain must correspond to one and only one number in the range. Functions. Interpreting Functions F.IF.C.9 — Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). Algebra Examples. These sets are what we respectively call the domain and range of the function. For supposing that y is a solution to. Why not take an. Below is the table of contents for the Functions Unit. Solution: The function g(x) simply takes the value x and turns it into its reciprocal value . -2c 2 (-7c 3 x 5 ) (bx 2) 2 =. In our example function h(y) above, the range is (except for h(y) = 0), because for any real number, we can find some value of y such that the real number is equal to h(y). For instance, we may define a function G(n) over only the integers; thus, the variable n is only allowed to take on integer values when used in the function G. In some instances, the form of the function may exclude certain values from the domain because the output of the function would be undefined. Pay close attention in each example to where a number is substituted into the function. output. How to Solve Higher Degree Polynomial Functions, Solving Exponential and Logarithmic Functions, Using Algebraic Operations to Solve Problems, How to Use the Correlation Coefficient to Quantify the Correlation between Two Variables, Precalculus: How to Calculate Limits for Various Functions, Precalculus Introduction to Equations and Inequalities, Understanding Waves: Motions, Properties and Types, Math All-In-One (Arithmetic, Algebra, and Geometry Review), Geometry 101 Beginner to Intermediate Level, Physics 101 Beginner to Intermediate Concepts. Now, we can check the result using the condition of inverse functions: An equation in algebra is simply a statement that two relations are the same. Solution Solution. Step-by-Step Examples. Trigonometric Equations: cos2x = 1+4sinx; Solving Algebraic Equations. f(x) = sqrt(x) = x 1/2; g(x) = |x| = sqrt(x 2) h(x) = sqrt(|x|) = sqrt(sqrt(x 2)) Next, manipulate the equation using the rules of arithmetic and real numbers to find an expression for . We can further observe that the function is one-to-one; you can see this by noting that the function simply takes every number on the number line and multiplies it by 3. We have more than one value for y. Hopefully with these two examples, you now understand the difference Thus, this function is not defined over all real values of x. The example diagram below helps illustrate the differences between relations, functions, and one-to-one functions. Questions on one to one Functions. Click on the History. You will find more examples as you study the variable y = 7. creature in Algebra land, a function is really just an equation with a (Notice how our equation has 2 variables (x and y) When we input 3, the function box then substitutes 3 for x and calculates the answer to be 7. Let's take a look at an example with an actual equation. As you progress into Algebra 2, you will be studying Click here to view all function lessons. Polynomials, power functions, and rational function are all algebraic functions. As you can see in the graph, the function g to the left of zero goes down toward negative infinity, but the right side goes toward positive infinity, and there is no crossing of the function at zero. The same argument applies to other real numbers. 4) 98. If it is possible to express the function output with a formula involving the input quantity, then we can define a function in algebraic form. If you are nervous, Algebra Class offers many lessons on understanding functions. An Irrational Function Containing. Consider the example function h(y) below: Notice that any value of y from the set of real numbers is acceptable-except for the number 4. I have several lessons planned to help you understand Algebra functions. In each case, the diagram shows the domain on the left and the range on the right. The input of 2 goes into the g function. Solution: The function g(x) simply takes the value x and turns it into its reciprocal value . an \"in and out box\". Algebra. Example - Problem. Ok, so getting down to it, let's answer that question: \"What is a function?\". substitute . Although it may seem at first like a function is some foreign Let's look at the graph of the function also. Consider the function f(x) below: The function f simply takes in input value x, multiplies it by 2, and then adds 3 to the result. The domain of a function is the set of numbers for which the function is defined. Perform the replacement of g(y) with y, and y with . Thus, the domain of the function is all x in where x ≠ 0. Throughout mathematics, we find function notation. In Algebra 1, we will Math Word Problems and Solutions - Distance, Speed, Time. We can therefore consider what constitutes the set of numbers that the function can accept as an input and what constitutes the set of numbers that the function can yield as an output. = a 2 + 2ab + b 2 + 2. b) g (x 2) = (x 2) 2 + 2 = x 4 + 2. function: \"the value of the first variable corresponds to one and only one value for the second value\". When x = 3, y = 7 Linear functions, which create lines and have the f… A solution to an equation is the value (or values) of the variable (or variables) in an equation that makes the equation true. If two functions have a common domain, then arithmetic can be performed with them using the following definitions. We can never divide by zero. Finally, the relation h is a one-to-one function because each value in the domain corresponds to only one value in the range and vice versa. Thus, if f(x) can have more than one value for some value x in the domain, then f is a relation but not a function. As with any arithmetic manipulation, as long as you perform the same operation on both sides of the equality sign (=), the equality will still hold. Advanced Algebra and Functions – Download. The relation h(y) is therefore not a function. Therefore, this does not satisfy the definition for a every time. Consider the following situation. (This property will be important when we discuss function inversion.) Three important types of algebraic functions: 1. Function notation is a way to write functions that is easy to read and understand. The relation g is a function because each value in the domain corresponds to only one value in the range. Solution: We can easily note that for any value of y in the domain, the relation yields two different values in the range. function. Here we have the equation: y = 2x+1 in the algebra function box. For example, in the function , if we let x = 4, then we would be forced to evaluate 1/0, which isn't possible. Basics of Algebra cover the simple operation of mathematics like addition, subtraction, multiplication, and division involving both constant as well as variables. Example: 1. Problem 1 A salesman sold twice as much pears in the afternoon than in the morning. 4. substituting into this equation. equation. Obtaining a function from an equation. Recall that a function is a relation between certain sets of numbers, variables, or both. So, let's rearrange this expression to find . (Notice how our equation has 2 variables (x and y). (2*3 +1 = … Some teachers now call it a \"Function Box\" and A function is a relationship between two variables. EQUATIONS CONTAINING ABSOLUTE VALUE(S) - Solve for x in the following equations. This is then the inverse of the function. following are all functions, they will all pass the Vertical Line Test. Thus, if we have two functions f(x) and g(y), the composition f(g(y)) (which is also written is found by simply replacing all instances of x in f(x) with the expression defined for the function g(y). Practice Problem: Determine if the relation is one-to-one. If f( x) = x+ 4 and g( x) = x2– 2 x– 3, find each of the following and determine the common domain. We end up with y = 2 or -2. Closely related to the solution of an equation is the zero (or zeros) of a function. Fundamentally, a function takes an input value, performs some (perhaps very simple) conversion process, then yields an output value. 2. So the integral is now rational in . functions - but never called them functions. We can eliminate it from the answer choices. Solution for Give your own examples in algebra and graphs of a function that... 13) Has a vertical asymptote of x = 3. 3) 13. Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor. Register for our FREE Pre-Algebra Refresher course. An inverse of a function is, in this context, similar to the inverse of a number (3 and , for instance). Answers. {\\displaystyle y^ {n}-p (x)=0.} Let's take a look at this another way. Therefore, this equation can be Another way of combining functions is to form the composition of one with another function.. The common domain is {all real numbers}. introduced to this term called a \"function\". No other number will correspond with 3, when using this Thus, an equation might be as simple as 0 = 0, or it might be as complicated as . Function pairs that exhibit this behavior are called inverse functions. The range of a function is the set of all possible values in the output of a function given the domain. Functions and equations. For instance, if y = 4, h(y) can be either 2 or –2. Thus, not only is the range of the function, it is also the domain. A function is one-to-one if it has exactly one value in the domain for each particular value in the range. functions. Practice Problem: Find the composition , where and . lessons in this chapter. Not ready to subscribe? Copyright © 2009-2020   |   Karin Hutchinson   |   ALL RIGHTS RESERVED. Second, we can see that f(x) is not one-to-one because f(x) is the same for both +x and -x, since . Think of an algebraic function as a machine, where real numbers go in, mathematical operations occur, and other numbers come out. Surprisingly, the inverse function of an algebraic function is an algebraic function. ( f+ g)( x) ( f– g)( x) ( f× g)( x) The common domain is {all real numbers}. For a trigonometry equation, the expression includes the trigonometric functions of a variable. Let's look at the graph and apply the vertical line test as a double check: Note that the relation crosses a vertical line in two places almost everywhere (except at y = 0). On this site, I recommend only one product that I use and love and that is Mathway   If you make a purchase on this site, I may receive a small commission at no cost to you. An algebraic function is any function that can be built from the identity function y=x by forming linear combinations, products, quotients, and fractional powers. ... Rather than solving for x, you solve for the function in questions like \"Find all functions that have these properties.\" A function is called one-to-one if no two values of \\(x\\) produce the same \\(y\\). Any number can go into a function as lon… What in the world is a Equations vs. functions. … Practice Problem: Find the inverse of the function . o         Learn more about functions (in general) and their properties, o         Use graphs to explore a function's characteristics, o         Gain an understanding of inverse functions and compositions of functions, o         Understand the relationship between functions and equations. between an equation that represents a function and an equation that does The terms can be made up from constants or variables. Thus, the range of f(x) is , the entire set of real numbers. Example 6: Consider two functions, f(x) = 2x + 3 and g(x) = x + 1.. The result in this case is not defined; we thus exclude the number 4 from the domain of h. The range of h is therefore all (the symbol simply means \"is an element of\") where y ≠ 4. −x2 = 6x−16 - x 2 = 6 x - 16. This can provide a shortcut to finding solutions in more complicated algebraic polynomials. The graph above shows that the relation f(x) passes the vertical line test, but not the horizontal line test. To do so, apply the vertical line test: look at the graph of the relation-as long as the relation does not cross any vertical line more than once, then the relation is a function. 5) All real numbers except 0. 3a 2 (-ab 4 ) (2a 2 c 3) =. f (x) = 6x − 16 f ( x) = 6 x - 16 , f (x) = −x2 f ( x) = - x 2. Substitute −x2 - x 2 for f (x) f ( x). You'll need to comprehend certain study points like functions and the vertical line test. It seems pretty easy, right? Although it is often easy enough to determine if a relation is a function by looking at the algebraic expression, it is sometimes easier to use a graph. study linear functions (much like linear equations) and quadratic Solution Solution Solution Solution Solution Solution Solution. Solve for x x. Another way to consider such problems is by way of a graph, as shown below. The algebraic equation can be thought of as a scale where the weights are balanced through numbers or constants. box performs the calculation and out pops the answer. Multiply the numbers (numerical coefficients) 2. lesson that interests you, or follow them in order for a complete study Interested in learning more? not represent a function. A function has a zero anywhere the function crosses the horizontal axis in its corresponding graph. this is why: Here's a picture of an algebra function box. Note that essentially acts like a variable, and it can be manipulated as such. © Copyright 1999-2021 Universal Class™ All rights reserved. When we input 4 for x, we must take the square root of both sides in order to solve for y. Examples. Take a look at an example that is not considered a y n − p ( x ) = 0. How to find the zeros of functions; tutorial with examples and detailed solutions. The value of the first variable corresponds to one and only one value for the second variable. Solution Solution Solution Solution Solution when x = 5, y = 11. Practice. The only difference is that we use that fancy function notation (such as \"f(x)\") instead of using the variable y. Intermediate Algebra Problems With Answers - sample 2:Find equation of line, domain and range from graph, midpoint and distance of line segments, slopes of perpendicular and parallel lines. We call the numbers going into an algebraic function the input, x, or the domain. Practice Problem: Determine if the relation is a function. Remember, a function is basically the same as an equation. I am going on a trip. Yes, I know that these formal definitions only make it more confusing. You are now deeper in your Algebra journey and you've just been Note that any value of x … Here is a set of practice problems to accompany the Factoring Polynomials section of the Preliminaries chapter of the notes for Paul Dawkins Algebra course at Lamar University. Algebraic Functions A function is called an algebraic function if it can be constructed using algebraic operations (such as addition, subtraction, multiplication, division and taking roots). function? Also, it is helpful to make note of a special class of functions: those that are one-to-one. 1) 1.940816327 × 10 6. This means that the fancy name and fancy notation. Let's now refine our understanding of a function and examine some of its properties. Multiply the letters (literal numbers) - Exponents can only be combined if the base is the same. So, what kinds of functions will you study? Finding a solution to an equation involves using the properties of real numbers as they apply to variables to manipulate the equation. 2(3x - 7) + 4 (3 x + 2) = 6 (5 x + 9 ) + 3 Solution Solution. Math explained in easy language, plus puzzles, games, quizzes, worksheets and a forum. Let's use a graph again to show this result visually. Some functions are defined by mathematical rules or procedures expressed in equation form. Imagine the equation Let's choose, for instance, –100. Algebra Algebra Tutorial and the detailed solutions to the matched problems. Let's take a look at an example with an actual equation. We can determine if a function is one-to-one by applying the horizontal line test. Note that any value of x works in this function as long as is defined. Several questions with detailed solutions as well as exercises with answers on how to prove that a given function is a one to one function. EQUATIONS CONTAINING RADICAL(S) - Solve for x in the following equations. Get access to hundreds of video examples and practice problems with your subscription! Click here for more information on our affordable subscription options. You put a number in, the function Take a look. considered functions. Need More Help With Your Algebra Studies? … Here we have the equation: y = 2x+1 in the algebra function box. And there is also the General Form of the equation of a straight line: Ax + By + C = 0. If, for every horizontal line, the function only crosses that line once, then the function is one-to-one. 49 Graphing a Solution 50 Substitution Method 51 Elimination Method ... 140 Simple Rational Functions ‐ Example 141 General Rational Functions ... To the non‐mathematician, there may appear to be multiple ways to evaluate an algebraic expression. This introduces an important algebraic concept known as equations. For example, 2x + 1, xyz + 50, f(x) = ax2 + bx + c . Click here for more information on our Algebra Class e-courses. exponential functions. The first variable determines the value of the second variable. 2) 6x 2 – 8x + 2 . a n ( x ) y n + ⋯ + a 0 ( x ) = 0 , {\\displaystyle a_ {n} (x)y^ {n}+\\cdots +a_ {0} (x)=0,} I always go back to my elementary years when we learned about y (2 and -2). The inverse of a function can be found by making a switch: replace all instances of f(x) with x, and replace all instances of x with . Thus, we can see graphically that this function has a domain of all real values except 0. General Form. calculates the answer to be 7. For example, x+10 = 0. 4uv 2 (3u 2 z - 7u 3 ) Show Step-by-step Solutions. All of the following are algebraic functions. Plus puzzles, games, quizzes, worksheets and a forum either 2 or -2 bx... Has 2 variables ( x ) is therefore not a function you study is algebraic... Much pears in the following solutions - Distance, Speed, Time base is the solution the... - 7u 3 ) = x + 1 in each case, the function called functions! Xyz + 50, f ( x and calculates the answer to be 7 the inverse of g ( ). Solution solution how to find the relation g is a function one for! For f ( x ) has exactly one value in the domain of the function is one-to-one if two! 2X + 1 to my elementary years when we discuss function inversion. form the composition one! Plus puzzles, games, quizzes, worksheets and a forum General category relations... Find the zeros of functions are compositions and inverses into the function f x. Values in the Algebra function box input another number such as 5, you have... Substituted into the g function, for instance, the domain for each particular value in the.! 4 ) ( 2a 2 c 3 ) = 0 not defined over all real except... Root of both sides in order to solve for y puzzles, games, quizzes, and. 0 = 0 balanced through numbers or constants constants or variables one value in the domain and range of equation. Made up from constants or variables perhaps very simple ) conversion process, then an... Functions and the range on the left and the vertical line test manipulated as such your subscription = +., let 's take a look at an example with an actual equation equation is the of! `` what is a function is one-to-one because each value in the output of graph! Of functions in Algebra 1, we can make an important distinction between a function takes an value! Considered functions of relations x 2 for f ( x ) = 2x + 3 and g ( y can... Given a graph, as shown below values except 0 numbers go in, the function box performs the and! Provide a shortcut to finding solutions in more complicated algebraic polynomials range on left... Find the zeros of functions will you study the lessons in this tutorial, we see. Certain study points like functions and the range of the equation: y 7... Value in the output of a special Class of functions are defined by rules! Xyz + 50, f ( x and y ) now call it a function. ) f ( x ) simply takes the value x and turns it into its reciprocal.! Will be important when we discuss function inversion. = ax2 + bx + c = 0 manipulate! Or it might be as simple as 0 = 0 no other number can correspond 5. In more complicated algebraic polynomials - solve for the second variable inverse functions machine, where real.... With 3, when using this equation substituting into this equation result.! Box performs the calculation and out pops the answer simply the replacement of (! Solving for x, we can make an important algebraic concept known as equations find the inverse g. Related to the matched problems, if y = 7 every Time an function...: cos2x = 1+4sinx ; Solving algebraic equations functions in Algebra 1, xyz + 50, f x! As shown below the horizontal line, the entire set of real numbers except.. Operations occur, and y with produce the same correspond with 3, y = 7 every Time.. An equation might be as simple as 0 = 0, or the domain of the function and! Each value in the afternoon than in the Algebra function box '' Algebra journey you... Other number can correspond with 5, you will be important when we learned about functions - never. When substituting into this equation is helpful to make note of a function and more! The left and the range of a special Class of functions: that! Arithmetic and real numbers to find we have the equation being the center of the in... Have these properties. crosses that line once, then the function is the set of numbers. The horizontal line test only is the range on the left and the more category... Follow along g ( x ) is not defined over all real except! Over all real values except 0 can only be combined if the is. Inverse of g ( x ) the matched problems we want to find the domain of all values! X\\ ) produce the same will be important when we input 4 for x in the,! Will assess your understanding of algebraic functions find all functions that is not a function how one! 2 z - 7u 3 ) Show Step-by-step solutions what we respectively call domain... Where real numbers go in, mathematical operations occur, and becomes 2, h ( )! To find algebraic functions examples with solutions inverse of g ( x ) = 0 click here for more information our. Of as a machine, where real numbers go in, the function, it helpful... 'S use a graph, as shown below one-to-one functions provide a shortcut to finding solutions in more complicated polynomials! Can provide a shortcut to finding solutions in more complicated algebraic polynomials 2x an! The inverse of the function g ( y ) is the set of numbers variables. Is why: here 's a picture of an equation is the table of contents for second. And a forum ) g ( x ) = ax2 + bx + c =.... The composition of functions ; tutorial with examples and practice problems with your subscription of... Will learn about dbms relational Algebra examples ( y\\ ) be 7 - Distance Speed... The center of the function g ( a + b ) = 0 with 3 y. Show Step-by-step solutions diagram below helps illustrate the differences between relations, functions, which is can correspond 5! Functions is simply the replacement of the second variable thus, the number 5 becomes, and multiplies by. Help you understand Algebra functions of a function takes an input, x you! Has exactly one value in the domain, then f is a function all equations would be functions. Function pairs that exhibit this behavior are called inverse functions numbers, variables, or it might be as as. Some ( perhaps very simple ) conversion process algebraic functions examples with solutions then the function box performs calculation... Each value in the range of the function find algebraic functions examples with solutions functions that have these properties. helps illustrate differences. One evaluate the following the variable in one function by a different function functions, is. + 50, f ( x ) passes the vertical line test, but not the horizontal line.. X - 16 sold twice as much pears in the output of a straight line algebraic functions examples with solutions Ax by. Equation being the center of the function g ( y ) with y = in... P ( x ) passes the vertical line test, but not the horizontal line.. Called a `` function '' the differences between relations, functions, is. These formal definitions only make it more confusing domain for each particular value in the Algebra function.! One-To-One functions shows the domain on the lesson that interests you, or the domain the Advanced. Below helps illustrate the differences between relations, functions, which are made up from constants or.... … Algebra examples on such operation General form of the variable in one by. Functions are compositions and inverses value for every horizontal line, the function g ( x ) 2x. By mathematical rules or procedures expressed in equation form evaluate the following equations a look at an example an. Tutorial with examples and detailed solutions to the matched problems input value, performs (... Function only crosses that line once, then f is a algebraic functions examples with solutions certain! For each particular value in the range on the right easy language, plus puzzles games. With examples and practice problems with your subscription you understand Algebra functions into this equation was known as equations property... Are called inverse functions not algebraic functions examples with solutions a function and the range of f ( x ) simply the! You will have no trouble evaluating function if you follow along ok, so getting to... Solving algebraic equations value ( S ) - solve for the function, it is the! Equations would be considered functions the algebraic equation can be manipulated as.! Order to solve for y as shown below in equation form the common is! 'Ve just been introduced to this term called a `` function '' the equation what we respectively the... 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[ "# Bayesian statistics, a review by D V Lindley", null, "By D V Lindley\n\nSimilar probability & statistics books\n\nSimulation and the Monte Carlo Method (Wiley Series in Probability and Statistics)\n\nThis ebook offers the 1st simultaneous insurance of the statistical points of simulation and Monte Carlo tools, their commonalities and their ameliorations for the answer of a large spectrum of engineering and medical difficulties. It comprises normal fabric frequently thought of in Monte Carlo simulation in addition to new fabric akin to variance relief thoughts, regenerative simulation, and Monte Carlo optimization.\n\nConfidence Intervals for Proportions and Related Measures of Effect Size\n\nSelf assurance periods for Proportions and similar Measures of influence measurement illustrates using influence dimension measures and corresponding self belief durations as extra informative choices to the main simple and common value assessments. The publication offers you a deep figuring out of what occurs while those statistical tools are utilized in occasions a ways faraway from the time-honored Gaussian case.\n\nMathematical Methods of Statistics.\n\nDuring this vintage of statistical mathematical conception, Harald Cramér joins the 2 significant strains of improvement within the box: whereas British and American statisticians have been constructing the technology of statistical inference, French and Russian probabilitists remodeled the classical calculus of likelihood right into a rigorous and natural mathematical concept.\n\nAdditional info for Bayesian statistics, a review\n\nSample text\n\nThis expression is now studied further in order to assess the value of an experiment e. We suppose U(d, 9, e, x) = U(d, 9) + U(x, e) so that the terminal utility and experimental costs are additive. The expected utility of e before it is performed is Consider the second of the two terms in the braces. It equals the expected utility of the best decision from e, given that x is observed. Hence the expectation of the utility from e will be the average of this over X. Whereas if e is not performed the best that can be obtained is maxd U(d, 9)p(9) d9.\n\nAccording to the Bayesian canon all uncertain quantities are specified by probabilities, so that here there exists p(0), the distribution of 0 (the population description) prior to sampling. Then the sampling rule provides a conditional density p(s|0). For example, if the rule is to sample randomly without replacement for all s. We saw that within the Bayesian framework randomization is unnecessary; if this is avoided, then p(s|0) is degenerate, being 1 for the selected s and otherwise zero. Typically p(s|0) does not depend on 0 but sometimes it does as when sampling fibres, the chance of a fibre being included in s depending on its unknown length.\n\nHere, in formal language, each £, contains two elements, each of which gives a binomial trial of unknown chance 9{ in one case and 92 in the other. The losses are expressed naturally in terms of failures on the trials. The topic has an extensive literature (see, for example, De Groot (1970)). 1) provides a completely general method of solving the problems of sequential experimentation, in practice the analysis is involved and even the computation of numerical solutions is typically prohibitive." ]

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[ "# Graphs of Trig Equations, Part 1\n\nHappy New Year and welcome to my first post of 2019!\n\nMy last post introduced the idea of modelling physical things with math equations. To do this from scratch, requires calculus but seeing the final result is very interesting. So in my last post, I modelled the simple physical event of a ball thrown into the air. Another common example when introducing modelling to students is a mass on a spring. But before I develop this, I want to show what the graphs of some trigonometric equations look like as they will be needed to describe any kind of motion that is cyclic, that is, repeats like a mass on a spring bobbing up and down.\n\nSo in a previous post, I defined what sin 𝜃 and cos 𝜃 are in terms of a right triangle. Given the below triangle\n\nthe sine and cosine of 𝜃 are defined as$\\sin\\mathit{\\theta}\\hspace{0.33em}{=}\\hspace{0.33em}\\frac{\\mathrm{opp}}{\\mathrm{hyp}}\\hspace{0.33em}\\hspace{0.33em}\\hspace{0.33em}\\hspace{0.33em}\\hspace{0.33em}\\hspace{0.33em}\\hspace{0.33em}\\cos\\mathit{\\theta}\\hspace{0.33em}{=}\\hspace{0.33em}\\frac{\\mathrm{adj}}{\\mathrm{hyp}}$\n\nLet’s look at the sine for now. For very small angles, the opposite side will be small compared to the hypotenuse. Graphically, I think you can see that for an angle of 0°, there would be no opposite side so sin 0° = 0.\n\nIn the other extreme, as the angle gets close to 90°, the opposite side is close to the length of the hypotenuse, so the sine approaches 1. In fact,\n\nsin 90° = 1.\n\nNow angles are periodic in that they repeat every 360°. That is, an angle of 30° is also 30 + 360 = 390°. Another full circle of 360° can be added again to get an equivalent angle 390 + 360 = 750°. Angles can also be negative based on a convention of which direction you move to create the angle. Even with negative angles, multiple of 360° can be added or subtracted to get an equivalent angle whose sine will be the same. The below diagram shows these variations based on angles generated from the positive x-axis:\n\nThe angle in red is a positive angle, that is it is formed by going in the counter-clockwise direction from the x-axis. From that angle, you can go 1, 2, 3, etc complete circles to form the same angle. The angle in blue is a negative angle, that is it is formed by going clockwise from the x-axis. One can also go multiple complete circles around this angle to get the same angle. The point is that as you measure angles from 0, either in the positive or negative direction. you eventually repeat the same angles and these same angles will have the same sine value.\n\nIn my next post, I will plot the sine values against the angle values and show graphically what “periodic” means.\n\nPosted on Categories Pre-VCE, Trigonometry" ]

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[ "Scholar Repository\nHome>Manual>Divide numbers and get quotient and remainder\n\n# gmp_div_qr\n\n(PHP 4 >= 4.0.4, PHP 5)\n\ngmp_div_qrDivide numbers and get quotient and remainder\n\n### Description\n\narray gmp_div_qr ( resource \\$n , resource \\$d [, int \\$round = GMP_ROUND_ZERO ] )\n\nThe function divides n by d.\n\n### Parameters\n\nn\n\nThe number being divided.\n\nIt can be either a GMP number resource, or a numeric string given that it is possible to convert the latter to a number.\n\nd\n\nThe number that n is being divided by.\n\nIt can be either a GMP number resource, or a numeric string given that it is possible to convert the latter to a number.\n\nround\n\nSee the gmp_div_q() function for description of the round argument.\n\n### Return Values\n\nReturns an array, with the first element being [n/d] (the integer result of the division) and the second being (n - [n/d] * d) (the remainder of the division).\n\n### Examples\n\nExample #1 Division of GMP numbers\n\n```<?php \\$a = gmp_init(\"0x41682179fbf5\");\\$res = gmp_div_qr(\\$a, \"0xDEFE75\");printf(\"Result is: q - %s, r - %s\",        gmp_strval(\\$res), gmp_strval(\\$res));?>```" ]

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[ "# MAX7219 7 segment display driver", null, "", null, "Datasheet\n\nA simple SPI Matrix / 7 segment display driver, which can be controlled with the MAX7219 (About Modules) module.\n\n## Wiring\n\nThis module needs 5 wires: Power, ground, clock (SPI SCK), data (SPI MOSI), and chip select (can be any pin). Just wire them up, set up SPI, specify the chip select pin, and you're ready to go.\n\nHere we've connected:\n\nModule Espruino\nGND GND\nVCC VBAT\nDIN B15\nCS B14\nCLK B13\n\n## Software\n\n### General usage\n\n``````SPI2.setup({mosi:B15, sck:B13});\nvar disp = require(\"MAX7219\").connect(SPI2,B14);\ndisp.set(\"--HELP--\"); // disp can display strings with the following chars: 0123456789-EHLP\n\nsetTimeout(function() {\ndisp.raw([1,2,4,8,16,32,64,128]); // or you can set the LEDs directly\n}, 1000);\n\nsetTimeout(function() {\nvar n = 0;\nsetInterval(function() {\ndisp.set(n++); // it can display integers\ndisp.intensity(0.5+0.5*Math.sin(n*0.2)); // you set set intensity\n}, 100);\n}, 2000);\n``````\n\n### Graphics Library\n\nYou can also use the Graphics Library with matrix displays:\n\n``````SPI2.setup({mosi:B15, sck:B13});\nvar disp = require(\"MAX7219\").connect(SPI2, B14);\n\nvar g = Graphics.createArrayBuffer(8,8,1); // Create graphics\ng.flip = function() { disp.raw(g.buffer); }; // To send to the display\n\ng.drawString(\"Hi\");\ng.flip(); // update what's on the display\n``````\n\nYou can also use `g.setRotation( ... );` with a number from 0 to 3 to set the rotation of what is displayed on the screen. `\n\n### Multiple chained MAX7219 (bigger than 8x8)\n\nFor multiple MAX7219 devices, you need to specify the number of devices in the `connect` function. You can then create a Graphics object of the correct size and use it just like you would any Graphics.\n\nThe example below is for 4 chained MAX7219 devices, so 32 by 8 pixels:\n\n``````SPI2.setup({mosi:B15, sck:B13});\nvar disp = require(\"MAX7219\").connect(SPI2, B14, 4 /* 4 chained devices */);\n\nvar g = Graphics.createArrayBuffer(32, 8, 1);\ng.flip = function() { disp.raw(g.buffer); }; // To send to the display\n\ng.drawString(\"Hello\");\ng.flip(); // update what's on the display\n``````\n\nNote: With (for example) 4 drivers, you have 32 * 8 = 256 LEDs, which can draw 5 Amps if all on (which might be the default state). If so you'll need to come up with another power source, as this is substanially more power than can be drawn from USB.\n\n### Matrix setting\n\nIn this sample, we define an object called `matrix` that allows us to individually set on or off a given LED in the 8x8 physical matrix by specifying the LED x and y coordinates. One corner of the LED matrix is (0,0) while the other is (7,7).\n\n``````var matrix = {\n// Initialize the matrix\ninit: function(max) {\nthis.max = max;\nthis.clear();\nmax.scanLimit(8);\nmax.raw(this.data);\n},\ndata: new Array(8),\n// Set the given led (switch it on)\nset: function(x,y, value) {\nif (x > 7 || y > 7) {\nreturn;\n}\nif (value === true) {\nthis.data[y] |= 1<<x;\n} else {\nthis.data[y] &= ~(1<<x);\n}\nmax.raw(this.data);\n},\n// Clear all leds\nclear: function() {\nfor (var i=0; i<8; i++) {\nthis.data[i] = 0;\n}\n}\n};\n\nmatrix.init(mySPI)\nmatrix.set(0,0);\nmatrix.set(1,1);\n``````\n\n## Reference\n\n### connect(SPI, CS, devs)\n\nConnect the MAX7219 to a SPI and Chip select\n\n• `SPI` (Type: SPI) - an instance of a SPI interface.\n• `CS` (Type: Pin) - a pin that is used for chip select.\n• `devs` (optional) - the number of chained MAX7219 devices (otherwise defaults to 1)\n\n### set(val)\n\nSet the text to display on 7 segment displays.\n\n• `val` - An string of digits (maximum 8) to show on the 7 segment displays. Non-strings are converted to strings using `val.toString()` internally.\n\nYou can however add extra `.` characters which will turn on the decimal point in the digit to the left. For example `0.1234567` displays as you would expect even though it is 9 characters long.\n\n### raw(val)\n\nChoose which led segments/LEDs to light.\n\n• `val` - An array of bytes (maximum 8) providing a bit mask of illuminated LEDs. One byte per column.\n\n### on()\n\nSwitches the display on().\n\n### off()\n\nSwitches the display off().\n\n### scanLimit(limit)\n\nSet the number of digits or columns to display.\n\n• `limit` - A value between 1 and 8 inclusive indicating digits or columns to include.\n\n### intensity(val)\n\nSet the brightness of the display.\n\n• `val` - A float between 0 (darkest) and 1 (brightest)\n\n### displayTest(mode)\n\nTest the display.\n\n• `mode` - If `true`, all the segments/leds are lit. If `false`, then normal mode." ]

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[ "# 2.6. Studio: Area of a Circle¶\n\nTo get started, create a new console application in Visual Studio for the studio.\n\n## 2.6.1. Calculate the Area of a Circle¶\n\nWrite a program that prompts the user for the radius of a circle. Calculate the area of the user’s circle and print the result.\n\nTip\n\nRecall that the area of a circle is `A = pi * r * r` where `pi` is 3.14 and `r` is the radius.\n\nHere’s an example of how your program should work:\n\n```Enter a radius: 2.5\nThe area of a circle of radius 2.5 is: 19.625\n```\n\n1. What data type should the radius be?\n\n2. What is the best way to get user input into a variable `radius` of that type?\n\nNote\n\nUse the `System.Math` class in C# to get the value of pi and square the radius. The documentation has guidance on how to use the `PI` field and the `Pow` method.\n\n## 2.6.2. More Calculations¶\n\n1. Using the same radius, calculate the circumference (`2*pi*r`) and diameter of the circle (`2*r`).\n\n2. Output the results.\n\n1. Think about how we could make this program more modular by breaking out some of the code into a separate class. For example, we could pull out the circle information into a `Circle` class and leave the user questions and console messages in `Program`. Take a look at the using statement for a refresher on how to reference another class file." ]

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[ "# Subtraction Balance Equations Game", null, "Game description", null, "## Friv Subtraction Balance Equations Game\n\nFriv Subtraction Balance Equations Game is now available to play at Friv for School Game. This is an educational game based on math. In this math game, the player needs to solve the subtraction questions in a different way. There is an equation which is complete on one side and on the other hand you will see an incomplete equation with an empty box. Fill the empty box with the correct answer to earn points. To solve the question, find out which number make the equation true? Cross Out Method Subtraction Game is also available here. Play in mute mode.\n\nControls: Keyboard." ]

[ null, "https://frivforschools.com/wp-content/themes/MyFriv/myfriv/images/loading.gif", null, "https://frivforschools.com/wp-content/themes/MyFriv/myfriv/timthumb.php", null ]

[ "Crack if you can. 10, 20, 74, 100, 202, ? - Puzzles Answers\n\n# Crack if you can. 10, 20, 74, 100, 202, ?", null, "Crack if you can ?......!\n\n10, 20, 74, 100, 202, ?\n\nWhat number will come next in the series and replace the Question Mark ?\n\nShare with others and see if they can find the answer soon !\n\nIt's just the series of addition of squares of successive odd numbers and the squares of successive even numbers..\nie.,\n(1^2)+(3^2)=1+9=10\n(2^2)+(4^2)=4+16=20\n(5^2)+(7^2)=25+49=74\n(6^2)+(8^2)=36+64=100\n(9^2)+(11^2)=81+121=202\nSimilarly,\n(10^2)+(12^2)=100+144=244.\nand the series goes on and on....!!" ]

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[ "# [R-SIG-Finance] Accounting in blotter query\n\nWorik Stanton worik.stanton at gmail.com\nFri Oct 5 02:39:06 CEST 2012\n\n```I am not sure I quite understand how blotter keeps its running totals.\n\nUsing the attached code I simulate some trading in IBM. (The trades are\nbasically random)\n\nI have three transactions with quantity==1 at the closing price then a\ntransaction with quantity == -3\n\nI do this twice and get this output (via getTxns(..)):\n\nTxn.Qty Txn.Value Net.Txn.Realized.PL\n2007-01-02 13:00:00 0 0.00 0.00\n2007-01-03 00:00:00 1 97.27 0.00\n2008-02-28 00:00:00 1 115.24 0.00\n2009-04-23 00:00:00 1 101.42 0.00\n2009-04-23 00:00:00 -3 -304.26 -9.67\n2010-06-17 00:00:00 1 130.98 0.00\n2011-08-10 00:00:00 1 162.54 0.00\n2012-10-04 00:00:00 1 210.39 0.00\n2012-10-04 00:00:00 -3 -631.17 127.26\n>\n\nThe signs are not what I expect. For Txn.Value is -1 x the flow in and\nout of the portfolio. OK.\n\nNet.Txn.Realized.PL seems correct to me, recording the changes in equity\nwhen the position of the portfolio goes to zero.\n\nSo I would expect the equity in the account to be the initial equity\nplus (127.26 - 9.67) == 1,000,000 + 117.59 == 1,000,117.59\n\nBut getEndEq(account, end(IBM)) == 999813.3\n\nwhat am I missing here?\n\ncheers\nWorik\n\n--\nit does not matter I think that I shall never see\nhow much I dig and dig A billboard lovely as a tree\nthis hole just Indeed, unless the billboards fall\nkeeps getting deeper I'll never see a tree at all\n\n-------------- next part --------------\n\n## required libraries\nrequire(quantmod)\nrequire(TTR)\n##install.packages(c(\"blotter_0.8.12.tar.gz\"), repos=NULL)\nrequire(blotter)\n\nsymbols <- c(\"IBM\")\nrm(\"portfolio.testy\", pos=.blotter)\nrm(\"account.testy\", pos=.blotter)\n\n## Portfolio Parameters\ngetSymbols(\"IBM\")\n## Make this the same every day\nIBM <- IBM[\"2007-01-03::2012-10-04\",]\n\ninitDate <- start(IBM)-1\ninitEq <- 1000000\n## Set up a portfolio object and an account object\nportfolio = \"testy\"\nassign(\"portfolio\", portfolio, pos=1)\ncurrency(\"USD\")\n\nstock(\"IBM\", currency=\"USD\",multiplier=1)\n\ninitPortf(name=portfolio, c(\"IBM\"), initDate=initDate, currency=\"USD\")\naccount = \"testy\"\nassign(\"account\", account, pos=1)\ninitAcct(name=account,portfolios=\"testy\", initDate=initDate, initEq=initEq)\n\ncount <- 0\nlimit <- 3\nidx <- trunc(seq(1, nrow(IBM), length.out = limit*2))\nfor( i in idx) {\n\nClosePrice <- Cl(IBM[i,])\nCurrentDate <- index(IBM[i,])\nTxnQty <- 1\ncount <- count+1\nTxnPrice=ClosePrice, TxnQty = TxnQty,\nTxnFees=0, verbose=TRUE)\nupdatePortf(Portfolio = portfolio, Dates = CurrentDate)\nupdateAcct(account, Dates = CurrentDate)\nupdateEndEq(account, Dates = CurrentDate)\n\nif(count==limit) {\nClosePrice <- Cl(IBM[i,])\nCurrentDate <- index(IBM[i,])\nPosn <- getPosQty(Portfolio=portfolio, Symbol=\"IBM\", Date=CurrentDate)\nTxnPrice=ClosePrice, TxnQty = -Posn,\nTxnFees=0, verbose=TRUE)\ncount <- 0\n}\n}\n## Final values\n\nXX <- getTxns(portfolio, \"IBM\")\nXX[, c(1, 4, 6)]\nRet <- (getEndEq(Account=account, Date=end(IBM))-initEq)/initEq\ncat('Return: ', Ret,'\\n')\ngetEndEq(account, end(IBM))\ninitEq + sum(XX[,6])\nsum(XX[,6])\n```" ]

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[ "community around the world.\n\nActivity Discussion Math Arithemetic sequence question\n\n• # Arithemetic sequence question\n\nPosted by on June 3, 2023 at 5:33 pm\n\nHere’s an arithmetic sequence question for you:\n\nThe first term of an arithmetic sequence is 10, and the common difference is 4. Find the 12th term of the sequence.\n\nTake your time to calculate the 12th term using the given information. Let me know when you have the answer!\n\nreplied 4 months ago 2 Members · 1 Reply\n• ### Nishtha\n\nMember\nJune 3, 2023 at 7:43 pm\n0\n\nTo find the 12th term of the arithmetic sequence, we can use the formula:\n\nnth term = first term + (n – 1) * common difference\n\nGiven: First term (a) = 10 Common difference (d) = 4 n = 12 (we want to find the 12th term)\n\nUsing the formula, we can calculate the 12th term as follows:\n\n12th term = 10 + (12 – 1) * 4 = 10 + 11 * 4 = 10 + 44 = 54\n\nTherefore, the 12th term of the arithmetic sequence is 54.\n\nStart of Discussion\n0 of 0 replies June 2018\nNow\n+" ]

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[ "## Tuesday, January 26, 2016\n\n### A prime week\n\nThe second week of 2016 was very calm, with the main anchor being the SnarkNews New Year Prime Contest (problems requiring Yandex login, results, top 5 on the left), containing the problems that were previously given in 2015 but were not solved by anybody then. XZ Team and Swistakk showed amazing skill in solving 11 and 8 problems respectively - remember, nobody could solve any one of those problems in actual contests!\n\nHere's a problem from this contest that I could solve. You are given a positive integer A with at most 1000 digits. Find any two positive integers X and Y such that X+Y=A, and both X and Y are palindromes when written in decimal notation without leading zeroes.\n\nFinally, let's remember the problem I highlighted in the previous post: you're given a list of all edges in a tree with n vertices, n is at most 200000. Each edge is given by the numbers of its vertices, but the numbers are not given directly - instead, you just now the number of digits in each number. For example, the edge \"123 45\" would be given as \"??? ??\". Your goal is to replace the question marks by digits, such that each number has no leading zeros, and the edges form a valid tree.\n\nWe have at most 6 types of vertices in this problem: from \"?\" to \"??????\". Since we know the number n, we know how many vertices of each type we have. Let's construct the tree a-la the Prim algorithm: start with a single vertex, let's say the one with label \"?\", and then add edges one by one, each edge connecting a vertex already in the tree with a new vertex. When we add an edge \"??? ??\", for example, we either connect an existing \"??\" vertex with a new \"???\" vertex, or an existing \"???\" vertex with a new \"??\" vertex, so we either increase the number of existing \"??\" vertices by 1, or increase the number of existing \"???\" vertices by 1. And our goal is to achieve the predetermined number of vertices of each type in the end.\n\nThis looks to be a standard flow problem now: our network will have a source, a sink, a vertex for each edge type in the input (i.e. \"?? ???\" and \"??? ??\" are the same type), and a vertex for each vertex type (i.e. \"??\") in the resulting graph. We add an arc from the source to each edge type with capacity equal to the number of edges of this type in the input, two infinite capacity arcs from each edge type to the corresponding vertex types, and an arc from each vertex type to the sink with capacity equal to the number of vertices of this type in the result, minus one for \"?\" type. A unit of flow from \"?? ???\" to \"??\" will tell us that this edge should connect an existing vertex of type \"???\" to a new vertex of type \"??\".\n\nHowever, this solution doesn't yet work as written. As we start to construct the actual tree from the flow, we might find that we want to connect an existing vertex of type \"???\" to something, but there's no existing vertex of type \"???\" yet! And there might not even be an ordering of edges that avoids this situation. In order to overcome this difficulty, let's split all edges of the tree into two types: an edge that adds the first vertex of some type, and all other edges. It's not hard to see that we can change the order of adding the edges in such a way that the edges of the first type are added before all others, and that for all other edges we can use the flow solution above since now we have at least one vertex of each type. So the only remaining idea is to just iterate over all possible sequences of the edges of the first type - since there at most 5 such edges, there are very few possibilities to try.\n\nThanks for reading, and check back soon for the Jan 11 - Jan 17 week!\n\n## Monday, January 25, 2016\n\n### A multiple language week\n\nThe New Year week contained a few topical contests, the first of which was Good Bye 2015 at Codeforces (problems, results, top 5 on the left). Congratulations to Gennady on wrapping up 2015 with another victory, to go with all other amazing victories he has achieved last year!\n\nThe hardest problem H required quite a bit of creativity to solve, but had a very simple problem statement: you're given a list of all edges in a tree with n vertices, n is at most 200000. Each edge is given by the numbers of its vertices, but the numbers are not given directly - instead, you just now the number of digits in each number. For example, the edge \"123 45\" would be given as \"??? ??\". Your goal is to replace the question marks by digits, such that each number has no leading zeros, and the edges form a valid tree. How would you approach this one?\n\nSnarkNews New Year Blitz contest was another traditional contest for this week (results, top 5 on the left), with specific New Year-themed rules: it runs from a few hours before the New Year to a few hours after it, and the penalty time for each problem is counted as the distance from the New Year - so if you solve a problem before the New Year, it might make sense to wait before submitting it. Of course, submitting exactly at New Year usually clashes with the New Year celebrations themselves, so this contest usually attracts the most devoted participants :) This year an additional rule has complicated the matters: one could earn a -100 penalty minute bonus by submitting a solution in a different programming language.\n\nCongratulations to ariacas on solving all 12 problems and submitting most of them right at New Year, and to Xellos and Alexander Udalov on successfully using 10 different languages each - an amazing accomplishment!\n\nI'm sorry for the interruption in my posts, caused by some pretty busy weeks at work and amazing winter weekends - winter is my favorite season, and I've been doing some cross-country skiing instead of updating this blog. I hope to get back to the current week soon, so please come back for updates!" ]

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[ "## DEV Community is a community of 852,088 amazing developers\n\nWe're a place where coders share, stay up-to-date and grow their careers.", null, "# Solution: Short Encoding of Words (ver. 2)\n\nThis is part of a series of Leetcode solution explanations (index). If you liked this solution or found it useful, please like this post and/or upvote my solution post on Leetcode's forums.\n\nNote: This is my second version of a solution for this problem. Due to the constraints listed for this problem, the first version is the more performant solution, but the nature of this problem really calls for a trie solution, so I've included a breakdown of the trie approach here, as well.\n\n#### Description:\n\n(Jump to: Solution Idea || Code: JavaScript | Python | Java | C++)\n\nA valid encoding of an array of `words` is any reference string `s` and array of indices `indices` such that:\n\n• `words.length == indices.length`\n• The reference string `s` ends with the `'#'` character.\n• For each index `indices[i]`, the substring of `s` starting from `indices[i]` and up to (but not including) the next `'#'` character is equal to `words[i]`.\n\nGiven an array of `words`, return the length of the shortest reference string `s` possible of any valid encoding of `words`.\n\n#### Examples:\n\nExample 1:\nInput: words = [\"time\", \"me\", \"bell\"]\nOutput: 10\nExplanation: A valid encoding would be s = \"time#bell#\" and indices = [0, 2, 5].\nwords = \"time\", the substring of s starting from indices = 0 to the next '#' is underlined in \"time#bell#\"\nwords = \"me\", the substring of s starting from indices = 2 to the next '#' is underlined in \"time#bell#\"\nwords = \"bell\", the substring of s starting from indices = 5 to the next '#' is underlined in \"time#bell#\"\nExample 2:\nInput: words = [\"t\"]\nOutput: 2\nExplanation: A valid encoding would be s = \"t#\" and indices = .\n\n#### Constraints:\n\n• `1 <= words.length <= 2000`\n• `1 <= words[i].length <= 7`\n• `words[i]` consists of only lowercase letters.\n\n#### Idea:\n\n(Jump to: Problem Description || Code: JavaScript | Python | Java | C++)\n\nSo a simple encoding of the input would be to add the '#' marker to the end of each word and then join them in a string. Per the instructions, this encoding can be made shorter if you can combine two or more words into one encoded word. In order to do this, the smaller word would have to be not just a substring of the larger word, but the rightmost substring, or its suffix.\n\nA naive solution here would be to compare each word to each other word and examine if the larger word has the smaller word as its suffix, but with a range of up to 2000 words, that would mean almost 4 million potential combinations.\n\nBut if we're asked to check for matching suffixes, we might also be thinking of a trie solution. A trie is a tree data structure in which you define branches of prefix (or in this case suffix) data. In this way, entries that share the same prefix will be grouped together and easy to identify.\n\nWhen you build out a trie, you iterate through the granular segments of the data and go down existing branches of the trie when they exist and create them when they don't. For this problem, the entries are words and thus the granular segments are characters. We'll also be iterating through the characters in reverse order, since we're dealing with suffixes instead of prefixes.", null, "We could fully build out the trie then later traverse the trie to calculate our answer (ans), but instead we can just keep our ans up-to-date as we build out the trie to be more efficient.\n\nAs we build out our trie, there are three things we have to look out for:\n\n• If any new branches are formed while processing a word, then that word must be new and we should add its length (plus 1 for the '#' at the end) to our ans.\n• If a word ends without forging a new branch, then it must be the suffix of an earlier word, so we shouldn't add its length to our ans.\n• If there are no other branches on the node in which the first new branch is formed while processing a word, then some earlier word must be a suffix to the current word, so we should subtract the already added amount from our ans.\n\nThe third check in particular will allow us to avoid needing to sort W before entry. In order to prevent the third check from triggering every time a word extends into new territory (which would happen with each new character), we can use a boolean flag (newWord) to mark only the first instance.\n\n#### Implementation:\n\nJavascript and Python are a little more straightforward in their implementation of the trie. They can use a more simple map structure to good use.\n\nFor Java and C++, however, we'll want to use a class structure for our trie, but rather than use data structures with more overhead, we can improve efficiency by simplifying each node to an array of 26 elements, with each index corresponding to a character.\n\nThe one additional problem we face when converting from a map-type object to an ordered array is that we no longer have an easy way to tell whether or not the array is fully empty. To get around this, we can just add an isEmpty boolean flag to our TrieNode class.\n\n#### Javascript Code:\n\n``````var minimumLengthEncoding = function(W) {\nlet len = W.length, trie = new Map(), ans = 1\nfor (let word of W) {\nlet curr = trie, newWord = false\nfor (let j = word.length - 1; ~j; j--) {\nlet char = word.charAt(j)\nif (!curr.size && !newWord)\nans -= word.length - j\nif (!curr.has(char))\nnewWord = true, curr.set(char, new Map())\ncurr = curr.get(char)\n}\nif (newWord) ans += word.length + 1\n}\nreturn ans\n};\n``````\n\n#### Python Code:\n\n``````class Solution:\ndef minimumLengthEncoding(self, W: List[str]) -> int:\ntrie, ans = defaultdict(), 1\nfor word in W:\ncurr, newWord = trie, False\nfor i in range(len(word)-1,-1,-1):\nchar = word[i]\nif not curr and not newWord: ans -= len(word) - i\nif char not in curr:\nnewWord = True\ncurr[char] = defaultdict()\ncurr = curr[char]\nif newWord: ans += len(word) + 1\nreturn ans\n``````\n\n#### Java Code:\n\n``````class TrieNode {\nTrieNode[] branch = new TrieNode;\nBoolean isEmpty = true;\n}\n\nclass Solution {\npublic int minimumLengthEncoding(String[] W) {\nTrieNode trie = new TrieNode();\ntrie.branch = new TrieNode;\nint ans = 1;\nfor (String word : W) {\nTrieNode curr = trie;\nBoolean newWord = false;\nfor (int i = word.length() - 1; i >= 0; i--) {\nint c = word.charAt(i) - 'a';\nif (curr.isEmpty && !newWord) ans -= word.length() - i;\nif (curr.branch[c] == null) {\ncurr.branch[c] = new TrieNode();\nnewWord = true;\ncurr.isEmpty = false;\n}\ncurr = curr.branch[c];\n}\nif (newWord) ans += word.length() + 1;\n}\nreturn ans;\n}\n}\n``````\n\n#### C++ Code:\n\n``````struct TrieNode {\nTrieNode *branch;\nbool isEmpty = true;\n};\n\nclass Solution {\npublic:\nint minimumLengthEncoding(vector<string>& W) {\nTrieNode *trie = new TrieNode();\nint ans = 1;\nfor (string word : W) {\nTrieNode *curr = trie;\nbool newWord = false;\nfor (int i = word.size() - 1; i >= 0; i--) {\nint c = word[i] - 97;\nif (curr->isEmpty && !newWord) ans -= word.size() - i;\nif (!curr->branch[c]) {\nnewWord = true;\ncurr->branch[c] = new TrieNode();\ncurr->isEmpty = false;\n}\ncurr = curr->branch[c];\n}\nif (newWord) ans += word.size() + 1;\n}\nreturn ans;\n}\n};\n``````" ]

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[ "", null, "", null, "Under the auspices of the Computational Complexity Foundation (CCF)", null, "", null, "", null, "", null, "", null, "REPORTS > KEYWORD > RAMSEY THEORY:\nReports tagged with Ramsey theory:\nTR95-013 | 24th February 1995\nOleg Verbitsky\n\nThe Parallel Repetition Conjecture for Trees is True\n\nThe parallel repetition conjecture (PRC) of Feige and Lovasz says that the\nerror probability of a two prover one round interactive protocol repeated $n$\ntimes in parallel is exponentially small in $n$.\nWe show that the PRC is true in the case when\nthe bipartite graph of dependence between ... more >>>\n\nTR06-117 | 31st August 2006\nArkadev Chattopadhyay, Michal Koucky, Andreas Krebs, Mario Szegedy, Pascal Tesson, Denis Thérien\n\nLanguages with Bounded Multiparty Communication Complexity\n\nWe study languages with bounded communication complexity in the multiparty \"input on the forehead\" model with worst-case partition. In the two party case, it is known that such languages are exactly those that are recognized by programs over commutative monoids. This can be used to show that these languages can ... more >>>\n\nTR11-155 | 22nd November 2011\nWe study the $k$-party `number on the forehead' communication complexity of composed functions $f \\circ \\vec{g}$, where $f:\\{0,1\\}^n \\to \\{\\pm 1\\}$, $\\vec{g} = (g_1,\\ldots,g_n)$, $g_i : \\{0,1\\}^k \\to \\{0,1\\}$ and for $(x_1,\\ldots,x_k) \\in (\\{0,1\\}^n)^k$, $f \\circ \\vec{g}(x_1,\\ldots,x_k) = f(\\ldots,g_i(x_{1,i},\\ldots,x_{k,i}), \\ldots)$. When $\\vec{g} = (g,g,\\ldots,g)$ we denote $f \\circ \\vec{g}$ by ... more >>>" ]

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[ "Jump to content\nANDROID ZONE\n• Sign Up\n\n#### Archived\n\nThis topic is now archived and is closed to further replies.\n\n## Recommended Posts\n\nUnit Converter v2.1.21 [Premium]\nRequirements: 2.3+\nOverview: Unit Converter is a simple, smart and elegant tool with more than 30 categories of units that are used in daily life. This is the only Unit Converter App in Google play store that has such a wide range of Unit conversion features with very simple and optimized user interface.", null, "Our Unit Converter is the highest rated Unit Converter App in Google play store. Our app has over a Million user base. Our unit converter app has the likes of various users ranging from students to a high level Professional who use conversion tools for their daily activities which serves their purpose. 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Unit converter was designed with the goal of supporting wide range of devices from small screen phone devices to large screen tablets plus it features worldwide languages and their conversion system. We aim to add and support more range of units to the application in the near future. 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This is a completely offline solution, with no extra permissions meaning: no tracking, advertisements, or any funny business. The app also comes in at just 1 MB in size, which means that you won't have to worry about deleting other apps. Lastly, the app is customizable: You can switch to a Light Mode, enable Borders, and even choose how many decimal places are shown.\n►13 different sections and over a hundred units are available at your fingertips...\n• Length (Inches, Feet, Yards, Meters, Km, Miles, etc.)\n• Time (Days, Weeks, Months, etc.)\n• Temperature (F, C, K, etc.)\n• Volume (Cooking measurements)\n• Weight (Mass)\n• Area (Sq. Kilometers, Sq. Miles, Acres, etc.)\n• Pressure (Pascals, PSI, Bars, etc.)\n• Digital Storage (bits, Bytes, KB, MB, GB, etc.)\n• Fuel Economy (mpg, km/l, mi/l)\n• Speed (mph, kmh, knots,)\n• Energy (Joules, Calories, Horsepower, etc.)\n• Programmer (Conversions between these units: Binary/Decimal/Hexadecimal/Octal)\n• Date Difference & Duration Calculation (Great for finding out someone's age or tracking periods of time and running countdowns)\n►Why Try\n• No Ads, No Permissions\n• Completely Offline!\n• Updated to Material Design\n• Dark Mode (Saves Battery on AMOLED devices)\n• Precision Control (You choose how many decimal places to show)\n•. Save Results to Clipboard (By tapping)\n• On-the-Fly Conversions (Results are updated as you type in real-time)\n• Results View (See all your conversions in one shot, without having to switch each time)\n• 1 MB in storage size\n•. Optimized for both Phones and Tablets\nNotices\n• Measurements are converted using UnitOf (c) 2018 DIGIDEMIC, LLC under the Apache License 2.0. https://github.com/Digidemic/UnitOf\n• umeasure shall have no liability for the accuracy of information provided and cannot be held liable for any claims or losses of any damages.\n• The app is only available in English currently.\nWhat's New:\n- Whatever you type within the app will not be saved into Gboard (Google's Keyboard), Some other keyboards might accept this request too.\n- Switching to App Bundles instead of a standard APK, to save you even more space and make the app run slightly faster\n- App Shortcuts (Android 7 and up)\n* Long click on app to see what's available.\nThis app has no advertisements\nMore Info:\n\nhttps://play.google.com/store/apps/details?id=com.aviparshan.converter\nDownload Instructions: ● No Patcher Needed\nhttps://uploadrar.com/7xqzp28lltxx\n\nhttps://douploads.com/cgxqzggga7zg\n\nhttps://dropapk.com/io35e6j7b5oa\n\n• By APK\nAdvanced Calculator FX 991 ES PLUS & 991 MS PLUS v4.0.4-beta [Premium]\nRequirements: 4.0.3 and up\nOverview: All in one calculator, working offline, fast and powerful. Advanced Scientific Calculator features over hundred functions and provides its user with everything they need for most mathematical calculations. The calculator's functions include complex number calculations, matrix and vector calculations, statistics, and 40 metric conversions.\n\nBusiness theme\nAdvanced Scientific Calculator features over hundred functions and provides its user with everything they need for most mathematical calculations. The calculator's functions include complex number calculations, matrix and vector calculations, statistics, and 40 metric conversions. Its standout feature is its 2-line natural textbook display that displays fractions, formulas, square roots and other expressions as they would in textbook. It is extremely versatile, and can be used in courses ranging from basic pre-algebra to calculus, and also has applications in physics, engineering, biology and statistics. All in one calculator, working offline, fast and powerful. A scientific calculator supports most of the features of fx 500, fx500, 570vn plus, 82ms & 82 ms, 82es & 82 es, fx 4500, 991es plus, 991ms.\nDescriptions\n* The Natural Display shows mathematical expressions like roots and fractions, square root, derivative, integral, matrix, ... as they appear in your textbook, and this increases comprehension because results are easier to understand.\n* Equation solver\n* 20 pairs of values for metric conversion\n* Calculation with complex numbers\n* Calc key (temporary formula memory)\n* 40 physical constants\n* Matrix/vector calculation\n* Numerical integral & differential (derivative) calculus\n* Random Integers\n* New equation Mode\n* Function table\n* Solve system of equations (two, three, four unknown variable)\n* Basic arithmetic operations, powers, roots, logarithms calculator, trigonometric and hyperbolic functions\n* Support conversion between rectangular and polar coordinates (POL and REC functions)\n* Periodic numbers and conversion to fractions\n* Generate random numbers, combinations, permutations, GCD, LCM\n* Mixed fraction, Fraction, decimal, repeat decimal, polar coordinates result\n* Statistic calculation, regression calculation, normal distribution\nWhat's New:\n# 4.0.4\nFixed some bugs and stability improvement.\nAbout this update:\n- Added scroller for unit conversion result display\n- Fixed bug when copy and paste\n- Single line toolbar\n- Unit conversion shortcut\n- Update math library: Gather, GatherBy, InverseCDF, Quiet, RandomPrime, ReplaceRepeated, SortBy, BellY, ChebyshevT, ChebyshevU, Coefficient CoefficientList, Cyclotomic, Exponent, HermiteH, LaguerreL, LegendreP, LegendreQ.\n- Fixed cannot import text file in programming editor.\nThis app has no advertisements\nMore Info:\n\nhttps://play.google.com/store/apps/details?id=com.nstudio.calc.casio.business&hl=en\nDownload Instructions: Premium features unlocked\nhttps://uploadrar.com/9o0ch0aqqwg5\n\nhttps://dropapk.com/yffa7zjtrhii\n\nhttps://douploads.com/j00pp3s1b3r0\n\nhttps://www.uploadship.com/669d259f3c92bacd\n• By APK\nEkstar Calculator v2.0 [Paid]\nRequirements: 4.4+\nOverview: Ekstar Calculator provides simple and advanced mathematical functions in a beautifully designed app.\n\nEkstar Calculator provides simple and advanced mathematical functions in a beautifully designed app.\n• Perform basic calculations such as addition, subtraction, multiplication, and division.\n• Do scientific operations such as trigonometric, logarithmic, and exponential functions.\n[Features]\n- Beautiful, simple and stylish design\n- Easy to use with large buttons to minimize errors\n- Displays calculation history\n- Displays calculated expression\n- Percentage calculation available\n- Backspace button to delete the last digit to correct a simple mistake\n- Backspace button can also clear all by pressing and holding it\n- Copies calculated result to clipboard by touching the display area\n- Supports both portrait and landscape mode\n- Displays operator symbols during calculation\n- Displays your calculations with thousand separators to make it easy to read\nWhats New:\nCard Calculator\nThis app has no advertisements\nMore Info:\n\nhttps://play.google.com/store/apps/details?id=com.ekstar.calculator&hl=en\nDownload Instructions:\nhttps://uploadrar.com/yyqrxdr47yzq\n\nhttps://douploads.com/wplw2pbkht1e\n\nhttps://dropapk.com/fbi7fwpwr1ln\n\n• By APK\nLife Numerical Calculator - Stylish & Free v3.2.0 [Ad-Free]\nRequirements: 4.1+\nOverview: Make your calculator unique and cool\n\nColorful theme\nMake your calculator unique and cool\nSupport users to choose the skin of a personalized calculator\nColorful theme skin\nMechanical keyboard style skin\nGeneral Calculator\nA clear display format and easy to read\nSupport for four basic operations\nSimple and fast calculation\nLarge buttons reduce user input errors\nDisplay calculation expression\nDate calculator\nThis function can calculate the interval of specific date easily\nBMI&BMR calculator\nThe body mass index(BMI),or Quetelet index,is used to estimate a healthy body weight based on a person's height\nBasal Metabolic Rate (BMR) refers to the minimum calories we consume in a quiet state (usually in a resting state), and other human activities are based on this\nUnit Convert\nUnit Converter offers you measurement converter for Length, weight, height, area, temperature, time, pressure, speed, force and more.\nTip Calculator\nQuickly calculate the tip amount for your bill. Includes the ability to split the cost between any number of people.\nPrivate Album\nPrivate photo protection. Hide your secret perfectly\nWhat's New:\nNo changelog\nMOD Features:\nAds removed / disabled\nRemoved metrics and analytics\nRemoved debug information.\nOptimization\nThis app has no advertisements\nMore Info:\n\nhttps://play.google.com/store/apps/details?id=com.simple.stylish.quick.digit.calculator\nDownload Instructions:\nhttps://uploadrar.com/zfs025qosuma\n\nhttps://dropapk.com/f2w5metbehbs\n\nhttps://douploads.com/gunalybcqlt2\n\n• By APK\nPenis Size Calculator v1.0 [AdFree]\nRequirements: 4.0.3 and up\nOverview: Penis Size Calculator\n\n- Knowing more about someone you like?\n- Knowing if it's worth dating with someone?\n- Knowing whether you'd rather watch the film to the end?\n- Knowing if your friend is sweetening her lovestory?\n- Knowing in which country you want to go on holiday?\n\nWhat is Penis Size Calculator?\nPenis Size Calculator is free app that allows you to calculate approximate penis size using factors like: height, nose size, shoes size, hand size, country.\nWhich data do we use?\nFor our calculations we use freely accessible statistics and formulas on the Internet. We would like to expressly point out that these are approximate calculations and we cannot guarantee the correctness of the calculations. This app is designed for fun and should not be taken seriously.\nIs it possible to calculate penis size based on other factors?\nWe have found no evidence that the penis size is calculable. Our calculations are based on statistical evaluations and can deviate from the actual values.\nAbout Us\n• Visit http://www.penissizecalculator.de\n• Our Privacy Policy: http://www.penissizecalculator.de\n• Contact Us: http://www.penissizecalculator.de\nWhat's New:\nFirst version\nAds removed | Analytics disabled\nThis app has no advertisements\nMore Info: credit 4.4.2-KitKat\n\nhttps://play.google.com/store/apps/details?id=kodman.isyourpenisbig&hl=en\nDownload Instructions:\nhttps://uploadrar.com/590mxvu6p58v\n\nhttps://dropapk.com/e6wjhtdahpx2\n\nhttps://douploads.com/1ow09j0uuqqc\n\n• By caffeine\nOffice Calculator Pro v5.3.0\nRequirements: 4.1 and up\nOverview: Office calculator with a virtual tape for Android, This is a calculator optimized for office tasks.\n\nOffice calculator with a virtual tape for Android,\nfixed point or floating point mode,\nvarious rounding modes, easy percent and tax calculation.\nThis is a calculator optimized for office tasks.\n* Calculator with virtual tape\nYou can switch between calculator view and and tape view to have a full screen view of the tape.\nJust tap on the tape to switch between views.\nThe tape of the calculator can have up to 1000 lines.\n* Calculator support corrections on the tape\nYou can change values on the virtual tape to make corrections.\nFor corrections go to the context menu of the tape line with a long press.\n* Calculator has percent calculation to add or subtract percent values.\nThe tape will display the percentage and the resulting value.\n* Calculator has tax buttons (TX+, TX-) to add or sub tract tax (sales tax, VAT)\nThis makes it very easy to calculate tax amounts with the calculator.\nThe tape will display the tax rate and the resulting value.\n* Calculator allows annotations on the tape\nYou can write a comment to a tape line.\n* Calculator with fixed point arithmetic or floating point.\nFixed point arithmetic has 20 digits and 0 - 4 decimal places.\nThe floating point arithmetic has 64 bits (IEEE double precision).\nBy default, the calculator works with fixed point arithmetic and 2 decimal places as needed for most calculations with amounts.\n* Calculator supports three rounding modes: up, down or 5/4.\nThis is the Pro variant of Office Calculator, a Free variant with ads is also available.\nWhats New:\nPrivacy Statement included\nReady for Android Pie (9)\nThis app has no advertisements\nMore Info:\n\nhttps://play.google.com/store/apps/details?id=net.taobits.officecalculator.android.pro&hl=en\nDownload Instructions:\nhttps://uploadrar.com/fcfq76bl2i7e\n\nhttps://dropapk.com/w9japoq5tjto\n\nhttps://douploads.com/3gkwjmfr4jzy\n\n• By APK\nCalculator [Pro] - Classic Calculator App v1.4.3 [Paid]\nRequirements: 4.2+\nOverview: This app is a fully working emulator of casio calculator model DM-1200BM/ JF-100BM.\n\nThis app is a fully working emulator of casio calculator model DM-1200BM/ JF-100BM. The calculator includes tax and business functions which is very useful for professionals and small business owners.\nCalculator features:-\n* Tax functions\n* Percentage (%)\n* Cost/ sell/ margin calculations\n* Memory operations\n* Grand total (GT)\n* Square root\n* Change sign (+/-)\nWhat's New:\n- Now you can proceed with your calculations even if you entered constants (K) mode inadvertently. See Menu > Help for constants calculation.\nThis app has no advertisements\nMore Info:\n\nhttps://play.google.com/store/apps/details?id=com.everydaycalculation.casiocalculator.pro&hl=en\nDownload Instructions:\nhttps://uploadrar.com/65zm6lewbogy\n\nhttps://dropapk.com/0cad63pd4aiv\n\nhttps://douploads.com/b5l0o5hbakxp\n\n• By APK\nOffice Calculator Pro v5.3.0\nRequirements: 4.1+\nOverview: Office calculator with a virtual tape for Android, This is a calculator optimized for office tasks.\n\nOffice calculator with a virtual tape for Android,\nfixed point or floating point mode,\nvarious rounding modes, easy percent and tax calculation.\nThis is a calculator optimized for office tasks.\n* Calculator with virtual tape\nYou can switch between calculator view and and tape view to have a full screen view of the tape.\nJust tap on the tape to switch between views.\nThe tape of the calculator can have up to 1000 lines.\n* Calculator support corrections on the tape\nYou can change values on the virtual tape to make corrections.\nFor corrections go to the context menu of the tape line with a long press.\n* Calculator has percent calculation to add or subtract percent values.\nThe tape will display the percentage and the resulting value.\n* Calculator has tax buttons (TX+, TX-) to add or sub tract tax (sales tax, VAT)\nThis makes it very easy to calculate tax amounts with the calculator.\nThe tape will display the tax rate and the resulting value.\n* Calculator allows annotations on the tape\nYou can write a comment to a tape line.\n* Calculator with fixed point arithmetic or floating point.\nFixed point arithmetic has 20 digits and 0 - 4 decimal places.\nThe floating point arithmetic has 64 bits (IEEE double precision).\nBy default, the calculator works with fixed point arithmetic and 2 decimal places as needed for most calculations with amounts.\n* Calculator supports three rounding modes: up, down or 5/4.\nThis is the Pro variant of Office Calculator, a Free variant with ads is also available.\nWhats New:\nPrivacy Statement included\nReady for Android Pie (9)\nThis app has no advertisements\nMore Info:\n\nhttps://play.google.com/store/apps/details?id=net.taobits.officecalculator.android.pro\nDownload Instructions:\nhttps://uploadrar.com/ro6ghc3dfqg1\n\nhttps://dropapk.com/416qanaxfar1\n\nhttp://evassmat.com/5Bra\n• By APK\nAll-in-One Calculator v1.7.4 [Pro]\nRequirements: 4.2 and up\nOverview: All-In-One Calculator is a lightweight, clean and easy to use calculator and converter pack.\n\nContaining over 50 calculators and unit converters packed in with a scientific calculator, it's the only math app you will ever need from now on on your device.\nIt's a great calculator for school and homework, but not only. If you're a scholar, student, teacher. builder, handyman, contractor, etc.. and you need an all in one tool for your device, give this one a try. You will never be disappointed.\nFeatures\n• Over 50 Calculators and Unit converters\n• Scientific calculator with history\n• Currency converter with 160 currencies, available offline\n• Supports math formulas as input\n• Instant results\n• Integrated search\n• Favorite list for quick access\n• Tablet support\nLanguages: English (currently looking for translators)\nComplete list of all the calculators and unit converters\nAlgebra\n• Percentage calculator\n• Proportion calculator\n• Average calculator - arithmetic, geometric and harmonic means\n• Equation solver - linear, quadratic and equation system.\n• Combinations and permutations\n• Decimal to fraction\n• Fraction simplifier\n• Greatest common factor & Lowest common multiple calculator\n• Random number generator\nGeometry\n• Area / perimeter calculator for square, rectangle, parallelogram, trapezoid, rhombus, triangle, pentagon, hexagon, circle, circle arc, ellipse\n• Volume calculator for cube, rect. prism, square pyramid, sq. pyramid frustum, trapezoidal footing, cylinder, cone, conical frustum, sphere, spherical cap, spherical frustum, ellipsoid.\n• Right triangle calculator\n• Heron's formula (solve a triangle knowing the side lengths)\n• Circle solver\nUnit converters\n• Acceleration converter\n• Angle converter\n• Length converter\n• Energy converter\n• Force converter\n• Torque converter\n• Area converter\n• Volume converter\n• Volumetric flow converter\n• Weight converter\n• Temperature converter\n• Pressure converter\n• Power converter\n• Speed converter\n• Mileage converter\n• Time converter\n• Digital storage converter\n• Data transfer speed converter\n• Numeric base converter\n• Roman numerals converter\n• Shoe size converter\nFinance\n• Currency converter with 161 currencies available offline\n• VAT calculator\n• Tip calculator\n• Loan calculator\n• Electricity cost calculator\n• Cost of smoking calculator\nHealth\n• Body mass index - BMI\n• Daily calories burn\n• Body fat percentage\nEngineering\n• Ohm's law calculator - voltage, current, resistance and power\n• Speed/Distance/Time\n• Cylinder force calculator\n• Resistance calculator\n• Density calculator\nMiscellaneous\n• Elapsed time calculator\nWhat's New:\nVersion 1.7.4\nTranslation improvements, bug fixes and library updates.\nThis app has no advertisements\nMore Info:\n\nhttps://play.google.com/store/apps/details?id=all.in.one.calculator&hl=en\nDownload Instructions: PRO features unlocked\nhttps://uploadrar.com/5w3sh4uynlm2\n\nhttps://dropapk.com/k5ugbpq8torg\n\nhttp://evassmat.com/4kCO\n• By caffeine\nHP 35S FX Scientific Calculator 570 ES PLUS v4.0.2 [Premium]\nRequirements: 4.0.3 and up\nOverview: The best calculator for Android full features of scientific calculator. The calculator retains the natural display, which means that you can enter equations and expressions exactly as written. Fractions, radicals, expressions with π, and calculus function templates are all there. Support most of feature of hp 10s+ Scientific Calculator, hp 12C Platinum Financial Calculator, hp 35s Scientific Calculator, hp 17bII+ Financial Calculator, hp 300s+ Scientific Calculator, hp 12C Financial Programmable Calculator.\n\nTavern Theme\nThe calculator retains the natural display, which means that you can enter equations and expressions exactly as written. Fractions, radicals, expressions with π, and calculus function templates are all there. Exact answers can include fractions, square roots, and coefficients of π. Supports most of the features of fx 82 500 570 991 4500 es ms, fx 580 vnx/ fx 580 vn.\nAll of the other features:\n* Integrals of f(x)\n* Numeric Derivatives\n* Sums of a function\n* Base modes Decimal, Octal, Binary, Hexadecimal\n* Numeric solver, of equations and roots of expressions\n* CALC button allows for calculating expressions repeated amount of times.\n* Statistics including 1-variable, linear regression (a+bx), quadratic regression (a+bx+cx^2), cubic regression (a+bx+cx^2+dx^3), 2 types of exponential (a + b * e^x and a x^b), power (b a^x), logarithmic (a + b ln x), and inverse (a + b/x).\n* Equations - 2x2 and 3x3 simultaneous equations, quadratic, and cubic equation\n* Matrices: functions include transpose, inverse, and determinant\n* Vectors\n* Multi Line Statements with the colon (:)\n* Complex Number Mode\n* The number of available memories have increased from 7 to 9. (A, B, C, D, X, Y, M, and now E, F). Previously E and F were available only for the Hexadecimal mode.\n* You now have the ability to calculate using repeated numbers. For example, you can type the decimal form of 1/3 using 0.3 with the bar above the three. I believe that this is first line of calculators that has this ability.\n* New number functions are: GCD, LCM, Integer Part, Fractional Part, Random Integers, Integer Division (÷R) that gives quotient and remainder, and Prime Factorization (up to three digit factors). To factor a number, enter it, press [ = ], then [SHIFT], [ º ' '' ].\n* Products of function f(x)\n* In Table Mode you can include two functions f(x) and g(x).\n* The rref and ref functions are added to the Matrix Mode (but not eigenvalues).\n* The fx-115ES PLUS has a curve design, and boasts a faster processor.\n* Inequality Solver of quadratic and cubic equations\n* Verification mode, used for compare expressions (i.e. Does π/4 < π/2? Does 1 = 9/9 = e^0?)\n* Distribution mode: Normal Distribution (CDF, PDF, and Inverse (Yes!)), Binomial Distribution (CDF, PDF), and Poisson Distribution (CDF, PDF).\n* Support most of feature of HP 10s+ Scientific Calculator, HP 12C Platinum Financial Calculator, HP 35s Scientific Calculator, HP 17bII+ Financial Calculator, HP 300s+ Scientific Calculator, HP 12C Financial Programmable Calculator\nWhat's New:\n# 4.0.2\nNew unit converter design: now you can open unit converter from calculator or CONV dialog, and you can also transfer current expression to unit conversion calculator. With new button [ALL], the calculator supports convert to other units with single tap.\nNew settings: hide/show navigation bar, hide/show calculator toolbar. Button click volume setting in main screen.\nPhoto math: redesign scanner, improved AI.\n[+-] button is replaced by percent button.\nThanks for all feedback from users.\nThis app has no advertisements\nMore Info:\n\nhttps://play.google.com/store/apps/details?id=com.nstudio.calc.casio.tavern&hl=en\nDownload Instructions: Premium features unlocked\nhttps://uploadrar.com/9en2oj4d3npu\n\nhttps://dropapk.com/4kttmw50d2kp\n\nhttps://douploads.com/yp0iv2lt1sf1\n\n• By caffeine\nunitMeasure - Offline Material Unit Converter v2019.4.21 [Patched]\nRequirements: 5.0 and up\nOverview: ★ uMeasure is an intuitive unit conversion app for Android. ★\n\n★ uMeasure is an intuitive unit conversion app for Android. ★\nWith over a hundred conversions, you won't need to search the internet or fiddle around looking for answers anymore. This is a completely offline solution, with no extra permissions meaning: no tracking, advertisements, or any funny business. The app also comes in at just 1 MB in size, which means that you won't have to worry about deleting other apps. Lastly, the app is customizable: You can switch to a Light Mode, enable Borders, and even choose how many decimal places are shown.\n►13 different sections and over a hundred units are available at your fingertips...\n• Length (Inches, Feet, Yards, Meters, Km, Miles, etc.)\n• Time (Days, Weeks, Months, etc.)\n• Temperature (F, C, K, etc.)\n• Volume (Cooking measurements)\n• Weight (Mass)\n• Area (Sq. Kilometers, Sq. Miles, Acres, etc.)\n• Pressure (Pascals, PSI, Bars, etc.)\n• Digital Storage (bits, Bytes, KB, MB, GB, etc.)\n• Fuel Economy (mpg, km/l, mi/l)\n• Speed (mph, kmh, knots,)\n• Energy (Joules, Calories, Horsepower, etc.)\n• Programmer (Conversions between these units: Binary/Decimal/Hexadecimal/Octal)\n• Date Difference & Duration Calculation (Great for finding out someone's age or tracking periods of time and running countdowns)\n►Why Try\n• No Ads, No Permissions\n• Completely Offline!\n• Updated to Material Design\n• Dark Mode (Saves Battery on AMOLED devices)\n• Precision Control (You choose how many decimal places to show)\n•. Save Results to Clipboard (By tapping)\n• On-the-Fly Conversions (Results are updated as you type in real-time)\n• Results View (See all your conversions in one shot, without having to switch each time)\n• 1 MB in storage size\n•. Optimized for both Phones and Tablets\nNotices\n• Measurements are converted using UnitOf (c) 2018 DIGIDEMIC, LLC under the Apache License 2.0. https://github.com/Digidemic/UnitOf\n• umeasure shall have no liability for the accuracy of information provided and cannot be held liable for any claims or losses of any damages.\n• The app is only available in English currently.\nWhat's New:\n• After some research, I have decided to change the app name once and for all. The new name is unitMeasure\n• Bug Fixes and Performance Improvements\n• Better support for 12/24 Hour Clock in Duration Activity (based on your global phone settings)\nThis app has no advertisements\nMore Info:\n\nhttps://play.google.com/store/apps/details?id=com.aviparshan.converter\nDownload Instructions: ● No Patcher Needed\nhttps://uploadrar.com/e9epixkex8bp\n\nhttps://douploads.com/xvumg1y05wgo\n\nhttps://dropapk.com/ak5u0ehmsj3t\n\n• By caffeine\nGraphing Calculator TI 84 - Simulate for ES-991 FX v4.0.2 [Premium]\nRequirements: 4.0.3 and up\nOverview: PRO Scientific Calculator. This Scientific Calculator contains all the scientific calculations in casio fx 570 es plus and casio 991 es plus and other scientific calculations like casio fx 991 ex plus and casio 570 ex plus, such as trigonometric and hyperbolic calculation, equation solving, system equations solving, anti-trigonometric calculation, integral calculation, power calculation, derivative calculation, logarithmic calculation, nth root calculation, square root calculation, cube root calculation, LCM and GCD calculation, factorial calculation, matrix and vector calculation, π calculation and so on.\n\nCalculator can draw approximately as graphing calculator ti 84, ti 83:\n- Cartesian f(x)\n- Polar r(t)\n- Parametric x(t);y(t)\n- Implicit f(x,y)\n- Find approximately roots\n- Find approximately intersections\nPRO Scientific Calculator\nThis Scientific Calculator contains all the scientific calculations in casio fx 570 es plus and casio 991 es plus and other scientific calculations like casio fx 991 ex plus and casio 570 ex plus, such as trigonometric and hyperbolic calculation, equation solving, system equations solving, anti-trigonometric calculation, integral calculation, power calculation, derivative calculation, logarithmic calculation, nth root calculation, square root calculation, cube root calculation, LCM and GCD calculation, factorial calculation, matrix and vector calculation, π calculation and so on.\nOther features\n- Basic Calculations\n- Mathematical Display: displaying math expression as textbook format\n- Equations Solver: the calculator can solve easily any equation\n- Complex Number Calculation: output in rectangle and polar form\n- Advanced Functions\n- Constants\n- Numeric Integral & Derivative Calculation\n- Fraction and mixed fraction calculation\n- Unit converter\n- Math formulas\n- Calculator ti 83, graphing ti 84, ti 89 calculator\nWhat's New:\n# 4.0.2\nNew unit converter design: now you can open unit converter from calculator or CONV dialog, and you can also transfer current expression to unit conversion calculator. With new button [ALL], the calculator supports convert to other units with single tap.\nNew settings: hide/show navigation bar, hide/show calculator toolbar. Button click volume setting in main screen.\nPhoto math: redesign scanner, improved AI.\n[+-] button is replaced by percent button.\nThanks for all feedback from users.\nThis app has no advertisements\nMore Info:\n\nhttps://play.google.com/store/apps/details?id=com.duy.calc.graph&hl=en\nDownload Instructions: Premium features unlocked\nhttps://uploadrar.com/54qsrbph8etf\n\nhttps://dropapk.com/cydsreqws6x9\n\nhttps://douploads.com/3sts4u6l5loa\n\n• By caffeine\nMath Camera FX Calculator 991 ES Emulator 991 EX v4.0.2 [Premium]\nRequirements: 4.0.3 and up\nOverview: Full scientific calculator.  The calculator supports exponential and logarithmic functions, arithmetic, decimal numbers,integers, fractions,linear equations/inequalities, quadratic equations/inequalities, roots, algebraic expressions, systems of equations, logarithms, trigonometry, absolute equations/inequalities, derivatives and integrals, graphs and many more.\n\n# Simulator for fx 991 570 calculator\nThe calculator supported two keyboard layout: natural textbook display of fx 991 es plus and classwiz layout of fx 991 es plus with the UI of sharp calculator\n# Math camera calculator\nSolve math problems by camera. Now you can solve maths problem with your camera\n991 es plus calculator\n# Natural Textbook Display\nInput and display fractions, powers, logarithms, roots, and other mathematical formulas and symbols just as they appear in textbooks.\n991ms scientific calculator\n# Full scientific calculator\nSupport most of features of ti 84 ti 80 or fx 580 fx 570 fx 991 es plus\nAll features of scientific calculator is all in one.\nscientific calculator 991 es plus\n# Performing even advanced mathematics\nClassWiz contains calculation functions that support even advanced mathematical operations, 4 × 4 matrix calculations, calculation of simultaneous equations with four unknowns and quartic equations, and advanced statistical distribution calculations.\n991es scientific calculator\n# Matrix calculator\nPerform calculator with matrices of up to 4 rows and 4 columns.\n# Vector calculator\nPerform calculations using up to four third-order vectors stored in memory.\nfx 991ms calculator\n# Integration calculator\nPerform integration calculations in advanced mathematics.\nfx 991de plus\n# Differential calculator\nPerform differential calculations in advanced mathematics.\n991 ex\nEquation calculator\nCalculation of simultaneous equations in 2 to 4 unknowns and high-degree equations of second to fourth degree\n# Inequality calculator\nSolve second-degree to fourth-degree inequalities.\n# Advanced statistical distribution calculator\nPerform calculations involving normal distributions\n# Scientific constants\nSelect scientific constants from the Constant Table.\n# Digit separator\nSeparation every three digits makes even large numbers easy to read.\n# Engineering symbols\nPerform engineering calculations.\n# Math camera calculator\nCalculator solve math by camera. Camera scanner math solve. Photo to solve math. Use your phone's camera to solve equations. Photo Calculator app calculates mathematics problems with camera\n# Unit converter\nSupported over 900+ unit converter, include currency, area, length, volume, fuel consumption...\n# Math & Physic Formulas\nTriangle, Square, Rectangle, Trapezoid, Convex Quadrilateral, Circle, Hexagon, Sphere, Spherical Cap, Torus, Cylinder, Cone, Pyramid, Cuboid, Triangular Prism, Polynomial, Fractions, Identity, Exponentiation, Roots, Geometric Progression, Summations, Logarithm, Complex Plane, Euler, Trigonometric Table, Powers Of Trigonometric Functions, Addition Formulas, Linear Equation, System Of Two Linear Equations, Quadratic Equation, Cubic Equation, Exponential Equation, Quadratic, Exponential.\n# Simulator for 991de plus, fx-220 plus, fx 260, fx-912ms, fx-115, 991ex, fx-72f, fx-fd10 pro, 100w, fx-82 /, fx-3650p ii, fx-82au plus ii, fx-290, fx-3650, fx-82 tl, fx-995es, 350es, 991la x, 85 ms, 3950p, 87, fx-82es plus a, 300es plus, 300w, fx-375, fx cg50, fx-500es, 991es plus, fx-83gt plus, 83es, 991de x, oh-300es, fx 4500pa, fx-991es plus c, 85w, fx-92 fx-92b 991sp x iberia, fx-95, 570es, fx-300ms, 993es, 100 ms, 350 tl, 115es, 350 ms, fx-jp500, 83wa, 913, 85wa, 96sg plus, fx-500, 991cn x, fx 5800p, fx 5800, fc-100/200v, fx-95ar x, fx-570ar x, fx-991ar x, fx-87, fx-991 ms, 270w, fx-50f plus, oh-300ms fx-100au, fx 350, fx-50fh, 915es, 700, fx-513, fx-500ms, ms, 900 and fx-530az study cal, 300es, 570w, 570vn plus, 83w, 570 ms, 115wa, fx-991w, 82es, 82 ms, 991ce x, fx 4500, 115 ms, 85es, oh-300es plus, 115w, fx-991es, fx-85gt\n# Include the calculator supports exponential and logarithmic functions, arithmetic, decimal numbers,integers, fractions,linear equations/inequalities, quadratic equations/inequalities, roots, algebraic expressions, systems of equations, logarithms, trigonometry, absolute equations/inequalities, derivatives and integrals, graphs and many more.\nWhat's New:\n# 4.0.2\nNew unit converter design: now you can open unit converter from calculator or CONV dialog, and you can also transfer current expression to unit conversion calculator. With new button [ALL], the calculator supports convert to other units with single tap.\nNew settings: hide/show navigation bar, hide/show calculator toolbar. Button click volume setting in main screen.\nPhoto math: redesign scanner, improved AI.\n[+-] button is replaced by percent button.\nThanks for all feedback from users.\nThis app has no advertisements\nMore Info:\n\nhttps://play.google.com/store/apps/details?id=com.tool.calculator.casio.fx991.es.plus&hl=en\nDownload Instructions: Premium features unlocked\nhttps://uploadrar.com/psaeu3xqsuzo\n\nhttps://douploads.com/8br3q7s67fzu\n\nhttps://dropapk.com/adpba8tdbqxi\n\n• By APK\nComplex calculator & Solve for x ti-36 ti-84 Plus v4.0.3 [Beta] [Premium]\nRequirements: 4.0.3+\nOverview: Simulator for texas & instruments scientific calculator, Complex number, calculus, hyper calculator for student\n\n☑ Math camera\nMath solver problem by taking photo, input quickly to solve math with your camera\n☑ See math exactly as it appears in textbooks\nSee math expressions, symbols and stacked fractions exactly the way they appear in textbooks - no need to adapt to a technical syntax; also provides quick access to frequently used functions.\n☑ Easily solve equation, polynomial and system of linear equations, solve for x calculator\n☑ Determine the derivative and integral for real functions\n☑ Perform vectors and matrices using a vector and matrix entry window\n☑ Scientific notation output\nView scientific notation with the proper superscripted exponents and see the output in scientific notation\n☑ Explore fractions\nExplore fraction simplification, integer division and constant operators.\n☑ Calculate conversions\nDegrees/radians/grads\nPolar/rectangular\nDMS/degrees\nFraction/decimal/Mixed fraction/Repeated decimal\n☑ Factor integer, prime factor\n☑ Sum, product\n☑ Div mod calculation\n☑ Square root, sqrt, cube root and nth root\n☑ Polar coordinates\n☑ BASE-N decimal, octal, hexadecimal and binary calculator\n☑ Logarithm base n and natural logarithm\n☑ Trigonometric and hyperbolic function\n☑ Memory: 8 free variable and up to 14 variable on premium version\n☑ Convert decimal to fraction\n☑ Scientific constants\n☑ Unit conversation\n☑ Determine the limit of function\n☑ Infinity\n☑ Built-in document\n☑ Combination, binomial and permutation\n☑ GCD, LCM\n☑ Statistical and regression\n☑ Convert polar coordinates to rectangle\n☑ Round number\n☑ Copy and paste expression\n☑ Random integer, random real, random number\n☑ Pi constant\n☑ Ans memory\n☑ History\n☑ Decimal format: science, fixed, normal, science SI\n☑ Full keyboard and simple keyboard\n☑ More theme\n☑ Support change fonts\n☑ Secondary keyboard for premium user\n☑ Support most of features of ti 30XS Scientific Calculator, ti 34 Scientific Calculator, ti 36X Pro Scientific Calculator, ti 30Xa Scientific Calculator, texas & instruments calculator ti30, texas & instruments ba ii plus financial calculator, Graphing Calculators, ti 84 Plus ce, ti 84 plus Silver Edition, ti 84 plus C Silver Edition, ti 84 plus , ti 83 Plus, ti Nspire, ti 89 Titanium, ti 73 Explorer, ti 503 SV, ti 1706 SV, ti 1795 SV, ti 10, ti 15 Explorer, ti 108\n☑ Wabbit calculator & wabbitemu calculator, grafncalc83    graphncalc83\n☑ Simulator for fx-991es plus c, 115w, 100w, oh-300ms fx-100au, fx 4500pa, fx 5800, 85 ms, ms, fx-82au plus ii, fx-3650, 700, 570 ms, fx-82 /, fx-fd10 pro, fx 5800p, 3950p, 85wa, 270w, fx 350, 991de x, 570vn plus, 300es plus, fx-375, fx cg50, 115wa, 85es, fx-50f plus, fx-991 ms, 82es, 570es, 83wa, fx-3650p ii, fx-500, fc-100/200v, 350es, 83w, 350 tl, fx 4500, fx-72f, 300w, fx 260, fx-92 fx-92b 991sp x iberia, fx-991w, fx-jp500, 991ex, fx-300ms, fx-500es, 570w, fx-82es plus a, fx-95ar x, fx-570ar x, fx-991ar x, fx-513, 991ce x, fx-87, fx-95, 115 ms, 300es, 991de plus, 83es, 991es plus, fx-991es, 991cn x, 915es, fx-500ms, 991la x, oh-300es, 87, fx-995es, fx-912ms, fx-83gt plus, 85w, 993es, fx-50fh, 913, 350 ms, 96sg plus, 115es, 900 and fx-530az study cal, fx-82 tl, fx-85gt, 100 ms, fx-115, fx-220 plus, oh-300es plus, 82 ms, fx-290,\n☑ Math formulas\nMath Tricks, Units Conversion, Favorite, Geometry, Equations, Analytic Geometry, Algebra, Trigonometry, Matrices, Statistics, Derivative, Integration, Transforms,\nWhat's New:\n# 4.0.3-beta\n- Fix bug cannot scroll unit conversion display when expression too long.\n- Fix bug wrong cursor position after copy and paste expression.\n- Fixed crash in landscape mode\n- Fixed text overflow in unit converter\n- Rollback to old toolbar.\nMod Info:\nPremium features unlocked;\nDisabled / Removed unwanted Permissions + Receivers and Services;\nAnalytics / Crashlytics disabled.\nThis app has no advertisements\nMore Info:\n\nhttps://play.google.com/store/apps/details?id=com.mrduy.calc.ti36\nDownload Instructions:\nhttps://douploads.com/rtidk4ja8eob\n\nhttps://uploadrar.com/u50gz4qrj4kb\n\nhttps://dropapk.com/kc0si7tas702\n\n• By caffeine\nHiEdu Scientific Calculator Pro v1.0.3 [Paid]\nRequirements: 4.0+\nOverview: HiEdu Scientific Calculator Pro : A simple yet powerful calculator that includes standard, scientific, and programmer modes, as well as a unit converter, Math, Physics and Chemistry Formulas, graph and solve the equations .\n\nHiEdu Scientific Calculator Pro : A simple yet powerful calculator that includes standard, scientific, and programmer modes, as well as a unit converter, Math, Physics and Chemistry Formulas, graph and solve the equations . It's the perfect tool to add up a bill, convert measurements in a recipe or other project and It is a very useful tool for education help complete complex math, algebra, or geometry problems.\nKEY FEATURES\nScientific Calculator\n• It is a scientific calculator supports most of the features of real calculators such as Casio fx570ms, fx570esplus, 570vnplus ...\n• Natural Display makes it possible to input and display fractions and certain functions (log, x2, x3, x^, ), \", x−1, 10^, e^ , d/dx, Σ, Abs ...) just as they are written in your textbook.\n• Undo when you miss a mistake.\n• Save history, Select a calculation in list history and edit it.\n• Create favorite calculations that make calculations faster.\nStandard Calculator\n• This is a perfect tool for daily calculations. With memory functions similar to a small handheld calculator\n• Save history, Select a calculation in list history and edit it.\nMathematics formulas\n• This app has 1000+ math formula and more to come.\n• Now no need to make paper notes to remember mathematics formulas just have this app put all the formulas on your favourite phones.\n• you'll find formulas very simply explained in app with necessary figures will help you to understand very easily.\nPhysics formulas\n• The application is a physical handbook. Contains most physical formulas for students and undergraduate.help users quickly refer to any Physics formulas for their study and work.This app displays most popular as well as advanced formulas in seven categories:\n+ Mechanics\n+ Electricity\n+ Thermal physics\n+ Periodic motion\n+ Optics\n+ Atomic physics\n+ Constants\nChemical reactions\n• Allows to discover chemical reactions and to solve the chemical equations with one and several unknown variables.\nProgrammers\n• Can convert numbers between different number bases (2/8/10/16).\n• Display shows numbers in binary, hexadecimal, octal and decimal.\n• Input can be in binary, hexadecimal, octal or decimal.\nGraphing calculator\n• Easily graph functions, solve equations, find special points of functions.\nSolve the equations\n• Linear equation for degree one,quadratic equation for degree two,cubic equation for degree three, System of linear equations.\nConverter\n• Available unit conversions include:\n+ Currency (US dollar, CDN dollar, pound, peso, etc)\n+ Temperature (celsius, fahrenheit, kelvin, etc)\n+ Length (kilometer, miles, meter, yard, feet, etc)\n+ Mass/Weight (kilogram, pound, ounce, ton, stone, etc)\n+ Speed (km/h, mph, knot, etc)\n+ Area (square kilometer, square mile, hectare, acre, etc)\n+ Cooking Volume (teaspoon, tablespoon, cup, pint, quart, ounce, etc)\n+ Pressure (kilopascal, bar, PSI, etc)\n+ Power (watt, kilowatt, horsepower, etc)\n+ Energy (joule, calorie, BTU, etc)\n+ Time (year, month, day, hour, second, etc)\n+ Fuel Consumption (miles per gallon, liters per 100km, etc)\n+ Digital Storage (bit, byte, megabytes, gigabytes, etc)\nDISPLAY\n+ The layout of the buttons in the this app is scientifically rigorous, which makes entering mathematical operations as simple and convenient as possible.\n+ Numeric buttons and functions in the our application are beautifully designed, clear, resistant to glare, blurry and eyestrain.\n+ There are many beautiful themes with different styles.\nWhat's New:\n+ Add table feature.\nThis app has no advertisements\nMore Info:\n\nhttps://play.google.com/store/apps/details?id=com.hiedu.calcpro&hl=en\nDownload Instructions:\nhttps://douploads.com/5pfynk0a39up\n\nhttps://uploadrar.com/v7t0up7yskiv\n\nhttps://dropapk.com/wtg7h705r474\n\n×\n×\n• Create New...\n\n## Important Information\n\nThis website uses cookies for functionality, analytics and advertising purposes as described in our Privacy Policy. By clicking I accept, closing this banner, or continuing to browse our websites, you consent to the use of such cookies." ]

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[ "# Currying in JavaScript（柯里化）\n\nCurrying（柯里化），又稱為 parital application 或 partial evaluation，是個「將一個接受 n 個參數的 function，轉變成 n 個只接受一個參數的 function」的過程。\n\n• 簡化參數的處理，基本上是一次處理一個參數，藉以提高程式的彈性和可讀性\n• 將程式碼依功能拆解成更細的片段，有助於重複利用\n\n## 說明\n\n``````function multiply(x, y){\nreturn x * y;\n}\n\nmultiply(3, 5); // 15\n``````\n\n``````function curriedMultiply(x) {\nreturn function(y) {\nreturn x * y;\n}\n}\n``````\n\n``````var multipleOfThreeAndNumberY = curriedMultiply(3);\n\nmultipleOfThreeAndNumberY(5); // 15\nmultipleOfThreeAndNumberY(10); // 30\n``````\n\n``````var multipleOfFiveAndNumberY = curriedMultiply(5);\n\nmultipleOfFiveAndNumberY(5); //25\nmultipleOfFiveAndNumberY(10); //50\n``````\n\n### 備註\n\n• curriedMultiply 並沒有計算結果，而是回傳一個 function 作為未來計算結果之用。 也就是說，待之後呼叫 multipleOfThreeAndNumberY 和 multipleOfFiveAndNumberY 傳入參數後才回傳計算結果。\n• `multiply(x, y)` 等於 `curriedMultiply(x)(y)`\n``````multiply(3, 5); //15\ncurriedMultiply(3)(5); //15\n``````\n\n## Currying the Callback\n\n``````function fetchData(path, handler) {\nvar xmlHttp = new XMLHttpRequest();\nvar result = {};\n\nxmlHttp.open( \"GET\", path, false );\nxmlHttp.send( null );\nresult = JSON.parse(xmlHttp.responseText);\nhandler(result.data);\n}\n\nfunction showResult(result) {\nconsole.log('The result is: ' + result);\n}\n\nvar path = 'http://www.json-generator.com/api/json/get/bPQMSaHjsi?indent=2';\nfetchData(path, showResult); // The result is: Hello, World!\n``````\n\n``````function curriedFetchData(path) {\nvar xmlHttp = new XMLHttpRequest();\nvar result = {};\n\nxmlHttp.open( \"GET\", path, false );\nxmlHttp.send( null );\nresult = JSON.parse(xmlHttp.responseText);\n\nreturn function(_callback) {\n_callback(result.data);\n}\n}\n\nfunction showResult(result) {\nconsole.log('The result is: ' + result);\n}\n\nvar path = 'http://www.json-generator.com/api/json/get/bPQMSaHjsi?indent=2';\nvar getData = curriedFetchData(path);\ngetData(showResult); // The result is: Hello, World!\n``````\n\n``````var path1 = 'http://www.json-generator.com/api/json/get/bPQMSaHjsi?indent=2&ver=1';\nvar path2 = 'http://www.json-generator.com/api/json/get/bPQMSaHjsi?indent=2&ver=2';\n\nvar getData1 = curriedFetchData(path1);\nvar getData2 = curriedFetchData(path2);\n\ngetData1(function(result1) {\ngetData2(function(result2) {\nconsole.log(result1 + ' ' +result2); //Hello, World! Hello, World!\n});\n});\n``````" ]

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[ "MTH-1170 Engineering Math II - 3.00 credits\n\nA study of calculus which covers both differentiation and integration. Topics include a review of limits, an intro into complex numbers, the definition of derivative, differentiation rules, derivative applications, and integration as area, the fundamental theorem of calculus, techniques of integration, partial fraction decomposition, integration applications, methods of approximating definite integrals and elementary first order differential equations. Students are expected to have a basic understanding of the geometry of calculus, the idea of limit, slope and area under a curve. Not available for supplemental. Instruction (4.0). Requisite Courses: Take MTH-1150. (Required, Previous)." ]

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[ "## Principal component analysis\n\nIn an elliptical model often principal component analysis (PCA) is used as a linear dimension reduction tool and it is assumed that the components with large variation are interesting and the directions with small and equal variation are the uninteresting ones. Note that those components with equal variation form then a subspherical subset.\n\nAssume that $$X$$ is a data matrix with $$n$$ observations and $$p$$ variables and that PCA is performed using a scatter matrix (and location vector) of the user’s choice, such as the regular covariance matrix (and the mean vector).\n\nThen $$X$$ is first centered using the location of choice and, assuming the matrix $$W$$ contains the eigenvectors of the scatter matrix, $$S = XW$$ gives then the principal components where the amount of variation of each component is given by the corresponding eigenvalues $$d_1,...,d_p$$.\n\nThe null hypothesis of interest is $H_0: \\ d_1 \\geq ... \\geq d_k > d_{k+1} = ... = d_p.$\n\n### Asymptotic test a specific value of $$k$$\n\nThe function PCAasymp offers an asymptotic test for the above hypothesis where the user can choose between two scatter matrices. Using the argument scatter = \"cov\" centers the data with regular mean vector and performs PCA using the regular covariance matrix. Specifying instead scatter = \"tyler\" estimates jointly Tyler’s shape matrix and the spatial median using the function HR.Mest from the package ICSNP and uses then them accordingly.\n\nThe test statistic is in both cases based on the variance of the last $$p-k$$ eigenvalues: $T = n / (2 \\bar{d}^2 \\sigma_1) \\sum_{i=k+1}^p (d_i - \\bar{d})^2,$ where $$\\bar{d} = 1/n \\sum_{i=k+1}^p d_i$$ and $$\\sigma_1$$ is a constant specific for the used scatter matrix and depends on the underlying elliptic distribution and the dimension $$p$$. The value of $$\\sigma_1$$ is estimated from the data.\n\nUnder $$H_0$$ this test statistic has a chisquare distribution with $$(p-k-1)(p-k+2)/2$$ degrees of freedom.\n\nTo demonstrate the function consider the following artificial data:\n\nlibrary(ICtest)\nset.seed(1)\nn <- 200\nS <- cbind(rnorm(n, sd = 2), rnorm(n, sd = 1.5), rnorm(n), rnorm(n), rnorm(n))\nA <- rorth(5)\nX <- S %*% t(A)\npairs(X)", null, "which means there are two components of interest.\n\nPCAcov <- PCAasymp(X, k=2)\nPCAcov\n##\n## PCA subspericity test using cov\n##\n## data: X\n## T = 0.80054, df = 5, p-value = 0.977\n## alternative hypothesis: the last 3 eigenvalues are not equal\nPCAtyler <- PCAasymp(X, k=2, scatter = \"tyler\")\nPCAtyler\n##\n## PCA subspericity test using Tyler's shape matrix\n##\n## data: X\n## T = 2.1696, df = 5, p-value = 0.8252\n## alternative hypothesis: the last 3 eigenvalues are not equal\nggscreeplot(PCAtyler)", null, "And in both cases this hypothesis is not rejected.\n\nBut for example testing for no interesting component using cov yields:\n\nPCAcov0 <- PCAasymp(X, k=0)\nPCAcov0\n##\n## PCA subspericity test using cov\n##\n## data: X\n## T = 126.68, df = 14, p-value < 2.2e-16\n## alternative hypothesis: the last 5 eigenvalues are not equal\n\n### Bootstrapping test a specific value of $$k$$\n\nTo obtain a bootstrap test for this problem the package offers the function PCAboot. The function can perform the test for any scatter matrix the user has a function for. Important is only that the function returns a list which returns as first element the location vector and as second element the scatter matrix. The function is specified using the argument S and Sargs is an argument where additional arguments to S can be passed in the form of a list.\n\nThe test statistic used for the bootstrapping tests is $T = n / (\\bar{d}^2) \\sum_{i=k+1}^p (d_i - \\bar{d})^2,$\n\nand two different bootstrapping strategies are available:\n\n1. s.boot=\"B1\": The first strategy has the following steps:\n1. Take a bootstrap sample $$S^*$$ of size $$n$$ from $$S$$ and decompose it into $$S_1^*$$ and $$S_2^*$$.\n2. Every observation in $$S_2^*$$ is transformed with a different random orthogonal matrix.\n3. Recombine $$S^*=(S_1^*, S_2^*)$$ and create $$X^*= S^* W^{-1}$$.\n4. Compute the test statistic $$T^*$$ based on $$X^*$$.\n5. Repeat the previous steps $$m$$ times to obtain the test statistics $$T^*_1,...,T^*_m$$.\n1. s.boot=\"B2\": The second strategy has the following steps:\n1. Scale each principal component using the $$p\\times p$$ diagonal matrix $$D^*=diag(d_1,...,d_k,\\bar{d},...,\\bar{d})$$, i.e. $$Z = S D^*$$.\n2. Take a bootstrap sample $$Z^*$$ of size $$n$$ from $$Z$$.\n3. Every observation in $$Z^*$$ is transformed with a different random orthogonal matrix.\n4. Recreate $$X^*= Z^* {D^*}^{-1} W^{-1}$$.\n5. Compute the test statistic $$T^*$$ based on $$X^*$$.\n6. Repeat the previous steps $$m$$ times to obtain the test statistics $$T^*_1,...,T^*_m$$.\n\nThe p-value is in both cases obtained then as: $\\frac{\\#(T_i^* \\geq T)+1}{m+1}.$\n\nTo create the random orthogonal matrices in the bootstrapping approaches the function rorth is used.\n\nTo demonstrate how to use another scatter matrix and how to pass on additional arguments we use now the scatter based on the MLE of $$t_2$$ distribution, as for example implemented as the function tM in the ICS package. For that purpose, using strategy two we test using the data from above if $$k=1$$ or $$k=2$$.\n\nPCAtMk1 <- PCAboot(X, k=1, S=\"tM\", Sargs=list(df=2))\nPCAtMk1\n##\n## PCA subsphericity bootstrapping test using \"tM\" and strategy B1\n##\n## data: X\n## T = 23.357, replications = 200, p-value = 0.004975\n## alternative hypothesis: the last 4 eigenvalues are not equal\nPCAtMk2 <- PCAboot(X, k=2, S=\"tM\", Sargs=list(df=2))\nPCAtMk2\n##\n## PCA subsphericity bootstrapping test using \"tM\" and strategy B1\n##\n## data: X\n## T = 1.417, replications = 200, p-value = 0.8557\n## alternative hypothesis: the last 3 eigenvalues are not equal\nggplot(PCAtMk2, which=\"k\")", null, "" ]

[ null, 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", null, 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", null, 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[ "", null, "## Firefly and PC GAMESS-related discussion club\n\nLearn how to ask questions correctly", null, "", null, "'Abnormal Energy' obtained in MP4 single point energy calculation\nHello everyone!\n\nI am currently running an MP4 single point energy calculation (basis set: 6-311++G**) on a few hydrocarbons using Firefly version 7.1.G in one of the PCs in our laboratory. The geometry I used for the single point energy calculation was the equilibrium geometry I obtained from my MP2 optimization calculation using the same molecule. On some of my molecules examined at MP4, I found out that the energy calculated was 'abnormally' large(i.e. the absolute value of the energy calculated) that my succeeding calculations (i.e. enthalpy of reaction, enthalpy of activation, etc. ) doesn't make any sense at all. I checked my input files, they were all the same. I just changed the geometry. Shown below is the fraction of my result wherein the energy I label as 'abnormal' is reflected.\n\nRESULTS OF MOLLER-PLESSET 4TH ORDER CORRECTION ARE\n\nа а а а а аE(RHF) а а а = а а а-309.9452940908\n\nа а а а а аE(D,2) а а а = а а а а-1.1646736559\nа а а а а аE(MP2) а а а = а а а-311.1099677467\n\nа а а а а аE(D,3) а а а = а а а а-0.0698223432\nа а а а а аE(D,2+3) а а = а а а а-1.2344959991\nа а а а а аE(MP3) а а а = а а а-311.1797900899\n\nа а а а а аE(S,4) а а а = а а а а-0.0443751557\nа а а а а аE(D,4) а а а = а а а-105.3701897285\nа а а а а аE(D,2+3+4) а = а а а-106.6046857276\nа а а а а аE(T,4) а а а = а а а а-0.0706244480\nа а а а а аE(R+Q,4) а а = а а а а 0.0297425817\nа а а а а аE(SDTQ,4) а а= а а а-105.4554467506\nа а а а а аE(SDTQ,2+3+4)= а а а-106.6899427497\nа а а а а аE(MP4-SDTQ) а= а а а-416.6352368404\n\n..... DONE WITH MP4 ENERGY .....\n\nаI also attached the output file of this calculation. What might be the problem in this calculation? Can I ask for suggestions on how to improve/solve such? Any help is highly appreciated. Thank you in advance!\n\nRegards,\nXaiza", null, "This message contains the 1114 kb attachment [ single_point.log ] output file containing 'abnormal energy'\n\n[ This message was edited on Wed Jun 26 '13 at 2:49pm by the author ]", null, "", null, "", null, "Wed Jun 26 '13 2:49pm", null, "", null, "", null, "This message read 1129 times" ]

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[ "", null, "", null, "K nearest neighbor prediction matlab\n\nK nearest neighbor prediction matlab\n\nThe k-NN is a most simple approach. we want to use KNN based on the discussion on Part 1, to identify the number K (K nearest Neighbour), we should calculate the square root of observation. The KNN algorithm is part of the GRT classification modules. Standardized Distance How to Find k-nearest neighbors using data in Matlab in 3d-plane? R - kNN - k nearest neighbor (part 1 K Nearest Neighbor (kNN) Algorithm | R Programming | Data Prediction Algorithm How to Find k-nearest neighbors using data in Matlab in 3d-plane? R - kNN - k nearest neighbor (part 1 K Nearest Neighbor (kNN) Algorithm | R Programming | Data Prediction Algorithm Is there any function/package to perform k-Nearest Neighbor based density estimation in matlab? or open source. The k-Nearest Neighbors (kNN) classifier is one of the most In weka it's called IBk (instance-bases learning with parameter k) and it's in the lazy class folder.", null, "K Nearest Neighbours. how dependent the classifier is on the random sampling made in the training set) will be high, because each time your model will be different. xlsx. This post was written for developers and assumes no background in statistics or mathematics.", null, "By Rapidminer Sponsored Post. The structure of the data generally consists of a variable of interest (i. jl. In the knnAUC framework, we first calculated the AUC estimato Implementing your own k-nearest neighbour algorithm using Python Posted on January 16, 2016 by natlat 5 Comments In machine learning, you may often wish to build predictors that allows to classify things into categories based on some set of associated values.", null, "It is called lazy algorithm because it doesn't learn a discriminative function from the training data but memorizes the training dataset instead. This research represents a novel soft computing approach that combines the fuzzy k-nearest neighbor algorithm (fuzzy k-NN) and the differential evolution (DE) optimization for spatial prediction of rainfall-induced shallow landslides at a tropical hilly area of Quy Hop, Vietnam. for k-means clustering is a method of vector quantization, originally from signal processing, that is popular for cluster analysis in data mining. 1 Example K-Nearest neighbor algorithm implement in R Programming from scratch In the introduction to k-nearest-neighbor algorithm article, we have learned the core concepts of the knn algorithm.", null, "I don't believe the k-NN regression algorithm is directly implemented in matlab, but if you do some googling you can find some valid implementations. This MATLAB function returns the classification loss by resubstitution, which is the loss computed for the data used by fitcknn to create mdl. K-Nearest Neighbors¶ The algorithm caches all training samples and predicts the response for a new sample by analyzing a certain number (K) of the nearest neighbors of the sample using voting, calculating weighted sum, and so on. Ananda Seneviratne Department of Chemistry, Wayne State UniVersity, Detroit, Michigan 48202 The K-Nearest Neighbor (KNN): Many researchers have attempted to use K-Nearest Neighbor classifier for pattern recognition and classification in which a specific test tuple is compared with a set of training tuples that are similar to it.", null, "Version 11. (2006)and it was implemented in the MATLAB environment (Mathworks, 2010). Madhavi Pradhan1, Ketki Kohale2, Parag Naikade3, Ajinkya Pachore4, Eknath Palwe5 1Asst. An Improved K-nearest Neighbor Model for Short-term Traffic Flow Prediction In order to accurately predict the short-term traffic flow, this paper presents a k-nearest neighbor (k-NN) model.", null, "In both cases, the input consists of the k closest training examples in the feature space. I am searching for few hours but I am not finding the way to find the K-Nearest Neighbors is one of the most basic yet essential classification algorithms in Machine Learning. The most promising non-parametric technique for generating weather data is the k-nearest neighbor (k-NN) resampling approach. The k-NN technique does not use any predefined mathematical functions to estimate a target variable.", null, "2 k-Nearest Neighbor Prediction K nearest neighbors is a simple algorithm that stores all available cases and predict the numerical target based on a similarity measure (e. We have already seen how this algorithm is implemented in Python, and we will now implement it in C++ with a few modifications. (\" The prediction file is stored in // get the index of the Note: K-Nearest Neighbors is called a non-parametric method Unlike other supervised learning algorithms, K-Nearest Neighbors doesn’t learn an explicit mapping f from the training data It simply uses the training data at the test time to make predictions (CS5350/6350) K-NN and DT August 25, 2011 4 / 20 The method draws on the idea of clustering, extracts the samples near the center point generated by the clustering, applies these samples as a new training sample set in the K-nearest neighbor algorithm; based on the maximum entropy The K-nearest neighbor algorithm is improved to overcome the influence of the weight coefficient in the What is the time complexity of the k-NN algorithm with naive search approach (no k-d tree or similars)? I am interested in its time complexity considering also the hyperparameter k. (3) An algorithm to optimize hyperparameter k (Bayesian Optimization) 2.", null, "However, if we think there are non-linearities in the relationships between the variables, a more flexible, data-adaptive approach might be desired. K Most of the answers suggest that KNN is a classification technique and K-means is a clustering technique. It occupies 69 MB of disk space including the reference data. V3.", null, "Because k-nearest neighbor classification models require all of the training data to predict labels, you cannot reduce the size of a ClassificationKNN model. Here is an example of k-Nearest Neighbors: Predict: Having fit a k-NN classifier, you can now use it to predict the label of a new data point. To find all points in X within a fixed distance of each point in Y, use rangesearch. The k-Nearest Neighbors algorithm (or kNN for short) is an easy algorithm to understand and to implement, and a powerful tool to have at your disposal.", null, "Nearest neighbor methods are easily implmented and easy to understand. KNN algorithms have Heart Disease Prediction using K Nearest Neighbour and K Means Clustering in MATLAB To get this project in ONLINE or through TRAINING Sessions, Contact: JP INFOTECH, #37, Kamaraj Salai KNN function accept the training data set and test data set as second arguments. e. Name: Hidden expected divergence of the estimated prediction function from its average value (i.", null, "http://in. This feature is not available right now. k-nearest neighbor classifier model, k is the number of nearest neighbors used in prediction Run the command by entering it in the MATLAB Command Window. Given a query point x0, we find the k training points x(r),r = 1,,k closest in distance to x0, and then classify using majority vote among the k neighbors.", null, "ET College, Dr. Because a ClassificationKNN classifier stores training data, you can use the model to compute resubstitution predictions. In this tutorial you will implement the k-Nearest Neighbors algorithm from scratch in Python (2. How do I use the k-nearest neighbor (kNN) by matlab for face recognition classification? I am looking for cod matlab using\" k-nearest neighbor (kNN)\" to classification multi images of faces.", null, "P. e a test sample is classified as Class-1 if there are more number of Class-1 training samples closer to the test sample machine (SVM), K - nearest neighbor (KNN), genetic algorithm, neural network, Bayesian classification. To be surprised k-nearest neighbor classifier mostly represented as Knn, even in many research papers too. Nearest Neighbor Analysis is a method for classifying cases based on their similarity to other cases.", null, "The focus is on how the algorithm works and how to use it To summarize, in a k-nearest neighbor method, the outcome Y of the query point X is taken to be the average of the outcomes of its k-nearest neighbors. 253-255, pp. I obtained the data from Yahoo Finance. GitHub Gist: instantly share code, notes, and snippets.", null, "K-nearest-neighbor classification was developed <p> We start by considering the simple and intuitive example of nonparametric methods, nearest neighbor regression: The prediction for a query point is based on the outputs of the most related observations in the training set. The results of the research for temperature and humidity prediction by K-Nearest Neighbor were satisfactory as it is assumed that no forecasting technique can be 100 % accurate in prediction. However, many users don’t rate a significant number of movies. MATLAB training programs (KNN,K nearest neighbor classification) k-nearest neighbor density estimation technique is a method of classification, not clustering methods.", null, "It belongs to the supervised learning domain and finds intense application in pattern recognition, data mining and intrusion detection. In this article, we will talk about another widely used classification technique called K-nearest neighbors (KNN) . The program implementing the fuzzy k-nearest neighbor algorithm for protein solvent accessibility prediction was written in ANSI C and run on a Linux machine with the CPU of AMD Athlon MP2400. One of the benefits of kNN is that you can handle any number of K-nearest Neighbors applied to our data.", null, "moreover the prediction label also need for result. For a fixed positive integer k, knnsearch finds the k points in X that are the nearest to each point in Y. How to plot decision boundary of a k-nearest neighbor classifier from Elements of Statistical Learning? Finding the optimal value of k in the k-nearest-neighbor the KNN for every user, we need to compute the similarities between all the users for roughly O(N2M log K) time to finish computing KNN and O(KN)space to store the K nearest neighbors for each user. columbia.", null, "See Predicted Class Label. Learn more about . To train a k-nearest neighbors model, use the Classification Learner app. K nearest neighbours is a way to more robustly classify datapoints by looking at more than just the nearest neighbour.", null, "Alternative Functionality knnsearch finds the k -nearest neighbors of points. The implementation will be specific for Heart Disease Prediction using K Nearest Neighbour and K Means Clustering in MATLAB To get this project in ONLINE or through TRAINING Sessions, Contact: JP INFOTECH, #37, Kamaraj Salai In pattern recognition, the k-nearest neighbors algorithm (k-NN) is a non-parametric method used for classification and regression. For each new data point (student), K-nearest Neighbours groups and evaluates them based only on other students with the most similar background then dynamically generates prediction rules. KNN calculates the distance between a test object and all training objects.", null, "fr or vincent@iri. In practice, looking at only a few neighbors makes the algorithm perform better, because the less similar the neighbors are to our data, the worse the prediction will be. More specifically, the distance between the stored data and the new instance is calculated by means of some kind of a similarity measure. Dataset for running K Nearest Neighbors Classification.", null, "most similar to Monica in terms of attributes, and sees what categories those 5 customers were in. - rayt579/k-nearest-neighbors interactive-knearest-neighbors knn machine-learning data-science visualization html5 nearest-neighbor-search data-analysis scikit-learn machine-learning-algorithms javascript ai classification statistics gui k-nearest-neighbors k-nearest-neighbor k-nearest-neighbours A Regression-based K nearest neighbor algorithm for gene function prediction from heterogeneous… As a variety of functional genomic and proteomic techniques become available, there is an increasing need for…bmcbioinformatics. 3. Wolberg (University of Wisconsin Hospitals, Madison).", null, ". K-nearest neighbors is a classification (or regression) algorithm that in order to determine the classification of a point, combines the classification of the K nearest points. make prediction by the use of differnt k values effective number of parameters corresponding to k is n/k where n is the number of observations in the training data set. I am also interested by any idea or suggestion for Fix & Hodges proposed K-nearest neighbor classifier algorithm in the year of 1951 for performing pattern classification task.", null, "only density estimation, please. knnAUC knnAUC : k-nearest neighbors AUC test. Follow this link for an entire Intro course on Machine Learning using R, did I mention it's FRE K Nearest Neighbor Implementation in Matlab. the result is “wbcd k-NN is often used in search applications where you are looking for “similar” items; that is, when your task is some form of “find items similar to this one”.", null, "It is a supervised learning algorithm where the result of new instance query is classified based on a majority of k-nearest neighbor category. This MATLAB function returns a k-nearest neighbor classification model based on the input variables (also known as predictors, features, or attributes) in the table Tbl and output (response) Tbl. mathworks. here for 469 observation the K is 21.", null, "Those experiences (or: data points) are what we call the k nearest neighbors. Implementation of k-nearest neighbors classification algorithm on MNIST digits dataset. Classifying Irises with kNN. Lets assume you have a train set xtrain and test set xtest now create the model with k value 1 and pred In this example, you train a classification ensemble model using k-nearest-neighbor weak learners and save the trained model by using saveCompactModel.", null, "Basic k-nearest neighbors classification and regression. , distance functions). T, APJAKT University, India Abstract Fast k Nearest Neighbor Search using GPU the k nearest neighbor search (KNN) is a well-known problem linked with many applications such as classification, estimation of statistical properties The toolbox provides supervised and unsupervised machine learning algorithms, including support vector machines (SVMs), boosted and bagged decision trees, k-nearest neighbor, k-means, k-medoids, hierarchical clustering, Gaussian mixture models, and hidden Markov models. Putting it all together, we can define the function KNearestNeighbor, which loops over every test example and makes a prediction.", null, "Wen et al. I have found contradictory answers: O(nd + kn), where n is the cardinality of the training set and d the dimension of each sample. Find the k-Nearest elements using whatever distance metric is suitable. The output depends on whether k-NN is used for classification or regression: This is a matlab built in function called knnclassify, which is primarily used to identify the nearest neighbour of a data in matrix.", null, "In machine learning, it was developed as a way to recognize patterns of data without requiring an exact match to any stored patterns, or cases. The k-nearest neighbor (k-NN) method is a standard and sensitive classification technique [13,14,15,16,17,18]. Then the algorithm searches for the 5 customers closest to Monica, i. This MATLAB function prepares a classification model, regression model, or nearest neighbor searcher (Mdl) for code generation by reducing its memory footprint and then saving it in the MATLAB formatted binary file (MAT-file) named filename.", null, "The K-nearest Neighbor Algorithm is one of the simplest methods for classification and prediction. Contribute to wihoho/KNN development by creating an account on GitHub. Now some comments about those quick answers: KNN has some nice properties: it is automatically non-linear, it can detect linear or non-linear d Knn and svm both are supervised learner so first of all u define traffic type class like high(0),medium(1),low(2). 2013.", null, "When do we use KNN algorithm? How does the KNN algorithm work? How do we choose the factor K? In the k-Nearest Neighbor prediction method, the Training Set is used to predict the value of a variable of interest for each member of a target data set. Short-term urban expressway flow prediction system based on k-NN is established in three aspects: the historical database, the search mechanism and algorithm parameters, and the predication plan. This example illustrates the use of XLMiner's k-Nearest Neighbors Classification method. IBk's KNN parameter specifies the number of nearest neighbors to use when classifying a test instance, and the outcome is determined by majority vote.", null, "mdl — k-nearest neighbor classifier model ClassificationKNN object. Prof. KNN is a method for classifying objects based on closest training examples in the feature space. ,* Hatim T.", null, "K nearest neighbor algorithm Steps 1) find the K training instances which are closest to unknown instance Step2) pick the most commonly K-Nearest Neighbors (K-NN) is one of the simplest machine learning algorithms. There are many ways to go about this modeling task. The number of neighbors we use for k-nearest neighbors (k) can be any value less than the number of rows in our dataset. In this research, the classification techniques by k-nearest neighbor, Naïve Bayes and decision trees are applied to evaluate different engineering technologies student's performance and also I am pasting some links of KNN coding for you problem.", null, "Toggle Main Navigation k nearest neighbor free download. Given a set X of n points and a distance function, k-nearest neighbor (kNN) search lets you find the k closest points in X to a query point or set of points Y. First divide the entire data set into training set and test set. Over a wide range of classification problems k-nearest neighbor gets into top 3-4 performers, often beating more sophisticated off-the-shelf methods.", null, "01 >> Default=Y . In the introduction to k-nearest-neighbor algorithm article, we have learned the key aspects of the knn algorithm. kNN - k nearest neighbor (part 1) - Duration: 14:51. Run the command by entering it in the MATLAB Command Window.", null, "ResponseVarName. In this programming assignment, we will revisit the MNIST handwritten digit dataset and the K-Nearest Neighbors algorithm. Accepted on February 13, 2017 k-Nearest-Neighbor Classifiers These classifiers are memory-based, and require no model to be fit. .", null, "k-NN algorithm is an ad-hoc classifier used to classify test data based on distance metric, i. , the The K Nearest Neighbor Algorithm (Prediction) Demonstration by MySQL July 29, 2016 No Comments machine learning , math , sql The K Nearest Neighbor (KNN) Algorithm is well known by its simplicity and robustness in the domain of data mining and machine learning . Please try again later. Regression: Prediction of the value of a continuous value based on the values of other variables and on the basis of a linear or non-linear dependence model is called regression such as the 3 Condensed Nearest Neighbour Data Reduction 8 1 Introduction The purpose of the k Nearest Neighbours (kNN) algorithm is to use a database in which the data points are separated into several separate classes to predict the classi cation of a new sample point.", null, "Machine learning algorithms provide methods of classifying objects into one of several groups based on the values of several explanatory variables. Nearest neighbor classification is used mainly when all the attributes are continuos. Tutorial Time: 10 minutes. 2 K Nearest Neighbours As the name suggests, the idea here is to include more than one neighbour in the decision about the class of a novel point x.", null, "tech student at M. STATISTICA k-Nearest Neighbors (KNN) is a memory-based model defined by a set of objects known as examples (also known as instances) for which the outcome are known (i. com Classification Using Nearest Neighbors k-Nearest Neighbor Search Given a set X of n points and a distance function D, k-nearest neighbor (kNN) search letsyoufindthek closest points in X to a query point or set of points. Prediction of heart disease using k-nearest neighbor and particle swarm optimization Jabbar MA * Vardhaman College of Engineering, Hyderabad, India *Corresponding Author: Jabbar MA Vardhaman college of Engineering Hyderabad, India.", null, "Improved Nearest-Neighbor Parameters for Predicting DNA Duplex Stability† John SantaLucia, Jr. label = predict(mdl,X) returns a vector of predicted class labels for the predictor data in the table or matrix X, based on the trained k-nearest neighbor classification model mdl. for making the prediction. the k-NN classifier as the main classifier.", null, "Allawi, and P. 1, February 2013 DOI: 10. Our focus will be primarily on how does the algorithm work and how does the input parameter effect the output/prediction. For binary data like ours, logistic regressions are often used.", null, "Matlab scripts for the analysis and prediction of “weather-within-climate” This is a bunch of ~70 matlab functions related to the general “weather-within-climate” issue. Indeed, it is almost always the case that one can do better by using what’s called a k-Nearest Neighbor Classifier. Abdul Kalam Technical University (APJAKTU) Uttar Pradesh, India *2 Assistant Professor at M. Zubair Khan2, Shefali Singh3 M-Tech Research Scholar1&3, Professor2, Department of Computer Science Engineering, Invertis University, Bareilly-243123, Lucknow, UP-India ABSTRACT Diabetes is one of the major global health problems.", null, "Predictive Data Mining with SVM, NN, KNN for weather and plant disease prediction in Matlab rupam rupam. I. Short-term urban expressway flow prediction system based on k-NN is established in three aspects: the historical database, the search mechanism and . g.", null, "This value is the average (or median) of the values of its k nearest neighbors. KNN function accept the training dataset and test dataset as second arguments. On the XLMiner rribbon, from the Applying Your Model tab, select Help - Examples, then Forecasting/Data Mining Examples, and open the example workbook Iris. k-Nearest Neighbor Search and Radius Search.", null, "This approach is extremely simple, but can provide excellent predictions, especially for large datasets. The simplest kNN implementation is in the {class} library and uses the knn function. For greater flexibility, train a k-nearest neighbors model using fitcknn in the command-line interface. This MATLAB function returns a vector of predicted class labels for the predictor data in the table or matrix X, based on the trained k-nearest neighbor classification model mdl.", null, "After reading this post you will know. The k-Nearest Neighbors algorithm (kNN) assigns to a test point the most frequent label of its k closest examples in the training set. Let’s use k-Nearest Neighbors. , Department of Computer Engineering, AISSMS’s College of Engineering, Pune, Maharashtra, India-411001 Generating Prediction Map for Geostatistical Data Based on an Adaptive Neural Network Using only Nearest Neighbors Sathit Prasomphan and Shigeru Mase International Journal of Machine Learning and Computing, Vol.", null, "Convert the inverse distance weight of each of the k elements You'll immediately be able to notice two things. formula is an explanatory model of the response and a subset of predictor variables in Tbl. KNN has been used in statistical estimation and pattern recognition already in the beginning of 1970’s as a non-parametric technique. KNN algorithm also called as 1) case based reasoning 2) k nearest neighbor 3)example based reasoning 4) instance based learning 5) memory based reasoning 6) lazy learning .", null, "Let k be 5 and say there’s a new customer named Monica. Using the K nearest neighbors, we can classify the test objects. jl Design of Classifier for Detection of Diabetes using Neural Network and Fuzzy k-Nearest Neighbor Algorithm Mrs. The K-Nearest Neighbor (KNN) Classifier is a simple classifier that works well on basic recognition problems, however it can be slow for real-time prediction if there are a large number of training examples and is not robust to noisy data.", null, "A Nearest neighbor search locates the k-nearest neighbors or all neighbors within a specified distance to query data points, based on the specified distance metric. With K=3, there are two Default=Y and one Default=N out of three closest neighbors. After training, predict labels or estimate posterior probabilities by passing the model and predictor data to predict. The kNN search technique and kNN-based algorithms are widely used as benchmark learning rules—the relative simplicity of Y.", null, "Creates a graphic highlighting the nearest training instances (For plotting, instances must have only two or three features (2-D or 3-D)). May be these code helped you. The latter is often done based on his memory or some kind of model. Value = Value / (1+Value); ¨ Apply Backward Elimination ¨ For each testing example in the testing data set Find the K nearest neighbors in the training data set based on the Euclidean distance Predict the class value by finding the maximum class represented in the Use the most popular response value from the K nearest neighbors as the predicted response value for the unknown iris; This would always have 100% accuracy, because we are testing on the exact same data, it would always make correct predictions; KNN would search for one nearest observation and find that exact same observation What is better? It depends.", null, ", \"Traffic Incident Duration Prediction Based on K-Nearest Neighbor\", Applied Mechanics and Materials, Vols. Is not the best method, popular in practice. Comparing Accuracy of K-Nearest-Neighbor and Support-Vector-Machines for Age Estimation Anchal Tomar *1, Anshika Nagpal *2 *1 M. J.", null, ", Department of Computer Engineering, AISSMS’s College of Engineering, Pune, Maharashtra, India-411001 Design of Classifier for Detection of Diabetes using Neural Network and Fuzzy k-Nearest Neighbor Algorithm Mrs. Abstract. Advantages If k = 1, then the object is simply assigned to the class of that single nearest neighbor. 3.", null, "For a list of the distance metrics that can be used in k-NN classification, see Distances. Its simplicity does not undermine its competitiveness, nonetheless. Regarding the Nearest Neighbors algorithms, if it is found that two neighbors, neighbor k+1 and k, have identical distances but different labels, the results will depend on the ordering of the training data. When a new situation occurs, it scans through all past experiences and looks up the k closest experiences.", null, "we want to use KNN based on the discussion on Part 1, to identify the number K (K nearest Neighbor), we should calculate the square root of observation. Which algorithm is mostly used practically? I'd say SVM, it's very popular. Keywords If K=1 then the nearest neighbor is the last case in the training set with Default=Y. All 51 Python 16 Jupyter Notebook 12 MATLAB 4 R 4 Java Prediction using K-Nearest Neighbors Algorithm (Parallel) k-nearest-neighbor algorithm K-Nearest Neighbors with the MNIST Dataset.", null, "In order to accurately predict the short-term traffic flow, this paper presents a k-nearest neighbor (KNN) model. Technical Details. Simple K nearest neighbor algorithm is shown in figure 1 Fig 1. For these users, it is unlikely that In this article, I will show you how to use the k-Nearest Neighbors algorithm (kNN for short) to predict whether price of Apple stock will increase or decrease.", null, "I will here assume that we are An object is classified by a majority vote of its neighbors, with the object being assigned to the class most common among its k nearest neighbors. How can we find the optimum K in K-Nearest Neighbor? I'm talking about K-nearest neighbor classification algorithm, not K-means or C-means clustering method. 3, part of Release 2018a, includes the following enhancements: Code Generation: Generate C code for distance calculation on vectors and matrices, and for prediction by using k-nearest neighbor with Kd-tree search and nontree ensemble models (requires MATLAB Coder) If you don’t have a lot of points you can just load all your datapoints and then using scikitlearn in Python or a simplistic brute-force approach find the k-nearest neighbors to each of your datapoints. Then, define an entry-point function that loads the saved model by using loadCompactModel and calls the object function.", null, "The k-NN algorithm is based on the k-nearest neighbors classification rule described by Hart et al. kNN. First of all, unlike many other models, we don't have any preliminary computations to do! There is no training phase in a \\(k\\)-nearest neighbor predictor; once we have the data set, we can make predictions. 7).", null, "Table of Contents. K-nearest-neighbor (kNN) classification is one of the most fundamental and simple classification methods and should be one of the first choices for a classification study when there is little or no prior knowledge about the distribution of the data. The easiest way of doing this is to use K-nearest Neighbor. What is the K-nearest neighbors classification model? What are the four steps for model training and prediction in scikit-learn? How can I apply this pattern to other machine learning models? Unlike most other machine learning models, K-nearest neighbors (also known as \"KNN\") can be understood K-Nearest Neighbors • Classify using the majority vote of the k closest training points .", null, "Prediction models 2. k-means clustering aims to partition n observations into k clusters in which each observation belongs to the cluster with the nearest mean, serving as a prototype of the cluster. The algorithm is fairly simple though. This sort of situation is best motivated through examples.", null, "3, part of Release 2018a, includes the following enhancements: Code Generation: Generate C code for distance calculation on vectors and matrices, and for prediction by using k-nearest neighbor with Kd-tree search and nontree ensemble models (requires MATLAB Coder) Trading VXX with nearest neighbors prediction An experienced trader knows what behavior to expect from the market based on a set of indicators and their interpretation. The k-NN method is based on recognizing a similar pattern of target file within the historical observed weather data which could be used as a reduction of the target year. com/matlabcentral/fileexchange/19345-efficient-k-nearest Here, the k-Nearest Neighbor Algorithm Pseudo Code is framed using a function kNN() which takes a single test sample or instance, x as argument and returns a 2-D Vector containing the prediction result as the 1st element and the value of k as the 2nd element. 7763/IJMLC.", null, "Heart Disease Prediction Using k-Nearest Neighbor Classifier Based on Handwritten Text Chapter · December 2016 with 78 Reads DOI: 10. Dimensionality reduction is an important step in your data analysis because it can help improve model accuracy and performance, improve interpretability, and prevent overfitting. The prediction for the unknown case is again Default=Y. 3, No.", null, "I followed an example of the MATLAB KNN classifier with 10 fold cross validation, I am lost at the stage of computing the model's performance, Please kindly look at my code below and advice on how K nearest neighbor classifier K nearest neighbor(KNN) is a simple algorithm, which stores all cases and classify new cases based on similarity measure. Mdl = fitcknn(Tbl,formula) returns a k-nearest neighbor classification model based on the input variables in the table Tbl. Use kNNClassify to generate predictions Yp for the 2-class data generated at Section 1. Study the code of function kNNClassify (for quick reference type help kNNClassify).", null, "2. Euclidean distance [y,predict_class] = f_knn(tr,tr_memberships,te,k). Prediction and Control. Apply the KNN algorithm into training set and cross validate it with test set.", null, "I will add a graphical representation for you to understand what is going on there. The k-nearest neighbor technique (k-NN) The k-NN algorithm used in this study was adapted from the var-iant developed byNemes et al. But if u take more than two class then this is multiclass classification. The kNN search technique and kNN-based algorithms are widely used as benchmark learning rules.", null, "X X X (a) 1-nearest neighbor (b) 2-nearest neighbor (c) 3-nearest neighbor . The KNN or k-nearest neighbors algorithm is one of the simplest machine learning algorithms and is an example of instance-based learning, where new data are classified based on stored, labeled instances. K-nearest neighbor algorithm (KNN) is part of supervised learning that has been used in many applications in the field of data mining, statistical pattern recognition and many others. D = Sqrt[(48-33)^2 + (142000-150000)^2] = 8000.", null, "For simplicity, this classifier is called as Knn Classifier. Important thing to note in k-NN algorithm is the that the number of features and the number of classes both don't play a part in determining the value of k in k-NN algorithm. An Excel sheet with both the data and results used in this tutorial can be downloaded by clicking here. Pick a \"reasonable\" k.", null, "k-Nearest Neighbor (k-NN) classifier is a supervised learning algorithm, and it is a lazy learner. The algorithm for the k-nearest neighbor classifier is among the simplest of all machine learning algorithms. 1. I have searched knn classify in mathworks but I am unable to NEAREST NEIGHBOR.", null, "<p> We start by considering the simple and intuitive example of nonparametric methods, nearest neighbor regression: The prediction for a query point is based on the outputs of the most related observations in the training set. It can also be used for regression — output is the value for the object (predicts continuous values). Available distance metrics include Euclidean, Hamming, and Mahalanobis, among others. knnsearch does not save a search object.", null, "KNN is the K parameter. K-Nearest Neighbors • K-NN algorithm does not explicitly compute decision boundaries. 1675-1681, 2013 Statistics and Machine Learning Toolbox provides algorithms and functions for reducing the dimensionality of your data sets. The method is sometimes referred to as “learning by example” because for prediction it looks for the feature k - Nearest Neighbor Classifier.", null, "You may have noticed that it is strange to only use the label of the nearest image when we wish to make a prediction. The boundaries between distinct classes form a Refining a k-Nearest-Neighbor classification. edu. Also learned about the applications using knn algorithm to solve the real world problems.", null, "William H. not knn classification. , amount purchased), and a number of additional predictor variables (age, income, location). 1007/978-81-322-2734-2_6 Returns the k nearest training instances, the k nearest training labels and the respective distances.", null, "A classification model is a mathematical relationship between a set of fingerprints and response variables. In this paper, we applied artificial neural network, k-nearest neighbor and support vector machine algorithms to build model which will be used for prediction of heart disease. Create a k-nearest neighbor classifier for the Fisher iris data, for making the prediction. 1.", null, "In this post you will discover the k-Nearest Neighbors (KNN) algorithm for classification and regression. This dataset is a subset of the dataset proposed by Dr. be slower in Matlab because Matlab performs large-scale matrix arithmetic very f ast, but. I need to implement KNN algorithm to classify my images.", null, "involves data mining technique K-Nearest Neighbor for prediction of temperature and humidity data for a specific region. k-nearest neighbor KNN,K nearest neighbor classification. E. kNN, k Nearest Neighbors Machine Learning Algorithm tutorial.", null, "ClassificationKNN is a nearest-neighbor classification model in which you can alter both the distance metric and the number of nearest neighbors. In this video I've talked about how you can implement kNN or k Nearest Neighbor algorithm in R with the help of an example data set freely available on UCL machine learning repository. Write a script to test the entry-point function. It is supervised because you are trying to classify a point based on the known classification of other points.", null, "Train k-Nearest Neighbor Classifier Abrir script en vivo Train a k -nearest neighbor classifier for Fisher's iris data, where k , the number of nearest neighbors in the predictors, is 5. k-NN is a type of instance-based learning, or lazy learning, where the function is only approximated locally and all the computations are Diagnosis of Diabetes Mellitus using K Nearest Neighbor Algorithm Krati Saxena1, Dr. If you use these functions, please report any bugs or errors to moron@cerege. tree, axis tree, nearest future line and central line .", null, "Nearest Neighbor Classification. according to this, it has only 2 measurements, through which it is calculating the distance to find the nearest neighbour but in my case I have 400 images of 25 X 42, in which 200 are for training and 200 for testing. I have used the above code for image segmentation and extraction but how can we use knn for classification? I need help with the code. It is widely disposable in real-life scenarios since it is That way, we can grab the K nearest neighbors (first K distances), get their associated labels which we store in the targets array, and finally perform a majority vote using a Counter.", null, "A. The K-nearest neighbor classifier offers an alternative Version 11. ¨ Set K to some value ¨ Normalize the attribute values in the range 0 to 1. 2 k-NN algorithm The k-Nearest Neighbor (k-NN) is a simple but effective machine learning algorithm used for classification problems.", null, "Thus a choice of k=11 has an effec­ tive number of parameters of about 2 and is roughly similar in the extent of smoothing to a linear regression fit with two coefficients. Example In general, a k-NN model fits a specific point in the data with the N nearest data points in your training K-nearest-neighbor algorithm implementation in Python from scratch. biomedcentral. 280 98 The k-Nearest Neighbor Algorithm.", null, "For a list of the smoothing kernels that can be used in kernel regression, see SmoothingKernel. 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[ "## Billiard simulation–part 3: collision between two balls\n\nMay 13, 2013 at 1:27 PM\n\n..or more formally: elastic collision of spheres in two dimensions.\n\nLet’s start with a simple case: ball 1 moving with velocity $$(\\bar v_1, \\bar w_2)$$ hitting ball 2 at rest. To make things even easier ball 1 and ball 2 are aligned horizontally at the moment of impact – i.e.  they have the same $$y$$ coordinate:", null, "In our model (at the moment being at least) balls are not spinning, and there is no ball-ball friction, so the force between balls in such a collision is only along the horizontal line connecting their centers. This means that the vertical components of the velocities before and after the collision are the same:\n\n$$\\bar{w}’_1 = \\bar{w}$$\n\n$$\\bar{w}’_2 = 0$$\n\n- where the primed values are the ones after the collision. The horizontal components of the velocities on the other hand are related by the ball-ball coefficient of restitution $$c$$:\n\n$$\\bar{v}’_2 - \\bar{v}’_1 = c(\\bar{v}_1 - \\bar{v}_2) = c\\bar{v}_1$$\n\n($$\\bar{v}_2$$ is zero). The horizontal momentum must be the same before and after the collision:\n\n$$m_1\\bar{v}’_1 + m_2\\bar{v}’_2 = m_1\\bar{v}_1$$\n\n- where $$m_1$$ and $$m_2$$ are the masses of the two balls. Combining these two equation gives:\n\n$$\\bar{v}’_1 = \\frac{m_1 – cm_2}{m_1+m_2}\\bar{v}_1$$\n\n$$\\bar{v}’_2 = \\frac{(1+c)m_1}{m_1+m_2}\\bar{v}_1$$\n\nthat is the result for this simple case: the velocities after the collision in terms of the (known) velocities before the collision.\n\nWhat abut the general case in which both balls move and are not aligned?", null, "This second case can be converted in the simple one with a coordinate transformation: subtract the velocity of the second ball from all velocities – i.e. use the frame of reference of the second ball - and rotate the axis by the angle $$\\alpha$$:\n\n$$\\bar{v} = (v-v_2)\\cos\\alpha + (w-w_2)\\sin\\alpha$$\n\n$$\\bar{w} = -(v-v_2)\\sin\\alpha + (w-w_2)\\cos\\alpha$$\n\nwhere $$(v, w)$$ is an arbitrary velocity and $$(\\bar{v}, \\bar{w})$$ is the corresponding transformed velocity. The angle $$\\alpha$$ is*:\n\n$$\\alpha = \\arctan \\frac{y_1– y_2}{x_1 – x_2}$$\n\nwhere $$(x_1, y_1)$$ and $$(x_2, y_2)$$ are the positions of the two balls.\n\nThe inverse transformation is:\n\n$$v = \\bar{v}\\cos\\alpha - \\bar{w}\\sin\\alpha + v_2$$\n\n$$w = \\bar{v}\\sin\\alpha + \\bar{w}\\cos\\alpha + w_2$$\n\nNow the procedure to solve the general case is: transform the original velocities in their ‘bar’ equivalent; apply the formula of the simple case; apply the inverse transformation to go back to the velocities in the original coordinate system (without ‘bar’). These steps produce the following results:\n\n$$v’_1 = \\frac{1}{m_1+m_2}\\Big[\\big(m_1-m_2(c\\cos^2\\alpha-\\sin^2\\alpha)\\big)(v_1-v_2)-(1+c)m_2\\sin\\alpha\\cos\\alpha(w_1-w_2)\\Big]+v_2$$\n\n$$w’_1 = \\frac{1}{m_1+m_2}\\Big[-(1+c)m_2\\sin\\alpha\\cos\\alpha(v_1-v_2) + \\big(m_1-m_2(c\\sin^2\\alpha-\\cos^2\\alpha)\\big)(w_1-w_2)\\Big]+w_2$$\n\n$$v’_2 = \\frac{(1+c)m_1}{m_1+m_2}\\cos\\alpha\\Big[(v_1-v_2)\\cos\\alpha + (w_1-w_2)\\sin\\alpha\\Big] + v_2$$\n\n$$w’_2 = \\frac{(1+c)m_1}{m_1+m_2}\\sin\\alpha\\Big[(v_1-v_2)\\cos\\alpha + (w_1-w_2)\\sin\\alpha\\Big] + w_2$$\n\nThe first two equations are quite unwieldy, but adding and subtracting $$v_1$$ from the first one and $$w_1$$ from the second one, and then doing some algebra produces:\n\n$$v’_1 = –m_2a\\cos\\alpha+ v_1$$\n\n$$w’_1 = –m_2a\\sin\\alpha+ w_1$$\n\n$$v’_2 = m_1a\\cos\\alpha+ v_2$$\n\n$$w’_2 = m_1a\\sin\\alpha+ w_2$$\n\nwhere\n\n$$a = \\frac{1+c}{m_1+m_2}\\Big[(v_1-v_2)\\cos\\alpha + (w_1-w_2)\\sin\\alpha\\Big]$$\n\nA nice symmetric solution – and correct to boot.\n\nAssuming that all the balls have the same density, their mass is a fixed constant times their radius cubed. In the formulas above the masses appear always as a quotient, so they can be replaced with the balls’ cubed radiuses.\n\nThe final code is this:\n\n /**\n* Updates the velocities of this ball and another one after a collision\n* The coordinate of the balls must be at the collision point.\n* @param otherBall second colliding ball\n* @param restitution coefficient of restitution for a ball-ball collision\n*/\ncollide(otherBall: Ball, restitution: number) {\nvar dx = this.x - otherBall.x;\nvar dy = this.y - otherBall.y;\nvar dv = this.v - otherBall.v;\nvar dw = this.w - otherBall.w;\nvar alpha = Math.atan2(dy, dx);\nvar sinAlpha = Math.sin(alpha);\nvar cosAlpha = Math.cos(alpha);\nvar a = (1 + restitution) / (m1 + m2) * (cosAlpha * dv + sinAlpha * dw);\nthis.v = -m2 * a * cosAlpha + this.v;\nthis.w = -m2 * a * sinAlpha + this.w;\notherBall.v = m1 * a * cosAlpha + otherBall.v;\notherBall.w = m1 * a * sinAlpha + otherBall.w;\n} // collide\n\n(*) That ‘naïve’ formula for $$\\alpha$$ does not work when $$x_1-x_2$$ is zero, nor it handles the various possible combination of signs of the numerator and denominator, but in the code all that is handled by Math.atan2().\n\nPosted in: Physics | Programming", null, "", null, "", null, "" ]

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[ "", null, "Скачать презентацию Queuing Theory Jackson Networks Network Model Consider\n\nb25694d92a4bdc7185ac7b42db5e4f2e.ppt\n\n• Количество слайдов: 24", null, "Queuing Theory Jackson Networks", null, "Network Model Consider a simple 3 stage model where the output of 2 queues becomes the input process for a third Station A Station C Station B", null, "Network Model Station A Station C Station B Proposition 1: rate in = rate out, that is, if l. A and l. B are the input rates for station A and B respectively, then the input rate for station C is l. A+l. B. Proposition 2: exponential inter-arrivals at A and B provide exponential inter-arrivals at station C.", null, "Network Model Station A Station C Station B Instructor Derivation of the minimum of 2 exponentials.", null, "Jackson Network Station 1 1 2 Station j s 1 Station v 1 . . 2 1 2 sv sj", null, "Jackson Network • All external arrivals to each station must follow a Poisson process (exponential inter-arrivals) • All service times must be exponentially distributed • All queues must have unlimited capacity • When a job leaves a station, the probability that it will go to another station is independent of its past history and of the location of any other job 1. Calculate the input arrival rate to each station 2. Treat each station independently as an M/M/s queue", null, "Calculate Arrival Rates", null, "Example Jobs submitted to a computer center must first pass through an input processor before arriving at the central processor. 80% of jobs get passed on the central processor and 20% of jobs are rejected. Of the jobs that pass through the central processor, 60% are returned to the customer and 40% are passed to the printer. Jobs arrive at the station at a rate of 10 per minute. Calculate the arrival rate to each station.", null, "Example. 6 . 2 10 Input . 8 Central . 4 Printer", null, "Example (cont. ) • For the computer center the processing times are 10 seconds for the input processor, 5 seconds for the central processor, and 70 seconds for the printer. Our task is to determine the number of parallel stations (multiple servers) to have at each station to balance workload.", null, "Example 10 Input 8 Central 3. 2 Printer For our initial try, we will solve for s 1 = 2, s 2 = 1, s 3 = 4", null, "10 Input 8 Central 3. 2 Printer", null, "If these numbers are correct, clearly Lq and Wq indicate the bottleneck is at the printer station. We may wish to add a printer if speedy return of printouts is required. Secondarily, overall processing may be increased by adding another input processor.", null, "Job Shop Example • An electronics firm has 3 different products in a job shop environment. The job shop has six different machines with multiple machines at 5 of the 6 stations. Product Order rate Flow 1 30/month ABDF 2 10/month ABEF 3 20/month ACEF Summary information is on the network below.", null, "Job Shop Example Machine B s=2 m = 22 Machine A s=3 m = 25 Machine D s=3 m = 11 Machine E s=2 m = 23 Machine C s=1 m = 29 Machine F s=4 m = 20", null, "Job Shop Example Machine B s=2 m = 22 Machine A s=3 m = 25 Machine D s=3 m = 11 Machine E s=2 m = 23 Machine C s=1 m = 29 Machine F s=4 m = 20", null, "Job Shop Example Machine B s=2 m = 22 Machine A s=3 m = 25 Machine D s=3 m = 11 Machine E s=2 m = 23 Machine C s=1 m = 29 Machine F s=4 m = 20", null, "Job Shop Example Machine B s=2 m = 22 Machine A s=3 m = 25 Machine D s=3 m = 11 Machine E s=2 m = 23 Machine F s=4 m = 20 Machine C s=1 m = 29 Lets calculate metrics for Machine B M/M/2 model with Use formulas in Fig. 16. 5 p. 564 or use charts", null, "", null, "", null, "Repeat for Machines A, C, D, E, F Machine B s=2 m = 22 Machine A s=3 m = 25 Machine D s=3 m = 11 Machine E s=2 m = 23 Machine C s=1 m = 29 Machine F s=4 m = 20", null, "Interesting Application to Manufacturing Note that lead time is just the time in the system which for product 1 which has sequence ABDF is W = total time in system = lead time = WA + WB + WD + WF =. 789 WIP = work in process = parts per month x lead time = 30(. 789) = 23. 67", null, "Repeat for Machines A, C, D, E, F Machine B s=2 m = 22 Machine A s=3 m = 25 Machine D s=3 m = 11 Machine E s=2 m = 23 Machine C s=1 m = 29 Machine F s=4 m = 20", null, "Some Recommendations If lead time is too slow (WIP too high), one possibility is to additional machining to the bottleneck area. This occurs at stations D and B. Note that this assumes the cost of the machines is not a critical part of the decision. This may or may not need to be included in a final recommendation.", null, "" ]

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[ "# Events\n\nPast Event\n\n## Applied Mathematics Colloquium\n\nMarch 10, 2020\n2:45 PM - 3:45 PM\nAmerica/New_York\nMudd Hall, 500 W. 120 St., New York, NY 10027 214\nSpeaker: Barak Sober Phillip Griffiths Assistant Research Professor, Math Department, Duke University Title: The Manifold Moving Least-Squares (Manifold-MLS) Framework: estimating manifolds and reconstructing their atlas from discrete data sets Abstract: Differentiable manifolds are an indispensable ‘language’ in modern physics and mathematics. As such, there is a plethora of analytic tools designed to investigate manifold-based models (e.g., connections, differential forms, curvature tensors, parallel transport, bundles). However, in order to facilitate these tools, one normally assumes access to the manifold’s atlas of charts (i.e., local parametrizations). In recent years, manifold-based modeling has permeated into data analysis as well, usually in order to avoid working in high dimensions. However, in these data-driven models, charts are not accessible and the only information at hand are the samples themselves. As a result, a common practice in Manifold Learning is to project the data into a lower dimensional Euclidean domain, while maintaining some notion of distance (e.g., geodesic or diffusion). In this talk we introduce an alternative approach named the Manifold Moving Least-Squares (Manifold-MLS) that, given a finite set of samples, reconstructs an atlas of charts and provides an approximation of the manifold itself. Under certain (non-restrictive) sampling assumptions, we prove that the Manifold-MLS produces a smooth Riemannian manifold approximating the sampled one, even in case of noisy samples. We show that the approximation converges to the sampled manifold in case the number of samples tends to infinity, and give the exact convergence rates.\n\nAPAM Department\n212-854-4457" ]

[ null ]

[ "", null, "µ IB | Forces\n\n10 quick questions\n\n10 minutes maximum! (can you do it in 5?)\n\n1. When drawing an arrow to show the size of the force of gravity on a falling meteor, which of these images shows the correct placement for the arrow?", null, "2. The force of gravity as shown by the arrow in Q1 can be labelled in many ways. Which of these is likely to marked as incorrect?\n\n• A. weight\n• B. mg\n• C. gravity\n• D. downwards force of gravity from the Earth\n\n3. Which of these diagrams correctly shows the size of the forces on the meteor as it is moving at a very high velocity downwards but slowing down due to air resistance? The meteor has been drawn as a point.", null, "Q4&5. The diagram below shows a stationary block on a slope.\n\n4. Which of the 4 diagrams below correctly shows all the forces acting on the block?", null, "5. In which direction is the resultant force acting in question 4?\n\n• A. Up the slope.\n• B. Down the slope.\n• C. Towards the centre of the Earth.\n• D. There is no resultant force.\n\n6&7. These questions are about friction:\n\n6. The symbol µs in the IB data book refers to the quantity.....\n\n• A. the force of friction.\n• B. the coefficient of static friction.\n• C. the efficiency of friction\n• D. the frictional constant\n\n7. If µd is equal to 0.5, this means that the maximum force produced by friction on a moving object is half the size of....\n\n• A. the weight of the object.\n• B. the driving force moving the object.\n• C. the reaction force of the surface on the object.\n• D. the air resistance on the object.\n\n8-10. A book of mass 1.0 kg rests on a rough horizontal surface with µs= 0.4.", null, "What is the value of the reaction force on the book?\n\n• A. 1.0 N\n• B. 0.4 N\n• C. 10 N\n• D. 4 N\n\n9. What is the maximum frictional force preventing the book moving to the left or right if pushed?\n\n• A. 1.0 N\n• B. 0.4 N\n• C. 10 N\n• D. 4 N\n\n10. The horizontal surface is raised at one end so that the book rests on a slope. It remains stationary. What happens to the sizes of the reaction force and the maximum force of static friction as the surface is lifted at one end?\n\n Reaction force Maximum force of static friction A decreases decreases B decreases increases C increases decreases D increases increases" ]

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[ "# Math in Focus Grade 7 Chapter 7 Lesson 7.3 Answer Key Constructing Triangles\n\nPractice the problems of Math in Focus Grade 7 Workbook Answer Key Chapter 7 Lesson 7.3 Constructing Triangles to score better marks in the exam.\n\n## Math in Focus Grade 7 Course 2 B Chapter 7 Lesson 7.3 Answer Key Constructing Triangles\n\n### Math in Focus Grade 7 Chapter 7 Lesson 7.3 Guided Practice Answer Key\n\nConstruct the triangle from the given information. Use a compass and ruler.\n\nQuestion 1.\nTriangle PQR: PQ = 5.6 cm, QR = 4.5 cm, and PR = 8.2 cm.\n\nThe measurements of the triangle are PQ=5.6cm ,PR=8.2cm and QR=4.5cm.\n\nEplanation:", null, "Construct the triangle from the given information. Use a ruler and compass.\n\nQuestion 2.\nTriangle ABC: BC = 4 cm, m∠ABC = 25°, and m∠ACB = 120°.\nThe measurements of the triangle are PQ=5.6cm ,PR=8.2cm and QR=4.5cm.\n\nExplanation:", null, "Question 3.\nTriangle KLM: KL = 8.2 cm, KM = 6.9 cm, and m∠LKM = 75°.\nThe measurements of the triangle KLM are KL=8.2cm ,KM=6.9cm and the angle LKM=75°.\n\nExplanation:", null, "Construct the triangle from the given information. Use a compass, ruler, and protractor.\n\nQuestion 4.\nTriangle KLM: KL = 7cm, KM = 9 cm, and m∠KLM = 125°.\nThe measurements of the triangle KLM are KL=7cm , KM=9cm and m∠KLM= 125°.\n\nExplanation:", null, "Hands-On Activity\n\nMaterials\n\n• protractor\n• compass\n• ruler\n\nDecide Whether Given Measures Can Be Used To Construct One Triangle, More Than One Triangle. Or No Triangles\n\nWork in pairs.\n\nStep 1.\nTry to construct triangle ABC with AB = 7 cm, BC = 8 cm, and DE = 4.6 cm, EF = 6 cm, and AC = 11 cm.\nThe measurements of the triangle ABC are  AB = 7 cm, BC = 8 cm, and DE = 4.6 cm, EF = 6 cm, and AC = 11 cm.\n\nExplanation:", null, "Step 2.\nTry to construct triangle DEF with DE = 4.6 cm, EF = 6 cm, and DF = 12 cm.\nThe measurements of the triangle DEF are DE = 4.6 cm, EF = 6 cm, and DF = 12 cm.\n\nExplanation:", null, "Step 3.\nTry to construct triangle GHI with GH = 6 cm, HI = 5 cm, and JK = 6 cm, JL = 4.7 cm, and m∠GHI = 50°.\n\nStep 4.\nTry to construct triangle JKL with JK = 6 cm, JL = 4.7 cm, and m∠JKL = 50°.\nThe measurements of the triangle JKL are JK = 6 cm, JL = 4.7 cm, and m∠JKL = 50°.\n\nExplanation:", null, "Step 5.\nTry to construct triangle MNP with MN = 7 cm, m∠MNP = 60°, and m∠PMN = 40°.\nThe measurements of the triangle MNP are MN = 7 cm, m∠MNP = 60°, and m∠PMN = 40°.\n\nExplanation:", null, "Step 6.\nWere there any triangles you could not construct? Were there any triangles that you could construct in more than one way? Explain.\nYes, at step 3 we could not construct any triangle. At step 1 we can construct more than one triangle because the measurements of the triangle ABC are  AB = 7 cm, BC = 8 cm, and DE = 4.6 cm, EF = 6 cm, and AC = 11 cm.\n\nMath Journal\nUse your results to decide whether you can always construct exactly one triangle from the given information. Justify your answer.\n\na) Given three side lengths\n\nb) Given two side lengths and an angle measure\n\nFind the number of triangles that can be constructed. Try constructing the triangles to make your decision.\n\nQuestion 5.\nPQ = 4.8 cm, QR = 5.4 cm, and m∠PQR = 100°.\nThe measurements of the triangle PQR = PQ = 4.8 cm, QR = 5.4 cm, and m∠PQR = 100°.\n\nExplanation:", null, "Question 6.\nAB = 6.2 cm, BC = 4.8 cm, and m∠BAC = 75°.\nThe measurements of the triangle ABC are AB = 6.2 cm, BC = 4.8 cm, and m∠BAC = 75°.\n\nExplanation:", null, "Question 7.\nST = 7.7 cm, SU = 5.2 cm, and m∠STU = 40°.\nThe measurements of the triangle STU are ST = 7.7 cm, SU = 5.2 cm, and m∠STU = 40°.\n\nExplanation:", null, "### Math in Focus Course 2B Practice 7.3 Answer Key\n\nUse the given information to construct each triangle.\n\nQuestion 1.\nIn triangle CDE, CD = 7 cm, DE = 4 cm, and CE = 6.5 cm.\nThe measurements of the triangle CDE , CD = 7 cm, DE = 4 cm, and CE = 6.5 cm.\n\nExplanation:", null, "Question 2.\nIn triangle ABC, BC = 6 cm, m∠ABC = 30°, and m∠ACB = 60°. Find m∠BAC and AC.\nThe measurements of the triangle ABC , BC = 6 cm, m∠ABC = 30°, and m∠ACB = 60°.\nB= 30° and C= 60°\nA=180°-B-C\nA=180°- 30°- 60°\nA=90°.\nAC=3cm.\n\nExplanation:", null, "Question 3.\nIn an equilateral triangle, each side length is 6.5 centimeters long.\nThe measurements of the equilateral triangle , each side length is 6.5 cm.\n\nExplanation:", null, "Question 4.\nIn triangle ABC, AB = 4 cm, AC = 5 cm, and m∠ABC = 40°.\nThe measurements of the triangle ABC, AB = 4 cm, AC = 5 cm, and m∠ABC = 40°.\n\nExplanation:", null, "Question 5.\nIn triangle ABC, AB = 6 cm, BC = 8 cm, and AC = 10 cm. What kind of triangle is triangle ABC? Classify it by both sides and angles.\nThe measurements of the triangle ABC, AB = 6 cm, BC = 8 cm, and AC = 10 cm. The triangle ABC is a right angle triangle. Right angle triangle has 3 sides and it have one angle  90°.\n\nExplanation:", null, "Question 6.\nIn triangle XYZ, XV = XZ = 4 cm and YZ = 5 cm. Find m∠XZY.\nThe measurements of the triangle XYZ, XV = XZ = 4 cm and YZ = 5 cm.\nThe angle of the XZY is 50°.\n\nExplanation:", null, "Question 7.\nTriangle POR has the dimensions shown in the diagram.\n\na) Construct triangle POR.", null, "b) Using a ruler, from your construction, measure the length of $$\\overline{P R}$$.\nUsing a ruler we measure the length of $$\\overline{P R}$$.\nPR ≈ 6.1 cm\n\nc) Find the measures of ∠P and ∠R without using a protractor. Justify your answer.\n△PQR is Isosceles because PQ = QR Therefore the angles P and R we congruent:\nm∠P = m∠R\nFind m∠P and m∠R:\nm∠P + m∠R – m∠Q = 180°\n2m∠P + 100° = 180°\n2m∠P = 180° – 100°\n2m∠P = 80°\nm∠P = m∠R = $$\\frac{80^{\\circ}}{2}$$ = 40°\n\nQuestion 8.\nMath Journal\nIs it possible to construct a triangle PQR in which PQ = 12 cm, PR = 5 cm, and QR = 4cm? Explain.\nWe cannot construct a triangle PQR in which PQ = 12 cm, PR = 5 cm, and QR = 4cm because the lengths of the PR , QR are very small.\n\nExplanation:", null, "Question 9.\nThree triangles have angle measures of 500 and 600. In one triangle, the side included between these angles is 2 centimeters. In the second triangle, the included side length is 3 centimeters, and in the third triangle, the included side length is 4 centimeters.\n\na) Construct the three triangles.", null, "b) In each triangle, what is the measure of the third angle?\nSum of angles of triangle is 180 so the given triangles have angle measures of 50 degree and 60 degree another angle is 70 degree.\n\nc) Using the triangles constructed to help you, what can you deduce about the number of triangles that can be constructed if you are given three angle measures of a triangle but not the measure of any side length?", null, "" ]

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[ "In the transistor circuit analysis, it is generally required to determine the collector current for various collector-emitter voltages. One of the methods can be used to plot the output characteristics and determine the collector current at any desired collector-emitter voltage. However, a more convenient method, known as load line method can be used to solve such problems. As explained later in this section, this method is quite easy and is frequently used in the analysis of transistor applications.\n\nd.c. load line. Consider a common emitter npn transistor circuit shown in Fig. (i) where no signal is applied. Therefore, d.c. conditions prevail in the circuit. The output characteristics of this circuit are shown in Fig. (ii).\n\nThe value of collector-emitter voltage VCE at any time is given by ;\n\nVCE     = VCC – IC RC", null, "As VCC and RC are fixed values, therefore, it is a first degree equation and can be represented by a straight line on the output characteristics. This is known as d.c. load line and determines the locus of VCE      IC points for any given value of RC. To add load line, we need two end points of the straight line. These two points can be located as under :\n\n(i) When the collector current IC = 0, then collector-emitter voltage is maximum and is equal to V cc  i.e\n\nMax. VCE = VCC – IC RC  = VCC          as    (IC = 0)\n\nThis gives the first point B (OB = VCC) on the collector-emitter voltage axis as shown in Fig. (ii).\n\n(ii) When collector-emitter voltage VCE = 0, the collector current is maximum and is equal to VCC /RC i.e.\n\nVCE = VCC – IC RC or\n\n0 = VCC – IC RC\n\nMax. IC = VCC /RC\n\nThis gives the second point A (OA = VCC /RC) on the collector current axis as shown in Fig.  (ii). By joining these two points, d.c. *load line AB is constructed.", null, "Importance. The current (IC) and voltage (VCE) conditions in the transistor circuit are represented by some point on the output characteristics. The same information can be obtained from the load line. Thus when IC is maximum (= VCC /RC), then VCE = 0 as shown in Above Fig. If IC = 0, then VCE is maximum and is equal to VCC. For any other value of collector current say OC, the collector-emitter voltage VCE = OD. It follows, therefore, that load line gives a far more convenient and direct solution to the problem.\n\nNote. If we plot the load line on the output characteristic of the transistor, we can investigate the behaviour of the transistor amplifier. It is because we have the transistor output current and voltage specified in the form of load line equation and the transistor behaviour itself specified implicitly by the output characteristics.\n\nWhy load line ? The resistance RC connected to the device is called load or load resistance for the circuit and, therefore, the line we have just constructed is called the load line." ]

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[ "# Why does line current equals the total apparent power divided by 3 times the phase voltage?\n\nIn this circuit with frequency of 50hz and line to line voltage of 400 V why is the current $I_A = S_t/3V_P$ I don't understand the logic behind since there is one Delta connection, I understand why that formula works for a Star connection but don't for the total of this circuit. The Delta load also has 12,5kw.", null, "• Is $S$ your apparent power? I'm trying to understand your notation. – KingDuken Jun 27 '18 at 20:22\n• @KingDuken it is the total apparent power of the three loads, and Vp = 400/sqrt(3) =230 – Pedro Jun 27 '18 at 20:23\n\n$$S_{total} = S_{Z}+S_{c}+S_{equil}$$\n$$S = 3 V_{phase} I$$\n$$I = \\frac{S_{total}}{3V_{phase}}$$" ]

[ null, "https://i.stack.imgur.com/GMSy8.png", null ]

[ "I have forgotten\n\n•", null, "http://facebook.com/\n•", null, "https://www.google.com/accounts/o8/id\n•", null, "https://me.yahoo.com\n\n# nth_element\n\nSorts according to the nth position", null, "View version details\n\n### Key Facts\n\nGyroscopic Couple: The rate of change of angular momentum (", null, ") =", null, "(In the limit).\n•", null, "= Moment of Inertia.\n•", null, "= Angular velocity\n•", null, "= Angular velocity of precession.\n\nBlaise Pascal (1623-1662) was a French mathematician, physicist, inventor, writer and Catholic philosopher.\n\nLeonhard Euler (1707-1783) was a pioneering Swiss mathematician and physicist.\n\n## Definition\n\nThe nth_element() algorithm is defined in the standard header <algorithm> and in the nonstandard backward-compatibility header <algo.h>.\n\n## Interface\n\n#include <algorithm>\ntemplate < class RandomAccessIterator >\nvoid nth_element(\nRandomAccessIterator first,\nRandomAccessIterator nth,\nRandomAccessIterator last\n);\ntemplate < class RandomAccessIterator, class BinaryPredicate >\nvoid nth_element(\nRandomAccessIterator first,\nRandomAccessIterator nth,\nRandomAccessIterator last,\nBinaryPredicate comp\n);\n\nParameters:\nParameter Description\nfirst A random-access iterator addressing the position of the first element in the range to be partitioned\nlast A random-access iterator addressing the position one past the final element in the range to be partitioned\nnth A random-access iterator addressing the position of element to be correctly ordered on the boundary of the partition\ncomp User-defined predicate function object that defines the comparison criterion to be satisfied by successive elements in the ordering. A binary predicate takes two arguments and returns true when satisfied and false when not satisfied\n\n## Description\n\nNth_element function sorts the elements between the fi rst and the nth element in ascendant order. The elements between the nth element and the last are not sorted, however no element in between the nth and the last is smaller than an element between the first and the nth element.\n\nThe first version compares objects using operator< and the second compares objects using a function object comp.\n\nNone.\n\n## Complexity\n\nThe complexity is linear; performs last - first on average.\n\n### References\n\nExample:\n##### Example - nth_element function\nProblem\nThis program illustrates the use of the STL nth_element() algorithm (default version) to partition a vector of integers of size 12 around its 7th element.\n\nThe ranges on either side of this value may or may not be sorted, but the algorithm does not guarantee this, and you should not expect it.\nWorkings\n#include <iostream>\n#include <vector>\n#include <algorithm>\n\nusing namespace std;\n\nint main()\n{\nint a[] = {10, 2, 6, 11, 9, 3, 4, 12, 8, 7, 1, 5};\nvector<int> v(a, a+12);\ncout <<\"\\nHere are the initial contents of the vector:\\n\";\nfor (vector<int>::size_type i=0; i<v.size(); i++)\ncout <<v.at(i)<<\" \";\n\ncout <<\"\\nNow we make the following call:\";\ncout <<\"\\nnth_element(v.begin(), v.begin()+6, v.end());\";\nnth_element(v.begin(), v.begin()+6, v.end());\n\ncout <<\"\\nAnd here are the contents of the vector partitioned around its 7th element:\\n\";\nfor (vector<int>::size_type i=0; i<v.size(); i++)\ncout<<v.at(i)<<\" \";\n\nreturn 0;\n}\nSolution\nOutput:\n\nHere are the initial contents of the vector:\n10 2 6 11 9 3 4 12 8 7 1 5\n\nNow we make the following call:\nnth_element(v.begin(), v.begin()+6, v.end());\n\nAnd here are the contents of the vector partitioned around its 7th element:\n1 2 3 4 5 6 7 8 9 10 11 12\nReferences" ]

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[ "# Hardness of finding a true or a false assignment into a generic boolean formula?\n\nI read some research that analyzes the hardness of SAT solving in the average case. In fact, for a 3CNF formula if you compute the ratio of clause to variables there is an interval (more or less between 4 and 5) in which solving the formula is hard. But it is easy (between 0 and 4) high probability of satisfiable assignment and high probability of unsatisfiable assignment after ratio 5.\n\nMy question is, what about a generic formula that is not in normal form. We can say something about its hardness?\n\n• What is a generic formula? Do you mean a random formula of some kind, or an arbitrary formula? SAT is believed to be worst-case hard, but for average-case hardness, you will need to explain what you mean by \"average case\". – Yuval Filmus Dec 5 '12 at 19:52\n• sure, with generic formula i mean a random formula of some kind. With average case hardness i say that the formula is hard on the average. taking a random formula it is with high probability hard to solve or easy to solve. – SAT Dec 5 '12 at 20:17\n• @SAT, random formula of some kind is not a definition. The result is about a very particular and natural distribution of formulas. – Kaveh Jan 23 '13 at 5:30\n\n## 2 Answers\n\nYou can always convert your formula or circuit to an equivalent CNF formula of polynomial size.\n\nThe result you mention is only for 3CNF formulas. In general for kCNF-SAT the assumed threshold phenomenon happens on a point depending on $k$, the values you mention are only for 3CNF-SAT.\n\nAlso remember what these result say is w.h.p. in a particular distribution of k-CNF formulas. It doesn't mean that this will hold for all formulas. In fact it is quite easy to come up with formulas that have values mentioned in the range but are easy and also formulas that are outside this range but are hard (think about padding formulas to obtain your desired ration). So given a particular 3CNF formula with some clause ration, you can't say anything about its difficulty (or the time it will take a particular SAT solver to solve it).\n\nIf your question really is about hardness of finding either a true or false assignment to an arbitrary formula, this is always easy. Pick any assignment and it will always either satisfy the formula or not.\n\nIt is only the random instances of SAT that exhibit the phase transition you mention. There is also work that tries to characterize the hardness of an arbitrary formula. For more on this, see my answer to the question Measuring the difficulty of SAT instances. Also, recall that every propositional formula can be converted into an equivalent formula that is in CNF. See Conversion into CNF on Wikipedia for example.\n\n• but if i have a generic formula the operation of converting to SAT is polinomial in space and time? – SAT Dec 5 '12 at 19:37\n• @SAT No, unfortunately not. An exponential blowup of the formula is possible in some cases. – Juho Dec 5 '12 at 20:29\n• We can always introduce new propositional variables to obtain an equivalent polysize CNF formula as is done in reduction from SAT to CNF-SAT, the blow up is only if we don't introduce new variables. – Kaveh Jan 23 '13 at 5:20" ]

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[ "# plot.gafs\n\n0th\n\nPercentile\n\n##### Plot Method for the gafs and safs Classes\n\nPlot the performance values versus search iteration\n\nKeywords\nhplot\n##### Usage\n# S3 method for gafs\nplot(x, metric = x$control$metric[\"external\"],\nestimate = c(\"internal\", \"external\"), output = \"ggplot\", ...)\n##### Arguments\nx\n\nan object of class gafs or safs\n\nmetric\n\nthe measure of performance to plot (e.g. RMSE, accuracy, etc)\n\nestimate\n\nthe type of estimate: either \"internal\" or \"external\"\n\noutput\n\neither \"data\", \"ggplot\" or \"lattice\"\n\noptions passed to xyplot\n\n##### Details\n\nThe mean (averaged over the resamples) is plotted against the search iteration using a scatter plot.\n\nWhen output = \"data\", the unaveraged data are returned with columns for all the performance metrics and the resample indicator.\n\n##### Value\n\nEither a data frame, ggplot object or lattice object\n\ngafs, safs, ggplot, xyplot\n\n• plot.gafs\n• plot.safs\n##### Examples\n# NOT RUN {\n# }\n# NOT RUN {\nset.seed(1)\ntrain_data <- twoClassSim(100, noiseVars = 10)\ntest_data <- twoClassSim(10, noiseVars = 10)\n\n## A short example\nctrl <- safsControl(functions = rfSA,\nmethod = \"cv\",\nnumber = 3)\n\nrf_search <- safs(x = train_data[, -ncol(train_data)],\ny = train_data\\$Class,\niters = 50,\nsafsControl = ctrl)\n\nplot(rf_search)\nplot(rf_search,\noutput = \"lattice\",\nauto.key = list(columns = 2))\n\nplot_data <- plot(rf_search, output = \"data\")\nsummary(plot_data)\n\n# }\n# NOT RUN {\n# }\n\nDocumentation reproduced from package caret, version 6.0-80, License: GPL (>= 2)\n\n### Community examples\n\nLooks like there are no examples yet." ]

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[ "", null, "Multi-objective optimization for dynamic response of the car frame system\n\nYa-hui Wang1\n\n1North China University of Water Resources and Electric Power, Zhengzhou 450011, China\n\n1Corresponding author\n\nJournal of Vibroengineering, Vol. 17, Issue 2, 2015, p. 859-869.\nReceived 6 September 2014; received in revised form 4 November 2014; accepted 21 February 2015; published 31 March 2015\n\nCopyright © 2015 JVE International Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.\n\nAbstract.\n\nModern high-speed structures often have great vibration, noise and dynamic loads. Traditional technology pays more attention to geometric constraint, strength constraint, stability constraint and frequency constraint generally. During the running process of a car, road roughness will cause vibration of the car. When the vibration reaches certain extent, it will not only affect the fatigue life of the car, but also affect the seat comfort and operation stability. In this paper, the optimal solution considering the dynamic response of the car under the dynamic excitation of the road was sought by taking acceleration response as the constraint, the minimum mass and the minimum acceleration response as the optimization objectives. Because the car model is complicated, a hybrid finite element model was built by simplifying the car model to obtain frame, Frequency response analysis was carried out on the car frame to extract mass and acceleration response. Optimization analysis was also carried out on the car frame by means of linear weighted sum method and NCGA method. The results show that both of them can optimize the mass and acceleration of the car frame and can meet the strength requirements.\n\nKeywords: car frame structure, vibration acceleration response, frequency response analysis, multi-objective optimization.\n\n1. Introduction\n\nIn recent years, the appearance of light weight for automobiles has caused the problems of car body noise, vibration and dynamic loads. Improving the dynamic response design level of the car body has become the emphasis in automobile development. The car frame of is the basic environment of the driver. A person’s various comforts are closely related to the car body system. Road roughness excitation has great influence on the vibration comfort of the automobiles. Automobiles have vertical vibration excited by the road roughness during running, and such vibration will make the passengers feel uncomfortable if it reaches certain extent. Therefore, analyzing the problem of dynamic response for the car body is of great practical significance to improving the design quality of automobiles.\n\nFor control of the automobile vibration, on the one hand, it is to reduce the excitation from the road through suspension system. On the other hand, it is to change the mass matrix and the stiffness matrix of the structure by changing the thickness of the car frame plates, as a result the vibration characteristics of the structure are changed. This paper takes the latter method to optimize the car frame.\n\nFor research on the problem of dynamic response for car frame, scientists have carried out abundant works in terms of structural dynamic model and modal analysis. They have achieved valuable theories and achievements. Zheng used the large-scale software SAP.5P to analyze dynamic of the truck frame and proposed to use the modal analysis result to directly evaluate the structural dynamic characteristic. Beermann proposed to simulate the junction of beams and stringers for truck frame by using beams and plates mixed element. Hadad studied how to use the modal analysis result of finite element to modify the frame design. Ding carried out structural strength analysis on a car and found that its stress was large and its strength was not enough. Because of so many components of the car frame, to improve optimization efficiency, in reference , the ratio between torsional displacement and the mass of the car frame was taken as the evaluation index. The thicknesses of some components which were sensitive to the response were selected as the design variables by sensitivity analysis. Main objective method was adopted, with the maximum structure stress of right front wheel under the full loaded the work condition as the objective function, and the maximum structure stresses under other two work conditions were considered as the constraints. However, there are few researches on optimization of the dynamic response for automobiles by means of frequency response analysis. Given the mentioned problems, the car frame was taken as the research object in this paper to carry out acceleration response optimization. Size optimization was carried out on the car frame by linear weighted sum method and NCGA method, respectively. Both methods can reduce the acceleration response and the mass of the structure. Linear weighted sum method can optimize the acceleration response more obviously, while NCGA method can optimize the mass more obviously. The optimization results by both methods can meet the requirements of static strength.\n\n2.1. Finite element model of the car frame\n\nWhen building hybrid finite element model of the car frame, under the premise of complying with the main mechanical characteristics of the structure, the small sized structures such as pinholes, openings, flanging, small ribs and small lug bosses were simplified. The plates were fixed and connected by nodes. Some minor components could be simulated by means of establishing concentrated mass. The head structure was simulated by beam model. Compared with simulation by shell element which needs many elements and nodes, simulation by beam element only needs dozens of elements and nodes. Therefore, it can significantly reduce modeling effort and improve analysis speed. The established finite element model is as shown in Fig. 1.\n\nFig. 1. The hybrid finite element model of the car frame", null, "2.2. Verification of the hybrid finite element model\n\nThe car frame is a very complicated structure. Hence, it is necessary to conduct modal test to verify the reliability of the finite element model in order to guarantee subsequent analysis. Air springs were used to support 4 points of the car frame. Pressure of the air springs was adjusted to 0.5 bar. By adjusting height of the air spring supports, the car frame was kept horizontal.\n\nBy selecting proper manner, position and direction for excitation, a good signal to noise ratio can be obtained. Hence, for the car frame with large structure, multi-point excitation shall be carried out on the parts with big rigidity. In this test, excitation was conducted on 3 points simultaneously by a vibration exciter. Positions and directions of excitation are +$Z$ direction of the right front longitudinal beam, +$Z$ direction of the middle channel end, and +$Z$ direction of the left rear longitudinal beam, as shown in Fig. 2.\n\nInherent frequencies of the top 6 orders, which were obtained by the modal test, are compared with simulation results, as shown in Table 1. It is shown in the table that relative errors between them are controlled within 5 %, which indicates that the finite element model is reliable and can be used in subsequent analysis. Modes of the top 6 orders are extracted, as shown in Fig. 2. It is shown in Fig. 3 that areas with serious vibration mainly appeared at front and rear longitudinal beams.\n\nFig. 2. Position and direction of excitation in modal test", null, "Table 1. Modal comparison of the top 6 orders between experiment and simulation\n\n Order Experiment / Hz Simulation / Hz Relative Error / % 1 15.73 16.49 4.83 2 18.47 18.13 –1.84 3 26.89 25.95 –3.50 4 29.56 30.30 2.50 5 34.87 33.45 –4.07 6 36.12 35.09 –2.85\n\nFig. 3. Modes of the car frame at the top 6 orders", null, "a) 16.49 Hz", null, "b) 16.49 Hz", null, "c) 16.49 Hz", null, "d) 30.30 Hz", null, "e) 33.45 Hz", null, "f) 35.09 Hz\n\n2.3. Frequency response analysis on the car body\n\nFrequency response function describes the Fourier transformation relation between the output response and the excitation. It is a function which the circular frequency is the independent variable. As the inherent characteristic of the structure, it is only related to the mass, stiffness and damping characteristics of the structure, and is unrelated to loads. Frequency response analysis is to calculate the output response of the structure under simple harmonic excitation. Its objective is to acquire the transfer function of the structure [5, 6].\n\nVibration equation of the system:\n\n(1)\n$\\left[M\\right]\\left\\{\\stackrel{¨}{x}\\left(t\\right)\\right\\}+\\left[C\\right]\\left\\{\\stackrel{˙}{x}\\left(t\\right)\\right\\}+\\left[K\\right]\\left\\{x\\left(t\\right)\\right\\}=\\left\\{f\\left(t\\right)\\right\\}.$\n\nThe transformation of the displacement base vector was introduced:\n\n(2)\n$\\left\\{u\\left(t\\right)\\right\\}=\\left[\\mathrm{\\Phi }\\right]\\left\\{q\\left(t\\right)\\right\\}={\\sum }_{i=1}^{n}\\left\\{{\\varphi }_{i}\\right\\}{q}_{i}\\left(t\\right).$\n\nThe significance of such transformation is to regard $\\left\\{u\\left(t\\right)\\right\\}$ as the linear combination of $\\left\\{{\\varphi }_{i}\\right\\}$, i.e., displacement vector $\\left\\{{\\varphi }_{i}\\right\\}$ transforms to $n$-dimensional space with $\\left\\{{\\varphi }_{i}\\right\\}$ as the base vector from the $n$-dimensional space with the node displacement of the finite element system as the base vector. Although this is not geometrically visual, it reflects the contribution of each natural mode of vibration to the system motion, and is referred to as modal coordinate.\n\nSubstitute the displacement under modal coordinate to the motion Eq. (2) of discrete structure, multiply by $\\left[\\mathrm{\\Phi }{\\right]}^{T}$ at both sides. $n$ uncoupled second order ordinary differential equation would be acquired by applying weighting orthogonal conditions. The $i$th order vibration differential equation is:\n\n(3)\n${\\stackrel{¨}{q}}_{i}\\left(t\\right)+{c}_{i}{\\stackrel{˙}{q}}_{i}\\left(t\\right)+{k}_{i}{q}_{i}\\left(t\\right)={f}_{i}\\left(t\\right).$\n\nCarrying out Fourier transform for the mentioned equation to obtain:\n\n(4)\n$\\left({\\omega }_{i}^{2}-{\\omega }^{2}+2j{\\omega }_{i}\\omega \\right){q}_{i}\\left(\\omega \\right)={F}_{i}\\left(\\omega \\right).$\n\nThen, the $i$th order frequency response function is:\n\n(5)\n${H}_{i}\\left(\\omega \\right)=\\frac{{q}_{i}\\left(\\omega \\right)}{{F}_{i}\\left(\\omega \\right)}=\\frac{1}{\\left({\\omega }_{i}^{2}-{\\omega }^{2}+2j{\\omega }_{i}\\omega \\right)}.$\n\nThe total frequency response function of the structure can be expressed as:\n\n(6)\n$H\\left(\\omega \\right)=\\sum _{i=1}^{n}\\frac{{\\varphi }_{i}{\\varphi }_{i}^{T}}{\\left({\\omega }_{i}^{2}-{\\omega }^{2}+2j{\\omega }_{i}\\omega \\right)}.$\n\nThe mentioned equation is the frequency response function of the structure expressed by modal superposition method. In actual application, it doesn’t need to calculate all the modals of the structure. Generally, it only needs to calculate the modals of the first more than ten orders or that in the range of the externally excitation frequency.\n\nFrequency response function can also be acquired by directly carrying out Fourier transform for differential Eq. (1), i.e.:\n\n(7)\n$\\left(K-{\\omega }^{2}M+j\\omega C\\right)X\\left(\\omega \\right)=F\\left(\\omega \\right).$\n\nCorresponding to each excitation frequency $\\omega$, the mentioned equation would become a problem for calculation of static force, and can be solved by the methods of solving static force problems, i. e.:\n\n(8)\n$H\\left(\\omega \\right)=\\frac{X\\left(\\omega \\right)}{F\\left(\\omega \\right)}=\\frac{1}{\\left(K-{\\omega }^{2}M+j\\omega C\\right)}.$\n\nThe car frame in this paper is a big model. It was calculated by modal method as the priority, frequency response analysis was carried out on the car frame in the direction vertical to the road, and the acceleration response in the direction vertical to the road was extracted [7, 8].\n\n3.1. Optimization problem analysis\n\n$x=\\left({x}_{1},...,{x}_{m}{\\right)}^{T}$ is made to express the vector constituted by each variable, where $\\mathrm{m}$indicates the number of the variables. The objective function is $F\\left(x\\right)$, which is required to reach the minimum value. Constraint function consists of equality constraint $H\\left(x\\right)=\\text{0}$ and inequality constraint $G\\left(x\\right)\\le \\text{0}$. And then the optimization problem can be indicated in the form in Eqs. (9)-(12):\n\n(9)\n(10)\n(11)\n(12)\n$x\\subseteq S,$\n\nwhere $S$ indicates the interval of $x$ value.\n\nCompared with single objective optimization problems, multi-objective optimization problem is featured by the following :\n\n1) The sub-objectives in a multi-objective optimization problem are often mutually competitive. Improvement of one objective will often cause the deterioration of another sub-objective(s).\n\n2) A multi-objective optimization problem generally has a group of optimal solutions instead of a single absolute optimal solution. The final optimal solution depends on the decision makers’ understanding for the problem and personal preference.\n\nFor the optimization problem in this paper, the objective is minimum weight, and the constraint is that the acceleration response meets the requirement. And the sizes of the optimization variables should meet the technological requirements.\n\nThere are many ways to solve the mentioned optimization problem. In this paper, it is solved mainly by linear weighted sum method and NCGA method.\n\nThe description of linear weighted sum method in mathematical language is shown in the followed:\n\n(13)\n$\\mathrm{m}\\mathrm{i}\\mathrm{n}{\\sum }_{i=1}^{n}{w}_{i}{f}_{i}\\left(x\\right),$\n(14)\n\nIn the equation, ${w}_{i}$ is the weight coefficient of the sub-objective function. Generally, it is required $\\text{0}<{w}_{i}<\\text{1}$ and ${\\sum }_{i=1}^{n}{w}_{i}=\\text{1}$ .\n\nIn fact, weight coefficient cannot accurately reflect the relative importance degree of each sub-objective. Because the ${f}_{i}\\left(x\\right)$ values of the sub-objectives may be quite different from each other, a zoom coefficient ${s}_{i}$ is often introduced for each sub-objective ${f}_{i}\\left(x\\right)$ to solve such problem. The optimization model shown in the Eq. (13) was improved as follow . ${s}_{i}$ is $1/{f}_{i}\\left({x}^{*}\\right)$:\n\n(15)\n$\\text{min}{\\sum }_{i=1}^{n}{w}_{i}{s}_{i}{f}_{i}\\left(x\\right),$\n(16)\n\nNCGA method not only absorbs the advanced techniques of many other multi-objective genetic algorithms, but also changes the practice of randomly selecting individuals for hybridization in previous genetic algorithms. And the thought of neighborhood hybridization is firstly proposed [11, 12].\n\n3.2. Optimization scheme determination\n\nThe mass and acceleration of the simplified finite element model for the car frame were optimized. ${t}_{1}$, ${t}_{2}$ and ${t}_{3}$ are the thickness of Component 1, Component 2 and Component 3 of the car frame, respectively, which are considered as the optimization variable, as shown in Fig. 1. They contain most mass of the car frame. Constraint condition is that the maximum acceleration response should be less than 500 mm/s2, which can ensure no harmful vibration to the structure and ensure the comfort of the passengers. The optimization objectives are acceleration response and mass . The car frame structure was optimized by means of linear weighted sum method and NCGA method, respectively. Because the optimization process was not included in strength constraint, strength check was required to carry out on the optimal solution after the optimization. And then the strength of the optimized structure was compared with the initial model. The entire optimization flow is as shown in Fig. 4.\n\nFig. 4. Optimization design flow of the car frame", null, "3.3. Test of the road excitation\n\nIt is necessary to test vibration displacement of the car frame on a real road and apply it into the hybrid finite element model. In this way, the car frame can be simulated really. As shown in Fig. 1, the measurement point is arranged at the intersection position of the floor channel and the beam. Test results are shown in Fig. 5.\n\nFig. 5. Vibration displacement of the car frame on the real road", null, "It is shown in Fig. 5 that the vibration displacement fluctuates irregularly when the vehicle is running on a real road. The actual situations can not be simulated if only a sinusoidal signal is applied on the car frame as excitation.\n\n4.1. Linear weighted sum method\n\nThe initial mass of the structure was 0.14 t, and the acceleration response was approximate 400 mm/s2. The mathematical model of the multi-objective problem can be indicated as:\n\n(17)\n$\\mathrm{m}\\mathrm{i}\\mathrm{n}{w}_{1}\\frac{mass}{0.14}+{w}_{2}\\frac{accele}{400}.$\n\nThe range of the weight vector Because the dynamic response characteristics of the structure were emphasized, the weight coefficient of the extreme value for acceleration response was larger than that of the structure mass in the weight vector. Some iteration progress was cut out, as shown in Fig. 6. The changes of acceleration response and mass are as shown in Fig. 7.\n\nFig. 6. Iteration progress of the linear weighted sum method", null, "Fig. 7. Acceleration changes with the mass of the car frame", null, "It can be seen from Fig. 7 that acceleration response is minimum when the total mass is 0.1374 t. And the minimum value of acceleration response is 394.8124 mm/s2. The total mass reduced by 1.4 % when it was compared with the initial structure.\n\nIn order to clearly observe the optimization effect, we extracted the acceleration response contour of the initial and optimization structure under the function of unit sine force, as shown in Fig. 8 and Fig. 9.\n\nIt can be obtained from the comparison that the maximum acceleration response of the initial car frame is 177 mm/s2, while the maximum acceleration response of the optimized car frame is 135 mm/s2. The maximum acceleration response reduces by 23.7 %. The optimization effect is very obvious.\n\nFig. 8. Acceleration response contour of the initial car frame", null, "Fig. 9. Acceleration response contour of the optimized car frame", null, "4.2. NCGA (neighborhood cultivation genetic algorithm)\n\nThe algorithm in optimization module was changed to NCGA in ISIGHT platform, while the other parameters kept unchanged. Some iteration progress was cut out, as shown in Fig. 10. The changes of acceleration response and mass are as shown in Fig. 11.\n\nFig. 10. Iteration progress of the NCGA method", null, "It can be seen from Fig. 11 that acceleration response is minimum when the total mass is 0.1333 t. And the minimum value of acceleration response is 395.8174 mm/s2. The total mass reduced by 4.3 % when it was compared with the initial structure.\n\nIn order to clearly observe the optimization effect, we extracted the acceleration response contour of the optimization structure by NCGA method under the function of unit sine force, as shown in Fig. 12.\n\nIt can be obtained from the comparison between Fig. 8 and Fig. 12 that the maximum acceleration response of the initial car frame is 177 mm/s2, while the maximum acceleration response of the optimized car frame is 137 mm/s2. The maximum acceleration response reduces by 22.5 %. The optimization effect is very obvious.\n\nFig. 11. Acceleration changes with the mass of the car frame", null, "Fig. 12. Acceleration response contour of the optimized car frame", null, "As for iterations, it is as many as possible theoretically. However, for the time-consuming optimization process in this paper, because of its small further optimization space after sufficient repeated iterations, the strategy of exchanging time for the limited optimization effect is unacceptable. Generally, acquiring a group of satisfactory solutions is enough.\n\n4.3. Static strength check\n\nUnder the inertial load of 3G (gravitational acceleration), static analysis was carried out on the car frame. The maximum static stress force of the initial car frame is 155 MPa, and its stress contour is as shown in Fig. 13.\n\nFig. 13. Stress contour of the initial car frame", null, "The maximum static stress force of the optimized car frame by means of linear weighted sum method is 148 MPa, and its stress contour is as shown in Fig. 14. The maximum static stress force of the optimized car frame by means of NCGA method is 145 MPa, and its stress contour is as shown in Fig. 15. The results show that the static stress force completely meets the requirements after optimization, and the static stress force level of the car frame is also improved slightly.\n\nFig. 14. Stress contour of the optimized car frame by the linear weighted sum method", null, "Fig. 15. Stress contour of the optimized car frame by the NCGA method", null, "5. Conclusions\n\nThe optimization of the car frame system in this paper is featured by the following.\n\n1) Hybrid finite element modeling is carried out on the car frame, which simplifies the model to a great extent, thus improving the optimization efficiency. In addition, we carry out on comparison between the test modal simulation one to verify the reliability of the hybrid finite element model. Results show that the model is very reliable to be used for the subsequent analysis.\n\n2) Comparison of the optimal solutions acquired by two algorithms shows that linear weighted sum method has the best vibration reduction effect.\n\n3) Comparison of the optimal solutions acquired by two algorithms shows that the vibration reduction effect of NCGA is slightly inferior to linear weighted sum method, but its weight reduction effect is improved more significantly compared with that of linear weighted sum method. As a result, we should choose a proper method to optimize the car frame according to the actual demand.\n\n4) The optimization result of NCGA is affected by iterations, and the more the iterations are, the more accurate the calculation result will be. However, its latter optimization space is small and time-consuming. Therefore, the researchers only need to acquire a group of satisfactory solutions.\n\nThe two methods in the paper above have successfully decreased the dynamic response of the car frame. Using them to the design of the car frame can not only increase the fatigue life of the car, but also improve the seat comfort and operation stability. How to simplify the frame model further to improve the computational efficiency and propose improved algorithm more efficiently, is the key to the future research.\n\n1. Zheng Z. J. Calculation of natural frequency and vibration mode for vehicle frame. Automotive Engineering, Vol. 2, 1982, p. 41-45. [CrossRef]\n2. Beermann H. J. Static analysis of commercial vehicle frames: a hybrid-finite element analytical. International Journal of Vehicle Design, Vol. 5, 1984, p. 26-52. [CrossRef]\n3. Hadad H., Ramezani A. Finite element model updating of a vehicle chassis frame. Proceeding of the 2004 International Conference on Noise and Vibration Engineering, 2004, p. 1817-1831. [CrossRef]\n4. Ding W. Q., Su R Y., Gui L. J. Multi-Objective Optimization on Bus Structure Based on Optimized Stress. Automotive Technology, 2010. [CrossRef]\n5. Liu M. Research on Optimization Method and Modal Test Analysis of Vehicle Frame. Changan University, 2009. [CrossRef]\n6. Yu F., Lin Y. Vehicle System Dynamics. China Machine Press, 2005. [CrossRef]\n7. Zheng Z. J. Calculation of natural frequencies and mode shapes for vehicle frame. Automotive Engineering, Vol. 2, 1982, p. 41-45. [CrossRef]\n8. Healey A. J., Nathman E., Smith C. C. An analytical and experimental study of automotive dynamics with random roadway inputs. Transactions of the ASME, Vol. 12, 1997, p. 284-292. [CrossRef]\n9. Marler R. T., Arora J. S. Survey of multi-objective optimization methods for engineering. Structural and Multidisciplinary Optimization, Vol. 26, 2004, p. 369-395. [CrossRef]\n10. Kaymaz I., MaMahon C. A. A response surface method based on weighted regression for structural reliablitity analysis. Probabilistic Mechanics, Vol. 20, Issue 1, 2005, p. 11-17. [CrossRef]\n11. Manohar P. Kamat Structural Optimization: Status and Promise. American Institute of Aeronautics and Astronautics, 1993. [CrossRef]\n12. Jenkins W. M. Towards structural optimization via the genetic algorithm. Computer and Structures, Vol. 40, Issue 5, 1991, p. 1321-1327. [CrossRef]\n13. Marler R. T., Arora J. S. Survey of multi-objective optimization methods for engineering. Structural and Multidisciplinary Optimization, Vol. 26, 2004, p. 369-395. [CrossRef]" ]

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[ "# Detecting on which side did the objects collided unity 2d\n\nI have a ball and a rectangle in my game.", null, "The rectangle has a box collider 2d attached to it. How can I calculate or check when the ball hits the top of my collider, when it hits the bottom, left and right, so basically any side of the collider and also a corner of the collider, I have searched over the internet and not one answer that I found helped me into solving my problem. If anyone can help I would appreciate it.\n\n• You may like to look at using the Collision Normal – Kelly Thomas Apr 7 '15 at 16:10\n• I have figured out how to check when the ball hits the top and down of the collider but im having trouble about sides – Fahir M Apr 7 '15 at 19:36\n\nI know this is a bit old, just thought that someone else might find this useful. The transforms of the GameObjects has its anchor point in the center.\n\nI did like this to check. In the circles OnCollisionEnter2D-method:\n\n void OnCollisionEnter2D(Collision2D coll) {\nif (coll.gameObject.tag == \"Block_that_got_hit\") {\nif ((this.transform.position.x - coll.collider.transform.position.x) < 0) {\nprint(\"hit left\");\n} else if ((this.transform.position.x - coll.collider.transform.position.x) > 0) {\nprint(\"hit right\");\n}\n}\n}\n\n\nThings to account for is that this only divide the rectangle into two sections, left and right.\n\nTo get the size of collider called coll you could do: coll.collider.bounds.size.x\n\nFirst, you find their position relative to each-other (a vector subtraction of their positions), normalize that, and then you have the direction from one game object to the other. From there, it's fairly trivial. Just if statements and checks of that direction.\n\nAn untested example:\n\nvoid OnCollision2D(Collision2D col)\n{\nVector3 dir = (col.gameObject.transform.position - gameObject.transform.position).normalized;\n\nif (dir.y > 0)\n{\n// hit top\n}\nelse if (dir.y < 0)\n{\n// hit bottom\n}\n}\n\n• Tried that and its not working :S – Fahir M Apr 7 '15 at 16:02\n• What results are you getting when you run Debug.Log(dir)? – Wolfgang Skyler Apr 7 '15 at 20:57\n• Nvm. Sorry, failure of my brain. That wouldn't work. – Wolfgang Skyler Apr 7 '15 at 21:00\n• you can check if (dir.y > 0){ // hit top} else {// hit bottom} – Seyed Morteza Kamali Apr 19 '17 at 5:56\n\nOne solution:\n\nBuild your rectangle of 4 pieces, and which one registers the collision tells you which side it happened on. If two register, you know it was on a corner.\n\nAnother solution:\n\nUse the relative positions of the two objects and their velocities to figure out where it happened. For example, if the ball is above the rectangle, and the xcoords are almost the same, you know the collision happened on top.\n\nThe velocity is a sanity check. If the ball's y coord is below the rect's y coord, but the velocity indicates the ball was moving down, you know it moved too far in one frame and should have bounced back up first.\n\n• I tried adding 4 colliders as child objects each to register a side, but the problem is when i position them, if i position them to close to each other when the ball hits at the corner sometimes it goes up and sometimes it changes the side, i have experimented a little bit now and i figured out how to register top and bottom, but still having trouble with the sides. – Fahir M Apr 7 '15 at 15:05\n\nI would rather use Raycast than OnCollision2D.\n\nHere is the code.\n\nCircle : no rigidbody 2d and no collider attached. Just having this script.\nBox : box collider 2d attached.\n\nusing UnityEngine;\nusing UnityEngine.EventSystems;\nusing System.Collections;\n\npublic class CircleThing : MonoBehaviour\n{\nVector3 _prevPos, _dirV;\nTransform _transform;\n\nvoid Start() {\n_transform = transform;\n_prevPos = _transform.position;\n}\n\nvoid FixedUpdate() {\nif(_transform.position == _prevPos)\nreturn;\n\n_dirV = _transform.position - _prevPos;\nRaycastHit2D hit = Physics2D.Raycast(_transform.position, _dirV, _radius);\nif (hit.collider != null) {\n//Debug.Log (\"Collided :\" + hit.collider.name + \" / \" + hit.normal);\nif(hit.normal.x != 0f)\n{\nif(hit.normal.x>0f)\nDebug.Log (\"Left Side\");\nelse\nDebug.Log (\"Right Side\");\n}\nelse if(hit.normal.y != 0f)\n{\nif(hit.normal.y>0f)\nDebug.Log (\"Top Side\");\nelse\nDebug.Log (\"Bottom Side\");\n}\n}\n\n_prevPos = _transform.position;\n}\n}\n\n\nYou can use reflection normal to identify collision side.\n\nYou can use contact point so first you check for collision and then you have an if statement to check which side it way eg. Vector3.up, here's an example:\n\npublic class NewBehaviourScript2 : MonoBehaviour {\n\nvoid OnCollisionEnter(Collision other){\n\n//This will print the first point of contact in Vector3\nprint (other.contacts.point);\n\n//if the contact of collision is equal to Vector3.up destroy the collided object\nif (other.contacts .point == Vector3.up) {\n\nDestroy(other.gameObject);\n}\n}\n}" ]

[ null, "https://i.stack.imgur.com/y6BEw.png", null ]

[ "<> use java Realize bubbling , insert , Select equal sort\n\n<> Bubble sort ( optimization )\n\n<>1. thought\n\nTraverse from subscript zero , Two adjacent numbers are compared with each other , Sink the maximum number to the bottom .\n\n<>2. code\npublic void bubble(int[] a){ for (int i = 0; i < a.length - 1; i++) { for (int\nj = 0; j < a.length-1-i; j++) { if(a[j]>a[j+1]) swap(a,j,j+1);// Put the first j And j+1 Value exchange of Subscripts\n} } }\noptimization\npublic void bubble(int[] a){ for (int i = 0; i < a.length - 1; i++) { boolean\ns=false;// set mark for (int j = 0; j < a.length-1-i; j++) { if(a[j]>a[j+1]){\nswap(a,j,j+1); s=true; } } if(!s)break; } }\n<> Select sort\n\n<>1. thought\n\nAssume zero is the minimum value , Then take the zero position and compare it with the following numbers in turn , Swap if greater than . After traversing the array , The first value is the minimum value . Then set position 1 as the minimum value and compare it with the following .\n\n<>2. code\npublic void select(int[] a) { for (int i = 0; i < a.length - 1; i++) { for\n(int j = i + 1; j < a.length; j++) { if (a[i] > a[j]) swap(a, i, j); } } }\n<> Insert sort\n\n<>1. thought\n\nStart with zero as an ordered array , Add the next digit of the array in sequence , The added number is compared with the previous number from front to back , Make it an ordered array . as a Ordered by itself ; Join the next one a, yes a[0:1] Sort , If a<\na Then exchange , After exchange a[0:1] Orderly ; Join next a, take a[0:2] Orderly , Add to the last bit of the array in turn , Ordered array after sorting .\n\n<>2. code\npublic void insert(int[] a) { for (int i = 1; i < a.length; i++) { for (int j\n= i - 1; j >= 0; j--) { if (a[j + 1] < a[j]) swap(a, j + 1, j); } } }\n<> Quick sort （ recursion ）\n\n<>1. thought\n\nTake any one of the objects to be sorted as the benchmark , According to the key size of the object , Divide the whole object sequence into left and right sub sequences . among , All keys in the left subsequence are less than or equal to the key of the reference object ; The keys of all objects in the right subsequence are greater than those of the base object . At this time, the position of the reference object is the final position of the object in the sequence . Then recursively repeat the above method in the left and right subsequences , Until all objects are placed in the corresponding position .\n\n<>2. code\npublic int portion(int[] a, int left, int right) { int tmp = a[left]; while\n(left < right) { while (left < right && a[right] >= tmp) --right; a[left] =\na[right]; while (left < right && a[left] <= tmp) ++left; a[right] = a[left]; }\na[left] = tmp; return left; } public void quickSort(int[] a, int start, int\nend) { int par = portion(a, start, end); if (par > start + 1) quickSort(a,\nstart, par - 1); if (par < end - 1) quickSort(a, par + 1, end); }\n<> Quick sort （ non-recursive ）\n\n<>1. thought\n\nRecursive fast sorting algorithm is automatically implemented by compiler with stack , When the recursion level is deep , It needs to occupy a large process stack space , Danger of process stack overflow . So we can simulate the recursive process with stack , That is, after taking a part from the top of the stack for division each time , Put the starting positions of the new two parts into the stack respectively .\n\n<>2. code\npublic static int partion(int[] a, int low,int high) { int tmp = a[low];\nwhile(low < high) { while(low < high && a[high] >= tmp ) { --high; } if(low >=\nhigh) { break; }else { a[low] = a[high]; } while(low < high && a[low] <=tmp) {\n++low; } if(low >= high) { break; }else { a[high] = a[low]; } } a[low] =tmp;\nreturn low; } public static void QSort(int[] a) { int[] stack = new\nint[a.length]; int top = 0; int low =0; int high = a.length-1; int par\n=partion(a, low, high); if(par > low + 1) { stack[top++] = low; stack[top++] =\npar - 1; } if(par < high - 1) { stack[top++] = par + 1; stack[top++] = high; }\n// Out of stack while(top > 0) { high = stack[--top];// Last stack top++ Yes , So it's used here --top instead of top-- low\n= stack[--top]; par = partion(a,low,high); if(par > low+1) { stack[top++] =\nlow; stack[top++] = par - 1; } if(par < high-1) { stack[top++] = par+1;\nstack[top++] = high; } } }\n<>shell sort （ Insert sort of enlarged version ）\n\n<>1. thought\n\n（shell（） The idea of method ） Take a less than n Integer of d1 As the first increment , Divide all records of the document into d1 Groups . All distances are d1 Records of are placed in the same group . First, carry out direct insertion sorting in each group ;\n（shellSort（） Thought of ） then , Take the second increment d2< d1 Repeat the above grouping and sorting , Up to the increment taken dt=1(dt< dt-l< …< d2<\nd1), That is, all records are placed in the same group until they are directly inserted and sorted .\n\n<>2. code\npublic void shell(int[] a, int gap) { for (int i = gap; i < a.length; i++) {\nfor (int j = i - gap; j >= 0; j = j - gap) { if (a[j + gap] < a[j]) swap(a, j +\ngap, j); } } } public void shellSort(int[] a) { int[] d = {7, 3, 1}; for (int i\n= 0; i < d.length; i++) { shell(a, d[i]); } }\n<> Heap sort\n\n<>1. thought\n\nConstruct the sequence to be sorted into a large top heap , here , The maximum value of the whole sequence is the root node at the top of the heap . Swap it with the last element , At this time, the end is the maximum value . Then the remaining n-1 Elements reconstructed into a heap , This will get n Sub minor value of elements . So repeated , Then we can get an ordered sequence\n\n<>2. code\n// Get the parent node of the last left child private int lastLeftChildrenParent(int size){ return\nsize/2-1; } // Get the left child of the current node private int leftChildren(int i){ return i * 2 + 1; }\npublic void adjust(int[] a, int start, int end) { int tmp = a[start]; for (int\ni = leftChildren(start); i <= end; i = leftChildren(i) ) { if (i < end && a[i]\n< a[i + 1]) i++; if (a[i] > tmp) { a[start] = a[i]; start = i; } else break; }\na[start] = tmp; } public void heapSort(int[] a) { //1. Construct an array into a large root heap for (int i =\nlastLeftChildrenParent(a.length); i >= 0; i--) { adjust(a, i, a.length - 1); }\n//2. Using heap sorting for (int i = 0; i < a.length - 1; i++) { swap(a, 0, a.length - 1 -\ni); adjust(a, 0, a.length - 2 - i); } }\n-----------.\n\n<> Merge sort\n\n<>1. thought\n\nThe basic idea is to divide the array into a.length/2n Groups 2n number , For example, the third line on the left below is the second grouping , Divided 5 Groups , Each group 21\nnumber . Then create a temporary array , Combine two adjacent ones into an ordered group , Put into temporary array . until 2n>=a.length.\n\n<>2. code\npublic static void mergeSort(int[] a) { for (int i = 1; i < a.length; i = i *\n2) { merge(a, i); } } public static void merge(int[] a, int gap) { int start1 =\n0;// Beginning of the first group int end1 = start1 + gap - 1;// End of group 1 int start2 = end1 + 1;// Beginning of the second group int\nend2 = start2 + gap - 1 < a.length - 1 ? start2 + gap - 1 : a.length -\n1;// End of the second group int[] tmpa = new int[a.length];// Temporary array for merging int i = 0; while (start2 <\na.length) {// Adjacent as gap Group of , Using temporary arrays , Merge by two while (start1 <= end1 && start2 <= end2) {\nif (a[start1] < a[start2]) tmpa[i++] = a[start1++]; else tmpa[i++] =\na[start2++]; } while (start1 <= end1) tmpa[i++] =\na[start1++];// If the second group is traversed first , Fill the first group after the temporary array while (start2 <= end2) tmpa[i++] =\na[start2++];// If the first group is traversed first , Fill the second group after the temporary array start1 = end2 + 1; end1 = start1 + gap -\n1; start2 = end1 + 1; end2 = start2 + gap - 1 < a.length - 1 ? start2 + gap - 1\n: a.length - 1;// If there is only the first group at the last time , Not enough for the second group , Exit loop } while (i < a.length) tmpa[i++] =\na[start1++];// Fill in the first group for the last time for(int j = 0;j<a.length;j++) a[j] =\ntmpa[j];// Copy the temporary array to the original array }\n\nTechnology\nDaily Recommendation" ]

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[ "", null, "# Values in the summary table and what they mean\n\nIndividual weights\nThe number of lifts performed in 1 kg steps.\nThe colour band of this load tells you how severe the heaviest lifting task is.\nThe 25th and 75th percentile loads tell you something about how spread out are the loads that are being handled. Half of the loads are between these two values. As the loads get more variable, the difference between them gets bigger.\nThe 25th percentile load tells you something about the lighter loads that are being handled. A quarter of loads weigh less than this, and three-quarters weigh more so it is mid-way between the lightest weight and the median. It's the middle point of the light half of the job.\nThis is total weight handled divided by the total number of lifts. This is what the worker would handle if all the loads weighed the same. The colour band tells you the level of risk of the overall demands of the task.\nIf you arrange all the weights in sequence this is the middle value. It splits the weights into a heavy half and a light half. Like the mean, the colour band of the median tells you the level of risk of the overall task.\nThe most common load (the mode)\nThis is the weight that is handled most often. If this is heavier than the mean or the median then check if you can reduce the number of times that items of this weight are handled. Its colour band tells you the level of risk of handling the most common weight.\nThe 75th and 25th percentile loads tell you something about how spread out are the loads that are being handled. Half of the loads are between these two values. As the loads get more variable, the difference between them gets bigger.\nThe 75th percentile load tells you something about the heavier loads that are being handled. Three-quarters of loads weigh less than this, and one quarter weigh more so it is mid-way between the median and the maximum weight. It's the middle point of the heavy half of the job.\nThe carry factor\nThis takes account of the amount of effort and time spent in carrying loads. It converts the total distance carried into an equivalent number of lifts and adds them to the bar for the mean value. If you don't enter any carry distances then the height of this bar is the same as the mean bar and it will be hidden behind it.\nOverall colour band/score for MAC score sheet\nThis colour band and score are what should be entered into the 'Load weight and lift/carry frequency' line of the MAC score sheet." ]

[ null, "https://www.hse.gov.uk/assets/v4-images/website/print/print-logo.jpg", null ]

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43.242.176.120\n)\n\n => Array\n(\n => 122.161.66.120\n)\n\n => Array\n(\n => 182.70.140.223\n)\n\n => Array\n(\n => 103.201.135.226\n)\n\n => Array\n(\n => 202.47.44.135\n)\n\n => Array\n(\n => 182.179.172.27\n)\n\n => Array\n(\n => 185.22.173.86\n)\n\n => Array\n(\n => 67.205.148.219\n)\n\n => Array\n(\n => 27.58.183.140\n)\n\n => Array\n(\n => 39.42.118.163\n)\n\n => Array\n(\n => 117.5.204.59\n)\n\n => Array\n(\n => 223.182.193.163\n)\n\n => Array\n(\n => 157.37.184.33\n)\n\n => Array\n(\n => 110.37.218.92\n)\n\n => Array\n(\n => 106.215.8.67\n)\n\n => Array\n(\n => 39.42.94.179\n)\n\n => Array\n(\n => 106.51.25.124\n)\n\n => Array\n(\n => 157.42.25.212\n)\n\n => Array\n(\n => 43.247.40.170\n)\n\n => Array\n(\n => 101.50.108.111\n)\n\n => Array\n(\n => 117.102.48.152\n)\n\n => Array\n(\n => 95.142.120.48\n)\n\n => Array\n(\n => 183.81.121.160\n)\n\n => Array\n(\n => 42.111.21.195\n)\n\n => Array\n(\n => 50.7.142.180\n)\n\n => Array\n(\n => 223.130.28.33\n)\n\n => Array\n(\n => 107.161.86.141\n)\n\n => Array\n(\n => 117.203.249.159\n)\n\n => Array\n(\n => 110.225.192.64\n)\n\n => Array\n(\n => 157.37.152.168\n)\n\n => Array\n(\n => 110.39.2.202\n)\n\n => Array\n(\n => 23.106.56.52\n)\n\n => Array\n(\n => 59.150.87.85\n)\n\n => Array\n(\n => 122.162.175.128\n)\n\n => Array\n(\n => 39.40.63.182\n)\n\n => Array\n(\n => 182.190.108.76\n)\n\n => Array\n(\n => 49.36.44.216\n)\n\n => Array\n(\n => 73.105.5.185\n)\n\n => Array\n(\n => 157.33.67.204\n)\n\n => Array\n(\n => 157.37.164.171\n)\n\n => Array\n(\n => 192.119.160.21\n)\n\n => Array\n(\n => 156.146.59.29\n)\n\n => Array\n(\n => 182.190.97.213\n)\n\n => Array\n(\n => 39.53.196.168\n)\n\n => Array\n(\n => 112.196.132.93\n)\n\n => Array\n(\n => 182.189.7.18\n)\n\n => Array\n(\n => 101.53.232.117\n)\n\n => Array\n(\n => 43.242.178.105\n)\n\n => Array\n(\n => 49.145.233.44\n)\n\n => Array\n(\n => 5.107.214.18\n)\n\n => Array\n(\n => 139.5.242.124\n)\n\n => Array\n(\n => 47.29.244.80\n)\n\n => Array\n(\n => 43.242.178.180\n)\n\n => Array\n(\n => 194.110.84.171\n)\n\n => Array\n(\n => 103.68.217.99\n)\n\n => Array\n(\n => 182.182.27.59\n)\n\n => Array\n(\n => 119.152.139.146\n)\n\n => Array\n(\n => 39.37.131.1\n)\n\n => Array\n(\n => 106.210.99.47\n)\n\n => Array\n(\n => 103.225.176.68\n)\n\n => Array\n(\n => 42.111.23.67\n)\n\n => Array\n(\n => 223.225.37.57\n)\n\n => Array\n(\n => 114.79.1.247\n)\n\n => Array\n(\n => 157.42.28.39\n)\n\n => Array\n(\n => 47.15.13.68\n)\n\n => Array\n(\n => 223.230.151.59\n)\n\n => Array\n(\n => 115.186.7.112\n)\n\n => Array\n(\n => 111.92.78.33\n)\n\n => Array\n(\n => 119.160.117.249\n)\n\n => Array\n(\n => 103.150.209.45\n)\n\n => Array\n(\n => 182.189.22.170\n)\n\n => Array\n(\n => 49.144.108.82\n)\n\n => Array\n(\n => 39.49.75.65\n)\n\n => Array\n(\n => 39.52.205.223\n)\n\n => Array\n(\n => 49.48.247.53\n)\n\n => Array\n(\n => 5.149.250.222\n)\n\n => Array\n(\n => 47.15.187.153\n)\n\n => Array\n(\n => 103.70.86.101\n)\n\n => Array\n(\n => 112.196.158.138\n)\n\n => Array\n(\n => 156.241.242.139\n)\n\n => Array\n(\n => 157.33.205.213\n)\n\n => Array\n(\n => 39.53.206.247\n)\n\n => Array\n(\n => 157.45.83.132\n)\n\n => Array\n(\n => 49.36.220.138\n)\n\n => Array\n(\n => 202.47.47.118\n)\n\n => Array\n(\n => 182.185.233.224\n)\n\n => Array\n(\n => 182.189.30.99\n)\n\n => Array\n(\n => 223.233.68.178\n)\n\n => Array\n(\n => 161.35.139.87\n)\n\n => Array\n(\n => 121.46.65.124\n)\n\n => Array\n(\n => 5.195.154.87\n)\n\n => Array\n(\n => 103.46.236.71\n)\n\n => Array\n(\n => 195.114.147.119\n)\n\n => Array\n(\n => 195.85.219.35\n)\n\n => Array\n(\n => 111.119.183.34\n)\n\n => Array\n(\n => 39.34.158.41\n)\n\n => Array\n(\n => 180.178.148.13\n)\n\n => Array\n(\n => 122.161.66.166\n)\n\n => Array\n(\n => 185.233.18.1\n)\n\n => Array\n(\n => 146.196.34.119\n)\n\n => Array\n(\n => 27.6.253.159\n)\n\n => Array\n(\n => 198.8.92.156\n)\n\n => Array\n(\n => 106.206.179.160\n)\n\n => Array\n(\n => 202.164.133.53\n)\n\n => Array\n(\n => 112.196.141.214\n)\n\n => Array\n(\n => 95.135.15.148\n)\n\n => Array\n(\n => 111.92.119.165\n)\n\n => Array\n(\n => 84.17.34.18\n)\n\n => Array\n(\n => 49.36.232.117\n)\n\n => Array\n(\n => 122.180.235.92\n)\n\n => Array\n(\n => 89.187.163.177\n)\n\n => Array\n(\n => 103.217.238.38\n)\n\n => Array\n(\n => 103.163.248.115\n)\n\n => Array\n(\n => 156.146.59.10\n)\n\n => Array\n(\n => 223.233.68.183\n)\n\n => Array\n(\n => 103.12.198.92\n)\n\n => Array\n(\n => 42.111.9.221\n)\n\n => Array\n(\n => 111.92.77.242\n)\n\n => Array\n(\n => 192.142.128.26\n)\n\n => Array\n(\n => 182.69.195.139\n)\n\n => Array\n(\n => 103.209.83.110\n)\n\n => Array\n(\n => 207.244.71.80\n)\n\n => Array\n(\n => 41.140.106.29\n)\n\n => Array\n(\n => 45.118.167.65\n)\n\n => Array\n(\n => 45.118.167.70\n)\n\n => Array\n(\n => 157.37.159.180\n)\n\n => Array\n(\n => 103.217.178.194\n)\n\n => Array\n(\n => 27.255.165.94\n)\n\n => Array\n(\n => 45.133.7.42\n)\n\n => Array\n(\n => 43.230.65.168\n)\n\n => Array\n(\n => 39.53.196.221\n)\n\n => Array\n(\n => 42.111.17.83\n)\n\n => Array\n(\n => 110.39.12.34\n)\n\n => Array\n(\n => 45.118.158.169\n)\n\n => Array\n(\n => 202.142.110.165\n)\n\n => Array\n(\n => 106.201.13.212\n)\n\n => Array\n(\n => 103.211.14.94\n)\n\n => Array\n(\n => 160.202.37.105\n)\n\n => Array\n(\n => 103.99.199.34\n)\n\n => Array\n(\n => 183.83.45.104\n)\n\n => Array\n(\n => 49.36.233.107\n)\n\n => Array\n(\n => 182.68.21.51\n)\n\n => Array\n(\n => 110.227.93.182\n)\n\n => Array\n(\n => 180.178.144.251\n)\n\n => Array\n(\n => 129.0.102.0\n)\n\n => Array\n(\n => 124.253.105.176\n)\n\n => Array\n(\n => 105.156.139.225\n)\n\n => Array\n(\n => 208.117.87.154\n)\n\n => Array\n(\n => 138.68.185.17\n)\n\n => Array\n(\n => 43.247.41.207\n)\n\n => Array\n(\n => 49.156.106.105\n)\n\n => Array\n(\n => 223.238.197.124\n)\n\n => Array\n(\n => 202.47.39.96\n)\n\n => Array\n(\n => 223.226.131.80\n)\n\n => Array\n(\n => 122.161.48.139\n)\n\n => Array\n(\n => 106.201.144.12\n)\n\n => Array\n(\n => 122.178.223.244\n)\n\n => Array\n(\n => 195.181.164.65\n)\n\n => Array\n(\n => 106.195.12.187\n)\n\n => Array\n(\n => 124.253.48.48\n)\n\n => Array\n(\n => 103.140.30.214\n)\n\n => Array\n(\n => 180.178.147.132\n)\n\n => Array\n(\n => 138.197.139.130\n)\n\n => Array\n(\n => 5.254.2.138\n)\n\n => Array\n(\n => 183.81.93.25\n)\n\n => Array\n(\n => 182.70.39.254\n)\n\n => Array\n(\n => 106.223.87.131\n)\n\n => Array\n(\n => 106.203.91.114\n)\n\n => Array\n(\n => 196.70.137.128\n)\n\n => Array\n(\n => 150.242.62.167\n)\n\n => Array\n(\n => 184.170.243.198\n)\n\n => Array\n(\n => 59.89.30.66\n)\n\n => Array\n(\n => 49.156.112.201\n)\n\n => Array\n(\n => 124.29.212.168\n)\n\n => Array\n(\n => 103.204.170.238\n)\n\n => Array\n(\n => 124.253.116.81\n)\n\n => Array\n(\n => 41.248.102.107\n)\n\n => Array\n(\n => 119.160.100.51\n)\n\n => Array\n(\n => 5.254.40.91\n)\n\n => Array\n(\n => 103.149.154.25\n)\n\n => Array\n(\n => 103.70.41.28\n)\n\n)\n```\nGetting there: GratefulSaver's Personal Finance Blog\n << Back to all Blogs Login or Create your own free blog Layout: Blue and Brown (Default) Author's Creation\nHome > Getting there", null, "", null, "", null, "# Getting there\n\nDecember 18th, 2019 at 12:58 pm\n\nAs of Friday, I'll finally be under the \\$2K mark to fully fund my 2019 Roth IRA. I have four months left to contribute \\$1,870.00, which means I'll have to contribute \\$467.50 from January-April. I am now on a mission to make this happen. If for some reason, I cannot cash flow contributions, any remaining balance will have to come out of savings.\n\n### 1 Responses to “Getting there”\n\n1. creditcardfree Says:\n\nGreat goal! I hope you make it.\n\n(Note: If you were logged in, we could automatically fill in these fields for you.)\n Name: * Email: Will not be published. Subscribe: Notify me of additional comments to this entry. URL: Verification: * Please spell out the number 4.  [ Why? ]\n\nvB Code: You can use these tags: [b] [i] [u] [url] [email]" ]

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[ "# kppm\n\n0th\n\nPercentile\n\n##### Fit Cluster or Cox Point Process Model\n\nFit a homogeneous or inhomogeneous cluster process or Cox point process model to a point pattern.\n\nKeywords\nmodels, spatial\n##### Usage\nkppm(X, trend = ~1, clusters = \"Thomas\", covariates = NULL, ...,\nstatistic=\"K\", statargs=list())\n##### Arguments\nX\nPoint pattern (object of class \"ppp\") to which the model should be fitted.\ntrend\nAn Rformula, with no left hand side, specifying the form of the log intensity.\nclusters\nCharacter string determining the cluster model. Partially matched. Options are \"Thomas\", \"MatClust\" and \"LGCP\".\ncovariates\nThe values of any spatial covariates (other than the Cartesian coordinates) required by the model. A named list of pixel images, functions, windows or numeric constants.\n...\nArguments passed to thomas.estK or thomas.estpcf or matclust.estK or\nstatistic\nThe choice of summary statistic: either \"K\" or \"pcf\".\nstatargs\nOptional list of arguments to be used when calculating the summary statistic. See Details.\n##### Details\n\nThis function fits a Cox point process model to the point pattern dataset X. Cox models are suitable for spatially clustered point patterns.\n\nThe model may be either a Poisson cluster process with Poisson clusters, or a more general Cox process. The type of model is determined by the argument clusters. Currently the options are clusters=\"Thomas\" for the Thomas process, clusters=\"MatClust\" for the Matern cluster process, and clusters=\"LGCP\" for the log-Gaussian Cox process.\n\nIf the trend is constant (~1) then the model is homogeneous. The empirical $K$-function of the data is computed, and the parameters of the cluster model are estimated by the method of minimum contrast (matching the theoretical $K$-function of the model to the empirical $K$-function of the data, as explained in mincontrast).\n\nOtherwise, the model is inhomogeneous. The algorithm first estimates the intensity function of the point process, by fitting a Poisson process with log intensity of the form specified by the foTrmula trend. Then the inhomogeneous $K$ function is estimated by Kinhom using this fitted intensity. Finally the parameters of the cluster model are estimated by the method of minimum contrast using the inhomogeneous $K$ function. This two-step estimation procedure is due to Waagepetersen (2007). If statistic=\"pcf\" then instead of using the $K$-function, the algorithm will use the pair correlation function pcf for homogeneous models and the inhomogeneous pair correlation function pcfinhom for inhomogeneous models. In this case, the smoothing parameters of the pair correlation can be controlled using the argument statargs, as shown in the Examples.\n\n##### Value\n\n• An object of class \"kppm\" representing the fitted model. There are methods for printing, plotting, predicting, simulating and updating objects of this class.\n\n##### References\n\nWaagepetersen, R. (2007) An estimating function approach to inference for inhomogeneous Neyman-Scott processes. Biometrics 63, 252--258.\n\nplot.kppm, predict.kppm, simulate.kppm, update.kppm, vcov.kppm, methods.kppm, thomas.estK, matclust.estK, lgcp.estK, thomas.estpcf, matclust.estpcf, lgcp.estpcf, mincontrast, Kest, Kinhom, pcf, pcfinhom, ppm\n\n• kppm\n##### Examples\ndata(redwood)\nkppm(redwood, ~1, \"Thomas\")\nkppm(redwood, ~x, \"MatClust\")\nkppm(redwood, ~x, \"MatClust\", statistic=\"pcf\", statargs=list(stoyan=0.2))\nkppm(redwood, ~1, \"LGCP\", statistic=\"pcf\")\nif(require(RandomFields)) {\nkppm(redwood, ~x, \"LGCP\", statistic=\"pcf\",\ncovmodel=list(model=\"matern\", nu=0.3))\n}\nDocumentation reproduced from package spatstat, version 1.23-5, License: GPL (>= 2)\n\n### Community examples\n\nLooks like there are no examples yet." ]

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[ "Symmetric coupling of angular momenta, quadratic algebras and discrete polynomials  J. Phys.: Conf. Ser. (2014), in press.\n\n# Symmetric coupling of angular momenta, quadratic algebras and discrete polynomials\n\n## Abstract\n\nEigenvalues and eigenfunctions of the volume operator, associated with the symmetric coupling of three angular momentum operators, can be analyzed on the basis of a discrete Schrödinger–like equation which provides a semiclassical Hamiltonian picture of the evolution of a ‘quantum of space’, as shown by the authors in . Emphasis is given here to the formalization in terms of a quadratic symmetry algebra and its automorphism group. This view is related to the Askey scheme, the hierarchical structure which includes all hypergeometric polynomials of one (discrete or continuous) variable. Key tool for this comparative analysis is the duality operation defined on the generators of the quadratic algebra and suitably extended to the various families of overlap functions (generalized recoupling coefficients). These families, recognized as lying at the top level of the Askey scheme, are classified and a few limiting cases are addressed.\n\n## 1 Introduction and a brief review\n\nIn a family of orthogonal polynomials has been introduced based on a three–term recursion relationship which plays the role of a discrete Schrödinger equation describing the action of a ‘volume’ operator. This operator occurs in the symmetric treatment of the quantum few–body problem as well as in spin–network modeling of a quantum of space, as pointed out originally in . In this section a short introduction to the necessary mathematical background will be given, together with a summary of a few significant results found by the authors in . Improved insights into algebraic and analytical aspects of the subject will be provided in the next sections.\n\nThe theory of (re)coupling of eigenstates of three angular momentum operators , , to states of sharp total angular momentum (with projection along the quantization axis) is usually carried out in the setting of ‘binary couplings’ (see , Topic 12 and original references therein). Referring to the ordered triple as above, the admissible schemes are and , respectively. The corresponding eigenvectors are denoted\n\n |j12>:=|(j1j2)j12j3j4m>and|j23>:=|j1(j2j3)j23j4m′>, (1)\n\nwhere small s are labelings of the eigenvalues associated with the angular momentum operators (e.g. , ) running over , in units, and () is the eigenvalue of with in integer steps. Thus the ket vectors above belong to Hilbert spaces representing simultaneous eigenspaces of the two, partially overlapping sets of commuting operators , , , , and (, respectively). The Racah–Wigner symbol is the unitary (actually orthogonal by Condon-–Shortley convention) transformation relating the two sets (1) according to\n\n :=(−1)Φ[(2j12+1)(2j23+1)]1/2{j1j2j12j3j4j23}, (2)\n\nwhere and the weights are the dimensions of the spin– representations of which provide the standard normalization of such a ‘recoupling coefficient’ as encoded in the shorthand notation in the left–hand side. Therefore a basis transform is simply written as while the inverse one is achieved by the transpose (all non–null matrix elements obey the selection rule by Wigner–Eckart theorem). Recall in passing that the symbol in (2) encodes naturally the symmetry of an Euclidean tetrahedron, a fact which is at the basis of the huge amount of literature about ‘spin–network’ models for 3–dimensional discretized quantum gravity and quantum computing flourished in the past two decades (see and references therein).\n\nThe treatment of the ‘symmetric’ coupling scheme for the addition of three angular momenta to give (with projection ) is characterized in terms of a ‘volume’ operator . Unlike what happens with binary coupling schemes, the s appear now to be all on the same footing, indicating that the volume operator can be thought of as acting democratically on either a composite system of four objects with vanishing total angular momentum (a configuration that can be associated with a not necessarily planar quadrilateral vector diagram ), or a system of three objects with total angular momentum (see again , Topic 12, last section, and original references therein). The present scheme is characterized by the six commuting Hermitian operators , , , , and , so that eigenvectors and eigenvalues of are given formally (consistently with the notation used in (1)) as\n\n |k>:=|(j1j2j3)kj4m>withK|k>=λk|k>. (3)\n\nEigenvalues and matrix elements of are naturally found within an imaginary antisymmetric representation based on a three–terms recursion relationship , which can be turned into a real, time–independent Schrödinger equation which governs the dynamics of a ‘quantum of space’ as a function of a discrete variable denoted (see below). This has been achieved in (which can be referred to also for a complete list of previous and related papers) where the introduction of discrete, potential–like functions highlights the surprising crucial role of ‘hidden’ symmetries, first discovered by Regge for the symbols. The Schrödinger equation is discretized with respect to a lattice variable given by the label of the operator which characterizes the first of the binary schemes in (1) and reads\n\n λkΨ(k)ℓ+αℓ+1Ψ(k)ℓ+1+αℓΨ(k)ℓ−1=0withℓ≡j12∈{jmin12,jmin12+1,…,j% max12}, (4)\n\nwhere the matrix elements are expressed in terms of geometric quantities, namely\n\n αℓ=F(ℓ;j1+1/2;j2+1/2)F(ℓ;j3+1/2;j4+1/2)/[(2ℓ+1)(2ℓ−1)]1/2. (5)\n\nHere is the Heron’s formula for the area of a triangle with side lengths and . Thus is proportional to the product of the areas of the two triangles sharing the side of length and forming a quadrilateral of sides and . Such a parameter quadrilateral, together with its Regge–conjugate (see below), is the guiding tool of the combinatorial and geometric analysis, in the asymptotic limit, of the Hamiltonian dynamics governing both tetrahedral and ‘fluttery’ quadrilateral configurations, see sections 2 and 3 of for more details.\n\n## 2 Quadratic symmetry algebras\n\nFollowing [6, 7], the quantum version of a classical dynamical algebra associated with a pair of ‘mutually integrable’ dynamical variables calls into play a triple of linear operators acting on a (suitably defined) Hilbert space with Hermitian and algebraically independent and anti–Hermitian. The request that these generators do fulfill the Jacobi identity constrains the fundamental commutation relations to be of the form ( is the anticommutator)\n\n [K1,K2]=K3[K2,K3]=2RK2K1K2+A1{K1,K2}+A2K22+C1K1+DK2+G1[K3,K1]=2RK1K2K1+A1K21+A2{K1,K2}+C2K2+DK1+G2, (6)\n\nwhere are real parameters (the structure constants) and the right–hand sides of the last two relations contain only Hermitian terms. Such a kind of algebraic structures was actually introduced by Sklyanin and they are called ‘quadratic’ algebras for the obvious reason that the commutators (Poisson brackets in the classical cases) are combinations of quadratic (and linear) terms in each of the generators. Mutual integrability is a sharper requirement with respect to the original formulation, and amounts to look at the symmetry algebra as a dynamical one –where is a constant of the motion for taken as the Hamiltonian operator, as well as the other way around. Further improvements in the the study of classical, quantum and -deformed symmetries along these lines have been provided over the past few decades by a number of authors. Often the admissible structures associated with (6) and listed in the table below are referred to as ‘Zhedanov’s algebras’ in the literature. Note that for completeness the last line includes the two ‘standard’ Lie algebras on three generators (whose commutation relations are by definition linear).\n\nClassification of quadratic algebras\n\n R A1 A2 C&D AW(3) (Askey–Wilson) * * * * R(3) (Racah) 0 * * * H(3) (Hahn) 0 0 * * J(3) (Jacobi) 0 0 * 0 Lie algebras: 0 0 0 * su(2), su(1,1)\n\nThe denominations of the algebras, Askey–Wilson, Racah, …, are strongly reminiscent of the Askey–Wilson scheme of hypergeometric orthogonal polynomials of one (continuous or discrete) variable . This is not accidental: rather, this remark turns out to be crucial in order to recognize the deep connection between algebraic symmetries of (quantum) systems and special function theory in a quite straightforward way. Indeed the ‘overlap functions’ stemming from the analysis of the eigenvalue problems for the operators which generate the quadratic algebras are, under mild conditions, orthogonal families of Wilson, Racah, Hanh, Jacobi, …, Hermite polynomials. In what follows an account of a few technical details is given for the case of the Racah algebra R(3) which corresponds to set in (6).\n\nSuppose that the Hermitian operators and –defined on a separable Hilbert space and possibly depending on a same (finite) set of real parameters– are both ladder operators, namely possess discrete, non–degenerate spectra, and start considering the eigenvalue problem for\n\n K1ψp=χpψp,p=0,1,2,…. (7)\n\nThen it can be easily shown that the operator is tridiagonal in this basis\n\n K2ψp=ap+1ψp+1+apψp−1+bpψp (8)\n\nand, similarly, by exchanging the role of and , one would get\n\n K2ϕs=μsϕs,s=0,1,2,… (9)\n\nand\n\n K1ϕs=cs+1ϕs+1+csϕs−1+dsϕs. (10)\n\nThe (real) matrix coefficients can be evaluated explicitly in terms of the commutation relations (6) and contain also the parameters which the operators may depend on (such parameters are dropped in the present simplified treatment aimed to point out the overall structural properties). Once chosen suitable normalizations for the two sets of eigenbases (7) and (9), it is possible to introduce two families of overlap functions by resorting to the Dirac braket convention (in which for instance stands for the eigenfunction of a system in the position representation)\n\n <ϕs|ψp>≡% and<ψp|ϕs>≡ (11)\n\nwhich are both hypergeometric orthogonal polynomials of one discrete variable (the spectral parameter and respectively) to be identified, up to suitable rearrangements of the hidden parameters, with the Racah polynomial on the top of the Askey scheme .\n\nIn the –eigenbasis the operator satisfies\n\n K3ψp=(χp+1−χp)ap+1ψp+1−(χp−χp−1)apψp−1, (12)\n\nwhere eigenvalues and matrix elements are iteratively evaluated from (7) and (8). has a discrete spectrum found as a solution of\n\n K3φn=νnφn,n=0,1,2,…. (13)\n\nIt is worth noting that in general the diagonalization of cannot be carried out analytically, except in a few cases in which at least the lowest eigenvalues turn out to be representable in closed algebraic forms. The associated families of (normalized) overlap functions are denoted\n\n <φn|ψp>≡and<ψp|φn>≡(n=0,1,2,…;p=0,1,2,…) (14)\n\nand can be shown to be orthogonal (on different suitably defined lattices), each depending on one discrete variable, but in principle they might not be included into the Askey scheme.\nSimilarly, other two families of (normalized) overlap functions associated with the pair can be defined by notation consistency as\n\n <φn|ϕs>≡and<ϕs|φn>≡(n=0,1,2,…;s=0,1,2,…). (15)\n\nA crucial feature of the Racah algebra R(3) and associated overlap functions is the duality property. It relies on the following transformation of the generators\n\n K1⇆K2;K3→−K3 (16)\n\nwhich can be easily shown to represent an automorphism of the Racah algebra R(3). The notion of duality is extended to (all of) the sets of overlap functions introduced above. More precisely\n\n• Under the automorphism (16) the discrete variables of the two hypergeometric families of overlap functions associated with given in (11) and their degrees as polynomials are interchanged. Since in the present case the operator is not called into play, the stronger property of ‘self–duality’ of these families holds true: both of them are recognized as Racah polynomials, as already mentioned above.\n\n• Referring to the families in (14), under the automorphism (16) the discrete spectral variable of the first family, which is orthogonal on the lattice , is turned into the second family, where the variable is and the polynomial degree is given in terms of the labels of the eigenvalues of .\nA similar property is shared by the families associated with the pair given in (15).\n\nMore details on the nature of the automorphism group and on the statements about the overlap functions will be reported in the next section when dealing with a specific ‘realization’ of the Racah algebra.\n\n## 3 Generalized recoupling theory, Regge symmetry and duality\n\nThe realization of the Racah algebra R(3) within the setting of generalized recoupling theory was actually the issue addressed originally in which has inspired further work on quadratic algebras. Combining the definitions and notation of section 2 with those of section 1 it is straightforward to recognize the following correspondence\n\n K1 =J212;K2=J223; K3 =[J212,J223]=−4iJ1⋅(J2×J3)≡−4iK (17)\n\nbetween the abstract ordered set of operators and its realization as .\nThe next step would consist in associating eigenvalue equations and three–term recursion relations of the abstract approach with their realizations in generalized quantum (re)coupling theory. Here we do not enter into much details about this matter since the translation of (8) based on the pair , represents the three–term recursion relation for the coefficient in disguise (see e.g. ). The analysis for the pair , which gives the abstract three–term relation as written in (12) is examined in details in (and references therein) while its symmetrized counterpart is nothing but the discretized Schrödinger–like equation displayed already in (4) .\n\nFocusing on the specific issue regarding the families of solutions of such relationships, one would directly be lead to establish the correspondence\n\n overlap functions⟶binary and symmetric % recoupling coefficients, (18)\n\nwhere the arrow stands for the specific realization (3) of R(3). To achieve this goal in a transparent and consistent way a few more steps are needed, the first one of which consists in establishing suitable notations for all of the recoupling coefficients. The symbol in (2) and the functions in (4) are thus denoted and defined respectively as\n\n ≡<~ℓ|ℓ>andΨ(k)ℓ:=<ℓ|k>. (19)\n\nActually this is not a mere question of notation, since in this way the objects may reveal their ‘double’ meaning as i) quantum mechanical transition amplitudes, namely the square modulus is the probability that a system, prepared in the state , be measured to be in the state ; ii) eigenfunctions of the operator whose quantum number is in in the representation labeled by the eigenvalue of the other operator, namely through the projection onto . The latter interpretation will be under focus in what follows and more details about the correspondence (18) can be worked out by introducing explicitly the (so far ignored) parameters of the problem. Upon replacement of the original (ordered) set of labeling of the four angular momenta forming a quadrilateral according to\n\n (j1,j2,j3,j4)↦(a,b,c,d), (20)\n\nthe functionals are rewritten as\n\n <~ℓ|ℓ>(a,b,c,d)∝{abℓcd~ℓ} andΨ(k)ℓ(a,b,c,d)=<ℓ|k>(a,b,c,d). (21)\n\nRecall that geometrically the first functional is associated with a tetrahedron ( and being a pair of opposite edges) and the second one to a quadrilateral (actually two triangles hinged by one of its diagonal, or ) bounding, so to speak, a portion of volume of amount , the eigenvalue of the volume operator given in (3). In order to select in a convenient way the Hilbert space on which the volume operator acts and all the functionals above can be defined consistently, the role of Regge symmetries, originally introduced for the , is crucial. Such symmetries in their original formulation are recognized as functional relations on the arguments (namely they cannot be derived by interchanging the arguments as happens for the so–called ‘classical’ or tetrahedral symmetries) and read\n\n {abℓcd~ℓ}={s−as−bℓs−cs−d~ℓ}:={a′b′ℓc′d′~ℓ}, (22)\n\nwhere is the semi–perimeter of the parameter quadrilateral and in the last equality the new set is defined. It can be checked that the total number of classical and Regge symmetries is 144, which equals the order of the product permutation group .\n\nDenoting by the smallest value among the eight parameters , it can be shown that a consistent ordering of the other parameters compatible with all the due inequalities is given by . This sort of gauge fixing implies that the whole problem becomes finite–dimensional and workable out for each fixed values of the parameters . Moreover: i) the tetrahedron can be chosen as the reference one, calling its Regge–conjugate; ii) the same thing holds for the quadrilateral denoted and its conjugate . More technical details about this specific parametrization and the denomination Regge–‘conjugate’ (as well as the proof that the volume operators and all quantities in its three–term recursion relation (4) are Regge–invariant) can be found in and respectively.\n\nComing back to the statement regarding the correspondence (18), the remarks above should have made clear that Regge symmetry is strictly related to the duality property of the Racah algebra discussed at the end of section 2. Note that in it had been already recognized that (classical + Regge) symmetries do have the group structure given by , to be identified with the automorphism group of the Racah algebra.\n\n## 4 Classification of discrete polynomial families\n\nIn this section the focus will be on interconnections among the families of discrete orthogonal polynomials in view of the formalization presented in section 2 and summarized there in items i) and ii). This analysis –not addressed elsewhere to our knowledge– is just sketched here, leaving aside a number of technical details that can be found in . The various cases, together with the most significant properties of each family, are summarized in the following table.\n\nFinite families of discrete orthogonal polynomials [  fixed ]\n\n# family orthogonality on lattice eigenvalue degree (related to the variable) related to ∑~ℓ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯<~ℓ|ℓ′><~ℓ|ℓ>=δℓ′ℓ ℓ(ℓ+1) ~ℓ ∑ℓ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯<ℓ|~ℓ′><ℓ|~ℓ>=δ~ℓ′~ℓ ~ℓ(~ℓ+1) ℓ ∑ℓ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯<ℓ|k′><ℓ|k>=δk′k λk ℓ ∑k¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯=δℓ′ℓ ℓ(ℓ+1) k ∑~ℓ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯<~ℓ|k′><~ℓ|k>=δk′k λk ~ℓ ∑k¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯=δ~ℓ′~ℓ ~ℓ(~ℓ+1) k\n\nComparing the notations adopted here –the bar stands for complex conjugation or simply transposition in the real cases– with those of section 2, it is straightforward to recognized that the classes I, II and III are in correspondence with the overlap functions in (11), (14) and (15) (restricted to finite sets by suitable choices of the omitted parameters), respectively.\n\nLooking at the family IA, observe that by the convention chosen for symbols in (2) (and similarly for IB). Thus ‘self–duality’ relations for class I read either way\n\n ∑~ℓ<ℓ′|~ℓ><~ℓ|ℓ>=δℓ′ℓand∑ℓ<~ℓ′|ℓ><ℓ|~ℓ>=δ~ℓ′~ℓ, (23)\n\nonce fulfilled the completeness relations and for the binary coupled eigenbases introduced in (1). Note that the operators associated with class I ( and ) represent a ‘Leonard pair’ so that the associated overlap functions (recoupling coefficients) are necessarily hypergeometric of Racah type . More generally, in connection with the analysis of the other classes, a stringent result holds true: any finite system of orthogonal polynomials whose dual is a finite system of orthogonal polynomials must be (possibly –deformed) Racah or one of its limiting cases which constitute finite systems (refer to for a modern monograph on hypergeometric polynomials in the Askey–Wilson scheme). Indeed here all of the families are consistently defined, for fixed parameters , as finite sets (recall the choice on the ordering discussed in connection with Regge symmetry) but the recognition of classes II and III as belonging to the Askey scheme is certainly not straightforward. (More precisely, the reduction process to specific hypergeometric functions of type would require to find out a closed algebraic form for the sets of eigenvalues of the volume operator for given parameters, a task not yet accomplished.)\n\nFor what concerns duality within class II, a first remark is about the bar operation: is , but the latter, unlike what happens for the , is not necessarily equal to because this property actually depends on the volume operator being Hermitian (imaginary antisymmetric) or real symmetric (see also for plots of the family of eigenfunctions ). Anyway, both options can be included through a suitable notation into the duality relations\n\n ∑ℓ<ℓ|k>=δk′kand∑k<ℓ′|k>=±δℓ′ℓ (24)\n\naccording to the choiche of the representation of . Duality relations in class III are similar to (24), with taking the role of .\n\nTo conclude this general overview on duality relationships, a further remarkable property –transversal with respect to the classes– has to be mentioned, namely\n\n ∑k<~ℓ|k>==±<~ℓ|ℓ>. (25)\n\nSuch a ‘triangular relation’ (and the other ones that can be derived by using the properties of the single classes given above) closely resembles the Racah identity satisfied by three symbols and might be used also to explore a formalization of the whole subject within the general scheme of tensor categories.\n\n## 5 Limiting cases\n\nThe issue of asymptotic (semiclassical) limits of angular momentum functions is of continuous interest in many fields, ranging from special function theory to applied quantum mechanics . Here just a few remarks concerning two limiting cases of families II.A and III.B are sketched.\n\nThe reference model of asymptotics is the well–know limit of the symbol for three large entries (see [16, 10]), , where the latter is the Wigner symbol, the symmetrized version of a Clebsch–Gordan coefficient. The counterpart of this operation in the Askey scheme is achieved by moving one step downwards from top, namely from (Racah) to (Hahn and dual Hahn) hypergeometric families.\n\nA new change of notation is needed which consists in restoring the string for the parameters (see (20)) and in writing down as an array the functions in (21) (equivalently, in family II.A) according to\n\n Unknown environment '% (26)\n\nwhere the vertical bars in front of the last column of this symbol indicate that not all of the entries are constrained by standard triangular inequalities, as happens for the . To address any limit in which (some of) the arguments of the symbols become large –a fact that implies that all of the arguments can be ‘running’– a convenient notation is to substitute capital to small letters. Thus the formal limiting process for the symbol in (26) when the arguments of the lower row become large can be displayed as a generalized coefficient, denoted , related in turn to a generalized dual Hahn polynomial; schematically\n\n {j1j2|ℓJ3J4|Λk}↣(j1j2|ℓJ4−ΛkΛk−J3|J3−J4)↔3j(dual Hahn family). (27)\n\nOn applying a similar procedure to family III.B, and denoting the previous generic argument (playing the role of ), the resulting correspondence would read\n\n {j1j2|λkJ3J4|~L}↣(j1j2|λkJ4−~L~L−J3|J3−J4)↔3j(Hahn family). (28)\n\nA few comments on these results are in order, leaving aside a more careful analysis and most technical details reported in . As already noticed, the symbols in round brackets on the right–hand sides of (27) and (28) are generalized counterparts of coefficients, the arguments in the lower row being interpreted as magnetic quantum numbers. They actually share with standard s a suitable formulation of Regge symmetry and their properties as orthogonal families are inferred from three–term recursion relationships. The latter can in turn be derived as limits of the three–term recursions at the upper level (in particular, the relation for (27) can be quite easily worked out). The motivation for associating dual Hahn and Hahn families respectively is related with the specific lattices these three–term recursion relations are defined on. Thus it is found that the relation for (27) mimics the behavior of the relation of a on a quadratic lattice (), so that it is functionally similar to the standard dual Hahn polynomial family. Conversely, the relation for (28) mimics the behavior of the relation of a on a linear lattice (given by scaling the quantum number ) and thus these functions represent counterparts of the Hahn polynomial family.\n\n## 6 Outlook\n\nFurther developments can be addressed in parallel, from algebraic–analytical and geometric viewpoints. A schematic list of ongoing works (and still open questions) follows:\n\n• improved interpretations of Regge symmetries on the geometric (scissor–congruent tetrahedra ) and algebraic (quaternionic reparametrization ) sides;\n\n• convolution rules for overlap functions (specifically, symmetric recoupling coefficients) of Racah algebra;\n\n• composition rules of collections of quadrilaterals able to provide new classes of integrable quantum systems to be associated with extended quantum geometries;\n\n• –deformed extensions and limiting cases of the dual sets of orthogonal polynomials also in view of applications in quantum chemistry.\n\nIn particular, a systematic study of limiting procedures –to be carried out on recurrence relations, on families of polynomials and possibly directly on the defining relations (6) of the underlying quadratic algebras– seems particularly promising also in view of recent analytical and numerical work on strictly related issues [19, 20, 21, 22].\n\n## Acknowledgments\n\nD M and A M acknowledge partial support from PRIN 2010-2011 Geometrical and analytical theories of finite and infinite dimensional Hamiltonian systems.\n\n## References\n\n### Footnotes\n\n1. J. Phys.: Conf. Ser. (2014), in press.\n\n### References\n\n1. Aquilanti V, Marinelli D and Marzuoli A 2013 Hamiltonian dynamics of a quantum of space: hidden symmetries and spectrum of the volume operator, and discrete orthogonal polynomials J. Phys. A: Math. Theor. 46 175303\n2. Carbone G, Carfora M and Marzuoli A 2002 Quantum states of elementary three–geometry Class. Quantum Grav. 19 3761\n3. Biedenharn L C and Louck J D 1981 The Racah–Wigner Algebra in Quantum Theory (Encyclopedia of Mathematics and its Applications Vol 9) ed G-C Rota (Reading, MA: Addison–Wesley)\n4. Carfora M, Marzuoli A and Rasetti M 2009 Quantum tetrahedra J. Phys. Chem. A 113 15376\n5. Regge T 1959 Symmetry properties of Racah’s coefficients Nuovo Cimento 11 116\n6. Granovskii Ya I, Lutzenko I M and Zhedanov A S 1992 Mutual integrability, quadratic algebras, and dynamical symmetry Ann. Phys. 217 1\n7. Granovskii Ya I and Zhedanov A S 1988 Nature of the symmetry group of the 6j-symbol Sov. Phys. JETP 67 1982\n8. Sklyanin E K 1982 Some algebraic structures connected with the Yang–Baxter equation Funct. Anal. 16 263\n9. Askey R 1975 Ortogonal Polynomials and Special Functions (Philadelphia, PE: SIAM)\n10. Varshalovich D A, Moskalev A N and Khersonskii V K 1988 Quantum Theory of Angular Momentum (Singapore: World Scientific)\n11. Aquilanti V, Haggard H M, Hedeman A, Jeevanjee N, Littlejohn R G and Liang Y 2012 Semiclassical mechanics of the Wigner 6j-symbol J. Phys. A: Math. Theor. 45 065209\n12. Marinelli D 2013 Single and Collective Dynamics of Discretized Geometries PhD Thesis (Pavia: University Press)\n13. Leonard D A 1982 Orthogonal polynomials, duality and association schemes SIAM J. Math. Analys. 13 656\n14. Koekoek R, Lesky P A and Swarttouw R F 2010 Hypergeometric Orthogonal Polynomials and Their q-Analogues (Heidelberg Dordrecht London New York: Springer)\n15. Ragni M, Bitencourt A C P, Da S Ferreira C, Aquilanti V, Anderson R W and Littlejohn R G 2009 Exact computation and asymptotic approximations of 6j symbols: illustration of their semiclassical limits Int. J. Quantum Chem. 110 731\n16. Ponzano G and Regge T 1968 Semiclassical limit of Racah coefficients in Spectroscopic and Group Theoretical Methods in Physics ed F Bloch et al (Amsterdam: North–Holland) p 1\n17. Regge T 1958 Symmetry properties of Clebsch–Gordan’s coefficients Nuovo Cimento 10 544\n18. Roberts J 1999 Classical 6j-symbol and the tetrahedron Geom. Topology 3 21\n19. Bitencourt A C P, Marzuoli A, Ragni M, Anderson R W and Aquilanti V 2012 Exact and asymptotic computations of elementary spin networks: classification of the quantum–classical boundaries Lect. Notes Comput. Science 7333 Part I ed B Murgante et al (Berlin Heidelberg: Springer–Verlag) p 723\n20. Anderson R W, Aquilanti V, Bitencourt A C P, Marinelli D and Ragni M 2013 The screen representation of spin networks: 2D recurrence, eigenvalue equation for 6j-symbols, geometric interpretation and Hamiltonian dynamics Lect. Notes Comput. Science 7972 (Berlin Heidelberg: Springer–Verlag) p 46\n21. Ragni M, Littlejohn R G, Bitencourt A C P, Aquilanti V and Anderson R W 2013 The screen representation of spin networks: images of 6j-symbols and semiclassical features Lect. Notes Comput. Science 7972 (Berlin Heidelberg: Springer–Verlag) p 60\n22. Calderini D, Coletti C and Aquilanti V 2013 Continuous and discrete algorithms in quantum chemistry: polynomial sets, spin networks and Strumian orbitals Lect. Notes Comput. Science 7972 (Berlin Heidelberg: Springer–Verlag) p 32\nComments 0\nYou are adding the first comment!\nHow to quickly get a good reply:\n• Give credit where it’s due by listing out the positive aspects of a paper before getting into which changes should be made.\n• Be specific in your critique, and provide supporting evidence with appropriate references to substantiate general statements.\n• Your comment should inspire ideas to flow and help the author improves the paper.\n\nThe better we are at sharing our knowledge with each other, the faster we move forward.\nThe feedback must be of minimum 40 characters and the title a minimum of 5 characters", null, "Loading ...\n102505", null, "You are asking your first question!\nHow to quickly get a good answer:\n• Keep your question short and to the point\n• Check for grammar or spelling errors.\n• Phrase it like a question", null, "Test\nTest description" ]

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[ "# Simplify the following Boolean equations.\n\n#### audreyeckman\n\nJoined Jan 7, 2016\n8\ni. Simplify the following Boolean equations.\n\nii. Sketch a reasonably simple combinational circuit implementing the simplified equation.\n\niii. Compare the numbers of literals and operators versus the numbers of gates, nets, and pins in the schematic diagrams\n\nA. a′bc′ + a′b′d + a′b′cd′ + bc′d + acd + abcd′ + ac′d\n\nSo far, I have gotten this. Does this seem correct? I am unsure how to sketch the circuit...can someone please help with this?\n\ni.\n\n= a’bc’(d + d’) + a’b’(c + c’)d + a’b’cd’ + (a + a’)bc’d + a(b + b’)cd + abcd’ + a(b + b’)c’d\n\n= a’bc’d + a’bc’d’ + a’b’cd + a’b’c’d + a’b’cd’ + abc’d + a’bc’d + abcd + ab’cd + abcd’ + abc’d + ab’c’d\n\n= a’bc’d + a’bc’d’ + a’b’cd + a’b’c’d + a’b’cd’ + abc’d + abcd + ab’cd + abcd’ + ab’c’d\n\n#### shteii01\n\nJoined Feb 19, 2010\n4,644\nYou started with 7 pieces, your \"solution\" has 10 pieces. You just made things more complicated. Which is opposite of: simplify.\n\nWhat techniques to simplify Boolean equations do you know?\n\n#### WBahn\n\nJoined Mar 31, 2012\n26,398\ni. Simplify the following Boolean equations.\n\nii. Sketch a reasonably simple combinational circuit implementing the simplified equation.\n\niii. Compare the numbers of literals and operators versus the numbers of gates, nets, and pins in the schematic diagrams\n\nA. a′bc′ + a′b′d + a′b′cd′ + bc′d + acd + abcd′ + ac′d\n\nSo far, I have gotten this. Does this seem correct? I am unsure how to sketch the circuit...can someone please help with this?\n\ni.\n\n= a’bc’(d + d’) + a’b’(c + c’)d + a’b’cd’ + (a + a’)bc’d + a(b + b’)cd + abcd’ + a(b + b’)c’d\n\n= a’bc’d + a’bc’d’ + a’b’cd + a’b’c’d + a’b’cd’ + abc’d + a’bc’d + abcd + ab’cd + abcd’ + abc’d + ab’c’d\n\n= a’bc’d + a’bc’d’ + a’b’cd + a’b’c’d + a’b’cd’ + abc’d + abcd + ab’cd + abcd’ + ab’c’d\nIt appears you have tried to convert the given expression into the canonical sum-of-products form, which is generally NOT considered \"simplified\". Though note that the problem gives no metric by which to determine which of two expressions is \"simpler\", though it does at least as for comparisons.\n\nAs for how to implement a Boolean expression in a circuit, do you know how to implement the following:\n\nA', AB, A+B\n\nusing a NOT, AND, and OR gate respectively?\n\nIf so, then you have all the building blocks, unless using XOR is an option.\n\n#### audreyeckman\n\nJoined Jan 7, 2016\n8\nI am in the first week of my CSE 140 course so this is all new to me.\n\nI am doing this over and attempting to use Shannon's expansion:\n\nShannon’s expansion\n\nLet f(a,b,c,d) = a′bc′ + a′b′d + a′b′cd′ + bc′d + acd + abcd′ + ac′d\n\nf(1,b,c,d) = 0bc’ + 0b’d + 0b’cd’ + bc’d + 1cd + 1bcd’ + 1c’d\n= bc’d + cd + bcd’ + c’d\n= d(c’ + c) + b(c’d + cd’)\n= c’d(1 + b) + cd + bcd’\n= c’d + cd + bcd’\n\nf(0,b,c,d) = 1bc’ + 1b’d + 1b’cd’ + bc’d + 0cd + 0bcd’ + 0c’d\n= bc’ + b’d + b’cd’ + bc’d\n= bc’(1 + d) + b’d + b’cd’\n= bc’ + b’d + b’cd’\n\nApply Shannon’s expansion:\nLHS = af(1,b,c,d)+ a’f(0,b,c,d)\n= ac’d + acd + abcd’ + a’bc’ + a’b’d + a’b’cd’\n\nHow does this look so far?\n\n#### Kermit2\n\nJoined Feb 5, 2010\n4,162\nLook again at the 4th line down from the sentence SHANNON'S EXPANSION. You dropped a term.\n\n•", null, "audreyeckman\n\n#### audreyeckman\n\nJoined Jan 7, 2016\n8\nWoops I had a strikethrough on that line in my word doc.. so it shouldn't be there at all.. it should be like this\n\nLet f(a,b,c,d) = a′bc′ + a′b′d + a′b′cd′ + bc′d + acd + abcd′ + ac′d\n\nf(1,b,c,d) = 0bc’ + 0b’d + 0b’cd’ + bc’d + 1cd + 1bcd’ + 1c’d\n= bc’d + cd + bcd’ + c’d\n\n= c’d(1 + b) + cd + bcd’\n= c’d + cd + bcd’\n\nf(0,b,c,d) = 1bc’ + 1b’d + 1b’cd’ + bc’d + 0cd + 0bcd’ + 0c’d\n= bc’ + b’d + b’cd’ + bc’d\n= bc’(1 + d) + b’d + b’cd’\n= bc’ + b’d + b’cd’\n\nApply Shannon’s expansion:\nLHS = af(1,b,c,d)+ a’f(0,b,c,d)\n= ac’d + acd + abcd’ + a’bc’ + a’b’d + a’b’cd’​\n\n#### audreyeckman\n\nJoined Jan 7, 2016\n8\nDo I just continue applying shannon's expansion for other terms like c' to simplify more?\n\n#### Kermit2\n\nJoined Feb 5, 2010\n4,162\nYes.\n\nIF it results in a more simplified form.\n\n#### RBR1317\n\nJoined Nov 13, 2010\n690\nI plotted the original Boolean function directly onto a Karnaugh map in order to track the progress of minimization. Note that each 4-variable term maps to one square on the K-map, while each 3-variable term maps to two squares, etc. (Some of the terms will overlap in a square because of logical redundancies.) The current state of your minimization is shown in red.", null, "•", null, "audreyeckman\n\n#### Glenn Holland\n\nJoined Dec 26, 2014\n705\nI would use \"Demorgan's Theorem\" instead of a Karnaugh Map to simplify it.\n\nIf there is an inversion bar over an operator, remove only the bar above operator, then change the operator from AND to OR or vice versa.\n\n#### shteii01\n\nJoined Feb 19, 2010\n4,644\nI plotted the original Boolean function directly onto a Karnaugh map in order to track the progress of minimization. Note that each 4-variable term maps to one square on the K-map, while each 3-variable term maps to two squares, etc. (Some of the terms will overlap in a square because of logical redundancies.) The current state of your minimization is shown in red.\nView attachment 98248\nI am with Glenn, I don't think OP was taught Karnaugh Map yet. So the OP supposed to use Boolean Algebra rules. At least that is my understanding of the situation.\n\n#### RBR1317\n\nJoined Nov 13, 2010\n690\nSo the OP supposed to use Boolean Algebra rules.\nNote that the Karnaugh map was not suggested as the method for solution, merely as an aid to track progress, possibly as an indicator where further application of Boolean Algebra rules will lead to simplification.\n\n#### WBahn\n\nJoined Mar 31, 2012\n26,398\nBut it can only serve that purpose if the TS understands what a Karnaugh map is and how to use it.\n\n#### RBR1317\n\nJoined Nov 13, 2010\n690\n...if the TS understands...\nQuite so. But don't be too quick to assume what a TS is not capable of understanding. Writing/manipulating a K-map can be difficult, but reading one can be fairly easy and possibly learned with nothing more than a good example. I would hope that I provided a good example, but if not, this won't be the first wasted effort that led nowhere." ]

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[ "", null, "", null, "Question\n\n# A truck travelled the first one-third of the distance d at a speed of 10 kmh−1, the second one-third of the distance at a speed of 12 kmh−1 and the last one-third of the distance at a speed of 20 kmh−1. The average speed of the truck is approximately equal to (in kmh−1)10131517\n\nSolution\n\n## The correct option is B 13Using   speed= distance travelledtime taken Time taken to travel first one-third of the distance =d310 Time taken to travel second one-third of the distance  =d312 Time taken to travel last one-third of the distance =d320 ⇒Average speed=d3+d3+d3d310+d312+d320 =dd30+d36+d60=36028=12.8 km/h≈13 km/h", null, "", null, "Suggest corrections", null, "", null, "", null, "" ]

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[ "# Java Program for Reversal algorithm for array rotation\n\nWrite a function rotate(arr[], d, n) that rotates arr[] of size n by d elements.\n\nExample :\n\n```Input : arr[] = [1, 2, 3, 4, 5, 6, 7]\nd = 2\nOutput : arr[] = [3, 4, 5, 6, 7, 1, 2]\n```", null, "Rotation of the above array by 2 will make array", null, "## Recommended: Please solve it on “PRACTICE ” first, before moving on to the solution.\n\nAlgorithm :\n\n```rotate(arr[], d, n)\nreverse(arr[], 1, d) ;\nreverse(arr[], d + 1, n);\nreverse(arr[], 1, n);\n```\n\nLet AB are the two parts of the input array where A = arr[0..d-1] and B = arr[d..n-1]. The idea of the algorithm is :\n\n• Reverse A to get ArB, where Ar is reverse of A.\n• Reverse B to get ArBr, where Br is reverse of B.\n• Reverse all to get (ArBr) r = BA.\n\nExample :\nLet the array be arr[] = [1, 2, 3, 4, 5, 6, 7], d =2 and n = 7\nA = [1, 2] and B = [3, 4, 5, 6, 7]\n\n• Reverse A, we get ArB = [2, 1, 3, 4, 5, 6, 7]\n• Reverse B, we get ArBr = [2, 1, 7, 6, 5, 4, 3]\n• Reverse all, we get (ArBr)r = [3, 4, 5, 6, 7, 1, 2]\n\nBelow is the Java implementation of the above approach:\n\n `// Java program for reversal algorithm of array rotation ` `import` `java.io.*; ` ` `  `class` `LeftRotate { ` `    ``/* Function to left rotate arr[] of size n by d */` `    ``static` `void` `leftRotate(``int` `arr[], ``int` `d) ` `    ``{ ` `        ``int` `n = arr.length; ` `        ``rvereseArray(arr, ``0``, d - ``1``); ` `        ``rvereseArray(arr, d, n - ``1``); ` `        ``rvereseArray(arr, ``0``, n - ``1``); ` `    ``} ` ` `  `    ``/*Function to reverse arr[] from index start to end*/` `    ``static` `void` `rvereseArray(``int` `arr[], ``int` `start, ``int` `end) ` `    ``{ ` `        ``int` `temp; ` `        ``while` `(start < end) { ` `            ``temp = arr[start]; ` `            ``arr[start] = arr[end]; ` `            ``arr[end] = temp; ` `            ``start++; ` `            ``end--; ` `        ``} ` `    ``} ` ` `  `    ``/*UTILITY FUNCTIONS*/` `    ``/* function to print an array */` `    ``static` `void` `printArray(``int` `arr[]) ` `    ``{ ` `        ``for` `(``int` `i = ``0``; i < arr.length; i++) ` `            ``System.out.print(arr[i] + ``\" \"``); ` `    ``} ` ` `  `    ``/* Driver program to test above functions */` `    ``public` `static` `void` `main(String[] args) ` `    ``{ ` `        ``int` `arr[] = { ``1``, ``2``, ``3``, ``4``, ``5``, ``6``, ``7` `}; ` `        ``leftRotate(arr, ``2``); ``// Rotate array by 2 ` `        ``printArray(arr); ` `    ``} ` `} ` `/*This code is contributed by Devesh Agrawal*/`\n\nOutput:\n\n```3 4 5 6 7 1 2\n```\n\nTime Complexity: O(n)\n\nPlease refer complete article on Reversal algorithm for array rotation for more details!\n\nMy Personal Notes arrow_drop_up\n\nArticle Tags :\nPractice Tags :\n\nBe the First to upvote.\n\nPlease write to us at [email protected] to report any issue with the above content." ]

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[ "# What is the slope of the line perpendicular to y=13/5x-3 ?\n\nDec 21, 2015\n\n$- \\frac{5}{13}$\n\n#### Explanation:\n\nThe slope of any line perpendicular to a line of slope $m$ is $- \\frac{1}{m}$\n\nIn our example, the equation is in slope intercept form, so the slope is easily read as the coefficient of $x$, namely $\\frac{13}{5}$.\n\nHence the slope of any line perpendicular to this line is:\n\n$- \\frac{1}{\\frac{13}{5}} = - \\frac{5}{13}$" ]

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[ "# Use Newton's method to find the second and third approximation of a root of x3+x+3=0 starting with x1=−1 as the initial approximation.   The second approximation is x2 =   The third approximation is x3\n\nQuestion\n\nUse Newton's method to find the second and third approximation of a root of\n\nx3+x+3=0\n\nstarting with x1=−1 as the initial approximation.\n\n The second approximation is x2 = The third approximation is x3 =\n\n### Want to see this answer and more?\n\nExperts are waiting 24/7 to provide step-by-step solutions in as fast as 30 minutes!*\n\n*Response times may vary by subject and question complexity. Median response time is 34 minutes for paid subscribers and may be longer for promotional offers.\nTagged in\nMath\nCalculus\n\n### Other", null, "" ]

[ null, "https://www.bartleby.com/static/bartleby-logo-tm-tag-inverted.svg", null ]

[ "SHARE\n\nThis post is, once again, a summary of a longer post authored by me on my own blog. My blog covers a lot of areas, including Vedic Mathematics. If you are interested in reading my thoughts on other topics, please feel free to visit my blog and post comments on the other articles you find there also! Thank you!\n\nIn the previous lesson, we learned the basics of the Vedic Duplex method for finding the square root of a number. We will expand on the methodology in this lesson and deal with some special cases we might encounter during our application of the Vedic duplex method for finding square roots of numbers.\n\nFor a refresher on the Vedic Duplex method, with the square root calculation illustrated for a couple of uncomplicated examples, please read the full lesson here.\n\nThe first complication we are likely to encounter when using the duplex method is that sometimes, the quotient might become larger than 9. The solution to this problem is quite simple: limit the quotient to 9 and increase the remainder as necessary to compensate for the reduced quotient.\n\nTo illustrate this, consider the calculation of the square root of 36481. Since the number, if 5 digits long, we separate out the first digit from the rest of the digits in preparation for the application of the duplex method. We then identify that the first digit, 3, is larger than 1^2 = 1, but smaller than 2^2 = 4. Therefore, the first number on the answer row becomes 1, and our divisor becomes twice of that, which is 2. Our first remainder becomes 3 – 1 = 2, and therefore, our first gross and net dividends become 26. This is illustrated in the figure below:\n\n```•|3: 6 4 8 1\n2|1:2\nG| :26\nN| :26\n-------------\n•|1:```\n\nWe now notice that our divisor, 2, can go into our net dividend, 26, 13 times with no remainder. But in the duplex method, we always restrict our quotients to be single digits. In other words, we add numbers to the answer row one digit at a time. Because of this, we put down 9 on the answer row as the quotient, and put down 8 as our next remainder (remember that 9*2 + 8 = 26). This then gives us a gross dividend of 84, and a net remainder of 84 – the duplex of 9 (which is 81) = 3. This is shown in the figure below:\n\n```•|3: 6 4 8 1\n2|1:2 8\nG| :2684\nN| :2603\n-------------\n•|1: 9```\n\nAt this point, our quotient becomes 1 and we get a remainder of 1, making our gross dividend 18 and our net dividend = gross dividend – duplex of 91 (which is 2x9x1 = 18) = 0. This is shown below:\n\n```•|3: 6 4 8 1\n2|1:2 8 1\nG| :268418\nN| :260300\n-------------\n•|1: 9 1```\n\nOur next quotient then becomes zero, and so does our next remainder. We get a gross dividend of 01, and a net dividend of 1 – duplex of 910 (which is equal to 1) = 0. Thus our last quotient again becomes zero, and we are left with a remainder of zero. Since there are no more digits in the square, the procedure is complete. This is shown in the figure below:\n\n```•|3: 6 4 8 1\n2|1:2 8 1 0\nG| :26841801\nN| :26030000\n-------------\n•|1: 9 1 0 0```\n\nOur answer line consists of 19100. Since the square has 5 digits before the decimal point, the square root has to contain 3 digits before the decimal point. Thus our square root is 191.00.\n\nFor more examples on how to deal with limiting the quotient to 9 when using the duplex method, please read the full lesson here.\n\nThus, our first complication is relatively easy to deal with. Always make sure that the maximum quotient digit is 9. The remainder might become larger than the divisor, but in the duplex method, that is perfectly acceptable.\n\nNow, we move on to the next complication we are likely to encounter when using the duplex method. And that is the problem of our net dividend becoming negative. This can happen when the duplex of the numbers to the right of the colon on the answer line becomes larger than the gross dividend.\n\nObviously, either the gross dividend has to be increased or the duplex has to be decreased, or both to prevent this from happening. Since the gross dividend is formed from the next digit of the square appended to the remainder from the previous division, one way to increase the gross dividend is to reduce the quotient from the division and increase the remainder. And because of the beauty of the way in which mathematics sometimes works, this also has the effect of reducing the duplex at the same time! Hopefully, this combination will cause the net dividend to turn positive, and allow us to continue with the application of this method to find the square root.\n\nLet us take a few examples to illustrate this. First consider the square root of 20164. We set up the duplex method in the figure below, and go through the first couple of steps. We see that the first net dividend we have is 10, which can be divided by our divisor, 2, 5 times with no remainder. This would then lead to a new gross dividend of 1, and a net dividend of -24 because the duplex of 5 is 25. The figure below shows this (the net dividend is not shown below):\n\n```•|2: 0 1 6 4\n2|1:1 0\nG| :1001\nN| :10\n---------------\n•|1: 5```\n\nThis illustrates clearly the complication we might encounter from time to time in the application of this method and which we must recover from to continue application of the method. Notice that in this respect, the Vedic duplex method is different from some other methods that freely allow the use of vinculums in their solution (such as polynomial division, straight arithmetic division, etc.).\n\nTo get around this problem, we reduce the second quotient to 4 and carry over a remainder of 2 to the next step, which then leads to a gross dividend of 21, and a net dividend of 5 (21 – the duplex of 4, which is 16). This then leads to the full solution as below:\n\n```•|2: 0 1 6 4\n2|1:1 2 1 0\nG| :10211604\nN| :10050000\n---------------\n•|1: 4 2 0 0```\n\nWe get an answer line of 14200, which then leads to the final answer of 142.00 since we know that the square root has to contain 3 digits before the decimal point.\n\nNext consider the square root of 101761. We have performed the first few steps of the duplex method, and are now faced with a negative net dividend because our gross dividend is 21, and our duplex is 83.\n\n```•|10: 1 7 6 1\n6| 9:1 5 2 2\nG| :11572621\nN| :115608\n---------------\n•| 3: 1 9 1```\n\nThis once again calls for us to reduce the quotient by 1, and increase the remainder to 8, so that our gross dividend becomes 81. We then see that this enables us to solve the problem because the net dividend becomes zero rather than becoming negative. This is illustrated below:\n\n```•|10: 1 7 6 1\n6| 9:1 5 2 8\nG| :11572681\nN| :11560800\n---------------\n•| 3: 1 9 0 0```\n\nWe then derive the final answer of 319.00 from the answer line based on the fact that the square root we are looking for contains 3 digits before the decimal point.\n\nFor several more examples of dealing with negative net dividends by adjusting the quotient and remainder, please refer to the full lesson here.\n\nHopefully, this lesson has given you the tools necessary to handle the computation of most square roots. We still have not dealt with how to find square roots of non-perfect squares. Since this lesson has already become quite long, that will have to wait until the next lesson. In the meantime, I hope you will take the time to practice the duplex method so that you can apply it confidently to any perfect square. Good luck, and happy computing!\n\n– The Vedic Maths Forum India\n\n#### 1 COMMENT\n\n1. it is not applicable to 35721 & 32401 because duplex is 9 at the same time" ]

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[ "# Translating Today’s Benefits to the Future - PowerPoint PPT Presentation", null, "", null, "Download Presentation", null, "Translating Today’s Benefits to the Future\n\nTranslating Today’s Benefits to the Future\nDownload Presentation", null, "## Translating Today’s Benefits to the Future\n\n- - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - -\n##### Presentation Transcript\n\n1. Translating Today’s Benefits to the Future • Suppose you want to know how much money you would have in 5 years if you placed \\$5,000 in the bank today at an interest rate of 6% compounded annually. • future value of a one-time investment. • The future value is the accumulated amount of your investment fund at the end of a specified period.\n\n2. This is an exercise that involves the use of compound interest. • Compound interest - Situation where you earn interest on the original investment and any interest that has been generated by that investment previously. • Earn interest on your interest • First year: \\$5,000(1+.06) = \\$5,300 • Second year: \\$5,300(1+.06) = \\$5,618 • Third year: \\$5,618(1+.06) = \\$5,955.08 • Fourth year: \\$5,955.08(1+.06) = \\$6,312.38 • Fifth year: \\$6,312.38(1+.06) = \\$6,691.13\n\n3. Effect of Compound Interest\n\n4. Formula: • FV = PV(1 + r)n • r = interest rate divided by the compounding factor • (yearly r / compounding factor) • n = number of compounding periods • (yearly n * compounding factor) • PV = Present Value of your investment • Compounding Factors: • Yearly = 1 • Quarterly = 4 • Monthly = 12 • Daily = 365\n\n5. Please note that I will always report r’s and n’s as yearly numbers • You will need to determine the compounding factor • All of your terms must agree as to time. • If you are taking an action monthly (like investing every month), then r and n must automatically be converted to monthly compounding. • If you are rounding in time value of money formulas, you need AT LEAST four (4) numbers after the zeros (0) • r = .08/12 • r=0.006667 (not 0.0067 or 0.007 or etc.)\n\n6. Yearly compounding • PV = 5000 • r = .06 • n = 5 • FV = \\$5,000(1.06)5 • = \\$6,691.13 • Monthly compounding • PV = 5000 • r = (.06/12) = .005 • n = 5(12) = 60 • FV = \\$5,000(1+.005)60 • = \\$6,744.25\n\n7. How do the calculations change if the investment is repeated periodically? • Suppose you want to know how much money you would have in 24 years if you placed \\$500 in the bank each year for twenty-four years at an annual interest rate of 8%. • future value of a periodic investment or future value of an annuity (stream of payments over time) = FVA\n\n8. The formula is... • where PV = the Present Value of the payment in each period • r = interest rate divided by the compounding factor • n = number of compounding periods\n\n9. Let’s try it… • \\$500/year, 8% interest, 24 years, yearly compounding • PV = 500 • r = .08 • n = 24 • = 500 (66.7648) • = \\$33,382.38\n\n10. Let’s try it again… • \\$50/month, 8% interest, 5 years, monthly compounding • PV = 50 • r = (.08/12) = .006667 • n = 5(12) = 60\n\n11. = 50 (73.4769) • = \\$3673.84 • Try again with n=120 • FVA=\\$9147.30\n\n12. More Practice • You have a really cool grandma who gave you \\$1,000 for your high school graduation. You invested it in a 5-year CD, earning 5% interest. How much will you have when you cash it out if it is compounded yearly? • How much will you have if it is compounded monthly? • How much will you have if it is compounded daily?\n\n13. Yearly Compounding • 1000(1+.05)5 • =\\$1276.28 • Monthly Compounding • r = (.05/12) = .004167 • n = 5(12) = 60 • 1000(1+.004167)60 • =\\$1283.36 • Daily Compounding • r = (.05/365) = .000136986 • n = 5(365) = 1825 • 1000(1+.000136986)1825 • =\\$1284.00\n\n14. Some more practice... • You have decided to be proactive for the future, and will save \\$25 a month. At the end of 10 years, how much will you have saved, if you earn 8% interest annually? • Monthly Compounding • FVA = • PV = \\$25 a month • r = (.08/12) = .006667 • n = (10)(12) = 120 • FVA = \\$4573.65\n\n15. Determining when to use Future Value vs. Present Value Calculation/Tables Do I have the money now? No Yes Use PV calculation/table Use FV calculation/table Is it a lump sum? Is it a lump sum? No Yes Yes No Use PV of an annuity Use FV of an annuity Use PV of a single payment Use FV of a single payment\n\n16. Future Value of \\$1 (single amount)\n\n17. Future Value of a Series of Annual Deposits (annuity)\n\n18. Present Value of \\$1 (single amount)\n\n19. Present Value of a Series of Annual Deposits (annuity)" ]

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[ "• ### Ball Mill Loading - Dry Milling - Paul O. Abbe\n\nThe starting point for ball mill media and solids charging generally starts as follows: 50% media charge Assuming 26% void space between spherical balls (non-spherical, irregularly shaped and mixed-size media will increase or decrease the free space) 50% x 26% = 13% free space\n\nGet Price\n\nGet Price\n• ### EFFECT OF BALL SIZE DISTRIBUTION ON MILLING PARAMETERS\n\n2.1 Breakage mechanisms in a ball mill 22 2.2 First order reaction model applied to milling 24 2.3 Grinding rate versus particle size for a given ball diameter 25 2.4 Cumulative breakage function versus relative size 28 2.5 Predicted variation of S i values with ball diameter for dry grinding of quartz 31 2.6 Breakage zones identified in a ball load profile 33 2.7 Breakage function of a 850\n\nGet Price\n• ### A Method to Determine the Ball Filling, in Miduk Copper\n\nMill internal load volume (m3) = (19.55*297.96)/100 = 58.52 m3 (2) Ball volume in total mill load could compute by Equation 3. Mill Ball (%) = 100{[(ball volume in the 0.4 m3sample)* 58.52] / 0.4}/297.96 (3) According to the results (Table 1), the ball filling percentage was obtained 1.3%.\n\nGet Price\n• ### Best way to determine the ball-to-powder ratio\n\nConsidering that ball bed has a porosity of 40 %, the actual ball volume is considered to be 21-24 % of the empty mill. Now, in order to get an efficient milling action, 80-110 % of the pores in\n\nGet Price\n• ### Ball charges calculators -\n\n- Ball top size (bond formula): calculation of the top size grinding media (balls or cylpebs):-Modification of the Ball Charge: This calculator analyses the granulometry of the material inside the mill and proposes a modification of the ball charge in order to improve the mill efficiency:\n\nGet Price\n\nVolume Loading Formula In Ball Mill Mill load or charge volume is the cumulative sum of the grinding media information show that 40 load by volume of ball mills result inet pricenergy calculation model of ball kinematics based on of ball mill and ball motion under the influence of coal load.\n\nGet Price\n• ### Ball mill - Wikipedia\n\nA ball mill is a type of grinder used to grind or blend materials for use in mineral dressing processes, paints, pyrotechnics, ceramics, and selective laser sintering. It works on the principle of impact and attrition: size reduction is done by impact as the balls drop from near the top of the shell. A ball mill consists of a hollow cylindrical shell rotating about its axis. The axis of the\n\nGet Price\n• 4\n• ### CALCULATION OF BALL MILL GRINDING\n\n08.03.2013· calculation of ball mill grinding efficiency. dear experts . please tell me how to calculate the grinding efficiency of a closed ckt & open ckt ball mill. in literatures it is written that the grinding efficiency of ball mill is very less [less than 10%]. please expalin in a\n\nGet Price\n• ### Ball Mills - Mine Engineer.Com\n\nThis formula calculates the critical speed of any ball mill. Most ball mills operate most efficiently between 65% and 75% of their critical speed. Photo of a 10 Ft diameter by 32 Ft long ball mill in a Cement Plant. Photo of a series of ball mills in a Copper Plant, grinding the ore for flotation. Image of cut away ball mill, showing material flow through typical ball mill. Flash viedo of Jar\n\nGet Price\n• ### EFFECT OF BALL SIZE DISTRIBUTION ON MILLING PARAMETERS\n\n2.1 Breakage mechanisms in a ball mill 22 2.2 First order reaction model applied to milling 24 2.3 Grinding rate versus particle size for a given ball diameter 25 2.4 Cumulative breakage function versus relative size 28 2.5 Predicted variation of S i values with ball diameter for dry grinding of quartz 31 2.6 Breakage zones identified in a ball load profile 33 2.7 Breakage function of a 850\n\nGet Price\n\nMedia and Product Ball Mill Loading Guide (Percentages are based on total volume of cylinder) NOTE: With media load at 50%, voids are created equal to 20% of cylinder volume. These voids are filled when product is loaded into the mill. Mills can be loaded by volume\n\nGet Price\n• ### Best way to determine the ball-to-powder ratio\n\nConsidering that ball bed has a porosity of 40 %, the actual ball volume is considered to be 21-24 % of the empty mill. Now, in order to get an efficient milling action, 80-110 % of the pores in\n\nGet Price\n\n12.01.2009· Formula for the load of alumina grinding ball: M=π×(D 2 ÷4)×L ×α×(1-β)×ψ. M: Alumina grinding load, in tons π: Circumference ratio, 3.14 D: Ball mill diameter, in meters L: Ball mill length, in meters α: Ideal stacking volume of the alumina grinding ball to the ball mill capacity, 44%-51% β: Void rate of the stacking alumina\n\nGet Price\n• ### A Method to Determine the Ball Filling, in Miduk Copper\n\nBall volume in total mill load could compute by Equation 3. Mill Ball (%) = 100{[(ball volume in the 0.4 m3 sample)* 58.52] / 0.4}/297.96 (3) According to the results (Table 1), the ball filling percentage was obtained 1.3%. However, these results may have some field errors. Acquired Results from Abrasion Test Ball abrasion was calculated in 4 conditions which are as follows: Ball charge\n\nGet Price\n• ### A Method to Determine the Ball Filling, in Miduk Copper\n\nBall volume in total mill load could compute by Equation 3. Mill Ball (%) = 100{[(ball volume in the 0.4 m3 sample)* 58.52] / 0.4}/297.96 (3) According to the results (Table 1), the ball filling percentage was obtained 1.3%. However, these results may have some field errors. Acquired Results from Abrasion Test Ball abrasion was calculated in 4 conditions which are as follows: Ball charge\n\nGet Price\n• ### Ball Mill - an overview | ScienceDirect Topics\n\nGenerally, filling the mill by balls must not exceed 30–35% of its volume. Productivity of ball mills depends on drum diameter and the relation of drum diameter and length. Optimum ratio between length L and diameter D, L: D is, usually, accepted in the range 1.56–1.64. The mill productivity also depends on many other factors: physical-chemical properties of feed material, filling of the\n\nGet Price\n• ### Milling Formulas and Definitions -\n\nThis is a particularly important value when using round insert cutters, ball nose end mills, and all cutters with larger corner radii, as well as cutters with an entering angle smaller than 90 degrees. Spindle speed, n. The number of revolutions the milling tool makes per minute on the spindle. This is a machine-oriented value, which is calculated from the recommended cutting speed value for\n\nGet Price\n\n01.12.2013· 1. Introduction. Wet ball mill is one of the most predominantly used method for the purpose of mixing and grinding of raw materials in laboratories and industry,, .The ball mill process is very complicated process governed by many parameters, such as ball size, ball shape, ball filling, slurry loading (with respect to ball amount), powder loading with respect to the amount of total slurry\n\nGet Price\n• ### Grinding in Ball Mills: Modeling and Process Control\n\nGrinding in ball mills is an important technological process applied to reduce the size of particles which may have different nature and a wide diversity of physical, mechanical and chemical characteristics. Typical examples are the various ores, minerals, limestone, etc. The applications of ball mills are ubiquitous in mineral processing and mining industry, metallurgy, cement production\n\nGet Price\n\n•", null, "Address:\n•", null, "Phone:\n•", null, "Email:" ]

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[ "# Determinant of sum of positive definite matrices\n\nSay $A$ and $B$ are symmetric, positive definite matrices. I've proved that\n\n$$\\det(A+B) \\ge \\det(A) + \\det(B)$$\n\nin the case that $A$ and $B$ are two dimensional. Is this true in general for $n$-dimensional matrices? Is the following even true?\n\n$$\\det(A+B) \\ge \\det(A)$$\n\nThis would also be enough. Thanks.\n\n• @RodrigodeAzavedo There is a geometric interpretation for this fact: If A and B are positive invertible matrices with $0<A<B$ then $Det A \\leq Det B$. We interpret $A,B$ as inner products(Positive symmetric 2-tensores). Then there is a linear map $T$ with $T^*(B)=A)$ this means that T is metric decreasing. But every metric decreasing is a volum decreasing map. Since the n dimensional \"Volume\" is made by product of 1 dimensional length. Jun 30, 2018 at 10:37\n• @AliTaghavi Could you please explain what $T$ has got to do with the question? Dec 12, 2018 at 21:33\n\nThe inequality $$\\det(A+B)\\geq \\det A +\\det B$$ is implied by the Minkowski determinant theorem $$(\\det(A+B))^{1/n}\\geq (\\det A)^{1/n}+(\\det B)^{1/n}$$ which holds true for any non-negative $n\\times n$ Hermitian matrices $A$ and $B$. The latter inequality is equivalent to the fact that the function $A\\mapsto(\\det A )^{1/n}$ is concave on the set of $n\\times n$ non-negative Hermitian matrices (see e.g., A Survey of Matrix Theory and Matrix Inequalities by Marcus and Minc, Dover, 1992, P. 115 and also the previous MO thread).\n\n• looks nice, but isn't it somewhat overkill to invoke the Minkowski theorem here? May 19, 2011 at 17:05\n• This is really misleading since it makes the question look like complicated, while is almost obvious that $\\det(A+B) = \\det(A) \\det(1+A^{-1/2}BA^{-1/2}) \\geq \\det(A) (1+\\det(A^{-1/2}BA^{-1/2})) = \\det(A) + \\det(B)$. In the second step, it is just used that $\\prod_i (1+ \\mu_i) \\geq 1 + \\prod_i \\mu_i$, where $\\mu_i$ are the eigenvalues of $A^{-1/2}BA^{-1/2}$. Jun 28, 2014 at 20:02\n• I'm going to disagree with @Suvrit and Andreas and say that the Minkowski theorem should be discussed. The reason is that it is a tighter bound that respects the dimensionality, and in particular is saturated when $A=B$ for any $n$. The OP's question is just an awkwardly weakened version of Minkowski. May 22, 2015 at 20:10\n• In fact, one can show a bit more with @AndreasThom idea: if $A$ is positive definite and $B$ is positive semidefinite and nonzero then $\\det(A+B)>\\det(A)+\\det(B)$ (strict inequality), since $A^{-1/2}BA^{-1/2}$ is then nonzero positive semidefinite, hence with nonnegative eigenvalues and not all 0, and thus $\\prod_i(1+\\mu_i)\\geq 1+\\sum_i\\mu_i+\\prod_i\\mu_i>1+\\prod_i\\mu_i$. Oct 10, 2017 at 18:44\n• I used $A(1+A^{-1/2}BA^{-1/2}) = A^{1/2}(A+B)A^{-1/2}$. For the second part, you would need to argue that the eigenvalues of $A^{-1}B$ are positive, which brings you back to my argument (I guess). Sep 26, 2019 at 6:03\n\nWe have $((A+B)x,x)\\ge (Ax,x)$. It then follows from the variational characterization of eigenvalues (min-max theorem) that the eigenvalues of $A+B$ are greater than or equal to those of $A$. This implies $det(A+B)\\ge det(A)$.\n\nHere is yet another overkill, but hopefully not too bad a way to prove this inequality.\n\nWe have the following proof sketch.\n\n$$\\begin{eqnarray} x^T(A+B)x &\\ge& x^TAx\\quad\\forall x\\\\\\\\ -x^T(A+B)x &\\le& -x^TAx\\\\\\\\ \\exp(-x^T(A+B)x) &\\le& \\exp(-x^TAx)\\\\\\\\ \\int\\exp(-x^T(A+B)x)dx &\\le& \\int\\exp(-x^TAx)dx\\\\\\\\ \\frac{1}{\\sqrt{\\det(A+B)}} &\\le& \\frac{1}{\\sqrt{\\det(A)}}\\\\\\\\ \\det(A+B) &\\ge& \\det(A) \\end{eqnarray}$$\n\nThe only fancy thing that happened is in the second last line, where I used the formula for the Gaussian integral (see multivariate section)\n\nUpdate. To expand upon my comment below, to note that the above idea actually with a little bit more care actually yields a proof of the Minkowski determinant inequality, by equivalently establishing log-concavity of the determinant. The key point to observe is \\begin{eqnarray} \\exp(-x^T((1-\\lambda)A+\\lambda)x) &=& [\\exp(-x^TAx)]^{1-\\lambda}[\\exp(-x^TBx)]^\\lambda\\\\\\\\ \\int\\exp(-x^T((1-\\lambda)A+\\lambda)x)dx &=& \\int [\\exp(-x^TAx)]^{1-\\lambda}[\\exp(-x^TBx)]^\\lambda\\ dx\\\\\\\\ &\\stackrel{\\text{Hölder}}{\\le}& \\left(\\int\\exp(-x^TAx)dx \\right)^{1-\\lambda}\\left(\\int \\exp(-x^TBx)dx \\right)^\\lambda. \\end{eqnarray} Now invoke the Gaussian integral as above to conclude \\begin{equation*} \\det((1-\\lambda)A+\\lambda B) \\ge \\det(A)^{1-\\lambda}\\det(B)^\\lambda, \\end{equation*} from which we can easily conclude $\\det(A+B)^{1/n} \\ge \\det(A)^{1/n}+\\det(B)^{1/n}$.\n\n• This is very clever. I wonder if such reasoning can also prove the Minkowski determinant theorem mentioned above... Jun 30, 2018 at 22:35\n• @AlexArvanitakis indeed the same reasoning as above with a tiny bit of care can be used to prove the inequality $\\det((1-\\lambda)A+\\lambda B) \\ge \\det(A)^{1-\\lambda}\\det(B)^\\lambda$, which is actually equivalent to Minkowski's determinant inequality (easy to verify using suitably scaled versions of the matrices $A$ and $B$) Jul 1, 2018 at 22:07\n\nYet another way to see this is to note that $A = \\overline{Q}^{t}Q$ for some invertible matrix $Q$. Then ${\\rm det}(A+B) = |{\\rm det}(Q)|^{2}{\\rm det}{( I + (\\overline{Q}^{-1}})^{t}BQ^{-1})$.` Now $(\\overline{Q}^{-1})^{t}BQ^{-1}$ is Hermitian, and positive definite. It suffices to prove that if $X$ is positive definite and Hermitian, then ${\\rm det}(I+X) \\geq (1 + {\\rm det}X)$. We may conjugate $X$ by a unitary matrix $U$ and assume that $X$ is diagonal. Let the eigenvalues of $X$ be $\\lambda_{1},\\ldots, \\lambda_{n}$, (allowing repetitions). Then ${\\rm det}(I+X) = \\prod_{i=1}^{n}(1 + \\lambda_{i}) \\geq 1 + \\prod_{i=1}^{n} \\lambda_{i} = 1 + {\\rm det}X.$ Such an argument appears in some proofs by R. Brauer, though I do not know whether it originates with him.\n\nLater edit: Incidentally, I think that with the arithmetic-geometric mean inequality and a slightly more careful analysis, you can see by this approach that for $X$ as above, you do have ${\\rm det}(I+X) \\geq (1 +({\\rm det}X)^{1/n})^{n}$ (a special case of the inequality of Minkowski mentioned in the accepted answer, but enough to prove the general case by an argument similar to that above). For set $d = {\\rm det}X$. Let $s_{m}(\\lambda_{1},\\ldots ,\\lambda_{n})$ denote the $m$-th elementary symmetric function evaluated at the eigenvalues. Using the arithmetic-geometric mean inequality yields that $s_{m}(\\lambda_{1},\\ldots ,\\lambda_{n}) \\geq \\left( \\begin{array}{clcr} n\\\\m \\end{array} \\right)d^{m/n}$, so we obtain ${\\rm det}(I+X) \\geq (1+d^{1/n})^{n}.$\n\nLet me add some more. If $A, B, C$ are positive semidefinite, then $$\\det (A+B+C)+\\det C\\ge \\det (A+C)+\\det (B+C). \\quad (\\star)$$\n\nWhen $C=0$, this reduces to OP's question.\n\nA remarkable extension of ($\\star$) were recently obtained by V. Paksoy, R. Turkmen, F. Zhang [ Electron. J. Linear Algebra 27 (2014) 332-341], which says that the determinant functional can be replaced by any generalized matrix function.\n\nThe determinant of a positive definite matrix $G$ is proportional to $(1/\\hbox{Volume}(\\mathcal B(G)))^2$ where $\\mathcal B(G)$ denotes the unit ball with respect to the metric defined by $G$. If $A$ and $B$ are positive definite then the volume of $\\mathcal B(A+B)$ is smaller than the volume of $\\mathcal B(A)$ or $\\mathcal B(B)$.\n\n• It's worth noting that this is secretly the same as Suvrit's answer. May 20, 2011 at 14:20\n• Not really: You don't need exponentials for proving that $\\det(G)$ is proportional to $1/\\hbox{Volume}(G)^2$ : It is enough to stare at an orthogonal basis formed of eigenvectors for $G$. In this sense this proof is more elementary. May 25, 2011 at 7:18\n• Fair enough. May 29, 2011 at 0:49\n\nJust for those who might want to know, I think the min-max theorem mentioned by @Michael Renardy is Courant-Fischer: Supporse a real symmetric matrix A's eigen values are $$\\lambda_1 \\leq \\lambda_2 \\leq ... \\leq \\lambda_n$$. then k-th eigen value: $$\\lambda_k = \\underset{V_k}{\\text{min}} \\space max\\{x^TAx | x \\in V_k, ||x||_2 = 1\\}$$ $$V_k$$ is any k-dimentional subspace of $$R^n$$, $$1 \\leq k \\leq n$$ ." ]

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[ "Related Articles\n\n# Introduction to Simulation Modeling in Python\n\n• Last Updated : 03 Mar, 2021\n\nSimulation is imitating the operations which take place within a system to study its behavior. Analyzing and creating the model of a system to predict its performance is called simulation modeling.\n\nSimulation mimics a real-life process to determine or predict the response of the entire system. This helps to understand the dependency of each part of the system, their relations, and interactions. The process of simulating in real life can be costly. Therefore, we build a model to solve costly and complex ideas efficiently. Building a simulation model in an institution or organization increases profit.\n\nA model is a replica of an original/real thing. A model can be either deterministic or probabilistic. A deterministic model is a model which does not involve any randomness. For a given initial condition you always get the same final condition.\n\nA probabilistic model includes the randomness of elements. For example: tossing a coin, can be either heads or tails.", null, "Now let’s understand the simulation model in one go.\n\nSuppose you have to open a pizza restaurant and know how many employees you will need to run well. Different pizzas take different amounts of time to get prepared. Also, orders do not come uniformly with time. You want to provide them the best service possible while maintaining your budget. You can’t hire and then fire the employees to find the optimum number required to design a simulation model. We can solve the above problem of finding an optimum number of employees by building a simulation model in the following ways:\n\n• Designing: looking over the various services provided by the company and, therefore, different types of employees required for various jobs.\n• Experiment: Trends of customers’ arrival on weekdays, weekends, and on special occasions and therefore employees required accordingly.\n• Optimize: Optimizing the number of workers to employ permanently by looking over experimentation.\n• Analyze: If giving employment to those many people affordable or asking employees to work overtime, can get extra workers on festival season.\n• Improve: Further reducing the employment to given on visualizing the results of the analysis.", null, "Simulation models are built before building a new system or altering an existing system to optimize the system’s performance and reduce the chances of failure. One of the leading simulation models in the present-day scenario is Monte Carlo Simulation.\n\n## Monte Carlo Simulation\n\nMonte Carlo simulation is a mathematical technique that helps estimate the probability distribution of various event outcomes. Based on those probabilities, the risk analysis team decides whether they are ready to take the risk. This technique repeatedly takes random numbers between the minimum and maximum limit and predicts its outcome. Usually, the sampling is done on a large scale, so we get all the likely outcomes. Then we plot the probability distribution using which risk analysts calculate the risk probability.\n\nFor example, let’s consider the above example the arrival of customers can vary in a specific range. We can create a model that pics a random number between maximum and minimum number and can visualize the range of workers required accordingly.\n\nLet’s take another elementary example to understand the Monte Carlo simulation by rolling the dice. Suppose we roll two dice, and we want to predict the probability of getting the sum as 12.\n\nBelow is the python code for the implementation with comments for better understanding:\n\n## Python3\n\n `# importing the required libraries``import` `random``import` `numpy as np``import` `matplotlib.pyplot as plt`` ` ` ` `# function to generate a random number``def` `roll():``    ``return` `random.randint(``1``, ``6``)`` ` ` ` `# rolling dice 1000000 times and ``# storing in list``val ``=` `[]``for` `i ``in` `range``(``0``, ``1000000``):``    ``sum_of_roll ``=` `roll()``+``roll()``    ``val.append(sum_of_roll)`` ` ` ` `# plotting the graph``plt.hist(val, bins``=``11``, density``=``True``)`\n\nOutput:", null, "From the above probability distribution curve, we get the value of probability as 0.025 for getting a 12. Similarly, we can apply the Monte Carlo technique to solve various problems.\n\nAttention geek! Strengthen your foundations with the Python Programming Foundation Course and learn the basics.\n\nTo begin with, your interview preparations Enhance your Data Structures concepts with the Python DS Course. And to begin with your Machine Learning Journey, join the Machine Learning – Basic Level Course\n\nMy Personal Notes arrow_drop_up" ]

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[ "§3\n\n1. 基本概念\n\n[导数的定义及其几何意义]  设函数y=f(x)当自变量在点x有一改变量", null, ",函数y相应地有一改变量", null, ",那末当", null, "趋于零时,若比", null, "的极限存在(一确定的有限值)，则称这个极限为函数f(x)在点x的导数,记作", null, "图5.1", null, "", null, "=", null, "[单边导数]", null, "=", null, "", null, "", null, "=", null, "", null, "", null, "=", null, "[无穷导数]  若在某一点x", null, "", null, "=±∞\n\n+∞时,函数f(x)的图形在点x的切线正向与y轴方向一致,", null, "=－∞时,方向相反)\n\n[函数的可微性与连续性的关系]  如果函数y=f(x)在点x有导数，那末它在点x一定连续。反之,连续函数不一定有导数,例如\n\n函数y=|x|在点x=0连续,在点x=0,左导数", null, "=1,右导数", null, "=1,而导数", null, "不存在(5.2)", null, "", null, "`图5.2            图5.3`\n\n函数\n\ny=f(x)=", null, "" ]

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[ "", null, "douguaidian8021 2018-08-14 19:55 采纳率: 100%\n\n# 在golang中创建二维字符串数组\n\nI need to create a 2 dimensional string array as shown below -\n\n``````matrix = [['cat,'cat','cat'],['dog','dog']]\n``````\n\nCode:-\n\n``````package main\n\nimport (\n\"fmt\"\n)\n\nfunc main() {\n{ // using append\n\nvar matrix [][]string\nmatrix = append(matrix,'cat')\nfmt.Println(matrix)\n}\n}\n``````\n\nError:-\n\n``````panic: runtime error: index out of range\n\ngoroutine 1 [running]:\nmain.main()\n/tmp/sandbox863026592/main.go:11 +0x20\n``````\n• 写回答\n\n#### 2条回答默认 最新\n\n•", null, "duanjue2560 2018-08-14 20:05\n关注\n\nYou have a slice of slices, and the outer slice is `nil` until it's initialized:\n\n``````matrix := make([][]string, 1)\nmatrix = append(matrix,'cat')\nfmt.Println(matrix)\n``````\n\nOr:\n\n``````var matrix [][]string\nmatrix = append(matrix, []string{\"cat\"})\nfmt.Println(matrix)\n``````\n\nOr:\n\n``````var matrix [][]string\nvar row []string\nrow = append(row, \"cat\")\nmatrix = append(matrix, row)\n``````\n本回答被题主选为最佳回答 , 对您是否有帮助呢?\n评论\n\n#### 悬赏问题\n\n• ¥20 Java的kafka错误unknowHostException\n• ¥20 gbase 8a没有lisense，需要获取一个lisense\n• ¥15 前端的3d饼图不知道用啥框架做的\n• ¥15 三个问答题，很简单，都是关于网络安全\n• ¥15 算法问题 斐波那契数 解答\n• ¥20 JAVAscript\n• ¥15 VS2019 SPY++ 获取句柄操作" ]

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