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https://www.enjoyalgorithms.com/tags/coding-interview-concepts/
[ "All content related to coding-interview-concepts", null, "Introduction to Data Structures: Types, Classifications and Applications\n\nThe code structure of a well-designed algorithm using data structure is just like a structure of a good house. So a design of an algorithm must be based on a good understanding of data structures: properties, structure, implementation techniques, and efficiency of its critical operations. The fact is: Data structures are the core building blocks of algorithms and real-life applications.", null, "Binary Indexed Tree or Fenwick Tree\n\nA Fenwick tree or Binary indexed tree is a data structure that can efficiently update elements and calculate prefix sums in a table of numbers. Boris Ryabko proposed this structure in 1989, with a further modification published in 1992.", null, "Dynamic Array\n\nIn computer science, a dynamic array is a random access, the variable-size data structure that allows elements to be added or removed. It is supplied with standard libraries in many modern mainstream programming languages.", null, "Array In Data Structures\n\nAn array is a contiguous block of memory of the same type of elements where the size is equal to the number of elements in that array, which must be fixed. It is a structure of data such that each element can be efficiently located by its index or memory address.", null, "Introduction to Heap Data Structure\n\nA heap is a complete binary tree structure where each element satisfies a heap property. We learn two types of the heap in programming: 1) max-heap, which satisfies max heap property 2) min-heap, which satisfies min heap property.", null, "Sorting Algorithms Comparison\n\nComparison of sorting algorithms based on different parameters helps us choose an effcient sorting method in various problem-solving scenarios. You will get an answer to the following questions: how to compare two sorting algorithms? Which sorting is best in terms of properties like efficiency, in-place, stability, online vs. offline, etc.", null, "Introduction to Hashing\n\nHashing is an effcient searching technique that maps keys and values into the hash table using a hash function. Explore this blog to learn: how do we perform hash mapping in data structures? How do hash maps work? What are some popular hash functions in programming?", null, "Recursive Tree Traversals of a Binary Tree: Preorder, Inorder and Postorder Traversal\n\nTo process data stored in a binary tree, we need to traverse each tree node, and the process to visit all nodes is called binary tree traversal. In this blog, we will be discussing three popular recursive tree traversals: preorder, inorder and postorder traversals. These traversals are also called depth-first search traversal or dfs traversal in data structures.", null, "Iterative Binary Tree Traversal using Stack: Preorder, Inorder and Postorder\n\nIn recursive DFS traversals of a binary tree, we have three basic elements to traverse— root, left subtree, and right subtree. The traversal order depends on the order in which we process the root node. Here recursive code is simple and easy to visualize — only one function parameter and 3–4 lines of code. So critical question would be — How can we convert it into iterative code using stack? To simulate the recursive traversal into an iterative traversal, we need to understand the flow of recursive calls.", null, "Level Order Traversal of a Binary Tree :  Breadth First Search\n\nLevel order traversal accesses nodes in level by level order. This is also called breadth-first search traversal or BFS traversal. Here we start from the root node and process it, then process all the nodes at the first level, then process all the nodes at the second level, and so on. In other words, we explore all nodes at the current level before moving on to the nodes at the next level.", null, "Time complexity analysis in Data Structure and Algorithms\n\nExplore this blog to answer these questions related to complexity analysis: why time complexity analysis is important? What are the criteria to define the complexity of an algorithm? How do we analyze the time complexity of an algorithm? How do we represent algorithm time complexity in the form of big O notation?", null, "Analysis of Recursion in Data Structure and Algorithms\n\nLearning analysis of recursion is critical to understand the time complexity analysis of recursive algorithms. We will discuss these concepts related to the recursion analysis: Recurrence relations of recursive algorithms, steps to analyze the time complexity of recursion, Recursion tree method, and master theorem to analyze divide and conquer algorithms.", null, "Analysis of loop in Programming\n\nThere are several loop patterns in programming like a loop running constant time, a loop running n times, a loop growing exponentially, a loop running based on the specific condition, consecutive single loops, two nested loops, three nested loops, consecutive single loop with nested loops, etc. So for designing a better algorithm or optimizing the code, we should learn to analyze the time complexity of the loop in terms of Big-O notation.", null, "Introduction to Sorting Algorithms: Bubble Sort, Selection Sort and Insertion Sort\n\nSorting algorithms are the most fundamental problems to study in data structure and algorithms. But the critical question is - why we learn the design, code, and analysis of the sorting algorithms? Explore and Think!", null, "Iteration and Loop in Programming\n\nIteration is a process to repeat a sequence of code instructions a specified number of times or until a specific condition is met. It helps us to solve several coding problems in data structure and algorithms. We implement iteration using the two most common types of loops in programming languages: the while loop and the for loop.", null, "Step by Step Guide for Cracking the Coding Interview\n\nA comprehensive guide to master data structures and algorithms and crack the coding interview. This could help programmers prepare a step-by-step learning plan for the coding interview preparation. Explore and Enjoy!", null, "What is an Algorithm? Properties and Applications of Algorithms in real life\n\nThe concept of algorithm is essential for building high-performance software applications and cracking the coding interview to get a high-paying job in the software industry. So learning data structure and algorithms is one of the important career skills for programmers. Definition of the algorithm: An algorithm is a step-by-step procedure to transform a given input to the desired output and solve a computational problem.", null, "Recursion Explained: How recursion works in Programming?\n\nRecursion means solving the problem via the solution of the smaller sub-problem. This blog will answer some critical questions like - what is recursion? What are its advantages and disadvantages? How do you identify recursion problems? What is the difference between recursion and iteration? etc.", null, "How to develop algorithmic thinking in data structure and algorithms?\n\nAlgorithmic thinking definition: It is a method for solving algorithms and data structure problems based on a clear definition of the steps logically and repeatedly. Therefore, thinking algorithmically is essential for learning data structures and algorithms and solve various coding interview questions.", null, "Why should we learn data structures and algorithms?\n\nThere are four critical importance to learn data structures and algorithms: 1) An algorithm is a technology 2) It is at the core of library functions and several APIs 3) For cracking the coding interview 4) Algorithms are beautiful! This blog answer one of the critical questions: how do we develop a long-term motivation to learn data structures and algorithms?" ]
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http://typeocaml.com/2015/01/25/memoize-rec-untying-the-recursive-knot/
[ "# Recursive Memoize & Untying the Recursive Knot", null, "When I wrote the section of When we need later substitution in Mutable, I struggled. I found out that I didn't fully understand the recursive memoize myself, so what I had to do was just copying the knowledge from Real World OCaml. Luckily, after the post was published, glacialthinker commented in reddit:\n\n(I never thought before that a recursive function can be split like this, honestly. I don't know how to induct such a way and can't explain more. I guess we just learn it as it is and continue. More descriptions of it is in the book.)\n\nThis is \"untying the recursive knot\". And I thought I might find a nice wikipedia or similiar entry... but I mostly find Harrop. :) He actually had a nice article on this many years back in his OCaml Journal. Anyway, if the author swings by, searching for that phrase may turn up more material on the technique.\n\nIt greatly enlightened me. Hence, in this post, I will share with you my futher understanding on recursive memoize together with the key cure untying the recursive knot that makes it possible.\n\n# Simple Memoize revamped\n\nWe talked about the simple memoize before. It takes a non-recursive function and returns a new function which has exactly the same logic as the original function but with new new ability of caching the argument, result pairs.\n\nlet memoize f =\nlet table = Hashtbl.Poly.create () in\nlet g x =\nmatch Hashtbl.find table x with\n| Some y -> y\n| None ->\nlet y = f x in\ny\nin\ng", null, "The greatness of memoize is its flexibility: as long as f takes a single argument, memoize can make a memo version out of it without touching anything inside f.\n\nThis means while we create f, we don't need to worry about the ability of caching but just focus on its own correct logic. After we finish f, we simply let memoize do its job. Memoization and functionality are perfectly separated.\n\nUnfortunately, the simple memoize cannot handle recursive functions. If we try to do memoize f_rec, we will get this:", null, "f_rec is a recursive function so it will call itself inside its body. memoize f_rec will produce f_rec_memo which is a little similar as the previous f_memo, yet with the difference that it is not a simple single call of f_rec arg like we did f arg. Instead, f_rec arg may call f_rec again and again with new arguments.\n\nLet's look at it more closely with an example. Say, arg in the recursive process will be always decreased by 1 until 0.\n\n1. Let's first od f_rec_memo 4.\n2. f_rec_memo will check the 4 against Hashtbl and it is not in.\n3. So f_rec 4 will be called for the first time.\n4. Then f_rec 3, f_rec 2, f_rec 1 and f_rec 0.\n5. After the 5 calls, result is obtained. Then 4, result pair is stored in Hashtbl and returned.\n6. Now let's do f_rec_memo 3, what will happen? Obviously, 3 won't be found in Hashtbl as only 4 is stored in step 5.\n7. But should 3, result pair be found? Yes, it should of course because we have dealt with 3 in step 4, right?\n8. Why 3 has been done but is not stored?\n9. ahh, it is because we did f_rec 3 but not f_rec_memo 3 while only the latter one has the caching ability.\n\nThus, we can use memoize f_rec to produce a memoized version out of f_rec anyway, but it changes only the surface not the f_rec inside, hence not that useful. How can we make it better then?\n\n# Recursive Memoize revamped\n\nWhat we really want for memoizing a recursive function is to blend the memo ability deep inside, like this:", null, "Essentially we have to replace f_rec inside with f_rec_memo:", null, "And only in this way, f_rec can be fully memoized. However, we have one problem: **it seems that we have to change the internal of f_rec.\n\nIf we can modify f_rec directly, we can solve it easily . For instance of fibonacci:\n\nlet rec fib_rec n =\nif n <= 1 then 1\nelse fib_rec (n-1) + fib_rec (n-2)\n\n\nwe can make the memoized version:\n\nlet fib_rec_memo_trivial n =\nlet table = Hashtbl.Poly.create () in\nlet rec fib_rec_memo x =\nmatch Hashtbl.find table x with\n| Some y -> y\n| None ->\nlet y = fib_rec_memo (x-1) + fib_rec_memo (x-2) in\ny\nin\nfib_rec_memo\n\n\nIn the above solution, we replaced the original fib_rec inside with fib_rec_memo, however, we also changed the declaration to fib_rec_memo completely. In fact, now fib_rec is totally ditched and fib_rec_memo is a new function that blends the logic of memoize with the logic of fib_rec.\n\nWell, yes, fib_rec_memo_trivial can achieve our goal, but only for fib_rec specificly. If we need to make a memoized version for another recursive function, then we need to change the body of that function again. This is not what we want. We wish for a memoize_rec that can turn f_rec directly into a memoized version, just like what the simple memoize can do for f.\n\nSo we don't have a shortcut. Here is what we need to achieve:\n\n1. we have to replace the f_rec inside the body of f_rec with f_rec_memo\n2. We have keep the declaration of f_rec.\n3. We must assume we can't know the specific logic inside f_rec.\n\nIt sounds a bit hard. It is like giving you a compiled function without source code and asking you to modify its content. And more imporantly, your solution must be generalised.\n\nFortunately, we have a great solution to create our memoize_rec without any hacking or reverse-engineering and untying the recursive knot is the key.\n\n# Untying the Recursive Knot\n\nTo me, this term sounds quite fancy. In fact, I never heard of it before 2015-01-21. After I digged a little bit about it, I found it actually quite simple but very useful (this recursive memoize case is an ideal demonstration). Let's have a look at what it is.\n\nEvery recursive function somehow follows a similar pattern where it calls itself inside its body:", null, "Once a recursive function application starts, it is out of our hands and we know it will continue and continue by calling itself until the STOP condition is satisfied. What if the users of our recursive function need some more control even after it gets started?\n\nFor example, say we provide our users fib_rec without source code, what if the users want to print out the detailed trace of each iteration? They are not able unless they ask us for the source code and make a new version with printing. It is not that convenient.\n\nSo if we don't want to give out our source code, somehow we need to reform our fib_rec a little bit and give the space to our users to insert whatever they want for each iteration.\n\nlet rec fib_rec n =\nif n <= 1 then 1\nelse fib_rec (n-1) + fib_rec (n-2)\n\n\nHave a look at the above fib_rec carefully again, we can see that the logic of fib_rec is already determined during the binding, it is the fib_recs inside that control the iteration. What if we rename the fib_recs within the body to be f and add it as an argument?\n\nlet fib_norec f n =\nif n <= 1 then 1\nelse f (n-1) + f (n-2)\n\n(* we actually should now change the name of fib_norec\nto something like fib_alike_norec as it is not necessarily\ndoing fibonacci anymore, depending on f *)\n\n\nSo now fib_norec won't automatically repeat unless f tells it to. Moreover, fib_norec becomes a pattern which returns 1 when n is <= 1 otherwise add f (n-1) and f (n-2). As long as you think this pattern is useful for you, you can inject your own logic into it by providing your own f.\n\nGoing back to the printing requirement, a user can now build its own version of fib_rec_with_trace like this:\n\nlet rec fib_rec_with_trace n =\nPrintf.printf \"now fibbing %d\\n\" n;\nfib_norec fib_rec_with_trace n\n\n\nUntying the recusive knot is a functional design pattern. It turns the recursive part inside the body into a new parameter f. In this way, it breaks the iteration and turns a recursive function into a pattern where new or additional logic can be injected into via f.", null, "It is very easy to untie the knots for recusive functions. You just give an addition parameter f and replace f_rec everywhere inside with it. For example, for quicksort:\n\nlet quicksort_norec f = function\n| [] | _::[] as l -> l\n| pivot::rest ->\nlet left, right = partition_fold pivot rest in\nf left @ (pivot::f right)\n\nlet rec quicksort l = quicksort_norec quicksort l\n\n\nThere are more examples in Martin's blog, though they are not in OCaml. A formalized description of this topic is in the article Tricks with recursion: knots, modules and polymorphism from The OCaml Journal.\n\nNow let's come back to recursive memoize problem with our new weapon.\n\n# Solve Recursive Memoize\n\nAt first, we can require that every recursive function f_rec must be supplied to memoize_rec in the untied form f_norec. This is not a harsh requirement since it is easy to transform f_rec to f_norec.\n\nOnce we get f_norec, we of course cannot apply memoize (non-rec version) on it directly because f_norec now takes two parameters: f and arg.\n\nAlthough we can create f_rec in the way of let rec f_rec arg = f_norec f_rec arg, we won't do it that straightforward here as it makes no sense to have an exactly the same recursive function. Instead, we can for now do something like let f_rec_tmp arg = f_norec f arg.\n\nWe still do not know what f will be, but f_rec_tmp is non-recursive and we can apply memoize on it: let f_rec_tmp_memo = memoize f_tmp.\n\nf_rec_tmp_memo now have the logic of f_norec and the ability of memoization. If f can be f_rec_tmp_memo, then our problem is solved. This is because f is inside f_norec controlling the iteration and we wished it to be memoized.\n\nThe magic that can help us here is making f mutable. Because f needs to be known in prior and f_rec_tmp_memo is created after, we can temporarily define f as a trivial function and later on after we create f_rec_tmp_memo, we then change f to f_rec_tmp_memo.\n\nLet's use a group of bindings to demonstrate:\n\n(* trivial initial function and it should not be ever applied in this state *)\nlet f = ref (fun _ -> assert false)\n\nlet f_rec_tmp arg = f_norec !f arg\n\n(* memoize is the simple non-rec version *)\nlet f_rec_tmp_memo = memoize f_rec_tmp\n\n(* the later substitution made possible by being mutable *)\nf := f_rec_tmp_memo\n\n\nThe final code for memoize_rec is:\n\nlet memo_rec f_norec =\nlet f = ref (fun _ -> assert false) in\nlet f_rec_memo = memoize (fun x -> f_norec !f x) in\nf := f_rec_memo;\nf_rec_memo" ]
[ null, "http://typeocaml.com/content/images/2015/01/knot-1.jpg#hero", null, "http://typeocaml.com/content/images/2015/01/simple_memoize-1.jpg", null, "http://typeocaml.com/content/images/2015/01/simple_memoize_rec.jpg", null, "http://typeocaml.com/content/images/2015/01/memoize_rec_wish-1.jpg", null, "http://typeocaml.com/content/images/2015/01/transform-1.jpg", null, "http://typeocaml.com/content/images/2015/01/single_f_rec.jpg", null, "http://typeocaml.com/content/images/2015/01/untie_f_rec.jpg", null ]
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https://kexue.fm/archives/1995
[ "Matlab是为了数值计算（尤其是矩阵运算）而生的，因此它并不擅长处理符号计算。这就给我们编程带来了困难。在网上随便一搜，就可以发现，网上的Matlab牛顿法程序都是要求用户同时输入方程及其导函数，这显然是不方便的，因为Matlab本身就具备了求导功能。下面我们来分析一下困难在哪里。\n\ndiff(x^2) \n\nf=@(x) x^2 \n\nf=inline(x^2,'x')\n\ndiff(f(x)) \n\ndf=inline(diff(f(x)),'x') \n\nfunction f=jfc(g)\n\nsyms x\np=0.000001; %定义精度\nn=0; %计算迭代次数\n\ns=inline(g,'x'); %定义函数\nds=inline(diff(s(x)),'x'); %定义导函数\n\nx=1; %初始值\ne=s(x);\n\n%下面是迭代过程\nwhile abs(e)>p\nn=n+1;\nx=x-s(x)/ds(x);\ne=s(x);\nend\n\n%输出\n[x n e]\n\njfc(x^2-2)\n\n\nf=subs(x^2,'5',x)\n\n\nfunction f=jfc(g)\n\np=0.000001;\nx=1;\nn=0;\n\nds=diff(s);\ne=subs(s,'x',x);\n\nwhile abs(e)>p\nn=n+1;\nds0=subs(ds,'x',x);\nx=x-e/ds0;\ne=subs(s,'x',x);\nend\n\n[x n p]" ]
[ null ]
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https://mathbig.com/all-prime-factors-of-a-number-pages/prime-factors-of-902
[ "# Prime Factors of 902\n\nPrime Factors of 902 are 2, 11, and 41\n\n#### How to find prime factors of a number\n\n 1.   Prime Factorization of 902 by Division Method 2.   Prime Factorization of 902 by Factor Tree Method 3.   Definition of Prime Factors 4.   Frequently Asked Questions\n\n#### Steps to find Prime Factors of 902 by Division Method\n\nTo find the primefactors of 902 using the division method, follow these steps:\n\n• Step 1. Start dividing 902 by the smallest prime number, i.e., 2, 3, 5, and so on. Find the smallest prime factor of the number.\n• Step 2. After finding the smallest prime factor of the number 902, which is 2. Divide 902 by 2 to obtain the quotient (451).\n902 ÷ 2 = 451\n• Step 3. Repeat step 1 with the obtained quotient (451).\n451 ÷ 11 = 41\n41 ÷ 41 = 1\n\nSo, the prime factorization of 902 is, 902 = 2 x 11 x 41.\n\n#### Steps to find Prime Factors of 902 by Factor Tree Method\n\nWe can follow the same procedure using the factor tree of 902 as shown below:\n\nSo, the prime factorization of 902 is, 902 = 2 x 11 x 41.\n\n#### How do you define Prime Factors of a number?\n\nPrime numbers, in mathematics are all those natural numbers greater than 1 that have exactly 2 factors which are 1 and the number itself. When we express any number as the product of these prime numbers than these prime numbers become prime factors of that number. Eg- Prime Factors of 902 are 2 x 11 x 41.\n\n#### Properties of Prime Factors\n\n• Two prime factors of a given number are always coprime to each other.\n• 2 is the only even prime factor any number can have.\n• Two prime factors are always coprime to each other.\n• 1 is neither a prime number nor a composite number and also 1 is the factor of every given number. So, 1 is the factor of 902 but not a prime factor of 902.\n\n• Which is the smallest prime factor of 902?\n\nSmallest prime factor of 902 is 2.\n\n• Is 902 a perfect square?\n\nNo 902 is not a perfect square.\n\n• What is the prime factorization of 902?\n\nPrime factorization of 902 is 2 x 11 x 41.\n\n• What are the factors of 902?\n\nFactors of 902 are 1 , 2 , 11 , 22 , 41 , 82 , 451 , 902.\n\n• What is the product of all prime factors of 902?\n\nPrime factors of 902 are 2 x 11 x 41. Therefore, their product is 902.\n\n• What numbers are the prime factors of 902?\n\nPrime factors of 902 are 2 , 11 , 41.\n\n• What is the sum of all odd prime factors of 902?\n\nPrime factors of 902 are 2 , 11 , 41, out of which 11 , 41 are odd numbers. So, the sum of odd prime factors of 902 is 11 + 41 = 52.\n\n• Is there any even prime factor of 902?\n\nYes there is a even prime factor of 902.\n\n• What is the product of all odd prime factors of 902?\n\nPrime factors of 902 are 2 , 11 , 41, out of which 11 , 41 are odd numbers. So, the product of odd prime factors of 902 is 11 x 41 = 451." ]
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https://encyclopediaofmath.org/wiki/Parallel_transport
[ "# Parallel transport\n\n2010 Mathematics Subject Classification: Primary: 53C05 [MSN][ZBL]\n\nA topological or differential geometric construction generalizing the idea of parallel translation in affine spaces to fibers of general bundles, see connection. In contrast with the affine case, the result of parallel transport along a closed path may in general be nontrivial, leading thus to the notion of curvature.\n\n## Parallel transport (translation) in flat spaces\n\nSome smooth manifolds are naturally equipped with a possibility to freely move tangent vectors from one point to another.\n\n### (Genuine) parallel translation in vector and affine spaces\n\nIf $A$ is an affine space associated with the vector space $V=\\Bbbk^n$ (over the field $\\Bbbk$, usually $\\Bbbk=\\R$), then $V$ acts on $A$ by parallel translations $\\{t_w:w\\in V\\}$: $$\\forall x=(a_1,\\dots,a_n)\\in A^n,\\ \\forall w=(w_1,\\dots,w_n)\\in V\\qquad t_w x=(a_1+w_1,\\dots,a_n+ w_n).$$ This action induces the (almost trivial) action of parallel transport on tangent vectors. If $TA\\simeq V\\times A\\simeq\\Bbbk^{2n}=\\{(v,a)\\}$ is the tangent bundle, the collection of vectors $v$ attached to different points $a\\in A$, then the parallel transport acts on $TA$ by its differential, $$\\forall v\\in T_aA,\\ \\forall w\\in V,\\qquad \\rd t_w(a)\\cdot v=v\\in T_{t_w(a)}=T_{a+w} A.$$ Consequently, if $w_1,\\dots,w_k\\in V$ are vectors such that $w=w_1+\\cdots+w_k=0$, then the action $t_{w_k}\\circ\\cdots\\circ t_{w_1}:T_a A\\to T_a A$ is the identity for any point $a$.\n\nThese trivial observations indicate some of the properties that will fail for general parallel transport.\n\n### Parallel transport on Lie groups\n\nThe idea of parallel transport uses the Lie group structure on $\\R^n$ but the commutativity in fact is not necessary.\n\nLet $G$ be a (finite-dimensional) Lie group with $\\mathfrak g=T_e G$ the tangent space at the unity. For any element $g\\in G$ denote by $r_g:G\\to G$ the right action, $r_g(x)=x\\cdot g$. This action is transitive and free by the smooth diffeomorphisms. The differential $\\rd r_g:T_e G\\to T_g G$ is a bijection of the tangent spaces, which allows to identify them. For any ordered tuple of elements $g_1,\\dots,g_k\\in G$ whose product is equal to $e$, $g_1\\cdots g_k=e$, the composition $r_{g_k}\\circ\\cdots \\circ r_{g_1}$ is the identical transformation and the corresponding self-map $T_x G\\to T_x G$ the identity map.\n\nThe same obviously holds also for the left action $l_g:x\\mapsto g\\cdot x$ of $G$ on itself and for any free transitive action of $G$ on the corresponding homogeneous space $F$.\n\n## Parallel transport in topological bundles and fibrations\n\nLet $\\pi:E\\to B$ be a topological bundle with a generic fiber $F$, with all three topological spaces eventually having some additional structures defined on them. Usually we will assume that $E,B,F$ are smooth (finite-dimensional) manifolds with $\\pi$ a differentiable map of full rank, in which case $\\pi$ is often called fibration.\n\n### Motivation\n\nAlthough the definition of a bundle requires the bundles to depend \"regularly\" (continuously or differentiably) on the point in the base, there is no canonical way to identify between themselves points on different fibers.\n\nExample. Consider a smooth surface $B^2$ embedded in the affine space $\\R^3$. The tangent space $T_a B$ to the surface at a variable point $a$ depends smoothly on the point, yet there is no obvious way to \"translate\" a vector tangent to $S$ at one point, to another. However, one can construct such \"parallel transport\" using the Euclidean structure as follows: if $a_0,a_1$ are two sufficiently close points, then there exists a unique segment $\\gamma=[a,b]\\subseteq S$ of shortest length connecting them. This segment is smooth and it has well defined velocity vectors $v_i\\in T_{a_i}S$. The linear map $\\tau_0^1:T_{a_0}S\\to T_{a_1}S$ which sends $v_0$ to $v_1$ and is an orientation-preserving isometry, is uniquely defined by these two conditions. This defines the \"parallel transport\" between two tangent spaces at close points. However, if $a_0,a_1,\\dots,a_{n-1}, a_n=a_0$ are $n$ points (even sufficiently close to each other) and $\\tau_i^{i+1}:T_{a_i}S\\to T_{a_{i+1}}S$ is the corresponding \"parallel transport\" operator, then the result of the composition $\\tau_{n-1}^0\\circ \\tau_{n-2}^{n-1}\\circ\\cdots\\circ\\tau_1^2\\circ\\tau_0^1$ is in general a nontrivial rotation.\n\nIn this article we discuss differential geometric constructions which allow to introduce and study different ways of parallel transport.\n\n### Formal definition\n\nA connection in the topological bundle is a correspondence which allows to associate with any simple path $\\gamma:[0,1]\\to B$ in the base a family of homeomorphisms $\\tau_t^s:\\pi^{-1}(\\gamma(t))\\to\\pi^{-1}(\\gamma(s))$ between the respective fibers $F_t=\\pi^{-1}(\\gamma(t))$ and $F_s=\\pi^{-1}(\\gamma(s))$ such that:\n\n• $\\tau_t^s\\circ \\tau_r^t=\\tau_{r}^s$ for all values $r,t,s\\in[0,1]$ in any order, $\\tau_t^t\\equiv\\operatorname{id}$,\n• the homeomorphisms $\\tau_{t}^s$ continuously depend on $t,s\\in[0,1]$,\n• the homemorphisms $\\tau_t^s$ preserve the additional structure on the fibers, if any.\n\nThe homeomorphism $\\tau_\\gamma=\\tau_0^1:F_a\\to F_b$, $a=\\gamma(0)$, $b=\\gamma(1)$, is called the parallel transport along the path $\\gamma$. By the natural extension, it is defined for closed paths $\\gamma$ beginning and ending at any point $a$ as a self-map of the fiber $F_a$.\n\n### Parallel transport for coverings: covering homotopy\n\nIf the generc fiber $F$ of a bundle $\\pi:E\\to B$ has discrete topology, i.e., the only continous maps $[0,1]\\to F$ are constants, then there is only one way to choose the point $x(t)\\in \\pi^{-1}(\\gamma(t))$ continuously depending on $t$. In other words, if the fiber $F$ is discrete, the only continuous sections are locally constant.\n\nThus any covering of a (sufficiently regular) base $B$ admits a natural connection. This connection is locally flat: the result of parallel transport along a sufficiently small closed loop is the identical transformation. In a standard way this implies that the parallel transport between two (distant) fibers depends only on the homotopy class of the path chosen for the parallel transport.\n\nThus for any fixed point $a\\in B$ there is a natural representation of the fundamental group $\\pi_1(B,a)$ by bijections of the fiber $F_a\\simeq F$, called the group of covering transformations. Change of the base point $a$ results in a conjugate representation (assuming the base $B$ is connected).\n\nExample. Let $\\pi:E\\to B$ is a fibration of smooth manifolds with a compact fiber $F$. Then any two sufficiently close fibers $F_a$ and $F_b$ are diffeomorphic (not canonically), however, the respective homology groups $H_k(F_a,\\Z)$, $k\\le \\dim F$, considered as elements of a lattice with discrete topology, are canonically isomorphic. This allows to transport cycles of all dimensions on the fibers $F_a$ along any path in the base in a unique way. This connection together with the covariant derivation which it induces on the dual bundle $H^k_{\\rd R}(F_a,\\R)$ (especially in the algebraic context) (especially in the algebraic context) is called the Gauss-Manin connection.\n\n### Smooth connections on fibrations\n\nMain article: Connection.\n\nIn the case where $\\pi$ is a smooth bundle (fibration), it is natural to require that connections are differentiable maps between the fibers, differentiably depending also on the \"transport time\". This leads to the infinitesimal (tangent) construction known as the Ehresmann connection.\n\n#### Covariant derivation via connection\n\nLet $\\pi$ be a fibration and $s:B\\to E$ a smooth section, a differentiable map selecting a point $z=s(a)$ in each fiber $F_a$. A connection on the bundle $E$ allows to differentiate $s$ along a smooth path $\\gamma:(\\R^1,0)\\to (B,a)$, with the derivative (at the initial point $a$) being a \"vertical\" vector tangent to the fiber $F_a$ at the point $z=s(a)\\in E$.\n\nThe construction goes as follows: for every $t\\in (\\R^1,0)$ the parallel transport map $\\tau_t^0=(\\tau_0^t)^{-1}$ maps the point $s(\\gamma(t))\\in F_{\\gamma(t)}$ back into the fiber $F_a=F_{\\gamma(0)}$, defining thus a continuous curve $$(\\R^1,0)\\owns t\\mapsto f(t)=\\tau_t^0(s(\\gamma(t))\\in F_a.\\tag{TC}$$ If the section and the transport curve $\\gamma$ are smooth (the condition that should be verified in the local trivializing charts), then the curve $t\\mapsto f(t)$ is a smooth parametrized curve in the fiber $F_a$ which has a well-defined velocity vector $w\\in T_z F\\subseteq T_z E$, $z=f(0)=s(a)$.\n\nLinearization (computing the differentials) of all maps occurring in (TC) provides the linear relationships between the vectors $u=\\dot \\gamma(0)\\in T_a B$, its image $v=\\rd s(a) u$ and its \"vertical projection\" $w\\in T_z F\\subset T_z F$, $z=s(a)$. Thus the parallel transport in the tangential (linear) approximation provides us with the splitting of the space $T_z E$, the linear projection $P_z:T_z E\\to T_z F$ on the vertical subspace $T_z F$, the kernel of $\\rd \\pi(z):T_z E\\to T_a B$.\n\nThe directional derivative of a section $s(\\cdot)$ along a curve $\\gamma$ tangent to the vector $u=\\dot\\gamma(a)$ at the point $a$ of the base is therefore the vector $w=P_z\\cdot\\rd s(a)\\cdot\\dot\\gamma(a)$, with the operators $\\{P_z:T_zE\\to \\operatorname{Ker}\\rd\\pi(z)\\}$ giving the complete infinitesimal description of the connection.\n\nIn practice instead of the family of operators $\\{P_z\\}$ one uses the distribution of their null spaces, a sub-bundle $\\Gamma\\subset TE$ of the total bundle. Subspaces $\\{\\Gamma_z\\subseteq T_z E\\}$ from this distribution are referred to as horizontal subspaces should be complementary to the vertical subspaces $\\{V_z=T_z E\\}$ tangent to the fibers of the projection $\\pi$. This means that $\\dim\\Gamma=\\dim B$ and the differential $\\rd \\pi$ restricted on these subspaces is invertible.\n\n#### Ehresmann connection\n\nThe Ehresmann connection on the fiber bundle $\\pi:E\\to B$ is a horizontal distribution $\\Gamma\\subset TE$ complementary (transversal) to the vertical distribution $V=\\operatorname{Ker}\\rd \\pi\\subset TE$.\n\nThe Ehresmann connection defines the parallel transport along any smooth path $\\gamma:[0,1]\\to B$ in the base as follows. For any point $z\\in E$ over the curve, $\\pi(z)=\\gamma(t)$, there is a unique \"horizontal lift\", the vector $v(z)\\in\\Gamma_z$, which \"covers\" the velocity vector $\\dot\\gamma(t)$, $\\rd \\pi(z)v(z)=\\dot\\gamma(t)$. The corresponding vector field is defined on the induced bundle $\\gamma^*\\pi$ over the segment $[0,1]$; by construction, the flow of this field commutes with the projection on the base, hence maps fibers to fibers and defines the family of transport maps $\\tau_t^s$.\n\n#### Integrability and flatness\n\nThe parallel transport between two fibers $F_0=\\pi^{-1}(\\gamma(0))$ and $F_1=\\pi^{-1}(\\gamma(1))$ defined by a horizontal distribution $\\Gamma$ in general depends on the whole curve $\\gamma$ and changes with the curve even if its endpoints remain fixed.\n\nThere is one particular case when the parallel transport is (locally) independent of the path. Assume that the horizontal distribution is involutive and by the Frobenius theorem it admits integral submanifolds through each point $z\\in E$. By definition, these manifolds are transversal to the fibers and hence locally diffeomorphic to the base: each such manifold is the graph of a locally constant section $s$, whose graph is tangent to the distribution. If the generic fiber is compact, this implies that for any point $a\\in B$ on the base, there exists a small neighborhood $U\\owns a$ in $B$ such that each fiber $F_b=\\pi^{-1}(b)$ is canonically diffeomorphic to $F_a$. The diffeomorphism maps every point $z\\in F_a$ to the value $s_z(b)\\in F_b$, where $s_z(\\cdot)$ is the uniquely defined horizontal section of $\\pi$ such that $s_z(a)=z$. In particular, the parallel transport of the fiber $F_a$ on itself is identical for any closed loop with $\\gamma(0)=\\gamma(1)=a$ (smooth or only continuous) which entirely belongs to $U$, $\\gamma([0,1])\\subset U$.\n\nConnections with the property that the parallel translation along any sufficiently small (contractible) loop on the base is identical, are called (locally) flat connections. The local flatness, however, does not guarantee that the parallel transport along a \"large\" (non-contractible) loop in the base will be identical. Ditto for singular connections exhibiting singularities on small subsets of the base.\n\n#### Holonomy\n\nFor a fixed base point $a\\in B$ and the corresponding fiber, one may consider all self-maps of $F_a$ which appear as the result of parallel transport along closed curves with the beginning and end at $a$. The result clearly has the structure of a topological group, which in many interesting cases turns out to be finite-dimensional (eventually, discrete) Lie group. This group is called the holonomy group of the connection.\n\n## Connections on principal and vector bundles\n\nNon-involutive distributions produce parallel transport that is non-identical even for arbitrarily small simple closed loops: the deviation from the identity is generally referred to as the curvature of the connection.\n\n$\\def\\e{\\varepsilon}$ To separate the contribution of different elements of the construction, consider two non-collinear vectors $u_1,u_2\\in T_a B$ tangent to the base, and a small loop $\\gamma_\\e$ which (say, in a given chart $U$ on the base) corresponds to oriented boundary the parallelogram with the edges $\\e u_1$ and $\\e u_2$ for a sufficiently small real number $\\e>0$. Although the loop $\\gamma_\\e$ is only piecewise-smooth, one can attempt to compute the corresponding parallel transport map $\\tau_\\e=\\tau_{\\gamma_\\e}:F_a\\to F_a$. An easy estimate made in the trivializing coordinates shows that if the generic fiber $F$ is compact, then $\\tau_\\e$ is a self-diffeomorphism of the fiber, $O(\\e^2)$-close to the identity.\n\nIn absence of another structure on the generic fiber $F$ it is difficult to say more, in particular to study how the properly normalized displacement $\\lim_{\\e\\to0}\\e^{-2}(\\tau_\\e(x)-x)$ depends on the point $x\\in F_a$ and the two vectors $u_1,u_2$ (see Non-linear connection). However, for the special cases where the generic fiber is \"flat\" (a nicely parallelizable homogeneous space, see above, e.g., for vector or principal G-bundles) the computation leads to the notion of the curvature tensor, resp., curvature form.\n\nThe notions and constructions which are formulated in terms of connections and parallel transport, are central for many areas of geometry and mathematical physics. We mention only few keywords, referring to the corresponding articles for more information.\n\n• An affine connection on the tangent bundle $TM$ defines the class of \"auto-parallel curves\" on $M$, called geodesic lines. The tangent vector of a geodesic curve remains parallel to itself along these curves. The dynamical properties of the respective geodesic flows are radically different for manifolds of positive and negative curvature.\n• The tangent bundle of a Riemannian manifold admits a unique Levi-Civita connection which generates isometric parallel transport. Geodesic curves if this connection are local extremals for the Riemannian length functional. Similar \"distinguished\" connections exist also for Kähler manifolds.\n• Using connections, one can define certain characteristic classes, which measure various aspects of the nontriviality of the vector bundles on which they are defined.\n\n1. E.g., if all fibers are linear or Euclidean spaces, then $\\tau_t^s$ must be linear, resp., linear orthogonal operators.\n2. Assuming the base $B$ not very pathological, e.g., locally simply connected.\n3. I.e., $s(a)=\\operatorname{const}$ in any trivializing chart.\n4. It should be stressed that the linear projection $P_z$ of a tangent space onto its subspace is not a differential of any suitable smooth map.\n5. Note that the vertical distribution is integrable (involutive), while the integrability of $\\Gamma$ is not postulated.\n\nHow to Cite This Entry:\nParallel transport. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Parallel_transport&oldid=30961" ]
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https://www.impan.pl/pl/wydawnictwa/czasopisma-i-serie-wydawnicze/studia-mathematica/all/205/3/90746/operator-ideal-properties-of-vector-measures-with-finite-variation
[ "JEDNOSTKA NAUKOWA KATEGORII A+\n\n# Wydawnictwa / Czasopisma IMPAN / Studia Mathematica / Wszystkie zeszyty\n\n## Operator ideal properties of vector measures with finite variation\n\n### Tom 205 / 2011\n\nStudia Mathematica 205 (2011), 215-249 MSC: 28B05, 46B15, 46B42, 47B10, 47L20. DOI: 10.4064/sm205-3-2\n\n#### Streszczenie\n\nGiven a vector measure $m$ with values in a Banach space $X$, a desirable property (when available) of the associated Banach function space $L^1 (m)$ of all $m$-integrable functions is that $L^1 (m)= L^1(|m|)$, where $|m|$ is the $[0,\\infty ]$-valued variation measure of $m$. Closely connected to $m$ is its $X$-valued integration map $I_m : f \\mapsto \\int f \\, d m$ for $f \\in L^1 (m)$. Many traditional operators from analysis arise as integration maps in this way. A detailed study is made of the connection between the property $L^1 (m)= L^1(|m|)$ and the membership of $I_m$ in various classical operator ideals (e.g., the compact, $p$-summing, completely continuous operators). Depending on which operator ideal is under consideration, the geometric nature of the Banach space $X$ may also play a crucial role. Of particular importance in this regard is whether or not $X$ contains an isomorphic copy of the classical sequence space $\\ell ^1$. The compact range property of $X$ is also relevant.\n\n#### Autorzy\n\nKambah, ACT 2902, Australia\ne-mail\n• Werner J. RickerMath.-Geogr. Fakultät\nD-85072 Eichstätt, Germany\ne-mail", null, "" ]
[ null, "https://www.impan.pl/pl/wydawnictwa/czasopisma-i-serie-wydawnicze/studia-mathematica/all/205/3/90746/operator-ideal-properties-of-vector-measures-with-finite-variation", null ]
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https://academicnerds.com/2022/04/25/1-for-a-population-that-has-a-standard-deviation-of-24-fig/
[ "NEED A PERFECT PAPER? PLACE YOUR FIRST ORDER AND SAVE 15% USING COUPON:\n\n4.8/5\n\n1. For a population that has a standard deviation of 24, figure the standard deviation of the sampling distribution of samples of sizes a) 3, b)4, and d)12. Type all formulas and steps in calculation in order to receive full credits (parts (a) through (c).2. For a population that has a known standard deviation of 22, figure the 95% confidence interval (that is, the lower and upper confidence limits for part(a) through (b). Assume that in each case the researcher’s sample has a mean of 98 and the population is known to follow a normal curve. (parts (a) through (b).One can be 95% confident that for a sample size of 6, the true population mean is between ………… and ………..One can be 95% confident that for a sample size of 14, the true population mean is between ………… and ………..3. For each of the following samples that were given an experimental treatment, test whether the sample represents populations that score significantly higher than the general population. Make sure to indicate your conclusion. It is known that the general population of individuals has a mean of 78, a standard deviation of 6, and follows a normal distribution. Type all formulas and steps in calculation.A sample of 102 with a mean of 80.A sample of 9 with a mean of 83.4. 22 Women between ages of 70 and 80 were randomly selected from general population of women in this age group to take part in a study that examined the simple reaction time. The sample of women selected for the study had an average reaction time of 1.4 seconds. It is known that the mean reaction time of the population of women in this age group is 1.8 with a standard deviation of 0.4 seconds. Was the mean reaction time of the women participated in the study was significantly lower than the general population? Type all formulas, critical values, and steps in calculation.5. In a completed study, there is a known population with a normal distribution, μ=30, and σ=11. What is the estimated effect size if a sample given an experimental procedure that has a mean of  223040For each part also indicate whether the effect is approximately small, medium, or large. Type all formulas and steps in calculation Parts (a) through (c).6. On an intelligent test, the mean number of raw items correct is 240 and standard deviation is 38.  What are the raw scores on the test for people with standardized IQ scores of a)115, b) 85, and c) 130. To solve this problem, first figure the Z score for the particular IQ score, then use that Z score to find the raw score. Note that IQ scores have a mean of 100 and a standard deviation of 15. Type all formulas and steps in calculation.\n\n##### ******CLICK ORDER NOW BELOW TO GET THE ANSWER TO THIS ASSIGNMENT OR ANY OTHER ASSIGNMENT, DISCUSSION, ESSAY, HOMEWORK OR QUESTION*******.\"", null, "" ]
[ null, "https://i0.wp.com/academicnerds.com/wp-content/uploads/2023/04/Order-Now.png", null ]
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https://www.global-sci.com/intro/article_detail/cicp/10520.html
[ "Volume 23, Issue 1\nDispersive Shallow Water Wave Modelling. Part II: Numerical Simulation on a Globally Flat Space\n\nCommun. Comput. Phys., 23 (2018), pp. 30-92.\n\nPublished online: 2018-01\n\nPreview Full PDF 693 3476\nExport citation\n\nCited by\n\n• Abstract\n\nIn this paper we describe a numerical method to solve numerically the weakly dispersive fully nonlinear SERRE–GREEN–NAGHDI (SGN) celebrated model. Namely, our scheme is based on reliable finite volume methods, proven to be very efficient for the hyperbolic part of equations. The particularity of our study is that we develop an adaptive numerical model using moving grids. Moreover, we use a special form of the SGN equations where non-hydrostatic part of pressure is found by solving a linear elliptic equation. Moreover, this form of governing equations allows to determine the natural form of boundary conditions to obtain a well-posed (numerical) problem.\n\n• Keywords\n\nNonlinear dispersive waves, non-hydrostatic pressure, moving adaptive grids, finite volumes, conservative finite differences.\n\n76B15, 76M12, 65N08, 65N06\n\n• BibTex\n• RIS\n• TXT\n@Article{CiCP-23-30, author = {}, title = {Dispersive Shallow Water Wave Modelling. Part II: Numerical Simulation on a Globally Flat Space}, journal = {Communications in Computational Physics}, year = {2018}, volume = {23}, number = {1}, pages = {30--92}, abstract = {\n\nIn this paper we describe a numerical method to solve numerically the weakly dispersive fully nonlinear SERRE–GREEN–NAGHDI (SGN) celebrated model. Namely, our scheme is based on reliable finite volume methods, proven to be very efficient for the hyperbolic part of equations. The particularity of our study is that we develop an adaptive numerical model using moving grids. Moreover, we use a special form of the SGN equations where non-hydrostatic part of pressure is found by solving a linear elliptic equation. Moreover, this form of governing equations allows to determine the natural form of boundary conditions to obtain a well-posed (numerical) problem.\n\n}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2016-0179b}, url = {http://global-sci.org/intro/article_detail/cicp/10520.html} }\nTY - JOUR T1 - Dispersive Shallow Water Wave Modelling. Part II: Numerical Simulation on a Globally Flat Space JO - Communications in Computational Physics VL - 1 SP - 30 EP - 92 PY - 2018 DA - 2018/01 SN - 23 DO - http://doi.org/10.4208/cicp.OA-2016-0179b UR - https://global-sci.org/intro/article_detail/cicp/10520.html KW - Nonlinear dispersive waves, non-hydrostatic pressure, moving adaptive grids, finite volumes, conservative finite differences. AB -\n\nIn this paper we describe a numerical method to solve numerically the weakly dispersive fully nonlinear SERRE–GREEN–NAGHDI (SGN) celebrated model. Namely, our scheme is based on reliable finite volume methods, proven to be very efficient for the hyperbolic part of equations. The particularity of our study is that we develop an adaptive numerical model using moving grids. Moreover, we use a special form of the SGN equations where non-hydrostatic part of pressure is found by solving a linear elliptic equation. Moreover, this form of governing equations allows to determine the natural form of boundary conditions to obtain a well-posed (numerical) problem.\n\nGayaz Khakimzyanov, Denys Dutykh, Oleg Gusev & Nina Yu. Shokina. (2020). Dispersive Shallow Water Wave Modelling. Part II: Numerical Simulation on a Globally Flat Space. Communications in Computational Physics. 23 (1). 30-92. doi:10.4208/cicp.OA-2016-0179b\nCopy to clipboard\nThe citation has been copied to your clipboard" ]
[ null ]
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http://connection.ebscohost.com/c/articles/4710007/apparatus-low-frequency-study-high-loss-dielectrics
[ "TITLE\n\nApparatus for low-frequency study of high-loss dielectrics\n\nAUTHOR(S)\nJanik, P.; Tomawski, L.; Ziolo, J.\nPUB. DATE\nJuly 2001\nSOURCE\nReview of Scientific Instruments;Jul2001, Vol. 72 Issue 7, p3019\nSOURCE TYPE\nDOC. TYPE\nArticle\nABSTRACT\nThe measurement setup for studying complex dielectric permittivity in a region of frequency between 10[sup -3] to 10[sup 5] Hz. Loss factor, tan δ of the sample can be very high, from 10 to 10[sup 4], because the loss resistance is compensated by negative resistance, realized by a negative impedance converter. When loss resistance is compensated by negative resistance then oscillations are excited in the circuit. An inductance is simulated by electronic inductance simulator, which quality factor Q is high and the region of setting value of inductance is eight orders wide. The unknown value of capacitance of the sample is calculated from the oscillations frequency and the unknown value of parallel loss resistance from the parameters setting on the negative impedance converter. © 2001 American Institute of Physics.\nACCESSION #\n4710007\n\nShare" ]
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https://exoai.github.io/software/taurex/forward/transmission/
[ "# TauREx Tranmission Forward Model\n\nTo generate a transmission forward model, first make sure your parameter file is set to transmission\n\n``````[General]\ntype = transmission\n``````\n\nThe forward model is then simply run with\n\n``````python create_spectrum.py -p [PARAMETER FILE]\n``````\n\nThis will create an ascii file `SPECTRUM_out.dat` in the output path specified in your parameter file (`[Output] > path`).\n\nIf you would like to plot your spectrum, add the `--plot` flag. If you would like to save the `.pickle` instance `SPECTRUM_INSTANCE_out.pickle` containing all of the internal states (see here), then add the flag `--save_instance`.\n\n``````python create_spectrum.py -p [PARAMETER FILE] --plot --save_instance\n``````\n\nDocumentation on additional flags can be found with\n\n``````python create_spectrum.py --help\n``````\n\n### For C/O equilibrium chemistry models\n\nTauREx uses the Atmospheric Chemical Equilibrium (ACE) model (Agundez et al. 2012, A&A, 548, A73) using the thermochemical data by Venot et al (2012, A&A,546,A43).\n\nIf you run the model for the first time, you may need to compile it first (see here)).\n\nTo run the C/O forward model, set the following parameters:\n\n``````[General]\nace = true\n\n[Atmosphere]\nace_metallicity = 1 #metallicity. Change to whatever, 1 = 1x solar, 10 = 10x solar\nace_co = 0.54954 #C/O ratio\n``````\n\nBelow is an example:\n\n``````python create_spectrum.py -p tests/test_0_transmission_ace/test_fm.par --plot\n``````\n\nUpdated:" ]
[ null ]
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https://getfreecourses.co/learn-complete-calculus-1-from-scratch-1/
[ "## Learn everything from Calculus 1.It carries 42.5 hrs content, 59 Sections, 327 areas, 556 solved numerical problems\n\nCalculus 1\n\nWhat you’ll learn\n\n• Function, Domain and Range, Vertical line/Horizontal line/Ordered pair tests, Graphing of function, Inverse of a function, Parabola\n• Limit, Limit of trig functions, Limit of infinity, One-sided/Two-sided limits from the graphs and equations, Limit of multi variable function, Continuity and Discontinuity\n• Derivative rule, Chain rule, Power, Product and Quotient rule, Derivative of trig functions, inverse trig, hyperbolic, inverse hyperbolic, Composite functions,\n• Implicit differentiation, Asymptote, Vertical, horizontal asymptote and Hole, Point-slope, Slope-intercept, Standard form of equation,\n• Circle, Logarithmic rules, Logarithmic differentiation, Least square lines/ Regression lines, Squeeze theorem\n\nRequirements\n\n• Be able to know the very basics of calculus, algebra and trigonometry\n\n#### Description\n\nBe a master of calculus 1. Learn Calculus 1 through animation ,The course includes videos explanation with basics, graphical and mathematical proofs. It carries hundreds of numerical practice problems with complete solutions. The lectures are appealing, fancy (graphic designing), fast and take less time to walk you through the content. A prefect choice for students who take high school and college.\n\nWhy I want you to join this course?\n\n1. It carries 42.5 hours content\n2. 59 Sections\n3. 370+ lectures\n4. 327 areas that have been included\n5. 325 Figures and tables\n6. 556 solved numerical problems with complete solutions\n7. Animation has been used throughout the course\n8. Suitable background (Neither very sharp nor very dark)\n9. It took me full year to complete this course\n\nSo join me here and do it in a quick and easy way.\n\nList of content:\n\n• Function\n• Domain & Range\n• Inverse function\n• Vertical line test\n• Horizontal line test\n• Ordered pair test\n• Graphing of function\n• Transformation of function\n• Parabola\n• Inverse parabolic function\n• Circle\n• Center and Radius of a circle\n• Radian and Degree of a circle\n• Least squares method\n• Least square lines/Regression lines\n• Limit\n• Limit of Trigonometric functions\n• Limit of infinity\n• One-sided limit\n• Two-sided limit\n• Limit of multi variable functions\n• Continuity & Discontinuity\n• Asymptote\n• Vertical Asymptote\n• Horizontal Asymptote\n• Hole\n• Point-slope form of the equation\n• Slope-intercept form of the equation\n• Standard form of the equation\n• Tangent and normal lines\n• Derivative Rule\n• Chain Rule\n• Power Rule\n• Product Rule\n• Quotient Rule\n• Derivative of Trigonometric functions\n• Inverse Trigonometric functions\n• Hyperbolic functions\n• Inverse hyperbolic functions\n• Composite functions\n• Implicit Differentiation\n• Logarithmic and exponential Rules\n• Logarithmic and exponential differentiation\n• Squeeze Theorem\n• Modeling and solving the equations\n\n#### Who this course is for:\n\n• Beginner at high school/college\n\nCreated by Moein Ud Din\n\nLast updated 10/2020\nEnglish\n\nSize: 17.65GB\n\nhttps://www.udemy.com/course/calculus-1-pre-calculus/" ]
[ null ]
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https://www.mathwarehouse.com/solved-problems/quadratic-roots/find-the-roots-of-19x-squared-minus-1000x-860
[ " [SOLVED] the roots of y=19x^2-1000x-860. All the work, all the steps and the graph\n\n# [SOLVED] the root of y=19x^2-1000x-860\n\n### All the work, steps and graph of this equation\n\n${}$\n\n${}$\n\n${}$\n\nChange the three numbers below and , and our tool will tell you what the root of the equation!\n\n### See similar equations:\n\nThe roots of :\n\n300,000,000,000 calculated quadratic equations\nSee all quadratic equations\n\n### Ultimate Math Solver (Free)\n\nFree Algebra Solver ... type anything in there!" ]
[ null ]
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https://stats.stackexchange.com/tags/svm/hot
[ "# Tag Info\n\nThe condition of independent identical distributions (iid) refers to the $(x,y)$ data points. Independence means: $$p((x_i, y_i), (x_k, y_k)) = p((x_i, y_i)) p((x_k, y_k)),$$ i.e. the sampling of \\$(..." ]
[ null ]
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https://www.kumarweb28.com/opa-june19-unix-code
[ "", null, "# OPA JUNE 19 Unix\n\nStudent details are stored in following format:\n\nRoll no, Name, Standard, Science_Score, Mathematics_Score, SchoolName\nWrite the unix command to display all the fields in the same order as above for all the students whose score is more than 80 in mathematics and mathematics score should be the top score, among all the subjects for the respective student . The student details are to be displayed sorted in the ascending order of Standard (in which student studying) and ascending order of Mathematics score(If first sort parameter value is same for two or more students).\n\nRefer sample test case below for more details.\n\nThe student details are provided as command line argument when the file containing your command will run. Use appropriate command line argument(\\$1,\\$2)\nInput:\n\n♦ Sample test case\n\nTest case Input\n\n1,RajaR,9,60,85,SM\n2,Pooja,10,85,80,DAV\n3,RaghuRam,10,95,92,DAV\n4,Akhil,9,60,55,SM\n5,Bharath,10,80,88,SM\n6,Chandra,9,75,92,DAV\n\nTest case output:\n\n1|RajaR|9|60|85|SM\n\n6|Chandra|9|75|92|DAV\n\n5|Bharath|10|80|88|SM\n\nExplanation\n\nThe students , whose score is greater than 80 in mathematics and the Mathematics score is more than other subject(science) score are: RajaR ,Chandra,Bharath, After sorting the filtered records as per given requirement the output will be as below.\n11RajaRI9160185ISM 61Chandra19175192IDAV 51Bharathl10180188ISM\nThe above records displayed 9th class students first and later 10th class students nect but there are two students with 9th standard and hence the two records inturn sorted in the ascending order of Mathematics score. Here records are sorted using two sort parameters (standard and Mathematics score) in one go, ie two level sorting. Note: Extra line of space should not be there in between the output records .\nTwo level sorting means , Records will be sorted using second sort parameter / argument(Mathematics in this example) if and only if there are multiple records having the same value(for a field / column) after first level of sorting wrt the first sort parameter(Standard in this example).\n\nSolutions:" ]
[ null, "https://static.wixstatic.com/media/bdf5eb_21f30e4e767f47ffa6fd9af5ec3412b1~mv2.jpg/v1/fill/w_980,h_343,al_c,lg_1,q_80/bdf5eb_21f30e4e767f47ffa6fd9af5ec3412b1~mv2.jpg", null ]
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https://mathopenref.com/triangleareaperim.html
[ "# Area vs Perimeter of a triangle\n\nA triangle with a fixed perimeter can have many different areas.\nTry this Drag the orange dot on the triangle below. The triangle will have a fixed perimeter, but the area will vary.\n\nA common error is to assume that a triangle that has a fixed perimeter must also have a fixed area. This is definitely not the case as can be seen from the figure above. As you drag the orange point A, the triangle will maintain a fixed perimeter. But as you can see, the area varies quite a bit.\n\nWhen A is half way between B and C, the area is at a maximum. As you drag it around towards one side you can see the area decreasing, both in the formula at the top and by noticing that fewer and fewer squares can fit inside it. Eventually, when A is in line with B and C, the area is zero.\n\nThe area is at a maximum when the triangle is isosceles. That is, when both sides have the same length. Carefully adjust A above to create an isosceles triangle and note the area is the greatest when AC and AB are both the same length (9.0)\n\n## Try it with string\n\nMake a loop of string and pass it around two pins (corresponding to the two points B and C above). Pull the string taut with a third pin to make a triangle. As you move any pin with the string tight, you will be making triangles with different areas but the perimeter is fixed (the length of the string loop).\n\n## The Ellipse Connection\n\nIn the figure above, select the \"Show trail\" checkbox, then drag point A all the way around the base line. The resulting shape is an ellipse.\n\nWhy is this? The definition of an ellipse is\n\n\"A line forming a closed loop, where the sum of the distances from two points (foci) to every point on the line is constant\"\nPoints B and C form the two foci. Since the distance from B to C is fixed, and the perimeter is fixed, then the sum of the distances AB and AC are constant - the condition required to form an ellipse.\n\nThe string experiment described above is actually a practical way to draw an ellipse. See Drawing an ellipse using string and 2 pins. For more on ellipses, see also Definition of an ellipse." ]
[ null ]
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https://www.colorhexa.com/92ffa9
[ "# #92ffa9 Color Information\n\nIn a RGB color space, hex #92ffa9 is composed of 57.3% red, 100% green and 66.3% blue. Whereas in a CMYK color space, it is composed of 42.7% cyan, 0% magenta, 33.7% yellow and 0% black. It has a hue angle of 132.7 degrees, a saturation of 100% and a lightness of 78.6%. #92ffa9 color hex could be obtained by blending #ffffff with #25ff53. Closest websafe color is: #99ff99.\n\n• R 57\n• G 100\n• B 66\nRGB color chart\n• C 43\n• M 0\n• Y 34\n• K 0\nCMYK color chart\n\n#92ffa9 color description : Very light lime green.\n\n# #92ffa9 Color Conversion\n\nThe hexadecimal color #92ffa9 has RGB values of R:146, G:255, B:169 and CMYK values of C:0.43, M:0, Y:0.34, K:0. Its decimal value is 9633705.\n\nHex triplet RGB Decimal 92ffa9 `#92ffa9` 146, 255, 169 `rgb(146,255,169)` 57.3, 100, 66.3 `rgb(57.3%,100%,66.3%)` 43, 0, 34, 0 132.7°, 100, 78.6 `hsl(132.7,100%,78.6%)` 132.7°, 42.7, 100 99ff99 `#99ff99`\nCIE-LAB 91.905, -49.028, 31.554 54.773, 80.492, 50.184 0.295, 0.434, 80.492 91.905, 58.304, 147.235 91.905, -51.082, 53.118 89.718, -48.031, 29.638 10010010, 11111111, 10101001\n\n# Color Schemes with #92ffa9\n\n• #92ffa9\n``#92ffa9` `rgb(146,255,169)``\n• #ff92e8\n``#ff92e8` `rgb(255,146,232)``\nComplementary Color\n• #b2ff92\n``#b2ff92` `rgb(178,255,146)``\n• #92ffa9\n``#92ffa9` `rgb(146,255,169)``\n• #92ffe0\n``#92ffe0` `rgb(146,255,224)``\nAnalogous Color\n• #ff92b2\n``#ff92b2` `rgb(255,146,178)``\n• #92ffa9\n``#92ffa9` `rgb(146,255,169)``\n• #e092ff\n``#e092ff` `rgb(224,146,255)``\nSplit Complementary Color\n• #ffa992\n``#ffa992` `rgb(255,169,146)``\n• #92ffa9\n``#92ffa9` `rgb(146,255,169)``\n• #a992ff\n``#a992ff` `rgb(169,146,255)``\n• #e8ff92\n``#e8ff92` `rgb(232,255,146)``\n• #92ffa9\n``#92ffa9` `rgb(146,255,169)``\n• #a992ff\n``#a992ff` `rgb(169,146,255)``\n• #ff92e8\n``#ff92e8` `rgb(255,146,232)``\n• #46ff6d\n``#46ff6d` `rgb(70,255,109)``\n• #5fff81\n``#5fff81` `rgb(95,255,129)``\n• #79ff95\n``#79ff95` `rgb(121,255,149)``\n• #92ffa9\n``#92ffa9` `rgb(146,255,169)``\n• #acffbd\n``#acffbd` `rgb(172,255,189)``\n• #c5ffd1\n``#c5ffd1` `rgb(197,255,209)``\n• #dfffe5\n``#dfffe5` `rgb(223,255,229)``\nMonochromatic Color\n\n# Alternatives to #92ffa9\n\nBelow, you can see some colors close to #92ffa9. Having a set of related colors can be useful if you need an inspirational alternative to your original color choice.\n\n• #96ff92\n``#96ff92` `rgb(150,255,146)``\n• #92ff97\n``#92ff97` `rgb(146,255,151)``\n• #92ffa0\n``#92ffa0` `rgb(146,255,160)``\n• #92ffa9\n``#92ffa9` `rgb(146,255,169)``\n• #92ffb2\n``#92ffb2` `rgb(146,255,178)``\n• #92ffbb\n``#92ffbb` `rgb(146,255,187)``\n• #92ffc4\n``#92ffc4` `rgb(146,255,196)``\nSimilar Colors\n\n# #92ffa9 Preview\n\nThis text has a font color of #92ffa9.\n\n``<span style=\"color:#92ffa9;\">Text here</span>``\n#92ffa9 background color\n\nThis paragraph has a background color of #92ffa9.\n\n``<p style=\"background-color:#92ffa9;\">Content here</p>``\n#92ffa9 border color\n\nThis element has a border color of #92ffa9.\n\n``<div style=\"border:1px solid #92ffa9;\">Content here</div>``\nCSS codes\n``.text {color:#92ffa9;}``\n``.background {background-color:#92ffa9;}``\n``.border {border:1px solid #92ffa9;}``\n\n# Shades and Tints of #92ffa9\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, #000902 is the darkest color, while #f4fff6 is the lightest one.\n\n• #000902\n``#000902` `rgb(0,9,2)``\n• #001c06\n``#001c06` `rgb(0,28,6)``\n• #00300a\n``#00300a` `rgb(0,48,10)``\n• #00440e\n``#00440e` `rgb(0,68,14)``\n• #005712\n``#005712` `rgb(0,87,18)``\n• #006b17\n``#006b17` `rgb(0,107,23)``\n• #007e1b\n``#007e1b` `rgb(0,126,27)``\n• #00921f\n``#00921f` `rgb(0,146,31)``\n• #00a623\n``#00a623` `rgb(0,166,35)``\n• #00b927\n``#00b927` `rgb(0,185,39)``\n• #00cd2b\n``#00cd2b` `rgb(0,205,43)``\n• #00e02f\n``#00e02f` `rgb(0,224,47)``\n• #00f434\n``#00f434` `rgb(0,244,52)``\n• #09ff3d\n``#09ff3d` `rgb(9,255,61)``\n• #1cff4c\n``#1cff4c` `rgb(28,255,76)``\n• #30ff5c\n``#30ff5c` `rgb(48,255,92)``\n• #44ff6b\n``#44ff6b` `rgb(68,255,107)``\n• #57ff7b\n``#57ff7b` `rgb(87,255,123)``\n• #6bff8a\n``#6bff8a` `rgb(107,255,138)``\n• #7eff9a\n``#7eff9a` `rgb(126,255,154)``\n• #92ffa9\n``#92ffa9` `rgb(146,255,169)``\n• #a6ffb8\n``#a6ffb8` `rgb(166,255,184)``\n• #b9ffc8\n``#b9ffc8` `rgb(185,255,200)``\n• #cdffd7\n``#cdffd7` `rgb(205,255,215)``\n• #e0ffe7\n``#e0ffe7` `rgb(224,255,231)``\n• #f4fff6\n``#f4fff6` `rgb(244,255,246)``\nTint Color Variation\n\n# Tones of #92ffa9\n\nA tone is produced by adding gray to any pure hue. In this case, #c4cdc6 is the less saturated color, while #92ffa9 is the most saturated one.\n\n• #c4cdc6\n``#c4cdc6` `rgb(196,205,198)``\n• #c0d1c4\n``#c0d1c4` `rgb(192,209,196)``\n• #bcd5c1\n``#bcd5c1` `rgb(188,213,193)``\n• #b8d9bf\n``#b8d9bf` `rgb(184,217,191)``\n• #b4ddbc\n``#b4ddbc` `rgb(180,221,188)``\n• #afe2ba\n``#afe2ba` `rgb(175,226,186)``\n• #abe6b8\n``#abe6b8` `rgb(171,230,184)``\n• #a7eab5\n``#a7eab5` `rgb(167,234,181)``\n• #a3eeb3\n``#a3eeb3` `rgb(163,238,179)``\n• #9ff2b0\n``#9ff2b0` `rgb(159,242,176)``\n• #9af7ae\n``#9af7ae` `rgb(154,247,174)``\n• #96fbab\n``#96fbab` `rgb(150,251,171)``\n• #92ffa9\n``#92ffa9` `rgb(146,255,169)``\nTone Color Variation\n\n# Color Blindness Simulator\n\nBelow, you can see how #92ffa9 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" ]
[ null ]
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http://theandyzone.com/flightblog/?p=387
[ "# Flying a CTSW with Flat Plate Wings: Analyzing “Impact Lift”\n\nI wrote a blog a little while ago entitled “One Form of Lift” which talked about the generation of lift and how there was, from an engineering standpoint, no such thing as “impact lift”. Classical engineering analysis only uses lift (which is primarily generated by pressure flows around the wing) and drag. My assertion is that most or all of the force people are calling “impact lift” is really drag, but was there a way to prove it by using a real world example? To take a look at that, I decided to analyze what happens if I stick a set of flat plate wings on my light sport aircraft, a Flight Design CTSW.\n\nWe will assume that the wings on the CTSW are mounted so that they are at zero degrees angle of attack (and angle of incidence) when the airplane is sitting level. The wing area of a CTSW is 107.4 square feet and the airplane’s max gross weight is 1320 pounds.\n\nThe equation for lift is: Lift = ½ D V2 S CL where D= air density, S = wing area, V2= the velocity squared, and CL = the coefficient of lift.\n\nThe equation for drag is of the same form, i.e., Drag = ½ V2 S CD where = air density, S = area being analyzed for drag, and CD = coefficient of drag.\n\nFor these formulas, lift=weight, the density of air at sea level is used, and S= 107.4 sq ft.\n\nA flat plate has a lift coefficient, and the curve maximum hits a CL = 0.7 at an angle of attack of approximately 12 degrees.", null, "SOURCE:http://home.planet.nl/~kpt9/The%20boundary%20layer.htm\n\nAt twelve degrees’ angle of attack, then:\nLift = ½ (.002378 slugs/ft3) V2 (107.4) (0.7)\n\nFor the airplane to fly, lift must equal to weight, so:\n1320 = ½ (.002378) V2 (107.4) (0.7)\n\n2640/(.002378*107.4*.7) = V2\n\n2640/0.17877804 = V2\n\n14,767 = V2\n\n121.5 = V (feet per second) or 72 knots\n\nThis would get my CTSW with a flat plate wing off the ground at 72 knots while nibbling at the stall. Let’s say you understand this will be the case and elect to back off on the liftoff a bit, flying off at approximately 8 degrees angle of attack. (I believe you will either strike the tail of the CTSW at 12 degrees or be very much at risk of it.) So, when would you want to rotate? At that 8 degrees, you have a lift coefficient of 0.6. That gives you:\n\n2640/.153238 = V2\n\n17,228.1 = V2\n\n131.25 =V (fps) or 77 knots\n\nSince the CT actually gets airborne as low as 42 knots with flaps and about 50 without, you get an idea of the work a good airfoil design (using Bernoulli’s) is doing for you. You can “reverse engineer” the lift coefficient at those speeds by substituting them in for V and solving for CL.\n\nDoing so for the no flap configuration and 50 knots yields a CL = 1.45; in other words, the shaping of the airfoil increases the “flat plate” lift coefficient by slightly over 100%. (The use of flaps yields a lift coefficient of 2.06…which is part of the reason why it leaps off the runway and feels like you’re in an elevator going straight up…)\n\nBut, let’s go back to flying by the flat plate alone since our real target is to examine the idea of “impact lift”. As I said in an earlier blog, the only way to do this from an engineering standpoint is to use drag as the “impact lift” force. There is no accounting for such a thing in conventional performance analysis (which should tell you something in and of itself about the rigor of the idea, despite some folks trying to discount how engineers do it).\n\nLet’s see how we might be able to generate enough “impact lift” (drag) to fly. A flat plate has a drag coefficient of 1.28. Since the equations for lift and drag are the same and we’re considering the same area in both equation sets (i.e., only the area of the wings), then we can shortcut the calculation of the total drag force the wings can generate by simply taking a ratio of 1.28/0.7 = 1.83. Then, that same 1320 lbs of total force…now as drag instead of lift…would be generated at 72/1.83 = 39 knots. But this would be for a CTSW wing deflected at 90 degrees to the windstream (and the fuselage). Since we’re just trying to use “impact lift” (i.e., drag) to get airborne, the max lift would occur at a wing inclined 45 degrees to the windstream. The “lift” would be equal to the sine of 45 degrees times the total force. The sine of 45 degrees is 0.707. So, then the speed at which you’d have just enough drag acting vertically to lift off would be: 39 knots/0.707 = 56 knots.\n\nHowever, for this to occur, the drag acting in the horizontal direction would also be 1320 lbs (sine and cosine of 45 degrees…the horizontal and vertical force components would be the same). Let’s see if the Rotax 912 can get there.\n\nUsing Thrust = (HP*efficiency*326)/KTAS and assuming we have a 0.8 propeller efficiency:\n\n1320 = (100*.8*326)/KTS\n\n1320 KTS = 26,080\n\nKTS = 19.75\n\nThis is the speed the Rotax could attain in this “lift/drag” configuration. This is a conservative answer since the airplane will have more drag area than this, i.e., we did not account for the frontal area of the fuselage or other components. This puts us well short of the approximate 56 knots it would take to get airborne. To see how big an engine it would take, let’s use the same formula and solve for HP.\n\n1320= (HP*.8*326) / (56)\n\n1320 = (260.8HP)/ (56)\n\n1320*56 = 260.8 HP\n\n73920 = 260.8 HP\n\n283.4 = HP\n\nSo, it would take an engine producing almost three times the horsepower the CT has available which would increase the weight and cause us to do all these calculations over again. Keep in mind, too, that we are only talking about the power it would take to get the CT into the air since climb rate is a function of excess horsepower. The engine would have to be bigger still. (At least a 300HP IO-540…) What the numbers are telling you is that the idea of impact lift doesn’t work, and that’s before we try to consider the flying characteristics and design of the flight controls for such a beast. We know that increasing camber (curvature) of an airfoil causes an increase in lift and that’s what makes ailerons and elevators work; how do you explain what’s happening if “impact lift” (drag) is the only force?\n\n“Impact lift” is a misnomer and a popular myth, like saying you can discount Bernoulli’s principles and just use Newton’s laws to easily explain how airfoils work. Good luck with either. From both an engineering and piloting standpoint, it’s better and proper to see lift as a result of Bernoulli’s (i.e., pressure distributions) principles and drag as something that needs to be overcome and is not your friend (except when trying to slow down). You’ll not only stay safer that way but you’ll teach your kids the right concepts, making sure it is “as simple as possible but no simpler”.\n\nAUTHOR’S NOTE: Many thanks to Dave Witwer, Jim Gardner, and Matt Zwack for their review of the drafts of this blog. They’re all pilots and aerospace engineers (Dave, Jim and I worked at Johnson Space Center and Matt works out at Marshall Spaceflight Center.) Great guys I’m honored to know as colleagues and friends!" ]
[ null, "http://theandyzone.com/flightblog/wp-content/uploads/2016/12/image002-300x211.gif", null ]
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http://git.megacz.com/?p=coq-hetmet.git;a=blob;f=src/Extraction.v;h=542b5d49d7fc8d462a8666b19ad4722467951b80
[ "1 (* need this or the Haskell extraction fails *)\n2 Set Printing Width 1300000.\n4 Require Import Coq.Lists.List.\n5 Require Import Coq.Strings.Ascii.\n6 Require Import Coq.Strings.String.\n7 Require Import Main.\n11 Open Scope string_scope.\n14 (* I try to reuse Haskell types mostly to get the \"deriving Show\" aspect *)\n15 Extract Inductive option => \"Prelude.Maybe\" [ \"Prelude.Just\" \"Prelude.Nothing\" ].\n16 Extract Inductive list   => \"([])\" [ \"([])\" \"(:)\" ].\n17 (*Extract Inductive vec    => \"([])\" [ \"([])\" \"(:)\" ].*)\n18 (*Extract Inductive Tree   => \"([])\" [ \"([])\" \"(:)\" ].*)\n19 Extract Inlined Constant map => \"Prelude.map\".\n20 Extract Inductive string => \"Prelude.String\" [ \"([])\" \"(:)\" ].\n21 Extract Inductive prod   => \"(,)\" [ \"(,)\" ].\n22 Extract Inductive sum    => \"Prelude.Either\" [ \"Prelude.Left\" \"Prelude.Right\" ].\n23 Extract Inductive sumbool => \"Prelude.Bool\" [ \"Prelude.True\" \"Prelude.False\" ].\n24 Extract Inductive bool    => \"Prelude.Bool\" [ \"Prelude.True\" \"Prelude.False\" ].\n25 Extract Inductive unit    => \"()\" [ \"()\" ].\n26 Extract Inlined Constant string_dec => \"(==)\".\n27 Extract Inlined Constant ascii_dec => \"(==)\".\n28 Extract Inductive string => \"Prelude.String\" [ \"[]\" \"(:)\" ].\n30 (* adapted from ExtrOcamlString.v *)\n31 Extract Inductive ascii => \"Prelude.Char\"\n32 [\n33 \"{- If this appears, you're using Ascii internals. Please don't -} (\\ b0 b1 b2 b3 b4 b5 b6 b7 ->   let f b i = if b then 1 `shiftL` i else 0 in Data.Char.chr (f b0 0 .|. f b1 1 .|. f b2 2 .|. f b3 3 .|. f b4 4 .|. f b5 5 .|. f b6 6 .|. f b7 7))\"\n34 ]\n35 \"{- If this appears, you're using Ascii internals. Please don't -} (\\ f c -> let n = Char.code c in let h i = (n .&. (1 `shiftL` i)) /= 0 in f (h 0) (h 1) (h 2) (h 3) (h 4) (h 5) (h 6) (h 7))\".\n36 Extract Constant zero  => \"'\\000'\".\n37 Extract Constant one   => \"'\\001'\".\n38 Extract Constant shift => \"\\ b c -> Data.Char.chr (((Char.code c) `shiftL` 1) .&. 255 .|. if b then 1 else 0)\".\n40 Unset Extraction Optimize.\n41 Unset Extraction AutoInline.\n43 Definition coqCoreToStringPass (s:@CoreExpr CoreVar) : string\n44    := \"FIXME\".\n45 (*\n46 Definition coqCoreToCorePass (s:CoreExpr CoreVar) : CoreExpr CoreVar\n47    :=\n48 *)\n50 Extraction \"Extraction.hs\" coqCoreToStringPass." ]
[ null ]
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https://virallistclub.com/27502/
[ "# How Many Yards Is 100 Meters\n\nby -90 views\n\nValue in yards value in meters 10936132983377. How much is 100 meters in feet.", null, "Conversion Chart For Inches Yardage And Meters Sewing Basics Sewing Hacks Sewing Measurements\n\n### It is an English unit predecessor of imperial units and the term was derived from gerd in Old English the.", null, "How many yards is 100 meters. To calculate 100 Yards to the corresponding value in Meters multiply the quantity in Yards by 09144 conversion factor. Here is a solution for your problem plus a conversion chart and an easy to use conversion calculator. A yard is a unit of length equal to 3 feet or exactly 09144 meters.\n\nThe United States is one notable exception in that it largely uses US customary units such as yards inches feet and miles instead of meters in everyday use. 100 Meters x 10936132983377 10936132983377 Yards 100 Meters is equivalent to 10936132983377 Yards. Yd is a unit of length in both the imperial and US customary systems of measurement.\n\nWhat is 100 meters in inches feet meters km miles mm yards etc. Since 1959 a yard has been defined as exactly 09144 meters. 1 meter to yards.\n\nAnother way is saying that 1009 meters is equal to 1 00090624380574827 yards. 100 m to miles. 100 m to in.\n\nHow to convert 100 meters to yards To calculate a value in meters to the corresponding value in yards just multiply the quantity in meters by 10936132983377 the conversion factor. A meter is the basic unit of length in the metric system also known as the International System of Units. Likewise the question how many meter in 100 yard has the answer of 9144 m in 100 yd.\n\nUse this page to learn how to convert between metres and yards. For example to calculate how many yards is 100 meters multiply 100 by 10936133 that makes 10936133 yards is 100 meters. Since 1959 a yard has been defined as exactly 09144 meters.\n\nYd is a basic unit of length which is commonly used in United States customary units Imperial units and the former English units. 100 m 109361 yd An alternative is also that one yard is approximately zero point zero zero nine times one hundred meters. How many inches in 100 meters.\n\nA yard is a unit of length equal to 3 feet or exactly 09144 meters. A meter or metre is the fundamental unit of length in the metric system from which all other length units are based. Yd is a unit of length in both the imperial and US customary systems of measurement.\n\nHow much are 100 yards in meters. That means that to convert yard measurements you should multiply the figure by 09144. To calculate 100 Meters to the corresponding value in Yards multiply the quantity in Meters by 10936132983377 conversion factor.\n\nIn formulaic terms 1 meter is equal to 100009144 yards and 100 meters is equal to 100 100009144 yards. It is equal to 100 centimeters 11000th of a kilometer or about 3937 inches. 100 m to mm.\n\nAnother way is saying that 1008 meters is equal to 1 00090714285714286 yards. Note that rounding errors may occur so always check the results. 100 m to yd conversion.\n\n100 meters is equal to 10936 yards. 100 M to yards 100 109361 109361 yd. Another way is saying that 1007 meters is equal to 1 00090804369414101 yards.\n\nIt is defined as the length of the path travelled by light in. 1 metre is equal to 1 m or 10936132983377 yards. In this case 1 yard is equal to 00090804369414101 1007 meters.\n\nHow far is 100 yards in meters. Type in your own numbers in the form to convert the units. 1 meter equals 109361 yards or there are 109361 yd in a m.\n\n100 m to feet. It is also equal to 3 feet or 36 inches. It is equal to 3 feet or 36 inches defined as 9144 centimeters.\n\n100 yd to m conversion. 100 Yards x 09144 9144 Meters 100 Yards is equivalent to 9144 Meters. 100 m to km.\n\nThe meter symbol m is the fundamental unit of length in the International System of Units SI. How many yards are in 100 meters. A meter or metre is the fundamental unit of length in the metric system from which all other length units are based.\n\n1 Meter m is equal to 10936133 yards. 100 m to yd. In this case 1 yard is equal to 00090714285714286 1008 meters.\n\nIn this case we should multiply 100 Meters by 10936132983377 to get the equivalent result in Yards. How long is it. Conversion chart for meters to yards.\n\nThe origin of the yard as a unit is unclear. What is 100 meters in feet. How far is 100 meters in yards.\n\nHow many yards in a meter. In this case 1 yard is equal to 00090624380574827 1009 meters. Here is the formula.\n\n100 m to cm. To convert meters to yards multiply the meter value by 10936133. Convert cm km miles yds ft in mm m.\n\nIt is equal to 100 centimeters 11000th of a kilometer or about 3937 inches. In this case we should multiply 100 Yards by 09144 to get the equivalent result in Meters. How to convert meters to yards.\n\nA common question is How many yard in 100 meter. Following is a meters to yards table to convert 1 meter up to 100 meters. We can say that one hundred meters is approximately one hundred nine point three six one yards.\n\nBoth numerical calculations extend to many decimal places. And the answer is 109361329834 yd in 100 m.", null, "T Shirt Yarn 109 Yards 100 Meters 6 8 Mm 350 Grams Blue Etsy T Shirt Yarn Fabric Yarn Yarn", null, "T Shirt Yarn 100 Meters 7 9 Mm 109 Yards 028 035 In Etsy T Shirt Yarn Ribbon Yarn Yarn", null, "How Many Yards In A Mile English Units Converting Measurements Metric Conversions", null, "Macrame Rope 3 Mm 100 Meters 109 Yards Rope Cord Knitting Rope Crochet Cord Crochet Yarn Basket Bag Carpet Polyester Cord Red By Cordandyarn On Etsy", null, "Cotton Rope 3 Mm 109 Yards 240 G 37 Colors Macrame Cord Cotton Etsy Macrame Cord Crochet Backpack Pattern Crochet Rope", null, "3 Mm Misty Cord Cotton 100 M Macrame Yarn Macrame Macrame Rope Multi Color 108 Yards 100m Chunky Yarn Bobbiny Dream Catcher Handmade Chair Macrame Swing", null, "5mm Eucalyptus Green Single Twist Cord 108 Yards 100 Meters Bobbiny Single Twist Macrame Stri 1 Singles Twist Twist Macrame", null, "6mm Bonnie Braid 100 Yards Macrame Cord Bonnie Cotton Crafts", null, "Knitted Cord 3 Mm 100 Meters 109 Yards Rope Cordmacrame Etsy Crochet Cord Knitted Crochet Yarn", null, "6mm Macrame Cord 108 Yards 100 Meters Dusty Rose Macrame Rope Chunky Macrame Yarn Polyester Rope Macrame Cord Macrame Plant Hanger Patterns Small Wall Hangings", null, "3 Mm Cotton Filled 100 Meters 200 Grams 7 05 Oz 109 Yards Cotton Macrame Cord 100 Cotton Macra Products Cord Cott Rug Bag Knit Picks Writing Gifts", null, "T Shirt Print Yarn 109 100 Meters Home Textile Yarn Cotton Yarn Zpagetti Yarn T Shirt Yarn Basket Yarn Spaghetti Yarn T Shirt Yarn Fabric Yarn Tshirt Print", null, "3mm Bobbiny Cord Ecru Golden Macrame Meters Natural Ply Premium Single Twist Yards Bobbiny 3mm Golden Natural E Macrame Cord Singles Twist Macrame", null, "How To Convert Yarn Weights To Yardage Knitting Tutorial Knitting Techniques Knitting Instructions", null, "How Many Meters Yards Of Threads Required For Making One T Shirt Average Thread Consumption For Making T Shirt An How To Make Tshirts Sewing Thread Overlocker", null, "Baker S Twine Light Pink 100 Yards 100 Meters For Etsy Craft Projects Bakers Twine Twine", null, "5mm Mustard Cotton Cord 108 Yards 100 Meters Bobbiny Macrame Cord Chunky Yarn Cotton Rope Chunky Yarn Macrame Cord Chunky Crochet", null, "Fabric By Yards 100 Linen Fabric By Meters Cats Pattern Etsy Linen Fabric Cat Pattern Fabric\n\nREAD:   Which Of The Following Molecules Can Form Hydrogen Bonds?" ]
[ null, "https://i.pinimg.com/564x/b7/fc/08/b7fc086d32e70dffe7c903aaa0242e2a--quilt-in-a-day-measurement-chart.jpg", null, "https://i.pinimg.com/originals/5d/54/44/5d54449283cf4a0475c0769dee24c4b6.jpg", null, "https://i.pinimg.com/736x/44/29/b0/4429b03076174e37ed5ea2a5dd3b4f8e.jpg", null, "https://i.pinimg.com/736x/37/04/1f/37041f8bbab89ce0ca1352038fec09da.jpg", null, "https://i.pinimg.com/564x/41/b8/32/41b832a5e0e6f6ad872438a011d3538e.jpg", null, "https://i.pinimg.com/736x/c8/db/19/c8db1907602de28cdcfd870d5dc17a4e.jpg", null, "https://i.pinimg.com/originals/72/ed/7c/72ed7c826949b84bd2ff9b996fc1cb55.jpg", null, "https://i.pinimg.com/474x/16/fc/7d/16fc7d534eef3b61e28c76c35c235235.jpg", null, "https://i.pinimg.com/474x/8f/12/32/8f1232b09983da9f518509a2685870db.jpg", null, "https://i.pinimg.com/564x/c5/40/74/c54074456d3c5fe9417b2a922440cee1.jpg", null, "https://i.pinimg.com/736x/8d/bf/f5/8dbff5bf20fcc94c07e85ef0a96eeabf.jpg", null, "https://i.pinimg.com/originals/ae/14/5b/ae145bef2a2b4d46cca3567c39757e01.jpg", null, "https://i.pinimg.com/736x/1e/db/9c/1edb9c0c897afa1bb4924d62157f0906.jpg", null, "https://i.pinimg.com/originals/bc/1d/db/bc1ddb15d4d6ecb2b4ae1dc5534476ff.jpg", null, "https://i.pinimg.com/736x/56/01/04/56010454670c4d9c0eda85c8e6cc21dc.jpg", null, "https://i.pinimg.com/originals/5d/54/44/5d54449283cf4a0475c0769dee24c4b6.jpg", null, "https://i.pinimg.com/originals/a6/15/10/a6151055c8ca4c8ecb39e00d78d4b70d.png", null, "https://i.pinimg.com/originals/ca/aa/be/caaabe6f1047f68e0a8fa2437751abe3.jpg", null, "https://i.pinimg.com/736x/d5/9c/1e/d59c1eba66fde1a89f9429fb2a2e9446.jpg", null, "https://i.pinimg.com/originals/e1/d8/22/e1d822d8ea40bfa77f5e1a1bc2ec694f.jpg", null ]
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https://rookienerd.com/tutorial/c/c-boolean
[ "# C Boolean\n\nIn C, Boolean is a data type that contains two types of values, i.e., 0 and 1. Basically, the bool type value represents two types of behavior, either true or false. Here, '0' represents false value, while '1' represents true value.\n\nIn C Boolean, '0' is stored as 0, and another integer is stored as 1. We do not require to use any header file to use the Boolean data type in C++, but in C, we have to use the header file, i.e., stdbool.h. If we do not use the header file, then the program will not compile.\n\n### Syntax\n\nsnippet\n`bool variable_name;`\n\nIn the above syntax, bool is the data type of the variable, and variable_name is the name of the variable.\n\nLet's understand through an example.\n\nsnippet\n```#include <stdio.h>\n#include<stdbool.h>\nint main()\n{\nbool x=false; // variable initialization.\nif(x==true) // conditional statements\n{\nprintf(\"The value of x is true\");\n}\nelse\nprintf(\"The value of x is FALSE\");\nreturn 0;\n}```\n\nIn the above code, we have used <stdbool.h> header file so that we can use the bool type variable in our program. After the declaration of the header file, we create the bool type variable 'x' and assigns a 'false' value to it. Then, we add the conditional statements, i.e., if..else, to determine whether the value of 'x' is true or not.\n\nOutput\n\nOutput\nThe value of x is FALSE\n\n## Boolean Array\n\nNow, we create a bool type array. The Boolean array can contain either true or false value, and the values of the array can be accessed with the help of indexing.\n\nLet's understand this scenario through an example.\n\nsnippet\n```#include <stdio.h>\n#include<stdbool.h>\nint main()\n{\nbool b={true,false}; // Boolean type array\nfor(int i=0;i<2;i++) // for loop\n{\nprintf(\"%d,\",b[i]); // printf statement\n}\nreturn 0;\n}```\n\nIn the above code, we have declared a Boolean type array containing two values, i.e., true and false.\n\nOutput\n\nOutput\n1,0,\n\n## typedef\n\nThere is another way of using Boolean value, i.e., typedef. Basically, typedef is a keyword in C language, which is used to assign the name to the already existing datatype.\n\nLet's see a simple example of typedef.\n\nsnippet\n```#include <stdio.h>\ntypedef enum{false,true} b;\nint main()\n{\nb x=false; // variable initialization\nif(x==true) // conditional statements\n{\nprintf(\"The value of x is true\");\n}\nelse\n{\nprintf(\"The value of x is false\");\n}\nreturn 0;\n}```\n\nIn the above code, we use the Boolean values, i.e., true and false, but we have not used the bool type. We use the Boolean values by creating a new name of the 'bool' type. In order to achieve this, the typedef keyword is used in the program.\n\nsnippet\n`typedef enum{false,true} b;`\n\nThe above statement creates a new name for the 'bool' type, i.e., 'b' as 'b' can contain either true or false value. We use the 'b' type in our program and create the 'x' variable of type 'b'.\n\nOutput\n\nOutput\nThe value of x is false\n\n## Boolean with Logical Operators\n\nThe Boolean type value is associated with logical operators. There are three types of logical operators in the C language:\n\n&&(AND Operator): It is a logical operator that takes two operands. If the value of both the operands are true, then this operator returns true otherwise false\n\n||(OR Operator): It is a logical operator that takes two operands. If the value of both the operands is false, then it returns false otherwise true.\n\n!(NOT Operator): It is a NOT operator that takes one operand. If the value of the operand is false, then it returns true, and if the value of the operand is true, then it returns false.\n\nLet's understand through an example.\n\nsnippet\n```#include <stdio.h>\n#include<stdbool.h>\nint main()\n{\nbool x=false;\nbool y=true;\nprintf(\"The value of x&&y is %d\", x&&y);\nprintf(\"\\nThe value of x||y is %d\", x||y);\nprintf(\"\\nThe value of !x is %d\", !x);\n}```\n\nOutput\n\nOutput\nThe value of x&&y is 0 The value of x||y is 1 The value of !x is 1\nRelated Tutorial\nContents +" ]
[ null ]
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http://alegremath.com/algebra-1-math/trinomials/forgotten-algebra.html
[ "Try the Free Math Solver or Scroll down to Tutorials!\n\n Depdendent Variable\n\n Number of equations to solve: 23456789\n Equ. #1:\n Equ. #2:\n\n Equ. #3:\n\n Equ. #4:\n\n Equ. #5:\n\n Equ. #6:\n\n Equ. #7:\n\n Equ. #8:\n\n Equ. #9:\n\n Solve for:\n\n Dependent Variable\n\n Number of inequalities to solve: 23456789\n Ineq. #1:\n Ineq. #2:\n\n Ineq. #3:\n\n Ineq. #4:\n\n Ineq. #5:\n\n Ineq. #6:\n\n Ineq. #7:\n\n Ineq. #8:\n\n Ineq. #9:\n\n Solve for:\n\n Please use this form if you would like to have this math solver on your website, free of charge. Name: Email: Your Website: Msg:\n\n### Our users:\n\nI must say that I am extremely impressed with how user friendly this one is over the Personal Tutor. Easy to enter in problems, I get explanations for every step, every step is complete, etc.\nJonathan McCue, OH\n\nThe simple interface of Algebrator makes it easy for my son to get right down to solving math problems. Thanks for offering such a useful program.\nDavid Figueroa, NY.\n\nAs a user of both Algebrator 2.0 and 3.0 I have to say that the difference is incredible. I found the old Algebrator useful, but it was really difficult to enter more complex expression. With your new WYSIWYG interface that problem has been completely eliminated! It's like Word Equation Editor, just simpler. Also, thank you for not using the new new software as an excuse to jack up the price.\nGina Simpson, DE\n\nI really needed help with fractions, the program listed each of the steps, so I was able to get my homework finished in time. Thanks.\nG.O., Kansas\n\nBefore using Algebrator, I could barely do long division. Now Im like the best student in my algebra class and I never would have been able to get that result without it! Thank you so much!\nBilly Hafren, TX\n\n### Students struggling with all kinds of algebra problems find out that our software is a life-saver. Here are the search phrases that today's searchers used to find our site. Can you find yours among them?\n\n#### Search phrases used on 2011-07-03:\n\n• The Algebra Helper software\n• example math trivia\n• how to use casio calculators in solving math\n• factor tree for GCF and LCM template\n• matrix linear equation ti83\n• work sheets on permutation & combinations\n• online ellipse calculator algebra 2\n• java divisible by\n• probablity in pre algebra\n• factor tree worksheets\n• permutation combination quiz quizzes\n• matlab second order differential equation\n• how to solve amatyc\n• Multiplying Dividing Integers Worksheets\n• beginners Physics for College Students\n• When adding and subtracting rational expressions, why do you need a LCD?\n• 8% to a decimal\n• algebra identify expression\n• lineal metre/metre\n• math fraction poems\n• free print outs for 5th and 6th graders\n• free answers to larson's calculus 8th edition test forms\n• java method for number precision\n• mutliple variable system of nonlinear equations\n• free algebra clep practice\n• college worded problems in algebraic\n• MC DOUGAL LITTELL ALGRBRA 2\n• calculate greatest common divisor\n• free online trigonometry solver triangle\n• polynomial to rational equation using matlab\n• transformation worksheets graphs\n• vectors math test questions\n• math worksheets+order of operations\n• fractional exercises in singaporean math\n• trigonometric manual for 10th class\n• algebraic expression\n• Rational expression solver\n• calculate lowest common denominator in excel\n• simplifying equations with negative exponents\n• how you know which fraction bigger when comparing\n• free factoring polynomials calculator online\n• worksheet adding and subtracting integers\n• what is college algebra tutor with voice software\n• 10th class trigonometric formulas\n• math helper.com\n• adding and subtracting algebraic expressions worksheet\n• English Aptitude Questions\n• free worksheets graphing calculator\n• how do i store formulas into my Ti-84 Calculator\n• trinomial factor calculator\n• STEP BY STEP SQUARE ROOT SOLVER\n• volume math test online\n• algebraic proofs worksheet\n• simplyfying equations\n• java program to check if divisible by integer\n• ordered pairs junior High pictures\n• property of parabola square polynomial\n• clep college algebra\n• algebraic factorization quadratic higher gcse\n• mastering physics solutions manual pdf\n• x+3>8 solve inequalities calculator cheat\n• houghton mifflin algebra book for grade 7 quizzes\n• pre-algebra for 7th grade worksheets\n• free amswers to algebra 116\n• \"online graphing calculator\" flash application\n• solving problem in college algebra\n• logical reasoning worksheets\n• multiplying and dividing scientifc\n• algebra activity for 5th grade\n• What Is the Hardest Math Equation in the World\n• solve quadratic equations on ti-83 plus\n• y is the square of a number and z is the cube root of a number. The difference between the two numbers is the sum of the answers\n• how to solve combining equation\n• pre algebra help\n• combinations, permutations easy\n• algebric problems" ]
[ null ]
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https://matplotlib.org/1.4.1/mpl_toolkits/axes_grid/api/axes_size_api.html
[ "", null, "#### Previous topic\n\nThe Matplotlib AxesGrid Toolkit API\n\n#### Next topic\n\n`mpl_toolkits.axes_grid.axes_divider`\n\n# `mpl_toolkits.axes_grid.axes_size`¶\n\nclass `mpl_toolkits.axes_grid.axes_size.``Fixed`(fixed_size)\n\nSimple fixed size with absolute part = fixed_size and relative part = 0\n\nclass `mpl_toolkits.axes_grid.axes_size.``Scaled`(scalable_size)\n\nSimple scaled(?) size with absolute part = 0 and relative part = scalable_size\n\nclass `mpl_toolkits.axes_grid.axes_size.``AxesX`(axes, aspect=1.0, ref_ax=None)\n\nScaled size whose relative part corresponds to the data width of the axes multiplied by the aspect.\n\nclass `mpl_toolkits.axes_grid.axes_size.``AxesY`(axes, aspect=1.0, ref_ax=None)\n\nScaled size whose relative part corresponds to the data height of the axes multiplied by the aspect.\n\nclass `mpl_toolkits.axes_grid.axes_size.``MaxWidth`(artist_list)\n\nSize whose absolute part is the largest width of the given artist_list.\n\nclass `mpl_toolkits.axes_grid.axes_size.``MaxHeight`(artist_list)\n\nSize whose absolute part is the largest height of the given artist_list.\n\nclass `mpl_toolkits.axes_grid.axes_size.``Fraction`(fraction, ref_size)\n\nAn instance whose size is a fraction of the ref_size.\n\n```>>> s = Fraction(0.3, AxesX(ax))\n```\nclass `mpl_toolkits.axes_grid.axes_size.``Padded`(size, pad)\n\nReturn a instance where the absolute part of size is increase by the amount of pad.\n\n`mpl_toolkits.axes_grid.axes_size.``from_any`(size, fraction_ref=None)\n\nCreates Fixed unit when the first argument is a float, or a Fraction unit if that is a string that ends with %. The second argument is only meaningful when Fraction unit is created.:\n\n```>>> a = Size.from_any(1.2) # => Size.Fixed(1.2)\n>>> Size.from_any(\"50%\", a) # => Size.Fraction(0.5, a)\n```" ]
[ null, "https://s3.amazonaws.com/github/ribbons/forkme_right_orange_ff7600.png", null ]
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https://www.lesswrong.com/posts/uNjcYeMXXsnopajMg/thoughts-on-the-5-10-problem
[ "Frontpage\n\n# 5 dollars is better than 10 dollars\n\nThe 5-10 Problem is a strange issue in which an agent reasoning about itself makes an obviously wrong choice.\n\nOur agent faces a truly harrowing choice: it must decide between taking $5 (utility 5) or$10 (utility 10).\n\nHow will our agent solve this dilemna? First, it will spend some time looking for a proof that taking $5 is better than taking$10. If it can find one, it will take the $5. Otherwise, it will take the$10.\n\nFair enough, you think. Surely the agent will concede that it can't prove taking $5 is better than taking$10. Then, it will do the sensible thing and take the $10, right? Wrong. Our agent finds the following the following proof that taking$5 is better:\n\nLet's go over the proof.\n\nLine 1: Taking $5 gives you$5.\n\nLine 2: If F is true, then ~F->x is true for any x.\n\nLine 3: If you find a proof that taking $5 gives you$5 and take $10 gives you$0, you'd take the $5. Line 4: Combine the three previous lines Line 5: Löb's Theorem Line 6: Knowing that taking$5 gives you $5 and taking$10 gives you $0, you happily take the$5.\n\n# Simplified Example\n\nTo understand what went wrong, we'll consider a simpler example. Suppose you have a choice between drinking coffee (utility 1) and killing yourself (utility -100).\n\nYou decide to use the following algorithm: \"if I can prove that I will kill myself, then I'll kill myself. Otherwise, I'll drink coffee\".\n\nAnd because a proof that you'll kill yourself, implies that you'll kill yourself, by Lob's Theorem, you will kill yourself.\n\nHere, it is easier to see what went wrong-proving that you'll kill yourself is not a good reason to kill yourself.\n\nThis is hidden in the original 5-10 problem. The first conditional is equivalent to \"if I can prove I will take $5, then I'll take$5\".\n\nHopefully, it's now more clear what went wrong. How can we fix it?\n\n# Solution?\n\nI once saw a comment suggesting that the agent instead reason about how a similar agent would act (I can't find it anymore, sorry). However, this notion was not formalized. I propose the following formalization:\n\nWe construct an agent . Each time makes a decision, it increments an internal counter , giving each decision a unique identity. uses the following procedure to make decisions: for each action , it considers the agent . is a copy of (from when it was created), except that if would make a decision with id , it instead immediately takes action . Then, if can prove any of these agents has the maximum expected utility, it chooses the action corresponding to that agent.\n\nFrontpage" ]
[ null ]
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https://tenpy.readthedocs.io/en/latest/examples/advanced/mpo_exponential_decay.html
[ "# mpo_exponential_decay.py¶\n\n\"\"\"Demonstration of the mpo.MPO.from_grids method.\n\nWe construct a MPO model for a spin 1/2 Heisenberg chain with an infinite number of\n2-sites interactions, with strength that decays exponentially with the distance between the sites.\n\nBecause of the infinite number of couplings it is not possible to construct the MPO from a\ncoupling model. However the tensors that form the MPO have a surprisingly simple\nform (see the grid below).\n\nWe run the iDMRG algorithm to find the ground state and energy density of the\nsystem in the thermodynamic limit.\n\"\"\"\n# Copyright 2018-2021 TeNPy Developers, GNU GPLv3\n\nimport numpy as np\nimport tenpy.linalg.np_conserved as npc\n\nfrom tenpy.networks.mpo import MPO\nfrom tenpy.networks.mps import MPS\nfrom tenpy.networks.site import SpinHalfSite\nfrom tenpy.models.model import MPOModel\nfrom tenpy.models.lattice import Chain\nfrom tenpy.algorithms import dmrg\nfrom tenpy.tools.params import asConfig\n\nclass ExponentiallyDecayingHeisenberg(MPOModel):\nr\"\"\"Spin-1/2 Heisenberg Chain with exponentially decaying interactions.\n\n.. math ::\n\nH = \\sum_i \\sum_{j>i} \\exp(-\\frac{|j-i-1|}{\\mathtt{xi}}) (\n\\mathtt{Jxx}/2 (S^{+}_i S^{-}_j + S^{-}_i S^{+}_j)\n+ \\mathtt{Jz} S^z_i S^z_j ) \\\\\n- \\sum_i \\mathtt{hz} S^z_i\n\nAll parameters are collected in a single dictionary model_params.\n\nParameters\n----------\nL : int\nLength of the chain.\nJxx, Jz, hz, xi: float\nCoupling parameters as defined for the Hamiltonian above.\nbc_MPS : {'finite' | 'infinte'}\nMPS boundary conditions.\nconserve : 'Sz' | 'parity' | None\nWhat should be conserved. See :class:~tenpy.networks.Site.SpinHalfSite.\n\"\"\"\ndef __init__(self, model_params):\n# model parameters\nmodel_params = asConfig(model_params, \"ExponentiallyDecayingHeisenberg\")\nL = model_params.get('L', 2)\nxi = model_params.get('xi', 0.5)\nJxx = model_params.get('Jxx', 1.)\nJz = model_params.get('Jz', 1.5)\nhz = model_params.get('hz', 0.)\nconserve = model_params.get('conserve', 'Sz')\nif xi == 0.:\ng = 0.\nelif xi == np.inf:\ng = 1.\nelse:\ng = np.exp(-1 / (xi))\n\n# Define the sites and the lattice, which in this case is a simple uniform chain\n# of spin 1/2 sites\nsite = SpinHalfSite(conserve=conserve)\nlat = Chain(L, site, bc_MPS='infinite', bc='periodic')\n\n# The operators that appear in the Hamiltonian. Standard spin operators are\n# already defined for the spin 1/2 site, but it is also possible to add new\n# operators using the add_op method\nSz, Sp, Sm, Id = site.Sz, site.Sp, site.Sm, site.Id\n\n# yapf:disable\n# The grid (list of lists) that defines the MPO. It is possible to define the\n# operators in the grid in the following ways:\n# 1) NPC arrays, defined above:\ngrid = [[Id, Sp, Sm, Sz, -hz*Sz ],\n[None, g*Id, None, None, 0.5*Jxx*Sm],\n[None, None, g*Id, None, 0.5*Jxx*Sp],\n[None, None, None, g*Id, Jz*Sz ],\n[None, None, None, None, Id ]]\n# 2) In the form [(\"OpName\", strength)], where \"OpName\" is the name of the\n# operator (e.g. \"Sm\" for Sm) and \"strength\" is a number that multiplies it.\ngrid = [[[(\"Id\", 1)], [(\"Sp\",1)], [(\"Sm\",1)], [(\"Sz\",1)], [(\"Sz\", -hz)] ],\n[None , [(\"Id\",g)], None , None , [(\"Sm\", 0.5*Jxx)]],\n[None , None , [(\"Id\",g)], None , [(\"Sp\", 0.5*Jxx)]],\n[None , None , None , [(\"Id\",g)], [(\"Sz\",Jz)] ],\n[None , None , None , None , [(\"Id\",1)] ]]\n# 3) It is also possible to write a single \"OpName\", equivalent to\n# [(\"OpName\", 1)].\ngrid = [[\"Id\" , \"Sp\" , \"Sm\" , \"Sz\" , [(\"Sz\", -hz)] ],\n[None , [(\"Id\",g)], None , None , [(\"Sm\", 0.5*Jxx)]],\n[None , None , [(\"Id\",g)], None , [(\"Sp\", 0.5*Jxx)]],\n[None , None , None , [(\"Id\",g)], [(\"Sz\",Jz)] ],\n[None , None , None , None , \"Id\" ]]\n# yapf:enable\ngrids = [grid] * L\n\n# Generate the MPO from the grid. Note that it is not necessary to specify\n# the physical legs and their charges, since the from_grids method can extract\n# this information from the position of the operators inside the grid.\nH = MPO.from_grids(lat.mps_sites(), grids, bc='infinite', IdL=0, IdR=-1)\nMPOModel.__init__(self, lat, H)\n\ndef example_run_dmrg():\n\"\"\"Use iDMRG to extract information about the ground state of the system.\"\"\"\nmodel_params = dict(L=2, Jxx=1, Jz=1.5, xi=0.8)\nmodel = ExponentiallyDecayingHeisenberg(model_params)\npsi = MPS.from_product_state(model.lat.mps_sites(), [\"up\", \"down\"], bc='infinite')\ndmrg_params = {\n'mixer': True,\n'chi_list': {\n0: 100\n},\n'trunc_params': {\n'svd_min': 1.e-10\n},\n}\nresults = dmrg.run(psi, model, dmrg_params)\nprint(\"Energy per site: \", results['E'])\nprint(\"<Sz>: \", psi.expectation_value('Sz'))\n\nif __name__ == \"__main__\":\nimport logging\nlogging.basicConfig(level=logging.INFO)\nexample_run_dmrg()" ]
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https://en.m.wikipedia.org/wiki/Diffusion_equation
[ "Diffusion equation\n\nThe diffusion equation is a partial differential equation. In physics, it describes the behavior of the collective motion of micro-particles in a material resulting from the random movement of each micro-particle. In mathematics, it is applicable in common to a subject relevant to the Markov process as well as in various other fields, such as the materials sciences, information science, life science, social science, and so on. These subjects described by the diffusion equation are generally called Brown problems.\n\nStatement\n\nThe equation is usually written as:\n\n${\\frac {\\partial \\phi (\\mathbf {r} ,t)}{\\partial t}}=\\nabla \\cdot {\\big [}D(\\phi ,\\mathbf {r} )\\ \\nabla \\phi (\\mathbf {r} ,t){\\big ]},$\n\nwhere ϕ(r, t) is the density of the diffusing material at location r and time t and D(ϕ, r) is the collective diffusion coefficient for density ϕ at location r; and ∇ represents the vector differential operator del. If the diffusion coefficient depends on the density then the equation is nonlinear, otherwise it is linear.\n\nMore generally, when D is a symmetric positive definite matrix, the equation describes anisotropic diffusion, which is written (for three dimensional diffusion) as:\n\n${\\frac {\\partial \\phi (\\mathbf {r} ,t)}{\\partial t}}=\\sum _{i=1}^{3}\\sum _{j=1}^{3}{\\frac {\\partial }{\\partial x_{i}}}\\left[D_{ij}(\\phi ,\\mathbf {r} ){\\frac {\\partial \\phi (\\mathbf {r} ,t)}{\\partial x_{j}}}\\right]$\n\nIf D is constant, then the equation reduces to the following linear differential equation:\n\n${\\frac {\\partial \\phi (\\mathbf {r} ,t)}{\\partial t}}=D\\nabla ^{2}\\phi (\\mathbf {r} ,t),$\n\nalso called the heat equation.\n\nHistorical origin\n\nThe particle diffusion equation was originally derived by Adolf Fick in 1855.\n\nDerivation\n\nThe diffusion equation can be trivially derived from the continuity equation, which states that a change in density in any part of the system is due to inflow and outflow of material into and out of that part of the system. Effectively, no material is created or destroyed:\n\n${\\frac {\\partial \\phi }{\\partial t}}+\\nabla \\cdot \\mathbf {j} =0,$\n\nwhere j is the flux of the diffusing material. The diffusion equation can be obtained easily from this when combined with the phenomenological Fick's first law, which states that the flux of the diffusing material in any part of the system is proportional to the local density gradient:\n\n$\\mathbf {j} =-D(\\phi ,\\mathbf {r} )\\,\\nabla \\phi (\\mathbf {r} ,t).$\n\nIf drift must be taken into account, the Smoluchowski equation provides an appropriate generalization.\n\nDiscretization\n\nThe diffusion equation is continuous in both space and time. One may discretize space, time, or both space and time, which arise in application. Discretizing time alone just corresponds to taking time slices of the continuous system, and no new phenomena arise. In discretizing space alone, the Green's function becomes the discrete Gaussian kernel, rather than the continuous Gaussian kernel. In discretizing both time and space, one obtains the random walk.\n\nDiscretization (Image)\n\nThe product rule is used to rewrite the anisotropic tensor diffusion equation, in standard discretization schemes, because direct discretization of the diffusion equation with only first order spatial central differences leads to checkerboard artifacts. The rewritten diffusion equation used in image filtering:\n\n${\\frac {\\partial \\phi (\\mathbf {r} ,t)}{\\partial t}}=\\nabla \\cdot \\left[D(\\phi ,\\mathbf {r} )\\right]\\nabla \\phi (\\mathbf {r} ,t)+{\\rm {tr}}{\\Big [}D(\\phi ,\\mathbf {r} ){\\big (}\\nabla \\nabla ^{T}\\phi (\\mathbf {r} ,t){\\big )}{\\Big ]}$\n\nwhere \"tr\" denotes the trace of the 2nd rank tensor, and superscript \"T\" denotes transpose, in which in image filtering D(ϕ, r) are symmetric matrices constructed from the eigenvectors of the image structure tensors. The spatial derivatives can then be approximated by two first order and a second order central finite differences. The resulting diffusion algorithm can be written as an image convolution with a varying kernel (stencil) of size 3 × 3 in 2D and 3 × 3 × 3 in 3D." ]
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https://www.proofwiki.org/wiki/Uniform_Absolute_Convergence_of_Infinite_Product_of_Complex_Functions
[ "# Uniform Absolute Convergence of Infinite Product of Complex Functions\n\n## Theorem\n\nLet $X$ be a compact metric space.\n\nLet $\\sequence {f_n}$ be a sequence of continuous functions $X \\to \\C$.\n\nLet $\\ds \\sum_{n \\mathop = 1}^\\infty f_n$ converge uniformly absolutely on $X$.\n\nThen:\n\n$\\map f x = \\ds \\prod_{n \\mathop = 1}^\\infty \\paren {1 + \\map {f_n} x}$ converges uniformly absolutely on $X$\n$f$ is continuous\nthere exists $n_0 \\in \\N$ such that $\\ds \\prod_{n \\mathop = n_0}^\\infty \\paren {1 + \\map {f_n} x}$ has no zeroes.\n\n## Proof\n\n### Lemma\n\nLet $X$ be a set.\n\nLet $\\family {g_n}$ be a family of mappings $g_n : X \\to \\C$.\n\nLet $g_n$ converge uniformly to $g: X \\to \\C$.\n\nLet there be a constant $a \\in \\R$ such that $\\map \\Re {\\map g x} \\le a$ for all $x \\in X$.\n\nThen $\\exp g_n$ converges uniformly to $\\exp g$.\n\n$\\Box$\n\nBecause $\\ds \\sum_{n \\mathop = 1}^\\infty f_n$ converges uniformly, there exists $n_0 > 0$ such that $\\size {\\map {f_n} x} < \\dfrac 1 2$ for $n \\ge n_0$ and $x \\in X$.\n\nThen:\n\n$\\map \\Re {1 + \\map {f_n} x} > 0$\n$\\size {\\map \\log {1 + \\map {f_n} x} } \\le \\dfrac 3 2 \\size {\\map {f_n} x}$\n$\\size {\\map \\log {1 + \\size {\\map {f_n} x} } } \\le \\dfrac 3 2 \\size {\\map {f_n} x}$\n\nfor $n \\ge n_0$.\n\n$g = \\ds \\sum_{n \\mathop = n_0}^\\infty \\map \\log {1 + f_n}$\n\nand:\n\n$h = \\ds \\sum_{n \\mathop = n_0}^\\infty \\map \\log {1 + \\size {f_n} }$\n\nBy Uniform Limit Theorem, $g$ and $h$ are continuous.\n\nBy Continuous Function on Compact Subspace of Euclidean Space is Bounded, $g$ and $h$ are bounded\n\n$\\map \\exp g = \\ds \\prod_{n \\mathop = n_0}^\\infty \\paren {1 + f_n}$\n$\\map \\exp h = \\ds \\prod_{n \\mathop = n_0}^\\infty \\paren {1 + \\size {f_n} }$\n\nBy the lemma, the products converge uniformly.\n\nBy Uniform Limit Theorem, $\\map \\exp g$ is continuous.\n\nBecause the second product converges uniformly, the first converges uniformly absolutely.\n\nBy Image of Complex Exponential Function, $\\map \\exp g$ has no zeroes.\n\n$\\blacksquare$" ]
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https://rna.wlu.edu/bio297/08-ggplot2-slides.html
[ "Curated Data Sets\n\nHere are two data sets of particular note:\n\nGoal: Ask a question, answer it with a picture!\n\nSome ideas:\n\n• What is the distribution of gene or protein sizes across the yeast genome? Of introns? Of functional RNAs?\n• Are there correlations between the processes proteins are involved in and their size? Or location within the genome?\n• Are there biases in which genes contain introns?\n• Do short chromosomes have more or longer introns? [credit to Joseph]\n\nGrammar of Graphics in R (ggplot2)\n\nlibrary(ggplot2)\n\nConstructing a plot\n\n# Here's the structure of the diamonds dataset\n## carat cut color clarity depth table price x y z\n## 1 0.23 Ideal E SI2 61.5 55 326 3.95 3.98 2.43\n## 2 0.21 Premium E SI1 59.8 61 326 3.89 3.84 2.31\n## 3 0.23 Good E VS1 56.9 65 327 4.05 4.07 2.31\n## 4 0.29 Premium I VS2 62.4 58 334 4.20 4.23 2.63\n## 5 0.31 Good J SI2 63.3 58 335 4.34 4.35 2.75\n## 6 0.24 Very Good J VVS2 62.8 57 336 3.94 3.96 2.48\n# Construct a ggplot object to visualize the relationship between clarity and depth\np <- ggplot(diamonds, aes(clarity, depth))\np + geom_point()", null, "p + geom_boxplot()", null, "Single variable distributions\n\n# Visualize the distribution of the depth variable\np2 <- ggplot(diamonds, aes(depth))\n# Histogram\np2 + geom_histogram()\n## stat_bin: binwidth defaulted to range/30. Use 'binwidth = x' to adjust this.", null, "# Density distribution\np2 + geom_density()", null, "Setting axis limits\n\n# Set x-axis limits\np2 + geom_density() + xlim( c(55, 65) )\n## Warning: Removed 857 rows containing non-finite values (stat_density).", null, "Two quantitative variables\n\n# Visualize depth as a function of price\np3 <- ggplot( diamonds, aes(price, depth) )\n# Use points (scatter plot)\np3 + geom_point()", null, "Data grouping and secondary visualizations\n\n# Visualize depth as a function of price; use color to visualize clarity label\np4 <- ggplot( diamonds, aes(price, depth, color = clarity) )\n# Use points (scatter plot)\np4 + geom_point()", null, "For visualizations that use solid objects, you can also specify a fill argument:\n\np5 <- ggplot(diamonds, aes( price, fill = clarity) )\n# Setting the alpha channel to 50% makes the density plots transparent\np5 + geom_density(alpha = 0.5)", null, "" ]
[ null, 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", null, 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", null, 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", null, 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", null, 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", null, 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null, 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null, 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null ]
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https://www.fossilhunters.xyz/giant-planets/sfb.html
[ "# Sfb\n\nwhere To and po are reference temperatures and pressures; and SFB is a factor to be fitted or calculated (see below). The mean absorption coefficient k, may be expanded as k,(T)=k,(To) ('T)^exp\n\nwhere qr is 1.0 for linear molecules and 1.5 for nonlinear molecules. There are thus five independent parameters in the Goody-Voigt model: k„(T0), y0, 6/a(h, Ei, and SFB, which may either be fitted to laboratory transmission spectra, or alternatively derived from tabulated line listings such as HITRAN and GEISA. These parameters, while usually fitted directly to measured spectra, are related to the properties of the real absorption lines in the spectral band: kp (T0) is the integrated line strength of all the lines in the wavenumber range considered at the standard temperature; y0 is the mean ratio of pressure-broadened to Doppler-broadened linewidths at STP (standard temperature and pressure); S/a% is mean line spacing divided by the Doppler-broadened width at STP; Ei is the mean energy of lower states; and SFB is the mean self-broadening to foreign-broadening ratio of absorption lines.\n\nOnce band data have been tabulated, the transmission of homogeneous paths may be rapidly and accurately calculated. However, real atmospheres are inhomo-geneous in that pressure, temperature, and composition vary rapidly with altitude. How then may band models be applied? It may be shown that the mean transmission of a path though an inhomogeneous atmosphere may be well approximated by the mean transmission of an equivalent homogeneous path, whose path amount, mean pressure, and mean temperature are given by:\n\nThis is known as the Curtis-Godson approximation. Hence, to use band models to calculate thermal emission spectra, the inhomogeneous atmosphere is represented by a series of equivalent Curtis-Godson paths from space to progressively deeper levels in the atmosphere and the difference between the band-calculated mean transmissions used to find the mean transmission weighting function. In addition, since the absorption lines of different molecules are rarely correlated with each other, the total transmission of Curtis-Godson paths for all the gases concerned is simply found by multiplying the individual gas transmissions together, or equivalently summing the optical thicknesses. The band model approach is very fast, but is found to be useless for multiple scattering calculations and hence is mostly used in the mid-infrared to far-infrared where scattering is generally less important (as we shall see in Section 6.5.2).\n\n### Correlated-k approximation\n\nAn alternative approach to calculating finite resolution spectra is to use ^-distributions. For a path of absorber amount m in an atmosphere of uniform pressure p and T, the mean transmission is given by where the absorption coefficient at a particular wavelength is the summation of all the individual line contributions. Since the absorption coefficient k(,) is a rapidly varying function of a wavenumber, in order to numerically calculate the mean transmission accurately, a very fine wavenumber step must be chosen. However, when calculating the mean transmission in a spectral interval it does not matter which parts of the interval are actually highly or poorly absorbing. All we need to know is what fraction of the interval has low absorption, what fraction has high absorption, and so on. In other words, if we calculate a high-resolution absorption coefficient spectrum using a regularly spaced high-resolution grid, and then sort the absorption coefficients into order starting with the low absorption coefficients first and then working monotonic-ally through to the high absorption coefficients, the resulting integral of the sorted spectrum is identical to that of the original. The advantage of this approach is that the sorted spectrum, known as the k-distribution, k(g), is a smoothly varying function that is usually expressed in terms of the fraction of the interval g, which varies between 0 and 1. Since it is a smoothly varying function, the integral may be accurately integrated with far fewer quadrature points and thus calculation of mean transmission is very much faster. In practice ten to twenty quadrature points are usually found to be satisfactory and the mean transmission may be approximated by where kt is the k-distribution calculated at each of the N quadrature points; and Agi are the quadrature weights. The k-distributions may be pre-calculated for each gas for a range of temperatures and pressures found in real atmospheres and then stored in look-up tables for rapid interpolation and calculation of mean transmission. Since the absorption lines of different gases may be assumed to a good approximation to be uncorrelated, it is also reasonably straightforward to combine k-distributions together (Lacis and Oinas, 1991). The k-distribution look-up tables may be calculated\n\neither directly from line data or, if the available line data are of poor quality, indirectly from band data using the technique of exponential sums (e.g., Irwin et al., 1996). While we can see that ^-distributions can speed up transmission calculations for homogeneous paths, how can they help us for inhomogeneous paths? For monochromatic calculations, the transmission of an inhomogeneous path is found by splitting the path into small subpaths, calculating the transmission, and then multiplying all the transmissions together. However, for band-averaged transmissions, such as those used by band models, this multiplication is not possible and thus the Curtis-Godson approximation must be used. The Curtis-Godson approximation may also be used with ^-distributions, but there is then no advantage over the band model approach. Instead, it is found that regions of high and low absorption within the spectral band are spectrally correlated between various subpaths within the inhomogeneous path. This correlation exists between the ^-distributions also (Lacis and Oinas, 1991; Goody et al., 1989). Hence, the ^-distributions may effectively be multiplied together almost as though they were monochromatic to determine the mean transmission of the inhomogeneous path where the inhomogeneous path has been split into M subpaths. This is the correlated-k approximation and is found to have a similar accuracy to that of the Curtis-Godson approximation. The great advantage, however, lies in the fact that thermal emission and in particular scattering calculations (discussed in Section 6.6) may also be summed in exactly the same way. Hence, the technique of correlated-k allows for rapid calculation of spectra in multiply scattering atmospheres and is thus used extensively to simulate the near-IR reflectance spectra of the giant planets." ]
[ null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.93060684,"math_prob":0.9723787,"size":6739,"snap":"2020-24-2020-29","text_gpt3_token_len":1352,"char_repetition_ratio":0.1429844,"word_repetition_ratio":0.0019512195,"special_character_ratio":0.18548746,"punctuation_ratio":0.095117845,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9939845,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-05-30T05:52:02Z\",\"WARC-Record-ID\":\"<urn:uuid:58e8eca3-53fa-4712-b20e-52026484716d>\",\"Content-Length\":\"17051\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:85600107-3bbf-4571-ad12-d43346175195>\",\"WARC-Concurrent-To\":\"<urn:uuid:ac42e4a1-60de-46d2-aee7-76236d056350>\",\"WARC-IP-Address\":\"172.67.139.95\",\"WARC-Target-URI\":\"https://www.fossilhunters.xyz/giant-planets/sfb.html\",\"WARC-Payload-Digest\":\"sha1:YUF3OQY4HAFKSGZRJUJPVYMHGFAYML7V\",\"WARC-Block-Digest\":\"sha1:GPVPHQY2UVT47IF55IQSCWSCBZDG53AX\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-24/CC-MAIN-2020-24_segments_1590347407289.35_warc_CC-MAIN-20200530040743-20200530070743-00570.warc.gz\"}"}
https://physicsteacher.in/dc-circuits-hub-of-related-posts/
[ "# DC Circuits – Hub of related Posts\n\nHere goes the list of our posts on DC Circuits and related topics and subtopics.\n\n#### Measuring the resistance of a component – different ways\n\nIn this post, we are going to discuss different ways of measuring the resistance of a component. Resistance is defined as R = V/I. This obviously gives ways of measuring ...\n\n#### How to find resistance using Resistor Colour Codes\n\nSmall resistors use coloured or painted bands which represent their resistive value and tolerance. These coloured painted bands produce a system of identification generally known as a Resistors Colour Code ...\n\n#### How does alternating current differ from direct current?\n\nIn this post, we will find out the answer to a very common question: \"How does alternating current differ from direct current?\" Direct current implies that the current flows in ...\n\n#### Ammeters and Voltmeters – FAQs, connection, concepts\n\nAmmeters measure the current of a circuit, and voltmeters measure the voltage drop across a resistor. Ammeters and voltmeters are cleverly designed because it is important in the design to ...\n\n#### Capacitors & Capacitance – Formula & other FAQs\n\nCapacitors are components of electrical circuits that temporarily store electric charge. Capacitors are simple passive devices. The capacitor is a component that has the ability or \"capacity\" to store energy ...\n\n#### [pdf notes] Electric Circuits Grade 10 & Grade 11 Notes download | class 10 & class 11 physics notes on Electric Circuits\n\nThis Electric Circuits Notes [PDF download] is primarily for the 10th & 11th grade physics syllabus of different international boards. This also covers the class 10 and class 11 physics ...\n\n#### Potential dividers – how does it work? – explain with examples\n\nSometimes we want to use only part of the e.m.f. of a supply. To do this, we use an arrangement of resistors called a potential divider circuit. In other words, ...\n\n#### What is the Internal Resistance of cells?\n\nWhat is the Internal Resistance of cells & how it affects the current flow in a circuit? All electric cells are made of materials that have resistance. The resistance of ...\n\n#### How to define Voltages, Electromotive Force (emf), and Potential Difference (PD)?\n\nVoltages, Electromotive Force (emf), and Potential Difference (PD) - These 3 terms are often used while we discuss electrical circuits. Hence exactly knowledge about these certainly helps us to understand ...\n\n#### Symbols & functions of Common components of electrical circuits – How to get?\n\nThe following tables describe some of the common components of electrical circuits, their functions, images, and the symbols that are used to represent them in circuit diagrams. Figure 1 Figure ...\n\n#### Voltages in series circuits and parallel circuits – easy understanding\n\nVoltages in series circuits and parallel circuits - Let's see how total voltage in series circuits and parallel circuits are calculated. Voltages in series circuits A series circuit has no ...\n\n#### How current flows through series and parallel circuits? A quick reference\n\nHere we will see how current flows through series and parallel circuits. Currents in series circuits In a series circuit, devices are connected so there is only one closed path ...\n\n#### Equivalent resistance of a parallel circuit with derivation & numerical problems\n\nThe equivalent resistance of a parallel circuit is found using Kirchoff's junction rule, which states that the sum of the currents entering a branch (or junction) must be equal to ...\n\n#### Series Circuits, Resistors in series & equivalent resistance – numerical\n\nWhat is a series circuit? A series circuit consists of several resistors connected in sequence, one after the other. This increases the length of the conductor. Therefore total resistance increases ...\nScroll to top" ]
[ null ]
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https://ch.mathworks.com/help/vision/ug/subtract-image-background-using-opencv-code-in-matlab.html
[ "# Subtract Image Background by Using OpenCV in MATLAB\n\nThis example shows how to subtract the background in an image sequence or a video by using the prebuilt MATLAB interface to the OpenCV function `cv::BackgroundSubtractorKNN`. In this example, you also use the `createMat` utility function to define the input and output arrays, and the `getImage` utility function to read the output image returned by the OpenCV function. The input video must be have a static background and dynamic foreground objects.\n\nRead a video into the MATLAB workspace by using the `VideoReader` MATLAB function.\n\n```videoSample = VideoReader(\"atrium.mp4\"); videoSample.CurrentTime = 2.5;```\n\nAdd the MATLAB interface to OpenCV package names to the import list.\n\n```import clib.opencv.*; import vision.opencv.*;```\n\nSpecify the parameter values to compute the background by using the OpenCV function for k-Nearest Neighbor (KNN) background subtractor `cv::BackgroundSubtractorKNN`. Set these values:\n\n• Number of last frames to consider for computing the KNN background model `history` to `300`.\n\n• Threshold for differentiating the foreground and background pixels `threshold` to `400`.\n\n• `shadow` to `true`, to detect the shadow regions.\n\n```history = 300; threshold = 400; shadow = true;```\n\nCreate a MATLAB interface object by using the `getBasePtr` utility function to represent the `BackgroundSubtractorKNN` class.\n\n```cvPtr = cv.createBackgroundSubtractorKNN(history,threshold,shadow); kNNBase = util.getBasePtr(cvPtr);```\n\nYou can also set the parameter values for the background subtractor by accessing the public methods of the `BackgroundSubtractorKNN` class. Set the number of `k` nearest neighbors required for classifying a pixel as belonging to the background model to 2.\n\n`kNNBase.setkNNSamples(2);`\n\nFollow these steps to extract the foreground region by using the `apply` method of the OpenCV class `BackgroundSubtractorKNN`.\n\n• Create an `InputArray` and `OutputArray` class by using the `createMat` MATLAB utility function to store the input video frame and the output foreground mask respectively.\n\n• The `apply` method takes the video frames as inputs and then, computes the foreground pixels by using the k-NN algorithm. The `apply` method stores the mask containing the foreground pixel regions to the `OutputArray` class.\n\n• Export the output foreground mask returned by the `apply` method to MATLAB workspace by using the `getImage` MATLAB utility function.\n\n• Extract the desired foreground region by using the foreground mask and the input video frames.\n\n```foregroundmask = zeros(videoSample.Height,videoSample.Width,videoSample.NumFrames); while hasFrame(videoSample) frame = readFrame(videoSample); [inMat,imgInput] = util.createMat(frame); [outMat,outImg] = util.createMat(); kNNBase.apply(imgInput,outImg); foregroundmask = util.getImage(outImg); foregroundmask = rescale(foregroundmask); foregroundmask = cast(foregroundmask,\"like\",frame); foreground(:,:,1) = frame(:,:,1).*foregroundmask; foreground(:,:,2) = frame(:,:,2).*foregroundmask; foreground(:,:,3) = frame(:,:,3).*foregroundmask; image(foreground,Parent=gca); pause(0.01); end```", null, "" ]
[ null, "https://ch.mathworks.com/help/examples/opencvinterface/win64/SubtractBackgroundOpenCVCodeMATLABExample_01.png", null ]
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https://docs.aws.amazon.com/en_us/quicksight/latest/user/varpOver-function.html
[ "Amazon QuickSight\nUser Guide\n\nThe AWS Documentation website is getting a new look!\nTry it now and let us know what you think. Switch to the new look >>\n\nYou can return to the original look by selecting English in the language selector above.\n\n# varpOver\n\n`varpOver` calculates the variance of the specified measure, partitioned by the chosen attribute or attributes, based on a biased population.\n\n`varpOver` is supported for use with analyses based on SPICE and direct query data sets.\n\n## Syntax\n\nThe brackets are required. To see which arguments are optional, see the following descriptions.\n\n``````varpOver\n(\nmeasure\n,[ partition_field, ... ]\n,calculation level\n)``````\n\n## Arguments\n\nmeasure\n\nThe measure that you want to do the calculation for, for example `sum({Sales Amt})`. Use an aggregation if the calculation level is set to `NULL` or `POST_AGG_FILTER`. Don't use an aggregation if the calculation level is set to `PRE_FILTER` or `PRE_AGG`.\n\npartition field\n\n(Optional) One or more dimensions that you want to partition by, separated by commas.\n\nEach field in the list is enclosed in {} (curly braces), if it is more than one word. The entire list is enclosed in [ ] (square brackets).\n\ncalculation level\n\n(Optional) Specifies the calculation level to use:\n\n• `PRE_FILTER` – prefilter calculations are computed before the dataset filters.\n\n• `PRE_AGG` – preaggregate calculations are computed before applying aggregations and top and bottom N filters to the visuals.\n\n• `POST_AGG_FILTER` – (default) table calculations are computed when the visuals display.\n\nDefaults to `POST_AGG_FILTER` when blank. For more information, see Using Level-Aware Aggregations.\n\n## Example\n\nThe following example calculates the variance of `sum(Sales)`, partitioned by `City` and `State`, based on a biased population.\n\n``````varpOver\n(\nsum(Sales),\n[City, State]\n) ``````\n\nThe following example calculates the variance of ```Billed Amount``` over `Customer Region`, based on a biased population. This example uses the revenue sample dataset, located in an Amazon S3 bucket. The fields in the table calculation are in the field wells of the visual.\n\n``````varpOver\n(\nsum({Billed Amount}),\n[{Customer Region}]\n)``````" ]
[ null ]
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https://howtodoinjava.com/python-misc/compare-tuples/
[ "# Python – Comparing tuples\n\nIn Python, tuples are compared lexicographically (alphabetical order as seen in an English dictionary) by comparing corresponding elements of two tuples.\n\nIt means that the first item of the first tuple is compared to the first item of the second tuple; if they are not equal then that’s the result of the comparison. Else the second item is considered, then the third and so on.\n\n## 1. Rules for comparing tuples\n\nFor understanding the tuples comparison, focus on how words are compared and stored in an English dictionary. Here, each letter of the words can be considered an item in the tuple.\n\n1. Compare the n-th items of both tuple (starting with the zero-th index) using the == operator. If both are equal, repeat this step with the next item.\n2. For two unequal items, the item that is “less than” makes the tuple, that contains it, also “less than” the other tuple.\n3. If all items are equal, both tuples are equal.\n4. If one tuple runs out of items during step 1, the shorter tuple is “less than” the longer one.\n\n## 2. Simple comparison\n\nIn given example, `tuple1` and `tuple2` are compared by:\n\n• comparing `tuple1` to `tuple2` – which are equal\n• comparing `tuple1` to `tuple2` – which are equal\n• comparing `tuple1` to `tuple2` – which are NOT equal and decide the result of comparison\n```tuple1 = (1,2,3)\ntuple2 = (1,2,4)\n\nprint (tuple1 == tuple2)\t# False\n\nprint (tuple1 < tuple2)\t\t# True\n\nprint (tuple1 > tuple2)\t\t# False\n```\n\n## 2. Compare unequal tuples\n\nPython program to show comparison of tuples having an unequal number of items.\n\n```tuple1 = (1,2,3)\ntuple2 = (4,5,6,7)\n\nprint( tuple1 < tuple2 ) \t# True\n```\n\n## 3. All elements of tuple1 are greater than items of tuple2\n\nTwo compare two tuples such that all items in tuple1 are greater than tuple2, we need to use all() function and check comparison on items one by one, for corresponding items in both tuples.\n\n```tuple1 = (1,2,3)\ntuple2 = (4,5,6)\n\nresult = all(x < y for x, y in zip(tuple1, tuple2))\n\nprint( result ) \t# True\n```\n\n## 4. Compare tuples with heterogeneous items\n\nTuples comparison for `==` equality operator works for heterogeneous items. But `'less than'` and `'greater than'` operators does not work with different datatypes.\n\n```tuple1 = (1, 2, 3)\ntuple2 = (1, 2, \"6\")\t\t# \"3\" will be compared to 6\n\nprint( tuple1 == tuple2 ) \t# False\n```\n\nFor evaluating less than or greater than, if we know that tuples can contain items of different types, then we need to use `map()` function to convert all values both tuples into a single type.\n\n```tuple1 = (1,2,3)\ntuple2 = (4,5,\"6\")\n\ntuple1 = (1, 2, 3)\ntuple2 = (1, 2, \"6\")\n\nresult = tuple(map(int, tuple2)) < tuple1\n\nprint (result)\t\t\t\t# False\n\n# TypeError: '<' not supported between instances of 'int' and 'str'\nprint( tuple1 < tuple2 )\n```\n\nHappy Learning !!\n\nDiscover More\n\n### Related Articles And Resources\n\nSubscribe\nNotify of", null, "Inline Feedbacks" ]
[ null, "https://secure.gravatar.com/avatar/2a02a26f1d88570d969b459aced9a919", null ]
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https://export.arxiv.org/abs/1809.02975?context=math
[ "math\n\n# Title: A new geometric viewpoint on Sturm-Liouville eigenvalue problems\n\nAbstract: In Euclidean plane geometry, cycloids are curves which are homothetic to their respective bi-evolutes. In smooth normed planes, cycloids can be similarly defined, and they are characterized by their radius of curvature functions being solutions to eigenvalue problems of certain Sturm-Liouville equations. In this paper, we show that, for the eigenvalue {\\lambda} = 1, this equation is a previously studied Hill equation which is closely related to the geometry given by the norm. We also investigate which geometric properties can be derived from this equation. Moreover, we prove that if the considered norm is defined by a Radon curve, then the solutions to the Hill equation are given by trigonometric functions. Further, we give conditions under which a given Hill equation induces a planar Minkowski geometry, and we prove that in this case the geometry is Euclidean if an eigenvalue other than {\\lambda} = 1 induces a reparametrization of the original unit circle.\n Subjects: Classical Analysis and ODEs (math.CA); Metric Geometry (math.MG) MSC classes: 52A10, 52A21, 52A40, 53A35, 34B24 Cite as: arXiv:1809.02975 [math.CA] (or arXiv:1809.02975v1 [math.CA] for this version)\n\n## Submission history\n\nFrom: Vitor Balestro [view email]\n[v1] Sun, 9 Sep 2018 14:00:36 GMT (91kb)\n\nLink back to: arXiv, form interface, contact." ]
[ null ]
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https://indrajeetpatil.github.io/ggstatsplot/articles/web_only/purrr_examples.html
[ "You can cite this package/vignette as:\n\n\nTo cite package 'ggstatsplot' in publications use:\n\nPatil, I. (2021). Visualizations with statistical details: The\n'ggstatsplot' approach. Journal of Open Source Software, 6(61), 3167,\ndoi:10.21105/joss.03167\n\nA BibTeX entry for LaTeX users is\n\n@Article{,\ndoi = {10.21105/joss.03167},\nurl = {https://doi.org/10.21105/joss.03167},\nyear = {2021},\npublisher = {{The Open Journal}},\nvolume = {6},\nnumber = {61},\npages = {3167},\nauthor = {Indrajeet Patil},\ntitle = {{Visualizations with statistical details: The {'ggstatsplot'} approach}},\njournal = {{Journal of Open Source Software}},\n}\n\nThis is an extremely time-consuming vignette, and so it is not evaluated here. You can still use the code as a reference for writing your own purrr code.\n\n## Why use {purrr}?\n\nMost of the ggstatsplot functions have grouped_ variants, which are designed to quickly run the same ggstatsplot function across multiple levels of a single grouping variable. Although this function is useful for data exploration, it has two strong weaknesses-\n\n• The arguments applied to grouped_ function call are applied uniformly to all levels of the grouping variable when we might want to customize them for different levels of the grouping variable.\n\n• Only one grouping variable can be used to repeat the analysis when in reality there can be a combination of grouping variables and the operation needs to be repeated for all resulting combinations.\n\nWe will see how to overcome this limitation by combining ggstatsplot with the purrr package.\n\nNote:\n\n• While using purrr::pmap(), we must input the arguments as strings.\n\n• You can use ggplot2 themes from extension packages (e.g. ggthemes).\n\n• If you’d like some more background or an introduction to the purrr package, please see this chapter.\n\n## Introduction and methodology\n\nFor all the examples in this vignette we are going to build lists of things that we will pass along to purrr which will in turn return a list of plots that will be passed to combine_plots. As the name implies combine_plots merges the individual plots into one bigger plot with common labeling and aesthetics.\n\nWhat are these lists that we are building? The lists correspond to the parameters in our ggstatsplot function like ggbetweenstats. If you look at the help file for ?ggbetweenstats for example the very first parameter it wants is the data file we’ll be using. We can also pass it different titles of even ggtheme themes.\n\nYou can pass:\n\n• A single character string such as xlab = \"Continent\" or numeric such as nboot = 25 in which case it will be reused/recycled as many times as needed.\n\n• A vector of values such as nboot = c(50, 100, 200) in which case it will be coerced to a list and checked for the right class (in this case integer) and the right quantity of entries in the vector i.e., nboot = c(50, 100) will fail if we’re trying to make three plots.\n\n• A list; either named data = year_list or created as you go palette = list(\"Dark2\", \"Set1\"). Any list will be checked for the right class (in this case character) and the right quantity of entries in the list.\n\n## ggbetweenstats\n\nLet’s start with ggebtweenstats. We’ll use the gapminder dataset. We’ll make a 3 item list called year_list using dplyr::filter and split.\n\n## for reproducibility\nlibrary(ggstatsplot)\nset.seed(123)\n\n## let's split the data frame and create a list by years of interest\nyear_list <- gapminder::gapminder %>%\ndplyr::filter(year %in% c(1967, 1987, 2007), continent != \"Oceania\") %>%\nsplit(f = .$year, drop = TRUE) ## checking the length of the list and the names of each element length(year_list) names(year_list) Now that we have the data divided into the three relevant years in a list we’ll turn to purrr::pmap to create a list of ggplot objects that we’ll make use of stored in plot_list. When you look at the documentation for ?pmap it will accept .l which is a list of lists. The length of .l determines the number of arguments that .f will be called with. List names will be used if present. .f is the function we want to apply (here, .f = ggbetweenstats). Let’s keep building the list of arguments, .l. First is data = year_list, the x and y axes are constant in all three plots so we pass the variable name as a string x = \"continent\". Same with the label we’ll use for outliers where needed. For demonstration purposes let’s assume we want the outliers on each plot to be a different color. Not actually recommending it just demonstrating what’s possible. The rest of the code shows you a wide variety of possibilities and we won’t catalog them here. ## for reproducibility set.seed(123) library(ggstatsplot) ## creating a list of plots plot_list <- purrr::pmap( .l = list( data = year_list, x = \"continent\", y = \"lifeExp\", outlier.tagging = TRUE, outlier.label = \"country\", outlier.label.args = list( list(size = 3, color = \"#56B4E9\"), list(size = 2.5, color = \"#009E73\"), list(size = 3.5, color = \"#F0E442\") ), xlab = \"Continent\", ylab = \"Life expectancy\", title = list( \"Year: 1967\", \"Year: 1987\", \"Year: 2007\" ), type = list(\"r\", \"bf\", \"np\"), pairwise.display = list(\"s\", \"ns\", \"all\"), p.adjust.method = list(\"hommel\", \"bonferroni\", \"BH\"), conf.level = list(0.99, 0.95, 0.90), k = list(1, 2, 3), effsize.type = list( NULL, \"partial_omega\", \"partial_eta\" ), plot.type = list(\"box\", \"boxviolin\", \"violin\"), package = list(\"nord\", \"ochRe\", \"awtools\"), palette = list(\"aurora\", \"parliament\", \"bpalette\"), ggtheme = list( ggthemes::theme_stata(), ggplot2::theme_classic(), ggthemes::theme_fivethirtyeight() ) ), .f = ggbetweenstats ) The final step is to pass the plot_list object we just created to the combine_plots function. While each of the 3 plots already has labeling information combine_plots gives us an opportunity to add additional details to the merged plots and specify the layout in rows and columns. ## combining all individual plots from the list into a single plot using combine_plots function combine_plots( plotlist = plot_list, annotation.args = list(title = \"Changes in life expectancy across continents (1967-2007)\"), plotgrid.args = list(ncol = 1) ) ## ggwithinstats We will be using simulated data from then Attention Network Test provided in ANT dataset in ez package. ## for reproducibility set.seed(123) library(ggstatsplot) library(ez) data(\"ANT\") ## loading data from ez package ## let's split the data frame and create a list by years of interest cue_list <- ANT %>% split(f = .$cue, drop = TRUE)\n\n## checking the length of the list and the names of each element\nlength(cue_list)\n\n## creating a list of plots by applying the same function for elements of the list\nplot_list <- purrr::pmap(\n.l = list(\ndata = cue_list,\nx = \"flank\",\ny = \"rt\",\noutlier.tagging = TRUE,\noutlier.label = \"group\",\noutlier.coef = list(2, 2, 2.5, 3),\noutlier.label.args = list(\nlist(size = 3, color = \"#56B4E9\"),\nlist(size = 2.5, color = \"#009E73\"),\nlist(size = 4, color = \"#F0E442\"),\nlist(size = 2, color = \"red\")\n),\nxlab = \"Flank\",\nylab = \"Response time\",\ntitle = list(\n\"Cue: None\",\n\"Cue: Center\",\n\"Cue: Double\",\n\"Cue: Spatial\"\n),\ntype = list(\"p\", \"r\", \"bf\", \"np\"),\npairwise.display = list(\"ns\", \"s\", \"ns\", \"all\"),\np.adjust.method = list(\"fdr\", \"hommel\", \"bonferroni\", \"BH\"),\nconf.level = list(0.99, 0.99, 0.95, 0.90),\nk = list(3, 2, 2, 3),\neffsize.type = list(\n\"omega\",\n\"eta\",\n\"partial_omega\",\n\"partial_eta\"\n),\npackage = list(\"ggsci\", \"palettetown\", \"palettetown\", \"wesanderson\"),\npalette = list(\"lanonc_lancet\", \"venomoth\", \"blastoise\", \"GrandBudapest1\"),\nggtheme = list(\nggplot2::theme_linedraw(),\nhrbrthemes::theme_ft_rc(),\nggthemes::theme_solarized(),\nggthemes::theme_gdocs()\n)\n),\n.f = ggwithinstats\n)\n\n## combining all individual plots from the list into a single plot using combine_plots function\ncombine_plots(\nplotlist = plot_list,\nannotation.args = list(title = \"Response times across flank conditions for each type of cue\"),\nplotgrid.args = list(ncol = 1)\n)\n\n## ggscatterstats\n\nFor the next example lets use the same methodology on different data and using ggscatterstats to produce scatterplots combined with marginal histograms/boxplots/density plots with statistical details added as a subtitle. For data we’ll use movies_long which is from IMDB and part of the ggstatsplot package. Since it’s a large dataset with some relatively small categories like NC-17 we’ll sample only one quarter of the data and completely drop NC-17 using dplyr.\n\nThis time we’ll put all the code in one block-\n\n## for reproducibility\nset.seed(123)\n\nmpaa_list <- movies_long %>%\ndplyr::filter(mpaa != \"NC-17\") %>%\ndplyr::sample_frac(size = 0.25) %>%\nsplit(f = .$mpaa, drop = TRUE) ## creating a list of plots plot_list <- purrr::pmap( .l = list( data = mpaa_list, x = \"budget\", y = \"rating\", xlab = \"Budget (in millions of US dollars)\", ylab = \"Rating on IMDB\", title = list( \"MPAA Rating: PG\", \"MPAA Rating: PG-13\", \"MPAA Rating: R\" ), label.var = list(\"title\"), ## note that you need to quote the expressions label.expression = list( quote(rating > 7.5 & budget < 100), quote(rating > 8 & budget < 50), quote(rating > 8 & budget < 10) ), type = list(\"r\", \"np\", \"bf\"), xfill = list(\"#009E73\", \"#999999\", \"#0072B2\"), yfill = list(\"#CC79A7\", \"#F0E442\", \"#D55E00\"), ggtheme = list( ggthemes::theme_tufte(), ggplot2::theme_classic(), ggplot2::theme_light() ) ), .f = ggscatterstats ) ## combining all individual plots from the list into a single plot using combine_plots function combine_plots( plotlist = plot_list, annotation.args = list( title = \"Relationship between movie budget and IMDB rating\", caption = \"Source: www.imdb.com\" ), plotgrid.args = list(ncol = 1) ) The remainder of the examples vary in content but follow the exact same methodology as the earlier examples. ## ggcorrmat ## for reproducibility set.seed(123) ## splitting the data frame by cut and creating a list ## let's leave out \"fair\" cut ## also, to make this fast, let's only use 5% of the sample cut_list <- ggplot2::diamonds %>% dplyr::sample_frac(size = 0.05) %>% dplyr::filter(cut != \"Fair\") %>% split(f = .$cut, drop = TRUE)\n\n## checking the length and names of each element\nlength(cut_list)\nnames(cut_list)\n\n## running function on every element of this list note that if you want the same\n## value for a given argument across all elements of the list, you need to\n## specify it just once\nplot_list <- purrr::pmap(\n.l = list(\ndata = cut_list,\ncor.vars = list(c(\"carat\", \"depth\", \"table\", \"price\")),\ntype = list(\"pearson\", \"np\", \"robust\", \"bf\"),\npartial = list(TRUE, FALSE, TRUE, FALSE),\ntitle = list(\"Cut: Good\", \"Cut: Very Good\", \"Cut: Premium\", \"Cut: Ideal\"),\np.adjust.method = list(\"hommel\", \"fdr\", \"BY\", \"hochberg\"),\nlab.size = 3.5,\ncolors = list(\nc(\"#56B4E9\", \"white\", \"#999999\"),\nc(\"#CC79A7\", \"white\", \"#F0E442\"),\nc(\"#56B4E9\", \"white\", \"#D55E00\"),\nc(\"#999999\", \"white\", \"#0072B2\")\n),\nggtheme = list(\nggplot2::theme_linedraw(),\nggplot2::theme_classic(),\nggthemes::theme_fivethirtyeight(),\nggthemes::theme_tufte()\n)\n),\n.f = ggcorrmat\n)\n\n## combining all individual plots from the list into a single plot using\n## combine_plots function\ncombine_plots(\nplotlist = plot_list,\nguides = \"keep\",\nannotation.args = list(\ntitle = \"Relationship between diamond attributes and price across cut\",\ncaption = \"Dataset: Diamonds from ggplot2 package\"\n),\nplotgrid.args = list(nrow = 2)\n)\n\n## gghistostats\n\n## for reproducibility\nset.seed(123)\n\n## let's split the data frame and create a list by continent\n## let's leave out Oceania because it has just two data points\ncontinent_list <-\ngapminder::gapminder %>%\ndplyr::filter(year == 2007, continent != \"Oceania\") %>%\nsplit(f = .$continent, drop = TRUE) ## checking the length and names of each element length(continent_list) names(continent_list) ## running function on every element of this list note that if you want the same ## value for a given argument across all elements of the list, you need to ## specify it just once plot_list <- purrr::pmap( .l = list( data = continent_list, x = \"lifeExp\", xlab = \"Life expectancy\", test.value = list(35.6, 58.4, 41.6, 64.7), type = list(\"p\", \"np\", \"r\", \"bf\"), bf.message = list(TRUE, FALSE, FALSE, FALSE), title = list( \"Continent: Africa\", \"Continent: Americas\", \"Continent: Asia\", \"Continent: Europe\" ), effsize.type = list(\"d\", \"d\", \"g\", \"g\"), normal.curve = list(TRUE, FALSE, FALSE, TRUE), ggtheme = list( ggplot2::theme_classic(), hrbrthemes::theme_ipsum_tw(), ggplot2::theme_minimal(), hrbrthemes::theme_modern_rc() ) ), .f = gghistostats ) ## combining all individual plots from the list into a single plot using combine_plots function combine_plots( plotlist = plot_list, annotation.args = list( title = \"Improvement in life expectancy worldwide since 1950\", caption = \"Note: black line - 1950; blue line - 2007\" ), plotgrid.args = list(nrow = 4) ) ## ggdotplotstats ## for reproducibility set.seed(123) library(ggthemes) library(hrbrthemes) ## let's split the data frame and create a list by continent ## let's leave out Oceania because it has just two data points continent_list <- gapminder::gapminder %>% dplyr::filter(continent != \"Oceania\") %>% split(f = .$continent, drop = TRUE)\n\n## checking the length and names of each element\nlength(continent_list)\nnames(continent_list)\n\n## running function on every element of this list note that if you want the same\n## value for a given argument across all elements of the list, you need to\n## specify it just once\nplot_list <-\npurrr::pmap(\n.l = list(\ndata = continent_list,\nx = \"gdpPercap\",\ny = \"year\",\nxlab = \"GDP per capita (US$, inflation-adjusted)\", test.value = list(2500, 9000, 9500, 10000), type = list(\"p\", \"np\", \"r\", \"bf\"), title = list( \"Continent: Africa\", \"Continent: Americas\", \"Continent: Asia\", \"Continent: Europe\" ), effsize.type = list(\"d\", \"d\", \"g\", \"g\"), centrality.line.args = list( list(color = \"red\"), list(color = \"#0072B2\"), list(color = \"#D55E00\"), list(color = \"#CC79A7\") ), ggtheme = list( ggplot2::theme_minimal(base_family = \"serif\"), ggthemes::theme_tufte(), hrbrthemes::theme_ipsum_rc(axis_title_size = 10), ggthemes::theme_hc(bgcolor = \"darkunica\") ) ), .f = ggdotplotstats ) ## combining all individual plots from the list into a single plot using combine_plots function combine_plots( plotlist = plot_list, annotation.args = list(title = \"Improvement in GDP per capita from 1952-2007\"), plotgrid.args = list(nrow = 4), guides = \"keep\" ) ## ggpiestats ## for reproducibility set.seed(123) ## let's split the data frame and create a list by passenger class class_list <- Titanic_full %>% split(f = .$Class, drop = TRUE)\n\n## checking the length and names of each element\nlength(class_list)\nnames(class_list)\n\n## running function on every element of this list note that if you want the same\n## value for a given argument across all elements of the list, you need to\n## specify it just once\nplot_list <-\npurrr::pmap(\n.l = list(\ndata = class_list,\nx = \"Survived\",\ny = \"Sex\",\nlabel = list(\"both\", \"count\", \"percentage\", \"both\"),\ntitle = list(\n\"Passenger class: 1st\",\n\"Passenger class: 2nd\",\n\"Passenger class: 3rd\",\n\"Passenger class: Crew\"\n),\ncaption = list(\n\"Total: 319, Died: 120, Survived: 199, % Survived: 62%\",\n\"Total: 272, Died: 155, Survived: 117, % Survived: 43%\",\n\"Total: 709, Died: 537, Survived: 172, % Survived: 25%\",\n\"Data not available for crew passengers\"\n),\npackage = list(\"RColorBrewer\", \"ghibli\", \"palettetown\", \"yarrr\"),\npalette = list(\"Accent\", \"MarnieMedium1\", \"pikachu\", \"nemo\"),\nggtheme = list(\nggplot2::theme_grey(),\nggplot2::theme_bw(),\nggthemes::theme_tufte(),\nggthemes::theme_economist()\n),\nproportion.test = list(TRUE, FALSE, TRUE, FALSE),\ntype = list(\"p\", \"p\", \"bf\", \"p\")\n),\n.f = ggpiestats\n)\n\n## combining all individual plots from the list into a single plot using combine_plots function\ncombine_plots(\nplotlist = plot_list,\nannotation.args = list(title = \"Survival in Titanic disaster by gender for all passenger classes\"),\nplotgrid.args = list(ncol = 1),\nguides = \"keep\"\n)\n\n## ggbarstats\n\n## for reproducibility\nset.seed(123)\n\n## let's split the data frame and create a list by passenger class\nclass_list <- Titanic_full %>% split(f = .\\$Class, drop = TRUE)\n\n## checking the length and names of each element\nlength(class_list)\nnames(class_list)\n\n## running function on every element of this list note that if you want the same\n## value for a given argument across all elements of the list, you need to\n## specify it just once\nplot_list <-\npurrr::pmap(\n.l = list(\ndata = class_list,\nx = \"Survived\",\ny = \"Sex\",\ntype = \"bayes\",\nlabel = list(\"both\", \"count\", \"percentage\", \"both\"),\ntitle = list(\n\"Passenger class: 1st\",\n\"Passenger class: 2nd\",\n\"Passenger class: 3rd\",\n\"Passenger class: Crew\"\n),\ncaption = list(\n\"Total: 319, Died: 120, Survived: 199, % Survived: 62%\",\n\"Total: 272, Died: 155, Survived: 117, % Survived: 43%\",\n\"Total: 709, Died: 537, Survived: 172, % Survived: 25%\",\n\"Data not available for crew passengers\"\n),\npackage = list(\"RColorBrewer\", \"ghibli\", \"palettetown\", \"yarrr\"),\npalette = list(\"Accent\", \"MarnieMedium1\", \"pikachu\", \"nemo\"),\nggtheme = list(\nggplot2::theme_grey(),\nggplot2::theme_bw(),\nggthemes::theme_tufte(),\nggthemes::theme_economist()\n)\n),\n.f = ggbarstats\n)\n\n## combining all individual plots from the list into a single plot using combine_plots function\ncombine_plots(\nplotlist = plot_list,\nannotation.args = list(\ntitle = \"Survival in Titanic disaster by gender for all passenger classes\",\ncaption = \"Asterisks denote results from proportion tests: \\n***: p < 0.001, ns: non-significant\"\n),\nplotgrid.args = list(ncol = 1),\nguides = \"keep\"\n)\n\n## grouped_ variants\n\nNote that although all the above examples were written with the non-grouped variants of functions, the same rule holds true for the grouped_ variants of all the above functions.\n\nFor example, if we want to use the grouped_gghistostats across three different datasets, you can use purrr::pmap() function. For the sake of brevity, the plots are not displayed here, but you can run the following code and check the individual grouped_ plots (e.g., plotlist[]).\n\n## create a list of plots\nplotlist <- purrr::pmap(\n.l = list(\ndata = list(mtcars, iris, ToothGrowth),\nx = alist(wt, Sepal.Length, len),\nresults.subtitle = list(FALSE),\ngrouping.var = alist(am, Species, supp)\n),\n.f = grouped_gghistostats\n)\n\n## given that we had three different datasets, we expect a list of length 3\n## (each of which contains a grouped_ plot)\nlength(plotlist)\n\n## Repeating function execution across multiple columns in a data frame\n\n## setup\nset.seed(123)\nlibrary(ggstatsplot)\nlibrary(patchwork)\n\n## running the same analysis on two different columns (creates a list of plots)\nplotlist <- purrr::pmap(\n.l = list(\ndata = list(movies_long),\nx = \"mpaa\",\ny = list(\"rating\", \"length\"),\ntitle = list(\"IMDB score by MPAA rating\", \"Movie length by MPAA rating\")\n),\n.f = ggbetweenstats\n)\n\n## combine plots using patchwork\nplotlist[] + plotlist[]\n\n## Suggestions\n\nIf you find any bugs or have any suggestions/remarks, please file an issue on GitHub: https://github.com/IndrajeetPatil/ggstatsplot/issues" ]
[ null ]
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http://helpcenter.perpetuumsoft.com/kb/a622/how-to-calculate-time-difference-by-using-a-formula.aspx
[ "# How to calculate time difference by using a formula\n\nDate and time formulas are useful for managing features that are time or date dependent. Two data types are used for working with dates and time in MobiDB: these are Date and Time types. You can use operations like addition or subtraction on Date and Time values to calculate either a future date or elapsed time between two dates.\n\nThe date value acquired from the Date type field holds only date as such, but during the calculation, if you add a Time type value to a Date type value it is possible to get a combined Date/Time value.\n\nThe following properties are available when working with Date type:\n\nday – returns the day of the month of a given date (21.01.2015 12:01 -> 21)\nmonth – returns the month of given date (21.01.2015 12:01 -> 1)\nyear – returns the year of a given date (21.01.2015 12:01 -> 2015)\ndate – returns the date, that does not have a time shift (21.01.2015 12:01 -> 21.01.2015)\ntime – returns the time shift from 0:00 date (21.01.2015 12:01 -> 12:01)\n\nThe values of Date type do not have any methods.\n\nThe available operations include:\n\naddition to time – results in a date, shifted forward for a given time\nsubtraction of time from date – results in a date, shifted backward for a given time\nsubtraction of date from date – results in a time, elapsed from the subtracted date\n\nThe following comparison operators are supported: <, >, <=, >=\n\nTime type in general is represented by a time interval. When getting the time value from the Time type field the value can fall within 00:00:00 to 23:59:59, but during the expression calculation the result may be more than one day.\n\nThe following properties are available when working with Time type:\n\ndays – returns a number of days in a given time interval (1d 12:02:15 -> 1)\nhours – returns a number of hours in a given time interval (1d 12:02:15 -> 12)\nminutes – returns a number of minutes in a given time interval (1d 12:02:15 -> 2)\nseconds – returns a number of seconds in a given time interval (1d 12:02:15 -> 15)\ntotalhours – returns  a total number of hours of a given time interval (1d 12:01:15 -> 36)\ntotalminutes – returns  a total number of minutes of a given time interval (1d 12:01:15 -> 2161)\ntotalseconds – returns  a total number of seconds of a given time interval (1d 12:01:15 -> 129675)\n\nThe values of the Time type do not have any methods.\n\nThe available operations for Time type include:\n\nunary -, addition to another time interval, subtraction from time interval.\n\nLet’s have a look at the sample for better perception.\n\nTask. To calculate worktime hours by subtracting date and time values.\n\nIn this scenario we originally have the following fields in our database:\n\nStart date (‘date1’ field) of Date type\nStart time (‘time1’ field) of Time type\nEnd date (‘date2’ field) of Date type\nEnd time (‘time2’ field) of Time type\n\nTo calculate working hours (subtract Start date and time from End date and time) the following approach can be used:\n\n1.Use days property to get the number of days and multiply the result by 24 to get the number of hours\n2.Subtract Start time from End time and use hours property to get the number of hours\n3.Add the results  from step 1 and 2 to get the total working hours value\n\n(date2-date1).days*24+(time2-time1).hours" ]
[ null ]
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http://mizar.org/version/current/html/proofs/e_siec/33
[ "let N be e_net; :: thesis: ( (id ( the carrier of N \\ (rng the escape of N))) * ( the escape of N \\ (id the carrier of N)) = the escape of N \\ (id the carrier of N) & (id ( the carrier of N \\ (rng the entrance of N))) * ( the entrance of N \\ (id the carrier of N)) = the entrance of N \\ (id the carrier of N) )\nset T = the entrance of N;\nset C = the carrier of N;\nset E = the escape of N;\nset I = id the carrier of N;\nfor x, y being object st [x,y] in the escape of N \\ (id the carrier of N) holds\n[x,y] in (id ( the carrier of N \\ (rng the escape of N))) * ( the escape of N \\ (id the carrier of N))\nproof\nlet x, y be object ; :: thesis: ( [x,y] in the escape of N \\ (id the carrier of N) implies [x,y] in (id ( the carrier of N \\ (rng the escape of N))) * ( the escape of N \\ (id the carrier of N)) )\nassume A1: [x,y] in the escape of N \\ (id the carrier of N) ; :: thesis: [x,y] in (id ( the carrier of N \\ (rng the escape of N))) * ( the escape of N \\ (id the carrier of N))\nthen [x,y] in the escape of N by XBOOLE_0:def 5;\nthen A2: x in dom the escape of N by XTUPLE_0:def 12;\nA3: not x in rng the escape of N\nproof\nassume x in rng the escape of N ; :: thesis: contradiction\nthen ex z being object st [z,x] in the escape of N by XTUPLE_0:def 13;\nthen the escape of N * ( the escape of N \\ (id the carrier of N)) <> {} by ;\nhence contradiction by Def2; :: thesis: verum\nend;\ndom the escape of N c= the carrier of N by Th14;\nthen x in the carrier of N \\ (rng the escape of N) by ;\nthen [x,x] in id ( the carrier of N \\ (rng the escape of N)) by RELAT_1:def 10;\nhence [x,y] in (id ( the carrier of N \\ (rng the escape of N))) * ( the escape of N \\ (id the carrier of N)) by ; :: thesis: verum\nend;\nthen A4: the escape of N \\ (id the carrier of N) c= (id ( the carrier of N \\ (rng the escape of N))) * ( the escape of N \\ (id the carrier of N)) by RELAT_1:def 3;\nfor x, y being object st [x,y] in the entrance of N \\ (id the carrier of N) holds\n[x,y] in (id ( the carrier of N \\ (rng the entrance of N))) * ( the entrance of N \\ (id the carrier of N))\nproof\nlet x, y be object ; :: thesis: ( [x,y] in the entrance of N \\ (id the carrier of N) implies [x,y] in (id ( the carrier of N \\ (rng the entrance of N))) * ( the entrance of N \\ (id the carrier of N)) )\nassume A5: [x,y] in the entrance of N \\ (id the carrier of N) ; :: thesis: [x,y] in (id ( the carrier of N \\ (rng the entrance of N))) * ( the entrance of N \\ (id the carrier of N))\nthen [x,y] in the entrance of N by XBOOLE_0:def 5;\nthen A6: x in dom the entrance of N by XTUPLE_0:def 12;\nA7: not x in rng the entrance of N\nproof\nassume x in rng the entrance of N ; :: thesis: contradiction\nthen ex z being object st [z,x] in the entrance of N by XTUPLE_0:def 13;\nthen the entrance of N * ( the entrance of N \\ (id the carrier of N)) <> {} by ;\nhence contradiction by Def2; :: thesis: verum\nend;\ndom the entrance of N c= the carrier of N by Th14;\nthen x in the carrier of N \\ (rng the entrance of N) by ;\nthen [x,x] in id ( the carrier of N \\ (rng the entrance of N)) by RELAT_1:def 10;\nhence [x,y] in (id ( the carrier of N \\ (rng the entrance of N))) * ( the entrance of N \\ (id the carrier of N)) by ; :: thesis: verum\nend;\nthen A8: the entrance of N \\ (id the carrier of N) c= (id ( the carrier of N \\ (rng the entrance of N))) * ( the entrance of N \\ (id the carrier of N)) by RELAT_1:def 3;\n( (id ( the carrier of N \\ (rng the escape of N))) * ( the escape of N \\ (id the carrier of N)) c= the escape of N \\ (id the carrier of N) & (id ( the carrier of N \\ (rng the entrance of N))) * ( the entrance of N \\ (id the carrier of N)) c= the entrance of N \\ (id the carrier of N) ) by RELAT_1:50;\nhence ( (id ( the carrier of N \\ (rng the escape of N))) * ( the escape of N \\ (id the carrier of N)) = the escape of N \\ (id the carrier of N) & (id ( the carrier of N \\ (rng the entrance of N))) * ( the entrance of N \\ (id the carrier of N)) = the entrance of N \\ (id the carrier of N) ) by ; :: thesis: verum" ]
[ null ]
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http://www.self.gutenberg.org/articles/eng/Linear_canonical_transform
[ "", null, "#jsDisabledContent { display:none; } My Account | Register | Help", null, "Flag as Inappropriate", null, "This article will be permanently flagged as inappropriate and made unaccessible to everyone. Are you certain this article is inappropriate?          Excessive Violence          Sexual Content          Political / Social Email this Article Email Address:\n\nLinear canonical transform\n\nArticle Id: WHEBN0007438899\nReproduction Date:\n\n Title: Linear canonical transform", null, "Author: World Heritage Encyclopedia Language: English Subject: Collection: Publisher: World Heritage Encyclopedia Publication Date:\n\nLinear canonical transform\n\nIn Hamiltonian mechanics, the linear canonical transformation (LCT) is a family of integral transforms that generalizes many classical transforms. It has 4 parameters and 1 constraint, so it is a 3-dimensional family, and can be visualized as the action of the special linear group SL2(R) on the time–frequency plane (domain).\n\nThe LCT generalizes the Fourier, fractional Fourier, Laplace, Gauss–Weierstrass, Bargmann and the Fresnel transforms as particular cases. The name \"linear canonical transformation\" is from canonical transformation, a map that preserves the symplectic structure, as SL2(R) can also be interpreted as the symplectic group Sp2, and thus LCTs are the linear maps of the time–frequency domain which preserve the symplectic form.\n\nDefinition\n\nThe LCT can be represented in several ways; most easily, it can be viewed as a 2×2 matrix with determinant 1, i.e., an element of the special linear group SL2(R). Taking a matrix $\\left\\left(\\begin\\left\\{smallmatrix\\right\\}a & b\\\\c & d\\end\\left\\{smallmatrix\\right\\}\\right\\right),$ with ad − bc = 1, the corresponding integral transform is:\n\n $X_\\left\\{\\left(a,b,c,d\\right)\\right\\}\\left(u\\right) = \\sqrt\\left\\{-i\\right\\} \\cdot e^\\left\\{i \\pi \\frac\\left\\{d\\right\\}\\left\\{b\\right\\} u^\\left\\{2\\right\\}\\right\\} \\int_\\left\\{-\\infty\\right\\}^\\infty e^\\left\\{-i 2 \\pi \\frac\\left\\{1\\right\\}\\left\\{b\\right\\} ut\\right\\}e^\\left\\{i \\pi \\frac\\left\\{a\\right\\}\\left\\{b\\right\\} t^2\\right\\} x\\left(t\\right) \\; dt \\, ,$ when b ≠ 0, $X_\\left\\{\\left(a,0,c,d\\right)\\right\\}\\left(u\\right) = \\sqrt\\left\\{d\\right\\} \\cdot e^\\left\\{i \\pi cdu^\\left\\{2\\right\\}\\right\\} x\\left(du\\right) \\, ,$ when b = 0.\n\nSpecial cases\n\nMany classical transforms are special cases of the linear canonical transform:\n\n\n\n\\begin{bmatrix}\n\n a & b \\\\\nc & d\n\n\n\\end{bmatrix}\n\n=\n\n\n\\begin{bmatrix}\n\n 0 & 1 \\\\\n-1 & 0\n\n\n\\end{bmatrix}.\n\n\n\n\\begin{bmatrix}\n\n a & b \\\\\nc & d\n\n\n\\end{bmatrix}\n\n=\n\n\n\\begin{bmatrix}\n\n \\cos \\theta & \\sin \\theta \\\\\n-\\sin \\theta & \\cos \\theta\n\n\n\\end{bmatrix}.\n\n\n\n\\begin{bmatrix}\n\n a & b \\\\\nc & d\n\n\n\\end{bmatrix}\n\n=\n\n\n\\begin{bmatrix}\n\n 1 & \\lambda z \\\\\n0 & 1\n\n\n\\end{bmatrix}.\n\nwhere z is distance and λ is wave length.\n• The Laplace transform corresponds to rotation by 90° into the complex domain, and can be represented by the matrix:\n\n\n\\begin{bmatrix}\n\n a & b \\\\\nc & d\n\n\n\\end{bmatrix}\n\n=\n\n\n\\begin{bmatrix}\n\n 0 & i \\\\\ni & 0\n\n\n\\end{bmatrix}.\n\n• The Fractional Laplace transform corresponds to rotation by an arbitrary angle into the complex domain, and can be represented by the matrix:\n\n\n\\begin{bmatrix}\n\n a & b \\\\\nc & d\n\n\n\\end{bmatrix}\n\n=\n\n\n\\begin{bmatrix}\n\n i \\cos \\theta & i \\sin \\theta \\\\\ni \\sin \\theta & -i \\cos \\theta\n\n\n\\end{bmatrix}.\n\nComposition\n\nComposition of LCTs corresponds to multiplication of the corresponding matrices; this is also known as the \"additivity property of the WDF\".\n\nIn detail, if the LCT is denoted by OF(a,b,c,d), i.e.\n\n$X_\\left\\{\\left(a,b,c,d\\right)\\right\\}\\left(u\\right) = O_F^\\left\\{\\left(a,b,c,d\\right)\\right\\}\\left[x\\left(t\\right)\\right] \\,$\n\nthen\n\n$O_F^\\left\\{\\left(a2,b2,c2,d2\\right)\\right\\} \\left \\\\left\\{ O_F^\\left\\{\\left(a1,b1,c1,d1\\right)\\right\\}\\left[x\\left(t\\right)\\right] \\right \\\\right\\} = O_F^\\left\\{\\left(a3,b3,c3,d3\\right)\\right\\}\\left[x\\left(t\\right)\\right] \\, ,$\n\nwhere\n\n\n\n\\begin{bmatrix}\n\n a3 & b3 \\\\\nc3 & d3\n\n\n\\end{bmatrix}\n\n=\n\n\n\\begin{bmatrix}\n\n a2 & b2 \\\\\nc2 & d2\n\n\n\\end{bmatrix} \\begin{bmatrix}\n\n a1 & b1 \\\\\nc1 & d1\n\n\n\\end{bmatrix}.\n\nIn optics and quantum mechanics\n\nParaxial optical systems implemented entirely with thin lenses and propagation through free space and/or graded index (GRIN) media, are quadratic phase systems (QPS); these were known before Moshinsky and Quesne (1974) called attention to their significance in connection with canonical transformations in quantum mechanics. The effect of any arbitrary QPS on an input wavefield can be described using the linear canonical transform, a particular case of which was developed by Segal (1963) and Bargmann (1961) in order to formalize Fok's (1928) boson calculus.\n\nApplications\n\nCanonical transforms are used to analyze differential equations. These include diffusion, the Schrödinger free particle, the linear potential (free-fall), and the attractive and repulsive oscillator equations. It also includes a few others such as the Fokker–Planck equation. Although this class is far from universal, the ease with which solutions and properties are found makes canonical transforms an attractive tool for problems such as these.\n\nWave propagation through air, a lens, and between satellite dishes are discussed here. All of the computations can be reduced to 2×2 matrix algebra. This is the spirit of LCT.\n\nElectromagnetic wave propagation\n\nAssuming the system looks like as depicted in the figure, the wave travels from plane xi, yi to the plane of x and y. The Fresnel transform is used to describe electromagnetic wave propagation in air:\n\n$U_0\\left(x,y\\right) = - \\frac\\left\\{j\\right\\}\\left\\{\\lambda\\right\\} \\frac\\left\\{e^\\left\\{jkz\\right\\}\\right\\}\\left\\{z\\right\\} \\int_\\left\\{-\\infty\\right\\}^\\infty \\int_\\left\\{-\\infty\\right\\}^\\left\\{\\infty\\right\\} e^\\left\\{j \\frac\\left\\{k\\right\\}\\left\\{2z\\right\\} \\left[ \\left(x-x_i\\right)^2 +\\left(y-y_i\\right)^2 \\right] \\right\\} U_i\\left(x_i,y_i\\right) \\; dx_i\\; dy_i,$\n\nwith\n\n k = 2 π / λ : wave number; λ : wavelength; z : distance of propagation; j : imaginary unit.\n\nThis is equivalent to LCT (shearing), when\n\n\n\n\\begin{bmatrix}\n\n a & b \\\\\nc & d\n\n\n\\end{bmatrix} = \\begin{bmatrix}\n\n 1 & \\lambda z \\\\\n0 & 1\n\n\n\\end{bmatrix}.\n\nWhen the travel distance (z) is larger, the shearing effect is larger.\n\nSpherical lens\n\nWith the lens as depicted in the figure, and the refractive index denoted as n, the result is:\n\n$U_0\\left(x,y\\right) = e^\\left\\{jkn \\Delta\\right\\} e^\\left\\{-j \\frac\\left\\{k\\right\\}\\left\\{2f\\right\\} \\left[x^2 + y ^2\\right]\\right\\} U_i\\left(x,y\\right)$\n\nwith f the focal length and Δ the thickness of the lens.\n\nThe distortion passing through the lens is similar to LCT, when\n\n\n\n\\begin{bmatrix}\n\n a & b \\\\\nc & d\n\n\n\\end{bmatrix} = \\begin{bmatrix}\n\n 1 & 0 \\\\\n\\frac{-1}{\\lambda f} & 1\n\n\n\\end{bmatrix}.\n\nThis is also a shearing effect: when the focal length is smaller, the shearing effect is larger.\n\nSpherical Mirror\n\nThe spherical mirror—e.g., a satellite dish—can be described as a LCT, with\n\n\n\n\\begin{bmatrix}\n\n a & b \\\\\nc & d\n\n\n\\end{bmatrix} = \\begin{bmatrix}\n\n 1 & 0 \\\\\n\\frac{-1}{\\lambda R} & 1\n\n\n\\end{bmatrix}.\n\nThis is very similar to lens, except focal length is replaced by the radius of the dish. Therefore, if the radius is smaller, the shearing effect is larger.\n\nExample\n\nThe system considered is depicted in the figure to the right: two dishes – one being the emitter and the other one the receiver – and a signal travelling between them over a distance D. First, for dish A (emitter), the LCT matrix looks like this:\n\n\n\n\\begin{bmatrix}\n\n 1 & 0 \\\\\n\\frac{-1}{\\lambda R_A} & 1\n\n\n\\end{bmatrix}.\n\nThen, for dish B (receiver), the LCT matrix similarly becomes:\n\n\n\n\\begin{bmatrix}\n\n 1 & 0 \\\\\n\\frac{-1}{\\lambda R_B} & 1\n\n\n\\end{bmatrix}.\n\nLast, for the propagation of the signal in air, the LCT matrix is:\n\n\n\n\\begin{bmatrix}\n\n 1 & \\lambda D \\\\\n0 & 1\n\n\n\\end{bmatrix}.\n\nPutting all three components together, the LCT of the system is:\n\n\n\n\\begin{bmatrix}\n\n a & b \\\\\nc & d\n\n\n\\end{bmatrix} = \\begin{bmatrix}\n\n 1 & 0 \\\\\n\\frac{-1}{\\lambda R_B} & 1\n\n\n\\end{bmatrix} \\begin{bmatrix}\n\n 1 & \\lambda D \\\\\n0 & 1\n\n\n\\end{bmatrix} \\begin{bmatrix}\n\n 1 & 0 \\\\\n\\frac{-1}{\\lambda R_A} & 1\n\n\n\\end{bmatrix} = \\begin{bmatrix}\n\n 1-\\frac{D}{R_A} & - \\lambda D \\\\\n\\frac{1}{\\lambda} (R_A^{-1} + R_B^{-1} - R_A^{-1}R_B^{-1}D) & 1 - \\frac{D}{R_B}\n\n\n\\end{bmatrix} \\, ." ]
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https://www.pilishen.com/posts/vuejs-this-disable-solution
[ "``````axios.get('url').then( (response)=>{\nthis.data = response.data;\n}).catch( (error)=>{\n...\n});\n\n//vue-resource\nthis.\\$http.get('url').then((response)=>{\nthis.data = response.body;\n},(response)=>{\n...\n});\n``````\n\n``````axios.get('url').then( function(response){\nthis.data = response.data;\n\n}).catch(function(error){\nconsole.log(error)\n});\n``````\n\n### 2. 在http请求外层将vue实例所代表的this赋值给一个变量\n\n``````vm = this;\naxios.get('url').then( function(response){\nvm.data = response.data;\n}).catch();\n``````\n\n### 3. 在创建vue实例的时候，将vue实例赋值给一个变量\n\n``````var vm = new Vue({\n...\n\naxios.get('url').then(function(response){\nvm.data = response.data;\n\n}).catch();\n``````\n\n### 那this在上面两种环境下指的到底是什么呢？ 下面进入读文档的时间", null, "", null, "", null, "" ]
[ null, "https://github.githubassets.com/images/icons/emoji/unicode/1f604.png", null, "https://7xsku2.com1.z0.glb.clouddn.com/vueJs/6DW%7DS@@@Q@MR2%5DVY~XZDZKH.png", null, "https://7xsku2.com1.z0.glb.clouddn.com/vueJs/EN%28\\$B@RRK61VB7%29A1W%285%28PR.png", null ]
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http://www.cpearson.com/excel/returningarraysfromvba.aspx
[ "", null, "Returning Arrays From VBA User Defined Functions\n\nThis page describes returning arrays as the result of VBA User Defined Functions.", null, "Introduction\n\nThis page looks at a few issue that might arise when you are returning arrays from UDFs.", null, "Choosing The Right Return Array Size\n\nAt its simplest, the size of the returned array can be mandated by the function and require that the user use an array that size in order to get all the results. The Excel function LINEST function works this way. You must array-enter that function into a range of cells that is 5 rows tall and 2 columns wide. If you enter it into a larger range, Excel fills out the unused elements of the range with #N/A errors. If you enter it into a smaller range, you will not get all the values created by LINEST.\n\nTo mandate the size of the returned array, simply declare the array to that size and setting the result of the function to that array. For example,\n\n``` Function Test() As Variant\nDim V() As Variant\nDim N As Long\nDim R As Long\nDim C As Long\nReDim V(1 To 3, 1 To 4)\nFor R = 1 To 3\nFor C = 1 To 4\nN = N + 1\nV(R, C) = N\nNext C\nNext R\nTest = V\nEnd Function\n```\n\nThis function simply returns an array with 3 rows and 4 columns that contains the integers from 1 to 12.\n\nReturning such a fixed-size array can be useful if the number of results does not vary with the number and/or values of the inputs to the function. However, this is usually not the case.\n\nIn the majority of circumstances, if your UDF is going to return an array, that array will vary in size and the size will depend on any one or more of three things: the size of the range into which the UDF was entered, the number of elements passed into the function, and, of course, the nature and function of the UDF itself. The Application.Caller object, when used in a UDF called from a worksheet range, is a Range reference to the range from which your UDF was called.\n\nCAUTION: Application.Caller will be a Range object only when the function in which it appears was called from a worksheet cell. If the function was called from another VB procedure, Application.Caller will be an Error-type Variant and most any attempt to use it will result in a Type Mismatch (13) error. If the code containing Application.Caller was called via the OnAction property of a Shape object on a worksheet, Application.Caller will be a String containing the name of the sheet. Therefore, if your function might be called from another VB procedure rather than only from a worksheet cell, you should test Application.Caller with the IsObject function to ensure that it is indeed an object before attempting to access any of its properties.\n\nCAUTION: In Excel 2003, a new object, Application.ThisCell, was introduced. It is similar in nature to Application.Caller, but differs when a UDF is array entered into a range of more than one cell. Application.Caller will return the a Range reference to the entire range in which the UDF was array-entered. Application.ThisCell returns a reference to the first (upper left) cell in the range from which the UDF was called. Frankly, I'm not sure why Application.ThisCell was introduced in the first place.\n\nIn the example code on this page, we will not test Application.Caller with IsObject. For simplicity and brevity, we will assume that the function is being called from a worksheet.\n\nUsing Application.Caller, you can determine the number of rows and columns from which the function was called. For example,\n\n``` Function Test()\nDim CallerRows As Long\nDim CallerCols As Long\nWith Application.Caller\nCallerRows = .Rows.Count\nCallerCols = .Columns.Count\nEnd With\nTest = CallerRows * CallerCols\nEnd Function\n```\n\nIn this code, the variables CallerRows and CallerCols get the number of rows and columns in the range from which the function was called. If you want to return an array the same size as the range from which the function was called, you can use code like the following:\n```Function Test() As Variant\nDim CallerRows As Long\nDim CallerCols As Long\nDim Result() As Long\nDim N As Long\nDim RowNdx As Long\nDim ColNdx As Long\n\nWith Application.Caller\nCallerRows = .Rows.Count\nCallerCols = .Columns.Count\nEnd With\nReDim Result(1 To CallerRows, 1 To CallerCols)\nFor RowNdx = 1 To CallerRows\nFor ColNdx = 1 To CallerCols\nN = N + 1\nResult(RowNdx, ColNdx) = N\nNext ColNdx\nNext RowNdx\nTest = Result\nEnd Function\n```\n\nThis function returns an array with the same dimensions as the range from which the function was called, and simply fills those elements with the first Rows*Columns integers.\n\nYou can, of course, ignore the size of the range from which the function was called and return an array with the dimensions required by your function's purpose. In this case, if the function is entered into a range smaller than the result array of the function, the result array is trunctated on the bottom and on the right to the size of the calling range. If the function was entered into a range larger than the size of the returned array, Excel fills the unused cells with #N/A values. This is the normal behavior of Excel's own array functions. For example, if you array enter =ROW(A1:A3) into cells B1:B5, the result will be 1 2 3 #N/A #N/A. The ROW(A1:A3) returns an array with only three elements, so Excel fills in the rest of the calling range with #N/A values.", null, "Orienting An Array\n\nIf your UDF creates a 1-dimensional array as its result, it can orient the array as either a row vector or a column vector so that is will be properly displayed in the worksheet cells without requiring the user to wrap your UDF result in a TRANSPOSE function. If the function was called from a row vector of cells (e.g., A1:E1), it does not need to be transposed. If the function was called from a column vector of cells (e.g., A1:A5), the array needs to be transposed. The code below looks at Application.Caller.Rows.Count and if this is greater than 1, it tranposes the array before returning it to the caller. Note that this should be done only with single-dimensional arrays and only when the UDF is being called from a worksheet range. Therefore, you should first test Application.Caller with IsObject and then test Application.Caller.Rows.Count and Application.Caller.Columns.Count to test if it is being called from a row or column vector. For example,\n\n``` Function Test(NN As Long)\nDim Result() As Long\nDim N As Long\nReDim Result(1 To NN)\nFor N = 1 To NN\nResult(N) = N\nNext N\nIf Application.Caller.Rows.Count > 1 Then\nTest = Application.Transpose(Result)\nElse\nTest = Result\nEnd If\nEnd Function\n```\n\nYou can, of course, forego this and return the array as-is and leave it up to the user to use the TRANSPOSE function to properly orient the array." ]
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https://parasol-lab.gitlab.io/stapl-home/docs/sgl/creation/generators/make_random_neighborhood.html
[ "# make_random_neighborhood\n\nDefined in <stapl/containers/graph/generators/random_neighborhood.hpp>\n\ntemplate<typename GraphView>\nGraphView make_random_neighborhood(size_t n,size_t ef,size_t k,bool bidirectional)\n\n\n## Summary\n\nGenerates a random graph with N vertices.\n\nEach vertex can connect to others in its neighborhood (+/- k from a vertex's id defines the neighborhood). k=1 forms a circular list, while k=N forms an Erdos-Renyi random network. Each vertex connects to ef neighbors on average, this is not the guaranteed number of edges for a particular vertex. The diameter of the generated graph decreases as k increases.\n\nThe returned view owns its underlying container.\n\n#### Parameters\n\n• n: Number of vertices in the generated graph.\n• ef: Average number of outgoing edges per vertex.\n• k: Size of the neighborhood to which each vertex can connect.\n• bidirectional: True to add back-edges in a directed graph, false for forward edges only.\n\n#### Returns\n\nA view over the generated graph.\n\n#### Example\n\n using view_type = stapl::graph_view<stapl::multidigraph<int>>;\n\nauto v = stapl::generators::make_random_neighborhood<view_type>(\n128, 8, 4, true\n);" ]
[ null ]
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https://www.scribd.com/document/358878192/Analog-Electronics
[ "You are on page 1of 29\n\n# GATE SOLVED PAPER - IN\n\nANALOG ELECTRONICS\n\n## Q. 1 The i -v characteristics of the diode in the circuit given below are :\n\nv - 0.7 A v \\$ 0.7 V\ni = * 500\n0 A, v < 0.7 V\nThe current in the circuit is\n\n## (A) 10 mA (B) 9.3 mA\n\n(C) 6.67 mA (D) 6.2 mA\n\n## (A) Av . 200 (B) Av . 100\n\n(C) Av . 20 (D) Av . 10\n\n## Q. 3 The circuit shown is a\n\nmywbut.com\nGATE SOLVED PAPER - IN ANALOG ELECTRONICS\n\n^R1 + R2h C\n\nR1 C\n\nR1 C\n\n^R1 + R2h C\n\n## YEAR 2011 ONE MARK\n\nQ. 4 The amplifier shown below has a voltage gain of - 2.5 , an input resistance of\n10 kW, and a lower 3-dB cut-off frequency of 20 Hz. Which one of the following\nstatements is TRUE when the emitter resistance RE is doubled ?\n\n## (A) Magnitude of voltage gain will decrease\n\n(B) Input resistance will decrease\n(C) Collector bias current will increase\n(D) Lower 3-dB cut-off frequency will increase\n\n## Q. 5 Assuming base-emitter voltage of 0.7 V and b = 99 of transistor Q1 , the output\n\nvoltage Vo in the ideal opamp circuit shown below is\n\n## (A) - 1 V (B) - 1/3.3 V\n\n(C) 0 V (D) 2 V\n\nmywbut.com\nGATE SOLVED PAPER - IN ANALOG ELECTRONICS\n\n## Q. 6 Assuming zener diode D1 has current-voltage characteristics as shown below of\n\nthe right and forward voltage drop of diode D2 is 0.7 V, the voltage Vo in the\ncircuit shown below is\n\n## (A) 3.7 V (B) 2.7 V\n\n(C) 2.2 V (D) 0 V\n\n## Q. 7 The value of Vo of the series regulator shown below is\n\n(A) 24 V (B) 28 V\n(C) 30 V (D) 32 V\n\n## (A) low-pass filter (B) high-pass filter\n\n(C) band-pass filter (D) band-reject filter\n\n## Common Data For Questions 9 and 10 :\n\nM1 , M2 and M 3 in the circuit shown below are matched N-channel enhancement\nmode MOSFETs operating in saturation mode, forward voltage drop of each\ndiode is 0.7 V, reverse leakage current of each diode is negligible and the opamp\nis ideal.\n\nmywbut.com\nGATE SOLVED PAPER - IN ANALOG ELECTRONICS\n\n## Q. 9 The current Is in the circuit is\n\n(A) - 1 mA (B) 0.5 mA\n(C) 1 mA (D) 2 mA\n\n## Q. 10 For the computed value of current Is , the output voltage Vo is\n\n(A) 1.2 V (B) 0.7 V\n(C) 0.2 V (D) - 0.7 V\n\n## YEAR 2010 ONE MARK\n\nQ. 11 In the ideal op-amp circuit given in the adjoining figure, the value of R f is varied\nfrom 1 kW to 100 kW. The gain G = bV0 l will\nVi\n\n## (A) remain constant at + 1 (B) remain constant at - 1\n\n(C) vary as (R f /10, 000) (D) vary as (1 + R f /10, 000)\n\n## YEAR 2010 TWO MARKS\n\nQ. 12 The matched transistors Q1 and Q2 shown in the adjoining figure have b = 100.\nAssuming the base-emitter voltages to be 0.7 V, the collector-emitter voltage V2\nof the transistors Q2 is\n\n## (A) 33.9 V (B) 27.8 V\n\n(C) 16.2 V (D) 0.7 V\n\nmywbut.com\nGATE SOLVED PAPER - IN ANALOG ELECTRONICS\n\nQ. 13 An active filter is shown in the adjoining figure. The dc gain and the 3 dB cut-off\nfrequency of the filter respectively, are, nearly\n\n## R1 = 15.9kW, R2 = 159 kW, C1 = 1.0nF\n\n(A) 40 dB, 3,14 kHz (B) 40 dB, 1.00 kHz\n(C) 20 dB, 6.28 kHz (D) 20 dB, 1.00 kHz\n\n## Common Data For Questions 14 and 15 :\n\nA differential amplifier is constructed using an ideal op-amp as shown in the\nadjoining figure. The values of R1 and R2 are 47 kW and 470kW respectively.\n\nQ. 14 The input impedances seen looking into the terminals V1 and V2 with respect to\nground, respectively are\n(A) 47 kW 43 kW (B) 47 kW and 47 kW\n(C) 47 kW and 51 kW (D) 517 kW and 517 kW\n\n## Q. 15 V1 and V2 are connected to voltage sources having an open circuit of + 1V each\n\nand internal resistances of 13 kW and 3 kW respectively. The output voltage V0 is\n(A) 0 V (B) 0.15 V\n(C) 1.5 V (D) 10 V\n\n## Q. 16 The circuit shown in the figure is\n\nmywbut.com\nGATE SOLVED PAPER - IN ANALOG ELECTRONICS\n\n## (A) an all-pass filter (B) a band-pass filter\n\n(C) a high-pass filter (D) a low-pass filter\n\n## YEAR 2009 TWO MARKS\n\nQ. 17 In the circuit shown, the Zener diode has ideal characteristics and a breakdown\nvoltage of 3.2 V. The output voltage V0 for an input voltage Vi =+ 1V is closed to\n\n## (A) - 10 V (B) - 6.6 V\n\n(C) - 5 V (D) - 3.2 V\n\nQ. 18 The input resistance of the circuit shown in the figure assuming an ideal op-amp,\nis\n\n## (A) R/3 (B) 2R/3\n\n(C) R (D) 4R/3\n\nQ. 19 In the circuit shown in the figure, the switch S has been in Position 1 for a long\ntime. It is then moved to Position 2. Assume the Zener diodes to be idea. The\ntime delay between the switch moving to position 2 and the transition in the\noutput voltage V0 is\n\n## (A) 5.00 ms (B) 8.75 ms\n\n(C) 10.00 ms (D) 13.75 ms\n\nmywbut.com\nGATE SOLVED PAPER - IN ANALOG ELECTRONICS\n\n## Common Data For Questions 20 and 21 :\n\nThe figure shows a sample-and-hold circuit using a MOSFET as a switch. The\nthreshold voltage of the MOSFET as a switch. The threshold voltage of the\nMOSFET is + 2 V. It has zero leakage current in the off state. Assume that the\ncapacitor is ideal.\n\n## Q. 20 The input voltage Vi ranges from - 5 V to + 5 V. Appropriate values of Vsub , of\n\nVg during hold are, respectively,\n(A) + 12V \\$ + 7V and # - 3V (B) - 12V, \\$ + 3V, and # - 7V\n(C) + 12V, \\$ + 3V and # - 7V (D) - 12V, \\$ + 7V, and # - 3V\n\nQ. 21 The circuit is used at a sampling rate of 1 kHz, with an A/D converter having a\nconversion time of 200 ms. The op-amp has an input bias current of 10 nA. The\nmaximum hold error is\n(A) 1 mV (B) 2 mV\n(C) 5 mV (D) 10 mV\n\n## Common Data For Questions 22 and 23 :\n\nThe circuit shown in the figure uses three identical transistors with VBE = 0.7 V\nand b = 100 . Given R1 = R2 = R 3 = 1kW, kT/qe = 25mV\n.The collector current of transistor Q 3 is 2 mA.\n\n## Q. 22 The bias Voltage VB at the base of the transistor Q 3 is approximately\n\n(A) - 9.3 V (B) - 10.0 V\n(C) - 10.3 V (D) - 11.0 V\n\n## Q. 23 The small signal voltage gain of the circuit is\n\n(A) - 20 (B) - 40\n(C) 20 (D) 40\n\nmywbut.com\nGATE SOLVED PAPER - IN ANALOG ELECTRONICS\n\n## Q. 24 For a single BJT common base amplifier\n\n(A) Current gain as well as voltage gain can be greater than unity\n(B) Current gain can be greater than unity but voltage gain is always < unity.\n(C) Voltage gain can be greater than unity but current gain is always < unity\n(D) Current gain as well as voltage gain is always less than unity.\n\nQ. 25 In the circuit shown below, the ideality factor h of the diode is unity and the\nvoltage drop across it is 0.7 V. The dynamic resistance of the diode at room\ntemperature is approximately\n\n(A) 15 W (B) 25 W\n(C) 50 W (D) 700 W\n\n## Q. 26 An ideal op-amp has the characteristics of an ideal\n\n(A) Voltage controlled voltage source (B) Voltage controlled current source\n(C) Current controlled voltage sourec (D) Current controlled current source\n\n## YEAR 2008 TWO MARKS\n\nQ. 27 A differential amplifier shown below has a differential mode gain of 100 and a\nCMRR of 40 dB. If V1 = 0.55 and V2 = 0.45 V, the output V0 is\n\n## (A) 10 V (B) 10.5 V\n\n(C) 11 V (D) 15 V\n\n## (A) low-pass filter with a maximum gain of 1\n\n(B) low-pass filter with a maximum, gain of 2\n(C) high-pass filter with a maximum gain of 1\n(D) high-pass filter with a maximum gain of 2\n\nmywbut.com\nGATE SOLVED PAPER - IN ANALOG ELECTRONICS\n\nQ. 29 In the op-amp circuit shown below is that of Vin is gradually increased from - 10\nV to + 10 V. Assuming that the output voltage Vout saturates at - 10 V and + 10\nV, Vout will change from\n\n(A) - 10V to + 10V when Vin =- 1V (B) - 10V to + 10V when Vin =+ 1V\n(C) + 10V to - 10V when Vin =- 1V (D) + 10 V to - 10 V when Vin =+ 1 V\n\n## Q. 30 For the op-amp circuit shown below V0 is approximately equal to\n\n(A) - 10 V (B) - 5 V\n(C) + 5 V (D) + 10 V\n\nQ. 31 In the amplifier circuit shown below, assume VBE = 0.7 V and the b of the transistor\nand the values of C1 and C2 are extremely high. If the amplifier is designed such\nthat at the quiescent point its VCE = VCC , When VCC is the power supply voltage,\n2\nits small signal voltage gain Vout will be\nVin\n\nmywbut.com\nGATE SOLVED PAPER - IN ANALOG ELECTRONICS\n\n(C) 9 (D) 19\n\n## YEAR 2007 ONE MARK\n\nQ. 32 When the light falls on the photodiode shown in the following circuit, the reverse\nsaturation current of the photodiode changes form 100 mA to 200 mA .\n\nAssuming the op-amp to be ideal, the output voltage, Vout of the circuit.\n(A) does not change (B) changes from 1 V to 2 V\n(C) changes from 2 V to 1 V (D) changes from - 1V to - 2 V\n\n## If RB is shorted, the waveform at VC is\n\nmywbut.com\nGATE SOLVED PAPER - IN ANALOG ELECTRONICS\n\n## YEAR 2007 TWO MARKS\n\nQ. 34 Consider the linear circuit with and ideal op-amp shown in the figure below.\n\nThe Z-parameters of the two port feedback network are Z11 = Z22 = 11kW and\nZ12 = Z21 = 1kW . The gain of the amplifier is\n(A) + 110 (B) + 11\n(C) - 1 (D) - 120\n\n## The nature of feedback in the this circuit is\n\n(A) positive current (B) negative current\n(C) positive voltage (D) negative voltage\n\n## The b of the transistor and VCE are respectively\n\n(A) 19 and 2.8 V (B) 19 and 4.7 V\n(C) 38 and 2.8 V (D) 38 and 4.7 V\n\nmywbut.com\nGATE SOLVED PAPER - IN ANALOG ELECTRONICS\n\n## Which one of the following statements about the output is correct ?\n\n(A) V0 # 95 mV (B) 95 m V < V0 # 98 mV\n(C) 98 mV < V0 # 101 mV (D) V0 > 101 mV\n\nQ. 38 The three transistors in the circuit shown below are identical, with\nVBE = 0.7 V and b = 100 .\n\nThe voltage Vc is\n(A) 0.2 V (B) 2 V\n(C) 7.4 V (D) 10 V\n\nQ. 39 The input signal shown in the figure below is fed to a Schmitt trigger. The signal\nhas a square wave amplitude of 6 V p-p. It is corrupted by an additive by an\nadditive high frequency noise of amplitude 8V p-p.\n\nWhich one of the following is an appropriate choice for the upper and lower trip\npoints of the Schmitt trigger to recover a square wave of the same frequency from\nthe corrupted input signal Vi ?\n(A) !8.0 V (B) !2.0 V\n(C) !0.5 V (D) 0 V\n\nmywbut.com\nGATE SOLVED PAPER - IN ANALOG ELECTRONICS\n\n## The correct frequency response of the circuit is\n\nQ. 41 In the circuit shown below the switch (S) is closed whenever the input voltage (\nVin ) is positive and open otherwise.\n\nThe circuit is a\n(A) Low pass filter (B) Level shifter\n(C) Modulator (D) Precision rectifier\n\nmywbut.com\nGATE SOLVED PAPER - IN ANALOG ELECTRONICS\n\n## Q. 42 Consider the triangular wave generator shown below.\n\nAssume that the op-amps are idea and have !12 V power supply. If the input\nis a !5V 50 Hz square wave of duty cycle 50%, the condition that results in a\ntriangular wave of peak to peak amplitude 5 V and frequency 50 Hz at the output\nis\n(A) RC = 1 (B) R = 1\nC\n(C) R = 5 (D) C = 5\nC R\n\n## Common Data For Questions 43, 44 and 45 :\n\nConsider the op-amp circuit shown in the figure below.\n\n## Q. 43 If V1 = 0.2 V, V2 = 0.6 V and V0 =- 7 V , and the op-amp is ideal, the value of\n\nR1 is\n(A) 5 kW (B) 10 kW\n(C) 15 kW (D) 20 kW\n\n## Q. 44 Let V1 = V2 = Vc sin2pft and R1 = 20 kW . The op-amp has a slew rate of 0.5 V/\n\nms with its other parameter being idea. The values of Vc and f for which the\namplifier output will have not distortion are, respectively\n(A) 0.1 V and 300 kHz (B) 0.5 V and 300 kHz\n(C) 0.1 V and 300 kHz (D) 0.5 V and 30 kHz\n\n## Q. 45 Let V1 = V2 = 0 and R1 = 20 kW . Assume that the op-amp is ideal except for a\n\nnon-zero input bias current. What is the value of R2 for the output voltage of the\nop-amp to be zero ?\n(A) 2.2 kW (B) 9.1 kW\n(C) 20 kW (D) 100 kW\n\nmywbut.com\nGATE SOLVED PAPER - IN ANALOG ELECTRONICS\n\n## YEAR 2006 ONE MARK\n\nQ. 46 If the value of the resistance R in the following figure is increased by 50%, then\nvoltage gain of the amplifier shown in the figure will change by.\n\n(A) 50 % (B) 5%\n(C) - 50 % (D) Negligible amount\n\nQ. 47 When the switch S2 is closed the gain of the programmable gain amplifier shown\nin the following figure is\n\n(C) 4 (D) 8\n\n## YEAR 2006 TWO MARKS\n\nQ. 48 In the circuit shown in the following figure, the op-amp has input bias current\nIb < 10 nA , and input offset voltage Vio < 1. The maximum dc error in the output\nvoltage is\n\n## (A) 1.0 mV (B) 2.0 mV\n\n(C) 2.5 mV (D) 3.0 mV\n\nmywbut.com\nGATE SOLVED PAPER - IN ANALOG ELECTRONICS\n\nQ. 49 The potential difference between the input terminals of an op amp may be treated\nto be nearly zero, if\n(A) the two supply voltages are balanced\n(B) The output voltage is not saturated\n(C) the op-amp is used in a circuit having negative feedback\n(D) there is a dc bias path between each of the input terminals and the circuit\nground\n\nQ. 50 A dual op-amp instrumentation amplifier is shown below. The expression for the\noutput of the amplifier is given by.\n\nR1 R1\n\nR1 R2\n\n## Q. 51 An amplifier circuit is shown below. Assume that the transistor works in\n\nactive region. The low frequency small-signal parameters for the transistor are\ngm = 20 mS, b 0 = 50, r 0 = 3, r b = 0 . What is the voltage gain, AV = ` v0 j , of the\nvi\namplifier ?\n\n## (A) 0.967 (B) 0.976\n\n(C) 0.983 (D) 0.998\n\nmywbut.com\nGATE SOLVED PAPER - IN ANALOG ELECTRONICS\n\nQ. 52 The biasing circuit of a silicon transistor is shown below. If b = 80, then what is\nVCE for the transistor ?\n\n## (A) - 6.08 V (B) 0.2 V\n\n(C) 1.2 V (D) 6.08 V\n\n## Q. 53 An astable multi-vibrator circuit using a 555 IC is given in the following figure.\n\nThe frequency of oscillation is.\n\n## (A) 20 kHz (B) 30 kHz\n\n(C) 40 kHz (D) 45 kHz\n\n## Statement For Linked Answer Q. 54 and 55 :\n\nIn the Schmitt trigger circuit shown below, the Zener diodes have VZ (reverse\nsaturation voltage) = 6 V and VD (forward voltage drop) = 0.7 V.\n\nmywbut.com\nGATE SOLVED PAPER - IN ANALOG ELECTRONICS\n\nQ. 54 If the circuit has the input lower trip point (LTP) = 0 V, then value of R1 is\nR2\ngiven as.\n(A) 0.223 (B) 2.67\n(C) 4.67 (D) 3\n\n## Q. 55 The input upper trip point (UTP) of the Schmitt trigger is\n\n(A) 1.5 V (B) 2.1 V\n(C) 2.42 V (D) 6.7 V\n\n## YEAR 2005 ONE MARK\n\nQ. 56 The peak value of the output voltage V0 across the capacitor shown in the figure\nfor a 2230:9 transformer and a 230 V, 50 Hz, input assuming 0.7 V diode drop\nand an ideal transformer, is\n\n## (A) 12.73 (B) 11.33\n\n(C) 7.6 (D) 9.0\n\nQ. 57 In the circuit shown in the given figure the input voltage Vin (t) is given by 2\nsin (100pt). For RL in the range 0.5 kW to 1.5 kW to 1.5 kW, the current through\nRL is.\n\n## (A) + 2 sin (100pt) mA (B) - 2 sin (100pt) mA\n\n(C) + 0.5 sin (100pt) mA (D) 1.5 sin (100pt) mA\n\n## Q. 58 The input-output charcteristic of a Schmidt trigger has a hysteresis band of\n\n! 0.1 V . If the input voltage is 5 sin (100pt), the delay between the corresponding\nzero cross-over points of the output and input signals is\n(A) 6.37 ms (B) 0.02 ms\n(C) 63.7 ms (D) 2.0 ms\n\nmywbut.com\nGATE SOLVED PAPER - IN ANALOG ELECTRONICS\n\nQ. 59 In the circuit shown in the figure the input voltage Vi is a symmetrical saw-tooth\nwave of average value zero, positive slope and peak-to-peak value 20 V. The\naverage value of the output, assuming an ideal operational amplifier with peak-\nto-peak symmetrical swing of 30 V, is\n\n(A) 5 V (B) 10 V\n(C) - 5 V (D) 7.5 V\n\n## Q. 60 In the instrumentation amplifier shown in the figure if the switch SW is changed\n\nform position A to B, the values of the amplifier gain G before and after changing\nthe switch respectively are\n\n## (A) 45, 95 (B) 50, 100\n\n(C) 100, 200 (D) 90, 180\n\n## Q. 61 Figure shows a circuit which has a coil of resistance R and inductance L. At\n\nresonance, the Q-factor of the coil is given by\n\n(A) bV - V0 l (B) V0\nV V\n\n(C) bV - V0 l (D) V\nV0 V0\n\nmywbut.com\nGATE SOLVED PAPER - IN ANALOG ELECTRONICS\n\nQ. 62 For the circuit shown in the figure, IDSQ (in mA) and VGSQ (in V) are related\nthrough 2 IDSQ = (4 + VGSQ) 2 .\nThe following data is given :\nVDD = 15 V, R1 = 1.0 MW, R2 = 6.5 MW, RD = 2.0 kW, RS = 1.0 kW,\nIDSS = 8 mA. The value of IDSQ, assuming the gate current is negligible, is\napproximately equal to.\n\n## (A) 5 mA (B) 2.0 nA\n\n(C) 2.3 mA (D) 3.4 mA\n\nQ. 63 In the circuit shown in the figure, assuming ideal diose characteristics with zero\nforward resistance and 0.7 V forward drop, the average value of V0 when the input\nwaveform is as shown, is\n\n## (A) - 0.7 V (B) - 1.0 V\n\n(C) - 2.0 V (D) - 2.7 V\n\nQ. 64 For the RC circuit shown in the figure, the condition for obtaining an attenuation,\nVout Vin , of 1/3 at a frequency w rad/s is\n\n## (A) 3wCR 1 = 0 (B) 2wCR - 1 = 0\n\n(C) 3wCR - 2 = 0 (D) wCR - 1 = 0\n\nmywbut.com\nGATE SOLVED PAPER - IN ANALOG ELECTRONICS\n\n## Statement For Linked Answer Q. 65 and 66 :\n\nGiven figure shows a transistor circuit with feedback\n\nQ. 65 In the circuit, in order to get V0 in the range of 0-30 V, the range of Vin is\n(A) 0-30 V (B) 0.20 V\n(C) 0-15 V (D) 1.10 V\n\n## Q. 66 If Vin is generated using an n -bit DA converter, the minimum value of n required,\n\nso that the value of V0 can be set with in an accuracy of less than 20 mV is,\n(A) 9 (B) 10\n(C) 11 (D) 12\n\n## Q. 67 Assuming ideal diode characteristics, the input/output voltage relationship for\n\nthe circuit shown in Fig. is\n\n(A) v0 (t) = vi (t), for all vi (t) (B) v0 (t) = vi (t), for vi (t) vR\n= 0, otherwise\n(C) v0 (t) = vi (t), for vi (t), for vi (t) < vR (D) v0 (t) = vi (t), for vi (t) > vR\n= vR, otherwise = vR, otherwise\nQ. 68 The output of the op-amp in the circuit of Fig. is\n\n(A) 0 V (B) - 3 V\n(C) + 1.5 V (D) + 3 V\n\nmywbut.com\nGATE SOLVED PAPER - IN ANALOG ELECTRONICS\n\n## (A) Variac (B) Triac\n\n(C) Quadrac (D) Diac\n\n## Q. 70 The parameters of the JEET in Fig. gm = 1 mA/V , rd = 15 kW Neglecting the\n\neffect of the capacitor of A.C. analysis, the small signal A.C. voltage gain for the\ncircuit is.\n\n(A) - 30 (B) - 10\n(C) + 40 (D) + 60\n\n## Q. 71 The value of V0 in the circuit, shown in Fig. is\n\n(A) - 5 V (B) - 3 V\n(C) + 3 V (D) + 5 V\n\n## Q. 72 The gain ` v0 j of the amplifier circuit shown in Fig. is\n\nvi\n\n(A) 8 (B) 4\n(C) - 4 (D) 3RL\nR\n\nmywbut.com\nGATE SOLVED PAPER - IN ANALOG ELECTRONICS\n\n## Q. 73 The output voltage v0 in the circuit in Fig. is\n\n(A) R2 Vd (B) R2 Vd\nR R1\n(C) R2 V (D) R2 V\nR1 d R (1 + d)\nQ. 74 V1 and V2 are the input voltages of an instrumentation amplifier. The output of the\ninstrumentation amplifier is found to be 100 (V1 - V2) +10 - 4 (V1 + V2). The gain\nand the common mode rejection ratio (CMRR) of the instrumentation amplifier\nrespectively are\n(A) (50, 60 dB) (B) (50 120 dB)\n(C) (100, 60 dB) (D) (100, 120 dB)\n\n## Q. 75 The circuit in Fig. is a\n\n(A) Band-pass filter with lower cut-off wl = 1 and higher cut off w = 1\nH\nR1 C1 R2 C2\n(B) Band-reject filter with lower cut-off w1 = 1 and higher cut off wH = 1\nR1 C1 R2 C2\n(C) Band-pass filter with lower cut-off wl = 1 and higher cut off wH = 1\nR2 C2 R1 C1\n(D) Band-reject filter with lower cut-off wl = 1 and higher cut off\nR2 C2\nwH = 1\nR1 C1\n\nQ. 76 For the circuit shown in Fig. the diode D is ideal. The power dissipated by the\n300 W resistor is\n\n## (A) 0.25 W (B) 0.50 W\n\n(C) 0.75 W (D) 1.00 W\n\nmywbut.com\nGATE SOLVED PAPER - IN ANALOG ELECTRONICS\n\nQ. 77 Fig (a) shows a Schwitt trigger circuit and Fig (b) the corresponding hysteresis\ncharacteristics. The values of VTL and VTH are\n\n## YEAR 2003 ONE MARK\n\nQ. 78 An integrator circuit is shown in Fig. The op-amp is of type 741 and has an input\noffset current ios of 1 mA and R is 1 MW. If the input Vi is a 1 kHz square wave of\n1 V peak to peak, the output V0 , under steady state condition, will be.\n\n## (A) A square wave of 1 V peak to peak\n\n(B) A triangular wave of 1 V peak to peak\n(C) Positive supply voltage + Vcc\n(D) Negative supply voltage - Vcc\n\nQ. 79 The output of an op-amp whose input is a 2.5 MHz square wave is shown in Fig.\nThe slew rate of the op-amp is\n\n## (A) 0.8 V/ms (B) 8.0 V/ms\n\n(C) 20.0 V/ms (D) 40.0 V/ms\n\nmywbut.com\nGATE SOLVED PAPER - IN ANALOG ELECTRONICS\n\nQ. 80 The op-amp and the 1 mA current source in the circuit of Fig. are ideal. The\noutput of the op-amp is\n\n## (A) - 1.5 mA (B) - 1.5 V\n\n(C) - 7.5 V (D) + 1.5 V\n\n## YEAR 2003 TWO MARKS\n\nQ. 81 A forward-biased silicon diode when carry negligible current, has a voltage drop\nof 0.64 V. When the current is 1 A it dissipates 1 W. The ON-resistance of the\ndiode is\n(A) 0.36 W (B) 0.64 W\n(C) 0.72 W (D) 1.0 W\n\n## Q. 82 A transistor amplifier circuit is shown in Fig. The quescent collector current,\n\nrounded off to first decimal, is\n\n## (A) 2.6 mA (B) 2.3 mA\n\n(C) 2.1 mA (D) 2.0 mA\n\nQ. 83 The op-amp used in the inverting amplifier shown in Fig. has an equivalent input\noffset voltage Vios of 5 mV. The output offset voltage is.\n\n## (A) 5 mV (B) 280 mV\n\n(C) 285 mV (D) 560 mV\n\nmywbut.com\nGATE SOLVED PAPER - IN ANALOG ELECTRONICS\n\nQ. 84 In the circuit shown in Fig. the op-amps used are ideal. The output V0 is\n\n## (A) 3.0 V (B) 1.5 V\n\n(C) 1.0 V (D) 0.5 V\n\n## Q. 85 A 50 W power amplifier has a rated output of 30 Vr.m.s and a voltage gain of 40\n\ndB. It is connected to a 40 W loudspeaker having an internal resistance of 10W.\nDetermine the maximum input voltage that can be given to the power amplifier\nso that neither the power amplifier nor the loudspeaker is overloaded.\n(A) 40 V (B) 20 V\n(C) 0.4 V (D) 0.2 V\n\nQ. 86 The circuit shown in Fig. is that of a waveform generator. Assuming ideal devices\nand !12 V supply, the output V0 is a\n\n## (A) Triangular wave of period 120 ms and amplitude !6 V\n\n(B) Square wave of period 60 ms and amplitude !6 V\n(C) Square wave of period 120 ms and amplitude !6 V\n(D) Square wave of period 60 ms and amplitude !12 V\n\nQ. 87 The 5 V Zener diode in figure is ideal and the ammeter (A), of full-scale 1 mA,\nhas an internal resistance of 100W. The circuit shown, with terminal 1 positive,\nfunctions as a\n\n## (A) 0 - 1 VDC voltmeter (B) 0 - 1 mA DC ammeter\n\n(C) 0 - 6 VDC voltmeter (D) 0 - 5 VAC voltmeter\n\nmywbut.com\nGATE SOLVED PAPER - IN ANALOG ELECTRONICS\n\n## YEAR 2002 TWO MARKS\n\nQ. 88 A unity gain buffer amplifier has a bandwidth of 1 MHz . The output voltage of\nthe amplifier for an input of 2 V sinusoid of frequency 1 MHz will be\n(A) 2 V (B) 2 2 V\n(C) 2 V (D) 4 V\n2 2\nQ. 89 An amplifier of gain 10, with a gain-bandwidth product of 1 MHz and slew rate\nof 0.1 V/ms is fed with a 10 kHz symmetrical square wave of ! 1 V amplitude. Its\noutput will be\n(A) ! 10 V amplitude square wave (B) ! 2.5 V amplitude square wave\n(C) ! 10 V amplitude triangular wave (D) ! 2.5 V amplitude triangular wave\n\n## YEAR 2001 ONE MARK\n\nQ. 90 A sample and hold circuit has two buffers, one at the input and the other at the\noutput. The primary requirements for the buffers are\n(A) The input buffer should have high slew rate and the output buffer should\nhave low bias current\n(B) the input buffer should have low bias current and the output buffer should\nhave high slew rate\n(C) both the buffers should have low bias currents\n(D) both the buffers should have high slew rate\n\nQ. 91 A twisted pair of wires is used for connecting the signal source with the\ninstrumentation amplifier, as it helps reducing\n(A) the effect of external interference\n(B) the error due to bias currents in the amplifier\n(C) the loading of the source by the amplifier\n(D) the common mode voltage\n\n## Q. 92 For an input V ^ t h = 5 - 2 sin ^100 pt h - cos ^200 pt h the output of a full-wave\n\nrectifier average is\n(A) 2 (B) 4\n(C) 5 (D) 8\n\n## Q. 93 In figure, input offset voltage of the operational amplifier is 2 mV . The output\n\nDC error voltage is\n\nmywbut.com\nGATE SOLVED PAPER - IN ANALOG ELECTRONICS\n\n(A) 0 mV (B) 2 mV\n(C) 11 mV (D) 22 mV\n\n## YEAR 2000 ONE MARK\n\nQ. 94 An op-amp with a slew rate of 1 mVs has been used to build an amplifier of gain\n+ 10 . If the input to the amplifier is a sinusoidal voltage with peak amplitude of\n1 V , the maximum allowable frequency of the input signal for undistorted output\nis\n(A) 830 Hz (B) 15.92 kHz\n(C) 31.84 kHz (D) 1.0 MHz\n\nQ. 95 For a sinusoidal input of 50 V amplitude, the circuit shown in figure can be used\nas\n\n## (A) regulated DC power supply (B) square-wave generator\n\n(C) half-wave rectifier (D) full-wave rectifier\n\nQ. 96 In the DC millivoltmeter circuit shown in figure, the input voltage for full scale\ndeflection is\n\n(A) 10 V (B) 1 V\n(C) 100 mV (D) 10 mV\n\n## Q. 97 If both the junctions of a transistor are forward biased, it will be in\n\n(A) saturation mode (B) active mode\n(C) cut-ff mod (D) inversion mode\n\n**********\n\nmywbut.com\nGATE SOLVED PAPER - IN ANALOG ELECTRONICS\n\nANALOG ELECTRONICS\n1 2 3 4 5 6 7 8 9 10\n(D) (D) (B) (A) (C) (C) (C) (A) (B) (A)\n11 12 13 14 15 16 17 18 19 20\n(A) (B) (D) (C) (B) (A) (B) (A) (B) (D)\n21 22 23 24 25 26 27 28 29 30\n(C) (A) (C) (C) (B) (A) (B) (D) (D) (B)\n31 32 33 34 35 36 37 38 39 40\n(C) (B) (A) (D) (D) (A) (B) (C) (B) (C)\n41 42 43 44 45 46 47 48 49 50\n(D) (B) (B) (C) (B) (D) (B) (D) (C) (A)\n51 52 53 54 55 56 57 58 59 60\n(A) (B) (C) (C) (C) (B) (A) (A) (D) (C)\n61 62 63 64 65 66 67 68 69 70\n(B) (D) (B) (D) (D) (C) (D) (A) (B) (B)\n71 72 73 74 75 76 77 78 79 80\n(A) (A) (B) (D) (A) (C) (D) (D) (D) (B)\n81 82 83 84 85 86 87 88 89 90\n(A) (B) (C) (B) (D) (C) (C) (C) (D) (A)\n91 92 93 94 95 96 97\n(A) (C) (B) (B) (B) (D) (A)\n\nmywbut.com" ]
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https://www.sigmaaldrich.com/FR/en/technical-documents/technical-article/environmental-testing-and-industrial-hygiene/air-testing/function
[ "How Does the Diffusive Sampler Work? Why is it so Special?\n\nHow Does the Diffusive Sampler Work?\n\nThe diffusive sampler is a closed box, usually cylindrical. Of its two opposite sides, one is “transparent” to gaseous molecules which cross it, and are adsorbed onto the second side. The former side is named diffusive surface, the latter is the adsorbing surface (marked with S and A in the figure).", null, "In the diffusive sampler, the adsorbing and the diffusive surfaces are two opposing plane of a closed box. Driven by the concentration gradient, the gaseus molecules (coloured in the figure) pass through the diffusive surface and are trapped from the adsorbing surface.\n\nDriven by the concentration gradient dC/dl, the gaseous molecules cross S and diffuse towards A along the path l, parallel to the axis of the cylindrical box. The molecules, which can be trapped by the adsorbing material, are eventually adsorbed onto A according to the equation:", null, "where dm is the adsorbed mass during time dt and D is the diffusion coefficient. Let C be the concentration at the diffusive surface and C0 the concentration at the adsorbing surface, the integral of becomes", null, "If the concentration at the adsorbing surface is negligible, the equation can be approximated to", null, "Q is the sampling rate and has the dimensions of a gaseous flow (if m is expressed in μg, t in minutes and C in μg·l-1, Q is expressed in l·min-1).\n\nTherefore, if Q is constant and measured, to calculate the ambient air concentration you need only to quantify the mass of analyte trapped by the adsorbing material and to keep note of the time of exposure of the diffusive sampler.\n\nTo improve the analytical sensitivity the collected mass m should be increased by enlarging Q. As D is a constant term, one can only try to improve the S/l ratio, namely the geometrical constant of the sampler. Unfortunately, in the common axial simmetry sampler, if S is enlarged, the adsorbing surface A must be enlarged too, in order to keep the two parallel surfaces at a fixed distance. Since the analytes can be recovered from the axial sampler only by solvent extraction, any increase of A lead to a proportional increase of the extraction solvent volume, thus the improvement of Q is canceled out by the effect of dilution.\n\nThe value of distance l could also be reduced, but under the critical value of about 8 mm the diffusion law is no longer valid in the case of low air velocity values, since adsorption rate becomes higher than supplying rate of analyte molecules at the diffusive surface.\n\nCannot we improve Q then?\nThe answer is to improve the sampler geometry to a radial design. From this idea the radiello sampler has been developed, its cylindrical outer surface acting as diffusive membrane: the gaseus molecules move axially parallel towards an adsorbent bed which is cylindrical too and coaxial to the diffusive surface.\n\nWhen compared to the axial sampler, radiello shows a much higher diffusive surface without increase of the adsorbing material amount. Even if the adsorbing surface is quite smaller then the diffusive one, each point of the diffusive layer faces the diffusion barrier at the same distance.", null, "Diffusive and adsorbing surfaces are cylindrical and coaxial: a large diffusive surface\nfaces, at a fixed distance, the small surface of a little concentric cartridge.\n\nAs S=2πrh (where h is the height of the cylinder) and the diffusive path is as long as the radius r, we can then express equation as follows", null, "The integral of equation from rd (radius of the diffusive cylindrical surface) to ra (radius of the adsorbing surface) becomes", null, "the ratio", null, "is the geometrical constant of radiello. The calculated uptake rate is therefore proportional to the height of the diffusive cylinder and inversely proportional to the logarithm of the ratio of diffusive vs adsorbing cylinder radii.\n\nWhile ra can be easily measured, rd can only be calculated by exposure experiments. Actually the diffusive membrane has been designed with a thick tubular microporous layer. The actual diffusive path length is therefore\nmuch longer than the distance among the diffusive and adsorbing surfaces due to the tortuosity of the path through the pores. A diffusive cylinder of external diameter 8 mm, thickness 1.7 mm and average porosity of\n25 μm, coupled to an adsorbing cartridge with radius 2.9 mm creates a diffusive path of 18 mm instead of the straight line path estimation of (8-2.9) = 5.1 mm.\n\nThe sampling rate Q is function of diffusive coefficient D, which is a thermodynamic property of each chemical substance. D varies with temperature (T) and pressure (p); therefore also the sampling rate is a function of those variables according to", null, "Q values that will be quoted in the following have been measured at 25 °C and 1013 hPa. As a consequence, they should be corrected so as to reflect the actual sampling conditions.\n\nThe correction of Q for atmospheric pressure is usually negligible since its dependence is linear and very seldom we face variations of more than 30 hPa about the average value of 1013 hPa. In the worst case, if corrections for pressure are ignored you make an error of ±3%, usually it is within ±1.5%.\n\nOn the other hand, Q depends exponentially on temperature variations, therefore more relevant errors can be introduced if average temperature is significantly different from 25 °C. Moreover, when chemiadsorbing cartridge are used kinetic effects (variations of reaction velocities between analyte and chemiadsorbing substrate) can be evident, apart from thermodynamic ones (variation of D).\n\nIt is therefore very important to know the average temperature in order to ensure accuracy of experimental\ndata. how you can perform on-field temperature measurements on page B3.\n\nEven if some cartridges adsorb large quantities of water when exposed for a long time in wet atmosphere, generally this does not affect sampling by radiello. Some consequences, neverthless, can sometimes be felt on the analysis. As an example, a very wet graphitised charcoal cartridge could generate ice plugs during cryogenic focusing of thermally desorbed compounds or blow out a FID flame.\n\nIt is therefore important to protect radiello from bad weather. page B1 how this can be easily done.\n\nThe diffusive sampling does not involve the use of heavy and encumbering pumping systems, does not have energy\npower supply problems, does not require supervision, is noiseless, is not flammable and does not represent an explosion hazard, can be performed by everybody everywhere and with very low costs.\n\nMoreover, it is not subject to the breakthrough problem, which can be serious when active pumping is performed.", null, "In pumped sampling the adsorbed compound behaves as a chromatographic peak (top): air flow displaces it along the adsorbent bed and its concentration is distributed as a gaussian function. Eventually, the compound comes out from the opposite end. When its concentration in the outlet air is 10% of the concentration in the sampled air we say that the breakthrough has been reached or, with a misleading expression, that the tube has been saturated. Any further pumping leads to a loss of analyte and a consequent underestimation of the environmental concentration. The extent of this phenomenon depends weakly on the concentration of target compound but rather on the value of air flow, the overall sampling volume and the chemical compound involved.", null, "In the graph the case of benzene is displayed, sampled at 25 °C onto an activated charcoal adsorbent bed of the same volume of a code 130 (Product No. RAD130) radiello cartridge. The breakthrough is reached after 35, 44 or 49 liters of sampled air depending on benzene concentration in air (10, 50 or 100 μg·m-3 respectively).\n\nAn apparently similar phenomenon is shown by radiello also. In this case, however, we cannot speak of breakthrough, since no actual air flow is involved, but rather of backdiffusion. This consists of a decrease of the value of m·Q-1·t-1 (which is equal to the measured concentration (equation above). This term is constant and equal to the actual concentration until the adsorbed mass of analyte is far from the maximum amount allowed by the adsorbing medium\ncapacity. The extent of backdiffusion depends on concentration and exposure time but a decrease of 10% in them·Q-1·t-1 term is observed along with equivalent sampling volumes of magnitude bigger than those seen before: 1600, 2300 and 3050\nliters at the concentration of 10, 50 and 100 μg·m-3.", null, "For a traditional axial symmetry sampler the uptake rate increases linearly with tha ratio of diffusive surface vs diffusive path length, while for the radial symmetry sampler, the corresponding increase is exponential. This means that, let the diffusive surface vs diffusive path length ratio be 8:1, for the axial sampler the uptake rate value is 8 (regardless of dimensions) while for the radial one it is 45.\n\nWhy diffusive sampling has not been so extensively adopted up to now? This is due to the fact that the traditional axial symmetry sampler has generally poor sensitivity and reproducibility because of the limits set by its geometry. On one side, uptake rate values are generally low, on the other, they often vary depending on environmental conditions.\n\nThese limitations have been overcome by radiello.\n\nBy virtue of radial symmetry, uptake rate is:\n\n• High, since it does not vary linearly but exponentially with the ratio diffusive surface vs diffusive path length (quation ). With the same dimensions, radiello’s uptake rate is at least three times higher than that of any axial diffusive sampler.\n• Constant, due to the great adsorbing capacity of the adsorbing cartridge;\n• Reproducible, by virtue of the stiffness of the diffusive membrane and the cartridge and of the close tolerances characterizing all the components of radiello.\n• Invariable with air speed, due to the tortuosity of the diffusive path inside the microporous diffusive cylindrical surface.\n• Precisely measured, because it is not calculated but experimentally measured in a controlled atmosphere chamber in a wide range of concentration, temperature, relative humidity, air speed conditions and with or without interferents...." ]
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https://www.shaalaa.com/question-bank-solutions/the-diagonal-quadrilateral-shaped-field-24-m-perpendiculars-dropped-it-remaining-opposite-vertices-are-8-m-13-m-find-area-field-area-general-quadrilateral_15453
[ "Share\n\n# The Diagonal of a Quadrilateral Shaped Field is 24 M and the Perpendiculars Dropped on It from the Remaining Opposite Vertices Are 8 M and 13 M. Find the Area of the Field. - CBSE Class 8 - Mathematics\n\n#### Question\n\nThe diagonal of a quadrilateral shaped field is 24 m and the perpendiculars dropped on it from the remaining opposite vertices are 8 m and 13 m. Find the area of the field.", null, "#### Solution\n\nIt is given that,\n\nLength of the diagonal, = 24 m\n\nLength of the perpendiculars, h1 and h2, from the opposite vertices to the diagonal are h1 = 8 m and h2 = 13 m\n\nArea of the quadrilateral = 1/2 d(h_1 + h_2)\n\n= 1/2 (24m) x (13m + 8cm)\n\n= 1/2 (24 m)(21 m)\n\n= 252 m^2\n\nThus, the area of the field is 252 m2.\n\nIs there an error in this question or solution?\n\n#### APPEARS IN\n\nNCERT Solution for Mathematics Textbook for Class 8 (2018 to Current)\nChapter 11: Mensuration\nEx. 11.20 | Q: 4 | Page no. 178\nSolution The Diagonal of a Quadrilateral Shaped Field is 24 M and the Perpendiculars Dropped on It from the Remaining Opposite Vertices Are 8 M and 13 M. Find the Area of the Field. Concept: Area of a General Quadrilateral.\nS" ]
[ null, "https://www.shaalaa.com/images/_4:7c4758b7d2354691b3f4874e6e655399.png", null ]
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https://quant.stackexchange.com/questions/16094/gamma-is-always-positive-on-both-put-and-call
[ "# Gamma is always positive on both put and call\n\nI recently met the claim that for standard put and calls the gamma of the options are always positive. Is this a general result?\n\nI am hoping not to assume any model, especially not Black-Scholes.\n\n• I think that gamma is a model dependent concept. I once went to a talk by Musiela in which he discussed sufficient condition to make sure that it was positive. So I think the answer to your question is no. It is true for BS however. Jan 5 '15 at 20:25\n• @MarkJoshi Darn, thanks though :) I tried googling, but could not find his results. If you stumble on them I would love to know.\n– htd\nJan 6 '15 at 7:38\n• You can look at ElKaroui & al \"Robustness of the Black Scholes formula\". They give show that calls have positive Gamma in the local volatility model but that it can fail to be true in stoch vol.\n– AFK\nJan 8 '15 at 0:54\n\nI'll use a European call option as an example, I think you can easily generalize it for a put option.\n\nGiven underlying $S(t) = S_t$, maturity $T$, strike $K$ and risk-free rate $r$, the price of a call option as time $t$ under the rik-neutral measure $Q$ is\n\n\\begin{align} C(t, S_t) & = \\mathbb{E}^Q \\left[ e^{-r(T-t)} \\max (S_T - K, 0) \\right] \\\\ & = \\mathbb{E}^Q \\left[ e^{-r(T-t)} (S_T - K) \\cdot \\mathbb{1}_{S_T \\geq K} \\right] \\\\ & = \\mathbb{E}^Q \\left[ e^{-r(T-t)} S_T \\cdot \\mathbb{1}_{S_T \\geq K} \\right] - \\mathbb{E}^Q \\left[ K e^{-r(T-t)} \\cdot \\mathbb{1}_{S_T \\geq K} \\right] \\\\ & = e^{-r(T-t)} \\mathbb{E}^Q \\left[ S_T \\cdot \\mathbb{1}_{S_T \\geq K} \\right] - K e^{-r(T-t)} \\mathbb{E}^Q \\left[ \\mathbb{1}_{S_T \\geq K} \\right] \\\\ \\end{align}\n\nwhere $\\mathbb{1}_{S_T \\geq K}$ is a function values $1$ when $S_T \\geq K$ and $0$ otherwise. For the first expectation, we can change the probability measure to make it more manageable. Call $P$ the new measure; the Radon-Nikodym derivative between the $P$ and $Q$ is\n\n$$dQ = \\frac{S_t}{S_T} e^{r(T-t)} dP$$\n\nTherefore you get\n\n\\begin{align} C(t, S_t) & = e^{-r(T-t)} \\mathbb{E}^Q \\left[ S_T \\cdot \\mathbb{1}_{S_T \\geq K} \\right] - K e^{-r(T-t)} \\mathbb{E}^Q \\left[ \\mathbb{1}_{S_T \\geq K} \\right] \\\\ & = e^{-r(T-t)} \\mathbb{E}^P \\left[ S_T \\cdot \\mathbb{1}_{S_T \\geq K} \\cdot \\frac{S_t}{S_T} e^{r(T-t)} \\right] - K e^{-r(T-t)} \\mathbb{E}^Q \\left[ \\mathbb{1}_{S_T \\geq K} \\right] \\\\ & = e^{-r(T-t)} \\mathbb{E}^P \\left[ \\mathbb{1}_{S_T \\geq K} S_t e^{r(T-t)} \\right] - K e^{-r(T-t)} \\mathbb{E}^Q \\left[ \\mathbb{1}_{S_T \\geq K} \\right] \\\\ & = S_t \\mathbb{E}^P \\left[ \\mathbb{1}_{S_T \\geq K} \\right] - K e^{-r(T-t)} \\mathbb{E}^Q \\left[ \\mathbb{1}_{S_T \\geq K} \\right] \\\\ \\end{align}\n\nExpanding the expectations as integrals you get:\n\n\\begin{align} C(t, S_t) & = S_t \\int_K^{\\infty} f^P(S_T) dS_T - K e^{-r(T-t)} \\int_K^{\\infty} f^Q(S_T) dS_T \\\\ & = S_t P_1 - K e^{-r(T-t)} P_2 \\end{align}\n\nwhere $P_1, P_2$ highlight that the integrals are probabilities.\n\nNow the Greeks:\n\n\\begin{align} \\Delta & = \\frac{\\partial C}{\\partial S_t} = \\int_K^{\\infty} f^P(S_T) dS_T = P_1 \\\\ \\Gamma & = \\frac{\\partial^2 C}{\\partial S_t} = \\frac{\\partial \\Delta}{\\partial S_t} = f^P(S_t) \\frac{\\partial f^P(S_t)}{\\partial S_t} \\\\ \\end{align}\n\nThe derivative in $\\Gamma$ is the key. I don't think you can prove $\\Gamma$ to be positive for any probability density (i.e. any model).\n\n• How to assert the existence of measure $P$? Sep 21 '19 at 13:08" ]
[ null ]
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https://pages.mtu.edu/~msgocken/ma5630spring2003/lectures/global1/global1/node2.html
[ "", null, "", null, "", null, "Next: The steepest-descent method Up: Globalizing Newton's method: Descent Previous: Introduction\n\n# Descent Directions\n\nThe reader will recall that", null, "is a descent direction for f at x(k) if", null, "This condition implies that", null, "Indeed, if", null, "represents the one-dimensional slice'' of f in the direction of p,", null, "then the descent condition implies that", null, "and hence that", null, "for all", null, "sufficiently small (see Figure 1).", null, "Given x(k) and a descent direction p, it is possible to reduce f by moving in the direction of p, that is, by choosing an appropriate", null, "and defining", null, ". A procedure for choosing", null, "is referred to as a line search (since x(k+1) is found on the (half-)line parametrized as", null, "). I will discuss line searches (a solution to the third difficulty described above in the Introduction) later. For now, I want to concentrate on methods for producing descent directions.\n\nNewton's method produces the direction", null, "This is a descent direction if", null, "that is, if", null, "that is, if", null, "(1)\n\nCondition (1) will hold if", null, "is positive definite. The reader may recall that the eigenvalues of H-1 are simply the reciprocals of the eigenvalues of H,1 and therefore", null, "is positive definite if and only if", null, "is positive definite. Of course, if", null, "is positive definite, then it is nonsingular, and in this case the first two difficulties mentioned in the Introduction disappear. If", null, "is positive definite, then the Newton step is well-defined and represents a descent direction.\n\nThe following observation is essential: If H is any symmetric positive definite matrix, then", null, "is a descent direction for f at x(k). This suggests the following modification of Newton's method:", null, "(2)\n\nwhere Hk is a positive definite approximation of", null, "and", null, "is a step-length parameter that is chosen by a line search. An iteration of the form (2) is referred to as a quasi-Newton iteration. In order for the rapid local convergence of Newton's method to be preserved, Hk should be a good approximation to (or equal to)", null, "when x(k) is close to x*.\n\nI will now describe two specific quasi-Newton methods.", null, "", null, "", null, "Next: The steepest-descent method Up: Globalizing Newton's method: Descent Previous: Introduction\nMark S. Gockenbach\n2003-01-30" ]
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https://www.lmfdb.org/EllipticCurve/Q/116281/c/
[ "# Properties\n\n Label 116281.c Number of curves $2$ Conductor $116281$ CM no Rank $1$ Graph", null, "# Related objects\n\nShow commands for: SageMath\nsage: E = EllipticCurve(\"c1\")\n\nsage: E.isogeny_class()\n\n## Elliptic curves in class 116281.c\n\nsage: E.isogeny_class().curves\n\nLMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality\n116281.c1 116281b2 [1, 0, 1, -3490853, -2510792715] [] 2019600\n116281.c2 116281b1 [1, 0, 1, -2423, 179199] [] 183600 $$\\Gamma_0(N)$$-optimal\n\n## Rank\n\nsage: E.rank()\n\nThe elliptic curves in class 116281.c have rank $$1$$.\n\n## Complex multiplication\n\nThe elliptic curves in class 116281.c do not have complex multiplication.\n\n## Modular form 116281.2.a.c\n\nsage: E.q_eigenform(10)\n\n$$q + q^{2} - 2q^{3} - q^{4} + q^{5} - 2q^{6} - 2q^{7} - 3q^{8} + q^{9} + q^{10} + 2q^{12} - q^{13} - 2q^{14} - 2q^{15} - q^{16} + 5q^{17} + q^{18} + 6q^{19} + O(q^{20})$$\n\n## Isogeny matrix\n\nsage: E.isogeny_class().matrix()\n\nThe $$i,j$$ entry is the smallest degree of a cyclic isogeny between the $$i$$-th and $$j$$-th curve in the isogeny class, in the LMFDB numbering.\n\n$$\\left(\\begin{array}{rr} 1 & 11 \\\\ 11 & 1 \\end{array}\\right)$$\n\n## Isogeny graph\n\nsage: E.isogeny_graph().plot(edge_labels=True)\n\nThe vertices are labelled with LMFDB labels.", null, "" ]
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https://www.corelearningonline.com/documents/lessonLists/cm5.htm
[ "", null, "## UNIT 1: FRACTION CONCEPTS\n\nLesson 1.1 - Fractions and Mixed Numbers\n\n• The concept of a fraction\n• Numerator and denominator\n• Fractions in measurement\n• Fraction of a set\n• Fractions larger than one\n• Mixed numbers\n\nLesson 1.2 - Equivalent Fractions and Lowest Terms\n\n• Equivalent fractions\n• Using common multiples to create equivalent fractions\n• Reducing fractions to lowest terms\n• Using common factors to reduce fractions\n\nLesson 1.3 - Least Common Denominator\n\n• Common denominator\n• Making common denominators\n• Least common denominator\n• Using least common multiple to find equivalent fractions with common denominators\n\nLesson 1.4 - Comparison Symbols\n\n• Less than symbol\n• Greater than symbol\n\nLesson 1.5 - Comparing Fractions\n\n• Comparing fractions with the same denominators\n• Comparing fractions with different denominators by making equivalent fractions\nwith common denominators\n\nLesson 1.6 - Mixed Numbers and Improper Fractions\n\n• Mixed numbers and improper fractions\n• Converting a mixed number to an improper fraction\n• Converting an improper fraction to a mixed number\n\n## UNIT 2: ADDITION AND SUBTRACTION OF FRACTIONS\n\nLesson 2.1 - Adding and Subtracting Like Fractions\n\n• Like fractions with common denominators\n• Subtracting like fractions\n• Reducing to lowest terms in fractions calculations\n\nLesson 2.2 - Adding and Subtracting Unlike Fractions\n\n• Adding unlike fractions by creating equivalent fractions with common denominators\n• Subtracting unlike fractions by creating equivalent fractions with common\ndenominators\n• Using least common denominator in fractions calculations\n• Reducing to lowest terms in fractions calculations\n\nLesson 2.3 - Adding Mixed Numbers\n\n• Regrouping mixed numbers for addition\n• Converting mixed numbers to improper fractions for addition\n• Recording sum of mixed numbers as a mixed number\n\nLesson 2.4 - Subtracting Mixed Numbers\n\n• Regrouping mixed numbers for subtraction\n• Converting mixed numbers to improper fractions for subtraction\n• Recording the remainder of subtraction mixed numbers as a mixed number\n\nLesson 2.5 - Adding and Subtracting Fractions – Word Problems\n\n• Using addition where word problems combine or increase quantities\n• Using subtraction where word problems reduce or remove quantities\n\n## UNIT 3: MULTIPLICATION WITH FRACTIONS\n\nLesson 3.1 - Multiplying Whole Numbers by Fractions\n\n• Converting whole numbers to fractions to multiply by another fraction\n• Multiplying numerators and denominators of fraction numbers\n\nLesson 3.2 - Multiplying Fractions by Fractions\n\n• Multiplying numerators and denominators of fraction numbers\n• Reducing the product of multiplied fractions to lowest terms\n\nLesson 3.3 - Multiplying Mixed Numbers by Fractions\n\n• Converting mixed numbers to improper fractions for multiplication\n• Recording the product of multiplied mixed numbers as a mixed number\n\nLesson 3.4 - Multiplying by Fractions – Word Problems\n\n• Using multiplication where word problems combine or increase quantities many times\n\n## UNIT 4: DIVISION WITH FRACTIONS\n\nLesson 4.1 - Dividing Whole Numbers by Fractions\n\n• Divide by a fraction by multiplying the reciprocal of the fraction divisor – flip and multiply\n• Reducing the quotient in fraction form to lowest terms\n\nLesson 4.2 - Dividing Fractions by Fractions\n\n• Divide a fraction by another fraction by multiplying the reciprocal of the fraction divisor\n• Reducing the quotient in fraction form to lowest terms\n\nLesson 4.3 - Dividing Mixed Numbers\n\n• Converting mixed numbers to improper fractions for arithmetic operations\n• Divide an improper fraction by multiplying the reciprocal of the fraction divisor\n• Reducing the quotient in fraction form to lowest terms\n\nLesson 4.4 - Dividing with Fractions\n\n• Using division to separate something many times\n\n## UNIT 5: WORKING WITH FRACTIONS\n\nLesson 5.1 - Performing Fraction Arithmetic Operations\n\n• Rules for mixed operations\n• Adding and subtracting operations are done from left to right\n• Multiplying and dividing operations are done from left to right\n• If mixing operations, do multiplication and division before addition and subtraction\n• If brackets are used, do the operations in brackets first\n\nLesson 5.2 - Solving Fraction Word Problems\n\n• Standard steps for solving word problems: plan, model, calculate, check, answer\n\n## UNIT 6: DECIMAL BASICS\n\nLesson 6.1 - Decimal Numbers\n\n• Whole numbers and fractions\n• Mixed numbers\n• Decimal numbers\n• Decimal places\n• How to say decimals\n• Money and decimals\n\nLesson 6.2 - Changing Decimals to Fractions\n\n• Parts of a fraction\n• Changing decimals to fractions\n• Reducing fractions to lowest terms\n\nLesson 6.3 - Comparison Symbols\n\n• Greater than symbol\n• Less than symbol\n• Comparing whole numbers\n\nLesson 6.4 - Comparing Decimals\n\n• Showing decimal values in grids and pictures\n• Comparing decimal values in pictures\n• Comparing decimal numbers from left to right\n• Adding zeros to decimals to compare numbers of equal length\n\nLesson 6.5 - Rounding Decimals\n\n• Rounding to nearest whole number\n• Rounding to the nearest decimals for a selected decimal place value\n\nLesson 6.6 - Changing Fractions to Decimals\n\n• Changing fractions to decimals with denominators in base ten\n• Changing fractions to decimals by dividing the numerator by the denominator\n• Common fractions and equivalent decimal numbers\n\n## UNIT 7: ADDITION AND SUBTRACTION OF DECIMALS\n\n• Place value alignment in adding decimal numbers\n• Make decimal numbers the same length by adding zeros\n• Including decimal point after a whole number when adding to decimal numbers\n\nLesson 7.2 - Subtracting Decimals\n\n• Place value alignment in subtracting decimal numbers\n• Make decimal numbers the same length by adding zeros\n\nLesson 7.3 - Adding and Subtracting Decimals - Word Problems\n\n• Using addition in word problems to combine or increase quantities\n• Using subtraction in word problems to take away or find the difference in quantities\n• Using full statements and measurement units in answer to word problems\n\n## UNIT 8: MULTIPLICATION WITH DECIMALS\n\nLesson 8.1 - Multiplying Decimals by Tens\n\n• Moving decimal point to the right when multiplying decimals by base ten numbers\n\nLesson 8.2 - Multiplying Decimals by Tenths\n\n• Moving decimal point to the left when multiplying decimals by base ten decimal numbers\n• Adding a zero left of a decimal point if there is no whole number part\n\nLesson 8.3 - Multiplying Decimals\n\n• Counting decimal places in the numbers multiplied to use in the product\n• Multiplying dollars and rounding to two decimal places\n\nLesson 8.4 - Multiplying Decimals - Word Problems\n\n• Calculating area using decimals\n• Working with unit prices\n\n## UNIT 9: DIVISION WITH DECIMALS\n\nLesson 9.1 - Dividing by Tens or Tenths\n\n• Moving decimal point to the left when dividing by base ten\n• Moving decimal point to the left when dividing by decimal number in base ten\n\nLesson 9.2 - Dividing Decimals by Whole Numbers\n\n• Long division of decimal numbers by decimal numbers\n• Converting a decimal divisor to a whole number and changing the decimal place in the dividend and quotient\n• Adding zeros to dividend if needed to complete division\n• Repeating decimals\n\nLesson 9.3 - Dividing Decimals by Decimals\n\n• Regrouping mixed numbers for addition\n• Converting mixed numbers to improper fractions for addition\n• Recording sum of mixed numbers as a mixed number\n\nLesson 9.4 - Dividing Decimals - Word Problems\n\n• Using division in word problems to find a number of equal parts\n\n## UNIT 10: MIXED OPERATIONS\n\nLesson 10.1 - Doing Mixed Operations with Decimals\n\n• Do calculations left to right if only addition and subtraction\n• Do calculations left to right if only multiplication and division\n• Do multiplication and division before addition or subtraction\n• Do operations in brackets first\n\nLesson 10.2 - Doing Mixed Operations with Decimals - Word Problems\n\n• Using standard problem solving steps: plan, model, calculate, check, answer\n• Solving word problems with unit prices or costs\n• Solving word problems with time and distance\n\n## UNIT 11: RATIOS, PROPORTIONS, AND CONVERSION OF UNITS\n\nLesson 11.1 - Ratios\n\n• Using ratios to compare things\n• First term and second term in ratios\n\nLesson 11.2 - Calculating Proportions\n\n• Using proportions to compare things\n• Finding equivalent ratios by multiplying or dividing both terms by the same number\n• Finding equivalent ratios when the first or second terms are not 1\n\nLesson 11.3 - Converting Measurements\n\n• Units of measurement and measurement systems\n• Using conversion ratios to change measurements\n\nLesson 11.4 - Converting Money\n\n• Exchange rates and currency conversion ratios\n• Making currency conversions\n\n## UNIT 12: LINES AND ANGLES\n\nLesson 12.1 - Lines\n\n• Points and lines\n• Rays and line segments\n• Shapes made from points, lines, surfaces, and solids\n\nLesson 12.2 - Measuring Angles\n\n• Angles\n• How to measure angles\n• Angle rotation and degrees\n• Angle quarter turn; angle half turn; angle full turn\n• Angle vertex\n• Angle symbols\n• Size of angles\n\nLesson 12.3 - Types of Angles\n\n• Types of angles\n• Straight and right angles\n• Acute and obtuse angles\n• Reflex angles\n• Supplementary angles\n• Complementary angles\n\n## UNIT 13: PLANE SHAPES\n\nLesson 13.1 - Triangles\n\n• The properties of triangles\n• Vertices and interior angles in triangles\n• Acute triangles\n• Right triangles\n• Obtuse triangles\n• Use of a compass to draw arcs\n\n• Plane shapes\n• Squares, rhombi, parallelograms, and trapezoids\n\nLesson 13.3 - Polygons\n\n• Names of common polygons\n• Properties of polygons\n• Polygons, pentagons, hexagons, heptagons, octagons, nonagons, and decagons\n\nLesson 13.4 - Regular Polygons\n\n• Properties of regular polygons\n\nLesson 13.5 - Circles\n\n• The parts of a circle\n• Using a compass to draw a circle or draw arcs\n\nLesson 13.6 - Ellipses\n\n• Parts of an ellipse\n• Elliptical shapes\n• Lines of symmetry in ellipses\n\n## UNIT 14: SOLID SHAPES\n\nLesson 14.1 - Cubes, Prisms, Pyramids\n\n• Polyhedra\n• The properties of cube shapes\n• The properties of prism shapes\n• The properties of pyramid shapes\n\nLesson 14.2 - Cylinders, Cones, Spheres\n\n• The properties of cylinder shapes\n• The properties of cone shapes\n• The construction of sphere shapes\n\n## APPENDICES\n\n• Appendix A - Finding Lowest Terms\n• Appendix B - Multiplication Table\n• Appendix C - Customary Units\n• Appendix D - Metric Units" ]
[ null, "https://www.corelearningonline.com/kp_courseInfo/cm5/cm5_title.jpg", null ]
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https://ask.sagemath.org/question/9303/double-cosets-in-sage/?answer=14027
[ "# double cosets in Sage\n\nSuppose G is a group and H and I are two subgroup of it how can I compute the double cosets I\\G/H?\n\nedit retag close merge delete\n\nSort by » oldest newest most voted\n\nThe DoubleCoset function in GAP has not been wrapped yet, so this is currently \"not implemented\". But, you can always ask GAP to compute (double) cosets from within Sage:\n\nsage: gap.eval('g:=Group((1,2,3,4),(1,2));;')\nsage: gap.eval('u:=Subgroup(g,[(1,2,3),(1,2)]);;')\nsage: gap.eval('v:=Subgroup(g,[(3,4)]);;')\nsage: gap.eval('c:=DoubleCoset(u,(2,4),v);')\n'DoubleCoset(Group( [ (1,2,3), (1,2) ] ),(2,4),Group( [ (3,4) ] ))'\nsage: gap.eval('List(c);')\n'[ (2,3,4), (1,4,2), (1,3)(2,4), (2,4), (1,4,2,3), (1,3,4,2) ]'\n\nmore\n\nI think this could be easily wrapped, the return type is a list of tuples. It's just that no one has done it yet." ]
[ null ]
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http://talks.bham.ac.uk/talk/index/3181
[ "# The Kato Square Root Problem for Divergence Form Operators with Potential\n\n•", null, "Julian Bailey, Australian National University\n•", null, "Tuesday 17 April 2018, 14:00-15:00\n•", null, "Watson LTC.\n\nThe Kato square root problem for divergence form elliptic operators is the equivalence statement $\\left\\Vert \\sqrt { \\mathrm{div} \\left( A \\nabla \\right)}u \\right\\Vert \\simeq \\left\\Vert \\nabla u \\right\\Vert$, where $A$ is a complex matrix-valued function. In 2006, a few years after the first proof of this statement, A. Axelsson, S. Keith and A. McIntosh developed a general framework for proving square function estimates associated with Dirac-type operators and they showed that the Kato problem followed as an immediate application. In this talk I will give an overview of the Kato square root problem and run through a sketch of the proof of Axelsson, Keith and McIntosh. I will then discuss a generalisation of the Kato problem to include positive potentials $V$, namely $\\left\\Vert \\sqrt{-\\mathrm{div} \\left( A \\nabla \\right) + V}u \\right\\Vert \\simeq \\left\\Vert \\nabla u \\right\\Vert + \\left\\Vert V^{\\frac{1}{2}} u \\right\\Vert$. I will discuss how the Axelsson-Keith-McIntosh framework can be altered to allow for dependence of the Dirac-type operator on the potential. The Kato estimate for certain potentials will then follow as a result.\n\nThis talk is part of the Analysis seminar series." ]
[ null, "http://talks.bham.ac.uk/images/user.jpg", null, "http://talks.bham.ac.uk/images/clock.jpg", null, "http://talks.bham.ac.uk/images/house.jpg", null ]
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https://ncatlab.org/toddtrimble/published/Buildings+for+category+theorists
[ "Todd Trimble Buildings for category theorists\n\nThe notion of building, due to Jacques Tits, was invented to give a framework that unites two distinct developments: on the one hand, the structure and geometry of classical Lie groups via their Borel subgroups and maximal tori, and on the other, general forms of synthetic or axiomatic incidence geometry. It ranks as one of the most important concepts in 20th century geometry and group theory.\n\nThere are several ways of introducing this concept, none particularly easy. Perhaps the best way to learn about buildings is to play with examples first before embarking on the full-fledged definition which, however one cuts it, involves a certain amount of preface involving the details of Coxeter groups (roughly, symmetry groups generated by reflections). There are a number of good introductory texts available (such as those by Ken Brown and Richard Weiss), each providing several chapters of preparation before giving the actual definition.\n\nI myself began learning about buildings a few years ago through conversation with James Dolan, as part of the larger groupoidification project. Together we developed an alternative way of considering buildings which makes contact with enriched category theory and the theory of quantales, an approach which we felt would be congenial to (or at least readily apprehended by) category theorists. The purpose of these notes is to explain this approach, and tentatively suggest an enriched-category generalization of buildings which might be of interest.\n\nFor those who already know something about buildings, we can explain the rough idea as follows. A popular slogan in the so-called “local approach” due to Tits is that a building is like a metric space, except that “distances” between points are measured not by real numbers but by elements in Coxeter groups. To a categorist, this might recall Lawvere’s interpretation of metric spaces as categories enriched in a quantale of extended nonnegative reals, and the question arises whether Tits’s slogan can be similarly interpreted within a quantalic niche. This is indeed the case. To make it come out right, though, one needs to use certain “Coxeter monoids” equipped with a Bruhat ordering – certain quantales attached to a Coxeter diagram – instead of the associated Coxeter groups. (Curiously, there seems to be little mention of these monoids in the literature; they should be better known.) In the end, buildings are certain categories enriched in such Coxeter quantales, satisfying additional isometry conditions which are naturally understood in terms of homomorphisms which preserve both quantale products and internal homs. This forms the basis of a beautiful link between classical geometry and categorical logic.\n\nA brief rapport of Coxeter diagrams and associated structures\n\nA Coxeter diagram codes the same information as a Coxeter matrix but in easy-to-read form; we’ll start with Coxeter matrices.\n\nA Coxeter matrix indexed by a set $I$ is a function\n\n$m: I \\times I \\stackrel{m}{\\to} \\{1, 2, 3, \\ldots, \\infty\\}: (i, j) \\mapsto m_{i j}$\n\nsuch that $m_{i j} = m_{j i}$ and $m_{i j} = 1$ if and only if $i = j$.\n\nThe associated Coxeter diagram is a labeled simple graph whose set of vertices is $I$, and where there is an edge between vertices $i$ and $j$ (labeled $m_{i j}$) if and only if $m_{i j} \\geq 3$. In the literature it is standard to drop the label if $m_{i j} = 3$, and to draw instead two edges between $i$ and $j$ if $m_{i j} = 4$.\n\nThe associated so-called Coxeter group $W$ is a group presentation whose generators $s_i$ are in bijection with elements $i \\in I$, and whose relations are given by equations\n\n$(s_i s_j)^{m_{i j}} = 1$\n\nwhenever $m_{i j} \\lt \\infty$.\n\nIn particular, $(s_i)^2 = 1$ for all $i$. This also shows that the monoid presented by such equations is a group. It additionally follows that this monoid can be equivalently presented using the same generators and equations\n\n$s_i^2 = 1 \\qquad (1)$\n\n$\\,$\n\n$s_i s_j s_i \\ldots = s_j s_i s_j \\ldots \\qquad (2)$\n\nwhere each side of (2) is an alternating word of length $m_{i j}$.\n\nAn important general fact about Coxeter groups is that equality is decidable: there is an algorithm that decides whether two words in the $s_i$ are equivalent modulo the relator subgroup. Suppose given a word $w$ in letters $s_1, \\ldots, s_n$ and of length $k$; there are $n^k$ such words. If $w$ contains consecutive letters $s_i s_i$, then by relation (1) we may delete those letters to obtain an shorter word which is equivalent to $w$. We say the word $w$ is reducible. If $w$ is not reducible, we consider all words obtainable from $w$ in finitely many steps by replacing one side of an equation of type (2) with the other. Such replacements again produce a word of length $k$ in the letters $s_1, \\ldots, s_n$, and so there are only finitely many words obtainable from $w$ in this way. If none of these words is reducible, then $w$ is said to be reduced. We have the following results:\n\n• One can decide in finitely many steps whether a word is reduced.\n\n• Every word is equivalent to a reduced word.\n\n• Two reduced words are equivalent iff one is obtainable from the other by making replacements of type (2).\n\nThus whether two words are equivalent takes only finitely many steps to decide.\n\nThe Coxeter group carries the obvious involution given by inversion. It is therefore a $*$-monoid.\n\nCategorical definition of buildings\n\nLet $D$ be a Coxeter diagram. The Coxeter monoid $W_\\infty = W_\\infty(D)$ is the monoid presented using the same generators as the Coxeter group $W$, but subject to the equations\n\n$s_i^2 = s_i \\qquad (1')$\n\n$\\,$\n\n$s_i s_j s_i \\ldots = s_j s_i s_j \\ldots \\qquad (2)$\n\nThe concept of reduced word is the same as for the Coxeter group; the set of reduced words is the same for the Coxeter monoid $W_\\infty$ as for the Coxeter group $W$. Hence equality is decidable in the Coxeter monoid.\n\nIdentifying the underlying set of $W_\\infty$ with a set of equivalence classes of reduced words, $W_\\infty$ carries an anti-involution $w \\mapsto w^*$ where $w^*$ is the (reduced) word obtained by writing the (reduced) word $w$ in reverse.\n\nThe Coxeter monoid $W_\\infty$ carries a partial ordering, the smallest reflexive transitive relation for which $W_\\infty$ is a monoidal poset and the identity 1 is the bottom element. We usually write this as $x \\geq 1$, and we think more in terms of $(W_\\infty, \\geq)$, just we think of $([0, \\infty], \\geq)$ as the base of enrichment for metric spaces. The involution $(-)^*$ preserves the partial order. We call this the Bruhat order on $W_\\infty$.\n\nEvidently, then, $W_\\infty$ is a $*$-monoid in the bicategory $Ord$ of preorders and order-preserving maps. The free sup-lattice functor\n\n$P: Ord \\to sLat$\n\n(which takes the sup-lattice of downward-closed sets) is a strong monoidal functor which takes the $*$-monoid $W_\\infty$ in $Ord$ to a $*$-monoid $P(W_\\infty) = [W_{\\infty}^{op}, 2]$, also called a $*$-quantale. The quantalic multiplication is given by the usual Day convolution, which here takes the simple form\n\n$R \\cdot S = \\{r s: r \\in R, s \\in S\\}$\n\nfor $R$, $S$ down-closed subsets of $W_\\infty$. Alternatively, if\n\nThe functor $P: Ord \\to sLat$ factors through the Kleisli bicategory of the associated monad, which is equivalent to the cartesian bicategory of preorders and bimodules between preorders, denoted $OrdMod$.\n\nIf $X$ is any set, $X \\times X$ may be regarded as a $*$-monoid in the cartesian bicategory $Rel$ of sets and relations (and therefore in $OrdMod$, and therefore in $sLat$). Indeed, $Rel$ is compact, and the dual of any set $X$ is $X$ itself, so we have a monoid structure on\n\n$\\hom(X, X) = X^* \\times X = X \\times X$\n\nand a $*$-monoid where $f^*$ is the transpose of $f \\in \\hom(X^*, X^*) = \\hom(X, X)$. Thus, $P(X \\times X)$ is a $*$-quantale; the monoidal product is just composition of binary relations:\n\n$(R \\cdot S)(x, z) = \\exists_y R(x, y) \\wedge S(y, z)$\n\nand the transpose is just the taking of the opposite relation.\n\nAny quantale carries a residuated structure defined by operations $/$, $\\backslash$ that satisfy the adjunction conditions\n\n$u v \\leq w \\qquad iff \\qquad u \\leq w/v$\n\n$\\,$\n\n$u v \\leq w \\qquad iff \\qquad v \\leq u \\backslash w$\n\nAs examples we have:\n\n• In $P(X \\times X)$, we have $(T/S)(x, y) = \\forall_z S(y, z) \\Rightarrow T(x, z)$ and $(R \\backslash T)(y, z) = \\forall_x R(x, y) \\Rightarrow T(x, z)$.\n\n• In $P(W_\\infty)$, we have $T/S = \\{x \\in W_\\infty: \\forall_y y \\in S \\Rightarrow x y \\in T\\}$ and $R \\backslash T = \\{y \\in W_\\infty: \\forall_x x \\in R \\Rightarrow x y \\in T\\}$.\n\nDefinition\n\nLet $D$ be a Coxeter diagram. A $D$-building consists of a set $F$ and a bicontinuous homomorphism\n\n$[W_\\infty(D), 2] \\to [F \\times F, 2]$\n\nof residuated $*$-quantales.\n\nSome observations that clarify this definition:\n\n• Any bicontinuous map $[Y, 2] \\to [X, 2]$ is of the form $[f, 2]: [Y, 2] \\to [X, 2]$ for some $f: X \\to Y$, so the data of a $D$-building is given by a function\n\n$d: F \\times F \\to W_\\infty(D)$\n• A lax homomorphism of $*$-quantales\n\n$[d, 2]: [W_\\infty, 2] \\to [F \\times F, 2]$\n\ntakes an up-closed set $S \\subseteq W_\\infty$ to $\\{(f, f'): d(f, f') \\in S\\}$. This is the unique cocontinuous map which is determined by what it does to principal filters, i.e., by relations\n\n$\\{(f, f'): w \\leq d(f, f')\\}$\n\nand the lax homomorphism property says in part\n\n$\\exists_{f'} u \\leq d(f, f') \\wedge v \\leq d(f', f'') \\Rightarrow u v \\leq d(f, f')$\n\nin $W_{\\infty}^{op}$, which by Yoneda simply means\n\n$d(f, f')d(f', f'') \\qeq d(f, f'')$\n\nin $W_\\infty$. The other lax homomorphism condition is that\n\n$1 \\leq d(f, f)$\n\nin $W_{\\infty}^{op}$, or $1 \\geq d(f, f)$ in $W$, for all $f \\in F$. Since $1$ is the minimal element in the Bruhat order, this means $1 = d(f, f)$ for all $f$. Taken together, these just say $F$ is enriched in the monoidal poset $W_\\infty$. The condition that $[2, d]$ preserves the $*$ operation just means that $d(f', f) = d(f, f')^*$ for all $f, f' in F$.\n\n• Thus $F$ behaves like a $W$-valued pseudometric space, if $[d, 2]$ is lax $*$-monoidal. To say that $[d, 2]$ is strong $*$-monoidal means additionally that whenever\n\nRevised on September 8, 2010 at 15:42:48 by Todd Trimble" ]
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https://talema.com/smps-resonant-converters
[ "# Talema Blog\n\n## SMPS: Resonant Converters\n\nBy |\n\nThe increasing requirements of lighter, smaller and more efficient electronic products require power supply designers to develop AC-DC and DC-DC converters with high power density and efficiency. High switching frequency and high efficiency are the two methods used to improve power density and the profile of switched-mode power supplies (SMPS).\n\nThe effort to obtain ever-increasing power density in an SMPS has been limited by the size of passive components. Operation at higher frequencies considerably reduces the size of passive components such as transformers and filters; however, switching losses have been an obstacle to high-frequency operation.\n\nResonant techniques are used to reduce the switching losses in semiconductor devices and to allow for high-frequency operation. These techniques process power in a sinusoidal manner and the switching devices are softly commutated. Therefore, the switching losses and noise can be dramatically reduced because of its soft switching characteristics. Resonant techniques are used in both half-bridge and full-bridge converters.\n\nThe three most popular resonant converters are,\n\n• Series resonant converter\n• Parallel resonant converter\n• LLC resonant converter\n\n#### Series resonant converter\n\nIn a series resonant converter (SRC), the resonant inductor (Lr) and resonant capacitor (Cr) are in series and placed in series with the load. The resonant tank and the load act as a voltage divider.", null, "The impedance of the resonant tank can be changed by varying the frequency of driving voltage (Va).\n\nThe input voltage will be split between this impedance and the reflected load.  Since it is a voltage divider, the DC gain of an SRC is always lower than 1 (maximum gain happens at the resonant frequency).\n\nAt light load condition, the impedance of the load will be very large compared to the impedance of the resonant network and all the input voltage will be imposed on the load. This makes it difficult to regulate the output at light load. Theoretically, frequency should be infinite to regulate the output at no load.\n\n• Reduced switching loss and EMI through Zero Voltage Switching & Improved efficiency\n• Reduced magnetic components size by high-frequency operation\n\n• High circulating energy and high switching loss will occur at high input voltage. They are not suitable in application such (front end DC/DC application).\n• Pulsating rectifier current from the output capacitor so limitation for high output current application.\n• Cannot regulate the output at no load condition.\n\n#### Parallel Resonant Converter\n\nIn a parallel resonant converter (PRC), The resonant capacitor (Cr) is placed in parallel with the load, inevitability requiring large amounts of circulating current. This makes it difficult to use parallel resonant topologies in applications with high power density or large load variations.", null, "The impedance of the resonant tank can be changed by varying the frequency of driving voltage (Va). The transformer primary side is a capacitor, so an inductor is added on the secondary side to match the impedance.\n\n• No problem in output regulation at no load condition\n• Continuous rectifier current from the output inductor, Hence it is suitable for high output current application\n\n• The primary side current is almost independent of load condition, significant current may circulate through the resonant network, even at the no-load condition\n• High circulating energy and high switching loss will occur at high input voltage. They are not suitable in application such (front end DC/DC application)\n\n#### Half-Bridge LLC Resonant Converter\n\nThe half-bridge LLC topology consists of a square-wave generator, a series resonant tank, a transformer, an output rectifier circuit, and an output filter.", null, "The series resonant tank is composed of a series resonant inductor Lr, a series resonant capacitor Cr, and the Lm formed by the magnetizing inductance of transformer T1. The series resonant inductor can be an external component or the leakage inductance of T1. The rectifier circuit which includes D1 and D2 converts the resonant current into a unidirectional current. The output filter Co modulates the high-frequency ripple current.\n\nThe LLC resonant converter uses transformer magnetizing inductance for generating one more resonant frequency, which is much lower than the main resonant frequency comprising resonant tank Lr and Cr. The LLC resonant converter is designed to operate at a switching frequency higher than the resonant frequency of the resonant tank Lr and Cr.\n\nSwitches S1 and S2 operate at 50% duty cycle and the output voltage is regulated by varying the switching frequency of the converter. The converter has two resonant frequencies: a lower resonant frequency Fr2 (given by Lm, Lr, and Cr) and a fixed higher series resonant frequency Fr1 (given by Lr and Cr only).\n\nThe typical frequency response of an LLC resonant converter is:", null, "The two resonant frequencies are:", null, "", null, "The quality factor of the resonant tank is:", null, "", null, "RAC = Equivalent AC Resistance,  n = Turns ratio\n\nThe characteristics of an LLC resonant converter can be divided into three regions based on the operation.\n\nRegion 1 is similar to SRC operation. When the switching frequency is higher than Fr1, the converter is running at the ZVS region and the magnetizing inductance does not participate in the resonance. This region, which is also called the inductive load region, the voltage gain of the LLC resonant converter is always less than one.\n\nRegion 2 is the multi-resonant converter (MRC) region. Between Fr1 and Fr2, the load condition will determine the operation of the converter under ZVS and ZCS conditions, converter voltage gain reaches its maximum value. In this region, the energy stored in the magnetic components causes ZVS for the opposite switching device.\n\nRegion 3 is the overloaded region. When switching frequency is higher than Fr2, the converter always runs at ZCS condition. This region is called the capacitive mode region, switches S1 and S2 are under hard switching and have high switching losses. So ZCS  operation should always be avoided.\n\nIn general, the LLC resonant converter is designed to operate in Region 1 and 2 because of output regulation and ZVS operation. Switches S1 and S2 can be soft-switched for the entire load range by operating the converter under inductive load mode (ZVS region).  It can be either above or below the resonant frequency Fr1. The required gain is determined by the relationship between the input and output voltage, which can be represented by:", null, "g = Voltage gain for LLC resonant converter\n\nVo = Output voltage\n\nVIN = Input voltage\n\nFrom this equation, we can see that the lower the input voltage, the higher the voltage gain.\n\n• Narrow frequency variation over a wide line and load range, making this topology the best choice for front end DC-DC applications.\n• ZVS capability for entire load range, low turn-off current, therefore the switching loss is very low.\n• Zero voltage switching even at no load condition\n• All essential parasitic elements, including junction capacitances of all semiconductor devices and the leakage inductance of the transformer, are utilized to achieve soft-switching.\n• No output choke required, resulting in cost savings\n• Integrated magnetics: When a transformer is used in an LLC converter, the magnetizing inductance and leakage inductance can be used in resonant circuit instead of using a separate external inductor\n• High efficiency of > 96% and high power level up to 1 kW.\n\n• Higher ripple current on the secondary so lower ESR capacitors needed\n\nApplications\n\n• LED and LCD televisions\n• Computers and laptops\n• Industrial LED lighting\n• High-end audio\n• Home appliances\n• Industrial battery chargers", null, "Bhuvana Madhaiyan is a Design & Development Engineer with Talema India. She holds a bachelor’s degree in Electrical & Electronics Engineering from Anna University Chennai and has been a practicing engineer since 2006. Bhuvana joined the Talema team in 2007." ]
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http://encyclopedia2.thefreedictionary.com/arithmetic+sum
[ "# arithmetic sum\n\n## arithmetic sum\n\n[¦a·rith¦med·ik ′səm]\n(mathematics)\nThe result of the addition of two or more positive quantities.\nThe result of the addition of the absolute values of two or more quantities.\nMentioned in ?\nReferences in periodicals archive ?\nA ripple carry adder is a digital circuit that produces the arithmetic sum of two binary numbers.\nThis is a barometer for gauging the knowledge of students based on an individual's ability to write his/her name, read a paragraph in English, Urdu or in a regional language as well as solve two-digit arithmetic sum.\nThis arithmetic sum of GERB, the Reformist Bloc [RB], the Patriotic Front [PF] and ABV is not just unprincipled, but is an outright anti-European and anti-NATO concord which cannot be supported by the DPS,\" Mestan told reporters after his talks with Plevneliev.\nTotal resources - the arithmetic sum of 2P reserves and risked resources.\nThe consequences of choices made are expressed by a loss function construed as the arithmetic sum of squared estimation errors in each origin and development year.\nThe arithmetic sum of neither of these groups of figures is 70, and no explanation of the discrepancies is given.\nThe cumulative effect of what everyone is doing is greater than the arithmetic sum,\" he states.\n\nSite: Follow: Share:\nOpen / Close" ]
[ null ]
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http://eprints.iisc.ac.in/4425/
[ "", null, "Home | About | Browse | Latest Additions | Advanced Search | Contact | Help\n\n# Optical absorption and emission properties of $Pr^{3+}$ and $Er^{3+}$ in mixed alkali borate glasses\n\nVijayakumar, A and Chakradhar, RPS and Ratnakaram, YC (2006) Optical absorption and emission properties of $Pr^{3+}$ and $Er^{3+}$ in mixed alkali borate glasses. In: International Symposium on Non Oxide and new Optical Glasses (ISNOG), 10 - 14 April, 2006, Indian Institute of Science, Bangalore.", null, "", null, "Preview\nPDF\nhis article presents the optical absorption and emission properties of $Pr^{3+}$ and $Er^{3+}$ in mixed alkali borate glasses of the type $68B_2O_3.xLi_2O.(32-x)Cs_2O$ (where x= 8, 12, 16, 20 and 24 ). The variation of Judd-Ofelt intensity parameters $(\\Omega_{\\lambda})$, the peak wavelength of the hypersensitive transitions, radiative transition probabilities $(A_{rad})$ and peak emission cross-sections $(\\sigma_p)$ with x in the glass matrix has been discussed in detail. The changes in position of hypersensitive transition and intensity parameters with x are correlated to the structural changes in the host matrix. The estimated radiative lifetimes $(\\tau_R)$ of certain excited states of both $Pr^{3+}$ and $Er^{3+}$ in lithium cesium mixed alkali borate glasses are reported. Branching ratios $(\\beta)$ and integrated absorption cross sections $(\\Sigma)$ for certain important transitions are presented. Peak stimulated emission cross-sections $(\\sigma_p)$ are calculated for the observed emission peaks of $Pr^{3+}$ and $Er^{3+}$ ions in this glass matrix.", null, "View Item" ]
[ null, "http://eprints.iisc.ac.in/images/logo1.gif", null, "http://eprints.iisc.ac.in/style/images/fileicons/application_pdf.png", null, "http://eprints.iisc.ac.in/4425/1.haspreviewThumbnailVersion/Chakradhar1.pdf", null, "http://eprints.iisc.ac.in/style/images/action_view.png", null ]
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https://aimsciences.org/article/doi/10.3934/dcds.2010.28.511
[ "", null, "", null, "", null, "", null, "June  2010, 28(2): 511-517. doi: 10.3934/dcds.2010.28.511\n\n## The validity of the Euler-Lagrange equation\n\n 1 Dipartimento di Matematica e Applicazioni, Università degli Studi di Milano-Bicocca, Via R. Cozzi 53, I-20125 Milano, Italy, Italy\n\nReceived  December 2009 Revised  February 2010 Published  April 2010\n\nWe prove the validity of the Euler-Lagrange equation for a solution $u$ to the problem of minimizing $\\int_{\\Omega}L(x,u(x),\\nabla u(x))dx$, where $L$ is a Carathéodory function, convex in its last variable, without assuming differentiability with respect to this variable.\nCitation: Giovanni Bonfanti, Arrigo Cellina. The validity of the Euler-Lagrange equation. Discrete & Continuous Dynamical Systems - A, 2010, 28 (2) : 511-517. doi: 10.3934/dcds.2010.28.511\n Stefano Bianchini. On the Euler-Lagrange equation for a variational problem. Discrete & Continuous Dynamical Systems - A, 2007, 17 (3) : 449-480. doi: 10.3934/dcds.2007.17.449 Menita Carozza, Jan Kristensen, Antonia Passarelli di Napoli. On the validity of the Euler-Lagrange system. Communications on Pure & Applied Analysis, 2015, 14 (1) : 51-62. doi: 10.3934/cpaa.2015.14.51 Agnieszka B. Malinowska, Delfim F. M. Torres. Euler-Lagrange equations for composition functionals in calculus of variations on time scales. Discrete & Continuous Dynamical Systems - A, 2011, 29 (2) : 577-593. doi: 10.3934/dcds.2011.29.577 Yutian Lei, Zhongxue Lü. Axisymmetry of locally bounded solutions to an Euler-Lagrange system of the weighted Hardy-Littlewood-Sobolev inequality. Discrete & Continuous Dynamical Systems - A, 2013, 33 (5) : 1987-2005. doi: 10.3934/dcds.2013.33.1987 Guy V. Norton, Robert D. Purrington. The Westervelt equation with a causal propagation operator coupled to the bioheat equation.. Evolution Equations & Control Theory, 2016, 5 (3) : 449-461. doi: 10.3934/eect.2016013 Thierry Horsin, Peter I. Kogut, Olivier Wilk. Optimal $L^2$-control problem in coefficients for a linear elliptic equation. II. Approximation of solutions and optimality conditions. Mathematical Control & Related Fields, 2016, 6 (4) : 595-628. doi: 10.3934/mcrf.2016017 Sebastián Ferrer, Martin Lara. Families of canonical transformations by Hamilton-Jacobi-Poincaré equation. Application to rotational and orbital motion. Journal of Geometric Mechanics, 2010, 2 (3) : 223-241. doi: 10.3934/jgm.2010.2.223 Manuel de León, Juan Carlos Marrero, David Martín de Diego. Linear almost Poisson structures and Hamilton-Jacobi equation. Applications to nonholonomic mechanics. Journal of Geometric Mechanics, 2010, 2 (2) : 159-198. doi: 10.3934/jgm.2010.2.159 Thierry Horsin, Peter I. Kogut. Optimal $L^2$-control problem in coefficients for a linear elliptic equation. I. Existence result. Mathematical Control & Related Fields, 2015, 5 (1) : 73-96. doi: 10.3934/mcrf.2015.5.73 David Mumford, Peter W. Michor. On Euler's equation and 'EPDiff'. Journal of Geometric Mechanics, 2013, 5 (3) : 319-344. doi: 10.3934/jgm.2013.5.319 Mohammad Hassan Farshbaf-Shaker, Takeshi Fukao, Noriaki Yamazaki. Singular limit of Allen--Cahn equation with constraint and its Lagrange multiplier. Conference Publications, 2015, 2015 (special) : 418-427. doi: 10.3934/proc.2015.0418 S. Huff, G. Olumolode, N. Pennington, A. Peterson. Oscillation of an Euler-Cauchy dynamic equation. Conference Publications, 2003, 2003 (Special) : 423-431. doi: 10.3934/proc.2003.2003.423 Igor Kukavica, Amjad Tuffaha. On the 2D free boundary Euler equation. Evolution Equations & Control Theory, 2012, 1 (2) : 297-314. doi: 10.3934/eect.2012.1.297 M. Petcu. Euler equation in a channel in space dimension 2 and 3. Discrete & Continuous Dynamical Systems - A, 2005, 13 (3) : 755-778. doi: 10.3934/dcds.2005.13.755 Terence Tao. On the universality of the incompressible Euler equation on compact manifolds. Discrete & Continuous Dynamical Systems - A, 2018, 38 (3) : 1553-1565. doi: 10.3934/dcds.2018064 Ioan Bucataru. A setting for higher order differential equation fields and higher order Lagrange and Finsler spaces. Journal of Geometric Mechanics, 2013, 5 (3) : 257-279. doi: 10.3934/jgm.2013.5.257 In-Jee Jeong, Benoit Pausader. Discrete Schrödinger equation and ill-posedness for the Euler equation. Discrete & Continuous Dynamical Systems - A, 2017, 37 (1) : 281-293. doi: 10.3934/dcds.2017012 Juan Calvo. On the hyperbolicity and causality of the relativistic Euler system under the kinetic equation of state. Communications on Pure & Applied Analysis, 2013, 12 (3) : 1341-1347. doi: 10.3934/cpaa.2013.12.1341 Adnan H. Sabuwala, Doreen De Leon. Particular solution to the Euler-Cauchy equation with polynomial non-homegeneities. Conference Publications, 2011, 2011 (Special) : 1271-1278. doi: 10.3934/proc.2011.2011.1271 David González-Sánchez, Onésimo Hernández-Lerma. On the Euler equation approach to discrete--time nonstationary optimal control problems. Journal of Dynamics & Games, 2014, 1 (1) : 57-78. doi: 10.3934/jdg.2014.1.57\n\n2018 Impact Factor: 1.143\n\n## Metrics\n\n• PDF downloads (7)\n• HTML views (0)\n• Cited by (1)\n\n## Other articlesby authors\n\n• on AIMS\n• on Google Scholar\n\n[Back to Top]" ]
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https://www.physicsforums.com/threads/deriving-a-vector-identity-using-pauli-spin-matrices.384596/
[ "# Deriving a vector identity using Pauli spin matrices\n\n## Homework Statement\n\nI'm supposed to derive the following:\n\n$$\\left({\\bf A} \\cdot {\\bf \\sigma} \\right) \\left({\\bf B }\\cdot {\\bf \\sigma} \\right) = {\\bf A} \\cdot {\\bf B} I + i \\left( {\\bf A } \\times {\\bf B} \\right) \\cdot {\\bf \\sigma}$$\n\nusing just the two following facts:\n\nAny 2x2 matrix can be written in a basis of spin matrices:\n\n$$M = \\sum{m_\\alpha \\sigma_\\alpha}$$\n\nwhich means that the beta-th component is given by\n\n$$m_\\beta = \\frac{1}{2}Tr(M \\sigma_\\beta)$$\n\nlisted above...\n\n## The Attempt at a Solution\n\nIt should just be a left side= right side proof.\n\nI started by saying $$\\left({\\bf A} \\cdot {\\bf \\sigma} \\right) \\left({\\bf B }\\cdot {\\bf \\sigma} \\right) = \\left(\\sum_\\alpha a_\\alpha \\sigma_\\alpha \\cdot \\sigma \\right) \\left(\\sum_\\alpha b_\\alpha \\sigma_\\alpha \\cdot \\sigma \\right) = \\left( \\sum_\\beta a_\\alpha \\delta_{\\alpha \\beta} \\right) \\left( \\sum_\\gamma b_\\alpha \\delta_{\\alpha \\gamma} \\right) = \\sum_\\beta a_\\beta \\sum_\\gamma b_\\gamma = \\frac{1}{2} Tr(A \\sigma_\\beta) \\frac{1}{2} Tr(B \\sigma_\\gamma)$$\n\nNot sure if this is even the right way to start, and I can't see at all where I would go from here to get the appropriate RHS of the identity I'm proving. Any ideas?", null, "You can't expand A or B into Pauli matrices because neither of them are 2x2 matrices. They are both vectors of scalars.\n\nAlso, are you able to use any other info, such as the product of two Pauli matrices?\n\nThanks for the reply. I can use the usual commutation relations between the Pauli matrices. Also, I know the Pauli spin matrices are traceless... not sure if that's helpful or not.\n\nYes, that helps a lot. First you will need to make a 2-D matrix from the original equation. You had the right idea originally but expanded too much early on. You should do something like:\n\n$$(A\\cdot\\sigma)(B\\cdot\\sigma) = \\sum_{i} a_i \\sigma_i \\sum_{j} b_j \\sigma_j = \\sum_{ij}a_i b_j \\sigma_i \\sigma_j =M$$\n\nThat last term is now a 2d matrix. You will expand that in spin matrices including the identity. I suggest solving for the $$m_0$$ (identity piece) first, since that will give you your dot product. Be sure to use properties of the trace. For example, a_i and b_j are scalars. And you can break the sum of matrices in a trace up into a sum of traces of the individual matrices.\n\nLast edited:" ]
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https://brothersontech.com/isle-aux-morts/application-of-projectile-motion-in-engineering.php
[ "", null, "Projectile Motion Problem 1 - Kinematics of Particles Keyword 1Engineering Dynamics Projectile Motion Keyword 2 Engineering Dynamics Projectile Motion, Keyword 3 Engineering Dynamics Projectile Motion Keyword 4\n\n## Projectiles in Physics problemsphysics.com\n\nMotion of ProjectileStudy Material for IIT JEE askIITians. Motion in two dimensions - calculate the range of a projectile Resources, Tools and Basic Information for Engineering and Design of Technical Applications!, In this section we will discuss projectile motion, When we consider a projectile moving through the air we will assume that there Engineering & Maths. View.\n\nThis module introduces two-dimensional projectile motion and develops the related equations. The path equation, horizontal range and maximum height are some of the A projectile motion is a special case of two dimensional motion with constant acceleration. In this experiment, the group deciphers the importance of projectile and its application in our daily living.\n\nProjectile motion is the motion of an object subject only to the Engineering; Geosciences; The applications of projectile motion in physics and engineering SOCRATIC Subjects . Science What are some real life applications of projectile motion? Physics 2D Motion Projectile Motion.\n\nSOCRATIC Subjects . Science What are some real life applications of projectile motion? Physics 2D Motion Projectile Motion. Example John kicks the ball and ball does projectile motion with an angle of 53º to horizontal. Its initial velocity is 10 m/s, find the maximum height it can reach, …\n\nKeyword 1Engineering Dynamics Projectile Motion Keyword 2 Engineering Dynamics Projectile Motion, Keyword 3 Engineering Dynamics Projectile Motion Keyword 4 Another general and important area which is to do with projectile motion, is projectile Projectile motion is What are the application of projectile motion?\n\nProjectile motion is the motion of an object thrown or projected into the air, subject only to acceleration as a result of gravity. The applications of projectile motion in physics and engineering are numerous. Some examples include meteors as they enter Earth’s atmosphere, fireworks, and the … Recall that projectile motion is motion in which an object is moving through space only under the influence of the force of gravity. This moving object can be of any size, shape, and material composition, and is called a projectile. We have used two sets of formulas: the first to analyze motion along the x-axis,\n\nAn html 5 app may be used to interact with the concepts associated with projectiles. Projectile of Projectile (html 5 applet) Vertical Motion Engineering This module introduces two-dimensional projectile motion and develops the related equations. The path equation, horizontal range and maximum height are some of the\n\nAnother general and important area which is to do with projectile motion, is projectile Projectile motion is What are the application of projectile motion? Find and save ideas about Projectile motion on √ Application of Projectile Motion - Applications of calculus Classroom in which the motion of a projectile\n\nDownload Citation on ResearchGate Projectile dynamics in sport: Principles and applications How can we predict the trajectory of a baseball from bat to outfield? In this section we will discuss projectile motion, When we consider a projectile moving through the air we will assume that there Engineering & Maths. View\n\nIn this section we will discuss projectile motion, When we consider a projectile moving through the air we will assume that there Engineering & Maths. View acceleration distance equations of motion EV3 kinematics LEGO MINDSTORMS motion projectile projectile motion This engineering Describe projectile motion\n\nAnother general and important area which is to do with projectile motion, is projectile Projectile motion is What are the application of projectile motion? An object that is moving through the air without the aid of any external forces will follow a path that is governed by projectile motion. Mechanical Engineering\n\nPROJECTILE MOTION AND ITS APPLICATION ninayanapika. acceleration distance equations of motion EV3 kinematics LEGO MINDSTORMS motion projectile projectile motion This engineering Describe projectile motion, Using the equations of motion to figure out things about falling objects. Electrical engineering; Computing; Old videos on projectile motion. Projectile.\n\n### Projectile Motion An Integrated Lesson AP Central", null, "Engineering Dynamics Projectile Motion 2018 2019 2020. Find and save ideas about Projectile motion on √ Application of Projectile Motion - Applications of calculus Classroom in which the motion of a projectile, Find and save ideas about Projectile motion on √ Application of Projectile Motion - Applications of calculus Classroom in which the motion of a projectile.\n\nProjectile Motion – Kinematics & Dynamics – Engineering. Recall that projectile motion is motion in which an object is moving through space only under the influence of the force of gravity. This moving object can be of any size, shape, and material composition, and is called a projectile. We have used two sets of formulas: the first to analyze motion along the x-axis,, 2013-10-23 · A projectile is some object thrown in space or air. The Curved path along which the projectile travels is what is known as equation of path or trajectory. Projectile Motion is the free fall motion with acceleration due to ….\n\n### Projectile Launcher An Engineering Design Project for", null, "Projectile Motion Experiment Study.com. Download Citation on ResearchGate Projectile dynamics in sport: Principles and applications How can we predict the trajectory of a baseball from bat to outfield? https://en.wikipedia.org/wiki/Particle_mechanics Scientific Applications of Quadratic Functions. Problems involving gravity and projectile motion are typically dependent upon a second-order engineering, and.", null, "Motion in two dimensions - calculate the range of a projectile Resources, Tools and Basic Information for Engineering and Design of Technical Applications! Using the equations of motion to figure out things about falling objects. Electrical engineering; Computing; Old videos on projectile motion. Projectile\n\nUnderstanding The Concepts Of 2-D Kinematics. Application Of Projectile Motion AIPMT, COMED, BITS, Engineering & Medical entrance exams, The Projectile Motion Toolkit provides teachers with a collection Students use an online application to master three types of Science and Engineering\n\nStudents explore the relationships between displacement, velocity and acceleration and calculate simple projectile motion. The objective of this activity is to An html 5 app may be used to interact with the concepts associated with projectiles. Projectile of Projectile (html 5 applet) Vertical Motion Engineering\n\nWhat is 2D projectile motion? This is often done in a calculus-based engineering physics course. So for the horizontal direction we can use the following equation, Projectile Launcher: An Engineering projectile motion and The discussion then shifts to dynamics and the application of Newton’s 2nd law of motion2\n\nacceleration distance equations of motion EV3 kinematics LEGO MINDSTORMS motion projectile projectile motion This engineering Describe projectile motion Electrical engineering; Computing; Projectile motion (part 3 This isn't just math-- everything we're doing in math has kind of an application in the real\n\nDynamics is the branch of mechanics which deals with the study of bodies in motion. Branches of Dynamics (Projectile Motion) Engineering Mechanics. In this section we will discuss projectile motion, When we consider a projectile moving through the air we will assume that there Engineering & Maths. View\n\nAn object that is moving through the air without the aid of any external forces will follow a path that is governed by projectile motion. Mechanical Engineering What is 2D projectile motion? This is often done in a calculus-based engineering physics course. So for the horizontal direction we can use the following equation,\n\nThis lesson deals with the problem-solving approach to projectile motion where the use of the horizontal component of velocity and range calculation is primary. Components of initial velocity of parabolic throwing. Projectile motion is a form of motion in which an object or particle (in either case referred to as a projectile) is thrown near the Earth's surface, and it moves along a curved path under the action of gravity only.\n\n2016-08-20 · Problem 1 on Projectile Motion Video Lecture from Chapter Kinematics of Particles in Engineering Mechanics for First Year Engineering Students. Watch Projectile Launcher: An Engineering projectile motion and The discussion then shifts to dynamics and the application of Newton’s 2nd law of motion2\n\nStudying projectile motion allows for full application of kinematics, The motion of a projectile is a two-dimensional motion. and engineering topics. The Projectile Motion Toolkit provides teachers with a collection Students use an online application to master three types of Science and Engineering", null, "Recall that projectile motion is motion in which an object is moving through space only under the influence of the force of gravity. This moving object can be of any size, shape, and material composition, and is called a projectile. We have used two sets of formulas: the first to analyze motion along the x-axis, SOCRATIC Subjects . Science What are some real life applications of projectile motion? Physics 2D Motion Projectile Motion.\n\n## In Mechanical Engineering What is the difference between", null, "Engineering Dynamics Projectile Motion 2018 2019 2020. An html 5 app may be used to interact with the concepts associated with projectiles. Projectile of Projectile (html 5 applet) Vertical Motion Engineering, In this section we will discuss projectile motion, When we consider a projectile moving through the air we will assume that there Engineering & Maths. View.\n\n### Energizing Math with Engineering Applications\n\nProjectile dynamics in sport Principles and applications. Projectile motion (application. Motion of a projectile is described in a coordinate system, Do somebody tell me a best nano engineering book for beginners?, Projectile motion is the motion of an object subject only to the Engineering; Geosciences; The applications of projectile motion in physics and engineering.\n\nFind and save ideas about Projectile motion on √ Application of Projectile Motion - Applications of calculus Classroom in which the motion of a projectile Engineering Mechanics for 1st Year Engineering Students 4.5 Engineering Mechanics for 1st Year Engineering Students Projectile Motion Part-3\n\nElectrical engineering; Computing; Projectile motion (part 3 This isn't just math-- everything we're doing in math has kind of an application in the real PROJECTILE MOTION AND ITS APPLICATION TO DAILY LIFE Projectile Motion A projectile is any object that once projected or dropped continues in motion by its own inertia\n\nExample John kicks the ball and ball does projectile motion with an angle of 53º to horizontal. Its initial velocity is 10 m/s, find the maximum height it can reach, … Students explore the relationships between displacement, velocity and acceleration and calculate simple projectile motion. The objective of this activity is to\n\nUsing the equations of motion to figure out things about falling objects. Electrical engineering; Computing; Old videos on projectile motion. Projectile Understanding The Concepts Of 2-D AIPMT, COMED, BITS, Engineering & Medical entrance 2-D Kinematics Application of Projectile Motion Somesh Mohapatra\n\nIn this section we will discuss projectile motion, When we consider a projectile moving through the air we will assume that there Engineering & Maths. View Score a bull's eye with this cool science fair project on horizontal projectile motion. Guide a marble to its target and predict its trajectory using math!\n\nMotion in two dimensions - calculate the range of a projectile Resources, Tools and Basic Information for Engineering and Design of Technical Applications! Here's an easy solution to a real projectile motion exam problem Contact; Projectile Motion Problems (Physics 1 Exam Solution) The Engineering Degree\n\nSolving Projectile Motion Problems — Applying Kinematics Equations of Motion the new seventh edition of Engineering Mathematics has been thoroughly revised and Projectile motion is the motion of an object thrown or projected into the air, subject only to acceleration as a result of gravity. The applications of projectile motion in physics and engineering are numerous. Some examples include meteors as they enter Earth’s atmosphere, fireworks, and the …\n\nDynamics is the branch of mechanics which deals with the study of bodies in motion. Branches of Dynamics (Projectile Motion) Engineering Mechanics. Terminal ballistics the study of the projectile and Astrodynamics is the application of ballistics and Engineering Design Handbook: Ballistics\n\nThis lesson deals with the problem-solving approach to projectile motion where the use of the horizontal component of velocity and range calculation is primary. Components of initial velocity of parabolic throwing. Projectile motion is a form of motion in which an object or particle (in either case referred to as a projectile) is thrown near the Earth's surface, and it moves along a curved path under the action of gravity only.\n\nMotion in two dimensions - calculate the range of a projectile Resources, Tools and Basic Information for Engineering and Design of Technical Applications! Projectile Motion: An Integrated Lesson. concept and the images that illustrate the application of the concept. Projectile Motion in chemical engineering,\n\nWhat is 2D projectile motion? (article) Khan Academy. Dynamics is the branch of mechanics which deals with the study of bodies in motion. Branches of Dynamics (Projectile Motion) Engineering Mechanics., History of Projectile Motion - Download as Word Doc (.doc / .docx), PDF File (.pdf), Text File (.txt) or read online. bhjo.\n\n### Projectile Motion – Kinematics & Dynamics – Engineering", null, "In Mechanical Engineering What is the difference between. Scientific Applications of Quadratic Functions. Problems involving gravity and projectile motion are typically dependent upon a second-order engineering, and, In this experiment, you will learn how to create your own projectile motion experiment in order to calculate initial velocity of a horizontally....\n\nIn Mechanical Engineering What is the difference between. Scientific Applications of Quadratic Functions. Problems involving gravity and projectile motion are typically dependent upon a second-order engineering, and, Here's an easy solution to a real projectile motion exam problem Contact; Projectile Motion Problems (Physics 1 Exam Solution) The Engineering Degree.\n\n### Teacher Toolkits Projectile Motion", null, "ASEE PEER Projectile Motion with Aerodynamic Drag The. What is 2D projectile motion? This is often done in a calculus-based engineering physics course. So for the horizontal direction we can use the following equation, https://en.wikipedia.org/wiki/Particle_mechanics Download Citation on ResearchGate Projectile dynamics in sport: Principles and applications How can we predict the trajectory of a baseball from bat to outfield?.", null, "Projectile Launcher: An Engineering projectile motion and The discussion then shifts to dynamics and the application of Newton’s 2nd law of motion2 SOCRATIC Subjects . Science What are some real life applications of projectile motion? Physics 2D Motion Projectile Motion.\n\nExample John kicks the ball and ball does projectile motion with an angle of 53º to horizontal. Its initial velocity is 10 m/s, find the maximum height it can reach, … Download Citation on ResearchGate Projectile dynamics in sport: Principles and applications How can we predict the trajectory of a baseball from bat to outfield?\n\nIn this section we will discuss projectile motion, When we consider a projectile moving through the air we will assume that there Engineering & Maths. View Find and save ideas about Projectile motion on √ Application of Projectile Motion - Applications of calculus Classroom in which the motion of a projectile\n\nStudents explore the relationships between displacement, velocity and acceleration and calculate simple projectile motion. The objective of this activity is to Dynamics is the branch of mechanics which deals with the study of bodies in motion. Branches of Dynamics (Projectile Motion) Engineering Mechanics.\n\nacceleration distance equations of motion EV3 kinematics LEGO MINDSTORMS motion projectile projectile motion This engineering Describe projectile motion Projectile motion - is a motion of an item that being thrown from the ground and its falls back to the earth due to the gravity of the earth forming a curved path. Rocket motion - is a motion in which an object that can apply acceleration or thrust to itself. ‎\n\nProjectile motion is the motion of an object thrown or projected into the air, subject only to acceleration as a result of gravity. The applications of projectile motion in physics and engineering are numerous. Some examples include meteors as they enter Earth’s atmosphere, fireworks, and the … 2013-10-22 · √√ Application of Projectile Motion - Applications of calculus to the physics World A projectile is some object thrown in Projectile Motion\n\nScientific Applications of Quadratic Functions. Problems involving gravity and projectile motion are typically dependent upon a second-order engineering, and PROJECTILE MOTION AND ITS APPLICATION TO DAILY LIFE Projectile Motion A projectile is any object that once projected or dropped continues in motion by its own inertia\n\nProjectile motion is the motion of an object subject only to the Engineering; Geosciences; The applications of projectile motion in physics and engineering The Projectile Motion Toolkit provides teachers with a collection Students use an online application to master three types of Science and Engineering\n\nIn this section we will discuss projectile motion, When we consider a projectile moving through the air we will assume that there Engineering & Maths. View A projectile motion is a special case of two dimensional motion with constant acceleration. In this experiment, the group deciphers the importance of projectile and its application in our daily living.\n\nHere's an easy solution to a real projectile motion exam problem Contact; Projectile Motion Problems (Physics 1 Exam Solution) The Engineering Degree Scientific Applications of Quadratic Functions. Problems involving gravity and projectile motion are typically dependent upon a second-order engineering, and\n\nProjectile motion (application. Motion of a projectile is described in a coordinate system, Do somebody tell me a best nano engineering book for beginners? In this experiment, you will learn how to create your own projectile motion experiment in order to calculate initial velocity of a horizontally..." ]
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https://physics.stackexchange.com/questions/521295/adiabatic-process-and-2nd-law-violation
[ "# Adiabatic process and 2nd law violation\n\nConsider a gas which expands adiabatically and reversibly. Since there is no heat in the process, the gas transform some of it's internal energy into work. As no entropy is exchanged or created, the entropy of the gas is constant.\n\nNow, suppose we use the work given in the expansion to power a refrigerator. Assuming the refrigerator works in a cycle it creates no entropy. However, since refrigerator transfers heat from a cold reservoir to a hot one, this would mean a reduction in entropy.\n\nIn total, we obtain a reduction in entropy. Doesn't this violate the 2nd law of thermodynamics? If it does what is wrong with this scenario? I know that this cannot be done forever since our original gas cylinder ends up in a different state.\n\n• As you pointed out yourself, it's possible to reduce entropy locally. Every refrigerator does that. However, it's impossible to reduce the entropy of closed system. Dec 25 '19 at 16:21\n• I might be misunderstanding the scenario, but it seems to me like you are just analyzing one part of a cycle and assuming it describes the entire cycle? Dec 25 '19 at 16:31\n\nIf the refrigeration cycle is reversible, then the reduction in entropy of the low temperature reservoir from which heat is extracted equals the increase in entropy of the high temperature reservoir to which heat is transferred. For the reversible cycle the total entropy change is zero.\n\nThe change in entropy for the cold reservoir is\n\n$$\\Delta S_{cold}=$$.\n\nThe change in entropy of the hot reservoir is\n\n$$\\Delta S_{hot}=+\\frac{Q_H}{T_H}$$.\n\nFor a reversible refrigeration cycle (Carnot):\n\n$$\\frac{Q_C}{T_C}=\\frac{Q_H}{T_H}$$\n\nThus,\n\n$$\\Delta S_{tot}=+\\frac{Q_H}{T_H}-\\frac{Q_C}{T_C}$$\n\nFinally, $$Q_{H}=Q_{C}+W$$, where $$W$$ is the work input required to transfer heat to the hot reservoir.\n\nHope this helps.\n\n• You and Ofek are right, i forgot that even in the best case scenario when the fridge works as a Carnot cycle it cannot reduce the entropy since the heat taken from the cold reservoir is less that the heat given to the hot one. Dec 25 '19 at 17:01\n• @FranciscoLoyolaReyes That's correct. $\\frac{Q_C}{T_C}$ = $\\frac{Q_H}{T_H}$ and $Q_{H}=Q_{L}+W$. Dec 25 '19 at 17:12\n\nYou forgot that refrigerators deliver more heat into the heat reservoir than is taken out of the cool reservoir. Meaning the work you did by expanding the gas will go to heat up the heat reservoir. (And thus the net entropy gain will be 0 or positive, never negative)" ]
[ null ]
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https://www.algospot.com/judge/problem/read/SPETIAL
[ "## Spatial Concepts Test\n\n• 문제 ID\n• 시간 제한\n• 메모리 제한\n• 제출 횟수\n• 정답 횟수 (비율)\n• 출처\n• 분류\n\n#### 문제\n\nThe Flathead Testing Corporation (FTC) supplies various tests for Human Resources departments at many companies. One type of test they supply includes spatial concepts questions such as:\n\nWhen the following figure is folded back on the interior lines it forms a cube.", null, "Which of the following could be an image of one corner of the resulting cube?", null, "among the choices and another (given in the example) had two solutions among the choices (1 and 3).\n\nFTC needs a routine which will read in a specification of the unfolded cube and specifications of corner views and determine, for each corner view, whether it is a view of a corner of the cube specified in the unfolded part.\n\nFTC uses the following images as faces of each cube. Each image is symmetrical about the vertical axis and has a distinguished end (up in each image).", null, "The unfolded cube is specified by a string of six pairs of a letter indicating the image on the face and a number indicating the orientation of the distinguished end of the face: 1 is up, 2 is right, 3 is down and 4 is left. The faces are specified in the order given in the following figure with the orientations indicated in the square to the right:", null, "So the unfolded cube in the example is specified as “F3E4E2D3C2F3”. FTC has a routine which\nreads this specification and generates the unfolded image for the question.\n\nThe answer images are specified by three pairs of a letter and a digit indicating a face image and an orientation as indicated in the following diagram. The faces are specified in the order top, right, left (indicated by numbers in brackets in the figures), that is clockwise around the center vertex starting at the top. The orientation of the distinguished end of each face is indicated by the numbers on the edges in the diagram. They circle each face clockwise, starting at the center vertex.", null, "For the example, the answer figures are specified as “C2D2F2”, “E3F3C4”, “F2C2D2”, “D1E1F3” and “E1C1E1”. Again, FTC has a routine which reads this specification and generates each answer image for the question. They just need your routine to make sure there is exactly one correct answer to each question.\n\n#### 입력\n\nThe first line of input contains a single integer N, (1 ≤ N ≤ 1000) which is the number of datasets that follow.\nEach dataset consists of six lines of input. The first line of input is the specification for the folded out cube as described above. This line is followed by five lines, each of which gives the specification of one answer image as described above.\n\n#### 출력\n\nFor each dataset, output on a single line the dataset number, (1 through N), a blank, the number of answers which are solutions of the problem (corners of the cube specified in the folded out line), a blank and five ‘Y’ or ‘N’ characters separated by a blank indicating which of the answer images was a solution (‘Y’ for a solution, ‘N’ for not a solution).\n\n#### 예제 입력\n\n2\nF3E4E2D3C2F3\nC2D2F2\nE3F3C4\nF2C2D2\nD1E1F3\nE1C1E1\nA2F4F1A3A3C4\nC3A4A2\nF3F4A1\nF3C4A1\nA2C3A2\nA4A4F1\n\n#### 예제 출력\n\n1 2 Y N Y N N\n2 0 N N N N N" ]
[ null, "http://algospot.com/media/judge-attachments/143b96312fae537e53910428b6d5638d/aaa.jpg", null, "http://algospot.com/media/judge-attachments/c4979025ff31c581ec59ed80265caf23/anoa.jpg", null, "http://algospot.com/media/judge-attachments/293aa44b8d2291b890bdf69c78036feb/conda.jpg", null, "http://algospot.com/media/judge-attachments/874d3e640cf8579065c1189e47ff5e9b/whosad.jpg", null, "http://algospot.com/media/judge-attachments/749f266bfdff82e3e3f592a9174d0ec2/stris.jpg", null ]
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https://pballew.blogspot.com/2009/03/probably-interesting-problem.html
[ "## Sunday, 22 March 2009\n\n### Probably an Interesting Problem\n\nIt was a simple probability problem, but it teased me with its surprising answer, and led me on … but let me start at the beginning…\nA message on the AP discussion group from “Skerbie” (would I make this up?) asked…\n\nIf there are 4 red balls and 3 white balls in a container, and you remove them one at a time at random until one color is extinguished, what is the probability the remaining balls are red?\n\nThe simple answer, 4/7… soooo… would that always happen? And what is the math at work.\n\nI quickly tried several examples where the number of white and red differed by one and they all seemed to preserve the ratio. At first I thought that it would only work with a difference of one, but with a wake up reminder from Joshua Zucker I corrected my arithmetic flaws and figured out that, Yes, the probability of the smaller color being extinguished first is the ratio of red/(red+white). SO… to show why….\n\nOne of the first things that I thought was interesting and (at least by me) unsuspected is that the probability of drawing WWW is the same as drawing WRWRW, or RRWWW, or RWWRW or any of the possible outcomes that ends with white being exhausted first. For the original seven problem case, the probability of drawing WWW is (3/7) (2/6)(1/5)= 1/35…The same probability applies to, for example, WRWRW which is (3/7)(4/6)(2/5)(3/4)(1/3) because the last two fractions simply cancel out the impact of the red and we get 1/35 again… I picked up pretty quickly that the 35 in the denominator was the combination of 7 things taken 3 at a time. I checked a few other starting quantities and this was true of the others as well, if you had n white balls, and n+d red balls, the probability of any of the paths ending with white being exhausted first led to a probability of 1 over 2n+d choose n.\n\nAs I looked at counting the possible outcomes ending in white being exhausted, I realized that :\nThere was only one way to draw WWW\nThere were three ways to draw them with one red in the mix if the red could not be at the end\nRWWW; WRWW; WWRW\nAnd there were six ways to draw them with two reds in the mix.\nRRWWW, RWRWW; RWWRW; WRRWW; WRWRW; WWRRW\nAnd there were ten ways to draw them with three reds in the mix… this was the sequence of triangular numbers, in particular I realized that if the last one HAD to be white, the sequence was counting 2 choose 2, and then 3 choose 1; 4 choose 2; 5 choose 3. But since all of those had the same probability of occurring, then the total probability was just the sum of those multiplied by 1/35. And the sum of the numbers down that diagonal of Pascal’s arithmetic triangle was 20, which is 6 choose 3….\n\nI extended this to realize that as long as White had N balls, and Red had N+1, then there would be 2N choose N ways to order the outcomes, and each had a probability of 2N+1 choose N\n\nIn Pascal’s triangle, these were the successive numbers marked below:", null, "The first is for two reds and one white which leads to a probability of 2/3. The second is for three red and two white, and then for the four red, three white case. The 70/126 is the probability for starting with five red and four whites, and simplifies to the expected 5/9.\n\nWhen we expand the values for 2N choose N and 2N+1 choose N,", null, "we see why the result always leads to the result that the overall probably of white being exhausted first is Red/(Red + White) which, when there are N+1 Reds and N whites leads to (N+1) / (2N+1) .\n\nA very similar approach shows that when the difference between the number of Reds and Whites in the bowl is two, then we just move over one column in the arithmetic triangle to get :", null, "Ok, Maybe I’m the only old guy on the block who didn’t expect that…. But I bet a fistful of nickels that any bright kid in Alg II could look at what just happened and know where to go to find the answer if Red was three more than White…\n\nThey have the arithmetic triangle dating back to at least the thirteenth century, so why am I just finding this stuff out…." ]
[ null, "https://3.bp.blogspot.com/_PQZIFRiZz38/ScZxXTQ1dgI/AAAAAAAABl4/q2rPGK-DVyU/s400/prob1.jpg", null, "https://4.bp.blogspot.com/_PQZIFRiZz38/ScZxtrSVnYI/AAAAAAAABmA/GZX06WUeYLM/s400/prob2.jpg", null, "https://1.bp.blogspot.com/_PQZIFRiZz38/ScZx6_25VpI/AAAAAAAABmI/WmGNM8CreJA/s400/prob3.jpg", null ]
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https://itough2.lbl.gov/2019/02/27/manual-page-for-command-levenberg-marquardt/
[ "# Manual Page for Command >>> LEVENBERG-MARQUARDT\n\nSyntax\n>>> LEVENBERG-MARQUARDT (IDENTITY/EIGENVALUE) (SUPER/TRUNCATE (: (-)trunc))\n\nParent Command\n>> OPTION\n\nSubcommand\n-\n\nDescription\nThis command selects the Levenberg-Marquardt algorithm to minimize the objective function. This is the default minimization algorithm. The Levenberg-Marquardt algorithm combines the robustness of a steepest descent method with the efficiency of a Gauss-Newton step (see command >>> GAUSS-NEWTON):", null, "where the Tikhonov matrix D is a diagonal matrix with elements", null, "Alternatively, the Tikhonov matrix can be the identity matrix (keyword IDENTITY), or a diagonal matrix with the inverse of the squared eigenvalues of the Fisher Information matrix, scaled by the maximum squared eigenvalue (keyword EIGENVALUE). The parameter space can be truncated (keyword TRUNCATE) based on the eigenvalues of the Fisher Information matrix. Parameter trunc defines the cut-off value as a fraction of the eigenvalue to the maximum eigenvalue (default: 10-6). If given as an integer, the top INT(trunc) parameters will be selected. If trunc is a negative integer, more parameters are added as iterations proceed, with all parameters included for the final iteration. If keyword SUPER is present, superparameters will be created (see Tonkin and Doherty [WRR, 41, W10412, doi:10.1029/2005WR003995, 2005]).\n\nThe Levenberg-Marquardt method switches continuously from a gradient method (large lambda, see command >>> LEVENBERG) far from the minimum to a Gauss-Newton step as the minimum is approached and lambda is reduced.\n\nExample\n> COMPUTATION\n>> OPTION\n>>> use LEVENBERG-MARQUARDT minimization algorithm (default)\n<<<\n>> CONVERGE\n>>> initial LEVENBGERG parameter lambda is : 0.001 (default)\n>>> MARQUARDT parameter nue is : 10.000 (default)\n<<<\n<<" ]
[ null, "https://itough2.lbl.gov/wp-content/uploads/sites/9/2019/02/dpLevMar-LM.gif", null, "https://itough2.lbl.gov/wp-content/uploads/sites/9/2019/02/Dij-LM.gif", null ]
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https://file.scirp.org/Html/2-7402861_60340.htm
[ " The Harmonic Approximation in Heavy-Ion Reaction Study\n\nApplied Mathematics\nVol.06 No.11(2015), Article ID:60340,10 pages\n10.4236/am.2015.611161\n\nThe Harmonic Approximation in Heavy-Ion Reaction Study\n\nGodwin Joseph Ibeh1*, Elijah Dika Mshelia2\n\n1Department of Physics, Nigerian Defence Academy, Kaduna, Nigeria\n\n2Department of Physics, University of Abuja, Abuja, Nigeria\n\nEmail: *[email protected]\n\nCopyright © 2015 by authors and Scientific Research Publishing Inc.", null, "", null, "", null, "Received 15 August 2015; accepted 13 October 2015; published 16 October 2015\n\nABSTRACT\n\nThe derivation of the harmonic approximation of the Hamiltonian of a model of coupled three- dimensional harmonic oscillator is presented. It is shown how the splitting of the total Hamiltonian into the intrinsic and collective Hamiltonians leads to the description of the mechanism for energy dissipation in physical systems.\n\nKeywords:\n\nHarmonic Approximation, Energy Dissipation, Coupled Oscillators, Heavy-Ions, Dinuclear System, Cluster Model", null, "1. Introduction\n\nInvestigation into the mechanism of energy dissipation in heavy-ion reactions has been carried out by different authors from different approaches, an example is the quantum dynamical model of Diaz-Torres, Hinde, Dasgupta, Milburn and Tostevin, which is based on the dissipative dynamics of open quantum systems in this model both deep-inelastic process and quantum tunneling were treated with a quantum mechanical coupled-channels approach and . For some review papers and other approaches to heavy-ion collisions studies, see the following refs. - .\n\nMshelia, Scheid and Greiner formulated a nuclear energy dissipation theory to account for energy dissipation that occurs in heavy-ion collisions . This was described quantum mechanically as resulting from the coupling of collective degrees of freedom to intrinsic excitations. The formalism has been tested on several analytically solvable models of oscillators coupled to free motion in one-dimension . Recently, Ibeh and Mshelia presented a realistic but complex model for investigating the energy dissipation in physical systems , which was an extension of the one-dimensional models of previous work . The results obtained showed a marked improvement to the previous models comparative to the exact results.\n\nIn this paper, we consider some of the salient features in the complex model of Ibeh and Mshelia which consists of three-dimensional coupled oscillators located at the corners of a tetrahedron, three oscillators at the corner of the triangular base representing intrinsic motion while the one at the apex represents the collective motion . In Section 2, we present the derivation of the potential energy and the kinetic energy, leading to the equation of motion of the system. Section 3 deals with the quantization of the Hamiltonian of the dissipative system. In Section 4, the solution of the total and intrinsic Schrödinger equations is presented, while Section 5 consists of the method of determining the probability distribution function.\n\n2. The Classical Hamiltonian\n\nBy the symmetry consideration of the arrangement of four particles in space Figure 1 gives the schematic of the vibrating system, consisting of three-dimensional coupled oscillators located at the corners of a tetrahedron- three oscillators at the corners of the triangular base representing intrinsic motion while one at the apex representing collective motion. All oscillators are coupled to each other elastically. Their equilibrium positions are as follows: the particle of mass M is at the point", null, "at the apex of the tetrahedron while the other\n\nthree particles are positioned at", null, ",", null, ",", null, "located at the corners of the triangular base.\n\nFor harmonic vibration recall that in classical mechanics - , it is shown that near the equilibrium position the potential energy of the system may be developed in a Taylor series i.e.,", null, "(1)\n\nin this the only term of interest is the third term, which is sufficient for small amplitude of vibration, so that the harmonic potential energy is approximated to", null, "(2)\n\nin which the", null, "’s are constants given by", null, "(3)\n\nThe quantities", null, "form a symmetric matrix. Thus the potential energy of the system of Figure 1 about the equilibrium positions of the particles, becomes,", null, "(4)\n\nFigure 1. A system of three small mass coupled to each other and each coupled to a large mass.\n\nwhere the constants,", null, "and", null, ".\n\nSimilarly the quadratic kinetic energy of the system is", null, "(5)\n\nwhere,", null, ",", null, ", and, , are velocities. i = 1, 2, 3.\n\n3. The Quantum Energy Dissipation\n\nIn Ibeh and Mshelia the quantized Hamiltonian describing the dissipation of energy from the collective motion into intrinsic degrees of freedom is given as:\n\n(6)\n\nwhere the intrinsic and collective Hamiltonians are explicitly stated as:\n\n(7)\n\nand\n\n(8)\n\nThe collective Hamiltonian is assumed to be that of a free particle with mass, M and described by coordinates. The three oscillators in Figure 1 described by the coordinates have the same mass m and are elastically coupled to each other and to the collective motion. Energy can be dissipated from the collective degree of freedom into intrinsic excitations.\n\n3.1. Normal Modes of Vibration\n\nThe total Hamiltonian in Equation (6) is given in terms of Equations (7) and (8) as\n\n(9)\n\nFrom the above consideration we observe that the kinetic energy matrix is diagonal while the potential energy matrix is non-diagonal due to the products, , , , , , , , , , etc. these off-diagonal terms give rise to the coupling of the collective and intrinsic motions and the coupling of the intrinsic oscillators to each other. By a transformation to normal coordinates the quadratic forms of the kinetic and potential energies in Equation (9), can be reduced simultaneously to sums of squares in these coordinates and their derivatives and hence make the coupled-oscillator problem separable into independent motions, each with a particular normal frequencies - .\n\nThe normal frequencies are determined by the secular equation\n\n(10)\n\nwhere the coefficients and are the elements of the kinetic and potential energy matrices, respectively.\n\nUsing the matrices of the kinetic and potential energies according to Equation (9), we obtain from Equation (10) the following twelve eigenfrequencies:\n\n(11)\n\nwhere, the constants appearing in the eigenfrequencies above are defined as follows:\n\nNote the two double degenerate frequencies namely Ω1 = Ω3 and Ω2 = Ω4 and the two non-degenerate eigenfrequencies Ω5 and Ω6 describing the motion in which all the four particles vibrate about their common equilibrium configuration. The six eigenfrequencies: Ω7; Ω8; Ω9; Ω10; Ω11 and Ω12 which vanish are assumed to consists of the three zero eigenfrequencies Ω7, Ω8, Ω9, corresponding to the eigenmodes describing a uniform translational motion of the system as a whole, while the remaining three zero eigenfrequencies Ω10, Ω11 and Ω12 have no direct bearing on the theory of energy dissipation in this work. The corresponding transformations to normal coordinates are obtained as:\n\n(12)\n\nIn terms of the normal coordinates the quantum mechanical total Hamiltonian is\n\n(13)\n\n3.2. The Solutions of the Schrödinger Equation for the Total and Intrinsic Hamiltonians\n\nWe now obtain solutions of the time-independent Schrödinger equation with the decoupled total Hamiltonian H given by Equation (13).\n\n(14)\n\nSince H describes a free translational motion of the centre of mass and the decoupled harmonic oscillators in the g1, g2, g3, g4, g5 and g6 degrees of freedom the eigenvalues and eigenfunctions are obtained as,\n\n(15)\n\nand\n\n(16)\n\nwhere, the quantum numbers are. and, , are the wave numbers of the plane-wave functions for the centre of mass, normalized by means of the Dirac δ-function are given by\n\n(17)\n\nThe normalized, bound state, wave functions of the harmonic oscillators are written as\n\n(18)\n\nThe quantity is a Hermite polynomial of order and the s are the inverse oscillator lengths given by\n\n, (19)\n\nthe normalization constant occurring in Equation (19) is defined by\n\n. (20)\n\nThe total wave function in Equation (16) is normalized as follows:\n\n(21)\n\nThe intrinsic Hamiltonian can be stated in terms of intrinsic coordinates defined as following\n\n(22)\n\nThe resulting eigenvalue equation of the intrinsic Hamiltonian is\n\n(23)\n\nwhere are the intrinsic normal coordinates defined in terms of the intrinsic coordinates given in Equation (22).\n\nSolving Equation (23) results in the eigenvalues\n\n(24)\n\nAnd the following set of eigenfrequencies and eigenfunctions:\n\n(25)\n\nwhere, the constants appearing in the eigenfrequencies above are defined as follows:\n\nthe normalized intrinsic oscillator eigenfunctions:\n\n, (26)\n\nwhere, the intrinsic inverse oscillator lengths and normalization constants are respectively,\n\n, (27)\n\n(28)\n\nFrom Equation (26) the total intrinsic wave-function becomes\n\n(29)\n\n4. The Probability Density Functions\n\nThe fact that the intrinsic Hamiltonian eigenfunctions obtained form a complete set, by use of the completeness relation the total wave function is expanded in terms of the complete or-\n\nthonormal set of oscillator functions. The normalization of gives\n\n(30)\n\nsince the’s are orthonormal. The expansion coefficients represent the probability amplitude for excitation of the intrinsic motion .\n\nOn the other hand, the normalization of with respect to the variables g1, g2, g3, g4, g5 and g6 gives\n\n(31)\n\nThe relationship between the left hand and the right hand of Equations (30) and (31) is given by the transformation\n\n(32)\n\nWhen values are substituted the Jacobian is\n\n(33)\n\nComparing Equations (31), (32) and (33) the normalization condition\n\n(34)\n\nEquation (34) gives a measure for the probability for intrinsic excitation from collective motion . It should be noted that the derivation of Equation (34) demonstrates that the form of the collective amplitude, satisfy the normalization condition for the total wave function.\n\nThe collective amplitude is the expansion coefficient of the total wave function when expanded in terms of the complete orthonormal set of oscillator functions, and its form can be obtained by using Equations (12), (16), (17), (18) and (22), which then leads to the probability distribution as functions of interesting physical parameters for example, energy, intrinsic and collective quantum numbers, etc.\n\n5. Conclusions\n\nThis work has shown that the harmonic approximation of the Hamiltonian of coupled oscillators leads to a Schrödinger equation which describes the coupling of collective degree of freedom, represented by free motion with intrinsic degrees of freedom, represented by three coupled oscillators. This model explains the mechanism for energy dissipation in a physical system, based on the coupling of intrinsic and collective degrees of freedom. The model can be extended to nuclear fission and heavy-ion reactions, where the collective degree of freedom is the relative coordinates of the two heavy-ions and the intrinsic degrees of freedom are the single-particle degrees of freedom .\n\nFurthermore, of current interest and one which is an extension of the above model is the cluster model consisting of a dinuclear system which is not easily solvable analytically because it includes other degrees of freedoms such as butterfly, belly-dancer-type motions, γ-and β-vibrations, etc., of individual nuclei, this model is based on the assumption that cluster-type shapes are produced in the mass asymmetry of nuclear molecules. Theoretical and experimental evidences exist that show that this model is capable of explaining many of the features of deformed heavy nuclei - . An example of such features is the resent work of Adamian, Antonenko and Lenske, in which the linear response theory was used to calculate the mass parameters for collective variables of the dinuclear systems formed in cold fusion reactions and found that the microscopic mass parameter in the neck is larger than the one obtained using the hydrodynamical model .\n\nCite this paper\n\nGodwinJoseph Ibeh,Elijah DikaMshelia, (2015) The Harmonic Approximation in Heavy-Ion Reaction Study. Applied Mathematics,06,1831-1841. doi: 10.4236/am.2015.611161\n\nReferences\n\n1. 1. Diaz-Torres, A., Hinde, D.J., Dasgupta, M., Milburn, G.J. and Tostevin, J.A. (2008) Dissipative Quantum Dynamics in Low-Energy Collisions of Complex Nuclei. Physical Review C, 78, Article ID: 064604.\nhttp://dx.doi.org/10.1103/physrevc.78.064604\n\n2. 2. Diaz-Torres, A., Hinde, D.J., Dasgupta, M., Milburn, G.J. and Tostevin, J.A. (2009) Coupled-Channels Approach for Dissipative Quantum Dynamics in Near-Barrier Collisions. International Conference on New Aspects of Heavy-Ion Barrier, Chicago.\nhttp://dx.doi.org/10.1063/1.3108859\n\n3. 3. Swiatecki, W.J. and Bjфrnholm, S. (1972) Fission and Fusion Dynamics. Physics Reports, 4, 326-342.\nhttp://dx.doi.org/10.1016/0370-1573(72)90003-8\n\n4. 4. N&oumlrenberg, W. and Weidenmüller, H.A. (1976) Introduction to the Theory of Heavy-Ion Collisions. Lecture Notes in Physics 5, Springer-Verlag, Berlin.\n\n5. 5. Hasse, R.W. (1978) Approaches to Nuclear Friction. Reports on Progress in Physics, 41, 1027-1101.\nhttp://dx.doi.org/10.1088/0034-4885/41/7/002\n\n6. 6. Weidenmüller, H.A. (1980) Transport Theories of Heavy-Ion Reactions. Progress in Particle and Nuclear Physics, 3, 49.\nhttp://dx.doi.org/10.1016/0146-6410(80)90030-7\n\n7. 7. Mshelia, E.D. (1997) Nuclear Science and Technology in Human Progress. (Unpublished University Inaugural Lecture). Abubakar Tafawa Balewa University, Bauchi.\n\n8. 8. Aritomo, Y., Hagino, K., Nishio, K. and Chiba, S. (2012) Dynamical Approach to Heavy-Ion Induced Fission Using Actinide Target Nuclei at Energies around the Coulomb Barrier. Physical Review C, 85, Article ID: 044614.\nhttp://dx.doi.org/10.1103/PhysRevC.85.044614\n\n9. 9. Liu, Z.H. and Bao, J.D. (2013) Possibility to Produce Element 120 in the 54Cr+248Cm Hot Fusion Reaction. Physical Review C, 87, Article ID: 0344616.\nhttp://dx.doi.org/10.1103/PhysRevC.87.034616\n\n10. 10. Gontchar, I.I., Bhattacharya, R. and Chushnyakova, M.V. (2014) Quantitative Analysis of Precise Heavy-Ion Fusion Data at Above-Barrier Energies Using Skyrme-Hartree-Fock Nuclear Densities. Physical Review C, 89, Article ID: 034601.\nhttp://dx.doi.org/10.1103/PhysRevC.89.034601\n\n11. 11. Wen, K., Sakata, F., Li, Z.-X., Wu, X., Zhang, Y. and Zhou, S. (2014) Energy Dependence of the Nucleus-Nucleus Potential and the Friction Parameter in Fusion Reactions. Physical Review C, 90, Article ID: 054613.\nhttp://dx.doi.org/10.1103/PhysRevC.90.054613\n\n12. 12. Mshelia, E.D., Scheid, W. and Greiner, W. (1975) Theory of Energy Dissipation in Heavy-Ion Reactions. Il Nuovo Cimento A, 30, 589-608. http://dx.doi.org/10.1007/BF02730488\n\n13. 13. Mshelia, E.D., Haln, D. and Scheid, W. (1981) Energy Dissipation in a Model of Coupled Oscillators. Il Nuovo Cimento A, 61, 28-55.\nhttp://dx.doi.org/10.1007/BF02776606\n\n14. 14. Mshelia, E.D. and Ngadda, Y.H. (1989) A Stimulation for Energy Dissipation in Nuclear Reactions. Journal of Physics G: Nuclear and Particle Physics, 15, 1281-1290.\nhttp://dx.doi.org/10.1088/0954-3899/15/8/023\n\n15. 15. Ibeh, G.J. and Mshelia, E.D. (2014) Energy Dissipation in a Model of Coupled Three-Dimensional Harmonic Oscillator. Far East Journal of Mathematical Sciences, 88, 107-136.\n\n16. 16. Corben, H.C. and Stehle, P. (1960) Classical Mechanics. John Wiley, New York, 113-131, 364-372.\n\n17. 17. Wells, D.A. (1967) Theory and Problems of Lagrangian Dynamics. Schaum Publication, New York.\n\n18. 18. Marion, J.B. and Thornton, S.T. (1995) Classical Dynamics of Particles and Systems. 4th Edition, Saunders College Publications, New York.\n\n19. 19. Goldstein, H., Poole, C. and Safko, J. (2002) Classical Mechanics. 3rd Edition, Addison-Wesley, San Francisco, 238-258.\n\n20. 20. Wilson Jr., B., Decius, J.C. and Paul, C.C. (1980) Molecular Vibrations. Dover Publications, Inc., New York.\n\n21. 21. Desloge, E.A. (1982) Classical Mechanics. Volume II, Wiley-Interscience, New York, 665-707.\n\n22. 22. Mshelia, E.D. (1995) Method of Normal Coordinates in the Formulation of a System with Dissipation: The Harmonic Oscillator. Il Nuovo Cimento A, 108, 709-721.\nhttp://dx.doi.org/10.1007/BF02813376\n\n23. 23. Schiff, L.I. (1987) Quantum Mechanics. 3rd Edition, McGraw-Hill, New York, 50-52.\n\n24. 24. Greiner, W. (1994) Quantum Mechanics: An Introduction. 3rd Edition, Springer-Verlag, New York, 97-105.\n\n25. 25. Courant, R. and Hilbert, D. (1953) Methods of Mathematical Physics. Interscience Publishers, New York, 424.\n\n26. 26. Bromley, D.A. (1978) Nuclear Molecules. Scientific American, 239, 58-68.\nhttp://dx.doi.org/10.1038/scientificamerican1278-58\n\n27. 27. Volkov, V.V. (1978) Deep Inelastic Transfer Reaction—The New Type of Reactions between Complex Nuclei. Physics Reports, 44, 93-157.\nhttp://dx.doi.org/10.1016/0370-1573(78)90200-4\n\n28. 28. Iachello, F. and Jackson, A.D. (1982) A Phenomenological Approach to α-Clustering in Heavy Nuclei. Physics Letters B, 108, 151-154.\nhttp://dx.doi.org/10.1016/0370-2693(82)91162-5\n\n29. 29. Greiner, W., Park, J.Y. and Scheid, W. (1995) Nuclear Molecules. World Scientific, Singapore.\n\n30. 30. Buck, B., Merchant, A.C. and Perez, S.M. (1998) Systematic Study of Exotic Clustering in Even-Even Actinide Nuclei. Physical Review C, 58, 2049-2060.\nhttp://dx.doi.org/10.1103/physrevc.58.2049\n\n31. 31. Buck, B., Merchant, A.C. and Perez, S.M. (1999) Cluster Structure and Gamma Transitions in Actinides. Physical Review C, 59, 750-754.\nhttp://dx.doi.org/10.1103/PhysRevC.59.750\n\n32. 32. Adamian, G.G., Antonenko, N.V. and Scheid, W. (2000) Isotopic Dependence of Fusion Cross Sections in Reactions with Heavy Nuclei. Nuclear Physics A, 678, 24-38.\nhttp://dx.doi.org/10.1016/s0375-9474(00)00317-1\n\n33. 33. Mshelia, E.D. and Scheid, W. (2004) Collective Dynamics of a Dinuclear System. The European Physical Journal A, 20, 251-254.\nhttp://dx.doi.org/10.1140/epja/i2003-10102-7\n\n34. 34. Li, W., Nan, W., Fei, J., Hushan, X., Wei, Z., Li, Q.F., et al. (2006) Particle Transfer and Fusion Cross-Section for Super-Heavy Nuclei in Dinuclear System. Journal of Physics G, 32, 1143-1155.\nhttp://dx.doi.org/10.1088/0954-3899/32/8/006\n\n35. 35. Kalandarov, S.A., Adamian, G.G., Antonenko, N.V. and Scheid, W. (2011) Role of Angular Momentum in the Production of Complex Fragments in Fusion and Quasifission Reactions. Physical Review C, 83, Article ID: 054611.\nhttp://dx.doi.org/10.1103/PhysRevC.83.054611\n\n36. 36. Kalandarov, S.A., Adamian, G.G, Antonenko, N.V., Scheid, W., Heinz, S., Comas, V., Hofman, S., Khuyagbaatar, J., Ackermann, D., Heredia, J., HeBberger, F.P., Kindler, B., Lommel, B. and Mann, R. (2011) Emission of Cluster with Z > 2 from Excited Actinide Nuclei. Physical Review C, 84, Article ID: 054607.\nhttp://dx.doi.org/10.1103/PhysRevC.84.054607\n\n37. 37. Kalandarov, S.A., Adamian, G.G., Antonenko, N.V., Scheid, W. and Wieleczko, J.P. (2011) Role of the Entrance Channel in the Production of Complex Fragments in Fusion-Fission and Quasifission Reactions in the Framework of the Dinuclear System Model. Physical Review C, 84, Article ID: 064601.\nhttp://dx.doi.org/10.1103/PhysRevC.84.064601\n\n38. 38. Bansal, M., Sahila, C. and Rajk, G. (2012) Dynamical Cluster-Decay Model Using Various Formulations of a Proximity Potential for Compact Non-Coplanar Nuclei: Application to the 64Ni+100Mo Reaction. Physical Review C, 86, Article ID: 034604. http://dx.doi.org/10.1103/physrevc.86.034604\n\n39. 39. Adamian, G.G., Antonenko, N.V. and Lenske, H. (2015) Role of the Neck Degree of Freedom in Cold Fusion Reactions. Physical Review C, 91, Article ID: 054602. http://dx.doi.org/10.1103/PhysRevC.91.054602\n\nNOTES\n\n*Corresponding author." ]
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https://www.simplexety.com/
[ "# Simplexety V8.6\n\n## »The Calculator for Windows 10«\n\nSimplexety is a comprehensive freeware software utility specifically designed to help you perform various mathematical operations. Whether you are mathematics teacher, a student or an engineer, this utility proves it's not just a simple scientific calculator.\n\nComprehensive and rich-featured GUI\n\nAt first glance, the interface of the application may overwhelm you, because it contains numerous buttons, mathematical expressions, symbols and tabs that might get you confused, especially if you are a novice user. But once you get used to its layout, you can easily perform complex operations with just a few mouse clicks.\n\nCalculate textbook equations with ease\n\nSimplexety supports several dedicated parameters that enable you to perform various mathematical operations, such as subtraction, addition, division, multiplication, as well as trigonometric, parametric or polar functions.\n\nWith Simplexety, you can calculate integrals, derivatives and numerous equations based on well-known abstarct mathematical theories that can be found in science and mathematics textbooks.\n\nBesides being able to select the formula you want to compute, you can also edit equations accourding to your needs, but keep in mind that in order to use Greek characters, you need to double-click each symbol. The generated results can be copied to the Clipboard or the entire content can be saved as a file.\n\nKeep track of time while you perform calculations\n\nOther options, enable you to choose the measurement units for trigonometric functions or create custom functions and constants.\n\nThe application's built-in date and time parser allows you to perform various calculations to determine the current year, week, day, moon phase, season or epoch.\n\nFurthermore, you can use the Graph function to display each equation using the Cartesian coordinate pane.\n\nFully-featured mathematical calculator\n\nAll in all, Simplexety is a sophisticated software application contrary to what its name may suggest. It enables you to compute complex mathematical equations, while allowing you to create and run VBScript codes.\n\nSimplexety is established with four comfortable Formula/Code Editors and a plotting page to plot the functions and formulas.\n\n• Scientific Editor\n• Form Parser Editor\n• Date/Time Parser Editor\n• VBScript Editor\n• Plotting Formulas\n\nYou can edit the formulas and code, quickly and easily, either expressed in the Form or Scientific Editor. The VBScript Editor can be used to write short Visual Basic Script programs.\n\nYou can transfer the formula from the Form to the Scientific Editor and via command to the VBScript Editor.\n\nIf there is a fault on a formula string, then the program opens a separate window where you can see the position and the reason of the error.\n\nSimplexety was reviewed by Alexandra Savin, SOFTPEDIA" ]
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https://www.latin-is-simple.com/en/vocabulary/noun/3989/
[ "### Declension\n\nO-Declension / Gender: masculine\n\n### Forms\n\nSingular Plural\nNom. calculuscalculi\nGen. calculicalculorum\nDat. calculocalculis\nAcc. calculumcalculos\nVoc. calculecalculi\nAbl. calculocalculis" ]
[ null ]
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https://www.physicsforums.com/threads/why-launching-closer-to-the-equator-constitutes-an-advantage.993712/
[ "# Why launching closer to the equator constitutes an advantage\n\n• I\n\n## Summary:\n\nI would like to discuss why launching closer to the equator is physically the most efficient approach.\nI recently realized that some of the most used Space Centers (for instance the Kennedy Space Center, Merritt Island, FL (US), by NASA, the Guiana Space Center ,French Guiana, by ESA and the Baikonur Space Center ,Kazakhstan's area leased to Russia, by Roscosmos) are relatively close to the Equator and I was wondering why this is advantageous.\n\nI first thought that it may be related to energy efficiency and I indeed found a similar analysis here.\n\n$$\\frac{\\Delta E}{m} = \\frac{E_f - E_i}{m} = \\frac{E_f - (\\mathrm{KE}_i + \\mathrm{PE}_i)}{m}$$\n$$= -\\frac{GM}{r_f} - \\frac{1}{2} v_i^2 + \\frac{GM}{r_i} \\\\ = \\frac{GM}{R_E} \\left( 1 - \\frac{1}{\\alpha} \\right) - \\frac{1}{2} \\left( \\frac{2 \\pi R \\sin \\theta}{T} \\right)^2 \\tag{1}$$\n\nWhere\n\n$$PE=-\\int_{\\infty}^{r} \\vec F \\cdot d \\vec r'=-\\int_{\\infty}^{r} - \\frac{GMm}{r'^2} \\hat r' \\cdot d \\vec r' = -\\frac{GMm}{r}$$\n\n$$r_i=R_E, \\ r_f= \\alpha R_E, \\ \\alpha \\ \\text{is finite and greater than 1}$$\n\n$$v_i=\\frac{\\text{arc length}}{time}=\\frac{2 \\pi R \\sin \\theta}{T}$$\n\nWhere I've used the standard definition of latitude i.e.", null, "And I assumed ##\\theta## is small (as we are close to the equator), so that the chord is (approximately) equal to the arc length.\n\nSo based on the above analysis we see that the required energy per unit mass is maximum at the equator, which a priori means that launching from the equator is inefficient in terms of energy! (for those who check the link: tparker uses the an unconventional definition of latitude; he measures it from one of the poles; that is why he gets minimum energy at the Equator).\n\nOK so at this point I thought 'well so there must be another factor that compensates the inefficiency in terms of energy'. I suspect that is the fact that objects on the equator (i.e. at ##\\theta=0##) get the fastest rotational speed of any other ##\\theta##, which means they need to use less fuel. Does that really compensate?\n\n•", null, "etotheipi\n\nRelated Classical Physics News on Phys.org\n$$v_i=\\frac{\\text{arc length}}{time}=\\frac{2 \\pi R \\sin \\theta}{T}$$\nIf vi is the initial speed than it is\n\n$$v_i=\\frac{\\text{arc length}}{time}=\\frac{2 \\pi R \\cos \\theta}{T}$$\n\nwith the definition of latitude you are using.\n\nI suspect that is the fact that objects on the equator (i.e. at ##\\theta=0##) get the fastest rotational speed of any other ##\\theta##, which means they need to use less fuel.\nThat't what the amended equation above says. That means it is already included into the calculation. Other factors are the reduced gravity at the equator (due to the flattening of Earth) and the fact that many satellites go into equatorial orbits.\n\n•", null, "etotheipi and JD_PM\nkuruman\nHomework Helper\nGold Member\nI always thought it's because the apparent weight of the rocket is less nearer the equator because of the centrifugal force that is zero at the poles and increases as you go south or north fro there.\n\n@DrStupid thanks, now everything makes sense! (i.e. the required energy per unit mass is minimum at the equator).\n\nI always thought it's because the apparent weight of the rocket is less nearer the equator because of the centrifugal force that is zero at the poles and increases as you go south or north fro there.\nMmm I've read a bit on this.\n\nGravity would be weaker on the equator due to the centrifugal force i.e.\n\n$$g_{\\text{eff}}:= g - \\omega^2 R_E$$\n\nPlugging numbers into we get ##g_{\\text{eff}} \\sim 3 \\times 10^{-2} m/s^2##. However the experimental result is ##g_{\\text{eff}} \\sim 5 \\times 10^{-2} m/s^2##. Such a difference is justified by means of the centrifugal force.\n\njbriggs444\nHomework Helper\n2019 Award\nI always thought it's because the apparent weight of the rocket is less nearer the equator because of the centrifugal force that is zero at the poles and increases as you go south or north fro there.\nI do not think that it is helpful to adopt the rotating frame and consider potential resulting from the centrifugal force field. That potential diverges as one gets far from the Earth, so any conservation of energy argument is wasted.\n\nI do not think that it is helpful to adopt the rotating frame and consider potential resulting from the centrifugal force field. That potential diverges as one gets far from the Earth, so any conservation of energy argument is wasted.\nOf course the total energy is not conserved because the rotating frame is not inertial. However, the centrifugal force is conservative. Therefore it shouldn't be a problem to use the corresponding potential ##- {\\textstyle{1 \\over 2}}\\omega ^2 r^2##.\n\njbriggs444\nHomework Helper\n2019 Award\nOf course the total energy is not conserved because the rotating frame is not inertial. However, the centrifugal force is conservative. Therefore it shouldn't be a problem to use the corresponding potential ##- {\\textstyle{1 \\over 2}}\\omega ^2 r^2##.\nEnergy is conserved in the rotating frame. However, potential energy is not zero at infinity. It is, instead, infinite.\n\n•", null, "etotheipi\nEnergy is conserved in the rotating frame.\nIf you include the potential of the centrifugal force, than yes. I was under the impression that you don't want to do that.\n\nHowever, potential energy is not zero at infinity. It is, instead, infinite.\nI don't see the problem. The kinetic energy of a body at rest in an inertial system goes positive infinite in the rotating frame and the potential energy goes negative infinite. That fits together. Do I miss something?\n\n•", null, "etotheipi\nkuruman\nHomework Helper\nGold Member\nI asked about this a friend who is at JPL and he said that launch sites vary depending on the orbit, trajectory and mission. Near-equatorial sites are used for geosynchronous orbits because they provide a relatively higher tangential velocity component while for polar orbits launch sites are farther up north to minimize the tangential component, which is not needed, thus saving fuel.\n\n•", null, "vanhees71, Dale and etotheipi\njbriggs444\nHomework Helper\n2019 Award\nIf you include the potential of the centrifugal force, than yes. I was under the impression that you don't want to do that.\nDoing it is fine. Expecting it to be useful in a computation of energy needed to escape is questionable. If you need infinite energy to escape to infinity and you have infinite energy coming from the centrifugal field, how is a little bit of a boost to start with supposed to help?\n\n•", null, "etotheipi\nTo achieve orbit, you need to achieve orbital velocity (in inertial space). Whatever it is. Say 18000 mph (in inertial space). If you launch from the pole, the Earth rotation rate contributes zero to your velocity (in inertial space) If you launch with the Earth rotation, you are already going over 1000 MPH in inertial space, (to see this take the circumference of the Earth approx 25000 mile and divide by 24 hours; hence > 1000 mph)\n\nYou now need 18000 mph - 1000 mph or 17000 mph. Note if you launch the wrong way, you now need to add 19000 mph to get to 18000 mph (inertial).\n\nExpecting it to be useful in a computation of energy needed to escape is questionable. If you need infinite energy to escape to infinity and you have infinite energy coming from the centrifugal field, how is a little bit of a boost to start with supposed to help?\nRockets are usually not lauched to infinity. Most payloads go into Earth orbits. If a rotating frame is useful or not depends on the circumstances. In case of a geosynchronous orbit it would be my 1st choice.\n\n•", null, "jbriggs444" ]
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http://www.tuliaobiz.com/
[ "| 加入桌面 | 手机版 | 无图版", null, "", null, "• a\n• b\n• c\n• d\n• e\n• f\n• g\n• h\n• i\n• j\n• k\n• l\n• m\n• n\n• o\n• p\n• q\n• r\n• s\n• t\n• u\n• v\n• w\n• x\n• y\n• z", null, "", null, "站内信(0)", null, "会员服务 | 发布信息 | 会员中心 | 返回首页" ]
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https://infogalactic.com/info/Cubic_centimetre
[ "# Cubic centimetre\n\nA cubic centimetres (or cubic centimeters in US English) (SI unit symbol: cm3; non-SI abbreviations: cc and ccm) is a commonly used unit of volume that extends the derived SI-unit cubic metre, and corresponds to the volume of a cube that measures 1 cm × 1 cm × 1 cm. One cubic centimetre corresponds to a volume of 1/1,000,000 of a cubic metre, or 1/1,000 of a litre, or one millilitre; thus, 1 cm3 ≡ 1 ml. The mass of one cubic centimetre of water at 3.98 °C (the temperature at which it attains its maximum density) is closely equal to one gram. Note that SI supports only the use of symbols and deprecates the use of any abbreviations for units. Hence cm3 is preferred to cc or ccm.\n\nMany scientific fields have replaced cubic centimeters with milliliters. The medical and automotive fields in the United States still use the term cubic centimetre. Much of the automotive industry outside the U.S. has switched to litres. The United Kingdom uses millilitres in preference to cubic centimetres in the medical field, but not the automotive. Most other English-speaking countries follow the UK example.[citation needed]\n\nThere is currently a movement within the medical field to discontinue the use of cc in prescriptions and on medical documents, as it can be misread as \"00\". This could cause a hundredfold overdose of medication, which could be dangerous or even lethal. In the United States, such confusion accounts for 12.6% of all errors associated with medical abbreviations.", null, "One complete cycle of a four-cylinder, four-stroke engine. The volume displaced is marked in orange.\n\nIn automobile engines, \"cc\" refers to the total volume of its engine displacement in cubic centimetres. The displacement can be calculated using the formula", null, "$d = {\\pi \\over 4} \\times b^2 \\times s \\times n$\n\nwhere d is engine displacement, b is the bore of the cylinders, s is length of the stroke and n is the number of cylinders.\n\nConversions" ]
[ null, "https://infogalactic.com/w/images/thumb/8/8a/Displacement.gif/250px-Displacement.gif", null, "https://infogalactic.com/w/images/math/9/7/6/97674d0054e498e208c035c511f5dfb9.png ", null ]
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https://www.49ccscoot.com/calculators.html
[ "49ccScoot.Com\nCalculators\n\nThis is a collection of calculators that may be helpful to scooter enthusiasts.\n\n Fuel/Oil Mix Ratio Calculator Enter the amount of fuel and the desired mix ratio(__:1) and this calculator will tell you the amount of oil needed in both ounces and milliliters. Gallons of Fuel Ounces of Oil Desired Mix Ratio Milliliters of Oil\n Fuel/Oil Economy Calculator If you enter all the required fields, this calculator can tell you the fuel economy, fuel cost, oil cost for 2 strokes, and cost per mile for fuel and oil. If you are using this calculator for a 4 stroke you can leave the oil fields blank. MPG Miles Traveled Fuel Cost (Trip) Gallons of Fuel Used Oil Cost (Trip) Fuel Cost Per Gallon Fuel Cost Per Mile Oil Mix Ratio Oil Cost Per Mile Oil Cost Per Quart Total Cost Per Mile\nTire Diameter And Circumference\n\nEnter the tire width(mm), aspect ratio, and wheel diameter(in) and this calculator will tell you the tire's diameter and circumference in inches and millimeters. Circumference in mm is often used to calibrate aftermarket speedometers.\n\n 130/70P12 Width(mm) Aspect Ratio Wheel Diameter(in)\nWidth Diameter (in)\nAspect Ratio Diamter (mm)\nWheel Diameter Circumference (in)\nCircumference (mm)\n Speed Calculator Enter tire circumference(in), final drive ratio(__:1), and engine RPM and this calculator will give you the maximum speed for that setup. This may be a bit inaccurate for CVT driven scooters. You would actually need to know the RPM that the clutch bell is turning to be completely accurate. This calculator can give you a good idea of max speed differences using different tire sizes, different gear ratios, or setups that rev a little different. Tire Circumference Final Drive Ratio Speed RPM\n Speedometer Tire Size Correction Calculator This calculator can help you improve the accuracy of speedometers that require a tire size input for calibration. Enter the current tire size in your gauge (usually circumference in mm). Then you will need to have a trip odometer reading from a ride as well as a known accurate mileage from the same ride (usually GPS info) to enter. The calculator will output a corrected tire size for the gauge based on your inputs. Current Tire Size Speedometer Mileage Corrected Tire Size Actual Mileage\n Displacement Calculator Enter the bore and stroke in millimeters and the number of cylinders and this calculator will tell you the displacement in both cubic centimeters and cubic inches. Bore Displacement (cc) Stroke Displacement (ci) # of Cylinders\n Piston Ring End Gap Calculator Enter the bore in millimeters and this calculator will tell you the compression ring end gaps in inches for two-stroke and four-stroke engines. Bore 4T Top Ring 4T Second Ring 2T Rings\n Compression Ratio Calculator Enter the volume of the cylinder and the volume of the combustion chamber and this calculator will tell you the compression ratio (referred to as secondary compression in 2 strokes). For multi-cylinder engines, just use the columes from one cylinder. If you wish to find the effective (corrected) compression ratio of a 2 stroke engine, enter the effective cylinder volume instead of the total cylinder volume. Don't forget to add the volume of the cylinder head gasket to the volume of the combustion chamber. You can find the head gasket's volume by using the displacement calculator above (enter the gasket's thickness in mm into the stroke field). You also need to take deck height and the piston (dished, flat, or domed) into account. Cylinder Volume Compression Ratio Combustion Chamber Volume\n Combustion Chamber Volume This calculator will tell you the combustion chamber volume necessary to achieve your desired compression ratio (__:1). If you are using a head gasket, remember that it's volume needs to be subtracted from the combustion chamber volume shown here to get a correct result. Desired Compression Ratio Combustion Chamber Volume Cylinder Volume\n Primary Compression Ratio Enter the crankcase volume(cc) and cylinder volume(cc) and this calculator will show you the primary compression ratio of a 2 stroke engine. Crankcase Volume Primary Compression Cylinder Volume\n 1/4 Mile Calculator Enter 1/4 mile elapsed time (E.T.) in seconds and trap speed along with the vehicle weight with driver (lb) and this calculator will give you an estimate of horsepower and torqe to the wheel(s) as well as power to weight ratio (HP per lb). 1/4 Mile E.T. Horsepower (E.T. Method) 1/4 Mile Trap Speed Torque (E.T. Method) Vehicle Weight Horsepower (Trap Method) Engine RPM (Trap) Torque (Trap Method) Horsepwer (Average of ET and Trap Methods) Torque (Average of ET and Trap Mehods) Power To Weight Ratio (Average)" ]
[ null ]
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https://www.pasqal.com/articles/blog_january_15_2022
[ "Back\n\n# Decompositional QGNN", null, "Decompositional Quantum Graph Neural Network\n\nQuantum Machine Learning is a field that aims to solve Machine Learning problems with quantum algorithms and quantum computing. There exists a large variety of quantum algorithms used in solving such problems, with the most common being Quantum Neural Networks (QNNs). Varieties of QNNs include Quantum Convolutional Neural Network (QCNN), Quantum Generative Adversarial Network (QGAN), and Quantum Graph Neural Network (QGNN). As the names suggest, these algorithms are inspired from their classical counterparts. In this paper, the proposed algorithm is a hybrid quantum-classical algorithm for graph-structured data, which is called Decompositional Quantum Graph Neural Network (DQGNN), and is based on the classical GNN, which is one of the most popular learning tools, especially for dealing with non-Euclidean data. The main differentiator between the DQGNN and previous QGNN implementations is the decompositional aspect of this algorithm, that allows the computation of larger-sized graph-structured data with a fixed-sized quantum circuit with limited number of qubits, regardless of the size of the data. Algorithms based on GNNs have found applications in social network analysis, drug design, combinatorial optimization, and multi-agent learning.\n\nGNNs function on the basis of the neighborhood aggregation strategy, which involves updating the representation of a graph node by recursively aggregating the representations of its neighbors. So far, a variety of GNNs has been realized such as the Relational Graph Convolutional Networks (R-GCN), Graph Isomorphism Networks (GIN), edGNN, Random Walk Graph Neural Networks (RW-GNN), and Factorizable Graph Convolutional Networks (Factor GCN). However, these approaches embed nodes represented as points in a Euclidean space leading to significant structural distortion and information loss during computation. On the other hand, DQGNN is a hybrid quantum-classical algorithm for graph-structured data, that focuses on effective and scalable learning.\n\nDQGNN utilizes tensor and unitary matrices to implement a quantum GNN by designing a quantum circuit and replacing the Euclidean weight matrices of the GNN with unitary matrices, i.e. quantum gates. Utilizing tensor products offers two advantages: i) enlarges the node representation space exponentially such that nodes with different features can be mapped to different representations, and ii) requires significantly fewer model parameters than related deep learning models. DQGNN consists of the following processing steps; 1) A classical computer is used to decompose graphs into subgraphs. 2) The circuit of the mapping method is trained with node features. After training, the node features of the subgraphs are mapped into quantum states by applying the circuit. 3) The quantum circuit is implemented on a quantum device to compute the representations of the different subgraphs sequentially. 4) Finally, a classical computer computes the entropies of the individual representations and combines them. All these steps are iterated for obtaining graph representations for classification.\n\nBesides the proposed decompositional processing strategy, a trainable method is also proposed for mapping data from a Euclidean space to a Hilbert space, which can maintain distance relations and reduce information loss during the mapping.\n\nDQGNN is evaluated experimentally on six graph classification benchmarks. The compared methods include graph kernels, deep learning methods, and quantum machine learning methods. DQGNN is also compared with recent baselines for graph classification: 1) Kernel-based methods: WL subtree kernel, and Subgraph Matching Kernel (CSM), 2) Representative GCNs, including Deep Graph CNN’s (DGCNN) and Relational Graph Convolutional Networks (R-GCN), 3) Representative GNNs, i.e., Graph Isomorphism Network (GIN), edGNN, and RW-GNN. A derivative-free optimization method, UOBYQA is utilized for training DQGNN. A quantum simulator is used to implement quantum machine learning models on a classical computer utilizing codes by Qiskit and Tensorflow Quantum.\n\nThe results demonstrate that DQGNN achieves the best results on 5 out of 6 benchmarks with accuracy close to GNNs, while requiring fewer parameters in comparison. As compared to the GNN model with the least parameters referenced as DGCNN, the authors find that DQGNN achieves similar performance with only 1.68% parameters of the classical counterpart. The performance is also compared with alternative quantum machine learning methods like QSVM (Quantum-enhanced Support Vector Machine) and QCNN (Quantum Convolutional Neural Networks) using the graphlet count vector as the inputs (Gra+QSVM, Gra+QCNN). Results show that Gra+QSVM, Gra+QCNN and Gra+QCNN with the proposed trainable mapping method (Gra+QCNN w/M) demonstrate no improvement on DQGNN. However, as compared to Gra+QCNN, Gra+QCNN w/M achieve higher accuracy, therefore highlighting the effectiveness of the proposed mapping method. For example, in the case of the PROTEINS dataset, the accuracy achieved by DQGNN is 9% higher than that of DQGNN without the mapping. This improvement can be resulted from less information loss in the former case.\n\nDQGNN is a method that can be applied to any application that includes graph-structured data, and offers many advantages compared to other contemporary algorithms. The main advantage lies in the ability to divide the graph into sub-graphs and process each sub-graph one at a time with DQGNN, while using the same quantum circuit. Such methods can help with potential scalability issues that other algorithms might exhibit. Furthermore, it is speculated that the proposed mapping method can enhance the accuracy of alternative quantum machine learning methods, because of less information loss.\n\nDQGNN provides a good insight into transitioning to larger-sized graph-structured data during the NISQ era (limited qubits); requiring fewer parameters but having similar performance to other contemporary quantum algorithms." ]
[ null, "https://www.pasqal.com/_next/image", null ]
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http://blog.smaga.ch/cfa-level-i-buying-stocks-on-margin/
[ "# CFA Level I: Buying stocks on margin.\n\nHi everybody,\n\nToday I’ll try to write several posts on the different things I looked at during my time in Tel Aviv, which will come to an end very early tomorrow morning.\n\nI will also setup soon a page where I will display my progress in terms of score percentage in my practice sessions as time flows towards the exam day.\n\nThe posts I will be adding to the blog mostly concern things you can learn quickly and that will allow you to score easy points in the exam by just applying the formula. The first one of this series has actually been written already, it was concerning Basic and Diluted EPS.\n\nIn this post, I will talk about buying stocks on margin. This might seem at first glance quite complicated, but it’s in fact a quite simple concept. When you buy stocks, brokers will allow you to buy them on margin, that is, they will allow you not to deposit the full amount you would require to buy the stocks and lend you to rest of the amount for a given interest rate $r$. This allows you to gain leverage on the investment. As always when it comes to leverage, it’s a double-edged sword; your gains will be magnified by the leverage effect, but so will your losses.\n\nLet’s take an example which I will you throughout the post: I want to buy 100 stocks priced today at 10. Assuming my broker allow be to buy using an initial margin $m_i$ of 40%, I will have to deposit only $100 \\cdot 10 \\cdot 40\\% = 400$. Now if the price in a year is 11 (that is, a return of 10%) and I decide to sell the stock, I will make a profit on the stock price of $(11-10)*100=100$. The simple case assumes that the broker lend my the extra $600$ for an interest rate $r=0$. My return on the investment is hence $\\frac{400+100}{400} = 25\\%$. This is much bigger that the initial stock return. Another way to compute this simple case is to compute the leverage ratio $LR=\\frac{1}{m_i} = \\frac{1}{0.4}=2.5$ and then multiply it by the return of the stock to get the leveraged return: $10\\% \\cdot 2.5 = 25\\%$. Okay so that’s easy. The CFA Institute might be willing to make this a bit more complex by adding dividends $d=0.5$ to the stock, and setting $r=5\\%$ (the values are taken as examples). The reasoning is still the same:How much was I required to invest? still 400. How much do I get from the increase in price? still 100. How much dividend do I get? $100 \\cdot 0.5=50$. How much interests do I have to pay to the broker? $100 \\cdot 10 \\cdot (1-40\\%) \\cdot 5\\% = 30$. So you can compute the return on the investment as follows: $$\\frac{400+100 + 50 – 30}{400} -1 = \\frac{520}{400}-1 = 30\\%$$ Finally, the last typical question is about margin calls. The idea is that the broker (and the regulators) would want to make sure that you are able to pay your debt if the investment goes bad, as you did not deposit the full amount of the investment. Hence they have a maintenance margin $m_m$ which is a “limit” under which they do not want your margin to go. The price under which you will get a margin call (that is when the broker requires you to refill the account back to the initial margin requirement) is computed as follows: $$P_0 \\frac{1-m_i}{1-m_m}$$ So if we assume in our example that $m_m=25\\%$, then you will have a margin call when the price reaches $10 \\frac{0.6}{0.75} = 8$ So, with basically one formula to remember, you will get some very easy points in the exam!" ]
[ null ]
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https://matplotlib.org/3.1.0/_modules/matplotlib/dviread.html
[ "You are reading an old version of the documentation (v3.1.0). For the latest version see https://matplotlib.org/stable/_modules/matplotlib/dviread.html\n\n# Source code for matplotlib.dviread\n\n\"\"\"\nA module for reading dvi files output by TeX. Several limitations make\nthis not (currently) useful as a general-purpose dvi preprocessor, but\nit is currently used by the pdf backend for processing usetex text.\n\nInterface::\n\nwith Dvi(filename, 72) as dvi:\n# iterate over pages:\nfor page in dvi:\nw, h, d = page.width, page.height, page.descent\nfor x, y, font, glyph, width in page.text:\nfontname = font.texname\npointsize = font.size\n...\nfor x, y, height, width in page.boxes:\n...\n\"\"\"\n\nfrom collections import namedtuple\nimport enum\nfrom functools import lru_cache, partial, wraps\nimport logging\nimport os\nimport re\nimport struct\nimport textwrap\n\nimport numpy as np\n\nfrom matplotlib import cbook, rcParams\n\n_log = logging.getLogger(__name__)\n\n# Many dvi related files are looked for by external processes, require\n# additional parsing, and are used many times per rendering, which is why they\n# are cached using lru_cache().\n\n# Dvi is a bytecode format documented in\n# http://mirrors.ctan.org/systems/knuth/dist/texware/dvitype.web\n# http://texdoc.net/texmf-dist/doc/generic/knuth/texware/dvitype.pdf\n#\n# The file consists of a preamble, some number of pages, a postamble,\n# and a finale. Different opcodes are allowed in different contexts,\n# so the Dvi object has a parser state:\n#\n# pre: expecting the preamble\n# outer: between pages (followed by a page or the postamble,\n# also e.g. font definitions are allowed)\n# page: processing a page\n# post_post: state after the postamble (our current implementation\n# just stops reading)\n# finale: the finale (unimplemented in our current implementation)\n\n_dvistate = enum.Enum('DviState', 'pre outer inpage post_post finale')\n\n# The marks on a page consist of text and boxes. A page also has dimensions.\nPage = namedtuple('Page', 'text boxes height width descent')\nText = namedtuple('Text', 'x y font glyph width')\nBox = namedtuple('Box', 'x y height width')\n\n# Opcode argument parsing\n#\n# Each of the following functions takes a Dvi object and delta,\n# which is the difference between the opcode and the minimum opcode\n# with the same meaning. Dvi opcodes often encode the number of\n# argument bytes in this delta.\n\ndef _arg_raw(dvi, delta):\n\"\"\"Return *delta* without reading anything more from the dvi file\"\"\"\nreturn delta\n\ndef _arg(bytes, signed, dvi, _):\n\"\"\"Read *bytes* bytes, returning the bytes interpreted as a\nsigned integer if *signed* is true, unsigned otherwise.\"\"\"\nreturn dvi._arg(bytes, signed)\n\ndef _arg_slen(dvi, delta):\n\"\"\"Signed, length *delta*\n\nRead *delta* bytes, returning None if *delta* is zero, and\nthe bytes interpreted as a signed integer otherwise.\"\"\"\nif delta == 0:\nreturn None\nreturn dvi._arg(delta, True)\n\ndef _arg_slen1(dvi, delta):\n\"\"\"Signed, length *delta*+1\n\nRead *delta*+1 bytes, returning the bytes interpreted as signed.\"\"\"\nreturn dvi._arg(delta+1, True)\n\ndef _arg_ulen1(dvi, delta):\n\"\"\"Unsigned length *delta*+1\n\nRead *delta*+1 bytes, returning the bytes interpreted as unsigned.\"\"\"\nreturn dvi._arg(delta+1, False)\n\ndef _arg_olen1(dvi, delta):\n\"\"\"Optionally signed, length *delta*+1\n\nRead *delta*+1 bytes, returning the bytes interpreted as\nunsigned integer for 0<=*delta*<3 and signed if *delta*==3.\"\"\"\nreturn dvi._arg(delta + 1, delta == 3)\n\n_arg_mapping = dict(raw=_arg_raw,\nu1=partial(_arg, 1, False),\nu4=partial(_arg, 4, False),\ns4=partial(_arg, 4, True),\nslen=_arg_slen,\nolen1=_arg_olen1,\nslen1=_arg_slen1,\nulen1=_arg_ulen1)\n\ndef _dispatch(table, min, max=None, state=None, args=('raw',)):\n\"\"\"Decorator for dispatch by opcode. Sets the values in *table*\nfrom *min* to *max* to this method, adds a check that the Dvi state\nmatches *state* if not None, reads arguments from the file according\nto *args*.\n\n*table*\nthe dispatch table to be filled in\n\n*min*\nminimum opcode for calling this function\n\n*max*\nmaximum opcode for calling this function, None if only *min* is allowed\n\n*state*\nstate of the Dvi object in which these opcodes are allowed\n\n*args*\nsequence of argument specifications:\n\n'raw': opcode minus minimum\n'u1': read one unsigned byte\n'u4': read four bytes, treat as an unsigned number\n's4': read four bytes, treat as a signed number\n'slen': read (opcode - minimum) bytes, treat as signed\n'slen1': read (opcode - minimum + 1) bytes, treat as signed\n'ulen1': read (opcode - minimum + 1) bytes, treat as unsigned\n'olen1': read (opcode - minimum + 1) bytes, treat as unsigned\nif under four bytes, signed if four bytes\n\"\"\"\ndef decorate(method):\nget_args = [_arg_mapping[x] for x in args]\n\n@wraps(method)\ndef wrapper(self, byte):\nif state is not None and self.state != state:\nraise ValueError(\"state precondition failed\")\nreturn method(self, *[f(self, byte-min) for f in get_args])\nif max is None:\ntable[min] = wrapper\nelse:\nfor i in range(min, max+1):\nassert table[i] is None\ntable[i] = wrapper\nreturn wrapper\nreturn decorate\n\n[docs]class Dvi(object):\n\"\"\"\nA reader for a dvi (\"device-independent\") file, as produced by TeX.\nThe current implementation can only iterate through pages in order,\nand does not even attempt to verify the postamble.\n\nThis class can be used as a context manager to close the underlying\nfile upon exit. Pages can be read via iteration. Here is an overly\nsimple way to extract text without trying to detect whitespace::\n\n>>> with matplotlib.dviread.Dvi('input.dvi', 72) as dvi:\n... for page in dvi:\n... print(''.join(chr(t.glyph) for t in page.text))\n\"\"\"\n# dispatch table\n_dtable = [None] * 256\n_dispatch = partial(_dispatch, _dtable)\n\ndef __init__(self, filename, dpi):\n\"\"\"\nRead the data from the file named *filename* and convert\nTeX's internal units to units of *dpi* per inch.\n*dpi* only sets the units and does not limit the resolution.\nUse None to return TeX's internal units.\n\"\"\"\n_log.debug('Dvi: %s', filename)\nself.file = open(filename, 'rb')\nself.dpi = dpi\nself.fonts = {}\nself.state = _dvistate.pre\nself.baseline = self._get_baseline(filename)\n\ndef _get_baseline(self, filename):\nif rcParams['text.latex.preview']:\nbase, ext = os.path.splitext(filename)\nbaseline_filename = base + \".baseline\"\nif os.path.exists(baseline_filename):\nwith open(baseline_filename, 'rb') as fd:\nl = fd.read().split()\nheight, depth, width = l\nreturn float(depth)\nreturn None\n\ndef __enter__(self):\n\"\"\"\nContext manager enter method, does nothing.\n\"\"\"\nreturn self\n\ndef __exit__(self, etype, evalue, etrace):\n\"\"\"\nContext manager exit method, closes the underlying file if it is open.\n\"\"\"\nself.close()\n\ndef __iter__(self):\n\"\"\"\nIterate through the pages of the file.\n\nYields\n------\nPage\nDetails of all the text and box objects on the page.\nThe Page tuple contains lists of Text and Box tuples and\nthe page dimensions, and the Text and Box tuples contain\ncoordinates transformed into a standard Cartesian\ncoordinate system at the dpi value given when initializing.\nThe coordinates are floating point numbers, but otherwise\nprecision is not lost and coordinate values are not clipped to\nintegers.\n\"\"\"\nwhile self._read():\nyield self._output()\n\n[docs] def close(self):\n\"\"\"\nClose the underlying file if it is open.\n\"\"\"\nif not self.file.closed:\nself.file.close()\n\ndef _output(self):\n\"\"\"\nOutput the text and boxes belonging to the most recent page.\npage = dvi._output()\n\"\"\"\nminx, miny, maxx, maxy = np.inf, np.inf, -np.inf, -np.inf\nmaxy_pure = -np.inf\nfor elt in self.text + self.boxes:\nif isinstance(elt, Box):\nx, y, h, w = elt\ne = 0 # zero depth\nelse: # glyph\nx, y, font, g, w = elt\nh, e = font._height_depth_of(g)\nminx = min(minx, x)\nminy = min(miny, y - h)\nmaxx = max(maxx, x + w)\nmaxy = max(maxy, y + e)\nmaxy_pure = max(maxy_pure, y)\n\nif self.dpi is None:\n# special case for ease of debugging: output raw dvi coordinates\nreturn Page(text=self.text, boxes=self.boxes,\nwidth=maxx-minx, height=maxy_pure-miny,\ndescent=maxy-maxy_pure)\n\n# convert from TeX's \"scaled points\" to dpi units\nd = self.dpi / (72.27 * 2**16)\nif self.baseline is None:\ndescent = (maxy - maxy_pure) * d\nelse:\ndescent = self.baseline\n\ntext = [Text((x-minx)*d, (maxy-y)*d - descent, f, g, w*d)\nfor (x, y, f, g, w) in self.text]\nboxes = [Box((x-minx)*d, (maxy-y)*d - descent, h*d, w*d)\nfor (x, y, h, w) in self.boxes]\n\nreturn Page(text=text, boxes=boxes, width=(maxx-minx)*d,\nheight=(maxy_pure-miny)*d, descent=descent)\n\ndef _read(self):\n\"\"\"\nRead one page from the file. Return True if successful,\nFalse if there were no more pages.\n\"\"\"\nwhile True:\nbyte = self.file.read(1)\nself._dtable[byte](self, byte)\nif byte == 140: # end of page\nreturn True\nif self.state is _dvistate.post_post: # end of file\nself.close()\nreturn False\n\ndef _arg(self, nbytes, signed=False):\n\"\"\"\nRead and return an integer argument *nbytes* long.\nSignedness is determined by the *signed* keyword.\n\"\"\"\nstr = self.file.read(nbytes)\nvalue = str\nif signed and value >= 0x80:\nvalue = value - 0x100\nfor i in range(1, nbytes):\nvalue = 0x100*value + str[i]\nreturn value\n\n@_dispatch(min=0, max=127, state=_dvistate.inpage)\ndef _set_char_immediate(self, char):\nself._put_char_real(char)\nself.h += self.fonts[self.f]._width_of(char)\n\n@_dispatch(min=128, max=131, state=_dvistate.inpage, args=('olen1',))\ndef _set_char(self, char):\nself._put_char_real(char)\nself.h += self.fonts[self.f]._width_of(char)\n\n@_dispatch(132, state=_dvistate.inpage, args=('s4', 's4'))\ndef _set_rule(self, a, b):\nself._put_rule_real(a, b)\nself.h += b\n\n@_dispatch(min=133, max=136, state=_dvistate.inpage, args=('olen1',))\ndef _put_char(self, char):\nself._put_char_real(char)\n\ndef _put_char_real(self, char):\nfont = self.fonts[self.f]\nif font._vf is None:\nself.text.append(Text(self.h, self.v, font, char,\nfont._width_of(char)))\nelse:\nscale = font._scale\nfor x, y, f, g, w in font._vf[char].text:\nnewf = DviFont(scale=_mul2012(scale, f._scale),\ntfm=f._tfm, texname=f.texname, vf=f._vf)\nself.text.append(Text(self.h + _mul2012(x, scale),\nself.v + _mul2012(y, scale),\nnewf, g, newf._width_of(g)))\nself.boxes.extend([Box(self.h + _mul2012(x, scale),\nself.v + _mul2012(y, scale),\n_mul2012(a, scale), _mul2012(b, scale))\nfor x, y, a, b in font._vf[char].boxes])\n\n@_dispatch(137, state=_dvistate.inpage, args=('s4', 's4'))\ndef _put_rule(self, a, b):\nself._put_rule_real(a, b)\n\ndef _put_rule_real(self, a, b):\nif a > 0 and b > 0:\nself.boxes.append(Box(self.h, self.v, a, b))\n\n@_dispatch(138)\ndef _nop(self, _):\npass\n\n@_dispatch(139, state=_dvistate.outer, args=('s4',)*11)\ndef _bop(self, c0, c1, c2, c3, c4, c5, c6, c7, c8, c9, p):\nself.state = _dvistate.inpage\nself.h, self.v, self.w, self.x, self.y, self.z = 0, 0, 0, 0, 0, 0\nself.stack = []\nself.text = [] # list of Text objects\nself.boxes = [] # list of Box objects\n\n@_dispatch(140, state=_dvistate.inpage)\ndef _eop(self, _):\nself.state = _dvistate.outer\ndel self.h, self.v, self.w, self.x, self.y, self.z, self.stack\n\n@_dispatch(141, state=_dvistate.inpage)\ndef _push(self, _):\nself.stack.append((self.h, self.v, self.w, self.x, self.y, self.z))\n\n@_dispatch(142, state=_dvistate.inpage)\ndef _pop(self, _):\nself.h, self.v, self.w, self.x, self.y, self.z = self.stack.pop()\n\n@_dispatch(min=143, max=146, state=_dvistate.inpage, args=('slen1',))\ndef _right(self, b):\nself.h += b\n\n@_dispatch(min=147, max=151, state=_dvistate.inpage, args=('slen',))\ndef _right_w(self, new_w):\nif new_w is not None:\nself.w = new_w\nself.h += self.w\n\n@_dispatch(min=152, max=156, state=_dvistate.inpage, args=('slen',))\ndef _right_x(self, new_x):\nif new_x is not None:\nself.x = new_x\nself.h += self.x\n\n@_dispatch(min=157, max=160, state=_dvistate.inpage, args=('slen1',))\ndef _down(self, a):\nself.v += a\n\n@_dispatch(min=161, max=165, state=_dvistate.inpage, args=('slen',))\ndef _down_y(self, new_y):\nif new_y is not None:\nself.y = new_y\nself.v += self.y\n\n@_dispatch(min=166, max=170, state=_dvistate.inpage, args=('slen',))\ndef _down_z(self, new_z):\nif new_z is not None:\nself.z = new_z\nself.v += self.z\n\n@_dispatch(min=171, max=234, state=_dvistate.inpage)\ndef _fnt_num_immediate(self, k):\nself.f = k\n\n@_dispatch(min=235, max=238, state=_dvistate.inpage, args=('olen1',))\ndef _fnt_num(self, new_f):\nself.f = new_f\n\n@_dispatch(min=239, max=242, args=('ulen1',))\ndef _xxx(self, datalen):\nspecial = self.file.read(datalen)\n_log.debug(\n'Dvi._xxx: encountered special: %s',\n''.join([chr(ch) if 32 <= ch < 127 else '<%02x>' % ch\nfor ch in special]))\n\n@_dispatch(min=243, max=246, args=('olen1', 'u4', 'u4', 'u4', 'u1', 'u1'))\ndef _fnt_def(self, k, c, s, d, a, l):\nself._fnt_def_real(k, c, s, d, a, l)\n\ndef _fnt_def_real(self, k, c, s, d, a, l):\nn = self.file.read(a + l)\nfontname = n[-l:].decode('ascii')\ntfm = _tfmfile(fontname)\nif tfm is None:\nraise FileNotFoundError(\"missing font metrics file: %s\" % fontname)\nif c != 0 and tfm.checksum != 0 and c != tfm.checksum:\nraise ValueError('tfm checksum mismatch: %s' % n)\n\nvf = _vffile(fontname)\n\nself.fonts[k] = DviFont(scale=s, tfm=tfm, texname=n, vf=vf)\n\n@_dispatch(247, state=_dvistate.pre, args=('u1', 'u4', 'u4', 'u4', 'u1'))\ndef _pre(self, i, num, den, mag, k):\ncomment = self.file.read(k)\nif i != 2:\nraise ValueError(\"Unknown dvi format %d\" % i)\nif num != 25400000 or den != 7227 * 2**16:\nraise ValueError(\"nonstandard units in dvi file\")\n# meaning: TeX always uses those exact values, so it\n# should be enough for us to support those\n# (There are 72.27 pt to an inch so 7227 pt =\n# 7227 * 2**16 sp to 100 in. The numerator is multiplied\n# by 10^5 to get units of 10**-7 meters.)\nif mag != 1000:\nraise ValueError(\"nonstandard magnification in dvi file\")\n# meaning: LaTeX seems to frown on setting \\mag, so\n# I think we can assume this is constant\nself.state = _dvistate.outer\n\n@_dispatch(248, state=_dvistate.outer)\ndef _post(self, _):\nself.state = _dvistate.post_post\n# TODO: actually read the postamble and finale?\n# currently post_post just triggers closing the file\n\n@_dispatch(249)\ndef _post_post(self, _):\nraise NotImplementedError\n\n@_dispatch(min=250, max=255)\ndef _malformed(self, offset):\nraise ValueError(\"unknown command: byte %d\", 250 + offset)\n\n[docs]class DviFont(object):\n\"\"\"\nEncapsulation of a font that a DVI file can refer to.\n\nThis class holds a font's texname and size, supports comparison,\nand knows the widths of glyphs in the same units as the AFM file.\nThere are also internal attributes (for use by dviread.py) that\nare *not* used for comparison.\n\nThe size is in Adobe points (converted from TeX points).\n\nParameters\n----------\n\nscale : float\nFactor by which the font is scaled from its natural size.\ntfm : Tfm\nTeX font metrics for this font\ntexname : bytes\nName of the font as used internally by TeX and friends, as an\nASCII bytestring. This is usually very different from any external\nfont names, and :class:dviread.PsfontsMap can be used to find\nthe external name of the font.\nvf : Vf\nA TeX \"virtual font\" file, or None if this font is not virtual.\n\nAttributes\n----------\n\ntexname : bytes\nsize : float\nSize of the font in Adobe points, converted from the slightly\nsmaller TeX points.\nwidths : list\nWidths of glyphs in glyph-space units, typically 1/1000ths of\nthe point size.\n\n\"\"\"\n__slots__ = ('texname', 'size', 'widths', '_scale', '_vf', '_tfm')\n\ndef __init__(self, scale, tfm, texname, vf):\nif not isinstance(texname, bytes):\nraise ValueError(\"texname must be a bytestring, got %s\"\n% type(texname))\nself._scale = scale\nself._tfm = tfm\nself.texname = texname\nself._vf = vf\nself.size = scale * (72.0 / (72.27 * 2**16))\ntry:\nnchars = max(tfm.width) + 1\nexcept ValueError:\nnchars = 0\nself.widths = [(1000*tfm.width.get(char, 0)) >> 20\nfor char in range(nchars)]\n\ndef __eq__(self, other):\nreturn (type(self) == type(other)\nand self.texname == other.texname and self.size == other.size)\n\ndef __ne__(self, other):\nreturn not self.__eq__(other)\n\ndef __repr__(self):\nreturn \"<{}: {}>\".format(type(self).__name__, self.texname)\n\ndef _width_of(self, char):\n\"\"\"Width of char in dvi units.\"\"\"\nwidth = self._tfm.width.get(char, None)\nif width is not None:\nreturn _mul2012(width, self._scale)\n_log.debug('No width for char %d in font %s.', char, self.texname)\nreturn 0\n\ndef _height_depth_of(self, char):\n\"\"\"Height and depth of char in dvi units.\"\"\"\nresult = []\nfor metric, name in ((self._tfm.height, \"height\"),\n(self._tfm.depth, \"depth\")):\nvalue = metric.get(char, None)\nif value is None:\n_log.debug('No %s for char %d in font %s',\nname, char, self.texname)\nresult.append(0)\nelse:\nresult.append(_mul2012(value, self._scale))\nreturn result\n\n[docs]class Vf(Dvi):\nr\"\"\"\nA virtual font (\\*.vf file) containing subroutines for dvi files.\n\nUsage::\n\nvf = Vf(filename)\nglyph = vf[code]\nglyph.text, glyph.boxes, glyph.width\n\nParameters\n----------\nfilename : string or bytestring\n\nNotes\n-----\nThe virtual font format is a derivative of dvi:\nhttp://mirrors.ctan.org/info/knuth/virtual-fonts\nThis class reuses some of the machinery of Dvi\nbut replaces the _read loop and dispatch mechanism.\n\"\"\"\n\ndef __init__(self, filename):\nDvi.__init__(self, filename, 0)\ntry:\nself._first_font = None\nself._chars = {}\nself._read()\nfinally:\nself.close()\n\ndef __getitem__(self, code):\nreturn self._chars[code]\n\ndef _read(self):\n\"\"\"\nRead one page from the file. Return True if successful,\nFalse if there were no more pages.\n\"\"\"\npacket_char, packet_ends = None, None\npacket_len, packet_width = None, None\nwhile True:\nbyte = self.file.read(1)\n# If we are in a packet, execute the dvi instructions\nif self.state is _dvistate.inpage:\nbyte_at = self.file.tell()-1\nif byte_at == packet_ends:\nself._finalize_packet(packet_char, packet_width)\npacket_len, packet_char, packet_width = None, None, None\n# fall through to out-of-packet code\nelif byte_at > packet_ends:\nraise ValueError(\"Packet length mismatch in vf file\")\nelse:\nif byte in (139, 140) or byte >= 243:\nraise ValueError(\n\"Inappropriate opcode %d in vf file\" % byte)\nDvi._dtable[byte](self, byte)\ncontinue\n\n# We are outside a packet\nif byte < 242: # a short packet (length given by byte)\npacket_len = byte\npacket_char, packet_width = self._arg(1), self._arg(3)\npacket_ends = self._init_packet(byte)\nself.state = _dvistate.inpage\nelif byte == 242: # a long packet\npacket_len, packet_char, packet_width = \\\n[self._arg(x) for x in (4, 4, 4)]\nself._init_packet(packet_len)\nelif 243 <= byte <= 246:\nk = self._arg(byte - 242, byte == 246)\nc, s, d, a, l = [self._arg(x) for x in (4, 4, 4, 1, 1)]\nself._fnt_def_real(k, c, s, d, a, l)\nif self._first_font is None:\nself._first_font = k\nelif byte == 247: # preamble\ni, k = self._arg(1), self._arg(1)\nx = self.file.read(k)\ncs, ds = self._arg(4), self._arg(4)\nself._pre(i, x, cs, ds)\nelif byte == 248: # postamble (just some number of 248s)\nbreak\nelse:\nraise ValueError(\"unknown vf opcode %d\" % byte)\n\ndef _init_packet(self, pl):\nif self.state != _dvistate.outer:\nraise ValueError(\"Misplaced packet in vf file\")\nself.h, self.v, self.w, self.x, self.y, self.z = 0, 0, 0, 0, 0, 0\nself.stack, self.text, self.boxes = [], [], []\nself.f = self._first_font\nreturn self.file.tell() + pl\n\ndef _finalize_packet(self, packet_char, packet_width):\nself._chars[packet_char] = Page(\ntext=self.text, boxes=self.boxes, width=packet_width,\nheight=None, descent=None)\nself.state = _dvistate.outer\n\ndef _pre(self, i, x, cs, ds):\nif self.state is not _dvistate.pre:\nraise ValueError(\"pre command in middle of vf file\")\nif i != 202:\nraise ValueError(\"Unknown vf format %d\" % i)\nif len(x):\n_log.debug('vf file comment: %s', x)\nself.state = _dvistate.outer\n# cs = checksum, ds = design size\n\ndef _fix2comp(num):\n\"\"\"Convert from two's complement to negative.\"\"\"\nassert 0 <= num < 2**32\nif num & 2**31:\nreturn num - 2**32\nelse:\nreturn num\n\ndef _mul2012(num1, num2):\n\"\"\"Multiply two numbers in 20.12 fixed point format.\"\"\"\n# Separated into a function because >> has surprising precedence\nreturn (num1*num2) >> 20\n\n[docs]class Tfm(object):\n\"\"\"\nA TeX Font Metric file.\n\nThis implementation covers only the bare minimum needed by the Dvi class.\n\nParameters\n----------\nfilename : string or bytestring\n\nAttributes\n----------\nchecksum : int\nUsed for verifying against the dvi file.\ndesign_size : int\nDesign size of the font (unknown units)\nwidth, height, depth : dict\nDimensions of each character, need to be scaled by the factor\nspecified in the dvi file. These are dicts because indexing may\nnot start from 0.\n\"\"\"\n__slots__ = ('checksum', 'design_size', 'width', 'height', 'depth')\n\ndef __init__(self, filename):\n_log.debug('opening tfm file %s', filename)\nwith open(filename, 'rb') as file:\nheader1 = file.read(24)\nlh, bc, ec, nw, nh, nd = \\\nstruct.unpack('!6H', header1[2:14])\n_log.debug('lh=%d, bc=%d, ec=%d, nw=%d, nh=%d, nd=%d',\nlh, bc, ec, nw, nh, nd)\nheader2 = file.read(4*lh)\nself.checksum, self.design_size = \\\nstruct.unpack('!2I', header2[:8])\n# there is also encoding information etc.\nchar_info = file.read(4*(ec-bc+1))\nwidths = file.read(4*nw)\nheights = file.read(4*nh)\ndepths = file.read(4*nd)\n\nself.width, self.height, self.depth = {}, {}, {}\nwidths, heights, depths = \\\n[struct.unpack('!%dI' % (len(x)/4), x)\nfor x in (widths, heights, depths)]\nfor idx, char in enumerate(range(bc, ec+1)):\nbyte0 = char_info[4*idx]\nbyte1 = char_info[4*idx+1]\nself.width[char] = _fix2comp(widths[byte0])\nself.height[char] = _fix2comp(heights[byte1 >> 4])\nself.depth[char] = _fix2comp(depths[byte1 & 0xf])\n\nPsFont = namedtuple('Font', 'texname psname effects encoding filename')\n\n[docs]class PsfontsMap(object):\n\"\"\"\nA psfonts.map formatted file, mapping TeX fonts to PS fonts.\n\nUsage::\n\n>>> map = PsfontsMap(find_tex_file('pdftex.map'))\n>>> entry = map[b'ptmbo8r']\n>>> entry.texname\nb'ptmbo8r'\n>>> entry.psname\nb'Times-Bold'\n>>> entry.encoding\n'/usr/local/texlive/2008/texmf-dist/fonts/enc/dvips/base/8r.enc'\n>>> entry.effects\n{'slant': 0.16700000000000001}\n>>> entry.filename\n\nParameters\n----------\n\nfilename : string or bytestring\n\nNotes\n-----\n\nFor historical reasons, TeX knows many Type-1 fonts by different\nnames than the outside world. (For one thing, the names have to\nfit in eight characters.) Also, TeX's native fonts are not Type-1\nbut Metafont, which is nontrivial to convert to PostScript except\nas a bitmap. While high-quality conversions to Type-1 format exist\nand are shipped with modern TeX distributions, we need to know\nwhich Type-1 fonts are the counterparts of which native fonts. For\nthese reasons a mapping is needed from internal font names to font\nfile names.\n\nA texmf tree typically includes mapping files called e.g.\n:file:psfonts.map, :file:pdftex.map, or :file:dvipdfm.map.\nThe file :file:psfonts.map is used by :program:dvips,\n:file:pdftex.map by :program:pdfTeX, and :file:dvipdfm.map\nby :program:dvipdfm. :file:psfonts.map might avoid embedding\nthe 35 PostScript fonts (i.e., have no filename for them, as in\nthe Times-Bold example above), while the pdf-related files perhaps\nonly avoid the \"Base 14\" pdf fonts. But the user may have\nconfigured these files differently.\n\"\"\"\n__slots__ = ('_font', '_filename')\n\n# Create a filename -> PsfontsMap cache, so that calling\n# PsfontsMap(filename) with the same filename a second time immediately\n# returns the same object.\n@lru_cache()\ndef __new__(cls, filename):\nself = object.__new__(cls)\nself._font = {}\nself._filename = os.fsdecode(filename)\nwith open(filename, 'rb') as file:\nself._parse(file)\nreturn self\n\ndef __getitem__(self, texname):\nassert isinstance(texname, bytes)\ntry:\nresult = self._font[texname]\nexcept KeyError:\nfmt = ('A PostScript file for the font whose TeX name is \"{0}\" '\n'could not be found in the file \"{1}\". The dviread module '\n'can only handle fonts that have an associated PostScript '\n'font file. '\n'This problem can often be solved by installing '\n'a suitable PostScript font package in your (TeX) '\n'package manager.')\nmsg = fmt.format(texname.decode('ascii'), self._filename)\nmsg = textwrap.fill(msg, break_on_hyphens=False,\nbreak_long_words=False)\n_log.info(msg)\nraise\nfn, enc = result.filename, result.encoding\nif fn is not None and not fn.startswith(b'/'):\nfn = find_tex_file(fn)\nif enc is not None and not enc.startswith(b'/'):\nenc = find_tex_file(result.encoding)\nreturn result._replace(filename=fn, encoding=enc)\n\ndef _parse(self, file):\n\"\"\"\nParse the font mapping file.\n\nThe format is, AFAIK: texname fontname [effects and filenames]\nEffects are PostScript snippets like \".177 SlantFont\",\nfilenames begin with one or two less-than signs. A filename\nending in enc is an encoding file, other filenames are font\nfiles. This can be overridden with a left bracket: <[foobar\nindicates an encoding file named foobar.\n\nThere is some difference between <foo.pfb and <<bar.pfb in\nsubsetting, but I have no example of << in my TeX installation.\n\"\"\"\n# If the map file specifies multiple encodings for a font, we\n# follow pdfTeX in choosing the last one specified. Such\n# entries are probably mistakes but they have occurred.\n# http://tex.stackexchange.com/questions/10826/\n# http://article.gmane.org/gmane.comp.tex.pdftex/4914\n\nempty_re = re.compile(br'%|\\s*\\$')\nword_re = re.compile(\nbr'''(?x) (?:\n\"<$(?P<enc1> [^\"]+ )\" | # quoted encoding marked by [ \"< (?P<enc2> [^\"]+.enc)\" | # quoted encoding, ends in .enc \"<<? (?P<file1> [^\"]+ )\" | # quoted font file name \" (?P<eff1> [^\"]+ )\" | # quoted effects or font name <\\[ (?P<enc3> \\S+ ) | # encoding marked by [ < (?P<enc4> \\S+ .enc) | # encoding, ends in .enc <<? (?P<file2> \\S+ ) | # font file name (?P<eff2> \\S+ ) # effects or font name )''') effects_re = re.compile( br'''(?x) (?P<slant> -?[0-9]*(?:\\.[0-9]+)) \\s* SlantFont | (?P<extend>-?[0-9]*(?:\\.[0-9]+)) \\s* ExtendFont''') lines = (line.strip() for line in file if not empty_re.match(line)) for line in lines: effects, encoding, filename = b'', None, None words = word_re.finditer(line) # The named groups are mutually exclusive and are # referenced below at an estimated order of probability of # occurrence based on looking at my copy of pdftex.map. # The font names are probably unquoted: w = next(words) texname = w.group('eff2') or w.group('eff1') w = next(words) psname = w.group('eff2') or w.group('eff1') for w in words: # Any effects are almost always quoted: eff = w.group('eff1') or w.group('eff2') if eff: effects = eff continue # Encoding files usually have the .enc suffix # and almost never need quoting: enc = (w.group('enc4') or w.group('enc3') or w.group('enc2') or w.group('enc1')) if enc: if encoding is not None: _log.debug('Multiple encodings for %s = %s', texname, psname) encoding = enc continue # File names are probably unquoted: filename = w.group('file2') or w.group('file1') effects_dict = {} for match in effects_re.finditer(effects): slant = match.group('slant') if slant: effects_dict['slant'] = float(slant) else: effects_dict['extend'] = float(match.group('extend')) self._font[texname] = PsFont( texname=texname, psname=psname, effects=effects_dict, encoding=encoding, filename=filename) [docs]class Encoding(object): r\"\"\" Parses a \\*.enc file referenced from a psfonts.map style file. The format this class understands is a very limited subset of PostScript. Usage (subject to change):: for name in Encoding(filename): whatever(name) Parameters ---------- filename : string or bytestring Attributes ---------- encoding : list List of character names \"\"\" __slots__ = ('encoding',) def __init__(self, filename): with open(filename, 'rb') as file: _log.debug('Parsing TeX encoding %s', filename) self.encoding = self._parse(file) _log.debug('Result: %s', self.encoding) def __iter__(self): yield from self.encoding @staticmethod def _parse(file): lines = (line.split(b'%', 1).strip() for line in file) data = b''.join(lines) beginning = data.find(b'[') if beginning < 0: raise ValueError(\"Cannot locate beginning of encoding in {}\" .format(file)) data = data[beginning:] end = data.find(b']') if end < 0: raise ValueError(\"Cannot locate end of encoding in {}\" .format(file)) data = data[:end] return re.findall(br'/([^][{}<>\\s]+)', data) # Note: this function should ultimately replace the Encoding class, which # appears to be mostly broken: because it uses b''.join(), there is no # whitespace left between glyph names (only slashes) so the final re.findall # returns a single string with all glyph names. However this does not appear # to bother backend_pdf, so that needs to be investigated more. (The fixed # version below is necessary for textpath/backend_svg, though.) def _parse_enc(path): r\"\"\" Parses a \\*.enc file referenced from a psfonts.map style file. The format this class understands is a very limited subset of PostScript. Parameters ---------- path : os.PathLike Returns ------- encoding : list The nth entry of the list is the PostScript glyph name of the nth glyph. \"\"\" with open(path, encoding=\"ascii\") as file: no_comments = \"\\n\".join(line.split(\"%\").rstrip() for line in file) array = re.search(r\"(?s)\\[(.*)$\", no_comments).group(1)\nlines = [line for line in array.split(\"\\n\") if line]\nif all(line.startswith(\"/\") for line in lines):\nreturn [line[1:] for line in lines]\nelse:\nraise ValueError(\n\"Failed to parse {} as Postscript encoding\".format(path))\n\n[docs]@lru_cache()\ndef find_tex_file(filename, format=None):\n\"\"\"\nFind a file in the texmf tree.\n\nCalls :program:kpsewhich which is an interface to the kpathsea\nlibrary _. Most existing TeX distributions on Unix-like systems use\nkpathsea. It is also available as part of MikTeX, a popular\ndistribution on Windows.\n\n*If the file is not found, an empty string is returned*.\n\nParameters\n----------\nfilename : string or bytestring\nformat : string or bytestring\nUsed as the value of the --format option to :program:kpsewhich.\nCould be e.g. 'tfm' or 'vf' to limit the search to that type of files.\n\nReferences\n----------\n\n.. Kpathsea documentation <http://www.tug.org/kpathsea/>_\nThe library that :program:kpsewhich is part of.\n\"\"\"\n\n# we expect these to always be ascii encoded, but use utf-8\n# out of caution\nif isinstance(filename, bytes):\nfilename = filename.decode('utf-8', errors='replace')\nif isinstance(format, bytes):\nformat = format.decode('utf-8', errors='replace')\n\nif os.name == 'nt':\n# On Windows only, kpathsea can use utf-8 for cmd args and output.\n# The command_line_encoding environment variable is set to force it\n# to always use utf-8 encoding. See mpl issue #11848 for more info.\nkwargs = dict(env=dict(os.environ, command_line_encoding='utf-8'))\nelse:\nkwargs = {}\n\ncmd = ['kpsewhich']\nif format is not None:\ncmd += ['--format=' + format]\ncmd += [filename]\ntry:\nresult = cbook._check_and_log_subprocess(cmd, _log, **kwargs)\nexcept RuntimeError:\nreturn ''\nif os.name == 'nt':\nreturn result.decode('utf-8').rstrip('\\r\\n')\nelse:\nreturn os.fsdecode(result).rstrip('\\n')\n\n@lru_cache()\ndef _fontfile(cls, suffix, texname):\nfilename = find_tex_file(texname + suffix)\nreturn cls(filename) if filename else None\n\n_tfmfile = partial(_fontfile, Tfm, \".tfm\")\n_vffile = partial(_fontfile, Vf, \".vf\")\n\nif __name__ == '__main__':\nfrom argparse import ArgumentParser\nimport itertools\n\nparser = ArgumentParser()\nparser.add_argument(\"filename\")\nparser.add_argument(\"dpi\", nargs=\"?\", type=float, default=None)\nargs = parser.parse_args()\nwith Dvi(args.filename, args.dpi) as dvi:\nfontmap = PsfontsMap(find_tex_file('pdftex.map'))\nfor page in dvi:\nprint('=== new page ===')\nfor font, group in itertools.groupby(\npage.text, lambda text: text.font):\nprint('font', font.texname, 'scaled', font._scale / 2 ** 20)\nfor text in group:\nprint(text.x, text.y, text.glyph,\nchr(text.glyph) if chr(text.glyph).isprintable()\nelse \".\",\ntext.width)\nfor x, y, w, h in page.boxes:\nprint(x, y, 'BOX', w, h)" ]
[ null ]
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http://markusy.pl/forum/archive.php?54a05c=what-reaction-below-represents-the-balanced-chemical-equation-of-propanoic-acid-reacting-with-naoh
[ "what reaction below represents the balanced chemical equation of propanoic acid reacting with naoh\n5 years ago. The unbalanced chemical equation that describes this neutralization reaction looks like this #\"CH\"_ 3\"COOH\"_ ((aq)) + \"NaOH\"_ ((aq)) -> \"CH\"_ 3\"COONa\"_ ((aq)) + \"H\"_ 2\"O\"_ ((l))# Now, you could check to see if this chemical equation is balanced by counting the … GCSE Physics. Out of these cookies, the cookies that are categorized as necessary are stored on your browser as they are essential for the working of basic functionalities of the website.\n\nAcids and bases make a very important part of chemistry. Acid-Base Reaction.\n\nUse uppercase for the first character in the element and lowercase for the second character. We can get many common examples of acid base reactions in our daily life. Trevor H. Lv 7. Necessary cookies are absolutely essential for the website to function properly. The following equation will help you to know how the base gets dissociated in an aqueous solution.\n\n6789 Quail Hill Pkwy, Suite 211 Irvine CA 92603. Compound states [like (s) (aq) or (g)] are not required. Sodium + Water = Sodium Hydroxide + Dihydrogen, Na + H2O + Al + Ba(OH)2 = Ba(NaAlO2)2 + H2, Na + H2O + C14H14N3NaO3S = (N3)Na2(O3)S + C14H14OH + H2. Index The Reaction of Propanoic Acid with Alcohols to make Esters.. Propanoic acid will react with alcohols in the presence of concentrated sulfuric acid, to form esters. Now, you could check to see if this chemical equation is balanced by counting the number of atoms of each element present on both sides of the equation, or you could check by using the fact that sodium hydroxide is a strong base. 1 0. KHC8H4O4(aq) + NaOH(aq) --> KNaC8H4O4(aq) + H2O(l). So let’s see the equations and nature of acids and bases when they are mixed in water. a balanced equation would be nice too :) Answer Save. This was just a basic outline about the reactions but when you will move further, you may get many problems to solve related to these reaction. The compounds with a pH value above 7 are known as bases. ); The Gold Parsing System (Hats off!      In this ScienceStruck article we will discuss this type of reaction in detail with the help of some examples. Keep reading. To balance a chemical equation, enter an equation of a chemical reaction and press the Balance button.\n\nWe hope you are enjoying ScienceStruck!        These cookies will be stored in your browser only with your consent. (adsbygoogle = window.adsbygoogle || []).push({}); Propanoic water molecule and NaCl which is a salt. 1.54g of KHP is equivalent to 0.00754 mol of KHP. Compound states [like (s) (aq) or (g)] are not required. Replace immutable groups in compounds to avoid ambiguity. By the above given acid and base equations we can understand their dissociation in water. Examples: Fe, Au, Co, Br, C, O, N, F. Ionic charges are not yet supported and will be ignored. Like any other reaction, balancing acid base reactions is also very important. Examples of exothermic reaction are found in several daily activities. HCl(aq) + NaOH(aq) → H(aq)+ + Cl(aq)– + Na(aq)+ + OH(aq)– → NaCl(aq) + H2O(l). The balanced equation will appear above.\n\nDiscover the activities, projects, and degrees that will fuel your love of science. The balanced equation will appear above. The balanced equation will appear above.\n\nWe also use third-party cookies that help us analyze and understand how you use this website. ; A chemical reaction can be expressed in word equation and chemical equation. Replace immutable groups in compounds to avoid ambiguity. Read our article on how to balance chemical equations or ask for help in our chat.   53                                  Find out more about acid base reactions and their examples. acid will react with The Periodic Table Notice that the reactants' side has an undissociated acetate anion and the products' side has a dissociated acetate anion, so nothing to balance out here. URGENT?\n\nCH3CH2COOH + NaOH → CH3CH2COONa + H2O.\n\nreaction. Well, we're looking for good writers who want to spread the word.\n\nFor the best answers, search on … C3H7OH(aq)   +\n\nThis category only includes cookies that ensures basic functionalities and security features of the website. The salts produced by this reactions are neutral and when they are dissolved in water they behave as electrolytes and conduct electricity. We'll assume you're ok with this, but you can opt-out if you wish.\n\ngcsescience.com, Home +   propanoic acid   propyl propanoate  +  water. Have a look... Understanding some of the most common chemical reactions is essential to gain mastery of the deeper concepts in chemistry. Examples: Fe, Au, Co, Br, C, O, N, F. Ionic charges are not yet supported and will be ignored. If the pH value is less than 7, then the compound is said to be acidic and as the value falls below 7 the more acidic the compound is considered. ; The substance which are formed after a chemical reaction are called products. Compound states [like (s) (aq) or (g)] are not required. around the world. products : sodium propanoate and water. Which means if the reaction is between a strong acid and weak base then its result will vary from the reaction between a strong acid and strong base or a weak acid and a weak base. For example, C6H5C2H5 + O2 = C6H5OH + CO2 + H2O will not be balanced, but XC2H5 + O2 = XOH + CO2 + H2O will. So we can say that the chemical reaction between an acid and a base to give a neutralized product is known as an acid base reaction. This means that you can rewrite the chemical equation as, #\"CH\"_ 3\"COO\"color(red)(\"H\")_ ((aq)) + color(red)(\"OH\"_ ((aq))^(-)) -> \"CH\"_ 3\"COO\"_ ((aq))^(-) + color(red)(\"H\"_ 2\"O\"_ ((l)))#. propanoic acid is a weak acid with an ionization constant of 1.3 X 10^-5.What this means is in water nearly all the propanoic acid will remain as the acid form with ~ 1.0 % of the acid ionized if one starts with 0.1 M acid .\n\n." ]
[ null ]
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https://www.plumed.org/doc-master/user-doc/html/_p_a_t_h.html
[ "", null, "", null, "", null, "PATH\n This is part of the mapping module\n\nPath collective variables with a more flexible framework for the distance metric being used.\n\nThe Path Collective Variables developed by Branduardi and co-workers allow one to compute the progress along a high-dimensional path and the distance from the high-dimensional path. The progress along the path (s) is computed using:\n\n$s = \\frac{ \\sum_{i=1}^N i \\exp( -\\lambda R[X - X_i] ) }{ \\sum_{i=1}^N \\exp( -\\lambda R[X - X_i] ) }$\n\nwhile the distance from the path (z) is measured using:\n\n$z = -\\frac{1}{\\lambda} \\ln\\left[ \\sum_{i=1}^N \\exp( -\\lambda R[X - X_i] ) \\right]$\n\nIn these expressions $$N$$ high-dimensional frames ( $$X_i$$) are used to describe the path in the high-dimensional space. The two expressions above are then functions of the distances from each of the high-dimensional frames $$R[X - X_i]$$. Within PLUMED there are multiple ways to define the distance from a high-dimensional configuration. You could calculate the RMSD distance or you could calculate the amount by which a set of collective variables change. As such this implementation of the path CV allows one to use all the difference distance metrics that are discussed in Distances from reference configurations. This is as opposed to the alternative implementation of path (PATHMSD) which is a bit faster but which only allows one to use the RMSD distance.\n\nThe $$s$$ and $$z$$ variables are calculated using the above formulas by default. However, there is an alternative method of calculating these collective variables, which is detailed in . This alternative method uses the tools of geometry (as opposed to algebra, which is used in the equations above). In this alternative formula the progress along the path $$s$$ is calculated using:\n\n$s = i_2 + \\textrm{sign}(i_2-i_1) \\frac{ \\sqrt{( \\mathbf{v}_1\\cdot\\mathbf{v}_2 )^2 - |\\mathbf{v}_3|^2(|\\mathbf{v}_1|^2 - |\\mathbf{v}_2|^2) } }{2|\\mathbf{v}_3|^2} - \\frac{\\mathbf{v}_1\\cdot\\mathbf{v}_3 - |\\mathbf{v}_3|^2}{2|\\mathbf{v}_3|^2}$\n\nwhere $$\\mathbf{v}_1$$ and $$\\mathbf{v}_3$$ are the vectors connecting the current position to the closest and second closest node of the path, respectfully and $$i_1$$ and $$i_2$$ are the projections of the closest and second closest frames of the path. $$\\mathbf{v}_2$$, meanwhile, is the vector connecting the closest frame to the second closest frame. The distance from the path, $$z$$ is calculated using:\n\n$z = \\sqrt{ \\left[ |\\mathbf{v}_1|^2 - |\\mathbf{v}_2| \\left( \\frac{ \\sqrt{( \\mathbf{v}_1\\cdot\\mathbf{v}_2 )^2 - |\\mathbf{v}_3|^2(|\\mathbf{v}_1|^2 - |\\mathbf{v}_2|^2) } }{2|\\mathbf{v}_3|^2} - \\frac{\\mathbf{v}_1\\cdot\\mathbf{v}_3 - |\\mathbf{v}_3|^2}{2|\\mathbf{v}_3|^2} \\right) \\right]^2 }$\n\nThe symbols here are as they were for $$s$$. If you would like to use these equations to calculate $$s$$ and $$z$$ then you should use the GPATH flag. The values of $$s$$ and $$z$$ can then be referenced using the gspath and gzpath labels.\n\nExamples\n\nIn the example below the path is defined using RMSD distance from frames.\n\nClick on the labels of the actions for more information on what each action computes", null, "p1: PATH REFERENCEcompulsory keyword\na pdb file containing the set of reference configurations =file.pdb TYPEcompulsory keyword ( default=OPTIMAL-FAST )\nthe manner in which distances are calculated. =OPTIMAL LAMBDAcompulsory keyword ( default=0 )\nthe value of the lambda parameter for paths =500.0\nPRINT ARGthe input for this action is the scalar output from one or more other actions. =p1.spath,p1.zpath STRIDEcompulsory keyword ( default=1 )\nthe frequency with which the quantities of interest should be output =1 FILEthe name of the file on which to output these quantities =colvar FMTthe format that should be used to output real numbers =%8.4f\n\n\nThe reference frames in the path are defined in the pdb file shown below. In this frame each configuration in the path is separated by a line containing just the word END.\n\nATOM 1 CL ALA 1 -3.171 0.295 2.045 1.00 1.00\nATOM 5 CLP ALA 1 -1.819 -0.143 1.679 1.00 1.00\nATOM 6 OL ALA 1 -1.177 -0.889 2.401 1.00 1.00\nATOM 7 NL ALA 1 -1.313 0.341 0.529 1.00 1.00\nEND\nATOM 1 CL ALA 1 -3.175 0.365 2.024 1.00 1.00\nATOM 5 CLP ALA 1 -1.814 -0.106 1.685 1.00 1.00\nATOM 6 OL ALA 1 -1.201 -0.849 2.425 1.00 1.00\nATOM 7 NL ALA 1 -1.296 0.337 0.534 1.00 1.00\nEND\nATOM 1 CL ALA 1 -2.990 0.383 2.277 1.00 1.00\nATOM 5 CLP ALA 1 -1.664 -0.085 1.831 1.00 1.00\nATOM 6 OL ALA 1 -0.987 -0.835 2.533 1.00 1.00\nATOM 7 NL ALA 1 -1.227 0.364 0.646 1.00 1.00\nEND\n\n\nIn the example below the path is defined using the values of two torsional angles (t1 and t2). In addition, the $$s$$ and $$z$$ are calculated using the geometric expressions described above rather than the algebraic expressions that are used by default.\n\nClick on the labels of the actions for more information on what each action computes", null, "t1: TORSION ATOMSthe four atoms involved in the torsional angle =5,7,9,15\nt2: TORSION ATOMSthe four atoms involved in the torsional angle =7,9,15,17\npp: PATH TYPEcompulsory keyword ( default=OPTIMAL-FAST )\nthe manner in which distances are calculated. =EUCLIDEAN REFERENCEcompulsory keyword\na pdb file containing the set of reference configurations =epath.pdb GPATHcalculate the position on the path using trigonometry The final value can be referenced\nusing label.gpath. NOSPATH( default=off ) do not calculate the spath position NOZPATH( default=off ) do not calculate the zpath position\nPRINT ARGthe input for this action is the scalar output from one or more other actions. =pp.* FILEthe name of the file on which to output these quantities =colvar\n\n\nNotice that the LAMBDA parameter is not required here as we are not calculating $$s$$ and $$s$$ using the algebraic formulas defined earlier. The positions of the frames in the path are defined in the file epath.pdb. An extract from this file looks as shown below.\n\nREMARK ARG=t1,t2 t1=-4.25053 t2=3.88053\nEND\nREMARK ARG=t1,t2 t1=-4.11 t2=3.75\nEND\nREMARK ARG=t1,t2 t1=-3.96947 t2=3.61947\nEND\n\n\nThe remarks in this pdb file tell PLUMED the labels that are being used to define the position in the high dimensional space and the values that these arguments have at each point on the path.\n\nGlossary of keywords and components\nDescription of components\n\nBy default the value of the calculated quantity can be referenced elsewhere in the input file by using the label of the action. Alternatively this Action can be used to calculate the following quantities by employing the keywords listed below. These quantities can be referenced elsewhere in the input by using this Action's label followed by a dot and the name of the quantity required from the list below.\n\n Quantity Keyword Description gspath GPATH the position on the path calculated using trigonometry gzpath GPATH the distance from the path calculated using trigonometry\nCompulsory keywords\n REFERENCE a pdb file containing the set of reference configurations TYPE ( default=OPTIMAL-FAST ) the manner in which distances are calculated. More information on the different metrics that are available in PLUMED can be found in the section of the manual on Distances from reference configurations LAMBDA ( default=0 ) the value of the lambda parameter for paths\nOptions\n NUMERICAL_DERIVATIVES ( default=off ) calculate the derivatives for these quantities numerically SERIAL ( default=off ) do the calculation in serial. Do not use MPI TIMINGS ( default=off ) output information on the timings of the various parts of the calculation DISABLE_CHECKS ( default=off ) disable checks on reference input structures. NOZPATH ( default=off ) do not calculate the zpath position NOSPATH ( default=off ) do not calculate the spath position GPATH calculate the position on the path using trigonometry The final value can be referenced using label.gpath. You can use multiple instances of this keyword i.e. GPATH1, GPATH2, GPATH3... The corresponding values are then referenced using label.gpath-1, label.gpath-2, label.gpath-3..." ]
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https://numbermatics.com/n/9584156/
[ "# 9584156\n\n## 9,584,156 is an even composite number composed of two prime numbers multiplied together.\n\nWhat does the number 9584156 look like?\n\nThis visualization shows the relationship between its 2 prime factors (large circles) and 6 divisors.\n\n9584156 is an even composite number. It is composed of two distinct prime numbers multiplied together. It has a total of six divisors.\n\n## Prime factorization of 9584156:\n\n### 22 × 2396039\n\n(2 × 2 × 2396039)\n\nSee below for interesting mathematical facts about the number 9584156 from the Numbermatics database.\n\n### Names of 9584156\n\n• Cardinal: 9584156 can be written as Nine million, five hundred eighty-four thousand, one hundred fifty-six.\n\n### Scientific notation\n\n• Scientific notation: 9.584156 × 106\n\n### Factors of 9584156\n\n• Number of distinct prime factors ω(n): 2\n• Total number of prime factors Ω(n): 3\n• Sum of prime factors: 2396041\n\n### Divisors of 9584156\n\n• Number of divisors d(n): 6\n• Complete list of divisors:\n• Sum of all divisors σ(n): 16772280\n• Sum of proper divisors (its aliquot sum) s(n): 7188124\n• 9584156 is a deficient number, because the sum of its proper divisors (7188124) is less than itself. Its deficiency is 2396032\n\n### Bases of 9584156\n\n• Binary: 1001001000111110000111002\n• Base-36: 5PF6K\n\n### Squares and roots of 9584156\n\n• 9584156 squared (95841562) is 91856046232336\n• 9584156 cubed (95841563) is 880362676633920468416\n• The square root of 9584156 is 3095.8288066365\n• The cube root of 9584156 is 212.4147274933\n\n### Scales and comparisons\n\nHow big is 9584156?\n• 9,584,156 seconds is equal to 15 weeks, 5 days, 22 hours, 15 minutes, 56 seconds.\n• To count from 1 to 9,584,156 would take you about twenty-three 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 9584156 cubic inches would be around 17.7 feet tall.\n\n### Recreational maths with 9584156\n\n• 9584156 backwards is 6514859\n• The number of decimal digits it has is: 7\n• The sum of 9584156's digits is 38\n• More coming soon!\n\nMLA style:\n\"Number 9584156 - Facts about the integer\". Numbermatics.com. 2021. Web. 21 October 2021.\n\nAPA style:\nNumbermatics. (2021). Number 9584156 - Facts about the integer. Retrieved 21 October 2021, from https://numbermatics.com/n/9584156/\n\nChicago style:\nNumbermatics. 2021. \"Number 9584156 - Facts about the integer\". https://numbermatics.com/n/9584156/\n\nThe information we have on file for 9584156 includes mathematical data and numerical statistics calculated using standard algorithms and methods. We are adding more all the time. If there are any features you would like to see, please contact us. Information provided for educational use, intellectual curiosity and fun!\n\nKeywords: Divisors of 9584156, math, Factors of 9584156, curriculum, school, college, exams, university, Prime factorization of 9584156, STEM, science, technology, engineering, physics, economics, calculator, nine million, five hundred eighty-four thousand, one hundred fifty-six.\n\nOh no. Javascript is switched off in your browser.\nSome bits of this website may not work unless you switch it on." ]
[ null ]
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https://www.colorhexa.com/01f229
[ "# #01f229 Color Information\n\nIn a RGB color space, hex #01f229 is composed of 0.4% red, 94.9% green and 16.1% blue. Whereas in a CMYK color space, it is composed of 99.6% cyan, 0% magenta, 83.1% yellow and 5.1% black. It has a hue angle of 130 degrees, a saturation of 99.2% and a lightness of 47.6%. #01f229 color hex could be obtained by blending #02ff52 with #00e500. Closest websafe color is: #00ff33.\n\n• R 0\n• G 95\n• B 16\nRGB color chart\n• C 100\n• M 0\n• Y 83\n• K 5\nCMYK color chart\n\n#01f229 color description : Vivid lime green.\n\n# #01f229 Color Conversion\n\nThe hexadecimal color #01f229 has RGB values of R:1, G:242, B:41 and CMYK values of C:1, M:0, Y:0.83, K:0.05. Its decimal value is 127529.\n\nHex triplet RGB Decimal 01f229 `#01f229` 1, 242, 41 `rgb(1,242,41)` 0.4, 94.9, 16.1 `rgb(0.4%,94.9%,16.1%)` 100, 0, 83, 5 130°, 99.2, 47.6 `hsl(130,99.2%,47.6%)` 130°, 99.6, 94.9 00ff33 `#00ff33`\nCIE-LAB 83.792, -81.714, 74.358 32.163, 63.667, 12.692 0.296, 0.587, 63.667 83.792, 110.482, 137.698 83.792, -78.817, 98.646 79.792, -67.684, 46.424 00000001, 11110010, 00101001\n\n# Color Schemes with #01f229\n\n• #01f229\n``#01f229` `rgb(1,242,41)``\n• #f201ca\n``#f201ca` `rgb(242,1,202)``\nComplementary Color\n• #51f201\n``#51f201` `rgb(81,242,1)``\n• #01f229\n``#01f229` `rgb(1,242,41)``\n• #01f2a2\n``#01f2a2` `rgb(1,242,162)``\nAnalogous Color\n• #f20151\n``#f20151` `rgb(242,1,81)``\n• #01f229\n``#01f229` `rgb(1,242,41)``\n• #a201f2\n``#a201f2` `rgb(162,1,242)``\nSplit Complementary Color\n• #f22901\n``#f22901` `rgb(242,41,1)``\n• #01f229\n``#01f229` `rgb(1,242,41)``\n• #2901f2\n``#2901f2` `rgb(41,1,242)``\n• #caf201\n``#caf201` `rgb(202,242,1)``\n• #01f229\n``#01f229` `rgb(1,242,41)``\n• #2901f2\n``#2901f2` `rgb(41,1,242)``\n• #f201ca\n``#f201ca` `rgb(242,1,202)``\n• #01a61c\n``#01a61c` `rgb(1,166,28)``\n• #01bf20\n``#01bf20` `rgb(1,191,32)``\n• #01d925\n``#01d925` `rgb(1,217,37)``\n• #01f229\n``#01f229` `rgb(1,242,41)``\n• #0efe36\n``#0efe36` `rgb(14,254,54)``\n• #28fe4b\n``#28fe4b` `rgb(40,254,75)``\n• #41fe61\n``#41fe61` `rgb(65,254,97)``\nMonochromatic Color\n\n# Alternatives to #01f229\n\nBelow, you can see some colors close to #01f229. Having a set of related colors can be useful if you need an inspirational alternative to your original color choice.\n\n• #15f201\n``#15f201` `rgb(21,242,1)``\n• #01f201\n``#01f201` `rgb(1,242,1)``\n• #01f215\n``#01f215` `rgb(1,242,21)``\n• #01f229\n``#01f229` `rgb(1,242,41)``\n• #01f23d\n``#01f23d` `rgb(1,242,61)``\n• #01f251\n``#01f251` `rgb(1,242,81)``\n• #01f265\n``#01f265` `rgb(1,242,101)``\nSimilar Colors\n\n# #01f229 Preview\n\nThis text has a font color of #01f229.\n\n``<span style=\"color:#01f229;\">Text here</span>``\n#01f229 background color\n\nThis paragraph has a background color of #01f229.\n\n``<p style=\"background-color:#01f229;\">Content here</p>``\n#01f229 border color\n\nThis element has a border color of #01f229.\n\n``<div style=\"border:1px solid #01f229;\">Content here</div>``\nCSS codes\n``.text {color:#01f229;}``\n``.background {background-color:#01f229;}``\n``.border {border:1px solid #01f229;}``\n\n# Shades and Tints of #01f229\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, #000801 is the darkest color, while #f3fff5 is the lightest one.\n\n• #000801\n``#000801` `rgb(0,8,1)``\n• #001b05\n``#001b05` `rgb(0,27,5)``\n• #002f08\n``#002f08` `rgb(0,47,8)``\n• #00420b\n``#00420b` `rgb(0,66,11)``\n• #00560f\n``#00560f` `rgb(0,86,15)``\n• #006912\n``#006912` `rgb(0,105,18)``\n• #017d15\n``#017d15` `rgb(1,125,21)``\n• #019018\n``#019018` `rgb(1,144,24)``\n• #01a41c\n``#01a41c` `rgb(1,164,28)``\n• #01b71f\n``#01b71f` `rgb(1,183,31)``\n• #01cb22\n``#01cb22` `rgb(1,203,34)``\n• #01de26\n``#01de26` `rgb(1,222,38)``\n• #01f229\n``#01f229` `rgb(1,242,41)``\n• #09fe31\n``#09fe31` `rgb(9,254,49)``\n• #1cfe42\n``#1cfe42` `rgb(28,254,66)``\n• #30fe52\n``#30fe52` `rgb(48,254,82)``\n• #43fe62\n``#43fe62` `rgb(67,254,98)``\n• #57fe73\n``#57fe73` `rgb(87,254,115)``\n• #6afe83\n``#6afe83` `rgb(106,254,131)``\n• #7efe93\n``#7efe93` `rgb(126,254,147)``\n• #91ffa3\n``#91ffa3` `rgb(145,255,163)``\n• #a5ffb4\n``#a5ffb4` `rgb(165,255,180)``\n• #b8ffc4\n``#b8ffc4` `rgb(184,255,196)``\n• #ccffd4\n``#ccffd4` `rgb(204,255,212)``\n• #e0ffe5\n``#e0ffe5` `rgb(224,255,229)``\n• #f3fff5\n``#f3fff5` `rgb(243,255,245)``\nTint Color Variation\n\n# Tones of #01f229\n\nA tone is produced by adding gray to any pure hue. In this case, #718274 is the less saturated color, while #01f229 is the most saturated one.\n\n• #718274\n``#718274` `rgb(113,130,116)``\n• #688b6e\n``#688b6e` `rgb(104,139,110)``\n• #5e9567\n``#5e9567` `rgb(94,149,103)``\n• #559e61\n``#559e61` `rgb(85,158,97)``\n• #4ca75b\n``#4ca75b` `rgb(76,167,91)``\n• #42b155\n``#42b155` `rgb(66,177,85)``\n• #39ba4e\n``#39ba4e` `rgb(57,186,78)``\n• #30c348\n``#30c348` `rgb(48,195,72)``\n• #26cd42\n``#26cd42` `rgb(38,205,66)``\n• #1dd63c\n``#1dd63c` `rgb(29,214,60)``\n• #14df35\n``#14df35` `rgb(20,223,53)``\n• #0ae92f\n``#0ae92f` `rgb(10,233,47)``\n• #01f229\n``#01f229` `rgb(1,242,41)``\nTone Color Variation\n\n# Color Blindness Simulator\n\nBelow, you can see how #01f229 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" ]
[ null ]
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https://es.mathworks.com/help/symbolic/operators.html?s_tid=CRUX_lftnav
[ "# Operators and Elementary Operations\n\nPerform arithmetic, relational, and logical operations on symbolic objects\n\nSymbolic Math Toolbox™ includes functions for arithmetic, relational, and logical operations, as well as modulo and complex number operations, on symbolic objects. You can use these functions to perform simple operations like addition, multiplication, and calculating exponents, as well as other operations like finding the `n`th root, modulus, and finding the quotient and remainder of a division.\n\n## Functions\n\nexpand all\n\n `minus` Symbolic subtraction `plus` Symbolic addition `times` Symbolic array multiplication `ldivide` Symbolic array left division `rdivide` Symbolic array right division `power` Symbolic array power `nthroot` Nth root of symbolic numbers `mtimes` Symbolic matrix multiplication `mldivide` Symbolic matrix left division `mrdivide` Symbolic matrix right division `mpower` Symbolic matrix power `transpose` Symbolic matrix transpose `ctranspose` Symbolic matrix complex conjugate transpose\n\n#### Operators\n\n `eq` Define symbolic equation `ge` Define greater than or equal to condition `gt` Define greater than relation `le` Define less than or equal to condition `lt` Define less than relation `ne` Define inequality\n\n#### Functions\n\n `has` Check if expression contains particular subexpression `hasSymType` Determine whether symbolic object contains specific type `in` Numeric type of symbolic input `isAlways` Determine if symbolic conditions are true for all values of variables `isequal` Determine if symbolic inputs are equal `isequaln` Test symbolic objects for equality, treating `NaN` values as equal `isSymType` Determine whether symbolic object is specific type `max` Maximum elements of symbolic input `min` Minimum elements of symbolic input `piecewise` Conditionally defined expression or function\n\n#### Operators\n\n `and` Logical AND for symbolic expressions `not` Logical NOT for symbolic expressions `or` Logical OR for symbolic expressions `xor` Logical XOR for symbolic expressions\n\n#### Functions\n\n `all` Test whether all equations and inequalities represented as elements of symbolic array are valid `any` Test whether at least one of equations and inequalities represented as elements of symbolic array is valid `has` Check if expression contains particular subexpression `hasSymType` Determine whether symbolic object contains specific type `in` Numeric type of symbolic input `isAlways` Determine if symbolic conditions are true for all values of variables `isequaln` Test symbolic objects for equality, treating `NaN` values as equal `isfinite` Check whether symbolic array elements are finite `isinf` Check whether symbolic array elements are infinite `isnan` Check whether symbolic array elements are `NaN`s `isSymType` Determine whether symbolic object is specific type `logical` Determine if symbolic equation, inequality, or condition is true `symtrue` Symbolic logical constant true `symfalse` Symbolic logical constant false\n `mod` Symbolic modulus after division `powermod` Modular exponentiation `quorem` Quotient and remainder `rem` Remainder after division\n `abs` Symbolic absolute value (complex modulus or magnitude) `angle` Symbolic polar angle `conj` Complex conjugate of symbolic input `imag` Imaginary part of complex number `real` Real part of complex number" ]
[ null ]
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https://www.thefreelibrary.com/Obtaining+Desired+Vehicle+Dynamics+Characteristics+with+Independently...-a0531111179
[ "# Obtaining Desired Vehicle Dynamics Characteristics with Independently Controlled In-Wheel Motors: State of Art Review.\n\n1. INTRODUCTION\n\nDecreasing oil resources and increasing environmental problems have stimulated the need for research in alternative energy sources for automobiles. Electric vehicles have come up as a strong contender among all other alternate vehicles (Ruther. et al., 2015). They run on renewable energy source and are tail-pipe emission free. With ever increasing fuel prices and health impacts of internal combustion engines there is a demand for the eco-friendly means of transportation (Ji. et al., 2012: Rezvani, et al.,2015; Wideberg. et al., 2014). Unlike conventional vehicles, which were driven by an engine connected to a powertrain, the EVs are generally driven by individual wheel motors. The advantage of individual motor control is enhanced safety, comfort and improved handling dynamics.\n\nThere have been various vehicle dynamics control and torque vectoring algorithms available in literature. We analysed most relevant research that underwent in this area in order to develop a guideline to be followed while designing such a control system. As the torques can be controlled independently, direct yaw moment control and side slip control has come out as one of the most widely used technology for pro-actively preventing accidents.\n\nIn 1996, the world's first vehicle with a right-and-left torque vectoring type direct yaw moment control system was developed (Sawase & Sano., 1999). The focus is to develop a controller which can control Couple traction/braking ([T.sub.i] i= FL/FR/RL/RR) of the four in-wheel motors, from basic driving slogans, that are, steering angle, position of the accelerator and brake pedal as shown in Figure 1. Generally, all vehicle dynamics control (VDC) algorithms are based on a hierarchical structure, where, from the slogan of driving and vehicle information the vehicle's response (FOX vehicle in our case) is identified. This structure arises in several levels as shown in Figure 2.\n\nGenerally, the variables used by VDC algorithms to monitor the dynamic behavior of vehicle are:\n\nr: - Yaw rate; [beta]: - Slip angle\n\nThe system identifies whether the desired dynamics for the driver is within the range of operation of the vehicle. This further determines maximum grip between tires and ground. In case of detecting a discrepancy of the actual dynamics and the desired (and adjusted according to the maximum obtainable performance), a directional control is set to adjustr and [beta] to the desired values.\n\nThis directional control of the vehicle involves injection of a moment ([M.sub.z]) which is generated by traction/braking force difference in left-right wheels. Finally, longitudinal forces on each of the wheels are restricted to the maximum allowable value based on friction limit. There are three main control operation levels, namely,\n\n1. Supervisory Controller\n\n2. Upper-level Controller\n\n3. Lower-level Controller\n\nThese control levels described in detail in the adjoining sections.\n\n2. BACKGROUND\n\n2.1. Steps in Developing a Controller\n\nIn order to develop an algorithm for torque allocation the following steps are to be carried out.\n\n1. Characterization of the Desired Dynamic Response\n\nThis can be done in either two ways.\n\na. Simulation\n\nThis is based on the mathematical model of the vehicle developed in any of the vehicle dynamics simulation interface like, Adams-Car, CarSim, Matlab, etc. The vehicle is tested against a standard handling maneuver (for example: ISO 3888 Double lane change (Kanchwala, et al., 2014)).\n\nb. Field Testing\n\nThe vehicle can be tested according to the test criterion of a handling test (National Highway Traffic Safety Administration, Department of Transportation, April 6, 2007) along with a set of sensors mounted in order to get various response characteristics. The desired dynamics can be presented in several ways. Formulas from a simplified model can be represented as:\n\n[[[r.sub.desired] = [f.sub.1] ([delta], [V.sub.x])]; [[[beta].sub.desired] = [f.sub.2] ([delta], [V.sub.x])]]\n\n2. Deciding the Control Type and Layout\n\nSeries of works are needed to be carried out for developing the controller, namely,\n\na. Control of Yaw Rate and Side Slip Angle\n\nSliding mode, PID, Optimal LQ control, Fuzzy, etc.\n\nb. Torque Allocation\n\nTorque vectoring and wheel traction limits to be studied.\n\nc. Control of Wheel Dynamics\n\nControlling the longitudinal slip of different wheels.\n\nd. Characterization of the Electric Motors\n\nThis allows for sharing of pairs of traction / braking to optimize both efficiency/consumption and the dynamic response of the vehicle.\n\n2.2. Vehicle Dynamics Control - VDC\n\nVDC and stability control systems (Wang & Longoria, June, 20061 have attracted considerable attention from both academic and industry researchers. Main objective of VDC is to make the vehicle respond as intended by the driver (especially in adverse conditions) and to alleviate driver workload. This can be achieved by coordinating the actuation resources (tires) to expand the system operational envelope.\n\nWhile cornering at high lateral acceleration, tire forces approach to or are at the physical limit, i.e. road adhesion. The vehicle side-slip angle grows and the effectiveness of vehicle steering angle in generating yaw moment reduces significantly because of tire force saturation. This fact is first illustrated by the so-called [beta]-method (Shibahata, et al., 1993).The decrease of restoring yaw moment generated by tire lateral force at high side-slip is the main cause of vehicle unstable motion. By the addition of an external yaw moment the vehicle stability can be recovered. Generally, the number of actuation inputs (slip and slip angles of four tires) is more than the number of control variables (longitudinal, lateral velocities and yaw rate). Therefore, a hierarchically coordinated control structure with control allocation provides a suitable approach (Fredriksson, et al., 2004: Wang & Longoria, June, 2006).\n\nFrom vehicle dynamics point of view, yaw rate and side slip angle are closely related with vehicle maneuverability and lateral stability (Cho, et al.,2006). Based on driver steering input, desired yaw rate is determined, and correspondingly the desired yaw moment for this yaw rate is obtained. In coordinated VDC systems, reference model provides vehicle reference motions based on driver commands. The higher-level controller produces the generalized control efforts such as imposed forces and moments required to meet desired vehicle states. Control allocation optimally distributes the slip ratio and slip angle of each tire to simultaneously induce desired longitudinal and lateral forces (Li, et al.,2008: Li, et al., 2009). The task of a combined tire slip and slip angle tracking (Tire forces controller) controller is to manipulate driving/braking torque and steering angle of all wheels, independent of vehicle state. Corresponding vehicle states are fed back to higher level controller to close the loop. External yaw moment, independent of lateral forces and steering angle, is generated by the transverse distribution of vehicle braking force between left and right wheels. It is known as differential braking and is achieved using the main parts of anti-lock braking system (Van Zanten, et al., 1998). Longitudinal (braking and driving) forces for implementing VDC systems gives quick control action and is possible to integrate relevant hardware with existing anti-lock/spin systems (Van Zanten, 2000).\n\n2.3. State of Art: Control Law and Strategies\n\nThe key point in the strategy of yaw stability control law is to find required corrective yaw moment. Control laws, defined by the researchers in previous research, have the likeness of using yaw rate and vehicle slip angle as control variables. They differ in control strategies, which are addressed below.\n\nA fuzzy logic based direct yaw control for all wheel drive (AWD) EV is proposed in (Tahami, et al., 2003) which is taken as Case 1 (Figure 3) for discussion. A novel strategy is adopted where yaw rate and wheel slip ratio is controlled in the control loop. Separate fuzzy logic based controllers for yaw rate and wheels' slip ratio are used, where the yaw rate controller is determining the required torque. Corrective torque from yaw controller can saturate the tire force, to avoid this a slip controller is used to keep the slip ratio within the stable region. In yaw rate controller, reference yaw rate is generated by neural-network. It generates the reference yaw based on the vehicle speed and steering.\n\nIn case 2, (Figure 4), controller is designed to calculate the desire yaw moment from yaw rate error and vehicle slip angle error (Li, et al., 2008). Desired wheels' slip ratios are calculated based on desired yaw moment using fuzzy logic. It is assumed that ABS/TCS is available to manipulate braking or wheel traction. The key points in this paper realized are, the controller has used yaw rate and slip angle to find yaw moment and it is responsible for controlling the individual wheel sleep.\n\nIn Case 3, (Figure 5), for more robustness an active front steering controller is used. This controller is based on sliding mode control which provides the corrective steering angle (Zhao, et al., 2009). Rest of control architecture is same as Case 2. Use of steering control along with fuzzy controller is a novel strategy.\n\nA PID controller for lateral acceleration error, a sliding mode controller for yaw rate error and another PID controller for wheel sleep error is used by (Kim & Kim, 2006: Kim & Kim, 2007) which is taken as Case 6 (Figure 6). Corrective wheel torques, generated by these three controllers, is then combined and used as total corrective torque to control the yaw rate of the vehicle.\n\nFrom the above discussion, one can notice different strategies of torque based ESC for EVs. Several controllers like fuzzy, sliding mode control and neural network to control the system.\n\nDirect yaw moment control (DYC) introduced vehicle directional stability control under emergency situations (Mirzaei, 2010). It is shown that DYC is the most effective method of motion control compared with the other conventional control systems such as four wheel steering (4WS) (Abe, 1999: Selby, et al., 2001). The 4WS control, which depends on the relation between tire lateral force and the steer angle as a control command. It is efficient at small values of lateral acceleration, as the steer input has negligible effect on yaw moment when wheel force saturates. Despite the high efficiency of DYC in a wide range of operation, the external yaw moment (control input), should be kept as low as possible because of its some undesirable effects. It slows down the vehicle as corrective yaw moment is applied through the brakes. This effect must be kept to a minimum so that the driver can feel supported rather than overruled. Limiting excessive use of external yaw moment by integrating DYC and 4WS is studied by (Selby, et al., 2001).\n\nDepending on which variable is controlled, different control types of DYC have been proposed. The yaw rate control by DYC has been studied frequently (Esmailzadeh, et al., 2003: Mokhiamar & Abe, 2002: Mokhiamar & Abe, 2006). Some researchers have used the side-slip control type of DYC (Abe, 1999: Abe, et al., 2001). However, both variables have been controlled simultaneously by DYC (Park, et al., 2001: Ghoneim, et al., 2000).\n\nIn both side-slip control and yaw rate control by DYC, the desired (reference) models of these variables are established according to driver steering commands. Several researchers have used the steady-state behavior of linear vehicle model during a cornering maneuver as a desired model for the yaw rate with zero side slip (Esmailzadeh, et al., 2003: Geng, et al., 2009).\n\nThese models do not include the transient response for vehicle motions and therefore make large tracking errors at the beginning of maneuvers. Some researchers have used linear 2-DOF vehicle plane model (bicycle model) to be followed by the controller (Mokhiamar &Abe, 2006: Kanchwala, et al., 2015). Although the linear bicycle model shows a stable motion, it is unable to predict the tire/road conditions. It is desirable to develop a linear 2-DOF model with tire/road conditions.\n\nThere are several control methods to achieve the desired vehicle behavior using DYC in the literature. Ghoneim, et al., 2000 introduced a feedback control using yaw rate with proportional-derivative (PD) structure, while Geng, et al., 2009 used PID structure. Sliding mode control method has been also employed in finding the yaw moment control law (Abe, et al., 2001). In these methods, the optimization is not used as a main procedure in finding the control laws. A predictive optimal yaw stability controller based on a linearized vehicle model was by (Yamakawa & Watanabe, 2006). Some researchers have developed the well-known LQ theory to improve vehicle handling and stability using on-line numerical computations in optimization, but are not suitable for real-time implementation (Tark, et al., 2001). Esmailzadeh, et al., 2003 have presented an analytical solution for LQ problem, but the controller is based on tracking only reference yaw rate obtained from steady-state behavior of vehicle during cornering. In (Mirzaei, 2010), a complete LQ optimal problem is formulated to track the proposed desired model for both yaw rate and side-slip angle. The derived control law is developed in an analytical closed form which is easy to solve and implement. Also, different control forms are examined and effect of weighting factors on system performance is seen.\n\nApart from these control architectures researchers have also used model predictive control for direct yaw control (Kanchwala & Bordons, 2015). The wheel torques are independently controlled by using direct yaw moment and side slip control method to pro-actively improving vehicle handling. At high value of side slip the steering is no more capable of generating yaw moment and vehicle becomes laterally unstable. By unequal torque distribution a restoring yaw moment is generated and vehicle stability is ensured. The MPC monitors the Couple traction/braking torque of the four in-wheel motors, from basic driving slogans, which are, steering angle and desired speed. The model predictive control architecture has also been used to make the vehicle follow a desired path such as in the case of autonomous drive (Kanchwala & Ogai, 2016).\n\n3. REVIEW ON THREE MAJOR CONTROLLERS\n\nAs discussed in Section 1, there are three major levels of control operation namely,\n\n1. Supervisory controller\n\n2. Upper-level controller\n\n3. Lower-level controller\n\nSupervisory controller (Kang, et al., 2011) determines the control mode and dynamics for vehicle stability based on an admissible control region which is the relationship between the vehicle speed and the maximum curvature of the vehicle considering steering, sideslip, and rollover constraints (Yoon, et al., 2007: Cho, et al., 2010). Upper level controller computes the traction force input and the yaw moment input to track the desired dynamics (Baffet et al., 2006). Finally, the lower level controller is designed to obtain actual actuator commands (front and rear driving motor torques and independent brake torques), to apply upper level control inputs (Tahami, et al, 2004).\n\n3.1. Supervisory Controller\n\nThe Supervisory controller mainly determines the admissible control region.\n\nAdmissible Control Region\n\nThe admissible control region can be computed using the steering and sideslip constraints. These are described below:\n\n1. Steering Constraint\n\nThe steering constraint describes the limitation imposed by kinematic steering and handling properties on the attainable manoeuvre. The steering constraint can be obtained from a two degrees of freedom (2-DOF) bicycle model and the definition of slip angle.\n\n2. Sideslip Constraint\n\nIt describes the maximum curvature of the vehicle for lateral stability. Although some sideslip is expected and likely unavoidable, substantial slip causes large heading or trajectory tracking errors. Vehicle begins to skid when lateral traction force is equal to tire-road friction limit.\n\nIn unified chassis control (UCC) (Yoon, et al., 2010), the improvement of maneuverability and lateral stability is achieved by reducing the yaw rate error between actual and reference yaw rate (driver's steering input). Two types of reference yaw rates are derived according to control mode, i.e., the maneuverability mode, ESC-y (Electronic Stability Control) and lateral stability mode ESC-p. Each control mode generates a control yaw moment and longitudinal tyre force. The switching among control modes is performed based on the thresholds. For small sideslip angle, the controller is in the maneuverability mode, ESC-y and vice versa. The activation condition of the stability mode is determined by a phase plane analysis on the sideslip angle and sideslip angle rate. In ESC-y, a target yaw rate is generated based on the driver's steering input for maneuverability while in ESC-P, it is generated to reduce excessive sideslip angle for lateral stability.\n\nThe thresholds, [[gamma].sub.e,th] and [[beta.sub.th] are to be carefully determined. There have been several methods to determine the threshold for the sideslip angle. The most relevant method is to use the phase plane analysis (Chung and Yi, 2006). However, it requires the sideslip angle rate, which is difficult to measure or estimate. Hence, threshold value [[beta].sub.th] is used in the work of Yoon et al., 2010, and the value is set to 3[degrees] under the assumption of [micro] = 0.35 (Rajamani, et al., 2012). The threshold of yaw rate error [[gamma].sub.e,th] is set as 0.08 rad/s considering a case when vehicle undergoes a lane change at 60 kmph.\n\n3.2. Upper Level Controller\n\nThe upper level controller is designed to compute the desired traction force input [F.sub.x_des] and desired yaw moment input [M.sub.z_des] for desired dynamics tracked by Supervisory controller. Upper-controller systems are widely discussed (Tseng, et al., 1999: Yi, et al., 2003: Rajamani, et al., 2012). It mainly consists of three main parts, a traction force calculator, a speed controller, and a yaw rate controller (Kang, et al., 2011). The traction force calculator determines the traction force corresponding to the human driver's input, [F.sub.x_Human] (Accelerator/Brake pedal signal: APS/BPS, Figure 7). The upper level controller is further sub-divided into two parts, namely,\n\n1. Speed controller\n\n2. Yaw rate controller\n\nSpeed Controller\n\nIt follows the desired speed determined by the supervisory controller. The desired traction force is determined by traction force calculator or speed controller according to the control mode. It is designed based on sliding-mode control (SMC) method to obtain traction force\n\nYaw Rate Controller\n\nThe yaw rate controller computes the yaw moment input to track the desired yaw rate. It computes yaw moment input to reduce the yaw rate error again using SMC.\n\nIt is important to discuss to identify what are the required control parameters. If the controller is designed using only yaw rate as the control variable it would fail to stabilize the vehicle on the road where tire road adhesion is low (Al Emran Hasan, et al. 2013). At low friction vehicle slip angle increases rapidly without influencing lateral force, yaw rate and lateral acceleration. The controller should take both of the yaw velocity and slip angle as controller parameters else the vehicle would not achieve stability in critical situation (Kost, et al., Robert Bosch GmbH. 1996; Gutierrez, et al., 2011).\n\nThe Yaw Rate and Side slip controllers are discussed below.\n\n3.2.1. Yaw Rate Controller\n\nTo compensate the loss of vehicle stability in emergency situations due to nonlinear characteristics of tire forces, a linear 2DOF (Figure 8) vehicle plane model (bicycle model) with appropriate physical constraints is proposed as a desired model to be followed by the controller. The governing equations for the linear vehicle model, in the state space form, are expressed as (Wong. J.Y., 2008):\n\n[mathematical expression not reproducible] (1)\n\n[mathematical expression not reproducible] (2)\n\nIn the above equations, the vehicle side-slip angle [beta] and the yaw rate r are the two state variables. The front wheel steering angle d is considered as the driver input. Other parameters are:\n\n[C.sub.af], [C.sub.ar]: Cornering stiffness of the front and rear tires; [l.sub.1] [l.sub.2]: Distances of CG from front and rear axles; m: Vehicle mass; [I.sub.2]: Moment of inertia about vertical axis; [V.sub.x]. Longitudinal velocity.\n\nThe steady-state vehicle yaw rate and side slip during a constant cornering maneuver is obtained as,\n\n[mathematical expression not reproducible] (3)\n\n[mathematical expression not reproducible] (4)\n\nThe steady-state value of vehicle side-slip angle in terms of yaw rate is given by,\n\n[mathematical expression not reproducible] (5)\n\nReferring to the vehicle dynamics model, the term of lateral acceleration is defined as:\n\n[mathematical expression not reproducible] (6)\n\nwhere, [V.sub.y] is the lateral velocity. Therefore, steady-state value of yaw rate is defines as,\n\n[mathematical expression not reproducible] (7)\n\nSince the lateral acceleration of the vehicle in terms of 'g' units and it cannot exceed the maximum road coefficient of friction (Cho. et al., 2008) the maximum steady-state value of yaw rate [r.sub.ss] must be limited to,\n\n[mathematical expression not reproducible] (8)\n\nThe measured lateral acceleration a can be taken instead of [mu]g. Now, the constraint |[r.sub.ss|max] can be easily applied to the linear vehicle model. In this way, combination of the following condition with previous equations makes limits the desired yaw rate to a value compatible with tire/road conditions.\n\n[mathematical expression not reproducible] (9)\n\nTo increase the vehicle stability limit, an intentional modification of yaw rate response from second to first order model has been proposed (Mokhiamar & Abe, 2002). This modification is due to the fact that when side-slip angle converges to zero, yaw rate can be reduced to a first-order lag. As a result, the proposed yaw rate (dynamic response) by keeping its steady-state value is given by,\n\n[mathematical expression not reproducible] (10)\n\nThe yaw-rate error is,\n\n[[DELTA]r = [r - [r.sub.des]]] (11)\n\nFeedback of yaw-rate error is used to demand a desired yaw-rate torque from the lower controller. The moment command is generated based on the yaw rate error, where desired yaw rate is inferred from driver commanded steer angle rate (Hallowell & Ray, 2003). The moment is approximated as,\n\n[M = K[I.sub.zz]([r.sub.des] - r)] (12)\n\nWhere, K is the gain factor, [r.sub.des] is the desired yaw acceleration, and r is the actual yaw command.\n\nFor a real-time controller an actual yaw rate of a vehicle is measured directly using electronic yaw rate sensors. But for simulation actual yaw rate is found from vehicle model. Desired yaw rate is determined from steady state relation between steering angle and vehicle trajectory. In Unified chassis controller (Yoon, et al., 2010). ESC-[gamma] is designed to force vehicle to track a reference yaw rate generated by a driver's steering input. The dynamic equation of yaw rate can be presented as,\n\n[mathematical expression not reproducible] (13)\n\nTyre cornering stiffness ([C.sub.[alpha]f], [C.sub.[alpha]r]) is influenced by vertical load, slip angle and wheel slip. Since the tyre cornering stiffness has inherent nonlinearity and uncertainty, the sliding mode control (SMC) method has been used for the design of the desired yaw moment in order to incorporate directly the uncertainties in control design stage. Cornering stiffness deviation from actual value is bounded as,\n\n[|[C.sub.]alpha]i] - [C.sub.[alpha]i]| [less than or equal to] [F.sub.i] (i = f, r)] (14)\n\nWhere '[C.sub.[alpha]i]' indicates the best estimate of the actual value, of [C.sub.[alpha]i]. Defining a sliding surface, [S.sub.1] as\n\n[[[S.sub.1] = r - [r.sub.des]]; differentiating gives [[S.sub.1] = r - [r.sub.des]]] (15)\n\nSubstituting Equation (15) in (13) yields,\n\n[mathematical expression not reproducible] (16)\n\nThe equivalent control input that would achieve [S.sub.1] = 0 is given by,\n\n[mathematical expression not reproducible] (17)\n\nIn above equation the second discontinuous term is introduced to satisfy sliding condition regardless of model uncertainty ([C.sub.[alpha]f], [C.sub.[alpha]r]). Substituting Equation (17) into sliding condition ([S.sub.1][S.sub.1] [less than or equal to] [[eta].sub.1]|[S.sub.1]|), gives gain [k.sub.1],\n\n[mathematical expression not reproducible] (18)\n\nwhere, [[eta].sub.1] is a positive constant. In (Yoon et al.. 2010), [[eta].sub.1] is set as 10.\n\n3.2.2. Vehicle Side Slip Angle Controller\n\nVehicle body side slip angle is one of the most significant parameters in vehicle stability (Al Emran Hasan, et al., 2013). It is the angle between vehicle longitudinal axis and direction of velocity at CG\n\n[[beta] = [[V.sub.y]/[V.sub.x]]] (19)\n\nSide slip angle cannot be measured using any commercially available sensor. In real time, using lateral accelerometer along with a yaw rate sensor is used to estimate the side slip angle of the vehicle. Desired side slip angle [[beta].sub.des] can be obtained from steady state steering angle by equation (4). The measured side slip angle is compared with desired side slip angle and the error between them is fed to the control law of ESC-[beta] Using 2D bicycle model, vehicle lateral dynamics is expressed as,\n\n[m[V.sub.y] = -m[V.sub.x]r + 2[F.sub.yf]cos[delta] + 2[F.sub.yr]] (20)\n\nFrom Equation (20). assuming that [V.sub.x] [approximately equal to] 0, the sideslip angle dynamics can be arranged as follows:\n\n[mathematical expression not reproducible] (21)\n\nIf the reference yaw rate for the lateral stability is defined as,\n\n[mathematical expression not reproducible] (22)\n\nThen, body sideslip angle changes into a stable dynamics as shown in previous Equations, which implies that the body sideslip angle asymptotically converges to zero.\n\n[mathematical expression not reproducible] (23)\n\nWhere, [K.sub.[beta]] is a design parameter which is strictly positive. In this study, [K.sub.[beta]] is set to 3.\n\nSome researchers have used both Yaw rate error and side slip error to generate restoring yaw moment (Geng. et al.. 2009; Mirzaei. 2010; Al Emran Hasan, et al., 2013). The linear quadratic (LQ) method is considered as a suitable tool for solving such problem (Mirzaei. et al., 2008). In order to formulate a complete LQ problem, a performance index that penalizes the tracking errors and control expenditure is first considered in the following form:\n\n[mathematical expression not reproducible] (24)\n\nwhere, [w.sub.b], [w.sub.r] and [w.sub.u] are weighting factors indicating relative importance of corresponding terms. [M.sub.z] is the external yaw moment which must be determined from control law. The subscript d denotes the desired response. Minimizing J improve tracking accuracy with minimum external yaw moment.\n\nThe coefficient [w.sub.[beta]] (0 [less than or equal to] [w.sub.[beta]] [less than or equal to] 1) is introduced in the performance index as a weighting factor on [beta] deviation by Geng, 2009. It is defined as,\n\n[w.sub.b] = [q.sup.2][w.sub.[beta]] and [w.sub.r] = [q.sup.](1 - [w.sub.[beta]]) where,\n\n[mathematical expression not reproducible] (25)\n\nwhere, [[beta].sub.0] is a threshold value which has been set as 10[degrees] (Geng. et al., 2009).\n\nA sliding mode based control law has been chosen with the weighted combination of yaw rate error and slip angle error (Al Emran Hasan, et al., 2013). The control law is described below, where is the sliding surface, is the yaw rate, is the controller variable and is the actual side-slip of the vehicle.\n\n[S = r - [r.sub.des] + [epsilon]([beta] - [[beta].sub.des])] (26)\n\nController determines amount of required torque at each wheels to generate a corrective yaw moment to meet the targeted yaw rate determined desired value generator. From wheel torques rotational velocity of the wheel or tires is determined and then a lower controller can track the wheels' rotations. Simulations have been performed with the popular sine with dwell maneuver which has been used by transport authorities around the world for stability testing (Picot. et al., 2011).\n\n3.3. Lower Level Controller\n\nThe lower controller ensures that the yaw or side slip-mitigation correction commands of upper controller can be obtained from the torque-management devices. It is designed to obtain actual actuator commands, front and rear driving motor torques and independent brake torques. An optimization based control allocation strategy is used to map control inputs to actual actuator commands (Kang. et al., 2011). Lower level controller has to control speed and wheel slip (Traction control), perform torque estimation, allocate torques to the individual wheels. In addition to these it should take motor characteristics into account by precise motor modeling. A detailed state of the art survey is been given about lower level controller design and the method of operation in this section.\n\nThese are the four main steps to be followed while designing the lower level controller. These steps are briefly discussed below.\n\n3.3.1. Wheel Slip Control\n\nFirst role of the lower level controller iswheel slip control. A wheel slip controller is essentially a traction control system. It is designed to keep the wheel slip ratio [i.sub.x] of each wheel below [i.sub.x_max]. It is only activated when the magnitude of the wheel slip ratio is larger than [i.sub.x_max]. It determines the net torque command of wheel so that actual wheel speed tracks desired wheel speed for slip limitation.\n\nTraction control is developed to ensure the effectiveness of the torque output. It is necessarily an anti-slip control (Yin et al., 2009). In general traction control systems utilize the non-driven wheel velocities to provide an approximate vehicle velocity. However, this method is not applicable when the vehicle is accelerated by 4WD systems or decelerated by brakes. For this reason, the accelerometer measurement is used to calculate the velocity, but it cannot avoid offset and error issues. Other sensors, e.g., optical sensors (Turner & Austin, 2000), magnetic markers Tee & Tomizuka, 1996: Lee &\n\nTomizuka, 2003: Suryanarayanan & and Tomizuka, 2007), etc., can also obtain the chassis velocity. However, they are too expensive to be applied for an actual vehicle real-time control.\n\n(Tahami, et al., 2004) used a data fusion method for this purpose. The wheel linear speeds are used as pseudo sources of vehicle speed. Via integration of the acceleration another estimate for vehicle velocity is made available. For this purpose, an additional accelerometer is embedded in the vehicle in order to measure the vehicle longitudinal acceleration. The inputs are all fed into an estimator, where a Fuzzy logic determines which input is more reliable. Inputs are weighted and averaged to give the estimated speed. Figure 9 shows the block diagram of the estimator and it consists of two stages. In first stage preprocessing occurs, the wheel slips are calculated using the previous estimated vehicle speed and the measured wheel speeds. In next stage, wheel linear speeds and vehicle speed obtained by integration are weighted using Fuzzy rules.\n\nThe weighted values are averaged to give vehicle speed. Rule sets, which are used for weights are:\n\n1. In cruise driving, the integral of the vehicle acceleration is not reliable, since the accelerometer signal is comparable to offset and noise of the measuring circuit.\n\n2. In braking situation all wheel speeds are weighted low, because of large wheel slips.\n\nThe focus is on the development of a core traction control system based on the maximum transmissible torque estimation (MTTE) that requires neither chassis velocity nor information about tire-road conditions. In this system, only the torque reference and the wheel rotation speed is used to estimate the maximum transmissible torque. The differential equations for the calculation of longitudinal motion of the vehicle are described as:\n\n[[J.sub.w][omega] = T-r[F.sub.d]] (27)\n\n[m[V.sub.x] = [[F.sub.d] - [F.sub.dr]]] (28)\n\n[[V.sub.w] = r[omega]] (29)\n\n[[F.sub.d] ([i.sub.x]) = [mu]N] (30)\n\nWhere: [J.sub.w]: Wheel inertia; [V.sub.w]: Wheel velocity; [omega]: Wheel rotation speed; T: Driving Torque; r: Wheel radius; [F.sub.d]. Friction Force (Driving force); m: Vehicle Mass; N: Normal load; [V.sub.x]. Chassis Velocity (Vehicle velocity); [F.sub.dr] Driving resistance; [i.sub.x]. Slip ratio and [mu] Friction coefficient. The relation between slip ratio and friction coefficient can be described by various formulas. (Yin, et al., 20091 used widely used magic formula based tyre model (Pacejka & Bakker, 1992) to build a vehicle model for the simulations.\n\n3.3.2. Torque Estimation: MTTE (Maximum Transmissible Torque Estimation)\n\nTo avoid complicated [mu] - [i.sub.x] relation, only dynamic relation between tire and chassis is considered based on below considerations, which transform anti-slip control to max transmissible torque control.\n\n1. Kinematic relationship between wheel-chassis is fixed and known independent of road type.\n\n2. During acceleration, considering stability and tire slip, a well-managed control of difference of velocity between wheel and chassis is more important than mere pursuit of max acceleration.\n\n3. If wheel and chassis accelerations are well controlled, then the difference between wheel and chassis velocities, i.e., the slip, is also well controlled.\n\nThe driving force, i.e., the friction force between the tire and the road surface, can be calculated as (Kanchwala & Wideberg, 2016):\n\n[mathematical expression not reproducible] (31)\n\nIn normal road conditions, [F.sub.d] is less than the maximum friction force from the road. However, when slip occurs, [F.sub.d] equals the maximum friction force that the tire-road relation can provide and cannot increase with T. The difference between wheel and chassis velocities becomes more, i.e., the acceleration of wheel is more than that of chassis. Therefore, for slip not to start or become severe, the acceleration of the wheel must be close to that of the chassis. Moreover, considering [mu] - [i.sub.x] relation described in Magic Formula, appropriate difference between chassis velocity and wheel velocity is necessary to generate friction force. Accordingly, a relaxation factor, a is introduced as an approximation between chassis and wheel acceleration, given by,\n\n[mathematical expression not reproducible] (32)\n\nFor no or limited slip, [alpha] should be close to one. With a designed [alpha], when the vehicle enters a slippery road, [T.sub.max] must be reduced adaptively following the decrease of [F.sub.d] to satisfy, the no-slip condition. Since the friction force from road is available, the maximum transmissible torque [T.sub.max] is.\n\n[mathematical expression not reproducible] (33)\n\nThis formula allows a certain maximum torque output from the wheel (for given [F.sub.d]) so as not to increase the slip. Finally, the proposed controller uses [T.sub.max] to constrain torque reference if necessary. In lower level controller, optimal distribution algorithm is designed to generate actuator commands for efficient driving, minimization of the allocation error, and slip limitation. To distribute the actuator commands, the LQ constrained problem is formulated as a weighted least-squares (WLS).\n\n3.3.3. Torque Allocation\n\nIn torque controller (Figure 10), the limiter with a variable saturation value controls the torque output according to the dynamic situation. Under normal conditions, the torque reference pass through the controller without any effect, but on a slippery road, the controller constrains the torque output close to [T.sub.max]. At first, the estimator uses commanded torque into inverter and rotation speed of wheel to calculate friction force, and it then estimates maximum transmissible torque. Finally, it utilizes estimated torque value as a saturation value to limit the torque output.\n\nIt causes a phase shift, due to low resolution of the shaft encoder installed in wheel, a low-pass filter (LPF) with time constant of [[tau].sub.1] is introduced to smooth digital signal [V.sub.w] fed to the differentiator. In order to keep the filtered signals in phase, another LPF with a time constant of [x.sub.2] is also added.\n\nIn (Yamakawa. et al., 2007). a method of torque allocation and control for electric off-road vehicles based on a PD control is proposed. In order to examine optimal wheel torque distribution to the front and rear wheels on rough ground, a numerical vehicle model was constructed for the pitch plane.\n\nFor wheel torque distribution with the vehicle model, the following two methods are employed,\n\nA. Determining the torque on each wheel to control the speed of individual wheels; and\n\nB. Determining the torque on each wheel based on vertical load on wheel to control vehicle speed.\n\nIn order to compare efficiency, both numerical models drive the vehicle at same speed using speed feedback control. Motor torque is determined by the following feedback system with PI control.\n\n[mathematical expression not reproducible] (34)\n\nWhere, [K.sub.p] and [K.sub.i]: proportional and integral gains, [V.sup.T]: target velocity, and [V.sup.R]: wheel velocity. The integral control in the second term is added to reduce the system's steady-state error. Fig. 11 shows the block diagrams for the feedback systems A and B respectively. System A uses wheel speed feedback while System B applies feedback based on the vehicle's center of mass velocity to estimate the necessary total torque on the vehicle, and then allocates torque to each wheel based on the ratio of vertical loads. If wheel torque computed by the loop exceeds maximum torque available at each wheel, a block followed by PI blocks saturates (limits) wheel torque using the following algorithm.\n\n[mathematical expression not reproducible] (35)\n\nThe wheel torques obtained above have to be generated by the motor. Precise motor modelling is required to generate this torque. A permanent magnet motor model torque dynamics model is used in fZhao. et al., 2009) to provide demanded required torque by stability system of an all-wheel drive EV. A relatively similar second order motor torque dynamics model is used by (A1 Emran Hasan, et al., 2013) as.\n\n[mathematical expression not reproducible] (36)\n\n3.3.4. Handling Actuator Constraints\n\nIn the actuator constraints, actuator limits and the friction circle limit at each wheel should be considered. In most proposed model, the friction force is assumed to be determined by wheel slip. Let [F.sub.x] be longitudinal friction force and [F.sub.z] be vertical load. Then, tire/road friction coefficient is,\n\n[[[mu].sub.x] = [[F.sub.x]/[F.sub.z]]] (37)\n\nThe longitudinal wheel slip [i.sub.x] can be defined as,\n\n[mathematical expression not reproducible] (38)\n\nWhere, [r.sub.ef] is the effective wheel radius, [omega] is angular velocity. Normally, [[mu].sub.x] increases when vehicle velocity decreases or the road surface becomes rough. With given conditions, [[mu].sub.x] is a nonlinear function of [i.sub.x] with a distinct maximum (maximum of friction). The relationship of [[mu].sub.x] and [i.sub.x] can be clearly distinguished into two parts: the steady rising part of the [[mu].sub.x] - [i.sub.x] graph and the local sliding part in which [[mu].sub.x] gradually decreases to [[mu].sub.x_glide].\n\n4. CONCLUSIONS\n\nThe method of individual motor torque control has been investigated in this paper. The aim of this literature survey was to develop a path which can be followed while developing a torque vectoring system. Next step is the development and experimental testing of these novel control algorithms on actual vehicle. We were able to develop a systematic guideline of various works involved in developing such a system.\n\nThe paper began with steps in developing the controller. For most of the control applications a mathematical model of the vehicle is developed. The virtual vehicle model must be validated by field test results to ensure model accuracy. Next step was to decide control type and layout. Various control types are available in literature but we have found that an optimal LQ controller is most suitable in automotive control applications. The reason is that it is robust and relatively less significant to system parameter variabilities which are often encountered in an automobile.\n\nThe process of control law development is broadly divided in three sub-sections namely, Supervisory control, Upper level control and Lower level control design.\n\nSupervisory controller mainly determines the Admissible Control Region. For supervisory control, the unified chassis control (UCC) from (Yoon. et al., 2010) gives detailed explanation of setting the thresholds, [[gamma].sub.th] and [[beta].sub.th] for yaw rate and side slip errors. Upper level controller from (Kang, et al., 2011) is fairly detailed as it defines the relationship between the vehicle speed and the maximum curvature of the vehicle considering steering, sideslip, and rollover constraints. Finally, lower level controller is been discussed. There are the four main steps to be followed while designing the lower level controller. First step is longitudinal slip control design (traction control) for which the fuzzy logic based speed estimator of (Tahami, et al., 2004) is most appropriate for field applications as it is computationally very quick., torque allocation algorithm. Then comes the torque estimation algorithm which was discussed by maximum torque transmissibility equation. The torque allocation algorithm by (Yamakawa & Watanabe, 2006), proposes a method of torque allocation and control for electric off-road vehicles based on a PD control which is found to be most appropriate. Finally, motor torque characterisation and the process of doing the same is shown in section 3.3.4.\n\nYaw Rate and Side slip controller development methodology has also been discussed separately in a great detail. The mathematical model is been formulated and the equations are presented. Moreover, the wheel torque allocation based on the yaw rate and side slip controller is also been taken into account with the lower level controller model equations separately defined.\n\nThe works involved in development of a control system have been properly sub-divided in a logical fashion. From the vast amount of available literature, most relevant papers were selected and are discussed. We hope this guideline serves the needs of a vehicle control system designer.5.\n\n5. REFERENCES\n\n1. Abe, M., 1999. Vehicle dynamics and control for improving handling and active safety: from four-wheel steering to direct yaw moment control. Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics, 213(2), pp. 87-101.\n\n2. Abe, M. et al., 2001. Side-slip control to stabilize vehicle lateral motion by direct yaw moment. JSAE review, 22(4), pp. 413-419.\n\n3. Al Emran Hasan, M., Ektesabi, M. & Kapoor, A., 2013. An investigation into differential torque based strategies for electronic stability control in an in-wheel electric vehicle. Interantional Journal Engineering Innovative Technology, Volume 7, pp. 327-336.\n\n4. Baffet, G., Charara, A. & Stephant, J., 2006. Sideslip angle, lateral tire force and road friction estimation in simulations and experiments. IEEE International Conference on Control Applications, 2006 IEEE International Symposium on Intelligent Control, pp. 903-908.\n\n5. Cho, W. et al., 2006. An investigation into unified chassis control scheme for optimised vehicle stability and manoeuvrability. Vehicle System Dynamics, 46(S1), pp. 87-105.\n\n6. Cho, W. et al., 2008. An investigation into unified chassis control scheme for optimised vehicle stability and manoeuvrability. Vehicle System Dynamics, 46(S1), pp. 87-105.\n\n7. Cho, W. et al., 2010. Estimation of tire forces for application to vehicle stability control. IEEE Transactions on Vehicular Technology, 59(2), pp. 638-649.\n\n8. Esmailzadeh, E., Goodarzi, A. & Vossoughi, G., 2003. Optimal yaw moment control law for improved vehicle handling. Mechatronics, 13(7), pp. 659-675.\n\n9. Fredriksson, J., Andreasson, J. & Laine, L., 2004. Wheel force distribution for improved handling in a hybrid electric vehicle using nonlinear control. 43rd IEEE Conference on Decision and Control, Volume 4, pp. 4081-4086.\n\n10. Geng, C., Mostefai, L., Denai, M. & Hori, Y., 2009. Direct yaw-moment control of an in-wheel-motored electric vehicle based on body slip angle fuzzy observer. IEEE Transactions on Industrial Electronics, 56(5), pp. 1411-1419.\n\n11. Ghoneim, Y et al., 2000. Integrated chassis control system to enhance vehicle stability. International Journal of Vehicle Design, 23(1-2), pp. 124-144.\n\n12. Gutierrez, J., Romo, J., Canibano, E. & Merino, J., 2011. Control algorithm development for independent wheel torque distribution with 4 in-wheel electric motors. Fifth UKSim European Symposium on Computer Modeling and Simulation (EMS). IEEE, pp. 257-262.\n\n13. Hallowell, S. & Ray, L., 2003. All-wheel driving using independent torque control of each wheel. Proceedings of the American Control Conference, 2003. IEEE, Volume 3, pp. 2590-2595.\n\n14. Ji, S. et al., 2012. Electric vehicles in China: emissions and health impacts. Environmental science & technology, 46(4), pp. 2018-2024.\n\n15. Kanchwala, H. and Bordons, C., \"Improving Handling Performance of an Electric Vehicle Using Model Predictive Control,\" SAE Technical Paper 2015-01-0082, 2015, doi:10.4271/2015-01-0082.\n\n16. Kanchwala, H., Nan, W. & Ogai, H., 2014. Model Building Hardpoint Optimization & Experimental Correlation of a Single Seater EV-Toyota COMS. 2nd International Conference on Research in Science, Engineering and Technology (ICRSET2014), pp. 65-72.\n\n17. Kanchwala, H. and Ogai, H., \"Development of an Intelligent Transport System for EV,\" SAE Int. J. Passeng. Cars - Electron. Electr. Syst. 9(1):9-21, 2016, doi:10.4271/2015-01-9132.\n\n18. Kanchwala, H. & Wideberg, J., 2016. Pitch reduction and traction enhancement of an EV by real-time brake biasing and in-wheel motor torque control. International Journal of Vehicle Systems Modelling and Testing, 11(2), pp. 165-192.\n\n19. Kanchwala, H., Wideberg, J., Alba, C. B. & Marcos, D., 2015. Control of an independent 4WD electric vehicle by DYC method. International Journal of Vehicle Systems Modelling and Testing, 10(2), pp. 168-184.\n\n20. Kang, J., Yoo, J. & Yi, K., 2011. Driving control algorithm for maneuverability, lateral stability, and rollover prevention of 4WD electric vehicles with independently driven front and rear wheels. IEEE Transactions on vehicular technology, 60(7), pp. 2987-3001.\n\n21. Kim, D. & Kim, H., 2006. Vehicle stability control with regenerative braking and electronic brake force distribution for a four-wheel drive hybrid electric vehicle. Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering, 220(6), pp. 683-693.\n\n22. Kim, J. & Kim, H., 2007. Electric vehicle yaw rate control using independent in-wheel motor. Power Conversion Conference-Nagoya. PCC07. IEEE, pp. 705-710.\n\n23. Kost, F. et al., Robert Bosch GmbH, 1996. Control of vehicle side slip using yaw rate. U.S. Patent 5,480,219..\n\n24. Lee, H. & Tomizuka, M., 1996. Robust motion controller design for high-accuracy positioning systems. IEEE Transactions on Industrial Electronics, 43(1), pp. 48-55.\n\n25. Lee, H. & Tomizuka, M., 2003. Adaptive vehicle traction force control for intelligent vehicle highway systems (IVHSs). IEEE Transactions on Industrial Electronics, 50(1), pp. 37-47.\n\n26. Li, F., Wang, J. & Liu, Z., 2008. On the vehicle stability control for electric vehicle based on control allocation. Vehicle Power and Propulsion Conference, VPPC'08. IEEE, pp. 1-6.\n\n27. Li, F., Wang, J. & Liu, Z., 2009. Motor torque based vehicle stability control for four-wheel-drive electric vehicle. Vehicle Power and Propulsion Conference, VPPC09. IEEE, pp. 1596-1601.\n\n28. Mirzaei, M., 2010. A new strategy for minimum usage of external yaw moment in vehicle dynamic control system. Transportation Research Part C: Emerging Technologies, 18(2), pp. 213-224.\n\n29. Mirzaei, M., Alizadeh, G., Eslamian, M. & Azadi, S., 2008. An optimal approach to nonlinear control of vehicle yaw dynamics. Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, 222(4), pp. 217-229.\n\n30. Mokhiamar, O & Abe, M., 2002. Effects of model response on model following type of combined lateral force and yaw moment control performance for active vehicle handling safety. JSAE review, 23(4), pp. 473-480.\n\n31. Mokhiamar, O. & Abe, M., 2006. How the four wheels should share forces in an optimum cooperative chassis control. Control engineering practice, 14(3), pp. 295-304.\n\n32. National Highway Traffic Safety Administration, Department of Transportation, April 6, 2007. Federal motor vehicle safety standards. Fed. Reg, 72(66), pp. 17310-17350.\n\n33. Park, K., Heo, S. & Baek, I., 2001. Controller design for improving lateral vehicle dynamic stability. JSAE review, 22(4), pp. 481-486.\n\n34. Picot, N., Miller, B., Rizzo, M., and Klingler, T., \"FMVSS126 Electronic Stability Control Sine With Dwell Incomplete Vehicle Type 2 Analysis,\" SAE Int. J. Passeng. Cars - Mech. Syst. 4(1):713-721, 2011. doi:10.4271/2011-01-0956.\n\n35. Rajamani, R., Phanomchoeng, G., Piyabongkarn, D. & Lew, J., 2012. Algorithms for real time estimation on individual wheel tire-road friction coefficients. IEEE/ASME Transactions on Mechatronics, 17(6), pp. 1183-1195.\n\n36. Rezvani, Z., Jansson, J. & Bodin, J., 2015. Advances in consumer electric vehicle adoption research: A review and research agenda. Transportation research part D: transport and environment, Volume 34. pp. 122-136.\n\n37. Ruther, R. et al., 2015. Strategies for Plug-in Electric Vehicle-to-Grid (V2G) and Photovoltaics (PV) for Peak Demand Reduction in Urban Regions in a Smart Grid Environment. Plug In Electric Vehicles in Smart Grids. Springer Singapore, pp. 179-219.\n\n38. Sawase, K. & Sano., Y., 1999. Application of active yaw control to vehicle dynamics by utilizing driving/breaking force. JSAE review. 20(2), pp. 289-295.\n\n39. Selby, M., Manning, W., Brown, M., and Crolla, D., \"A Coordination Approach for DYC and Active Front Steering,\" SAE Technical Paper 2001-01-1275, 2001, doi:10.4271/2001-01-1275.\n\n40. Shibahata, Y., Shimada, K. & Tomari, T., 1993. Improvement of vehicle maneuverability by direct yaw moment control. Vehicle System Dynamics, 22(5-6), pp. 465-481.\n\n41. Suryanarayanan, S. & and Tomizuka, M., 2007. Appropriate sensor placement for fault-tolerant lane-keeping control of automated vehicles. IEEE/ASME Transactions on mechatronics, 12(4), pp. 465-471.\n\n42. Tahami, F., Farhangi, S. & Kazemi, R., 2004. Afuzzy logic direct yaw-moment control system for all-wheel-drive electric vehicles. Vehicle System Dynamics, 41(3), pp. 203-221.\n\n43. Tahami, F., Kazemi, R. & Farhanghi, S., 2003. A novel driver assist stability system for all-wheel-drive electric vehicles. IEEE Transactions on Vehicular Technology, 52(3), pp. 683-692.\n\n44. Tseng, H. et al., 1999. The development of vehicle stability control at Ford. IEEE/ASME transactions on mechatronics, 4(3), pp. 223-234.\n\n45. Turner, J. & Austin, L., 2000. Sensors for automotive telematics. Measurement Science and Technology, 11(2), p. R58.\n\n46. van Zanten, A., \"Bosch ESP Systems: 5 Years of Experience,\" SAE Technical Paper 2000-01-1633, 2000, doi:10.4271/2000-01-1633.\n\n47. van Zanten, A., Erhardt, R., Landesfeind, K., and Pfaff, G., \"VDC Systems Development and Perspective,\" SAE Technical Paper 980235, 1998, doi:10.4271/980235.\n\n48. Wang, J. & Longoria, R., June, 2006. Coordinated vehicle dynamics control with control distribution. American Control Conference, IEEE 2006, pp. 5348-5353.\n\n49. Wideberg, J. et al., 2014. Development and Experimental Validation of a Dynamic Model for Electric Vehicle with in Hub Motors. Procedia-Social and Behavioral Sciences, Volume 160, pp. 84-91.\n\n50. Wong, J.Y., 2008. Theory of ground vehicles. John Wiley & Sons.\n\n51. Yamakawa, J., Kojima, A. & Watanabe, K., 2007. A method of torque control for independent wheel drive vehicles on rough terrain. Journal of Terramechanics, 44(5), pp. 371-381.\n\n52. Yamakawa, J. & Watanabe, K., 2006. A method of optimal wheel torque determination for independent wheel drive vehicles. Journal of terramechanics, 43(3), pp. 269-285.\n\n53. Yi, K., Chung, T., Kim, J. & Yi, S., 2003. An investigation into differential braking strategies for vehicle stability control. Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering, 217(12), pp. 1081-1093.\n\n54. Yin, D., Oh, S. & Hori, Y., 2009. Anovel traction control for EV based on maximum transmissible torque estimation. IEEE Transactions on Industrial Electronics, 56(6), pp. 2086-2094.\n\n55. Yoon, J., Kim, D. & Yi, K., 2007. Design of arollover index-based vehicle stability control scheme. Vehicle system dynamics, 45(5), pp. 459-475.\n\n56. Yoon, J. et al., 2010. Design of an unified chassis controller for rollover prevention, manoeuvrability and lateral stability. Vehicle system dynamics, 48(11), pp. 1247-1268.\n\n57. Zhao, Y., Zhang, Y. & Zhao, Y., 2009. Stability control system for four-in-wheel-motor drive electric vehicle. Sixth International Conference on Fuzzy Systems and Knowledge Discovery, FSKD'09. IEEE, pp. 171-175.\n\nCONTACT INFORMATION\n\nCorresponding author:\n\nHusain Kanchwala\n\nSchool of Aerospace, Transport and Manufacturing\n\nCranfield University\n\nCranfield-MK43 0AL, United Kingdom\n\[email protected]\n\nPablo Luque-Rodriguez\n\nDepartment of Manufacturing and Engineering Construction\n\nUniversity of Oviedo\n\nOviedo-33071, Spain\n\nDaniel Alvarez-Mantaras\n\nDepartment of Manufacturing and Engineering Construction\n\nUniversity of Oviedo\n\nOviedo-33071, Spain\n\nJohan Wideberg\n\nDepartment of Transportation Engineering\n\nE.T.S.I. - University of Seville\n\nSeville-41092, Spain\n\nSagar Bendre\n\nNational Automotive Testing, Research and Infrastructure Project\n\nNATRIP\n\nIndore-452001, India\n\nHusain Kanchwala\n\nIITK\n\nPablo Luque Rodriguez and Daniel Alvarez Mantaras\n\nUniversity of Oviedo\n\nJohan Wideberg\n\nETSI\n\nSagar Bendre\n\nNATRIP\nCOPYRIGHT 2017 SAE International\nNo portion of this article can be reproduced without the express written permission from the copyright holder.\nCopyright 2017 Gale, Cengage Learning. All rights reserved.\n\nTerms of use | Privacy policy | Copyright © 2021 Farlex, Inc. | Feedback | For webmasters" ]
[ null ]
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http://glossary.ametsoc.org/wiki/Von_k%C3%A1rm%C3%A1n%27s_law
[ "# Logarithmic velocity profile\n\n(Redirected from Von kármán's law)\n\n## logarithmic velocity profile\n\nThe variation of the mean wind speed with height in the surface boundary layer derived with the following assumptions: 1) the mean motion is one-dimensional; 2) the Coriolis force can be neglected; 3) the shearing stress and pressure gradient are independent of height; 4) the pressure force can be neglected with respect to the viscous force; and 5) the mixing length l depends only on the fluid and the distance from the boundary, l = kz.\n\nNear aerodynamically smooth surfaces, the result is", null, "that is, the logarithmic velocity profile, where u* is the friction velocity and ν the kinematic viscosity. k ≅ 0.4 and has been called the Kármán constant or von Kármán's constant. The equation fails for a height z sufficiently close to the surface. For aerodynamically rough flow, molecular viscosity becomes negligible. The profile is then", null, "z0 is a constant related to the average height ε of the surface irregularities by z0 = ε/30 and is called the aerodynamic roughness length. Another derivation of the logarithmic profile was obtained by Rossby under the assumption that for fully rough flow the roughness affects the mixing length only in the region where z and z0 are comparable. Then l = k(z + z0) and", null, "For statically nonneutral conditions, a stability correction factor can be included (\nsee equation in definition of aerodynamic roughness length).\n\nHaugen, D. A. 1973. Workshop on Micrometeorology. Amer. Meteor. Soc., 392 pp.\n\nSutton, O. G. 1953. Micrometeorology. sect. 3.9.", null, "" ]
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http://num.bubble.ro/s/79/
[ "Substraction table for N = 79 - 0÷1\n\n79 - 0 = 79 [+]\n79 - 0.01 = 78.99 [+]\n79 - 0.02 = 78.98 [+]\n79 - 0.03 = 78.97 [+]\n79 - 0.04 = 78.96 [+]\n79 - 0.05 = 78.95 [+]\n79 - 0.06 = 78.94 [+]\n79 - 0.07 = 78.93 [+]\n79 - 0.08 = 78.92 [+]\n79 - 0.09 = 78.91 [+]\n79 - 0.1 = 78.9 [+]\n79 - 0.11 = 78.89 [+]\n79 - 0.12 = 78.88 [+]\n79 - 0.13 = 78.87 [+]\n79 - 0.14 = 78.86 [+]\n79 - 0.15 = 78.85 [+]\n79 - 0.16 = 78.84 [+]\n79 - 0.17 = 78.83 [+]\n79 - 0.18 = 78.82 [+]\n79 - 0.19 = 78.81 [+]\n79 - 0.2 = 78.8 [+]\n79 - 0.21 = 78.79 [+]\n79 - 0.22 = 78.78 [+]\n79 - 0.23 = 78.77 [+]\n79 - 0.24 = 78.76 [+]\n79 - 0.25 = 78.75 [+]\n79 - 0.26 = 78.74 [+]\n79 - 0.27 = 78.73 [+]\n79 - 0.28 = 78.72 [+]\n79 - 0.29 = 78.71 [+]\n79 - 0.3 = 78.7 [+]\n79 - 0.31 = 78.69 [+]\n79 - 0.32 = 78.68 [+]\n79 - 0.33 = 78.67 [+]\n79 - 0.34 = 78.66 [+]\n79 - 0.35 = 78.65 [+]\n79 - 0.36 = 78.64 [+]\n79 - 0.37 = 78.63 [+]\n79 - 0.38 = 78.62 [+]\n79 - 0.39 = 78.61 [+]\n79 - 0.4 = 78.6 [+]\n79 - 0.41 = 78.59 [+]\n79 - 0.42 = 78.58 [+]\n79 - 0.43 = 78.57 [+]\n79 - 0.44 = 78.56 [+]\n79 - 0.45 = 78.55 [+]\n79 - 0.46 = 78.54 [+]\n79 - 0.47 = 78.53 [+]\n79 - 0.48 = 78.52 [+]\n79 - 0.49 = 78.51 [+]\n79 - 0.5 = 78.5 [+]\n79 - 0.51 = 78.49 [+]\n79 - 0.52 = 78.48 [+]\n79 - 0.53 = 78.47 [+]\n79 - 0.54 = 78.46 [+]\n79 - 0.55 = 78.45 [+]\n79 - 0.56 = 78.44 [+]\n79 - 0.57 = 78.43 [+]\n79 - 0.58 = 78.42 [+]\n79 - 0.59 = 78.41 [+]\n79 - 0.6 = 78.4 [+]\n79 - 0.61 = 78.39 [+]\n79 - 0.62 = 78.38 [+]\n79 - 0.63 = 78.37 [+]\n79 - 0.64 = 78.36 [+]\n79 - 0.65 = 78.35 [+]\n79 - 0.66 = 78.34 [+]\n79 - 0.67 = 78.33 [+]\n79 - 0.68 = 78.32 [+]\n79 - 0.69 = 78.31 [+]\n79 - 0.7 = 78.3 [+]\n79 - 0.71 = 78.29 [+]\n79 - 0.72 = 78.28 [+]\n79 - 0.73 = 78.27 [+]\n79 - 0.74 = 78.26 [+]\n79 - 0.75 = 78.25 [+]\n79 - 0.76 = 78.24 [+]\n79 - 0.77 = 78.23 [+]\n79 - 0.78 = 78.22 [+]\n79 - 0.79 = 78.21 [+]\n79 - 0.8 = 78.2 [+]\n79 - 0.81 = 78.19 [+]\n79 - 0.82 = 78.18 [+]\n79 - 0.83 = 78.17 [+]\n79 - 0.84 = 78.16 [+]\n79 - 0.85 = 78.15 [+]\n79 - 0.86 = 78.14 [+]\n79 - 0.87 = 78.13 [+]\n79 - 0.88 = 78.12 [+]\n79 - 0.89 = 78.11 [+]\n79 - 0.9 = 78.1 [+]\n79 - 0.91 = 78.09 [+]\n79 - 0.92 = 78.08 [+]\n79 - 0.93 = 78.07 [+]\n79 - 0.94 = 78.06 [+]\n79 - 0.95 = 78.05 [+]\n79 - 0.96 = 78.04 [+]\n79 - 0.97 = 78.03 [+]\n79 - 0.98 = 78.02 [+]\nNavigation: Home | Addition | Substraction | Multiplication | Division       Tables for 79: Addition | Substraction | Multiplication | Division\n\nOperand: 1 2 3 4 5 6 7 8 9 10 20 30 40 50 60 70 80 90 100 200 300 400 500 600 700 800 900 1000 2000 3000 4000 5000 6000 7000 8000 9000\n\nSubstraction for: 1 2 3 4 5 6 7 8 9 10 20 30 40 50 60 70 71 72 73 74 75 76 77 78 79 80 90 100 200 300 400 500 600 700 800 900 1000 2000 3000 4000 5000 6000 7000 8000 9000" ]
[ null ]
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https://studycorgi.com/four-types-of-correlation-coefficients-comparison/
[ "# Four Types of Correlation Coefficients Comparison\n\n## Table\n\nTable 1. Four Correlation Coefficients and their Comparisons.\n\nWe will write a\ncustom essay\nspecifically for you\n\nfor only \\$16.05 \\$11/page\n308 certified writers online\n Statistical Method What the Statistical Method/Test Measures What type of research question would best apply to this method? Pearson’s r This is the parametric coefficient for determining relationships between variables, including their direction and magnitude, and making inferences about correlations between them (Jackson, 2017; Polit & Beck, 2017). This coefficient is supposed to be used with ratio or interval data with normal distributions; if these assumptions do not apply, the tests below this one should be considered. In general, the method would be used with a question that asks about correlations between variables that are likely to be measured with an interval or ratio scale. Example: is depression, as measured by the Beck Depression Inventory (ratio), correlated with anxiety, as measured by the Beck Anxiety Inventory (ratio). Spearman’s rho (ρ) The non-parametric option to the above-described test; it is also associated with testing correlations, but it can only be applied to ordinal data. If nominal data is involved, one should review the tests below. This method is applicable to a question that aims to test for correlations between variables which would use an ordinal scale. Example: the above-presented question that will employ specific Beck-defined categories (mild, moderate, severe depression and mild, moderate, severe anxiety) instead of ratio data. Point-Biserial (rpb) A coefficient for correlation-testing that can be used in case one of the variables is nominal and dichotomous. The other one is supposed to be on an interval or ratio scale (Gravetter, Wallnau, & Forzano, 2018; Jackson, 2016). If both variables are nominal, the last option in the table should be used. This coefficient is meant to test the correlations between a nominal and a ratio or interval variable, and its research question needs to reflect this fact. Example: is depression, as measured using the Beck Depression Inventory (ratio), more prevalent among men or women (nominal, dichotomous)? phi coefficient (φ) Another correlation coefficient; it is used to test for correlations between “dichotomous and nominal variables” (Jackson, 2016, p. 163). In other words, the phi coefficient is applicable to the variables that use nominal data and have only two values. This coefficient could use a question that focuses on correlations between variables which are nominal and have only two values. Example: is the adherence to physician recommendations pre-discharge correlated with the adherence to them post-discharge? The variables are nominal and dichotomous (one follows recommendations or does not).\n\n## Reflection and Summary\n\nThis paper is dedicated to an exercise of comparing correlation coefficients and their specific features. Table 1 summarizes the key information about them and offers examples of the questions that they can respond to; the following summary presents a reflection on the topic. The study of the four coefficients demonstrates that they are very similar, but the specific conditions of their applicability define their use by a researcher.\n\nFrom the literature on the topic, it is apparent that the four correlation coefficients are meant to work with the same general types of questions; specifically, they are correlation coefficients. As explained by Polit and Beck (2017), this statement means that the coefficients can help to determine if a relationship between variables that is found within a particular sample can be generalized and inferred for the studied population as a whole. Thus, the four coefficients are meant for the inferential testing of correlations between variables, which is why all their research questions will be concerned with particular variables and potential relationships between them.\n\nHowever, since the coefficients appear to reflect the types of variables that are used, the eventual questions are going to differ. In Table 1, the coefficients are arranged in the following order: the one that is meant for ratio or interval data is the first one, and it is followed by the coefficient that focuses on ordinal data and the two coefficients that can work with nominal data (Jackson, 2016; Polit & Beck, 2017). This arrangement can be useful since, as a parametric coefficient, Pearson’s r requires taking into account a greater number of assumptions and may be inapplicable to many datasets while also being the most powerful option (Polit & Beck, 2017). Upon determining that a dataset cannot use Pearson’s r, a researcher can check the non-parametric alternative (Spearman’s rho) and then the rest of the options.\n\nSince only specific variables are suitable for particular coefficients, the presented example questions attempt to reflect the differences between them. Thus, the first question inquires about correlations between depression and anxiety as measured by well-established inventories that produce ratio data (García-Batista, Guerra-Peña, Cano-Vindel, Herrera-Martínez, & Medrano, 2018; Oh et al., 2018).\n\nProvided that the study is carried out with a large enough sample to ensure normal distribution, this question should be able to use Pearson’s r. On the other hand, a researcher who uses the same question but instead employs ordinal data or has a small, non-normally distributed dataset would have to resort to the Spearman’s rho alternative. With the rest questions, the same conditions should be taken into account. Gender is the most obvious nominal and dichotomous variable (Jackson, 2016), which is why pairing it with another variable that uses a ratio scale would require the application of the point-biserial coefficient. Finally, two nominal variables, like the ones from the last example, require the phi coefficient.\n\nThus, the presented table can be used to demonstrate the differences between the coefficients in brief, and the example questions appear to illustrate their distinctions. In essence, the coefficients are the same, but they have different requirements for application, which mostly amount to the consideration of the types of data that they can test for correlations. Knowing their specific features is crucial for their correct use.\n\nGet your\n100% original paper\non any topic\n\ndone in as little as\n3 hours\n\n## References\n\nGarcía-Batista, Z., Guerra-Peña, K., Cano-Vindel, A., Herrera-Martínez, S., & Medrano, L. (2018). Validity and reliability of the Beck Depression Inventory (BDI-II) in general and hospital population of Dominican Republic. PLOS ONE, 13(6), e0199750. Web.\n\nGravetter, F., Wallnau, L., & Forzano, L. (2018). Essentials of statistics for the behavioral sciences (9th ed.). Boston, MA: Cengage Learning.\n\nJackson, S. L. (2016). Research methods and statistics: A critical thinking approach (5th ed.). Boston, MA: Cengage Learning.\n\nJackson, S. L. (2017). Statistics plain and simple (4th ed.). Boston, MA: Cengage Learning.\n\nOh, H., Park, K., Yoon, S., Kim, Y., Lee, S., Choi, Y., & Choi, K. (2018). Clinical utility of Beck Anxiety Inventory in clinical and nonclinical Korean samples. Frontiers in Psychiatry, 9, 1-10. Web.\n\nPolit, D.F., & Beck, C.T. (2017). Nursing research: Generating and assessing evidence for nursing practice (10th ed.). Philadelphia, PA: Lippincott, Williams & Wilkins.\n\n## Cite this paper\n\nSelect style\n\nReference\n\nStudyCorgi. (2021, August 10). Four Types of Correlation Coefficients Comparison. Retrieved from https://studycorgi.com/four-types-of-correlation-coefficients-comparison/\n\nWork Cited\n\n\"Four Types of Correlation Coefficients Comparison.\" StudyCorgi, 10 Aug. 2021, studycorgi.com/four-types-of-correlation-coefficients-comparison/.\n\n1. StudyCorgi. \"Four Types of Correlation Coefficients Comparison.\" August 10, 2021. https://studycorgi.com/four-types-of-correlation-coefficients-comparison/.\n\nBibliography\n\nStudyCorgi. \"Four Types of Correlation Coefficients Comparison.\" August 10, 2021. https://studycorgi.com/four-types-of-correlation-coefficients-comparison/.\n\nReferences\n\nStudyCorgi. 2021. \"Four Types of Correlation Coefficients Comparison.\" August 10, 2021. https://studycorgi.com/four-types-of-correlation-coefficients-comparison/.\n\nReferences\n\nStudyCorgi. (2021) 'Four Types of Correlation Coefficients Comparison'. 10 August.\n\nThis paper was written and submitted to our database by a student to assist your with your own studies. You are free to use it to write your own assignment, however you must reference it properly.\n\nIf you are the original creator of this paper and no longer wish to have it published on StudyCorgi, request the removal." ]
[ null ]
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https://quibbletown.piscatawayschools.org/our_school/staff_websites/zengerle__john/accelerated_math_7_syllabus
[ "• Select a School\n\n## Accelerated Math 7 Syllabus\n\n The Number System   Students will know… Operations and properties related to real numbers. The properties that apply to addition extend to include addition of negative numbers. Vocabulary related to the real number system. The relative magnitude of numbers. Operations can be modeled using concrete, symbolic, and pictoral methods. The properties that apply to multiplication extend to include addition of negative numbers. Numbers can be represented in many ways and these equivalent forms facilitate computation. The subsets of the Real Number system.   Students will be able to… Represent integer operations with concrete models and connect the actions with the models to standardized algorithms. Add and subtract integers. Solve multi-step problems involving integers. Represent integer operations with concrete models and connect the actions with the models to standardized algorithms. Multiply and Divide Integers fluently. Use the order of operations to solve multi-step problems involving integers. Convert, Compare, and Order rational numbers. Perform operations with rational numbers. Create a Venn diagram illustrating the subsets of the real number system Ratios and Proportional Relationships   Students will know… Ratios, Rates, Unit Rates, and Constants of Proportionality. Understand the equivalence of unit rates and constants of proportionality. Vocabulary related to percents. Values can be represented as percents, fractions, and decimals.   Students will be able to… Represent and solve proportional relationships. Calculate unit rates from rates. Represent constant rates of change from a table, verbal description, equation, or graph. Determine constant of proportionality in real-world situations. Use rates to solve problems. Represent and solve problems involving proportional relationships. Solve problems involving percent increase, percent decrease, and percent of change. Solve mark up and mark down problems. Use percents to find sales tax, tips, total cost, and simple interest. Covert units within a measurement system. Convert between percents, fractions, and decimals and determine which form is best to use in different situations. Use proportions, equations, and models to answer percent questions. QUARTERLY 1 Expressions, Equations, and Inequalities Students will know… The difference between expressions and equations. Balance is a required condition for equations. The limitations of a solution. The properties related to expressions and equations. Properties related to inequalities. The difference between equations and inequalities. Students will be able to… Write and solve two-step equations to represent real-world problems. Model situations involving linear relationships. Use algebraic properties to simplify expressions and solve equations. Write and solve two-step inequalities to represent real-world problems. Model situations involving inequalities. Use algebraic properties to solve inequalities. Geometry Students will know… The relationship between different types of angle pairs. The criteria for similar and congruent figures. The meaning of a scale factor. The equivalence of scale factor, constant of proportionality, and unit rate. The criteria to create two-dimensional shapes. The different parts of a circle and the relationship between them. Area formulas for different shapes. The relationship between the different methods for finding surface area. Students will be able to… Use ratios to determine if two figures are similar. Use similar shapes to find unknown measures. Construct triangles given three measures of angles or sides and determine when no triangle can be made. Write and solve equations using formulas and geometry concepts. Find the circumference of a circle. Find the area of a circle or a partial circle. Find the area of composite figures. Determine missing measurement given area or circumference. Find the surface area of a simple or composite figure using a net or a formula. Find the volume of prisms and composite solids. Statistics Students will know… Vocabulary related to data analysis. The difference between a population and a sample. The difference between a random and non-random sample. Students will be able to… Compare two sets of data displayed in dot plots or box plots. Find Mean Absolute Deviation. Use a sample to gain information about a population using random and non-random sampling. Make inferences from dot plots and box plots. Use data about a sample and proportional reasoning to make inferences or predictions about a population. Determine if an inference or prediction is valid. QUARTERLY 2 Probability Students will know… Probability is a value between zero and one that expresses the relative likelihood of an event occurring. The difference between theoretical and experimental probability. Students will be able to… Find the probability of a simple event and its complements. Find the experimental probabilities of simple and compound events. Use experimental probability to make a prediction. Create a sample space for an event. Find theoretical probability for simple and compound events. Compare theoretical and experimental probabilities. Use theoretical probability and proportional concepts to make predictions. Compare a prediction to results of an experiment. Use technology to conduct different simulations for simple and compound events and model events using diagrams, sample spaces, and symbols. Real Numbers, Exponents, and Scientific Notation Students will know… The relationship between subsets of real numbers. Square roots are the inverse of squaring and cube roots are the inverse of cubing. The square root of a non-perfect square is an irrational number. Numbers can be expressed in different forms and the different forms can be useful to answer questions in different contexts. The properties of exponents. Students will be able to… Express a rational number as a decimal and approximate the value of an irrational number. Compare and order rational and irrational numbers. Apply properties of integer exponents to evaluate expressions. Convert between standard notation and scientific notation. Add, Subtract, Multiply and Divide numbers which are expressed in Scientific Notation. Use properties to simplify exponential expressions. Compare and order values expressed in Scientific Notation. Linear Relations and Equations Students will know… The difference between proportional and non-proportional relationships. The equivalence of rate of change, constant of proportionality, unit rate, scale factor, and slope. Changes in slope and y-intercept affect the form of the graph. Equations can have no solutions, one solution, a limited number of solutions, or an infinite number of solutions. The difference between proportional and non-proportional relationships. Students will be able to… Represent linear situations with tables, graphs, and equations. Use data from a table or a graph to determine the rate of change or slope and y-intercept in mathematical and real-world situations. Graph linear relationships interpreting the unit rate as the slope of the line that models the relationship. Model linear relationships in graphs, tables, and equations. Comparing unit rates using tables, graphs, and equations. Change a graph by changing slope and/or y-intercept. Create a graphs, equations, tables, and situations given any one as a starting point. Determine if a point is a solution to an equation using a graph, table, or equation. Distinguish between proportional and non-proportional situations using tables, graph, and equations. Determine if a point is a solution to an equation using a graph, table, or equation using different methods. Model equations using concrete, pictoral, and symbolic methods. Write complex equations given real-world situations or tables. QUARTERLY 3 Transformational Geometry   Students will know… Properties of orientation and congruence of transformations in a coordinate plane. Transformations can be modeled using algebraic representations. The equivalence of scale factor, unit rate, slope, constant of proportionality, and rate of change. The relationship of the measures of angles and side lengths in similar figures.   Students will be able to… Model transformations using algebraic representations. Perform transformations in the coordinate plane. Write a series of transformations to create a given image from a pre-image. Compare and contrast the attributes of a shape and its dilation on a coordinate plane. Represent algebraically the effect of a scale factor applied to two-dimensional figure on a coordinate plane with the origin as the center of dilation. Write a series of transformations including dilation to create a given image from a pre-image. Find missing measures in similar figures. Determine if two shapes are similar given a diagram, measurements, or an equation. Find scale factor. Measurement Geometry   Students will know… The sum of the measures of the interior angles of a triangle is 180 degrees. Vocabulary related to parallel lines that are cut by a transversal. The volume of a Cylinder can be found using V=Bh where B is the area of the base and h is the height. The volume of a cone is 1/3 the volume of a cylinder with the same height and radius. The volume of a sphere is 2/3 the volume of a cylinder with the same radius and the height of twice the radius.   Students will be able to… Identify angle relationships in situations with parallel lines that are cut by a transversal. Find angle measures in situations involving parallel lines that are cut by a transversal. Determine the measures of the interior and exterior angels of a triangle. Determine if two triangles are similar or congruent given side lengths or angle measures. Use concepts of similar triangles to find missing measurements. Find the volume of a cylinder, cone, and sphere. Model the relationship between the volumes of cylinders, cones, and spheres. QUARTERLY 4" ]
[ null ]
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https://quantumgeometrydynamics.com/2013/09/
[ "# Archive for September, 2013\n\n## 2nd Edition of Introduction to Quantum-Geometry Dynamics Available\n\nIntroduction to Quantum-Geometry Dynamics 3rd Edition (new)\n\n## Mapping the Universe\n\nEverything we know about the universe we learned from photons. We detect cosmic photons with senses and instruments and from their physical properties we estimate the size, speed, direction, position and composition of each of their sources. In short, cosmic photons allow us to map out the Universe. The maps we now use have been drawn from interpretations of the signals we receive. And these interpretations are based on theories which are founded on the wave model of light.\n\nThe main tool used to determine position, direction and speed of a stellar object is provided by what is called the redshift effect. The redshift effect is simply the change in frequency of light attributed to the Doppler effect and is expected to occur when the emitting source is speeding away from us. The magnitude of redshift is understood to be proportional to speed of the source and is be used to calculate its distance from us. Maps of the observable universe are made by compiling data received from all observable sources. The problem, if QGD is correct, is that those maps are built on the assumption that light behaves like a wave and that, consequently, the Doppler effect applies. But if, as QGD suggests, light is singularly corpuscular, will a map based on QGD’s interpretation of the redshift and blueshift effects agree with the maps based on the wave model of light? Before answering the question we will first discuss how QGD explains the redshift effect.\n\n### Emission Spectrum of Atoms\n\nWe have shown that quantum-geometrical space itself exerts a force on an object and that any change in momentum of an object must be an integer multiple of the mass of the object (see QGD optics part 3). That is, for an object", null, "$a$ of mass", null, "${{m}_{a}}$,", null, "$\\Delta \\left\\| {{{\\vec{P}}}_{a}} \\right\\|=x{{m}_{a}}$ where", null, "$x\\in {{N}^{+}}$. This applies to the components of an atom that are bombarded by photons. For instance, if", null, "$a$ is an electron bombarded by a photon", null, "$b$ having mass", null, "${{m}_{b}}$, which momentum we have learned is equal to", null, "${{m}_{b}}c$, then", null, "$a$ will absorb", null, "$b$ only if", null, "${{m}_{b}}c=x{{m}_{a}}$. Similarly, the allowable changes in momentum", null, "$\\Delta \\left\\| {{{\\vec{P}}}_{a}} \\right\\|=x{{m}_{a}}$ must also apply to the emission of photons by an electron. The allowable changes in momentum determine the emission spectrum of the electrons of an atom.", null, "In the figure above, we have the visible part of the hydrogen emission spectrum. Here the first visible band correspond to a change in momentum of the electron", null, "$a$ by emission of a photon with momentum", null, "${{m}_{{{b}_{i}}}}c=i{{m}_{a}}$. Notice that the lowest possible value, which is at the far end of the spectrum is given when", null, "$i=1$ . Each emission line corresponds to allowable emission of a photon from an hydrogen atom’s single electron. In agreement with the laws of motion introduced earlier, each emitted photon has a specific momentum", null, "${{m}_{{{b}_{i}}}}c$ (hence, a specific mass", null, "${{m}_{{{b}_{i}}}}$ ). For values of", null, "$x and", null, "$x>i+3$ which are respectively towards the infrared and ultraviolet; the momentum puts them outside the boundaries of visible light.\n\nFor an atom", null, "$a$having", null, "$n$ components electrons", null, "${{a}_{i}}$in its outer orbits (the ones that will interact most with external photons) where", null, "$1 and having mass", null, "${{m}_{{{a}_{{{i}_{{}}}}}}}$the emission lines of its component electrons", null, "${{a}_{i}}$ corresponds to photons", null, "${{b}_{i}}$ such that", null, "${{m}_{b}}c={{x}_{i}}{{m}_{{{a}_{i}}}}$ and its spectrogram is the superposition of the emission lines of all its electrons. An example of the superimposition of the emission spectrums of the electrons of iron is shown in the illustration below. Note that an electron can have only one change in momentum at the time, emitting or absorbing a photon of corresponding momentum. So emission spectrograms are really composite images made from the emission of a large enough number of atoms to display the full emission spectrum of an element.", null, "### QGD’s Interpretation of the Redshift and Blueshift Effects\n\nNow that we have described and explained the emission spectrum of atoms we can deduce the cause the redshifts and blueshifts in the emission lines of the emission spectrum an atom. We saw earlier that the emission of a photon by and electron", null, "$a$ corresponds to a change in the electron’s momentum such that", null, "$\\Delta \\left\\| {{{\\vec{P}}}_{a}} \\right\\|=x{{m}_{a}}$ where", null, "$x\\in {{N}^{+}}$. So a redshift of the emission spectrum of an element implies that photons emitted by its electrons", null, "${{{a}'}_{i}}$are less massive than photons emitted by the electrons", null, "${{a}_{i}}$ of a reference atom of the same element (most often, the reference atom is on Earth). This means that", null, "$x{{m}_{{{{{a}'}}_{i}}}} sot that", null, "${{m}_{{{{{a}'}}_{i}}}}<{{m}_{{{a}_{_{i}}}}}$. That is, the mass of electron", null, "${{{a}'}_{i}}$ belonging to an atom of an element from a distance source is smaller than the mass of the corresponding electron", null, "${{a}_{i}}$ belonging to the atom of the same element on Earth. In the same way, the blueshift of the emission lines of the emission spectrum of an atom implies that", null, "${{m}_{{{{{a}'}}_{i}}}}>{{m}_{{{a}_{i}}}}$.\n\nSo, according to QGD, the redshift and blueshift effects imply that the electrons of the light emitting source are respectively less and more massive than the local reference electron", null, "$a$ . Therefore, quantum-geometry dynamics does not attribute the redshifts and blueshifts effects to a Doppler-like effect (which in the absence of a medium doesn’t make sense anyway) and, as a consequence, these effects are not speed dependant. Hence redshifts and blueshifts provide no indication of the speed or distance of their source.\n\nFrom the mechanisms of particle formation introduced earlier, we understand that though all electrons share the same basic structure they can have different masses. As matter aggregates though gravitational interactions, electrons absorb neutrinos, photons or preons(+) and gradually become more massive. It follows that redshifted photons must be emitted by sources at a stage of their evolution that precedes the stage of evolution of our reference source. Similarly, blueshifted photons being more massive were emitted at a stage of their evolution that succeeds that stage of evolution of our reference source. However, it can’t be assumed that sources of similarly redshifted photons are at similar distances from us unless they are part of a system within which they have simultaneously formed. The sources of similarly redshitted photons may be at greatly varying distances from us. Also, a source of blueshifted photons can be at the same distance as a source of redshifted photons would be. Therefore, there are important discrepancies between a map using QGD’s interpretation of the redshift and blueshift effects and one that is based on the classical wave interpretation of the same effects.\n\nSo though they provide no information about to the distance of their source (much less about their speed), redshifted or blueshifted photons inform us of the stage of evolution of their sources at the time they were emitted. Also, since sources of similarly redshifted (or similarly blueshifted) photons have similar mass, structure and luminosity, it is possible to establish the distance of one source of redshifted photons relative to a reference source of similarly redshifted photons by comparing the intensity of the light we receive from them.\n\n### Gravitational Telescopy\n\nAs we have seen, although we can indirectly estimate the distance of source of photons relative to another, there is no direct correlation between distance, direction or speed of a stellar object and how much the photons they emit are redshifted or blueshifted. However, according to QGD, it is theoretically possible to map the universe with great accurately by measuring the magnitude and direction gravitational interactions using a gravitational telescopy. And, unlike telescopes and radio-telescopes, gravitational telescope are not limited to the observation of photon emitting objects.\n\nMore importantly, if QGD’s prediction that gravity is instantaneous, then a map based on the observations of gravitational telescopes would represent all observed objects as they currently are and not as they were when they emitted the photons we receive from them.\n\n### Cosmological Implications\n\nThe notion that the universe is expanding is based on the classic interpretation of the redshift and blueshift effects, but if QGD is correct and redshift and blueshift effects are consequences of the stage of evolution of their source, then the expanding universe model loses its most important argument. The data then becomes consistent with the locally condensing universe proposed by quantum-geometry dynamics." ]
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https://proofsfromthebook.com/2012/11/24/polygon-angle-sum/
[ "# The Proof of the Polygon Angle Sum Theorem\n\nIntroduction\n\nWe have learned that the angle sum of a triangle is \\$latex 180^\\circ\\$. We have also learned that  the angle sum of a quadrilateral is \\$latex 360^\\circ\\$. In getting the angle sum of quadrilaterals, we divided the quadrilateral into two triangles by drawing a diagonal. In this post, we use this method to find the angle sum of the pentagon and other polygons.\n\nLet us extend the method stated above to pentagon (5-sided polygon). Clearly, we can divide the pentagon into three non-overlapping triangles by drawing two diagonals. Since each triangle has an angle sum of \\$latex 180^\\circ\\$, the angle sum of a pentagon, which is composed of three triangles, is \\$latex 540^\\circ\\$.", null, "Using the method above, we can see the pattern on the table below. The sum of a polygon with \\$latex n\\$ sides is \\$latex 180(n-2)\\$ degrees. Next, we summarize the polygon angle sum theorem and prove it.", null, "Theorem\n\nThe angle sum of a polygon with \\$latex n\\$ sides is 180(n-2) degrees.\n\nProof\n\nA polygon with \\$latex n\\$ sides can be divided into \\$latex n – 2\\$ triangles. Since the angle sum of a triangle is \\$latex 180^\\circ\\$, the angle sum of a polygon is \\$latex 180^\\circ (n-2)\\$.\n\nExercise\n\nIn the proof above, we have only considered the angle sum of a convex polygons. Does this theorem also hold on non-convex polygons? Explain your answer." ]
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http://www.kzoo.edu/catalog/?searched=Mathhttp://www.kzoo.edu/catalog/?searched=Mathematics&id=934
[ "# Mathematics\n\nProfessors: Barth, Cutter, Intermont, Nordmoe (Chair), Oloo, West\n\nThe mission of the Mathematics Program is to foster in all our students critical habits of mind: description, analysis and interpretation. The Program is designed to prepare its majors for successful lifetime engagement with mathematics whether it be through applied work in industry or government; research in mathematics, statistics, or one of the other mathematical sciences; teaching; or applying mathematics in the physical, computing, or social sciences. For non-majors, the Program builds substantive skills in quantitative and abstract reasoning and in their application to the study of modern society.\n\nFor purposes of course placement and prerequisites, a score of 4 or 5 on the AB calculus exam (or an AB subscore of the BC calculus exam) is regarded as equivalent to successful completion of MATH 112. A score of 4 or 5 on the BC calculus exam is equivalent to MATH 113. A score of 4 or 5 on the statistics exam is equivalent to MATH 260.\n\n## Transfer, Dual Enrollment, Study Abroad Credit\n\nCourses taken at other institutions will be awarded credit in mathematics if they meet one of the following criteria:\n\n1. The course is similar in content and rigor to an existing course in the Mathematics Department (and there are legitimate reasons why the student is not able to take the class at the College)\n2. The course covers some important topic of mathematics not offered at Kalamazoo College. .\n\nStudents are responsible for meeting with the department chair in advance to determine whether a course offered elsewhere will transfer back as a mathematics credit.\n\n## Requirements for the Major in Mathematics\n\nNumber of Units\nNine units of mathematics are required, exclusive of SIP and CS Cognate. Typically up to two units from outside courses (AP, transfer, dual enrollment, or study abroad) may count towards the major or minor in mathematics. MATH 260 and MATH 261 do not count for the major. Students who wish to apply additional external units toward the major must consult with the department.\n\nRequired Courses\nMATH 112-113 Calculus I and II\nMATH 214 Calculus III\nMATH 240 Linear Algebra and Vectors\n\nMATH 310 Complex and Vector Variables, MATH 316 Topics in Number Theory or MATH 318 Topics in Topology\nMATH 320 Real Analysis I or MATH 330 Abstract Algebra I\nOne two-term sequence beyond calculus (e.g., Real Analysis I and II, Abstract Algebra I and II, Probability and Mathematical Statistics, Abstract Algebra I and Linear Algebra II)\n\nRequired Cognate\nOne computer science course or one applied statistics course (MATH 260 or MATH 261)\n\nMajor Guidance\nAmong the courses we offer, MATH 320 and MATH 330 are at the highest level of abstraction. Before enrolling in one of these courses, students are strongly encouraged to complete MATH 310, MATH 316 or MATH318.\n\nFor students interested in graduate work in one of the mathematical sciences, additional work in MATH 280, 310, 314, 316, 320, 330, 420, 430, and 450 is appropriate. Those with a strong interest in computing should elect the minor in computer science in addition to MATH 300. For those students interested in applied work (mathematical biology, mathematical economics, operations research, etc.), election of MATH 270, 280, 310, 362, 365, 440, and at least two courses in computer science is appropriate. Other departments offer classes that use mathematical ideas: BIOL 112, 426, and 436; CHEM 310 and 410; ECON 305 and 412; PHIL 107; PHYS 340, 400, 410, and 420; and PSYC 390.\n\n## Mathematics Colloquium Credit\n\nIn addition to the requirements stated above, mathematics majors are required to complete the Mathematics Colloquium requirement. See the Mathematics Department for details.\n\n## Comprehensive Exams\n\nMathematics majors are required to satisfactorily complete the Sophomore Comprehensive exam and the Senior Comprehensive Exam. See the Mathematics Department for details.\n\n## Requirements for the Minor in Mathematics\n\nThere are four options for the minor in mathematics, each of which requires six units of credit in mathematics. Each of these options requires the \"core\" courses: Single variable calculus (MATH 112 and MATH 113), Multivariable Calculus (MATH 214), and Linear Algebra (MATH 240). The other required courses for each option are as follows:\n\nStatistics Option\nMATH 362 Probability\nMATH 365 Mathematical Statistics\n\nComputational Mathematics Option\nMATH 250 Discrete Mathematics or MATH 330 Abstract Algebra I\nMATH 300 Automata, Formal Languages, and Computability\n\nApplied Mathematics Option\nMATH 280 Differential Equations\nMATH 310 Complex and Vector Variables\n\nPure Mathematics Option\nMATH 320 Real Analysis I or MATH 330 Abstract Algebra I\nAnd one other mathematics course from the following list:\nMATH 310, MATH 314, MATH 316, MATH 318, MATH 320, MATH 330, MATH 362, or any\n400-level course in Mathematics\n\n**Note: MATH-260 and MATH-261 do not count for the Mathematics minor**\n\nStudents interested in mathematics are especially encouraged to consider the study abroad program in Budapest. The Budapest program is given in English; no prior knowledge of Hungarian is needed. It offers a number of mathematics courses as well as history, language, and literature courses. Mathematics majors have also studied mathematics in Erlangen, Quito, Perth, Aberdeen, and Lancaster. Early consultation with the department is strongly urged.\n\n## Mathematics courses\n\nMATH105Quantitative Reasoning and Statistical Analysis An introduction to some of the quantitative techniques used to clarify ordinary experience and to some of the statistical ideas used to shape public policy and human sciences, with emphasis on the concepts involved in producing, organizing, and drawing conclusions from data. Does not count toward the major or minor. Not open to students who already have credit from ANSO-212, MATH-260, or MATH-261.\nMATH110Calculus I with Review, Part 1 MATH 110 and 111 cover in two terms the material covered in Mathematics 112. In addition, topics from precalculus mathematics are reviewed and practiced as needed. Precalculus topics include: algebra and analytic geometry; linear, quadratic, polynomial and rational functions; and trigonometric functions. Enrollment is restricted to those who were advised to take Math 110-111 on the basis of the department's placement examination. The two-term Math 110-111 sequence serves as an alternate prerequisite for all college courses requiring MATH 112. Prerequisite: Placement into MATH-110 required\nMATH111Calculus I with Review, Part 2 This course continues the study of calculus begun in MATH 110. Review of precalculus mathematics continues as needed. Prerequisite: Take MATH-110 All course prerequisites must be met with a minimum grade of C-.\nMATH112Calculus I Differential calculus of single-variable functions: limits, derivatives, differentiation rules, related rates, optimization. An emphasis on problem solving using the tools of differential calculus with application to the natural and social sciences. Prerequisite: Math Placement Exam Required\nMATH113Calculus II Integral calculus of single-variable functions: the fundamental theorem of calculus, techniques of integration, infinite sequences and series. An emphasis on problem solving using the tools of integral calculus with application to the natural and social sciences. Prerequisite: MATH-112 All course prerequisites must be met with a minimum grade of C-.\nMATH214Calculus III Series, vectors in two and three dimensions, and integral and differential calculus of functions of several variables. Prerequisite: MATH-113 All course prerequisites must be met with a minimum grade of C-.\nMATH240Linear Algebra and Vectors Study of vector spaces, matrices, determinants, linear transformations, systems of equations and eigenvalues. Prerequisite: MATH-113 All course prerequisites must be met with a minimum grade of C-.\nMATH250Discrete Mathematics Introduction to formal structures and mathematical reasoning. Graphs, sets, logic, induction, structure of mathematical proof, counting, relations, and algebraic structures. Prerequisite: MATH-112 and one computer science course. All course prerequisites must be met with a minimum grade of C-.\nMATH260Applied Statistics I Introduction to statistics including methods of data collection and description, correlation and regression, chance, and statistical inference. The course makes extensive use of technology and is designed for students in the behavioral, biological, and social sciences. Does not count towards the major or minor in mathematics. Not open to students who already have credit from MATH-261Prerequisite: Not open to students who already have credit from MATH-261\nMATH261Biostatistics Introduction to statistics with particular attention to applications in biology and health sciences. Topics include sampling methods, design of experiments, exploratory data analysis, estimation, tests of significance, ANOVA, and correlation and regression analysis. BIOL 112 and 123 highly recommended. Does not count towards the major or minor in mathematics. Not open to students who already have credit from MATH-260Prerequisite: Not open to students who already have credit from MATH-260\nMATH/PHYS270Nonlinear Dynamics and Chaos Dynamical systems are mathematical objects used to model phenomena of natural and social phenomena whose state changes over time. Nonlinear dynamical systems are able to show complicated temporal, spatial, and spatiotemporal behavior. They include oscillatory and chaotic behaviors and spatial structures including fractals. Students will learn the basic mathematical concepts and methods used to describe dynamical systems. Applications will cover many scientific disciplines, including physics, chemistry, biology, economics, and other social sciences. Appropriate for Math or Physics Majors. Either MATH 305 or this course, but not both, may be counted towards the major in mathematics.\nMATH280Differential Equations and Numerical Methods Introduction to key concepts underlying analytical methods for the solution of ordinary differential equations and first-order systems studied together with techniques for constructing approximate numerical solutions. Prerequisite: MATH-214 and MATH-240 All course prerequisites must be met with a minimum grade of C-.\nMATH295Special Topics Living under the data deluge of the early 21st century, our challenge is no longer finding data, but instead transforming it into a format useful for addressing important questions. To that end, this course will focus on the use of the R statistics language and environment to access, visualize, transform and model data. Specific topics may include data scraping, data wrangling, graphical displays, reproducible research reports , and methods for modeling data including supervised and unsupervised learning.Prerequisite: MATH-260 or MATH-261 or COMP-210 or with instructor permission.\nMATH/COMP300Automata, Formal Languages, and Computability Study of automata as mathematical models of computation; of formal languages, which play a central role in the specification and translation of programming languages; and of the fundamental capabilities and limitations of computers.Prerequisite: MATH-250 or MATH-330, and 1 COMP course All course prerequisites must be met with a minimum grade of C-.\nMATH/IDSY305/PHYS 482Dynamic Models in Social Science The study of why mathematical and computational methods are important in understanding social phenomena, and how different social phenomena can be described by proper mathematical models. Specifically, applications of the theory of dynamical systems will be presented. Designed for math/science and social science students. Either MATH/PHYS 270 or this course, but not both, may be counted towards the major in mathematics.Prerequisite: MATH-113 All course prerequisites must be met with a minimum grade of C-.\nMATH310Complex and Vector Variables Generalizations of differentiation and integration to spaces of higher dimension: divergence, curl, and the classical integration theorems of multivariable calculus. Introduction to analytic functions of a complex variable, including Laurent series, Cauchy's formula, and conformal mapping. Prerequisite: MATH-214 and MATH-240 All course prerequisites must be met with a minimum grade of C-.\nMATH316Topics in Number Theory Study of classical number theory including distribution of primes, congruences, the Euler Phi function, and quadratic reciprocity. This course will also focus on developing proof writing skills. Prerequisite: MATH 214 and MATH 240\nMATH318Topics in Topology An introduction to topological spaces including the study of connectedness, metric spaces, and compactness. This course will also focus on developing proof writing skills.Prerequisite: MATH-214 MATH-240; All course prerequisites must be met with a minimum grade of C-.\nMATH320Real Analysis I Introduction to basic topological concepts in metric spaces followed by rigorous development of classical real analysis including sequences and series of functions, continuity, differentiability, and Reimann-Stieltjes integration. This course is among the most theoretical in our curriculum. Before enrolling, students are strongly encouraged to complete MATH 250, MATH 310, MATH 314, or MATH 318.Prerequisite: MATH-214 and MATH-240 All course prerequisites must be met with a minimum grade of C-.\nMATH330Abstract Algebra I Study of modern abstract algebra including groups, rings, fields, and other algebraic structures together with advanced topics of linear algebra. This course is among the most theoretical in our curriculum. Before enrolling, students are strongly encouraged to complete MATH 250, MATH 310, MATH 314, or MATH 318.Prerequisite: MATH-214 and MATH-240 All course prerequisites must be met with a minimum grade of C-.\nMATH360Applied Statistics II This course uses real data case studies to review descriptive statistics and to explore statistical inference for means, proportions, and transformations; analysis of variance; and regression. Statistical software is used throughout. The course is recommended both for students planning to do graduate coursework in the behavioral, biological, and social sciences and for mathematics majors seeking a comprehensive introduction to statistical methods.Prerequisite: 200-level math course. All course prerequisites must be met with a minimum grade of C-.\nMATH362Probability Study of mathematical theory of probability. Topics include data analysis, discrete and continuous sample spaces, combinatorial problems, random variables, probability densities and distributions, expected value, moment-generating functions, functions of a random variable, sampling distributions, and the central limit theorem. Prerequisite: MATH-113 All course prerequisites must be met with a minimum grade of C-.\nMATH365Mathematical Statistics Study of statistical inference. Topics include sampling theory, point and interval estimations, hypothesis testing, and regression. Stochastic processes, analysis of variance, simple experimental design, and nonparametric statistics may also be included. Prerequisite: MATH-362 All course prerequisites must be met with a minimum grade of C-.\nMATH420Real Analysis II Continuation of MATH 320. .Prerequisite: MATH-320 All course prerequisites must be met with a minimum grade of C-.\nMATH430Abstract Algebra II Continuation of MATH 330. Prerequisite: MATH-330 All course prerequisites must be met with a minimum grade of C-.\nMATH440Linear Algebra II Treatment of topics such as linear equations, orthogonal projections and least squares, pseudoinverses, eigenvalues and eigenvectors, diagonalization, canonical forms of linear transformations, positive definite matrices, the norm of a matrix, linear programming, and game theory.Prerequisite: MATH-240 All course prerequisites must be met with a minimum grade of C-.\nMATH450Topics in Pure and Applied Mathematics Readings in pure and applied mathematics. Content varies from year to year. Possible topics include: set theory, number theory, geometry, topology.Prerequisite: 1 COMP course and MATH-250 or MATH-316 or MATH-330 All course prerequisites must be met with a minimum grade of C-.\nMATH490Senior Seminar In this course we will explore some of the meta-themes of mathematics. In particular, we will examine how themes such as continuity and approximation are evident - or not - in various branches of mathematics. We will also reflect on such topics as the role of proof in mathematics versus the role of intuition, and what literacy in mathematics means.\nMATH593Senior Individualized Project Each program or department sets its own requirements for Senior Individualized Projects done in that department, including the range of acceptable projects, the required background of students doing projects, the format of the SIP, and the expected scope and depth of projects. See the Kalamazoo Curriculum -> Senior Individualized Project section of the Academic Catalog for more details.Prerequisite: Permission of department and SIP supervisor required.\nThis Academic Catalog is current as of Mar 18, 2019\n\nAn official catalog is produced each summer for the following academic year and stored in the Archives section of this site. These versions are used for degree audits. Throughout the year, approved changes are incorporated immediately. Updates that have been submitted and approved by early summer will be included in the archival catalog for the next academic year in mid-summer." ]
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https://stats.stackexchange.com/questions/118051/how-to-perform-residual-analysis-for-binary-dichotomous-independent-predictors-i
[ "# How to perform residual analysis for binary/dichotomous independent predictors in linear regression?\n\nI am performing the multiple linear regression below in R to predict returns on fund managed.\n\nreg <- lm(formula=RET~GRI+SAT+MBA+AGE+TEN, data=rawdata)\n\n\nHere only GRI & MBA are binary/dichotomous predictors; the remaining predictors are continuous.\n\nI am using this code to generate residual plots for the binary variables.\n\nplot(rawdata$GRI, reg$residuals)\nabline(lm(reg$residuals~rawdata$GRI, data=rawdata), col=\"red\") # regression line (y~x)\n\nplot(rawdata$MBA, reg$residuals)\nabline(lm(reg$residuals~rawdata$MBA, data=rawdata), col=\"red\") # regression line (y~x)\n\n\nMy Question: I know how to inspect residual plots for continuous predictors but how do you test assumptions of linear regression such as homoscedasticity when an independent variable is binary?\n\nResidual Plots:", null, "", null, "@NickCox has done a good job talking about displays of residuals when you have two groups. Let me address some of the explicit questions and implicit assumptions that lie behind this thread.\n\nThe question asks, \"how do you test assumptions of linear regression such as homoscedasticity when an independent variable is binary?\" You have a multiple regression model. A (multiple) regression model assumes there is only one error term, which is constant everywhere. It isn't terribly meaningful (and you don't have) to check for heteroscedasticity for each predictor individually. This is why, when we have a multiple regression model, we diagnose heteroscedasticity from plots of the residuals vs. the predicted values. Probably the most helpful plot for this purpose is a scale-location plot (also called 'spread-level'), which is a plot of the square root of the absolute value of the residuals vs. the predicted values. To see examples, look at the bottom row of my answer here: What does having \"constant variance\" in a linear regression model mean?\n\nLikewise, you don't have to check the residuals for each predictor for normality. (I honestly don't even know how that would work.)\n\nWhat you can do with plots of residuals against individual predictors is check to see if the functional form is properly specified. For example, if the residuals form a parabola, there is some curvature in the data that you have missed. To see an example, look at the second plot in @Glen_b's answer here: Checking model quality in linear regression. However, these issues don't apply with a binary predictor.\n\nFor what it's worth, if you only have categorical predictors, you can test for heteroscedasticity. You just use Levene's test. I discuss it here: Why Levene's test of equality of variances rather than F ratio? In R you use ?leveneTest from the car package.\n\nEdit: To better illustrate the point that looking at a plot of the residuals vs. an individual predictor variable does not help when you have a multiple regression model, consider this example:\n\nset.seed(8603) # this makes the example exactly reproducible\nx1 = sort(runif(48, min=0, max=50)) # here is the (continuous) x1 variable\nx2 = rep(c(1,0,0,1), each=12) # here is the (dichotomous) x2 variable\ny = 5 + 1*x1 + 2*x2 + rnorm(48) # the true data generating process, there is\n# no heteroscedasticity\n\nmod = lm(y~x1+x2) # this fits the model\n\n\nYou can see from the data generating process that there is no heteroscedasticity. Let's examine the relevant plots of the model to see if they imply problematic heteroscedasticity:", null, "Nope, nothing to worry about. However, let's look at the plot of the residuals vs. the individual binary predictor variable to see if it looks like there is heteroscedasticity there:", null, "Uh oh, it does look like there may be a problem. We know from the data generating process that there isn't any heteroscedasticity, and the primary plots for exploring this didn't show any either, so what is happening here? Maybe these plots will help:", null, "x1 and x2 are not independent of each other. Moreover, the observations where x2 = 1 are at the extremes. They have more leverage, so their residuals are naturally smaller. Nonetheless, there is no heteroscedasticity.\n\nThe take home message: Your best bet is to only diagnose heteroscedasticity from the appropriate plots (the residuals vs. fitted plot, and the spread-level plot).\n\n• Thanks! For the same regression I was doing I found that Residual Vs Y is homoscedastic but when I checked Residual Vs tenure(independent) it was a funnel shape. So i need to do some transformation to correct this right? Then in this context just wanted to understand why you mentioned that checking residual Vs independent variable is not necessary? – GeorgeOfTheRF Oct 14 '14 at 4:23\n• @mrcet007, no you don't need a transformation. If the res vs fitted shows no heteroscedasticity, you are OK. Perhaps an illustration will help you. I've edited my answer to add a demonstration. – gung - Reinstate Monica Oct 15 '14 at 2:05\n• Can you check this link people.duke.edu/~rnau/testing.htm . It says check residual Vs independent variable also. Just sharing for discussions sake. Can you comment on this? What i was thinking was we need to always check both residual Vs predicted as well as residual vs independent. homoscedasticity (constant variance) of the errors (a) versus time (in the case of time series data) (b) versus the predictions (c) versus any independent variable – GeorgeOfTheRF Oct 17 '14 at 13:45\n• My comment is that I have provided you with both a reason why you look at residual vs predicted graphs to check for heteroscedasticity & showed you an example of how looking at residual vs IV graphs can lead you astray. I don't know what else there is to say. – gung - Reinstate Monica Oct 17 '14 at 23:57\n\nIt's true that conventional residual plots are harder work in this case: it can be (much) more difficult to see whether the distributions are about the same. But there are easy alternatives here. You are just comparing two distributions, and there are many good ways to do that. Some possibilities are side-by-side or superimposed quantile plots, histograms or box plots. My own prejudice is that box plots unadorned are often over-used here: they usually will suppress the detail we should want to look at, even if we can often dismiss it as unimportant. But you can eat your cake and have it.\n\nYou use R, but nothing statistical in your question is R-specific. Here I used Stata for a regression on a single binary predictor and then fired up quantile box plots comparing the residuals for the two levels of the predictor. The practical conclusion in this example is that the distributions are about the same.", null, "More detail if the plot looks cryptic: For each distribution, we have a quantile plot, i.e. the ordered values are plotted versus their (fractional) rank. A box showing median and quartiles is superimposed. Hence each box is defined vertically in the usual way and horizontally because it is bounded by lines for fractional ranks $1/4$ and $3/4$.\n\nNote: See also How to present box plot with an extreme outlier? including @Glen_b's example of similar plots using R. Such plots should be easy in any decent software; if not, your software is not decent.\n\n• +1 Beautiful. Do you feel that there is a role for hypothesis testing on the residuals here as well? – Alexis Oct 6 '14 at 23:43\n• @gung I edited your edit. The original was evidently not clear enough if you misunderstood it. – Nick Cox Oct 6 '14 at 23:46\n• @Alexis Thanks! I am happy with the idea that a hypothesis of equal scatter is supported informally by the graph in this case. I am not of the school of thought that every small step in an analysis needs to be sanctified by a P-value. Unfortunately, it is never easy to be sure that you jump the right way, but I would in practice entertain other models too if I was in doubt. Here the example is just concocted for the question and not part of a serious analysis. – Nick Cox Oct 6 '14 at 23:48\n• My apologies, Nick. I misunderstood the point of that phrase. I thought it was a typo. It is clearer now. – gung - Reinstate Monica Oct 7 '14 at 1:20\n• @whuber That's fine by me. Some people find them confusing, or so I am told. – Nick Cox Oct 7 '14 at 17:43" ]
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http://ket-rt.ru/thevenins-teorem/
[ "Uncategorized\n\nThevenins teorem\n\nAs originally stated in terms of DC resistive circuits only, Thévenin’s theorem holds that:. Lastet opp av ProfTurgeGjennomgang av Thevenins teorem anvendt på et enkelt eksempel. Any combination of batteries and resistances with two terminals can be replaced by a single voltage source e and a single series resistor r. Thevenin’s Theorem states that it is possible to simplify any linear circuit, no matter how complex, to an equivalent circuit with just a single voltage source and . Electronics Tutorial using Thevenins Theorem to Analyse Complex DC Circuits including Thevenins Electrical Circuit Theory and Analysis.\n\nThevenin’s Theorem Easy Step by Step Procedure with Example Pictorial Views Thevenin’s Theorem may be stated below: Any Linear . Thevenin’s teorem er en måte å redusere en krets til en tilsvarende krets bestående av en enkelt spenningskilde, seriemotstan og last. If we think deeply about an electrical circuit, we can visualize the statements made in Thevenin theorem. Superposisjonsprinsippet er oppklart etter iherdig lesing og testing. Jeg tror det lønner seg å terpe på Thevenins teorem først og bli stø på denne.\n\nNorton er ikke annet en en dual til Thevenin. Thevenin’s Theorem is a very important and useful theorem. It is a method for the reduction of a portion of a complex circuit . Theory: In electrical circuit theory, Thevenin’s theorem for linear electrical networks states that any combination of voltage sources, current sources and resistors . General Idea: In circuit theory, Thévenin’s theorem for linear electrical networks states that any combination of voltage sources . Simply explained: Thevenin’s Theorem states that any network of voltage sources and resistors can be reduced to a single voltage source and a single resistor . How can I prove Thevenin’s and Norton’s theorem? Thévenin’s theorem can be used to convert any circuit’s sources and impedances to a . Norton’s Thereom is identical to Thevenin’s Theorem except that the equivalent. The thevenin’s theorem is named after a French engineer, M. Thevenin’s in 18and Norton’s theorem after a scientist E. These circuits demonstrate Thévenin’s theorem, which states that any combination of voltage sources, current sources, and resistors can be reduced to a single . In circuit analysis Thevenin’s theorem is very important.\n\nA large circuit can be replaced with an independent voltage source. Thevenin’s theorem is a procedure by which we change a complex network in to simple network called thevenin’s equivalent circuit. Thevenin’s theoreWelcome to our free internet course on AC/DC circuits using the TINA circuit simulation software.\n\nELECTRICAL PRINCIPLES TITLE: Thevenin’s Theorem Experiment Lecturer: Submission Form Signature: Hardcopy: Yes/No . Thevenin’s Theorem makes it easy to study complex networks by simplifying the circuit to be studied. It states that networks with voltage and current. Two powerful circuit analysis techniques are Thevenin’s theorem and Norton’s theorem. Both theories convert a complex circuit to a simpler series or parallel . Definition of Thevenin theorem by Electropedia.\n\nTHEVENIN’S THEOREConsider the following: Network. Thevenin’s theorem on ResearchGate, the professional network for scientists. Thevenin”s Theorem is one of the most widely used theorems in circuit analysis to simplify a circuit for ease of design and understanding.\n\nThis implies that voltage across load in figure 5. This implies: (see 5) \\$ v=c-(-K)i\\$ , that is, \\$ v=c+Ki\\$." ]
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https://uk.mathworks.com/matlabcentral/profile/authors/869968
[ "Community Profile", null, "# Dr. Murtaza Khan\n\n### Graduate of N.E.D University, Pakistan\n\n27 total contributions since 2009\n\nI did Ph.D. from Keio University, Japan in March 2008.\n\n* Book: Image and Video Data Compression using Spline and Quadtree (ISBN: 978-3-8383-2920-8)\n\n*Murtaza Ali Khan, \"A new method for video data\ncompression by quadratic Bézier curve fitting\",\nSignal, Image and Video Processing, online June 2010.\n\n* Murtaza Khan and Yoshio Ohno, \"Compression of Temporal Video Data by Catmull-Rom Spline and Quadratic Bezier Curve Fitting\", WSCG 2008 referred Proceeding, Plzen, Czech Republic, Feb. 2008.\n\n* Murtaza Khan and Yoshio Ohno, \"A hybrid image compression technique using quadtree decomposition and parametric line fitting for synthetic images\", Advances in Computer Science and Engineering, 1 (3), 263-283, Nov. 2007.\n\n* Murtaza Ali Khan and Yoshio Ohno, \"Compression of Video Data using Parametric Line and Natural Cubic Spline Block Level Approximation\", IEICE Transactions on Information and Systems, Vol.E90-D No.5 pp.844-850, May 2007.\nProfessional Interests: Spline/Curves,\n\nView details...\n\nContributions in\nView by\n\nMATRIX COFACTOR\nA = [ 2 4 1 4 3 7 2 1 3 ] detA = det(A) invA = inv(A) cofactorA = transpose(detA*invA)\n\n1 year ago | 2\n\nHow can i resize image stored in imageDatastore\n% % Resize images in data store using custom reader function clc, close all, clear all % % Read datastore already provided i...\n\n1 year ago | 0\n\nBar plot with bars in different colors\nmydata=rand(1,10) color= ['r','g','b','k']; figure, hold on % % if data is more than colors then colors will be repeated m =...\n\n2 years ago | 0\n\ncolor individual bar with different colors in bar plot\nmydata=rand(1,10) color= ['r','g','b','k']; figure, hold on % % if data is more than colors then colors will be repeated m...\n\n2 years ago | 0\n\nHow to change the color of individual bars in a bar chart?\nmydata=rand(1,10) color= ['r','g','b','k']; figure, hold on % % if data is more than colors then colors will be repeated m...\n\n2 years ago | 0\n\nError using vision.internal.Kdtree/index Invalid input class.\nI got the same error when my features matrix was of size M-by-1 in the custom feature extractor function. I changed it to size 1...\n\n2 years ago | 0\n\nhow to display multiple images and view them one after another in one axes\nThe attached code may help someone with the same need. It navigates though sequence of loaded images via Next and Previous push ...\n\n2 years ago | 0\n\nSubmitted\n\nCompression of motion capture data using quadratic Bezier curve\nCoding of MoCap signal using multidimensional quadratic Bezier curve fitting", null, "Submitted\n\nCompression of MoCap Data using DWT (GUI based)\nCompression of Motion Capture Data (ASF/AMC format) using Discrete Wavelet Transform", null, "Submitted\n\ncubic Bezier least square fitting\nApproximation of data using cubic Bezier curve least square fitting", null, "Submitted\n\nRainbow Colormap\nRainbow Colormap", null, "Submitted\n\nN Dimensional Cardinal Spline (Catmull-Rom) Spline Interpolation\nN -Dimensional cubic Cardinal spline (Catmull-Rom) Interpolation", null, "Submitted\n\nConstruction of cubic Bezier Patch and Surface\nConstruction of cubic Bezier Patch and Surface", null, "Submitted\n\nQuadtree decomposition (Encoding) and Decoding of RGB Image\nQuadtree decomposition (Encoding) and Decoding of RGB Image of size M-by-N-by-3.", null, "Submitted\n\nCardinal Spline (Catmull-Rom) Spline\nEvaluates and plot 2D Cardinal Spline (Catmull-Rom) Spline.", null, "Submitted\n\nEuler angles to Quaternion Conversion (for six basic sequence of rotations)\nAllowed rotations sequences: xyz, xzy, yxz, yzx, zxy, zyx\n\nSubmitted\n\n2D Cubic Beizer Curve\nEvaluate and plot 2D cubic bezier curve for given four control points.", null, "Submitted\n\nMerge two sorted vectors into a sorted vector\nMerge two sorted vectors 'a' and 'b' into a sorted vector 'c'\n\nSubmitted\n\nBinary Serach of rows of M-by-N Matrix\nBinary Search that is based on sum of column values of rows of input M-by-N Matrix", null, "Submitted\n\nReshape 1D to 2D with Balance\nReshapes 1D array to 2D array with size of rows and columns of B is balance", null, "Submitted\n\nApproximation of Circle Using Cubic Bezier Curve\nApproximation of unit radius circle with four parametrix bezier curves", null, "Submitted\n\nDCM from Euler angles\nComputes DCM from Euler angles for six basic sequence of rotations around X(Roll), Y(Pitch), Z(Ya)", null, "Submitted\n\nApproximation of 2-D Data by Natural Cubic Spline\nApproximation (Data Fitting) by Natural Cubic Spline.", null, "Submitted\n\nBinary Search for numeric vector\nSearch given value in a sorted vector, returns the index of location where the value is found.\n\nSubmitted\n\nBezier Interpolation in N-Dimension Space\nBezier interpolation for given four control points. Each control point can be in N-Dimensional.", null, "Submitted\n\nDifferential Encoding/Decoding\nBasic Differential Encoding/Decoding of input vector of numeric values", null, "" ]
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https://unapologetic.wordpress.com/2011/12/27/a-family-of-nontrivial-homology-classes-part-3/
[ "# The Unapologetic Mathematician\n\n## A Family of Nontrivial Homology Classes (part 3)\n\nSorry this didn’t go up as scheduled last week.\n\nWe must now show that the forms we’ve defined are closed, and thus that they indeed will define homology classes. That is,", null, "$d\\omega=0$. We must also show that they cannot be exact, and thus that the homology classes they define are nontrivial.\n\nWe defined", null, "$\\omega$ to be the pullback", null, "$\\pi^*\\hat{\\omega}$ of the form", null, "$\\hat{\\omega}$ on the sphere. Thus we can calculate", null, "$\\displaystyle d\\omega=d\\pi^*\\hat{\\omega}=\\pi^*d\\hat{\\omega}=\\pi^*0=0$\n\nwhich follows since", null, "$\\hat{\\omega}$ is an", null, "$n$-form on the", null, "$n$-dimensional sphere, and so no nontrivial", null, "$n+1$-form exists on", null, "$S^n$ to be equal to", null, "$d\\hat{\\omega}$.\n\nAs for exactness: if", null, "$\\omega=d\\eta$ for some", null, "$n-1$-form", null, "$\\eta$, then Stokes’ theorem tells us that", null, "$\\displaystyle\\int\\limits_{S^n}\\omega=\\int\\limits_{S^n}d\\eta=\\int\\limits_{\\partial S^n}\\eta=\\int\\limits_\\varnothing\\eta=0$\n\nSince the sphere has an empty boundary.\n\nBut it’s also possible to calculate this integral directly.", null, "\\displaystyle\\begin{aligned}\\int\\limits_{S^n}\\omega&=\\int\\limits_{S^n}\\pi^*\\hat{\\omega}\\\\&=\\int\\limits_{\\pi(S^n)}\\hat{\\omega}\\\\&=\\int\\limits_{S^n}\\iota_P(du^0\\wedge\\dots\\wedge du^n)\\end{aligned}\n\nNow, if", null, "$f:U^n\\to S^n$ is any parameterization of the sphere, we set", null, "$u^i=f^i(x)$ and calculate", null, "\\displaystyle\\begin{aligned}\\int\\limits_{S^n}\\omega&=\\int\\limits_{S^n}\\iota_P(du^0\\wedge\\dots\\wedge du^n)\\\\&=\\int\\limits_{U^n}f^*\\left(\\iota_P(du^0\\wedge\\dots\\wedge du^n)\\right)\\\\&=\\int\\limits_{U^n}\\left[du^0\\wedge\\dots\\wedge du^n\\right]\\left(P(f(x)),f_{*x}\\frac{\\partial}{\\partial x^1},\\dots,f_{*x}\\frac{\\partial}{\\partial x^n}\\right)\\\\&=\\int\\limits_{U^n}\\left[du^0\\wedge\\dots\\wedge du^n\\right]\\left(u^{i_0}\\frac{\\partial}{\\partial u^{i_0}},\\frac{\\partial u^{i_1}}{\\partial x^1}\\frac{\\partial}{\\partial u^{i_1}},\\dots,\\frac{\\partial u^{i_n}}{\\partial x^n}\\frac{\\partial}{\\partial u^{i_n}}\\right)\\end{aligned}\n\nWe extend", null, "$f$ to depend on a new variable", null, "$x_0$ which will vary in some small neighborhood of", null, "$1$ by defining", null, "$\\tilde{f}(x_0,x)=x_0f(x)$, so that we have", null, "$\\displaystyle\\frac{\\partial u^i}{\\partial x^0}=u^i$\n\nand so we can continue:", null, "\\displaystyle\\begin{aligned}\\int\\limits_{S^n}\\omega&=\\int\\limits_{U^n}\\left[du^0\\wedge\\dots\\wedge du^n\\right]\\left(\\frac{\\partial u^{i_0}}{\\partial x^0}\\frac{\\partial}{\\partial u^{i_0}},\\frac{\\partial u^{i_1}}{\\partial x^1}\\frac{\\partial}{\\partial u^{i_1}},\\dots,\\frac{\\partial u^{i_n}}{\\partial x^n}\\frac{\\partial}{\\partial u^{i_n}}\\right)\\\\&=\\int\\limits_{U^n}\\det\\left(\\frac{\\partial u^i}{\\partial x^j}\\right)\\left[du^0\\wedge\\dots\\wedge du^n\\right]\\left(\\frac{\\partial}{\\partial u^0},\\dots,\\frac{\\partial}{\\partial u^n}\\right)\\\\&=\\int\\limits_{U^n}\\det\\left(\\frac{\\partial u^i}{\\partial x^j}\\right)\\bigg\\vert_{x^0=1}\\,d(x^1,\\dots,x^n)\\end{aligned}\n\nNow, what is this integral calculating? The first column of the determinant is the vector", null, "$f(x)$ which, as the position vector of a point on the sphere, has unit length and points perpendicularly to its surface. The other columns form a basis of the tangent space to the sphere at", null, "$f(x)$. At any given point, then, we can change the basis so that the upper-left entry in the matrix is", null, "$1$ and all other entries in its row and column are zero. The determinant is thus the determinant of the rest of the matrix, which is the Jacobian determinant of the parameterization, and its integral is thus the volume of the image — the volume of the sphere.\n\nNow, we may not have a formula handy for the", null, "$n$-dimensional volume of the", null, "$n$-sphere, but it’s certainly not zero! Therefore the closed form", null, "$\\omega$ cannot have been exact, and so it must define a nontrivial homology class, just as asserted.\n\nDecember 27, 2011 - Posted by | Differential Topology, Topology\n\n1. i couldn’t get anything of it as the base of all this isn’t clear to me!", null, "Comment by harrins | December 29, 2011 | Reply\n\n2. Another terrific series! Cohomology isn’t nearly as scary as it sounds.\n\nI’m curious about what you said in (part 1), though, that these “provide models for every possible way a nontrivial homology class can arise” — could you elaborate on that (or point me to where I could learn more)?", null, "Comment by Joe English | January 3, 2012 | Reply\n\n3. It’s hard to be rigorous at this point, but the basic idea is that each of these describes a field that can exist around a certain kind of “hole”. For instance, if you can draw (something diffeomorphic to) a sphere around your hole, but that sphere can’t be drawn tight, then you’re looking at something like the three-dimensional version of this construction. If you can draw a circle around the hole that can’t be drawn tight, then you’re looking at the two-dimensional version. This goes for, say, tubular holes bored of a three-dimensional block, because you can draw a loop around them — inside the block — that can’t be drawn tight.\n\nAnyway, given any manifold and a closed form on the manifold, you draw loops of various dimensions around all the holes. If the form is exact, then the integrals around all these loops must be zero; nonzero results are the “obstruction” to the form being exact. But now for each dimension we have a model of a closed-but-not-exact form that just fails to be defined “inside a hole”.\n\nSo set up a copy of that model form in your space, with the singularity inside the hole. Scale the model form until the integral around your “test loop” is exactly the same as the integral you got from your original form. Subtract the scaled model form from the original form, and presto — you’ve resolved one obstruction. Do this for all the loops, and the resulting form must be exact. So your original form differs from an exact form by one real number parameter per independent test loop; the only reason wasn’t exact is that it “wrapped around a hole” more or less like one of our models.", null, "Comment by John Armstrong | January 3, 2012 | Reply\n\n4. “we may not have a formula handy for the n-dimensional volume of the n-sphere”", null, "Comment by John rood | January 5, 2018 | Reply\n• Read “we” as authorial, in the context of this one post, not the entire mathematical community. Deriving a single formula is notably more complicated, but not necessary for the result that", null, "$\\omega$ defines a nontrivial homology class.", null, "Comment by John Armstrong | January 5, 2018 | Reply" ]
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https://www.khanacademy.org/math/calculus-all-old/integration-calc/definite-integral-properties-calc/v/same-integration-bounds
[ "If you're seeing this message, it means we're having trouble loading external resources on our website.\n\nIf you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.\n\n# Definite integral over a single point\n\nAP.CALC:\nFUN‑6 (EU)\n,\nFUN‑6.A (LO)\n,\nFUN‑6.A.1 (EK)\n,\nFUN‑6.A.2 (EK)\n\n## Video transcript\n\n- [Voiceover] We've already taken definite integrals and we've seen how they represent or denote the area under a function between two points and above the X axis. But let's do something interesting. Let's think about a definite integral of F of X DX, It's the area under the curve, F of X, but instead of it being mean between two different X values, say A and B like we see in multiple times, let's say it's between the same one. Let's say it's between C and C. Let's say C is right over here. What do you think this thing right over here is going to be equal to? What does this represent? What is this equal to? I encourage you to pause the video and try to think about it. Well if you try to visualize it, you're thinking, well the area under the curve F of X, above the X axis, from X equals C to X equals C. So this region, I guess we could call it, that we think about it, does have a height. The height here is F of C. What's the width? Well there is no width, we're just at a single point. We're not going from C to C plus some delta X or C plus some even very small change in X or C plus some other very small a value. We're just, saying at the point C. When we're thinking about area we're thinking about how much two-dimensional space you're taking up. But this idea, this is just a one-dimensional, I think you could think of it as a line segment. What's the area of a line segment? Well a line segment has no area. So this thing right over here is going to be equal to zero. Now you might say, I get that. I see why that could make sense, why that makes intuitive sense. I'm trying to find the area of a rectangle where I know it's height, but it's width is zero. So that areas going to be zero is one way to think about it. But Sal, why are you even pointing this out to me? As well see, especially when we do more complex definite integration problems and solving things sometimes recognizing this will help you simplify an integration problem dramatically. Or you could work to be able to get to a point like this so that you can cancel things out. Or you can say, hey that thing right over there is just going to be equal to zero." ]
[ null ]
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https://www.chippiko.com/ina219-arduino
[ "# INA219 Arduino Basic Code, Library and Tutorial\n\nPosted on\n\n## INA219 Arduino\n\nAdafruit INA219 Arduino – How to Read the INA219 Sensor Module Using Arduino – The INA219 Sensor Module is a sensor that can measure current, voltage and power.\n\nThe voltages that can be read are the shunt voltage, the bus voltage and the load voltage.\n\nThe voltage will be read on a 0.1 ohm shunt resistor with a tolerance of 1% 2W.\n\nOn page 5 in the datasheet, it is written that the maximum voltage reading of the shunt resistor if PGA = 8 is ± 320mV, that means INA219 will be able to read a maximum current of ± 3.2A.\n\nThis INA219 sensor has a 12-bit internal ADC.\n\nThis means that the reading value will be divided into 4095 samples. If we use a maximum current of ± 3.2A, the value will be divided by 4095.\n\n3.2A / 4095 = 0.000781441 A\n\nSo, the sample will detect a current of 0.000781441 A or 0.78 mA (± 0.8mA). This will make a precise current reading.\n\nThe maximum voltage that can be read is up to ± 26VDC even though this module only uses 3 or 5V VCC source voltage.\n\nFor communication with a microcontroller, this sensor uses I2C communication which can be connected to the Arduino. we using 2 pins only, SDA on pin A4 and SCL on pin A5.\n\nThe INA219 sensor module has two input pins IN + and IN- connected to the shunt resistor. To be able to use this module, we need a library that will make Arduino programming easier.\n\n### INA219 Arduino Library\n\nThe INA2019 Sensor library is available in the Arduino IDE library manager. Please add it to your Arduino IDE with these steps:\n\n• Click Include Library\n• Click Manage Libary\n• Click install.\n\nA reference to this library, the I2C default address set in the library is 0x40. Jumper A0 and A1 are open. If jumper A0 is connected and A1 is not connected, use the address 0x41.\n\nIf jumper A0 is not connected and A1 is connected, use the address 0x44. If jumpers A0 and A1 are connected, use the address 0x45.\n\nThis library, in addition to measuring the current in the shunt resistor, can also read the NA219 Arduino Voltage shunt, load voltage and bus voltage. You can see this voltage difference in the following picture:\n\n### INA219 Arduino Wiring\n\nThe circuit between the Arduino Uno and INA219 is very simple, you just connect:\n\n• VCC to 5V or 3V.\n• SCA to A4 pin\n• SCL to pin A5\n• GND to GND\n\nConsider the following picture, in the example the load here is measuring the current flowing to the DC motor, you can replace this load into other devices such as LEDs, lamps, other electronic devices and so on:\n\n### Basic Code\n\nIn this article I connected jumper A0 then I used the I2C address of the sensor module is 0x41.\n\nYou can connect the jumpers or not, it’s up to you. because all conditions have their own address. The address can be set from the program.\n\n• If jumpers A0 and A1 are not connected, use the address 0x40\n• If jumper A0 is connected and A1 is not connected, use the address 0x41\n• If jumper A0 is not connected and A1 is connected, use the address 0x44\n• If jumpers A0 and A1 are connected, use the address 0x45\n\n``````#include <Wire.h>\n\nAdafruit_INA219 ina219 (0x41); // if A0 is jumpered\n// Adafruit_INA219 ina219 (0x44); // if A1 is jumpered\n// Adafruit_INA219 ina219 (0x45); // if A0 and A1 is jumpered\n\nvoid setup(void)\n{\nSerial.begin(9600);\n\nif (! ina219.begin()) {\nSerial.println(\"Failed to find INA219 chip\");\nwhile (1) {\ndelay(10);\n}\n}\n\n// By default the initialization will use the largest range (32V, 2A).\n\n// To use a slightly lower 32V, 1A range (higher precision on amps):\n//ina219.setCalibration_32V_1A();\n\n// Or to use a lower 16V, 400mA range (higher precision on volts and amps):\n//ina219.setCalibration_16V_400mA();\n}\n\nvoid loop(void)\n{\nfloat shuntvoltage = 0;\nfloat busvoltage = 0;\nfloat current_mA = 0;\nfloat power_mW = 0;\n\nshuntvoltage = ina219.getShuntVoltage_mV();\nbusvoltage = ina219.getBusVoltage_V();\ncurrent_mA = ina219.getCurrent_mA();\npower_mW = busvoltage * current_mA;\nloadvoltage = busvoltage + (shuntvoltage / 1000);\n\nSerial.print(\"BUS: \");\nSerial.print(busvoltage);\nSerial.print(\" V \");\n\nSerial.print(\"SHUNT: \");\nSerial.print(shuntvoltage);\nSerial.print(\" mV \");\n\nSerial.print(\" V \");\n\nSerial.print(\"CURRENT: \");\nSerial.print(current_mA);\nSerial.print(\" mA \");\n\nSerial.print(\"POWER: \");\nSerial.print(power_mW);\nSerial.print(\" mW\");\nSerial.print(\" or \");\nSerial.print(power_mW / 1000);\nSerial.println(\" W\");\n\ndelay(500);\n}``````\n\n1.", null, "dextrose says:" ]
[ null, "https://secure.gravatar.com/avatar/80235d4e41f30359fcb272b6c0c12adc", null ]
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https://www.groundai.com/project/gp-cake-effective-brain-connectivity-with-causal-kernels/
[ "1 Introduction\n\nAbstract\n\nA fundamental goal in network neuroscience is to understand how activity in one region drives activity elsewhere, a process referred to as effective connectivity. Here we propose to model this causal interaction using integro-differential equations and causal kernels that allow for a rich analysis of effective connectivity. The approach combines the tractability and flexibility of autoregressive modeling with the biophysical interpretability of dynamic causal modeling. The causal kernels are learned nonparametrically using Gaussian process regression, yielding an efficient framework for causal inference. We construct a novel class of causal covariance functions that enforce the desired properties of the causal kernels, an approach which we call GP CaKe. By construction, the model and its hyperparameters have biophysical meaning and are therefore easily interpretable. We demonstrate the efficacy of GP CaKe on a number of simulations and give an example of a realistic application on magnetoencephalography (MEG) data.\n\n\\DisableLigatures\n\n[f]encoding = *, family = *\n\nGP CaKe: Effective brain connectivity with causal kernels\n\nLuca Ambrogioni1, Max Hinne1, Marcel van Gerven1 and Eric Maris1\n\n1 Radboud University, Donders Institute for Brain, Cognition and Behaviour, Nijmegen, The Netherlands\n\n* [email protected]\n\n1 Introduction\n\nIn recent years, substantial effort was dedicated to the study of the network properties of neural systems, ranging from individual neurons to macroscopic brain areas. It has become commonplace to describe the brain as a network that may be further understood by considering either its anatomical (static) scaffolding, the functional dynamics that reside on top of that or the causal influence that the network nodes exert on one another [1, 2, 3]. The latter is known as effective connectivity and has inspired a surge of data analysis methods that can be used to estimate the information flow between neural sources from their electrical or haemodynamic activity[2, 4]. In electrophysiology, the most popular connectivity methods are variations on the autoregressive (AR) framework  . Specifically, Granger causality (GC) and related methods, such as partial directed coherence and directed transfer function, have been successfully applied to many kinds of neuroscientific data [6, 7]. These methods can be either parametric or non-parametric, but are not based on a specific biophysical model [8, 9]. Consequently, the connectivity estimates obtained from these methods are only statistical in nature and cannot be directly interpreted in terms of biophysical interactions . This contrasts with the framework of dynamic causal modeling (DCM), which allows for Bayesian inference (using Bayes factors) with respect to biophysical models of interacting neuronal populations . These models are usually formulated in terms of either deterministic or stochastic differential equations, in which the effective connectivity between neuronal populations depends on a series of scalar parameters that specify the strength of the interactions and the conduction delays . DCMs are usually less flexible than AR models since they depend on an appropriate parametrization of the effective connectivity kernel, which in turn depends on detailed prior biophysical knowledge or Bayesian model comparison.\n\nIn this paper, we introduce a new method that is aimed to bridge the gap between biophysically inspired models, such as DCM, and statistical models, such as AR, using the powerful tools of Bayesian nonparametrics . We model the interacting neuronal populations with a system of stochastic integro-differential equations. In particular, the intrinsic dynamic of each population is modeled using a linear differential operator while the effective connectivity between populations is modeled using causal integral operators. The differential operators can account for a wide range of dynamic behaviors, such as stochastic relaxation and stochastic oscillations. While this class of models cannot account for non-linearities, it has the advantage of being analytically tractable. Using the framework of Gaussian process (GP) regression, we can obtain the posterior distribution of the effective connectivity kernel without specifying a predetermined parametric form. We call this new effective connectivity method Gaussian process Causal Kernels (GP CaKe). The GP CaKe method can be seen as a nonparametric extension of linear DCM for which the exact posterior distribution can be obtained in closed-form without resorting to variational approximations. In this way, the method combines the flexibility and statistical simplicity of AR modeling with the biophysical interpretability of a linear DCM.\n\nThe paper is structured as follows. In Section 2 we describe the model for the activity of neuronal populations and their driving interactions. In Section 3 we construct a Bayesian hierarchical model that allows us to learn the causal interaction functions. Next, in Section 3.2, we show that these causal kernels may be learned analytically using Gaussian process regression. Subsequently in Section 4, we validate GP CaKe using a number of simulations and demonstrate its usefulness on MEG data in Section 5. Finally, we discuss the wide array of possible extensions and applications of the model in Section 6.\n\n2 Neuronal dynamics\n\nWe model the activity of a neuronal population using the stochastic differential equation\n\n Djxj(t)=Ij(t)+wj(t), (1)\n\nwhere is the total synaptic input coming from other neuronal populations and is Gaussian white noise with mean and variance . The differential operator specifies the internal dynamic of the neuronal population. For example, oscillatory dynamic can be modeled using the damped harmonic operator  , where is the peak angular frequency and is the damping coefficient.\n\nIn Eq. 1, the term accounts for the effective connectivity between neuronal populations. Assuming that the interactions are linear and stationary over time, the most general form for is given by a sum of convolutions:\n\n Ij(t)=N∑i=1(ci→j⋆xi)(t), (2)\n\nwhere the function is the causal kernel, modeling the effective connectivity from population to population , and indicates the convolution operator. The causal kernel gives a complete characterization of the linear effective connectivity between the two neuronal populations, accounting for the excitatory or inhibitory nature of the connection, the time delay, and the strength of the interaction. Importantly, in order to preserve the causality of the system, we assume that is identically equal to zero for negative lags ().\n\nInserting Eq. 2 into Eq. 1, we obtain the following system of stochastic integro-differential equations:\n\n Missing or unrecognized delimiter for \\big (3)\n\nwhich fully characterizes the stochastic dynamic of a functional network consisting of neuronal populations.\n\n3 The Bayesian model\n\nWe can frame the estimation of the effective connectivity between neuronal populations as a nonparametric Bayesian regression problem. In order to do this, we assign a GP prior distribution to the kernel functions for every presynaptic population and postsynaptic population . A stochastic function is said to follow a GP distribution when all its marginal distributions are distributed as a multivariate Gaussian . Since these marginals are determined by their mean vector and covariance matrix, the GP is fully specified by a mean and a covariance function, respectively and . Using the results of the previous subsection we can summarize the problem of Bayesian nonparametric effective connectivity estimation in the following way:\n\n ci→j(t)∼GP(0,K(t1,t2))wj(t)∼N(0,σ2)Djxj(t)=N∑i=1(ci→j⋆xi)(t)+wj(t), (4)\n\nwhere expressions such as mean that the stochastic process follows a GP distribution with mean function and covariance function .\n\nOur aim is to obtain the posterior distributions of the effective connectivity kernels given a set of samples from all the neuronal processes. As a consequence of the time shift invariance, the system of integro-differential equations becomes a system of decoupled linear algebraic equations in the frequency domain. It is therefore convenient to rewrite the regression problem in the frequency domain:\n\n ci→j(ω)∼CGP(0,K(ω1,ω2))wj(ω)∼CN(0,σ2)Pj(ω)xj(ω)=N∑i=1xi(ω)ci→j(ω)+wj(ω), (5)\n\nwhere is a complex-valued polynomial since the application of a differential operator in the time domain is equivalent to multiplication with a polynomial in the frequency domain. In the previous expression, denotes a circularly-symmetric complex normal distribution with mean and variance , while denotes a circularly-symmetric complex valued GP with mean function and Hermitian covariance function . Importantly, the complex valued Hermitian covariance function can be obtained from by taking the Fourier transform of both its arguments:\n\n K(ω1,ω2)=∫+∞−∞∫+∞−∞e−iω1t1−iω2t2K(t1,t2)dt1dt2. (6)\n\n3.1 Causal covariance functions\n\nIn order to be applicable for causal inference, the prior covariance function must reflect three basic assumptions about the connectivity kernel: I) temporal localization, II) causality and III) smoothness. Since we perform the GP analysis in the frequency domain, we will work with , i.e. the double Fourier transform of the covariance function.\n\nFirst, the connectivity kernel should be localized in time, as the range of plausible delays in axonal communication between neuronal populations is bounded. In order to enforce this constraint, we need a covariance function that vanishes when either or becomes much larger than a time constant . In the frequency domain, this temporal localization can be implemented by inducing correlations between the Fourier coefficients of neighboring frequencies. In fact, local correlations in the time domain are associated with a Fourier transform that vanishes for high values of . From Fourier duality, this implies that local correlations in the frequency domain are associated with a function that vanishes for high values of . We model these spectral correlations using a squared exponential covariance function:\n\n KSE(ω1,ω2)=e−ϑ(ω2−ω1)22+its(ω2−ω1)=e−ϑζ22+itsζ, (7)\n\nwhere . Since we expect the connectivity to be highest after a minimal conduction delay , we introduced a time shift factor in the exponent that translates the peak of the variance from to , which follows from the Fourier shift theorem. As this covariance function depends solely on the difference between frequencies , it can be written (with a slight abuse of notation) as .\n\nSecond, we want the connectivity kernel to be causal, meaning that information cannot propagate back from the future. In order to enforce causality, we introduce a new family of covariance functions that vanish when the lag is negative. In the frequency domain, a causal covariance function can be obtained by adding an imaginary part to Eq. 7 that is equal to its Hilbert transform . Causal covariance functions are the Fourier dual of quadrature covariance functions, which define GP distributions over the space of analytic functions, i.e. functions whose Fourier coefficients are zero for all negative frequencies . The causal covariance function is given by the following formula:\n\n KC(ζ)=KSE(ζ)+iHKSE(ζ). (8)\n\nFinally, as communication between neuronal populations is mediated by smooth biological processes such as synaptic release of neurotransmitters and dendritic propagation of potentials, we want the connectivity kernel to be a smooth function of the time lag. Smoothness in the time domain can be imposed by discounting high frequencies. Here, we use the following discounting function:\n\n f(ω1,ω2)=e−νω21+ω222. (9)\n\nThis discounting function induces a process that is smooth (infinitely differentiable) and with time scale equal to . Our final covariance function is given by\n\n Missing \\left or extra \\right (10)\n\nUnfortunately, the temporal smoothing breaks the strict causality of the covariance function because it introduces leakage from the positive lags to the negative lags. Nevertheless, the covariance function closely approximates a causal covariance function when is not much bigger than .\n\n3.2 Gaussian process regression\n\nIn order to explain how to obtain the posterior distribution of the causal kernel, we need to review some basic results of nonparametric Bayesian regression and GP regression in particular. Nonparametric Bayesian statistics deals with inference problems where the prior distribution has infinitely many degrees of freedom . We focus on the following nonparametric regression problem, where the aim is to reconstruct a series of real-valued functions from a finite number of noisy mixed observations:\n\n yt=∑iγi(t)fi(t)+wt , (11)\n\nwhere is the -th entry of the data vector , is an unknown latent function and is a random variable that models the observation noise with diagonal covariance matrix . The mixing functions are assumed to be known and determine how the latent functions generate the data. In nonparametric Bayesian regression, we specify prior probability distributions over the whole (infinitely dimensional) space of functions . Specifically, in the GP regression framework this distribution is chosen to be a zero-mean GP. In order to infer the value of the function at an arbitrary set of target points , we organize these values in the vector with entries . The posterior expected value of , that we will denote as , is given by\n\n mfj∣y=K×fjΓj(∑iΓiKfiΓi+D)−1y , (12)\n\nwhere the covariance matrix is defined by the entries and the cross-covariance matrix is defined by the entries  . The matrices are square and diagonal, with the entries given by .\n\nIt is easy to see that the problem defined by Eq. 5 has the exact same form as the generalized regression problem given by Eq. 11, with as dependent variable. In particular, the weight functions are given by and the noise term has variance . Therefore, the expectation of the posterior distributions can be obtained in closed from from Eq. 12.\n\n4 Effective connectivity simulation study\n\nWe performed a simulation study to assess the performance of the GP CaKe approach in recovering the connectivity kernel from a network of simulated sources. The neuronal time series are generated by discretizing a system of integro-differential equations, as expressed in Eq. 3. Time series data was then generated for each of the sources using the Ornstein-Uhlenbeck process dynamic, i.e.\n\n D(1)=ddt+α , (13)\n\nwhere the positive parameter is the relaxation coefficient of the process. The bigger is, the faster the process reverts to its mean (i.e. zero) after a perturbation. The discretization of this dynamic is equivalent to a first order autoregressive process. As ground truth effective connectivity, we used functions of the form\n\n ci→j(τ)=ai→jτe−τs , (14)\n\nwhere is a (non-negative) time lag, is the connectivity strength from to and is the connectivity time scale.\n\nIn order to recover the connectivity kernels we first need to estimate the differential operator . For simplicity, we estimated the parameters of the differential operator by maximizing the univariate marginal likelihood of each individual source. This procedure requires that the variance of the structured input from the other neuronal populations is smaller than the variance of the unstructured white noise input so that the estimation of the intrinsic dynamic is not too much affected by the coupling.\n\nSince most commonly used effective connectivity measures (e.g. Granger causality, partial directed coherence, directed transfer function) are obtained from fitted vector autoregression (VAR) coefficients, we use VAR as a comparison method. Since the least-squares solution for the VAR coefficients is not regularized, we also compare with a ridge regularized VAR model, whose penalty term is learned using cross-validation on separately generated training data. This comparison is particularly natural since our connectivity kernel is the continuous-time equivalent of the lagged AR coefficients between two time series.\n\n4.1 Recovery of the effective connectivity kernels\n\nWe explore the effects of different parameter values to demonstrate the intuitiveness of the kernel parameters. Whenever a parameter is not specifically adjusted, we use the following default values: noise level , temporal smoothing and temporal localization . Furthermore, we set throughout.", null, "Figure 1: Example of estimated connectivity. A. The estimated connectivity kernels for two connections: one present (2 → 1) and one absent (1 → 2). B. A three-node network in which node 1 feeds into node 2 and node 2 feeds into node 3. The disconnected edge from 1 to 3 is correctly estimated, as the estimated kernel is approximately zero. For visual clarity, estimated connectivity kernels for other absent connections (2 → 1, 3 →2 and 3 →1) are omitted in the second panel. The shaded areas indicate the 95% posterior density interval over 200 trials.\n\nFigure 1 illustrates connectivity kernels recovered by GP CaKe. These kernels have a connection strength of if feeds into and otherwise. This applies to both the two node and the three node network. As these kernels show, our method recovers the desired shape as well as the magnitude of the effective connectivity for both connected and disconnected edges. At the same time, Fig. 1B demonstrates that the indirect pathway through two connections does not lead to a non-zero estimated kernel. Note furthermore that the kernels become non-zero after the zero-lag mark (indicated by the dashed lines), demonstrating that there is no significant anti-causal information leakage.", null, "Figure 2: The effect of the the temporal localization, smoothness and noise level parameters on a present connection. A. The correlation and mean squared error between the ground truth connectivity kernel and the estimation by GP CaKe. B. The shapes of the estimated kernels as determined by the indicated parameter. Default values for the parameters that remain fixed are σ=0.05, ν=0.15 and ϑ=π. The dashed line indicates the zero-lag moment at which point the causal effect deviates from zero. The shaded areas indicate the 95% posterior density interval over 200 trials.\n\nThe effects of the different kernel parameter settings are shown in Fig. 2A, where again the method is estimating connectivity for a two node network with one active connection, with . We show the mean squared error (MSE) as well as the correlation between the ground truth effective connectivity and the estimates obtained using our method. We do this for different values of the temporal smoothing, the noise level and the temporal localization parameters. Figure 2B shows the estimated kernels that correspond to these settings. As to be expected, underestimating the temporal smoothness results in increased variance due to the lack of regularization. On the other hand, overestimating the smoothness results in a highly biased estimate as well as anti-causal information leakage. Overestimating the noise level does not induce anti-causal information leakage but leads to substantial bias. Finally, overestimating the temporal localization leads to an underestimation of the duration of the causal influence.", null, "Figure 3: The performance of the recovery of the effective connectivity kernels in terms of the correlation and mean squared error between the actual and the recovered kernel. Left column: results for the two node graph shown in Fig. 1A. Right column: results for the three node graph shown in Fig. 1B. The dashed line indicates the baseline that estimates all node pairs as disconnected.\n\nFigure 3 shows a quantitative comparison between GP CaKe and the (regularized and unregularized) VAR model for the networks shown in Fig. 1A and Fig. 1B. The connection strength was varied to study its effect on the kernel estimation. It is clear that GP CaKe greatly outperforms both VAR models and that ridge regularization is beneficial for the VAR approach. Note that, when the connection strength is low, the MSE is actually smallest for the fully disconnected model. Conversely, both GP CaKe and VAR always outperform the disconnected estimate with respect to the correlation measure.\n\n5 Brain connectivity\n\nIn this section we investigate the effective connectivity structure of a network of cortical sources. In particular, we focus on sources characterized by alpha oscillations (8–12Hz), the dominant rhythm in MEG recordings. The participant was asked to watch one-minute long video clips selected from an American television series. During these blocks the participant was instructed to fixate on a cross in the center of the screen. At the onset of each block a visually presented message instructed the participant to pay attention to either the auditory or the visual stream. The experiment also included a so-called ‘resting state’ condition in which the participant was instructed to fixate on a cross in the center of a black screen. Brain activity was recorded using a 275 channels axial MEG system.\n\nThe GP CaKe method can be applied to a set of signals whose intrinsic dynamic can be characterized by stochastic differential equations. Raw MEG measurements can be seen as a mixture of dynamical signals, each characterized by a different intrinsic dynamic. Therefore, in order to apply the method on MEG data, we need to isolate a set of dynamic components. We extracted a series of unmixed neural sources by applying independent component analysis (ICA) on the sensor recordings. These components were chosen to have a clear dipolar pattern, the signature of a localized cortical source. These local sources have a dynamic that can be well approximated with a linear mixture of linear stochastic differential equations . We used the recently introduced temporal GP decomposition in order to decompose the components’ time series into a series of dynamic components . In particular, for each ICA source we independently extracted the alpha oscillation component, which we modeled with a damped harmonic oscillator: . Note that the temporal GP decomposition automatically estimates the parameters and through a non-linear least-squares procedure .", null, "Figure 4: Effective connectivity using MEG for three conditions: I. resting state (R), II. attention to video stream (V) and III. attention to audio stream (A). Shown are the connections between occipital cortex, parietal cortex and left and right auditory cortices. A. The binary network for each of the three conditions. B. The kernels for each of the connections. Note that the magnitude of the kernels depends on the noise level σ, and as the true strength is unknown, this is in arbitrary units.\n\nWe computed the effective connectivity between the sources that corresponded to occipital, parietal and left- and right auditory cortices (see Fig. 4A) using GP CaKe with the following parameter settings: temporal smoothing , temporal shift , temporal localization and noise level . To estimate the causal structure of the network, we performed a -test on the maximum values of the kernels for each of the three conditions. The results were corrected for multiple comparisons using FDR correction with . The resulting structure is shown in Fig. 4A, with the corresponding causal kernels in Fig. 4B. The three conditions are clearly distinguishable from their estimated connectivity structure. For example, during the auditory attention condition, alpha band causal influence from parietal to occipital cortex is suppressed relative to the other conditions. Furthermore, a number of connections (i.e. right to left auditory cortex, as well as both auditory cortices to occipital cortex) are only present during the resting state.\n\n6 Discussion\n\nWe introduced a new effective connectivity method based on GP regression and integro-differential dynamical systems, referred to as GP CaKe. GP CaKe can be seen as a nonparametric extension of DCM  where the posterior distribution over the effective connectivity kernel can be obtained in closed form. In order to regularize the estimation, we introduced a new family of causal covariance functions that encode three basic assumptions about the effective connectivity kernel: (1) temporal localization, (2) causality, and (3) temporal smoothness. The resulting estimated kernels reflect the time-modulated causal influence that one region exerts on another. Using simulations, we showed that GP CaKe produces effective connectivity estimates that are orders of magnitude more accurate than those obtained using (regularized) multivariate autoregression. Furthermore, using MEG data, we showed that GP CaKe is able to uncover interesting patterns of effective connectivity between different brain regions, modulated by cognitive state.\n\nDespite its high performance, the current version of the GP CaKe method has some limitations. First, the method can only be used on signals whose intrinsic dynamics are well approximated by linear stochastic differential equations. Real-world neural recordings are often a mixture of several independent dynamic components. In this case the signal needs to be preprocessed using a dynamic decomposition technique . The second limitation is that the intrinsic dynamics are currently estimated from the univariate signals. This procedure can lead to biases when the neuronal populations are strongly coupled. Therefore, future developments should focus on the integration of dynamic decomposition with connectivity estimation within an overarching Bayesian model.\n\nThe model can be extended in several other directions. First, the causal structure of the neural dynamical system can be constrained using structural information in a hierarchical Bayesian model. Here, structural connectivity may be provided as an a priori constraint, for example derived from diffusion-weighted MRI , or learned from the functional data simultaneously  . This allows the model to automatically remove connections that do not reflect a causal interaction, thereby regularizing the estimation. Alternatively, the anatomical constraints on causal interactions may be integrated into a spatiotemporal model of the brain cortex by using partial integro-differential neural field equations  and spatiotemporal causal kernels. In addition, the nonparametric modeling of the causal kernel can be integrated into a more complex and biophysically realistic model where the differential equations are not assumed to be linear  or where the observed time series data are filtered through a haemodynamic  or calcium impulse response function .\n\nFinally, while our model explicitly refers to neuronal populations, we note that the applicability of the GP CaKe framework is in no way limited to neuroscience and may also be relevant for fields such as econometrics and computational biology.\n\nReferences\n\n1. A. Fornito and E. T. Bullmore, “Connectomics: A new paradigm for understanding brain disease.,” European Neuropsychopharmacology, vol. 25, pp. 733–748, 2015.\n2. K. Friston, “Functional and effective connectivity: A review,” Brain Connectivity, vol. 1, no. 1, pp. 13–35, 2011.\n3. S. L. Bressler and V. Menon, “Large-scale brain networks in cognition: Emerging methods and principles,” Trends in Cognitive Sciences, vol. 14, no. 6, pp. 277–290, 2010.\n4. K. E. Stephan and A. Roebroeck, “A short history of causal modeling of fMRI data.,” NeuroImage, vol. 62, no. 2, pp. 856–863, 2012.\n5. K. Friston, R. Moran, and A. K. Seth, “Analysing connectivity with Granger causality and dynamic causal modelling.,” Current Opinion in Neurobiology, vol. 23, no. 2, pp. 172–178, 2013.\n6. K. Sameshima and L. A. Baccalá, “Using partial directed coherence to describe neuronal ensemble interactions,” Journal of Neuroscience Methods, vol. 94, no. 1, pp. 93–103, 1999.\n7. M. Kamiński, M. Ding, W. A. Truccolo, and S. L. Bressler, “Evaluating causal relations in neural systems: Granger causality, directed transfer function and statistical assessment of significance,” Biological Cybernetics, vol. 85, no. 2, pp. 145–157, 2001.\n8. M. Dhamala, G. Rangarajan, and M. Ding, “Analyzing information flow in brain networks with nonparametric Granger causality,” NeuroImage, vol. 41, no. 2, pp. 354–362, 2008.\n9. S. L. Bressler and A. K. Seth, “Wiener–Granger causality: A well established methodology,” NeuroImage, vol. 58, no. 2, pp. 323–329, 2011.\n10. B. Schelter, J. Timmer, and M. Eichler, “Assessing the strength of directed influences among neural signals using renormalized partial directed coherence,” Journal of Neuroscience Methods, vol. 179, no. 1, pp. 121–130, 2009.\n11. K. Friston, B. Li, J. Daunizeau, and K. E. Stephan, “Network discovery with DCM,” NeuroImage, vol. 56, no. 3, pp. 1202–1221, 2011.\n12. O. David, S. J. Kiebel, L. M. Harrison, J. Mattout, J. M. Kilner, and K. J. Friston, “Dynamic causal modeling of evoked responses in EEG and MEG,” NeuroImage, vol. 30, no. 4, pp. 1255–1272, 2006.\n13. N. L. Hjort, C. Holmes, P. Müller, and S. G. Walker, Bayesian Nonparametrics. Cambridge University Press, 2010.\n14. C. E. Rasmussen, Gaussian Processes for Machine Learning. The MIT Press, 2006.\n15. L. Ambrogioni and E. Maris, “Complex–valued Gaussian process regression for time series analysis,” arXiv preprint arXiv:1611.10073, 2016.\n16. U. C. Täuber, Critical dynamics: a field theory approach to equilibrium and non-equilibrium scaling behavior. Cambridge University Press, 2014.\n17. L. Ambrogioni, M. A. J. van Gerven, and E. Maris, “Dynamic decomposition of spatiotemporal neural signals,” arXiv preprint arXiv:1605.02609, 2016.\n18. M. Hinne, L. Ambrogioni, R. J. Janssen, T. Heskes, and M. A. J. van Gerven, “Structurally-informed Bayesian functional connectivity analysis,” NeuroImage, vol. 86, pp. 294–305, 2014.\n19. M. Hinne, R. J. Janssen, T. Heskes, and M. A. J. van Gerven, “Bayesian estimation of conditional independence graphs improves functional connectivity estimates,” PLoS Computational Biology, vol. 11, no. 11, p. e1004534, 2015.\n20. S. Coombes, P. beim Graben, R. Potthast, and J. Wright, Neural Fields. Springer, 2014.\n21. K. J. Friston, A. Mechelli, R. Turner, and C. J. Price, “Nonlinear responses in fMRI: the Balloon model, Volterra kernels, and other hemodynamics,” NeuroImage, vol. 12, no. 4, pp. 466–477, 2000.\n22. C. Koch, Biophysics of computation: Information processing in single neurons. Computational Neuroscience Series, Oxford University Press, 2004.\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, "", null, "", null, "" ]
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http://www.nerdkits.com/forum/thread/2229/
[ "April 01, 2012 by Akeshish", null, "Hello everyone, From my understanding you system will not be stable(start to oscillate) if you have a 180 degree phase shift when your gain is 0 (or 1db). My question is why does this happen (physically with-in the circuit) i understand the math behind it. Im just trying to visually understand whats happening within the circuit to cause this effect. Im guessing it has to do with the capacitance and inductance! Hi Akeshish, This is a very deep question. If you understand why the math tells you that that a system is unstable with the above criteria then you are doing really well. If you want a physical idea of why this happens here is a slightly hand wavy explanation. Assume you have a circuit with negative feedback where the feedback path has 180 degrees of phase at unity gain at frequency 100hz. Now put a 100hz sine wave into it. If you take a sine wave, shift it by 180 degrees and subtract it from the original (because its negative feedback) you end up adding the same sine wave to itself. Since you are in a feedback loop your sine wave now twice as large goes around the feedback path again, gets shifted and added to itself again. From a circuit perspective it might help to explore how capacitors and inductors introduce a phase shift to a voltage (or current signal). This simple circuitlab example https://www.circuitlab.com/circuit/64ayuv/rc-time-domain-phase-shift-analysis/ can help you explore that. Run the time domain simulation, and notice how there is a 90 degree phase shift from the input to the output. If you sit and play with the equation of a capacitor (I=C*dv/dt) you can see the same phase shift come out of the math. So yes, capacitors and inductors do in fact introduce a phase shift, but they are certainly not the only elements that can change the phase of your signal. thank you very much ohh, by the way from your example wouldnt having a phase shift great than 180 to 359 degrees at unity gain also cause your system to be unstable? This is where im getting mixed up. Hi Akeshish, That's correct, having a phase of more than 180 degrees at crossover will result in an unstable system. I encourage you to not get too caught up thinking of the feedback loop in the time domain (my example was only mean to give you an idea of why the feedback loop blows up) and instead think of these systems in the frequency domain, and understand the math! Humberto thanks for the response, i think i get it. Lets say i have a circuit with three capacitors. I know that R = 1 / jwC or R= 1/SC. I can find the magnitude and phase of each capacitor based on frequency of the system. The one thing im having trouble understand is that if the capacitors are in parallel does the phase shift add together? If the capacitors are in series what happens to the phase shift (add, subtract, are in parallel)? Never mind i think i got it. you can take the magnitude and phase of your transfer function in order to find what im looking for. Thanks again" ]
[ null, "http://www.nerdkits.com/media/gravatar_mm_80.jpg", null ]
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https://www.combinatorics.org/ojs/index.php/eljc/article/view/v26i3p35
[ "# $1/k$-Eulerian Polynomials and $k$-Inversion Sequences\n\n• Ting-Wei Chao\n• Jun Ma\n• Shi-Mei Ma\n• Yeong-Nan Yeh\n\n### Abstract\n\nLet ${\\bf s} = (s_1, s_2, \\ldots, s_n,\\ldots)$ be a sequence of positive integers. An ${\\bf s}$-inversion sequence of length $n$ is a sequence ${\\bf e} = (e_1, e_2, \\ldots, e_n)$ of nonnegative integers such that $0 \\leq e_i < s_i$ for $1\\leq i\\leq n$. When $s_i=(i-1)k+1$ for any $i\\geq 1$, we call the ${\\bf s}$-inversion sequences the $k$-inversion sequences. In this paper, we provide a bijective proof that the ascent number over $k$-inversion sequences of length $n$ is equidistributed with a weighted variant of the ascent number of permutations of order $n$, which leads to an affirmative answer of a question of Savage (2016). A key ingredient of the proof is a bijection between $k$-inversion sequences of length $n$ and $2\\times n$ arrays with particular restrictions. Moreover, we present a bijective proof of the fact that the ascent plateau number over $k$-Stirling permutations of order $n$ is equidistributed with the ascent number over $k$-inversion sequences of length $n$.\n\nPublished\n2019-08-16\nArticle Number\nP3.35" ]
[ null ]
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https://www.physicsforums.com/threads/significant-figures.888050/
[ "Significant figures\n\nHomework Statement\n\nIn a physics lab, Logger Pro software generated statistical estimators such as the standard deviation σ = 0.04021 of a sample of size n = 29.\n\nAmong other things, I must calculate the standard error of the mean σmean.\n\nMy question is: Must σmean have four sig figs or two (i.e., do I account for the number of sig figs in the sample size, even though n has no error associated with it)?\n\nHomework Equations\n\nσmean = σ/sqrt(n)\n\nwhere σ is the standard deviation of the distribution and n is the sample size.\n\nThe Attempt at a Solution\n\nσmean = σ/sqrt(n) = 0.04021/sqrt(29) = 0.007467 or 0.0075?\n\nRUber\nHomework Helper\nSince your sample size is error free, you can consider that as an infinite number of sig. figs. and keep 4.\n\nSignificant figures is easiest to understand in scientific notation.\nIf you write it as 7.467 x 10^(-3), it is clear that this version has 4 significant figures.\n\ngneill\nMentor\nPresumably the count is accurate and must be an exact integer. It should be treated as though it has infinite precision.\n\nThanks all. In my lab report, I did it the correct way (i.e., reported the answer to 4 sig figs), but the TA docked me marks with the comment \"sig figs\", so I will have to take this up with the lab coordinator. Thanks again for your answers.\n\nDrClaude\nMentor\nIn a physics lab, Logger Pro software generated statistical estimators such as the standard deviation σ = 0.04021 of a sample of size n = 29.\nWhat was the number of significant digits in the data for which these σ were calculated?" ]
[ null ]
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https://dzone.com/articles/an-introduction-to-redis-ml-part-1
[ "{{announcement.body}}\n{{announcement.title}}\n\n# An Introduction to Redis-ML (Part 1)\n\nDZone 's Guide to\n\n# An Introduction to Redis-ML (Part 1)\n\n### Learn how to create a housing price prediction engine using Redis 4.0.0, the popular scikit Python package, and the Redis-ML module.\n\n· AI Zone ·\nFree Resource\n\nComment (0)\n\nSave\n{{ articles.views | formatCount}} Views\n\nDespite widespread interest in machine learning (ML), using it effectively in a real-time environment is a complex problem that hasn’t been given enough attention by framework developers. Nearly every language has a framework to implement the “learning” part of machine learning, but very few frameworks support the “predict” side of machine learning.\n\nOnce you’ve trained an ML model, how can you build a real-time application based on that model? With many toolkits, you have to build your own application. We are just starting to see frameworks focused on the prediction side of machine learning.\n\nIn this post, we’re going to dive deeper into machine learning, explain some of the techniques in an accessible way, and show how you can augment a machine learning pipeline with Redis. As an example, we will walk through the code for a sample program for predicting median housing prices from various features of a neighborhood.\n\nThe sample code in this post is written in Python 3 using a variety of freely available packages for machine learning. You will need to install the following packages using pip3 or your preferred package manager to run the samples:\n\n• scikit-learn (0.18.2)\n• numpy (1.13.1)\n• scipy (0.19.1)\n• redis (2.10.5)\n\nYou will also need a Redis 4.0.0 instance and the Redis-ML module. Shay Nativ, the developer behind the Redis-ML module, created a Docker container with Redis 4.0.0 and the Redis-ML module preloaded. To use that container in conjunction with the code in this post, launch the container using the command:\n\n``docker run -it -p 6379:6379 shaynativ/redis-ml``\n\nDocker will automatically download and run the container, mapping the default Redis port (6379) from the container to your computer.\n\nTo build our housing price predictor, we will use a machine learning technique known as linear regression.\n\nLinear regression was part of the statistician’s toolbox long before algorithmic machine learning was invented. With linear regression, we attempt to predict a result (sometimes called the dependent value) from one or more known quantities (explanatory variables). For linear regression to work, we must be able to accurately estimate our results with a straight line.", null, "Source\n\nIn the graph above, we can see how our data points cluster around an idealized line. This data set is a good candidate for linear regression. In practice, linear regression is used to model a variety of real-world problems where a linear relationship from observations can accurately predict a result, such as the price of a house based on square footage, or college GPA from high school GPA and SAT scores.\n\nFrom algebra, we know that a line is represented by an equation of the form y = b + ax, so to “learn” a model of this form, we need to apply an algorithm to discover the parameters of the line — the slope and intercept. Nothing incredibly fancy. In fact, prior to algorithmic machine learning, most statisticians would “fit” these models by hand. These days, it’s far more common to use a computer to find the line’s parameters and a variety of tool kits (i.e. TensorFlow, Scikit, Apache Spark) are available to solve a linear regression problem. The important thing to remember is that once we’ve learned a linear regression model, we have a mathematical formula for predicting results that could be implemented by any system.\n\nLet’s work through an example of performing a linear regression and discovering the model parameters using the popular Python scikit-learn package and the Boston Housing Dataset.\n\nThe Boston Housing Dataset is a classic data set used in teaching statistics and machine learning. The dataset predicts the median housing price for a neighborhood in the Boston area using neighborhood features like the average number of rooms in a house, the distance from main Boston employment centers, or crime rate. To make it easier to visualize the linear regression process, we’re going to work with a single feature of the data: the average rooms per dwelling (RM) column.\n\nThe Boston Housing Dataset is provided as part of the scikit-learning package, so, let’s start by plotting our data to visualize the relationship between room count (RM) and median price (MEDV):", null, "While not a perfect line, we can see a pretty strong linear relationship between the average number of rooms and the median house price in a neighborhood. We can even draw an idealized representation of the relationship and see how the data points cluster around it.", null, "The following code demonstrates how to load the Boston Housing dataset using scikit. The Boston Housing Dataset consists of twelve different features used to predict housing prices, so after loading the dataset, we extract data from the fifth column (the RM column) from the data for our sample.\n\n``````from sklearn.datasets import load_boston\n\nboston_RM = boston.data[:,5]\nboston_PRICE = boston.target``````\n\nNow we split our data into two sets: a training set and a test set. For our example, we create our training set from the first 400 samples and the test set from the remaining 106 samples.\n\n``````# slice the data into train and test sets\nx_train = boston_RM[:400].reshape(-1, 1)\nx_test = boston_RM[400:].reshape(-1, 1)\ny_train = boston.target[:400]\ny_test = boston.target[400:]``````\n\nThis method of splitting ensure ensures we always run with the same sets for reproducible results.\n\nNow that we’ve constructed our training and test sets, we can use the linear regression model supplied by scikit to fit a line to our data:\n\n``````lm = LinearRegression()\nlm.fit(x_train, y_train)\n\ncoef = lm.coef_\nint = lm.intercept_\nprint('Coef: {coef}, Intercept: {int}'.format(coef=coef, int=int))``````\n\nAfter running our code, we find that scikit has fit a line to our data with a coefficient of 9.40550212 and an intercept of -35.26094818316348.\n\nNow that we have these parameters, we can implement a linear model to predict housing prices in the Boston area based on the average number of rooms in a house in a neighborhood of interest. Now that I have this model, how can I build an application to make real-time predictions and use the functionality an app or a website?\n\nThe Scikit package provides a predict function to evaluate a trained model, but using a function within an application requires implementing a host of other services to make it fast and reliable. This is where Redis can augment your machine learning systems.\n\nThe Redis-ML module takes advantage of the new Modules API to add a standard linear regression as a native datatype. The module can create linear regressions as well as use them to predict values.\n\nTo add a linear regression to Redis, you need to use the `ML.LINREG.SET` command to add a linear regression to the database. The `ML.LINGREG.SET` command has the following form:\n\n``ML.LINREG.SET key intercept coeef [...]``\n\nBy convention, all of the commands in the Redis-ML module begin with the module’s identifier, ML. All linear regression commands are prefixed with `LINGREG`.\n\nTo setup Redis to be a predictive engine for Boston housing prices using the line we fit in scikit, we need to first load the Redis-ML module using the `loadmodule` directive.\n\n``redis-server --loadmodule /path/to/redis-ml/module.so``\n\nThen we set a key to represent our linear regression using the constants from scikit by executing the `ML.LINREG.SET` command. Remember that the intercept is the first value supplied and the coefficients are provided in feature order. From our scikit code to fit a regression line to the housing data, we determined our line had a coefficient of 9.40550212 for the RM variable and an intercept of -35.26094818316348. We can use the `ML.LINGREG.SET` command to set a Redis key to compute this linear relationship:\n\n``127.0.0.1:6379> ML.LINREG.SET boston_house_price:rm-only -35.26094818316348 9.40550212 OK``\n\nOnce our `boston_house_price:rm-only` key is created, we can repeatedly predict the median house price in a neighborhood by using the `ML.LINREG.PREDICT` command. To predict the median house price in a neighborhood that averages 6.2 rooms per housem we would run the command:\n\n``127.0.0.1:6379> ML.LINREG.PREDICT boston_house_price:rm-only 6.2 \"23.053164960836519”``\n\nRedis predicts a median house price of \\$23,053 (remember our housing prices are in thousands) for this neighborhood.\n\nIt’s helpful to understand how to work with the `ML.LINREG` commands from the redis-cli, but it is far more likely we would be doing this from an application. We can extend our Python code which fits the regression line to automatically create the `boston_house_price:rm-only` key in Redis. Once we’ve created the key in Redis, we implement a test that generates predictions from Redis using our test data.\n\n``````r = redis.StrictRedis('localhost', 6379)\nr.execute_command(\"ML.LINREG.SET\", \"boston_house_price:rm-only\", \"-35.26094818316348\", \"9.40550212\", )\n\nredis_predict = []\nfor x in x_test:\ny = r.execute_command(\"ML.LINREG.PREDICT\", \"boston_house_price:rm-only\", x)\nredis_predict.append(float(y))``````\n\nWe can also generate scikit’s predictions for the same set of data using the predict routine:\n\n``y_predict = lm.predict(x_test) ``\n\nFor comparison, we’ve plotted the results. In the graph below, the black circles represent the actual prices for the test data in our dataset. The blue markers (+) represent the values predicted by Scikit and the magenta markers (x) represent the values predicted by Redis.", null, "As you can see, Redis and scikit make the same predictions for median house price given the average number of rooms. While linear regression may not correctly predict the exact price of every data point, it provides a useful means of estimating an unknown price based on some observable features of a neighborhood.\n\nIn this post, we dug deeper into the linear regression feature of the Redis-ML. We looked at how to use the popular scikit Python package to fit a linear regression line to some housing data and then create a housing price prediction engine using Redis 4.0.0 and the Redis-ML module.\n\nIn the next part of the series, we will look at how Redis-ML can be used to implement an engine for classification, another kind of machine learning problem that attempts to determine the class of unknown data from previous examples.\n\nTopics:\nai ,machine learning ,predictive analytics ,redis ,linear regression ,algorithm ,tutorial ,data visualization\n\nComment (0)\n\nSave\n{{ articles.views | formatCount}} Views\n\nPublished at DZone with permission of Tague Griffith , DZone MVB. See the original article here.\n\nOpinions expressed by DZone contributors are their own." ]
[ null, "https://redislabs.com/wp-content/uploads/2017/07/Linear_regression.svg.png", null, "https://redislabs.com/wp-content/uploads/2017/07/Initial-Data.png", null, "https://redislabs.com/wp-content/uploads/2017/07/Data-with-Regression-Line.png", null, "https://redislabs.com/wp-content/uploads/2017/07/Comparison-Plot.png", null ]
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http://avagliano.info/3rd-grade-measurement-worksheets/grade-measurement-worksheets-inspirational-measuring-worksheet-for-3rd-science-and-geometry/
[ "Grade Measurement Worksheets Inspirational Measuring Worksheet For 3rd Science And Geometry", null, "grade measurement worksheets inspirational measuring worksheet for 3rd science and geometry.\n\nfree measurement worksheets grade 3 3rd science estimating common core,3rd grade measurement and geometry worksheets measuring inches second math for,3rd grade measurement and geometry worksheets measuring worksheet common core inches,3rd grade measuring length worksheets estimating measurement pdf for math,3rd grade measurement worksheets pdf and geometry kindergarten capacity images math great two page on mass measuring length,3rd grade common core measurement worksheets measuring inches science capacity,3rd grade estimating measurement worksheets math for inches printable and geometry,3rd grade science measurement worksheets free measuring inches length,inches worksheets 3rd grade measurement and geometry pdf science,3rd grade measurement and geometry worksheets impressive best images on math for i measuring length common core." ]
[ null, "http://avagliano.info/wp-content/uploads/2019/10/grade-measurement-worksheets-inspirational-measuring-worksheet-for-3rd-science-and-geometry.jpg", null ]
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https://pt.b-ok.org/book/2575425/570d2d
[ "Principal Fundamentals of Electric Power Engineering\n\n# Fundamentals of Electric Power Engineering\n\n,\nElectric power engineering has always been an integral part of electrical engineering education. Providing a unique alternative to existing books on the market, this text presents a concise and rigorous exposition of the main fundamentals of electric power engineering. Contained in a single volume, the materials can be used to teach three separate courses — electrical machines, power systems and power electronics, which are in the mainstream of the electrical engineering curriculum of most universities worldwide. The book also highlights an in-depth review of electric and magnetic circuit theory with emphasis on the topics which are most relevant to electric power engineering.\n\nCategories: Technique\\\\Energy\nAno: 2014\nEditora: World Scientific Publishing Company\nLíngua: english\nPáginas: 540\nISBN 10: 9814616583\nISBN 13: 9789814616584\nFile: PDF, 10.86 MB\n\n## You may be interested in\n\nPost a Review", null, "You can write a book review and share your experiences. Other readers will always be interested in your opinion of the books you've read. Whether you've loved the book or not, if you give your honest and detailed thoughts then people will find new books that are right for them.\n1\n\n### Bioprinting: Principles and Applications\n\nAno: 2015\nLíngua: english\nFile: PDF, 10.79 MB\n2\n\n### In the Hollow of the Wave: Virginia Woolf and Modernist Uses of Nature\n\nAno: 2012\nLíngua: english\nFile: PDF, 11.84 MB\n```\fFUNDAMENTALS OF\n\nELECTRIC POWER\nENGINEERING\n\n8582_9789814616584_TP.indd 1\n\n31/7/14 5:16 pm\n\nMay 2, 2013\n\n14:6\n\nBC: 8831 - Probability and Statistical Theory\n\nPST˙ws\n\nFUNDAMENTALS OF\n\nELECTRIC POWER\nENGINEERING\n\nIsaak D. Mayergoyz\n\n•\n\nPatrick McAvoy\n\nUniversity of Maryland, USA\n\nWorld Scientific\nNEW JERSEY\n\n•\n\nLONDON\n\n8582_9789814616584_TP.indd 2\n\n•\n\nSINGAPORE\n\n•\n\nBEIJING\n\n•\n\nSHANGHAI\n\n•\n\nHONG KONG\n\n•\n\nTA I P E I\n\n•\n\nCHENNAI\n\n31/7/14 5:16 pm\n\nWorld Scientific Publishing Co. Pte. Ltd.\n5 Toh Tuck Link, Singapore 596224\nUSA office: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601\nUK office: 57 Shelton Street, Covent Garden, London WC2H 9HE\n\nMayergoyz, I. D.\nFundamentals of electric power engineering / Isaak D. Mayergoyz, University of Maryland,\nUSA, Patrick McAvoy, University of Maryland, USA.\npages cm\nIncludes bibliographical references and index.\nISBN 978-9814616584 (hardbound : alk. paper) -- ISBN 9814616583 (hardbound : alk. paper) --\nISBN 978-9814616591 (e-book) -- ISBN 9814616591 (e-book) -\t\t ISBN 978-9814616607 (mobile) -- ISBN 9814616605 (mobile)\n1. Electric power systems. I. McAvoy, Patrick. II. Title.\nTK1001.M34 2014\n621.31--dc23\n\n2014028094\n\nBritish Library Cataloguing-in-Publication Data\nA catalogue record for this book is available from the British Library.\n\nCover illustration: High voltage switch gear for three phases, by Angie (Sawara, Japan) under CC\nBY 2.0, Wikimedia Commons\n\nAll rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means,\nelectronic or mechanical, including photocopying, recording or any information storage and retrieval\nsystem now known or to be invented, without written permission from the publisher.\n\nFor photocopying of material in this volume, please pay a copying fee through the Copyright Clearance\nCenter, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy\nis not required from the publisher.\n\nPrinted in Singapore\n\nChandra - Fundamentals of Electric Power.indd 1\n\n23/9/2014 10:57:42 AM\n\nSeptember 8, 2014\n\n11:16\n\nWorld Scientific Book - 9in x 6in\n\nTO OUR STUDENTS\n\nv\n\nmodified˙ws-book9x6\n\npage v\n\nMay 2, 2013\n\n14:6\n\nBC: 8831 - Probability and Statistical Theory\n\nPST˙ws\n\nSeptember 8, 2014\n\n11:16\n\nWorld Scientific Book - 9in x 6in\n\nmodified˙ws-book9x6\n\nPreface\n\nYou have in your hands an undergraduate text on fundamentals of electric\npower engineering. This text reflects the experience of the first author in\nteaching electric power engineering courses in the Electrical and Computer\nEngineering Department of the University of Maryland College Park during\nthe past thirty-four years. These courses have constituted the educational\ncore of the electric power engineering program. This program was originally\nestablished (in the early 1980s) with the financial support and sponsorship\nof Baltimore Gas and Electric (BGE) Company, Potomac Electric Power\nCompany (PEPCO), Virginia Electric Power Company (VEPCO), Bechtel Corporation and General Electric (GE) Foundation. This program has\nbeen designed as a sequence of senior elective courses in the area of electric\npower engineering. This design has two main advantages. First, students\nin such elective courses usually have strong interest in electric power and\nare really motivated to learn the related material. Second, senior students\nhave already been exposed to fundamentals in electric and electronic circuits, electromagnetics and control theory. This opens the opportunity to\ncover the material in power courses at sufficiently high level and with the\nsame mathematical and physical rigor which is now practiced in courses\non communication, control and electromagnetics. This text on fundamentals of electric power engineering reflects this approach to teaching power\ncourses.\nElectric power engineering has always been an integral part of electrical\nengineering education. This is especially true nowadays in view of renewed\nemphasis in the area of energy in general and electric power engineering in\nparticular. This textbook may provide a viable alternative to existing textbooks on the market by covering in one volume in a concise and rigorous\nmanner such topics as power systems, electrical machines and power elec-\n\nvii\n\npage vii\n\nSeptember 8, 2014\n\nviii\n\n11:16\n\nWorld Scientific Book - 9in x 6in\n\nmodified˙ws-book9x6\n\nFundamentals of Electric Power Engineering\n\ntronics. For this reason, this book can be used for teaching three different\ncourses such as Power Systems, Electrical Machines and Power Electronics. These power courses form the mainstream of electric power engineering\ncurriculum at most universities worldwide.\nThe book consists of three parts. The first part of the book deals with\nthe review of electric and magnetic circuits. This review stresses the topics\nwhich nowadays are usually deemphasized (or ignored) in required circuits\nand electromagnetics courses. Namely, the phasor diagrams for ac circuits and analysis of electric circuits with periodic non-sinusoidal sources\nare stressed. Phasor diagrams have practically disappeared from circuit\ncourses and textbooks, while these diagrams are still very instrumental in\nelectric power engineering. Analysis of electric circuits with periodic nonsinusoidal sources is very important in the study of steady-state operation\nof power electronics converters. The frequency-domain and time-domain\ntechniques for such analysis are presented in the book. In the review of\nmagnetic circuits, a special emphasis is made on the analysis of magnetic\ncircuits with permanent magnets. This is justified, on the one hand, by\nthe proliferation of permanent magnets in power devices and, on the other\nhand, by the insufficient discussion of this topic in the existing undergraduate textbooks. Furthermore, the analysis of nonlinear magnetic circuits\nand eddy current losses for circularly (or elliptically) polarized magnetic\nfields are presented. The former is important because magnetic saturation\nof ferromagnetic cores often occurs in power devices. The latter is of interest because ferromagnetic cores of ac electric machines are subject to\nrotating (not linearly polarized) magnetic fields.\nThe second part of the book can be used for teaching courses on power\nsystems and electrical machines. This part starts with a brief review of\nthe structure of power systems, analysis of three-phase circuits and the\ndiscussion of ac power and power factor. Next, the analysis of faults in\npower systems is presented. This analysis is first performed by using the\nThevenin theorem. Then, the concept of symmetrical components is introduced and the sequence networks are derived. Finally, the analysis of\nfaults based on sequence networks is discussed. The next chapter deals with\ntransformers. Here, the design and principle of operation of transformers\nare first considered along with the study of the ideal transformer. Then,\nthe equivalent circuit for a single-phase transformer is derived on the basis of equivalent mathematical transformation of coupled circuit equations\nand the importance of leakage inductances (leakage reactances) is stressed.\nNext, open-circuit and short-circuit tests are described as the experimen-\n\npage viii\n\nSeptember 8, 2014\n\n11:16\n\nWorld Scientific Book - 9in x 6in\n\nPreface\n\nmodified˙ws-book9x6\n\nix\n\ntal means of determining parameters of equivalent circuits. The chapter\nis concluded by the discussion of three-phase transformers. The following\nchapter deals with synchronous generators. Here, the design and principle\nof operation of synchronous generators with cylindrical rotors and salient\npole rotors are first considered. Then, the mathematical analysis of armature reaction magnetic fields of ideal cylindrical rotor generators is carried\nout. The results of this analysis are used in the discussion of the design of\nstator windings and in the computation of their synchronous reactance. It\nis stressed that stator windings are designed as filters of spatial and temporal harmonics. This is achieved due to their distributed nature, their\ntwo-layer structure and the use of fractional pitch. Next, the two-reactance\ntheory of salient pole synchronous generators is presented. The chapter\nis concluded by the derivation of formulas for the power of synchronous\ngenerators and by the discussion of static stability of these generators as\nwell as of their performance when connected to an infinite bus. The next\nchapter deals with the power flow analysis and dynamic (transient) stability of power systems. Here, the nonlinear power flow equations are first\nderived and then their numerical solutions by using Newton-Raphson and\ncontinuation techniques are discussed. The analysis of the transient stability is carried out by using the “swing” equation for mechanical motion of\nrotors of synchronous generators. This equation is presented in the Hamiltonian form, which leads to the phase portrait of rotor dynamics. This\nphase portrait results in a simple algebraic criterion for transient stability\nof rotor dynamics which contains as a particular case the celebrated equal\narea stability criterion. The last chapter of the second part deals with induction machines. In the past, induction machines have mostly been used\nas motors. However, recently induction machines have found applications\nas generators in wind energy systems. First, the design and principle of\noperation of induction machines is discussed. Then, by using the fact that\nin the induction machines the electromagnetic coupling between the rotor\nand stator windings is mostly realized through rotating magnetic fields, the\ncoupled circuit equations are derived. The equivalent mathematical transformation of these coupled circuit equations leads to the equivalent electric\ncircuits for induction machines. The chapter is concluded by the discussion\nof mechanical (torque-speed) characteristics of induction machines, which\nreveal the possibility of frequency control of speed of induction motors.\nThe third part of the book deals with power electronics and it consists of\nfour chapters. The first chapter covers the material related to power semiconductor devices. It starts with a brief review of the scope and nature\n\npage ix\n\nSeptember 8, 2014\n\nx\n\n11:16\n\nWorld Scientific Book - 9in x 6in\n\nmodified˙ws-book9x6\n\nFundamentals of Electric Power Engineering\n\nof power electronics and then provides the summary of basic facts of semiconductor physics. This is followed by the discussion of p-n junctions and\ndiodes, where all the basic relations are derived and characteristic features\nof power diodes are outlined. Then, the principles of operation and designs\nof bipolar junction transistors (BJTs) and thyristors (SCRs) are presented\nand the special emphasis is placed on the understanding of operation of\nthese devices as switches. Next, such devices as the MOSFET, power\nMOSFET and IGBT are discussed and their main advantages as power\nelectronics switches are articulated. The chapter is concluded with brief\ndescriptions of snubber circuits and resonant switches. The principles of\nzero-current switching (ZCS) and zero-voltage switching (ZVS) are outlined\nand it is stressed that the design of resonant (quasi-resonant) power converters is a very active and promising area of research. The next chapter deals\nwith rectifiers. Here, single-phase bridge rectifiers with RL, RC and RLC\nloads are first discussed along with center-tapped transformer rectifiers.\nThe time-domain technique is extensively used to derive analytical expressions for currents and voltages in such rectifiers. Then, three-phase diode\nrectifiers are studied and various circuit topologies of these rectifiers are\npresented along with derivation of analytical expressions for voltages and\ncurrents. The chapter is concluded with the discussion of phase-controlled\nrectifiers, and single-phase as well as three-phase versions of such rectifiers\nare studied in detail. The following chapter deals with inverters. It starts\nwith the discussion of single-phase bridge inverters, and the design of bidirectional (bilateral) switches needed for the operation of the inverters is\nmotivated and described. This is followed by the detailed study of pulsewidth modulation (PWM) and analytical expressions for spectra of PWM\nvoltages are derived. The chapter is concluded with the discussion of threephase inverters. The design of ac-to-ac converters by cascading three-phase\nrectifiers with three-phase inverters is then briefly outlined along with their\napplications in ac motor drives. The last chapter of the third part of the\nbook deals with dc-to-dc converters (choppers). Here, the buck converter,\nboost converter and buck-boost converter are first covered, and continuous\nand discontinuous modes of their operation are studied in detail. The chapter is concluded with the discussion of “flyback” and “forward” (indirect)\nconverters, and physical aspects of their operation are carefully described\nalong with all pertinent analytical formulas.\nEach part of the book is supplemented by a list of problems of varying\ndifficulty. Many of these problems are pointed questions related to the\ntheoretical aspects discussed in the text. It is hoped that this may motivate\n\npage x\n\nSeptember 19, 2014\n\n16:35\n\nWorld Scientific Book - 9in x 6in\n\nPreface\n\nmodified˙ws-book9x6\n\nxi\n\nreaders to go through the appropriate parts of the text again and again,\nwhich may eventually result in the better comprehension of the material.\nWe have made an effort to produce a relatively short book that covers the fundamentals of the very broad area of electric power engineering.\nNaturally, this can only be achieved by omitting some topics. We have\nomitted the discussion of transmission lines because this subject is usually\ncovered in courses on electromagnetics. We have also omitted the discussion of power system protection and economic operation (optimal dispatch)\nof generating resources. In our view, these topics are more suited for more\nadvanced courses. In the power electronics portion of the book, we have\nlimited our discussion to the most basic facts related to the circuit topology and principles of operation of power converters. This book has a strong\ntheoretical flavor with emphasis on physical and mathematical aspects of\nelectric power engineering fundamentals. It clearly reveals the multidisciplinary nature of power engineering and it stresses its connections with\nother areas of electrical engineering. It is believed that this approach can\nbe educationally beneficial.\nIn undertaking this project, we wanted to produce a student-friendly\ntextbook. We have come to the conclusion that students’ interests are best\nserved when the discussion of complicated concepts is not avoided. We have\ntried to introduce these concepts in a straightforward way and strived to\nachieve clarity and precision in exposition. We believe that material which\nis carefully and rigorously presented is better absorbed. It is for students\nto judge to what extent we have succeeded.\n\npage xi\n\nMay 2, 2013\n\n14:6\n\nBC: 8831 - Probability and Statistical Theory\n\nPST˙ws\n\nSeptember 8, 2014\n\n11:16\n\nWorld Scientific Book - 9in x 6in\n\nmodified˙ws-book9x6\n\nContents\n\nPreface\n\nPart I:\n\n1.\n\n3.\n\nReview of Electric and Magnetic\nCircuit Theory\n\nBasic Electric Circuit Theory\n1.1\n1.2\n1.3\n\n2.\n\nvii\n\n1\n3\n\nReview of Basic Equations of Electric Circuit Theory . . .\nPhasor Analysis of AC Electric Circuits . . . . . . . . . .\nPhasor Diagrams . . . . . . . . . . . . . . . . . . . . . . .\n\n3\n13\n22\n\nAnalysis of Electric Circuits with Periodic Non-sinusoidal\nSources\n\n31\n\n2.1\n2.2\n2.3\n\n31\n40\n51\n\nFourier Series Analysis . . . . . . . . . . . . . . . . . . . .\nFrequency-Domain Technique . . . . . . . . . . . . . . . .\nTime-Domain Technique . . . . . . . . . . . . . . . . . . .\n\nMagnetic Circuit Theory\n3.1\n3.2\n3.3\n3.4\n3.5\n\n61\n\nBasic Equations of Magnetic Circuit Theory . . . . . . . . 61\nApplication of Magnetic Circuit Theory to the Calculation\nof Inductance and Mutual Inductance . . . . . . . . . . . 77\nMagnetic Circuits with Permanent Magnets . . . . . . . . 87\nNonlinear Magnetic Circuits . . . . . . . . . . . . . . . . . 100\nHysteresis and Eddy Current Losses . . . . . . . . . . . . 110\n\nProblems\n\n123\nxiii\n\npage xiii\n\nSeptember 8, 2014\n\n11:16\n\nWorld Scientific Book - 9in x 6in\n\nxiv\n\nFundamentals of Electric Power Engineering\n\nPart II:\n1.\n\n3.2\n3.3\n\n4.2\n4.3\n4.4\n\nFault Analysis by Using the Thevenin Theorem. .\nSymmetrical Components . . . . . . . . . . . . .\nSequence Networks . . . . . . . . . . . . . . . . .\nAnalysis of Faults by Using Sequence Networks .\n\n159\n.\n.\n.\n.\n\n.\n.\n.\n.\n\n.\n.\n.\n.\n\n.\n.\n.\n.\n\n.\n.\n.\n.\n\n159\n171\n180\n188\n199\n\nDesign and Principle of Operation of the Transformer; The\nIdeal Transformer . . . . . . . . . . . . . . . . . . . . . . . 199\nCoupled Circuit Equations and Equivalent Circuit for the\nTransformer . . . . . . . . . . . . . . . . . . . . . . . . . . 205\nDetermination of Parameters of Equivalent Circuits;\nThree-Phase Transformers . . . . . . . . . . . . . . . . . . 218\n\nDesign and Principle of Operation of Synchronous\nGenerators . . . . . . . . . . . . . . . . . . . . . . . . . . .\nIdeal Cylindrical Rotor Synchronous Generators and Their\nArmature Reaction Magnetic Fields . . . . . . . . . . . .\nDesign of Stator Windings and Their Reactances . . . . .\nTwo-Reactance Theory for Salient Pole Synchronous Generators; Power of Synchronous Generators . . . . . . . . .\n\nPower Flow Analysis and Stability of Power Systems\n5.1\n5.2\n5.3\n\n6.\n\nBrief Overview of Power System Structure . . . . . . . . . 131\nThree-Phase Circuits and Their Analysis . . . . . . . . . . 138\nAC Power and Power Factor . . . . . . . . . . . . . . . . . 148\n\nSynchronous Generators\n4.1\n\n5.\n\n131\n\nTransformers\n3.1\n\n4.\n\n129\n\nFault Analysis\n2.1\n2.2\n2.3\n2.4\n\n3.\n\nPower Systems\n\nIntroduction to Power Systems\n1.1\n1.2\n1.3\n\n2.\n\nmodified˙ws-book9x6\n\n229\n229\n236\n245\n259\n275\n\nPower Flow Analysis . . . . . . . . . . . . . . . . . . . . . 275\nNewton-Raphson and Continuation Methods . . . . . . . . 281\nStability of Power Systems . . . . . . . . . . . . . . . . . . 293\n\nInduction Machines\n\n309\n\n6.1\n\n309\n\nDesign and Principle of Operation of Induction Machines\n\npage xiv\n\nSeptember 8, 2014\n\n11:16\n\nWorld Scientific Book - 9in x 6in\n\nmodified˙ws-book9x6\n\nContents\n\n6.2\n6.3\n\nxv\n\nCoupled Circuit Equations and Equivalent Circuits for Induction Machines . . . . . . . . . . . . . . . . . . . . . . . 317\nTorque-Speed Characteristics of the Induction Motor . . . 325\n\nProblems\n\n335\n\nPart III:\n1.\n\n1.2\n1.3\n1.4\n1.5\n\nIntroduction; Basic Facts Related to Semiconductor\nPhysics . . . . . . . . . . . . . . . . . . . . . . . . . .\nP-N Junctions and Diodes . . . . . . . . . . . . . . .\nBJT and Thyristor . . . . . . . . . . . . . . . . . . .\nMOSFET, Power MOSFET, IGBT . . . . . . . . . .\nSnubbers and Resonant Switches . . . . . . . . . . .\n\n.\n.\n.\n.\n.\n\n.\n.\n.\n.\n.\n\n.\n.\n.\n.\n.\n\nSingle-Phase Rectifiers with RL Loads . .\nSingle-Phase Rectifiers with RC and RLC\nThree-Phase Diode Rectifiers . . . . . . .\nPhase-Controlled Rectifiers . . . . . . . .\n\nSingle-Phase Bridge Inverter . . .\nPulse Width Modulation (PWM)\nThree-Phase Inverters; AC-to-AC\nMotor Drives . . . . . . . . . . .\n\n. . . .\n. . . .\n. . . .\n\n.\n.\n.\n.\n\n.\n.\n.\n.\n\n.\n.\n.\n.\n\n.\n.\n.\n.\n\n.\n.\n.\n.\n\nBuck Converter . . . . . . . . . .\nBoost Converter . . . . . . . . . .\nBuck-Boost Converter . . . . . .\nFlyback and Forward Converters\n\n389\n400\n411\n422\n435\n\n. . . . . . . . .\n. . . . . . . . .\nConverters and\n. . . . . . . . .\n\n. . . . . 435\n. . . . . 443\nAC\n. . . . . 456\n\nDC-to-DC Converters (Choppers)\n4.1\n4.2\n4.3\n4.4\n\n345\n358\n368\n378\n385\n389\n\nInverters\n3.1\n3.2\n3.3\n\n4.\n\n345\n\nRectifiers\n2.1\n2.2\n2.3\n2.4\n\n3.\n\n343\n\nPower Semiconductor Devices\n1.1\n\n2.\n\nPower Electronics\n\n467\n.\n.\n.\n.\n\n.\n.\n.\n.\n\n.\n.\n.\n.\n\n.\n.\n.\n.\n\n.\n.\n.\n.\n\n.\n.\n.\n.\n\n.\n.\n.\n.\n\n.\n.\n.\n.\n\n.\n.\n.\n.\n\n.\n.\n.\n.\n\n.\n.\n.\n.\n\n.\n.\n.\n.\n\n.\n.\n.\n.\n\n.\n.\n.\n.\n\n467\n478\n488\n495\n\nProblems\n\n509\n\nBibliography\n\n515\n\nIndex\n\n519\n\npage xv\n\nMay 2, 2013\n\n14:6\n\nBC: 8831 - Probability and Statistical Theory\n\nPST˙ws\n\nSeptember 8, 2014\n\n11:16\n\nWorld Scientific Book - 9in x 6in\n\nmodified˙ws-book9x6\n\nPART I\n\nReview of Electric and Magnetic\nCircuit Theory\n\n1\n\npage 1\n\nMay 2, 2013\n\n14:6\n\nBC: 8831 - Probability and Statistical Theory\n\nPST˙ws\n\nSeptember 8, 2014\n\n11:16\n\nWorld Scientific Book - 9in x 6in\n\nmodified˙ws-book9x6\n\nChapter 1\n\nBasic Electric Circuit Theory\n\n1.1\n\nReview of Basic Equations of Electric Circuit Theory\n\nIn circuit theory, there are two distinct types of basic mathematical relations. In the first type, these relations depend on the physical nature of\ncircuit elements and they are called terminal relations. The second type\nof relations reflects the connectivity of the electric circuit, namely, how the\ncircuit elements are interconnected. For this reason, they are sometimes\ncalled topological relations. These relations are based on the Kirchhoff\nCurrent Law (KCL) and Kirchhoff Voltage Law (KVL).\nelements: resistor, inductor, capacitor and ideal (independent) voltage and\ncurrent sources. These circuit elements are ubiquitous in power engineering\napplications. However, in power electronics, multi-terminal circuit elements\nare used as well. These multi-terminal circuit elements are models of power\nsemiconductor devices and they will be discussed in Chapter 1 of Part III.\nA two-terminal element is schematically represented in Figure 1.1. Each\ntwo-terminal element is characterized by the voltage v(t) across the terminals and by the current i(t) through the element. In order to write the\nmeaningful equations relating the voltages and currents in electric circuits,\nit is necessary to assign a polarity to the voltage and a direction to the\ncurrent. These assigned (not actual) directions and polarities are called\nreference directions and reference polarities. These reference directions and\npolarities are assigned arbitrarily. The actual current directions and voltage polarities are not known beforehand and they may change with time.\nThe reference direction for a current is indicated by an arrow, while the\nreference polarity is specified by placing plus and minus signs next to element terminals (see Figure 1.1). The reference directions and polarities are\n\n3\n\npage 3\n\nSeptember 8, 2014\n\n4\n\n11:16\n\nWorld Scientific Book - 9in x 6in\n\nmodified˙ws-book9x6\n\nFundamentals of Electric Power Engineering\n\nFig. 1.1\nusually coordinated by choosing the reference direction of the current from\nthe positive reference terminal to the negative reference terminal.\nAs discussed below, the reference directions and polarities are used in\nwriting KCL and KVL equations. These equations are then solved and the\nsigns of currents and voltages are found at any instant of time. If at time\nt a current is positive,\ni(t) > 0,\n\n(1.1)\n\nthen the actual direction of this current coincides with its reference direction. If, on the other hand, the found current is negative at time t,\ni(t) < 0,\n\n(1.2)\n\nthen the actual direction of this current at time t is opposite to its reference\ndirection.\nSimilarly, if a voltage is found to be positive,\nv(t) > 0,\n\n(1.3)\n\nthen the actual polarity coincides with its reference polarity. On the other\nhand, if the voltage is found to be negative,\nv(t) < 0,\n\n(1.4)\n\nthen the actual voltage polarity is opposite to its reference polarity. It is\nclear from the above discussion that the reference directions and polarities\nallow one to write KCL and KVL equations, then solve them and eventually\nfind actual directions and polarities of circuit variables.\nNow, we consider a resistor. Its circuit notation is shown in Figure 1.2.\nThe terminal relation for the resistor is given by Ohm’s law,\nv(t) = Ri(t),\n\n(1.5)\n\nwhere R is the resistance of the resistor. By using the terminal relation\n(1.5), we find the expression for instantaneous power p(t) for the resistor,\np(t) = v(t)i(t) = Ri2 (t),\n\n(1.6)\n\npage 4\n\nSeptember 8, 2014\n\n11:16\n\nWorld Scientific Book - 9in x 6in\n\nBasic Electric Circuit Theory\n\nmodified˙ws-book9x6\n\n5\n\nFig. 1.2\n\nFig. 1.3\nor\nv 2 (t)\n.\n(1.7)\nR\nIt is clear from the last two equations that in the case of the resistor the instantaneous power is always positive, which means that the resistor always\nconsumes electric power. This is the reason why resistors are often used in\nelectric power engineering to model irreversible losses of electric energy or\nits conversion into other forms of energy.\nNext, we discuss an inductor. Its circuit notation is shown in Figure 1.3.\nThe inductor is characterized by inductance L and its terminal relation is\ngiven by the formula\np(t) =\n\nv(t) = L\n\ndi(t)\n.\ndt\n\n(1.8)\n\nThe last equation implies that the current through an inductor is differentiable and, consequently, a continuous function of time. The latter means\nthat for any instant of time t0 the value of the current i(t0− ) immediately\nbefore t0 is equal to the value of the current i(t0+ ) immediately after t0 :\ni(t0− ) = i(t0+ ).\n\n(1.9)\n\nIt is clear from equation (1.8) that in the case of dc currents (i(t) = const)\nthe voltage across the inductor is equal to zero and the inductor can be\nreplaced by a “short-circuit” branch. On the other hand, if the inductor\n(as a part of a circuit) is connected by some switch to a source and the initial\ncurrent through the inductor before switching is zero, then according to the\n\npage 5\n\nSeptember 8, 2014\n\n6\n\n11:16\n\nWorld Scientific Book - 9in x 6in\n\nmodified˙ws-book9x6\n\nFundamentals of Electric Power Engineering\n\ncontinuity condition (1.9) the current through the inductor will remain zero\nimmediately after switching. This means that immediately after switching\nthe inductor is an “open-circuit” branch.\nIt is apparent from equation (1.8) that the instantaneous power p(t) for\nthe inductor is given by the formula\n\u0001\ndi(t)\nL d i2 (t)\np(t) = v(t)i(t) = Li(t)\n=\n.\n(1.10)\ndt\n2\ndt\nIt follows from the last equation that power is positive if the absolute value\nof inductor current increases with time and it is negative if the absolute\nvalue of the current decreases with time. This implies that when the absolute value of the inductor current is increasing with time, the electric power\nis being consumed and stored in the inductor’s magnetic field. On the other\nhand, when the absolute value of the inductor current is decreasing with\ntime, then the electric power is “given back” at the expense of the energy\npreviously stored in the magnetic field. This clearly suggests that the inductor is an energy storage element and it finds many applications as such\nin electric power engineering.\nAnother important application of the inductor is for “ripple suppression” in power electronics. Power electronics converters are switching-mode\nconverters in which semiconductor devices are used as switches that are\nrepeatedly (periodically) switched “on” and “off” to achieve the desired\nperformance of the converters. This periodic switching results in periodic\ncomponents of electric currents which manifest themselves as ripple in output converter voltages. These ripples can be suppressed by using inductors.\nIndeed, from equation (1.8) we find\nZ\n1 t\ni(t) = i(0) +\nv(τ )dτ.\n(1.11)\nL 0\nIf the current is a periodic function of time with period T , then\ni(0) = i(T )\n\n(1.12)\n\nand\nZ\n\nT\n\nv(τ )dτ = 0.\n\n(1.13)\n\n0\n\nIt is apparent that the second term in the right-hand side of equation (1.11)\ncan be construed as a ripple in electric current. It is clear from formula\n(1.11) that this ripple can be suppressed by increasing the value of inductance L. It is also clear from formulas (1.11) and (1.13) that the same\n\npage 6\n\nSeptember 8, 2014\n\n11:16\n\nWorld Scientific Book - 9in x 6in\n\nBasic Electric Circuit Theory\n\nmodified˙ws-book9x6\n\n7\n\nFig. 1.4\nripple can be suppressed by decreasing T , i.e., by increasing the frequency of\nswitching. This leads to the “trade-off” that is practiced in power electronics: the higher the frequency of switching of power semiconductor devices,\nthe smaller the value of inductance that is needed for the ripple suppression.\nNow, we proceed to the discussion of a capacitor. Its circuit notation is\nshown in Figure 1.4. The capacitor is characterized by capacitance C and\nits terminal relation is given by the formula\ndv(t)\n.\n(1.14)\ndt\nThe last equation implies that the voltage across a capacitor is differentiable\nand, consequently, a continuous function of time. The latter means that for\nany instant of time t0 the value of the voltage v(t0− ) immediately before t0\nis equal to the value of the voltage v(t0+ ) immediately after t0 :\ni(t) = C\n\nv(t0− ) = v(t0+ ).\n\n(1.15)\n\nIt is apparent from equation (1.14) that in the case of dc voltages (v(t) =\nconst) the current through the capacitor is equal to zero and the capacitor\nis an “open-circuit” branch. This is consistent with the fact that the current\nthrough the capacitor is a displacement current, which exists only when the\nelectric field in the capacitor varies with time.\nIn the case when an uncharged capacitor with zero voltage is connected\nthrough some switch to a source, then according to the continuity condition\n(1.15) the voltage across the capacitor will remain zero immediately after\nswitching. This means that immediately after switching the capacitor is\na “short-circuit” branch. This implies that capacitors connected in parallel with power equipment may protect this equipment from large initial\ntransient currents, which mostly flow through these capacitors.\nIt is apparent from equation (1.14) that the instantaneous power p(t)\nfor the capacitor is given by the formula\n\ndv(t)\nC d v 2 (t)\np(t) = v(t)i(t) = Cv(t)\n=\n.\n(1.16)\ndt\n2\ndt\n\npage 7\n\nSeptember 8, 2014\n\n8\n\n11:16\n\nWorld Scientific Book - 9in x 6in\n\nmodified˙ws-book9x6\n\nFundamentals of Electric Power Engineering\n\nFig. 1.5\nIt follows from the last equation that power is positive if the absolute value\nof capacitor voltage increases with time and it is negative if the absolute\nvalue of capacitor voltage decreases with time. This implies that, when\nthe absolute value of the capacitor voltage is increasing with time, the\nelectric power is being consumed and stored in the electric field within the\ncapacitor. On the other hand, when the absolute value of the capacitor\nvoltage is decreasing with time, then the electric power is “given back” at\nthe expense of energy stored in the electric field. This clearly reveals that\nthe capacitor is an energy storage element and it is used as such in many\npower-related applications.\nAnother important application of the capacitor is for “ripple suppression” in power electronics. Indeed, from equation (1.14) we derive\n\n1 t\nv(t) = v(0) +\ni(τ )dτ.\n(1.17)\nC 0\nIf the capacitor voltage is a periodic function of time with period T , then\nv(0) = v(T )\n\n(1.18)\n\nand\n\nT\n\ni(τ )dτ = 0.\n\n(1.19)\n\n0\n\nIt is clear that the second term in the right-hand side of formula (1.17)\ncan be construed as a ripple in capacitor voltage. It is apparent from\nformula (1.17) that this ripple can be suppressed by increasing the value\nof capacitance C. It is also apparent from formulas (1.17) and (1.19) that\nthe same ripple can be suppressed by decreasing T , i.e., by increasing the\nfrequency of switching. Hence, the trade-off: the higher the frequency of\nswitching of semiconductor devices in power converters, the smaller the\nvalue of the capacitance that is needed for ripple suppression.\nFinally, we shall discuss ideal (independent) voltage and current sources,\nwhose circuit notations are shown in Figures 1.5 and 1.6, respectively. An\n\npage 8\n\nSeptember 8, 2014\n\n11:16\n\nWorld Scientific Book - 9in x 6in\n\nBasic Electric Circuit Theory\n\nmodified˙ws-book9x6\n\n9\n\nFig. 1.6\nideal voltage source is a two-terminal element with the property that the\nvoltage across its terminals is specified at every instant of time,\nv(t) = vs (t),\n\n(1.20)\n\nwhere vs (t) is a given (known) function of time. It is apparent from the\ngiven definition that the terminal voltage does not depend on the current\nthrough the voltage source, which is reflected in the terminology independent voltage source.\nAn ideal current source is by definition a two-terminal element with the\nproperty that the current through this element is specified at every instant\nof time,\ni(t) = is (t),\n\n(1.21)\n\nwhere is (t) is a given (known) function of time. It is clear from the given\ndefinition that the terminal current does not depend on the voltage across\nthe current source; in this sense, this is an ideal (or independent) current\nsource.\nPreviously we discussed the terminal relations, which are determined by\nthe physical nature of the circuit elements. Now, we proceed to the brief\ndiscussion of the relations which are due to the connectivity of elements in\nan electric circuit. There are two types of such relations. We begin with\nthe Kirchhoff Current Law (KCL). KCL equations are written for nodes\nof electric circuits. A node of an electric circuit is a “point” where three\nor more elements are connected together. KCL states that the algebraic\nsum of electric currents at any node of an electric circuit is equal to zero\nat every instant of time. This is mathematically expressed as follows:\n\nik (t) = 0.\n(1.22)\nk\n\nThe term “algebraic sum” implies that some currents are taken with positive signs while others are taken with negative signs. Two equivalent rules\n\npage 9\n\nSeptember 8, 2014\n\n10\n\n11:16\n\nWorld Scientific Book - 9in x 6in\n\nmodified˙ws-book9x6\n\nFundamentals of Electric Power Engineering\n\ncan be used for sign assignments. One rule is that positive signs are assigned to currents with reference directions toward the node, while negative\nsigns are assigned to currents with reference directions from the node. KCL\nequations can be written for any node. However, only (n − 1) equations\nwill be linearly independent, where n is the number of nodes in a given circuit. The (n − 1) nodes for which KCL equations are written can be chosen\narbitrarily. The KCL equation for the last (n-th) node can be obtained\nby summing up the previously written KCL equations. This clearly suggests that the equation for the last (n-th) node is not linearly independent.\nA “point” in an electric circuit where only two elements are connected is\nnot qualified as a node because of the triviality of the KCL equation in\nthis case, which simply suggests that the same current flows through both\ncircuit elements, i.e., these two circuit elements are connected in series.\nNext, we discuss equations written by using the Kirchhoff Voltage Law\n(KVL). These equations are written for loops. A loop is defined as a set\nof branches that form a closed path with the property that each node is\nencountered only once as the loop is traced. A branch is defined as a\nsingle two-terminal element or several two-terminal elements connected in\nseries. KVL states that the algebraic sum of branch voltages around any\nloop of an electric circuit is equal to zero at every instant of time. This is\nmathematically expressed as follows:\nX\nvk (t) = 0.\n(1.23)\nk\n\nThe term “algebraic sum” implies that some branch voltages are taken with\npositive signs while others are taken with negative signs. The following\nrule can be used for sign assignment. If the tracing direction of the branch\ncoincides with the reference direction of the branch current then the positive\nsign is assigned to the branch voltage, otherwise the negative sign is assigned\nto the branch voltage.\nSince there may be many possible loops for any given circuit, determining which loops must be traced in order to write linearly independent KVL\nequations is not entirely obvious. One method which will always produce\nthe correct number of linearly independent KVL equations is based on the\nuse of a graph tree. By definition, a graph tree of an electric circuit is a\nsubset of branches with the property that all nodes of the circuit are connected together, but there are no closed loops formed by these branches.\nIt is clear that any graph tree of an electric circuit with n nodes contains\nn − 1 branches. By adding a new branch to the graph tree we create a new\n\npage 10\n\nSeptember 8, 2014\n\n11:16\n\nWorld Scientific Book - 9in x 6in\n\nBasic Electric Circuit Theory\n\nmodified˙ws-book9x6\n\n11\n\nloop and a new KVL equation can be written for the created loop. This\nKVL equation will contain a new variable – branch voltage for the added\nbranch. KVL equations written in this way will be linearly independent\nbecause each new equation contains a new variable. It is easy to see that\nthe total number of linearly independent KVL equations written in the described way is equal to b − (n − 1), where b is the total number of branches\nin the circuit. This is so because b − (n − 1) branches should be removed\nto form a graph tree and, consequently, b − (n − 1) loops will be formed by\nadding one by one the removed branches.\nIt is clear that the total number of linearly independent equations written by using KCL and KVL (i.e., the total number of equations (1.22)\nand (1.23)) is equal to the number b of branches. An additional b equations are obtained by using terminal relations (1.5), (1.8), (1.14), (1.20)\nand (1.21). Thus, the total number of equations is 2b, which is the total\nnumber of circuit variables, i.e., the total number of branch currents and\nbranch voltages. These are ordinary differential equations for which the\ninitial conditions can be found by using the continuity conditions (1.9) and\n(1.15). Thus, the framed equations (1.5), (1.8), (1.9), (1.14), (1.15), (1.20),\n(1.21), (1.22) and (1.23) form the foundation of electric circuit theory. In\nthis theory, various analysis techniques have been developed which exploit\nthe connectivity of electric circuits as well as the particular nature of excitation of these circuits. Some of these techniques will be discussed in this\nfirst part of the book due to their wide use in electric power engineering.\nIt is worthwhile to note that in electric circuit theory the basic (framed)\nrelations (1.5), (1.8), (1.9), (1.14), (1.15), (1.20), (1.21), (1.22) and (1.23)\nare treated as axioms (postulates) which are fully consistent with experimental facts. However, within the framework of electromagnetic field theory, all these fundamental circuit relations can be derived by using approximations relevant to the notion of electric circuits with lumped parameters.\nIt is worthwhile to stress in the conclusion of this section that electric\ncircuits are models for actual devices – models which are based on some\nsimplifications and approximations. This may lead in some cases to intrinsic (logical) contradictions between the basic circuit relations. We shall\nillustrate such possible contradictions for two cases of very simple electric\ncircuits shown in Figures 1.7 and 1.8. In Figure 1.7, at time t0 = 0 a\ndc current source is connected by switch (SW ) to an inductor and a resistor connected in series. It is clear that prior to the switching the current\n\npage 11\n\nSeptember 8, 2014\n\n12\n\n11:16\n\nWorld Scientific Book - 9in x 6in\n\nmodified˙ws-book9x6\n\nFundamentals of Electric Power Engineering\n\nFig. 1.7\n\nFig. 1.8\nthrough the inductor is equal to zero,\ni(0− ) = 0.\n\n(1.24)\n\nAccording to the continuity condition (1.9), the current i(0+ ) immediately\nafter switching must be equal to zero,\ni(0+ ) = 0.\n\n(1.25)\n\nHowever, according to KCL the same current must be equal to the current\nI0 of the current source,\ni(0+ ) = I0 \u001f= 0,\n\n(1.26)\n\nv(0+ ) = 0,\n\n(1.27)\n\nSimilarly, for the circuit shown in Figure 1.8, according to the continuity\ncondition (1.15) the voltage v(0+ ) across the capacitor is equal to zero,\nif the capacitor was not charged before switching. However, according to\nKVL the same voltage must be equal to the voltage V0 of the dc voltage\nsource,\n\nv(0+ ) = V0 \u001f= 0,\n\n(1.28)\n\npage 12\n\nSeptember 8, 2014\n\n11:16\n\nWorld Scientific Book - 9in x 6in\n\nBasic Electric Circuit Theory\n\nmodified˙ws-book9x6\n\n13\n\nThe above contradictions appear because in the circuits shown in Figures 1.7 and 1.8 some small parameters have been neglected. For instance,\nfor an actual (real) inductor there is always small parallel to L capacitance\nbetween the turns of the inductor. The presence of this capacitance will\nremove the contradiction between equations (1.25) and (1.26) because immediately after switching the current I0 will flow through this capacitance.\nSimilarly, the presence of a small resistance of connecting wires in the circuit\nshown in Fig. 1.8 will remove the contradiction between equations (1.27)\nand (1.28), because immediately after switching the voltage V0 will be applied across such resistance. The presented discussion suggests that in the\nactual devices represented by the circuits shown in Figures 1.7 and 1.8 the\ninitial stages of transients will be controlled by neglected small parameters.\nThis implies that small parameters can be important for proper modeling\nof the performance of actual devices. It is demonstrated later in this text\nthat the importance of small parameters is typical for such power devices\nas transformers and induction machines as well as boost and buck-boost\nchoppers.\n\n1.2\n\nPhasor Analysis of AC Electric Circuits\n\nIn many electric power applications, electric circuits are excited by ac (sinusoidal) sources. Under steady-state conditions, all voltages and currents\nin such circuits will be sinusoidal. A special and very useful circuit analysis\ntechnique exists which exploits this fact. It is known as the phasor technique and it uses complex numbers to represent time-harmonic sinusoidal\nquantities. The main advantage of the phasor technique is that it reduces\ncalculus operations on time-harmonic sinusoidal quantities to algebraic operations on complex numbers (phasors). As a result, the basic differential\nequations of electric circuits discussed in the previous section are reduced\nto linear algebraic equations with respect to phasors. This significantly\nsimplifies the analysis of electric circuits under ac steady-state conditions.\nThe central idea of the phasor technique can be described as follows. Every time-harmonic sinusoidal quantity is fully characterized by three numbers: its frequency, peak value and initial phase. In ac steady-state analysis, the frequency of sinusoidal quantities is fixed and known. Consequently,\nevery time-harmonic quantity of known frequency is fully characterized by\ntwo numbers: its peak value and initial phase. The same is true for complex numbers. In the polar form, each complex number is characterized\n\npage 13\n\nSeptember 8, 2014\n\n14\n\n11:16\n\nWorld Scientific Book - 9in x 6in\n\nmodified˙ws-book9x6\n\nFundamentals of Electric Power Engineering\n\nby its magnitude (absolute value) and polar angle. This suggests to represent any time-harmonic quantity by a phasor, which is a complex number\nwhose magnitude is equal to the peak value of the time-harmonic quantity\nand whose polar angle is equal to the initial phase of this time-harmonic\nquantity. This definition of the phasor is illustrated by the following two\nformulas for time-harmonic (sinusoidal) voltage and current, respectively,\nv(t) = Vm cos(ωt + ϕV ) ↔ V̂ = Vm ejϕV ,\n\n(1.29)\n\ni(t) = Im cos(ωt + ϕI ) ↔ Iˆ = Im ejϕI ,\n\n(1.30)\n\nwhere V̂ and Iˆ are the phasors of voltage and current, respectively. It is\nclear from the above formulas that if sinusoidal quantities are given then it\nis easy to write their phasors. On the other hand, if the phasor is known\nand represented in the polar form, then it is easy to write the corresponding\ntime-harmonic quantity.\nNow, it is easy to see that in the case of ac steady state all terminal\nrelations can be represented in the phasor form. Consider first a resistor.\nThen, by substituting sinusoidal voltage and current in formula (1.5), we\nfind\nVm cos(ωt + ϕV ) = RIm cos(ωt + ϕI ).\n\n(1.31)\n\nThe last equality implies that\nVm = RIm ,\n\n(1.32)\n\nϕV = ϕI .\n\n(1.33)\n\nThe last formula reveals that in the case of resistors, their time-harmonic\nvoltages and currents are in phase. From the last two formulas, we also\nderive\nˆ\nV̂ = Vm ejϕV = RIm ejϕI = RI.\n\n(1.34)\n\nThus, it is established that the terminal relation for the resistor can be\nwritten in the phasor form as follows:\nˆ\nV̂ = RI.\n\n(1.35)\n\nNext, we consider an inductor. Then, by substituting sinusoidal voltage\nand current in formula (1.8), we find\nVm cos(ωt + ϕV ) = −ωLIm sin(ωt + ϕI ),\n\n(1.36)\n\npage 14\n\nSeptember 8, 2014\n\n11:16\n\nWorld Scientific Book - 9in x 6in\n\nBasic Electric Circuit Theory\n\nmodified˙ws-book9x6\n\n15\n\nor\n\u0010\nπ\u0011\n.\nVm cos(ωt + ϕV ) = ωLIm cos ωt + ϕI +\n2\nThe last equality implies that\n\n(1.37)\n\nVm = ωLIm ,\n(1.38)\nπ\nϕV = ϕI + .\n(1.39)\n2\nThe last formula reveals that in the case of the inductor, its time-harmonic\nvoltage leads its time-harmonic current by π2 . Equivalently, the current lags\nbehind the voltage by π2 . From the last two formulas we also derive\nˆ\nV̂ = Vm ejϕV = ωLIm ej(ϕI +π/2) = jωLIm ejϕI = jωLI.\n\n(1.40)\n\nThus, it is established that the terminal relation for the inductor can be\nwritten in the phasor form as follows:\nˆ\nV̂ = jωLI.\n\n(1.41)\n\nFinally, we consider a capacitor. By substituting sinusoidal voltage and\ncurrent in formula (1.14), we find\nIm cos(ωt + ϕI ) = −ωCVm sin(ωt + ϕV ),\n\n(1.42)\n\nor\n\u0010\nπ\u0011\nIm cos(ωt + ϕI ) = ωCVm cos ωt + ϕV +\n.\n2\nThe last equality implies that\n\n(1.43)\n\nIm = ωCVm ,\n(1.44)\nπ\n(1.45)\nϕI = ϕV + .\n2\nThe last formula reveals that in the case of the capacitor, its time-harmonic\ncurrent leads its time-harmonic voltage by π2 . Equivalently, the voltage lags\nbehind the current by π2 . From the last two formulas we also derive\nIˆ = Im ejϕI = ωCVm ej(ϕV +π/2) = jωCVm ejϕV = jωC V̂ .\n\n(1.46)\n\nThus, it is established that the terminal relation for the capacitor can be\nwritten in the phasor form as follows:\nV̂ = −\n\nj ˆ\nI.\nωC\n\n(1.47)\n\npage 15\n\nSeptember 8, 2014\n\n11:16\n\nWorld Scientific Book - 9in x 6in\n\n16\n\nmodified˙ws-book9x6\n\nFundamentals of Electric Power Engineering\n\nIt is also clear that given sinusoidal voltage and current sources, they can\nbe written in phasor forms:\nvs (t) = Vms cos(ωt + ϕVs ) ↔ V̂s = Vms ejϕVs ,\nis (t) = Ims cos(ωt + ϕI ) ↔ Iˆs = Ims ejϕIs .\ns\n\n(1.48)\n(1.49)\n\nIt can be concluded that in the case of ac steady state all terminal relations\ncan be written in the algebraic phasor form.\nNow, we turn to KCL and KVL equations and write them in the phasor form. To do this we shall use the fact that the phasor of the sum\nof sinusoidal quantities is equal to the sum of the phasors of sinusoidal\nquantities being summed. The proof of this fact is based on the following\nmathematical relation between sinusoidal quantities and phasors:\nh\ni\nh\ni\nv(t) = Vm cos(ωt + ϕV ) = Re Vm ej(ωt+ϕV ) = Re V̂ ejωt .\n(1.50)\nIndeed, consider a sum of sinusoidal quantities of arbitrary physical nature\nX\ng(t) =\nGmk cos(ωt + ϕk )\n(1.51)\nk\n\nand we want to prove that\nĜ =\n\nX\n\nĜk .\n\n(1.52)\n\nk\n\nBy using the Euler formula and formula (1.50), we find\nh\ni X\nX\n\u0002\n\u0003\ng(t) =\nGmk Re ej(ωt+ϕk ) =\nRe Gmk ejϕk ejωt\nk\n\n=\n\nX\n\nk\n\nh\ni\nRe Ĝk ejωt = Re\n\nk\n\n\"\n\n!\nX\n\nĜk\n\n#\ne\n\njωt\n\nh\ni\n= Re Ĝejωt ,\n\n(1.53)\n\nk\n\nwhich proves the equality (1.52).\nHaving established the last fact, we can write KCL equations (1.22) and\nKVL equations (1.23) in the phasor form as follows:\nX\nIˆk = 0, [(n − 1) lin. ind. eqs.],\n(1.54)\nk\n\nX\n\nV̂k = 0,\n\n[b − (n − 1) lin. ind. eqs.].\n\n(1.55)\n\nk\n\nNext, we shall discuss the very important concept of impedance. To this\nend, consider a branch where a resistor, an inductor and a capacitor are\nconnected in series (see Figure 1.9). According to KVL, we have\n\npage 16\n\nSeptember 8, 2014\n\n11:16\n\nWorld Scientific Book - 9in x 6in\n\nBasic Electric Circuit Theory\n\nmodified˙ws-book9x6\n\n17\n\nFig. 1.9\nV̂ = V̂R + V̂L + V̂C .\n\n(1.56)\n\nBy using phasor relations (1.35), (1.41) and (1.47), we transform the last\nequation as follows:\n\u001b\n\u001a\n\u0019\u0018\n1\nj ˆ ˆ\nˆ\nˆ\nI = I R + j ωL −\n.\n(1.57)\nV̂ = RI + jωLI −\nωC\nωC\n\nNow, the impedance Z of the RLC branch can be naturally introduced by\nthe formula\n\u001a\n\u0019\n1\nZ = R + j ωL −\n(1.58)\n= R + jX,\nωC\nwhere\n\n1\n(1.59)\nωC\nis called the reactance of the branch and it is determined by the energy\nstorage elements in the branch.\nBy using the definition (1.58) of impedance, we shall write the terminal\nrelation for the RLC branch in the form\nX = ωL −\n\nˆ\nV̂ = IZ.\n\n(1.60)\n\nIn the polar form, the impedance can be written as\nZ = |Z|ejϕ .\n\n(1.61)\n\nBy substituting the last formula into equation (1.60), we find\nVm ejϕV = Im |Z|ej(ϕI +ϕ) ,\n\n(1.62)\n\nVm = Im |Z|,\n\n(1.63)\n\nϕV − ϕI = ϕ.\n\n(1.64)\n\nwhich implies that\n\npage 17\n\nSeptember 8, 2014\n\n11:16\n\n18\n\nWorld Scientific Book - 9in x 6in\n\nmodified˙ws-book9x6\n\nFundamentals of Electric Power Engineering\n\nThus, the magnitude of branch impedance relates peak values of branch\nvoltage and current, while the polar angle of the impedance is equal to the\nphase shift in time between branch voltage and current.\nFrom equations (1.58) and (1.61) the following useful expressions for |Z|\nand ϕ can be obtained:\ns\n\u00132\n\u0012\np\n1\n2\n2\n2\n,\n(1.65)\n|Z| = R + X = R + ωL −\nωC\n1\nωL − ωC\nX\n=\n.\n(1.66)\nR\nR\nThe branch shown in Figure 1.9 has the most general composition when\nthree physically distinct two-terminal elements are connected in series. The\nexpression (1.58) for the impedance of such a branch is naturally simplified\nwhen only one or two distinct two-terminal elements are present in the\nbranch. These simplifications are given by the following formulas:\n\ntan ϕ =\n\nZ = R,\n\n(1.67)\n\nif a branch contains only a resistor;\nZ = jωL,\n\n(1.68)\n\nif a branch contains only an inductor;\nZ=−\n\nj\n,\nωC\n\n(1.69)\n\nif a branch contains only a capacitor;\nZ = R + jωL\n\n(1.70)\n\nj\nωC\n\n(1.71)\n\nfor an RL branch;\nZ =R−\nfor an RC branch and\n\u0012\n\n1\nZ = j ωL −\nωC\n\n\u0013\n(1.72)\n\nfor an LC branch.\nThe last formula suggests that the impedance is equal to zero if\n1\n.\nω=√\nLC\n\n(1.73)\n\npage 18\n\nSeptember 8, 2014\n\n11:16\n\nWorld Scientific Book - 9in x 6in\n\nBasic Electric Circuit Theory\n\nmodified˙ws-book9x6\n\n19\n\nIt is also clear that under the condition (1.73), the impedance of the RLC\nbranch is given by the formula\nZ = R.\n\n(1.74)\n\nIn other words, under the condition (1.73) an RLC branch acts as a pure\nresistor and branch voltage and current are in phase. This phenomenon is\ncalled resonance and may have important implications.\nThe presented discussion can be summarized as follows. At ac steady\nstate, each branch can be characterized by impedance and the expression\nfor the branch impedance is determined by the composition of the branch.\nLet us consider a branch number k and let Zk be its impedance. Then, the\nphasor branch voltage V̂k and the phasor branch current Iˆk are related by\nthe formula (see (1.60))\nV̂k = Iˆk Zk .\n\n(1.75)\n\nFormula (1.75) can be used in the phasor form of KVL equations (1.55). In\nthese equations (as well as in equations (1.54)) we can also identify known\nphasors of voltage and current sources and move them with appropriate\nsigns to the right-hand sides. The described transformations eventually\nresult in the following ac steady-state equations for the phasors of branch\ncurrents:\nX\nX\n(1.76)\nIˆk = −\nIˆsk ,\nk\n\nX\nk\n\nIˆk Zk = −\n\nk\n\nX\n\nV̂sk .\n\n(1.77)\n\nk\n\nThese are simultaneous linear algebraic equations and it is apparent that\nthe total number of these equations is equal to the total number of passive\n(i.e., without sources) branches. By solving these equations, Iˆk can be found\nand then by using formula (1.75) the phasors of branch voltages V̂k can be\ndetermined. As soon as this is done, instantaneous voltages and branch\ncurrents can be computed by using formulas similar to (1.50). In the circuit\ntheory, various techniques have been developed which exploit connectivity\nof electric circuits. One example of such a technique is the method of\nequivalent transformations which exploits series and parallel connections of\nvarious branches to achieve the overall simplification of electric circuits.\nIt is interesting to mention that from the mathematical point of view\nthe phasor technique allows to find particular periodic solutions of ordinary\ndifferential equations (ODEs) which describe the performance of electric\n\npage 19\n\nSeptember 8, 2014\n\n20\n\n11:16\n\nWorld Scientific Book - 9in x 6in\n\nmodified˙ws-book9x6\n\nFundamentals of Electric Power Engineering\n\ncircuits in the case of their time-harmonic excitation. This phasor technique\nis more efficient and more powerful than the technique of undetermined\ncoefficients used in courses on ordinary differential equations. In this text,\nthe phasor technique will be frequently used to derive simple expressions\nfor particular periodic solutions of ODEs in cases when actual regimes are\nAs has been emphasized in our discussion, the main idea of the phasor\ntechnique is to reduce the operations of calculus on sinusoidal quantities to\nalgebraic operations on their phasors. It turns out that this idea can be\nextended to a broader class of voltages and currents.\nConsider the following voltage:\nv(t) = Vm eσt cos(ωt + ϕV ).\n\n(1.78)\n\nBy using the Euler formula, the last formula can be transformed as follows:\nh\ni\nh\ni\nv(t) = Vm eσt Re ej(ωt+ϕV ) = Re Vm ejϕV e(σ+jω)t .\n(1.79)\nNow, we introduce the voltage phasor V̂ ,\nV̂ = Vm ejϕV ,\n\n(1.80)\n\nas well as the complex frequency\ns = σ + jω.\nBy using the last two formulas in equation (1.79), we find\nh\ni\nv(t) = Re V̂ est .\n\n(1.81)\n\n(1.82)\n\nThe last formula extends the notion of phasors to voltages (1.78) which are\ncharacterized by complex frequency s. Similarly, for a current of complex\nfrequency s we have\nh\ni\nˆ st ,\ni(t) = Im eσt cos(ωt + ϕI ) = Re Ie\n(1.83)\nwhere as before Iˆ = Im ejϕI . Now, it can be shown that the phasor terminal\nrelations for resistors, inductors and capacitors in the case of voltages and\ncurrents of the same complex frequency s are similar to formulas (1.35),\n(1.41) and (1.47). Indeed, in the case of a resistor we have\nVm eσt cos(ωt + ϕV ) = RIm eσt cos(ωt + ϕI ).\nBy using formulas (1.79)-(1.83), we derive\nh\ni\nh\ni\nˆ st ,\nRe V̂ est = Re RIe\n\n(1.84)\n\n(1.85)\n\npage 20\n\nSeptember 8, 2014\n\n11:16\n\nWorld Scientific Book - 9in x 6in\n\nBasic Electric Circuit Theory\n\nmodified˙ws-book9x6\n\n21\n\nwhich implies that\nˆ\nV̂ = RI.\n\n(1.86)\n\nIn the case of an inductor, we find\nVm eσt cos(ωt + ϕV ) = σLIm eσt cos(ωt + ϕI )\n\u0010\nπ\u0011\n+ ωLIm eσt cos ωt + ϕI +\n.\n2\nThe last equality can be transformed as follows:\nh\ni\nh\ni\nˆ st ,\nRe V̂ est = Re (σ + jω)LIe\n\n(1.87)\n\n(1.88)\n\nor\nh\ni\nh\ni\nˆ st ,\nRe V̂ est = Re sLIe\n\n(1.89)\n\nwhich implies that\nˆ\nV̂ = sLI.\n\n(1.90)\n\nBy using the same line of reasoning, it can be shown that in the case of the\ncapacitor we have\n1 ˆ\nI.\n(1.91)\nsC\nBy using this algebraization of terminal relations, it can be demonstrated\nthat in the case of an RLC branch subject to a voltage (1.78) of complex\nfrequency s we have the branch current of the same complex frequency and\ntheir phasors are related by the impedance which is a function of the same\ncomplex frequency. Namely,\nV̂ =\n\nˆ\nV̂ = IZ(s),\n\n(1.92)\n\nwhere\n1\n.\n(1.93)\nsC\nIn applications, it is quite rare that electric circuits are excited by sources\nof complex frequency. However, voltages and currents of complex frequency\nregularly appear in the case of transients in electric circuits. For this reason,\nthe notion of complex frequency as well as the notion of impedance Z(s) as\na function of complex frequency s can be useful in the analysis of transients\nin electric circuits. Indeed, it can be shown that the complex frequencies of\ntransient response in RLC circuits are zeros of impedance Z(s) = 0. The\ndetailed discussion of this matter is beyond the scope of this section.\nZ(s) = R + sL +\n\npage 21\n\nSeptember 8, 2014\n\n22\n\n11:16\n\nWorld Scientific Book - 9in x 6in\n\nmodified˙ws-book9x6\n\nFundamentals of Electric Power Engineering\n\nFig. 1.10\n1.3\n\nPhasor Diagrams\n\nPhasor diagrams are ubiquitous in electric power engineering. They provide\ngeometric visualization for time phase shifts between different sinusoidal\nquantities and for their peak values. The starting point in the discussion\nof phasor diagrams is the representation of a sinusoidal quantity by a uniformly rotating vector. Consider a time-harmonic voltage\nv(t) = Vm cos(ωt + ϕV ).\n\n(1.94)\n\nWe can represent this voltage by a vector V̂ (called a phasor) whose length\nis equal to the peak value Vm of v(t) and whose initial angle with the x-axis\nof the Cartesian coordinate system is equal to the initial phase ϕV of v(t).\nThis angle is called “initial” because the vector V̂ is uniformly rotating in\nthe counterclockwise direction with constant angular velocity equal to the\nangular frequency ω of v(t). Thus, at time t the angle ϕV (t) between the\nvector V̂ and the x-axis (see Figure 1.10) is equal to\nϕV (t) = ωt + ϕV ,\n\n(1.95)\n\ni.e., angle ϕV (t) is the sum of the initial angle ϕV and the angle ωt through\nwhich the vector has rotated over the time t. If at any instant of time we\nconsider the projection of this vector onto the x-axis, it is clear that this\nprojection is equal to the instantaneous value of voltage v(t). In this sense,\nv(t) is represented by the uniformly rotating vector V̂ . Now consider a\ntime-harmonic current of the same angular frequency ω,\ni(t) = Im cos(ωt + ϕI ).\n\n(1.96)\n\nIt can also be represented by a uniformly rotating vector (phasor) Iˆ whose\nlength is equal to the peak value Im of i(t) and whose initial angle with the\nx-axis is equal to the initial phase ϕI of i(t). Since this vector is uniformly\n\npage 22\n\nSeptember 8, 2014\n\n11:16\n\nWorld Scientific Book - 9in x 6in\n\nBasic Electric Circuit Theory\n\nmodified˙ws-book9x6\n\n23\n\nFig. 1.11\nrotating in the counterclockwise direction with angular velocity ω, the angle\nϕI (t) between Iˆ and the x-axis at time t (see Figure 1.10) is equal to\nϕI (t) = ωt + ϕI .\n\n(1.97)\n\nAgain, it is apparent that at any instant of time t the projection of vector\nIˆ onto the x-axis is equal to the instantaneous value of current i(t). Now,\nthe important fact emerges. If we consider the angle ϕ between the two\nˆ we find according to formulas (1.95) and (1.97)\nrotating vectors V̂ and I,\nthat\nϕ = ϕV (t) − ϕI (t) = ϕV − ϕI = const.\n\n(1.98)\n\nThus, this angle ϕ does not change with time and it is equal to the phase\nshift in time between sinusoidal voltage v(t) and sinusoidal current i(t). In\nthis sense, one may say that the rotation of the vectors does not matter\nbecause it does not change the lengths of the vectors and the angle between\nthem. These lengths and the angle are the most important because they\nrepresent the peak values of the sinusoidal quantities and their phase shift\nin time. For this reason, the rotation of vectors (phasors) can be completely\nignored and we represent sinusoidal quantities by vectors (phasors) whose\nlengths are equal to the peak values of the sinusoidal quantities and the\nangles between the vectors are equal to the phase shifts in time between\nthe sinusoidal quantities. This is the central idea of the phasor diagrams,\ni.e., to represent the phase shifts in time by geometric angles between the\nvectors (phasors). This idea helps to visualize different relations between\nsinusoidal quantities and to use geometry in calculations.\nPhasor diagrams can be constructed for complicated electric circuits.\nThese constructions are based on generic phasor diagrams for the three basic two-terminal elements (resistor, inductor and capacitor). These generic\nphasor diagrams are shown in Figure 1.11. Consider first the resistor. According to formula (1.33), time-harmonic voltage across the resistor and\ntime-harmonic current through the resistor are in phase, i.e., the phase\nshift in time between the voltage and current is equal to zero. That is\n\npage 23\n\nSeptember 8, 2014\n\n24\n\n11:16\n\nWorld Scientific Book - 9in x 6in\n\nmodified˙ws-book9x6\n\nFundamentals of Electric Power Engineering\n\nFig. 1.12\nwhy a generic phasor diagram for the resistor has the form shown in Figure\n1.11a. This diagram is called generic because it reflects the main feature,\nzero phase shift, while the lengths of phasors V̂R and IˆR may vary from\nproblem to problem. Now consider the inductor. According to formula\n(1.39), time-harmonic voltage across the inductor leads the time-harmonic\ncurrent through the inductor by π2 . For this reason, in the generic phasor diagram the geometric angle between vectors V̂L and IˆL is equal to\nπ\n(as shown in Figure 1.11b) and vector V̂L leads vector IˆL in the sense\n2\nof counterclockwise rotation. Finally, consider the capacitor. According\nto formula (1.45), time-harmonic current through the capacitor leads the\ntime-harmonic voltage across the capacitor by π2 . This means that in the\ngeneric phasor diagram the geometric angle between vectors V̂C and IˆC is\nequal to π2 (as shown in Figure 1.11c) and vector IˆC leads vector V̂C in the\nsense of counterclockwise rotation.\nNow, through several examples we shall demonstrate how the phasor\ndiagrams can be constructed for actual circuits.\nExample 1. Consider the RLC circuit shown in Figure 1.12 excited by\ntime-harmonic voltage. First, we shall write the KVL equation for this\ncircuit,\nV̂ = V̂R + V̂L + V̂C .\n\n(1.99)\n\nThis equation implies that in the phasor diagram vector V̂ is the vectorial\nsum of vectors V̂R , V̂L and V̂C . As a general rule, we start the construction\nof the phasor diagram by identifying the quantity which is common to the\nresistor, inductor and capacitor. This quantity is the current, so we shall\nˆ Then, according to the generic diagram 1.11a, the vector\nfirst draw vector I.\nV̂R has the same direction as vector Iˆ (see Figure 1.13), while according to\nthe generic diagrams 1.11b and 1.11c vectors V̂L and V̂C are shifted from\nvector Iˆ by π2 in counterclockwise and clockwise directions, respectively.\nBy performing the vector addition of the three vectors V̂R , V̂L and V̂C , we\n\npage 24\n\nSeptember 8, 2014\n\n11:16\n\nWorld Scientific Book - 9in x 6in\n\nBasic Electric Circuit Theory\n\nmodified˙ws-book9x6\n\n25\n\nFig. 1.13\n\nFig. 1.14\narrive at the final form of the phasor diagram shown in Figure 1.13. In\nthis diagram, the geometric angle ϕ between vectors V̂ and Iˆ represents\nthe phase shift in time between the input voltage and input current.\nIt is of interest to consider a particular form of this phasor diagram\ncorresponding to the case of resonance. The resonance occurs under the\ncondition specified by formula (1.73). At resonance, the input voltage and\ncurrent are in phase. This leads to the phasor diagram shown in Figure\n1.14. It is apparent from this figure that the voltages across the inductor\nand capacitor have the same peak values but opposite phases (i.e., shifted\nin phase by π). For this reason, they compensate one another at any instant\nof time. It is also apparent from Figure 1.14 that the peak values of voltages\nacross the inductor and capacitor may be much higher than the peak value\nof the input voltage. This may never happen in dc circuits.\n\npage 25\n\nSeptember 8, 2014\n\n26\n\n11:16\n\nWorld Scientific Book - 9in x 6in\n\nmodified˙ws-book9x6\n\nFundamentals of Electric Power Engineering\n\nFig. 1.15\n\nFig. 1.16\nExample 2. Consider the RL circuit shown in Figure 1.15. Suppose that\nby using a voltmeter the peak values of the input voltage and the voltage\nacross the resistor have been measured and found to be 50 V and 30 V,\nrespectively. The question is what the peak value of the voltage across the\ninductor and the phase shift in time between the input voltage and input\ncurrent are.\nThe visualization of the phasor diagram for the above circuit appreciably\nfacilitates and simplifies the solution of this problem. A well-versed person\nwill visualize this phasor diagram in mind (without actually drawing it) to\ncome up with the immediate answers that the peak value of the voltage\nacross the inductor is 40 V, while the phase shift in time between the input\nvoltage and input current is arctan 4/3. For pedagogical reasons, we draw\nthis phasor diagram shown in Figure 1.16, which is a particular case (V̂C =\n0) of the phasor diagram shown in Figure 1.13. From the right triangle in\nFigure 1.16, the above-stated solution of the problem becomes immediately\napparent.\nExample 3. Consider a more complicated circuit shown in Figure 1.17.\n\npage 26\n\nSeptember 8, 2014\n\n11:16\n\nWorld Scientific Book - 9in x 6in\n\nBasic Electric Circuit Theory\n\nmodified˙ws-book9x6\n\n27\n\nFig. 1.17\nFirst, we shall write the relevant KCL and KVL equations:\nIˆ = IˆC + IˆR ,\nV̂ = V̂L + V̂12 ,\n\n(1.100)\n(1.101)\n\nwhere V̂12 is the phasor of the voltage across the nodes 1 and 2. These\nequations imply that vectorial sums of IˆC with IˆR and V̂L with V̂12 will\nresult in Iˆ and V̂ , respectively. Second, as a general rule, we start the\nconstruction of the phasor diagram from the “end” of the circuit where a\nresistor and a capacitor are connected in parallel and we identify the voltage\nV̂12 as the common quantity for R and C. So, we start the construction of\nthe phasor diagram by drawing the vector V̂12 . According to the generic\nphasor diagrams shown in Figures 1.11a and 1.11c, vector IˆR has the same\ndirection as V̂12 , while vector IˆC is perpendicular to V̂12 and “leads” it as\nfar as counterclockwise rotation is concerned. According to (1.100), the\nvectorial sum of IˆR and IˆC results in Iˆ as shown in Figure 1.18. According\nto the generic diagram shown in Figure 1.11b, vector V̂L is perpendicular\nto Iˆ and leads it in the sense of counterclockwise rotation. According\nto equation (1.101), the vectorial sum of V̂12 and V̂L results in V̂ . This\ncompletes the construction of the phasor diagram and the geometric angle\nϕ is equal to the phase shift in time between the input voltage and input\ncurrent.\nExample 4. Consider a circuit shown in Figure 1.19. First, we write\nrelevant KCL and KVL equations\nV̂12 = V̂R + V̂L2 ,\nIˆ = IˆR + IˆC ,\n\n(1.102)\n(1.103)\n\nV̂ = V̂L1 + V̂12 ,\n\n(1.104)\n\nwhere, as before, V̂12 is the phasor of the voltage across the nodes 1 and 2.\nSecond, as a general rule, we start the construction of the phasor diagram\n\npage 27\n\nSeptember 8, 2014\n\n28\n\n11:16\n\nWorld Scientific Book - 9in x 6in\n\nmodified˙ws-book9x6\n\nFundamentals of Electric Power Engineering\n\nFig. 1.18\n\nFig. 1.19\nfrom the “end” of the circuit, i.e., from the branch RL2 and we identify\nthe current IˆR as the quantity common to R and L2 . So, we draw vector IˆR . According to the generic phasor diagrams shown in Figure 1.11a\nand 1.11b, vector V̂R has the same direction as the vector IˆR , while vector\nV̂L2 is perpendicular to the vector IˆR and its orientation reflects that the\nvoltage across the inductor leads the current by π2 . According to equation\n(1.102), the vectorial sum of V̂R and V̂L2 results in V̂12 (see Figure 1.20).\nAccording to the generic diagram shown in Figure 1.11c, vector IˆC is per-\n\npage 28\n\nSeptember 8, 2014\n\n11:16\n\nWorld Scientific Book - 9in x 6in\n\nBasic Electric Circuit Theory\n\nmodified˙ws-book9x6\n\n29\n\nFig. 1.20\npendicular to vector V̂12 and “leads” it in the sense of counterclockwise\nrotation. The vectorial sum of IˆC and IˆR results according to equation\nˆ Finally, according to the generic diagram shown in Figure\n(1.103) in I.\n1.11b, vector V̂L1 is perpendicular to vector Iˆ and “leads” it. According to\nequation (1.104), the vectorial sum of V̂L1 and V̂12 results in V̂ , and this\ncompletes the construction of the phasor diagram.\nThis concludes the discussion of the phasor diagrams, which will be\nextensively used throughout this text.\n\npage 29\n\nMay 2, 2013\n\n14:6\n\nBC: 8831 - Probability and Statistical Theory\n\nPST˙ws\n\nSeptember 8, 2014\n\n11:16\n\nWorld Scientific Book - 9in x 6in\n\nmodified˙ws-book9x6\n\nChapter 2\n\nAnalysis of Electric Circuits with\nPeriodic Non-sinusoidal Sources\n\n2.1\n\nFourier Series Analysis\n\nIn power electronics, analysis of steady-state performance of switchingmode power converters is reduced to the analysis of electric circuits excited by time-periodic non-sinusoidal sources. There are two analytical\ntechniques that will be extensively used in this text for the analysis of such\ncircuits. The first one is the frequency-domain technique, which is based on\nthe Fourier series expansions of time-periodic functions (sources) and subsequent use of the phasor technique. The second one is the time-domain\ntechnique, which is based on the formulation of the steady-state circuit\nanalysis as a boundary value problem for ordinary differential equations\nwith periodic boundary conditions.\nWe begin with the frequency-domain technique and we first review in\nthis section the basic facts related to the Fourier series. These series are\nused for periodic functions. Below, we consider periodic functions of time,\nwhich is relevant to circuit analysis. However, the Fourier series are also\nvery instrumental in the design of windings of synchronous and induction\nmachines discussed in the second part of this book. In that case, Fourier\nseries are used for the expansion of periodic functions in space rather than\nin time.\nFunction f (t) is said to be periodic with period T (see Figure 2.1) if\nf (t + T ) = f (t).\n\n(2.1)\n\nIt is apparent that a multiple of T by any natural number is a period of f (t)\nas well. It will be assumed in the following that T is the smallest period of\nf (t). The fundamental angular frequency\n2π\nω=\n(2.2)\nT\n31\n\npage 31\n\nSeptember 8, 2014\n\n32\n\n11:16\n\nWorld Scientific Book - 9in x 6in\n\nmodified˙ws-book9x6\n\nFundamentals of Electric Power Engineering\n\nFig. 2.1\nwill be associated with this period. It turns out that under some general\nconditions periodic functions can be expanded into trigonometric Fourier\nseries\n∞\nX\nf (t) = c0 +\n(2.3)\n[an cos nωt + bn sin nωt] ,\nn=1\n\nwhere numbers c0 , an and bn are called the Fourier expansion coefficients.\nThe next step is to find the expression for these expansion coefficients in\nterms of function f (t). This can be accomplished by using the following\n“orthogonality” relations for trigonometric functions:\nZ T\ncos nωtdt = 0,\n(2.4)\n0\n\nZ\n\nT\n\nsin nωtdt = 0,\n\n(2.5)\n\ncos nωt sin mωtdt = 0,\n\n(2.6)\n\n0\nT\n\nZ\n0\n\nT\n\nZ\n\ncos nωt cos mωtdt =\n0\n\nZ\n\nT\n\n(2.7)\n\nT\nδnm ,\n(2.8)\n2\n0\nis the so-called Kronecker delta defined as follows:\n(\n1, if n = m,\n(2.9)\nδnm =\n0, if n 6= m.\nsin nωt sin mωtdt =\n\nwhere the symbol δnm\n\nT\nδnm ,\n2\n\npage 32\n\nSeptember 8, 2014\n\n11:16\n\nWorld Scientific Book - 9in x 6in\n\nmodified˙ws-book9x6\n\nAnalysis of Electric Circuits with Periodic Non-sinusoidal Sources\n\n33\n\nThese orthogonality conditions are easy to prove. Formulas (2.4) and (2.5)\nare immediately obvious because functions cos nωt and sin nωt are periodic\nwith period Tn , and the integrals of sine and cosine functions over any\nnumber of periods are equal to zero. The proof of formulas (2.6), (2.7) and\n(2.8) is only slightly more complicated. This proof is based on the wellknown trigonometric identities which reduce products of sine and cosine\nfunctions to sums of these functions with modified arguments, and then\nformulas similar to (2.4) and (2.5) can be used. This line of reasoning\ncan be followed when n 6= m. In the case when n = m, the trigonometric\nidentities relating squares of cosine and sine functions to cosine functions of\ndouble argument can be used to arrive at formulas (2.7) and (2.8). We omit\nthe details of the outlined derivations and encourage the reader to perform\nthese derivations, which will be beneficial for proper understanding of the\nmaterial.\nIn calling formulas (2.4)-(2.8) orthogonality conditions, we use geometric language which implies the analogy between formulas (2.4)-(2.8) and\northogonality of vectors. In this sense, the functional set consisting of a constant function and trigonometric functions is an orthogonal functional set,\nand formulas (2.4) and (2.5) can be understood as orthogonality relations\nbetween a constant function and cosine and sine functions. Orthogonal\nvectors are linearly independent and may be used as bases for expansions\nof an arbitrary vector. Similarly, the functional set consisting of a constant\nfunction and cosine and sine functions can be used as the functional basis for the expansion of an arbitrary function f (t), and formula (2.3) can\nbe understood as such an expansion. The Fourier expansion coefficients\ncan be interpreted as “projections” of f (t) on the “axes” identified with\na constant function and cosine and sine functions. This interpretation is\nconsistent with the following formulas for the expansion coefficients:\n1\nc0 =\nT\n\nZ\n\n2\nT\n\nZ\n\n2\nT\n\nZ\n\nan =\nbn =\n\nT\n\nf (t)dt,\n\n(2.10)\n\nf (t) cos nωtdt,\n\n(2.11)\n\nf (t) sin nωtdt.\n\n(2.12)\n\n0\nT\n\n0\nT\n\n0\n\nThese formulas can be derived by using the orthogonality relations. Indeed,\nby integrating both sides of formula (2.3) over T and by using formulas (2.4)\nand (2.5) we arrive at equation (2.10). In geometric language, it can be said\n\npage 33\n\nSeptember 8, 2014\n\n34\n\n11:16\n\nWorld Scientific Book - 9in x 6in\n\nmodified˙ws-book9x6\n\nFundamentals of Electric Power Engineering\n\nthat c0 is the projection of f (t) on the constant (unity) function. Similarly,\nby multiplying both sides of formula (2.3) by cos nωt, subsequently integrating both sides over T and using the orthogonality relations (2.4), (2.6)\nand (2.7), we arrive at the formula (2.11). In geometric language, it can\nbe said that an is the projection of f (t) on cos nωt. Finally, by multiplying\nboth sides of formula (2.3) by sin nωt, subsequently integrating both sides\nover T and using orthogonality relations (2.5), (2.6) and (2.8), we arrive\nat the formula (2.12). In geometric language, it can be said that bn is the\nprojection of f (t) on sin nωt.\nNext, the following two remarks are in order.\nRemark 1. Integrands in formulas (2.10), (2.11) and (2.12) are periodic\nfunctions of period T . It is apparent from the geometric point of view that\nintegrals of such functions over period T do not depend on the location of\nthe time interval of integration. Consequently, the last three formulas can\nalso be written in the following form:\n1\nc0 =\nT\n\nZ\n\n2\nan =\nT\n\nZ\n\n2\nT\n\nZ\n\nbn =\n\nT\n2\n\nf (t)dt,\n\n(2.13)\n\nf (t) cos nωtdt,\n\n(2.14)\n\nf (t) sin nωtdt.\n\n(2.15)\n\n− T2\nT\n2\n\n− T2\nT\n2\n\n− T2\n\nRemark 2. Under some general conditions, expansion coefficients an and\nbn tend to zero with the increase of n, i.e.,\nlim an = 0,\n\nn→∞\n\nlim bn = 0.\n\nn→∞\n\n(2.16)\n\nIt is interesting to note that formulas (2.16) are valid despite the fact that\nthe integrands in formulas (2.11) and (2.12) do not tend to zero. This raises\nthe question of the generic intuitive explanation for the validity of relations\n(2.16). The reason is that the functions cos nωt and sin nωt become very\nfast oscillating as n is increased. In other words, the period Tn of these functions becomes smaller and smaller. A sufficiently regular (normal) function\nf (t) can be accurately approximated by a piecewise constant function with\nconstant values in each time interval of Tn -duration. According to (2.4)\nand (2.5), for such piecewise constant functions, the integrals in (2.11) and\n(2.12) are equal to zero. A simple and rigorous proof of the validity of relations (2.16) can be given by assuming that f (t) is differentiable and using\n\npage 34\n\nSeptember 8, 2014\n\n11:16\n\nWorld Scientific Book - 9in x 6in\n\nmodified˙ws-book9x6\n\nAnalysis of Electric Circuits with Periodic Non-sinusoidal Sources\n\n35\n\nFig. 2.2\nintegration by parts in formulas (2.11) and (2.12). The reader is encouraged\nto carry out this proof.\nA periodic function f (t) may have some symmetry properties. These\nsymmetry properties may result in substantial simplifications of Fourier\nseries (2.3). Below, we shall discuss three types of symmetries: even symmetry, odd symmetry and half-wave symmetry.\na) Even symmetry\nA function f (t) is called even (or even symmetric) if for any t we have\nf (t) = f (−t).\n\n(2.17)\n\nAn example of the graph of such function is shown in Figure 2.2, and\nit is clear that this graph exhibits mirror symmetry with respect to the\nvertical axis. It is apparent from formula (2.17) as well as from Figure\n2.2 that for any even function we have\nT2\nT2\nf (t)dt = 2\nf (t)dt.\n(2.18)\n− T2\n\n0\n\nb) Odd symmetry\nA function f (t) is called odd (or odd symmetric) if for any t we have\nf (t) = −f (−t).\n\n(2.19)\n\nAn example of the graph of such function is shown in Figure 2.3, and\nit is clear that this graph exhibits rotational symmetry with respect to\nthe origin. It is apparent from formula (2.19) as well as from Figure 2.3\nthat for any odd function we have\nT2\nf (t)dt = 0.\n(2.20)\n− T2\n\npage 35\n\nSeptember 8, 2014\n\n36\n\n11:16\n\nWorld Scientific Book - 9in x 6in\n\nmodified˙ws-book9x6\n\nFundamentals of Electric Power Engineering\n\nFig. 2.3\n\nFig. 2.4\nRemark 3. It follows from the definitions (2.17) and (2.19) that the\nproduct of two even or two odd functions is an even function, while the\nproduct of an even function and an odd function is an odd function.\nc) Half-wave symmetry\nA periodic function f (t) is called a half-wave symmetric function if for\nany t we have\n\u001a\n\u0019\nT\nf t+\n= −f (t),\n(2.21)\n2\nwhere T is the period of f (t).\nAn example of the graph of such function is shown in Figure 2.4. It\nis apparent from the definition (2.21) and Figure 2.4 that a half-wave\nsymmetric function has two identical but of opposite sign half-cycles.\n\npage 36\n\nSeptember 8, 2014\n\n11:16\n\nWorld Scientific Book - 9in x 6in\n\nmodified˙ws-book9x6\n\nAnalysis of Electric Circuits with Periodic Non-sinusoidal Sources\n\n37\n\nFor this reason,\nT\n\nZ\n\nf (t)dt = 0.\n\n(2.22)\n\n0\n\nRemark 4. Half-wave symmetric functions are related to functions of\nperiod T2 . Indeed, it is easy to see that the product of two half-wave\nsymmetric functions is a function of period T2 , while the product of a\nhalf-wave symmetric function and a function of period T2 is a half-wave\nsymmetric function.\nNow, we demonstrate symmetry-related simplifications of Fourier series\n(2.3). We start with the case when f (t) is an even function. We recall that\ncos nωt are even functions, while sin nωt are odd functions. From the last\nobservation and Remark 3, we find that the integrands in formulas (2.13)\nand (2.14) are even functions, while integrands in formula (2.15) are odd\nfunctions. From these facts and formulas (2.18) and (2.20), we conclude\nthat\nbn = 0,\n\nf (t) = c0 +\n\n∞\nX\n\nan cos nωt,\n\n(2.23)\n\n(2.24)\n\nn=1\n\n2\nT\n\nZ\n\n4\nan =\nT\n\nZ\n\nc0 =\n\nT\n2\n\nf (t)dt,\n\n(2.25)\n\nf (t) cos nωtdt.\n\n(2.26)\n\n0\nT\n2\n\n0\n\nThe achieved simplification is twofold. First, only a constant term and\ncosine terms are present in the Fourier series expressions. Second, the\ncalculation of c0 and an requires the evaluation of integrals over T2 rather\nthan over T .\nNext, we consider the case when f (t) is an odd function. In this case,\naccording to Remark 3 the integrands in formulas (2.13) and (2.14) are odd\nfunctions, while the integrands in formulas (2.15) are even functions. From\nthese facts and formulas (2.18) and (2.20), we conclude respectively\nc0 = 0,\n\n(2.27)\n\nan = 0,\n\n(2.28)\n\npage 37\n\nSeptember 8, 2014\n\n11:16\n\nWorld Scientific Book - 9in x 6in\n\n38\n\nmodified˙ws-book9x6\n\nFundamentals of Electric Power Engineering\n\nf (t) =\n\n∞\nX\n\nbn sin nωt,\n\n(2.29)\n\nn=1\n\nbn =\n\n4\nT\n\nZ\n\nT\n2\n\nf (t) sin nωtdt.\n\n(2.30)\n\n0\n\nFinally, we consider the case when f (t) is a half-wave symmetric function. According to formulas (2.22) and (2.10), we immediately find\nc0 = 0.\n\n(2.31)\n\nTo achieve further simplification in Fourier series expansions, we observe\nthat for odd n functions cos nωt and sin nωt are half-wave symmetric functions, while for even n functions cos nωt and sin nωt are periodic with period\nT\n2 . From the last observation and Remark 4, we find that the integrands\nin formulas (2.11) and (2.12) are of half-wave symmetry for even n, while\nthese integrands are periodic functions of period T2 for odd n. Thus, according to (2.22) all even Fourier coefficients are equal to zero, while odd\nFourier coefficients are not equal to zero and integration over T can be\nreduced to double the integration over T2 . Thus, we arrive at the following\nsimplification of Fourier series:\n\nf (t) =\n\n∞\nX\n\n[a2n+1 cos(2n + 1)ωt + b2n+1 sin(2n + 1)ωt] ,\n\n(2.32)\n\nn=0\n\n4\nT\n\nZ\n\n4\n=\nT\n\nZ\n\na2n+1 =\nb2n+1\n\nT\n2\n\nf (t) cos(2n + 1)ωtdt,\n\n(2.33)\n\nf (t) sin(2n + 1)ωtdt.\n\n(2.34)\n\n0\nT\n2\n\n0\n\nIt is worthwhile to mention that the case of half-wave symmetric functions\nis encountered quite often in various electric power-related applications.\nWe conclude this section by the discussion of an alternative form of\nFourier series. This form is very convenient for the coupling of the Fourier\nseries expansion with the phasor technique. This coupling is the foundation\nof the frequency-domain technique for the analysis of electric circuits with\nperiodic non-sinusoidal sources.\nConsider one term of the infinite sum in Fourier series expansion (2.3)\n\npage 38\n\nSeptember 8, 2014\n\n11:16\n\nWorld Scientific Book - 9in x 6in\n\nmodified˙ws-book9x6\n\nAnalysis of Electric Circuits with Periodic Non-sinusoidal Sources\n\n39\n\nand perform the following transformations:\np\nan\nan cos nωt + bn sin nωt = a2n + b2n p\ncos nωt\n2\nan + b2n\n!\nbn\nsin nωt .\n+p\na2n + b2n\n\n(2.35)\n\nNext, we introduce ϕn by the formulas\nan\ncos ϕn = p\n,\n(2.36)\n2\nan + b2n\nbn\n,\n(2.37)\nsin ϕn = − p\na2n + b2n\nwhich means that\nbn\ntan ϕn = − .\n(2.38)\nan\nIt is easy to see that this introduction is consistent with trigonometric\nidentity\ncos2 ϕn + sin2 ϕn = 1.\n(2.39)\nWe shall also introduce the notation\np\n(2.40)\ncn = a2n + b2n .\nBy substituting formulas (2.36), (2.37) and (2.39) into equation (2.35), we\nobtain\nan cos nωt + bn sin nωt = cn (cos ϕn cos nωt − sin ϕn sin nωt)\n= cn cos(nωt + ϕn ).\n(2.41)\nBy using the last relation in formula (2.3), we arrive at the following alternative form of the Fourier series:\n∞\nX\nf (t) = c0 +\n(2.42)\ncn cos(nωt + ϕn ),\nn=1\n\nwhere c0 , cn and ϕn can be computed by using the following formulas:\nZ\n1 T\nc0 =\n(2.43)\nf (t)dt,\nT 0\nZ\n2 T\n(2.44)\nf (t) cos nωtdt,\nan =\nT 0\nZ T\n2\n(2.45)\nf (t) sin nωtdt,\nbn =\nT\np 0\n(2.46)\ncn = a2n + b2n ,\nbn\n(2.47)\ntan ϕn = − .\nan\nThis concludes the review of the Fourier series.\n\npage 39\n\nSeptember 8, 2014\n\n40\n\n11:16\n\nWorld Scientific Book - 9in x 6in\n\nmodified˙ws-book9x6\n\nFundamentals of Electric Power Engineering\n\nFig. 2.5\n\n2.2\n\nFrequency-Domain Technique\n\nIn this section, we consider the frequency-domain technique for the analysis\nof steady-state regimes of electric circuits excited by periodic non-sinusoidal\nsources. This technique is based on the combined usage of Fourier series\nexpansions and phasors. We first present the general description and justification of the frequency domain technique and then we illustrate this\ntechnique by two examples.\nConsider an electric circuit shown in Figure 2.5. Here, vs (t) is a given\nperiodic non-sinusoidal voltage source\n\nvs (t + T ) = vs (t),\n\n(2.48)\n\nwhile LEC is the abbreviation for a generic linear electric circuit with given\nlumped parameters. It is required to find the input electric current i(t) in\n\ni(t + T ) = i(t).\n\n(2.49)\n\nThe frequency-domain technique for the solution of the stated problem consists of the following three steps.\nStep 1. The given periodic function vs (t) is expanded into Fourier series\nby using formulas (2.42)-(2.47). These formulas in the notation relevant to\n\npage 40\n\nSeptember 8, 2014\n\n11:16\n\nWorld Scientific Book - 9in x 6in\n\nmodified˙ws-book9x6\n\nAnalysis of Electric Circuits with Periodic Non-sinusoidal Sources\n\n41\n\nour problem can be written as follows:\nvs (t) = Vs0 +\n\n∞\nX\n\nVsn cos(nωt + ϕsn ),\n\n(2.50)\n\nn=1\n\nVs0\n\n1\n=\nT\n\nZ\n\n2\nT\n\nZ\n\n2\nT\np\n\nZ\n\nan =\nbn =\n\nvs (t)dt,\n\n(2.51)\n\nvs (t) cos nωtdt,\n\n(2.52)\n\nvs (t) sin nωtdt,\n\n(2.53)\n\n0\nT\n\n0\nT\n\n0\n\na2n + b2n ,\nbn\n=− ,\nan\n\nVsn =\ntan ϕsn\n\nT\n\n(2.54)\n(2.55)\n\nwhere\nω=\n\n2π\n.\nT\n\n(2.56)\n\nEach term in the expansion (2.50) can be interpreted as a voltage source:\nvsn (t) = Vsn cos(nωt + ϕsn ),\n∞\nX\nvs (t) = Vs0 +\nvsn (t),\n\n(2.57)\n(2.58)\n\nn=1\n\nand the given voltage source can be interpreted as the series connection of\nthese voltage sources (see Figure 2.6).\nStep 2. Next, we shall use the superposition principle illustrated in Figure\n2.7 and consider the current i(t) as the sum of currents I0 and in (t) excited\nin LEC when only one of the voltage sources Vs0 or vsn (t), respectively, is\nactive:\ni(t) = I0 +\n\n∞\nX\n\nin (t).\n\n(2.59)\n\nn=1\n\nThe calculation of I0 requires dc analysis of LEC subject to dc voltage Vs0 .\nIn this analysis, inductors in LEC are replaced by short-circuit branches,\nwhile capacitors are replaced by open-circuit branches. Thus, the determination of I0 is reduced to the dc analysis of the resistive electric circuit\ncorresponding to LEC (see Figure 2.8).\n\npage 41\n\nSeptember 8, 2014\n\n42\n\n11:16\n\nWorld Scientific Book - 9in x 6in\n\nFundamentals of Electric Power Engineering\n\nFig. 2.6\n\nFig. 2.7\n\nFig. 2.8\n\nmodified˙ws-book9x6\n\npage 42\n\nSeptember 8, 2014\n\n11:16\n\nWorld Scientific Book - 9in x 6in\n\nmodified˙ws-book9x6\n\nAnalysis of Electric Circuits with Periodic Non-sinusoidal Sources\n\n43\n\nFig. 2.9\nThe calculation of in (t) can be carried out by using the phasor technique. Namely, the time-harmonic voltage source vsn (t) is represented by\nthe phasor\nvsn (t) = Vsn cos(nωt + ϕsn ) → V̂sn = Vsn ejϕsn ,\n\n(2.60)\n\neach branch of LEC is represented by its impedance evaluated at the angular\nfrequency nω and the phasor analysis technique is used to find the phasor\nIˆn in the impedance version of LEC (see Figure 2.9). Having found the\nphasor Iˆn = Imn ejϕIn , the current in (t) can be written as follows:\nIˆn = Imn ejϕIn → in (t) = Imn cos(nωt + ϕIn ).\n\n(2.61)\n\nStep 3. By using formulas (2.59) and (2.61), the final expression for i(t)\ncan be represented in the form\ni(t) = I0 +\n\n∞\n\nImn cos(nωt + ϕIn ).\n\n(2.62)\n\nn=1\n\nWe conclude the general description of the frequency-domain technique\nwith the following two remarks.\nRemark 1. In many power electronics-related applications, the first term\nin the right-hand side of formula (2.62) can be interpreted as the main\ndesired signal, while the infinite sum in (2.62) can be interpreted as undesirable “ripple.” Thus, the frequency-domain technique leads to the clear\nseparation between the main desired component of the signal and its ripple.\nRemark 2. In the presented general description of the frequency-domain\ntechnique, the calculation of the input current i(t) was discussed. It is easy\nto see that the same three steps can be applied to the calculation of any\nbranch current or any branch voltage of LEC.\nNow, we shall illustrate the frequency-domain technique by two examples.\n\npage 43\n\nSeptember 8, 2014\n\n11:16\n\n44\n\nWorld Scientific Book - 9in x 6in\n\nmodified˙ws-book9x6\n\nFundamentals of Electric Power Engineering\n\nFig. 2.10\n\nFig. 2.11\nExample 1. Consider the electric circuit shown in Figure 2.10, where the\nvoltage source vs (t) is a periodic sequence (train) of identical rectangular\npulses (see Figure 2.11). Thus, V0 , T , t0 , L and R are given, and it is\nrequired to find i(t) and vR (t) in the steady-state regime, i.e.,\ni(t + T ) = i(t),\n\nvR (t + T ) = vR (t).\n\nStep 1. We represent vs (t) as the following Fourier series:\n∞\n\nvs (t) = Vs0 +\nVsn cos(nωt + ϕsn ),\n\n(2.63)\n\n(2.64)\n\nn=1\n\nwhere\n\n2π\n.\n(2.65)\nT\nTo find Vs0 , Vsn and ϕsn , we sequentially use the formulas (2.51)-(2.55).\n\n1 T\n1 t0\nt0\nvs (t)dt =\nV0 dt = V0 .\n(2.66)\nVs0 =\nT 0\nT 0\nT\nBy introducing the notation D for so-called duty factor,\nt0\n(2.67)\nD= ,\nT\nwe find\nω=\n\nVs0 = DV0 .\n\n(2.68)\n\npage 44\n\nSeptember 8, 2014\n\n11:16\n\nWorld Scientific Book - 9in x 6in\n\nmodified˙ws-book9x6\n\nAnalysis of Electric Circuits with Periodic Non-sinusoidal Sources\n\n45\n\nNext,\nan =\n\n2\nT\n\nT\n\nZ\n\n2V0\n=\nT\n\nvs (t) cos nωtdt =\n0\n\n\u0012\n\n1\nsin nωt\nnω\n\n\u0013\n\nt0\n\n=\n0\n\n2V0\nT\n\nZ\n\nt0\n\ncos nωtdt\n0\n\n2V0\nsin nωt0 .\nnωT\n\n(2.69)\n\nTaking into account in the last formula the relation (2.65), we find\nV0\nan =\nsin nωt0 .\n(2.70)\nπn\nSimilarly,\nZ\nZ\n2V0 t0\n2 T\nvs (t) sin nωtdt =\nsin nωtdt\nbn =\nT 0\nT 0\n\u0013 t0\n\u0012\n2V0\n2V0\n1\n=\n=\ncos nωt\n(1 − cos nωt0 ).\n(2.71)\n−\nT\nnω\nnωT\n0\nInvoking again the relation (2.65), the last formula can be written as follows:\nV0\nbn =\n(1 − cos nωt0 ).\n(2.72)\nπn\nNext,\nq\np\nV0\nsin2 nωt0 + (1 − cos nωt0 )2\nVsn = a2n + b2n =\nπn\nr\nV0\nnωt0\nV0 p\n2(1 − cos nωt0 ) =\n4 sin2\n=\n,\n(2.73)\nπn\nπn\n2\nwhich implies that\nVsn =\n\n2V0\nnωt0\nsin\n.\nπn\n2\n\n(2.74)\n\nFinally,\ntan ϕsn =\n\ncos nωt0 − 1\n.\nsin nωt0\n\n(2.75)\n\nThus, the explicit analytical expressions are found for Vs0 , Vsn and ϕsn .\nThis concludes this first step.\nStep 2. First consider the dc analysis of the resistive version of the electric\ncircuit shown in Figure 2.10. This is illustrated by Figure 2.12. This\nanalysis is trivial and results in\nVs0\nDV0\nI0 =\n=\n,\nVR0 = DV0 .\n(2.76)\nR\nR\n\npage 45\n\nSeptember 8, 2014\n\n11:16\n\n46\n\nWorld Scientific Book - 9in x 6in\n\nmodified˙ws-book9x6\n\nFundamentals of Electric Power Engineering\n\nFig. 2.12\n\nFig. 2.13\nSecond, consider the phasor analysis of ac steady state in the circuit shown\nin Figure 2.13 at the frequency nω. Here, we find\nV̂sn = Vsn ejϕsn ,\n\n(2.77)\n\nand Vsn and ϕsn are given by formulas (2.74) and (2.75). Furthermore,\nV̂sn\n,\nIˆn =\nZn\n\n(2.78)\n\nwhere\nZn = R + jnωL =\nand\n\n\u0017\nR2 + n2 ω 2 L2 ejϕn\n\ntan ϕn =\n\nnωL\n.\nR\n\n(2.79)\n\n(2.80)\n\nBy substituting formulas (2.77) and (2.79) into equation (2.78), we end up\nwith\nIˆn = √\n\nVsn\nej(ϕsn −ϕn ) .\nR2 + n2 ω 2 L2\n\n(2.81)\n\nFrom the last formula, we find\nin (t) = √\n\nR2\n\nVsn\ncos(nωt + ϕsn − ϕn ).\n+ n2 ω 2 L2\n\n(2.82)\n\npage 46\n\nSeptember 8, 2014\n\n11:16\n\nWorld Scientific Book - 9in x 6in\n\nmodified˙ws-book9x6\n\nAnalysis of Electric Circuits with Periodic Non-sinusoidal Sources\n\n47\n\nStep 3. The input current i(t) is the sum of currents I0 and in (t) for all\ni(t) = I0 +\n\n∞\nX\n\nin (t),\n\n(2.83)\n\nn=1\n\nor\ni(t) =\n\n∞\n0\nsin nωt\n2V0 X\nDV0\n2\n√\n+\ncos(nωt + ϕsn − ϕn ),\nR\nπ n=1 n R2 + n2 ω 2 L2\n\n(2.84)\n\nwhere we have used formula (2.74) for Vsn in the equation (2.82). By\nmultiplying the last formula by R we find the voltage across the resistor\nvR (t) = DV0 +\n\n∞\n0\nsin nωt\n2V0 R X\n2\n√\ncos(nωt + ϕsn − ϕn ).\nπ n=1 n R2 + n2 ω 2 L2\n\n(2.85)\n\nIn some applications\nωL \u001d R,\n\n(2.86)\n\np\nR2 + n2 ω 2 L2 ≈ nωL.\n\n(2.87)\n\nand\n\nThis leads to the following simplification of formula (2.85):\nvR (t) ≈ DV0 +\n\n∞\n0\n2V0 R X sin nωt\n2\ncos(nωt + ϕsn − ϕn ).\nπωL n=1\nn2\n\n(2.88)\n\nIt is clear that due to the inequality (2.86) the second term (the ripple)\nin the right-hand side of formula (2.88) is small. It is also clear from the\nlast formula that the ripple suppression is controlled by the product ωL.\nThis implies the trade-off for ripple suppression between the value of L and\nthe frequency of switching used to produce the train of rectangular pulses\nshown in Figure 2.11. We point out that this trade-off has already been\ndiscussed in general terms in section 1 of Chapter 1.\nExample 2. Consider the electric circuit shown in Figure 2.14, where\nthe voltage source vs (t) is a periodic function of time shown in Figure 2.11.\nIt is assumed that V0 , T , t0 , R, L and C are given, and it is required to\nfind voltage vR (t) across the resistor in the steady-state regime, i.e.,\nvR (t + T ) = vR (t).\n\n(2.89)\n\npage 47\n\nSeptember 8, 2014\n\n48\n\n11:16\n\nWorld Scientific Book - 9in x 6in\n\nmodified˙ws-book9x6\n\nFundamentals of Electric Power Engineering\n\nFig. 2.14\nStep 1. As before, we represent vs (t) by the Fourier series\nvs (t) = Vs0 +\n\n∞\n\nVsn cos(nωt + ϕsn ),\n\n(2.90)\n\nn=1\n\nwhere ω = 2π\nT and Vs0 , Vsn and ϕsn can be computed by using formulas\n(2.68), (2.74) and (2.75). In other words, the first step in this example is\nidentical to the first step in the first example, because the electric circuits\nin these examples are excited by identical voltage sources.\nStep 2. The dc analysis of the electric circuit shown in Figure 2.14 and\nsubject to dc voltage source Vs0 (instead of voltage source vs (t)) leads to\nthe circuit shown in Figure 2.12. The result of this analysis is obvious:\nVR0 = Vs0 = DV0 .\n\n(2.91)\n\nNext, we consider the phasor analysis of ac steady state in the electric\ncircuit shown in Figure 2.15 at the frequency nω. Here, as before,\nV̂sn = Vsn ejϕsn\n\n(2.92)\n\nand Vsn and ϕsn are found in the first step (see formulas (2.74) and (2.75)).\nIt is apparent that the phasor Iˆn of the input current is equal to\nV̂sn\nIˆn =\n,\n(2.93)\nZn\nwhere Zn is the input impedance of the electric circuit shown in Figure\n2.15 at the frequency nω. It is clear that this input impedance is found as\nfollows:\nZn = jnωL +\n\nj\n− nωC\nR\n\nj\n− nωC\n+R\n\n.\n\n(2.94)\n\nBy using simple algebraic transformations, we find\nZn = jnωL +\n\nR − n2 ω 2 LCR + jnωL\nR\n=\n.\n1 + jnωCR\n1 + jnωCR\n\n(2.95)\n\npage 48\n\nSeptember 8, 2014\n\n11:16\n\nWorld Scientific Book - 9in x 6in\n\nmodified˙ws-book9x6\n\nAnalysis of Electric Circuits with Periodic Non-sinusoidal Sources\n\n49\n\nFig. 2.15\nBy substituting the last formula into (2.93), we arrive at\nIˆn = V̂sn\n\n1 + jnωCR\n.\nR − n2 ω 2 LCR + jnωL\n\n(2.96)\n\nNow, by using the current divider rule, we obtain\nIˆRn = Iˆn\n\n−j\nnωC\n−j\nnωC +\n\nR\n\n= Iˆn\n\n1\n.\n1 + jnωCR\n\n(2.97)\n\nBy substituting formula (2.96) into the last equation, we find\nIˆRn =\n\nV̂sn\n,\nR − n2 ω 2 LCR + jnωL\n\nV̂Rn = V̂sn\n\nR\nR−\n\nn2 ω 2 LCR\n\n+ jnωL\n\n(2.98)\n\n.\n\n(2.99)\n\nBy using formula (2.92) and simple transformations, the last equation can\nbe written as follows:\nVsn R\nej(ϕsn −ϕn ) ,\n(2.100)\nV̂Rn = \u0016\n2\n(n2 ω 2 LCR − R) + n2 ω 2 L2\nwhere\n\ntan ϕn =\nFrom formula (2.100) we obtain\nvRn (t) = \u0016\n\nnωL\n.\nR − n2 ω 2 LCR\n\nVsn R\n2\n\n(n2 ω 2 LCR − R) + n2 ω 2 L2\n\ncos(nωt + ϕsn − ϕn ).\n\n(2.101)\n\n(2.102)\n\nStep 3. Now, by using the superposition principle, we arrive at\nvR (t) = VR0 +\n\n∞\n\nn=1\n\nvRn (t).\n\n(2.103)\n\npage 49\n\nSeptember 8, 2014\n\n11:16\n\nWorld Scientific Book - 9in x 6in\n\n50\n\nmodified˙ws-book9x6\n\nFundamentals of Electric Power Engineering\n\nBy using in the last equation formula (2.91) for VR0 and formula (2.102)\nfor vRn (t) as well as formula (2.74) for Vsn , we obtain the final expression\nfor vR (t):\nvR (t) = DV0\n+\n\n∞\n0\nsin nωt\n2V0 R X\n2\nq\ncos(nωt + ϕsn − ϕn ).\nπ n=1\n2\nn (n2 ω 2 LCR − R) + n2 ω 2 L2\n\n(2.104)\nIn certain applications, the second term in the right-hand side of the last\nequation can be construed as a ripple. This ripple will be effectively suppressed if the lumped parameters of the circuit shown in Figure 2.14 are\nchosen in such a way that\nω 2 LC \u001d 1 and ω 2 C 2 R2 \u001d 1.\n(2.105)\nThe last inequalities imply, respectively, that\nn2 ω 2 LCR \u001d R\n(2.106)\nand\nn4 ω 4 L2 C 2 R2 \u001d n2 ω 2 L2 .\n(2.107)\nFormulas (2.106)\nand\n(2.107)\nmean\nthat\nq\n2\n\n(n2 ω 2 LCR − R) + n2 ω 2 L2 ≈ n2 ω 2 LCR.\nThis leads to the following simplification of equation (2.104):\n\n∞\n0\n2V0 X sin nωt\n2\ncos(nωt + ϕsn − ϕn ).\nvR (t) ≈ DV0 +\nπω 2 LC n=1\nn3\n\n(2.108)\n\n(2.109)\n\nNow, it is apparent that more efficient suppression of ripple can be achieved\nin the circuit shown in Figure 2.14 in comparison with the circuit shown\nin Figure 2.10. Indeed, each term in the infinite sum of formula (2.109)\ndecays as 1/n3 rather than 1/n2 as in formula (2.88). In addition, the\nsuppression of the ripple in formula (2.109) is controlled by the product\nω 2 LC rather than by the product ωL. This means that the increase in\nswitching frequency suppresses the ripple more efficiently in the circuit\nshown in Figure 2.14 as compared with the circuit shown in Figure 2.10.\nFinally, the dependence of ripple suppression on ω 2 LC reveals, as before,\nthe trade-off between the values of energy storage elements L and C and\nthe frequency of switching.\n\npage 50\n\nSeptember 8, 2014\n\n11:16\n\nWorld Scientific Book - 9in x 6in\n\nmodified˙ws-book9x6\n\nAnalysis of Electric Circuits with Periodic Non-sinusoidal Sources\n\n51\n\nFig. 2.16\n\nFig. 2.17\n2.3\n\nTime-Domain Technique\n\nNow, we proceed to the discussion of the time-domain technique for the\nanalysis of steady-state regimes of linear electric circuits excited by periodic non-sinusoidal sources. This technique is based on the formulation of\nsteady-state analysis as a boundary value problem for ordinary differential\nequations with periodic boundary conditions. We illustrate this technique\nby the following two examples.\nExample 1. Consider the electric circuit shown in Figure 2.16 excited by\nthe voltage source vs (t), where vs (t) is the periodic function of time shown\nin Figure 2.17. Here, V0 , T , t0 , L and R are given, and it is required to\nfind i(t) and vR (t) which are periodic with period T :\ni(t + T ) = i(t),\n\nvR (t + T ) = vR (t).\n\n(2.110)\n\nIt is apparent that this example is identical to Example 1 from the previous section. This is done on purpose in order for the reader to compare\ntechniques.\nThe time-domain technique can be presented as a sequence of three distinct steps.\n\npage 51\n\nSeptember 8, 2014\n\n52\n\n11:16\n\nWorld Scientific Book - 9in x 6in\n\nmodified˙ws-book9x6\n\nFundamentals of Electric Power Engineering\n\nStep 1. is to formulate the problem of steady-state analysis as a boundary\nvalue problem with periodic boundary conditions. To this end, we first\nwrite the KVL for the circuit shown in Figure 2.16:\ndi(t)\nL\n+ Ri(t) = vs (t).\n(2.111)\ndt\nIt is apparent from Figure 2.17 that the last equation can be written as two\ndistinct equations for two time intervals:\ndi(t)\n+ Ri(t) = V0 , if 0 < t < t0 ,\ndt\ndi(t)\nL\n+ Ri(t) = 0, if t0 < t < T.\ndt\nThese two equations can be complemented by two conditions\nL\n\n(2.112)\n(2.113)\n\ni(0) = i(T ),\n\n(2.114)\n\ni(t0− ) = i(t0+ ).\n\n(2.115)\n\nThe equation (2.114) is the periodic boundary condition which follows from\n(2.110) for t = 0, while the equation (2.115) is the interface condition which\nexpresses the continuity of electric current through the inductor.\nThe last four equations constitute the boundary value problem for differential equations (2.112) and (2.113) with periodic boundary and interface\nconditions (2.114) and (2.115), respectively. As soon as the solution of this\nboundary value problem is found, the value of i(t) can be found at any\ntime (i.e., not only in time interval [0, T ]) by using the first equation in\n(2.110). Indeed, by using this equation, we can extend the solution from\nthe time interval [0, T ] to the time interval [T, 2T ], and then from the time\ninterval [T, 2T ] to the time interval [2T, 3T ] and so on. In other words, by\nusing the first equation in (2.110), the solution of the boundary value problem (2.112)-(2.115) with periodic boundary condition can be periodically\nextended to the infinite time interval. It is clear that this periodically extended solution has the physical meaning of the steady state in the electric\ncircuit shown in Figure 2.16.\nStep 2. is to find general solutions of differential equations (2.112) and\nequation of first order with constant coefficients. Its general solution has\ntwo distinct components: a particular solution ip (t) of inhomogeneous equation (2.112) and a general solution ih (t) of the corresponding homogeneous\nequation. Namely,\ni(t) = ip (t) + ih (t),\n(2.116)\n\npage 52\n\nSeptember 8, 2014\n\n11:16\n\nWorld Scientific Book - 9in x 6in\n\nmodified˙ws-book9x6\n\nAnalysis of Electric Circuits with Periodic Non-sinusoidal Sources\n\n53\n\nwhere\nL\n\ndip (t)\n+ Rip (t) = V0 ,\ndt\n\n(2.117)\n\nwhile\ndih (t)\n+ Rih (t) = 0.\n(2.118)\ndt\nIn mathematics, the particular solution of inhomogeneous differential equation (2.117) is sought in the same form as the right-hand side of the equation:\nL\n\nip (t) = B = const.\n\n(2.119)\n\nBy substituting formula (2.119) into equation (2.117) we find\nRB = V0 ,\n\nB=\n\nV0\nR\n\n(2.120)\n\nand\nV0\n.\n(2.121)\nR\nIt is apparent that ip (t) is identical to the dc steady state in the electric\ncircuit shown in Figure 2.16 excited by the dc voltage V0 . This observation\nis very helpful and can be used for the calculation of particular solutions\nof differential equations for more complicated circuits excited by dc or ac\nvoltage sources. In the latter case, the phasor technique can be used for\nthe calculation of particular solutions.\nNow, we proceed to the calculation of ih (t) by using equation (2.118).\nWe look for a solution of this equation in the form\nip (t) =\n\nih (t) = A1 est ,\n\n(2.122)\n\nwhere A1 and s are some constants. By substituting the last formula into\nequation (2.118), we arrive at\nsLA1 est + RA1 est = 0,\n\n(2.123)\n\nsL + R = 0\n\n(2.124)\n\nand\nR\n.\nL\nThus, the general solution ih (t) has the form\ns=−\n\nR\n\nih (t) = A1 e− L t .\n\n(2.125)\n\n(2.126)\n\npage 53\n\nSeptember 8, 2014\n\n54\n\n11:16\n\nWorld Scientific Book - 9in x 6in\n\nmodified˙ws-book9x6\n\nFundamentals of Electric Power Engineering\n\nBy substituting formulas (2.121) and (2.126) into equation (2.116), we find\nthe general solution of equation (2.112):\nR\nV0\n(2.127)\ni(t) =\n+ A1 e− L t , if 0 < t < t0 .\nR\nNext, we consider the general solution of equation (2.113). This equation is\nidentical in structure to equation (2.118). Consequently, its general solution\nhas the form\nR\n\ni(t) = A2 e− L t ,\n\nif t0 < t < T,\n\n(2.128)\n\nwhere A2 is some constant.\nStep 3. is to find constants A1 and A2 from the periodic boundary condition (2.114) and interface boundary condition (2.115). These conditions\n\nRT\nV0\n\n\n\n(2.129)\n+ A1 = A2 e− L ,\nR\nRt0\nRt0\nV\n\n\n 0 + A1 e− L = A2 e− L .\n(2.130)\nR\nIndeed, by using formula (2.127) for the evaluation of i(0) and formula\n(2.128) for the evaluation of i(T ), we end up with equation (2.129). Similarly, by using equation (2.127) for the evaluation of i(t0− ) and formula\n(2.128) for the evaluation of i(t0+ ), we arrive at equation (2.130). The last\ntwo equations can be easily solved. Indeed, these equations can be written\nas follows:\n\nRT\nV0\n\n\nA1 − A2 e− L = − ,\n(2.131)\nR\nV0 Rt0\n\n\n\n(2.132)\nA1 − A2 = − e L .\nR\nBy subtracting the second equation from the first, we find\n\u0010\n\u0011\n\u0011 V \u0010 Rt0\nRT\n0\ne L −1\nA2 1 − e− L =\n(2.133)\nR\nand\nRt0\n\nV0 e L − 1\n.\n(2.134)\nR 1 − e− RT\nL\nNow, by substituting the last formula into equation (2.132), after simple\ntransformations we obtain\nA2 =\n\nR(t0 −T )\n\n−1\nV0 e L\nA1 =\n.\nR 1 − e− RT\nL\n\n(2.135)\n\npage 54\n\nSeptember 8, 2014\n\n11:16\n\nWorld Scientific Book - 9in x 6in\n\nmodified˙ws-book9x6\n\nAnalysis of Electric Circuits with Periodic Non-sinusoidal Sources\n\n55\n\nBy using the last two formulas in equations (2.127) and (2.128) we arrive\nat the final expression\n#\n \"\nR(t0 −T )\nL\n\n−\n1\ne\nV\nRt\n0\n\n\ne− L , if 0 < t < t0 ,\n1+\n\n− RT\nR\nL\n1\n−\ne\ni(t) =\n(2.136)\nRt0\n\n\nV0 e L − 1 − Rt\n\n\ne L,\nif t0 < t < T.\nR 1 − e− RT\nL\nBy taking into account that\nvR (t) = i(t)R,\n\n(2.137)\n\nwe find\n#\n \"\nR(t0 −T )\n```" ]
[ null, "https://pt.b-ok.org/img/loader.gif", null ]
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https://minuteshours.com/162-1-minutes-to-hours
[ "# 162.1 minutes to hours\n\n## Result\n\n162.1 minutes equals 2.7017 hours\n\nYou can also convert 162.1 minutes to hours and minutes.\n\n## Conversion formula\n\nMultiply the amount of minutes by the conversion factor to get the result in hours:\n\n162.1 min × 0.0166667 = 2.7017 hr\n\n## How to convert 162.1 minutes to hours?\n\nThe conversion factor from minutes to hours is 0.0166667, which means that 1 minutes is equal to 0.0166667 hours:\n\n1 min = 0.0166667 hr\n\nTo convert 162.1 minutes into hours we have to multiply 162.1 by the conversion factor in order to get the amount from minutes to hours. We can also form a proportion to calculate the result:\n\n1 min → 0.0166667 hr\n\n162.1 min → T(hr)\n\nSolve the above proportion to obtain the time T in hours:\n\nT(hr) = 162.1 min × 0.0166667 hr\n\nT(hr) = 2.7017 hr\n\nThe final result is:\n\n162.1 min → 2.7017 hr\n\nWe conclude that 162.1 minutes is equivalent to 2.7017 hours:\n\n162.1 minutes = 2.7017 hours\n\n## Result approximation\n\nFor practical purposes we can round our final result to an approximate numerical value. In this case one hundred sixty-two point one minutes is approximately two point seven zero two hours:\n\n162.1 minutes ≅ 2.702 hours\n\n## Conversion table\n\nFor quick reference purposes, below is the minutes to hours conversion table:\n\nminutes (min) hours (hr)\n163.1 minutes 2.718339 hours\n164.1 minutes 2.735005 hours\n165.1 minutes 2.751672 hours\n166.1 minutes 2.768339 hours\n167.1 minutes 2.785006 hours\n168.1 minutes 2.801672 hours\n169.1 minutes 2.818339 hours\n170.1 minutes 2.835006 hours\n171.1 minutes 2.851672 hours\n172.1 minutes 2.868339 hours\n\n## Units definitions\n\nThe units involved in this conversion are minutes and hours. This is how they are defined:\n\n### Minutes\n\nThe minute is a unit of time or of angle. As a unit of time, the minute (symbol: min) is equal to 1⁄60 (the first sexagesimal fraction) of an hour, or 60 seconds. In the UTC time standard, a minute on rare occasions has 61 seconds, a consequence of leap seconds (there is a provision to insert a negative leap second, which would result in a 59-second minute, but this has never happened in more than 40 years under this system). As a unit of angle, the minute of arc is equal to 1⁄60 of a degree, or 60 seconds (of arc). Although not an SI unit for either time or angle, the minute is accepted for use with SI units for both. The SI symbols for minute or minutes are min for time measurement, and the prime symbol after a number, e.g. 5′, for angle measurement. The prime is also sometimes used informally to denote minutes of time. In contrast to the hour, the minute (and the second) does not have a clear historical background. What is traceable only is that it started being recorded in the Middle Ages due to the ability of construction of \"precision\" timepieces (mechanical and water clocks). However, no consistent records of the origin for the division as 1⁄60 part of the hour (and the second 1⁄60 of the minute) have ever been found, despite many speculations.\n\n### Hours\n\nAn hour (symbol: h; also abbreviated hr.) is a unit of time conventionally reckoned as 1⁄24 of a day and scientifically reckoned as 3,599–3,601 seconds, depending on conditions. The seasonal, temporal, or unequal hour was established in the ancient Near East as 1⁄12 of the night or daytime. Such hours varied by season, latitude, and weather. It was subsequently divided into 60 minutes, each of 60 seconds. Its East Asian equivalent was the shi, which was 1⁄12 of the apparent solar day; a similar system was eventually developed in Europe which measured its equal or equinoctial hour as 1⁄24 of such days measured from noon to noon. The minor variations of this unit were eventually smoothed by making it 1⁄24 of the mean solar day, based on the measure of the sun's transit along the celestial equator rather than along the ecliptic. This was finally abandoned due to the minor slowing caused by the Earth's tidal deceleration by the Moon. In the modern metric system, hours are an accepted unit of time equal to 3,600 seconds but an hour of Coordinated Universal Time (UTC) may incorporate a positive or negative leap second, making it last 3,599 or 3,601 seconds, in order to keep it within 0.9 seconds of universal time, which is based on measurements of the mean solar day at 0° longitude." ]
[ null ]
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https://answers.everydaycalculation.com/simplify-fraction/140-7559
[ "Solutions by everydaycalculation.com\n\n## Reduce 140/7559 to lowest terms\n\n140/7559 is already in the simplest form. It can be written as 0.018521 in decimal form (rounded to 6 decimal places).\n\n#### Steps to simplifying fractions\n\n1. Find the GCD (or HCF) of numerator and denominator\nGCD of 140 and 7559 is 1\n2. Divide both the numerator and denominator by the GCD\n140 ÷ 1/7559 ÷ 1\n3. Reduced fraction: 140/7559\nTherefore, 140/7559 simplified to lowest terms is 140/7559.\n\nMathStep (Works offline)", null, "Download our mobile app and learn to work with fractions in your own time:" ]
[ null, "https://answers.everydaycalculation.com/mathstep-app-icon.png", null ]
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https://www.wantiku.com/jianzao2/guanli2/e/403281922?domain=exam8
[ "", null, "", null, "180:00", null, "2021年5月22日《建设施工管理》真题\n\n1\n(单项选择题)\n\n• A.\n\n重伤\n\n• B.\n\n轻伤\n\n• C.\n\n职业病\n\n• D.\n\n失能伤害\n\n• A\n• B\n• C\n• D\n\n2\n(单项选择题)\n\n• A.\n\n建设单位项目负责人\n\n• B.\n\n施工项目经理\n\n• C.\n\n施工项目技术负责人\n\n• D.\n\n监理工程师\n\n• A\n• B\n• C\n• D\n\n3\n(单项选择题)\n\n• A.\n\n参数法\n\n• B.\n\n综合单价法\n\n• C.\n\n分包法\n\n• D.\n\n工科单价法\n\n• A\n• B\n• C\n• D\n\n4\n(单项选择题)\n\n• A.\n\n最高管理者\n\n• B.\n\n项目经理\n\n• C.\n\n技术负责人\n\n• D.\n\n安全生产负责人\n\n• A\n• B\n• C\n• D\n\n5\n(单项选择题)\n\n• A.\n\n定期比较计划值和实际值，并采取纠偏措施\n\n• B.\n\n针对目标影响因素采取有效的预防措施\n\n• C.\n\n对进度目标由粗到细进行逐层分解\n\n• D.\n\n按照进度控制的要求，收集施工进度实际值\n\n• A\n• B\n• C\n• D\n\n6\n(单项选择题)\n\n• A.\n\n管理措施\n\n• B.\n\n组织措施\n\n• C.\n\n经济措施\n\n• D.\n\n技术措施\n\n• A\n• B\n• C\n• D\n\n7\n(单项选择题)\n\n• A.\n\n风险识别——风险评估——风险应对——风险监控\n\n• B.\n\n风险计划——风险分析——风险评估——风险应对\n\n• C.\n\n风险识别——风险分析——风险应对——风险监控\n\n• D.\n\n风险规划——风险评估——风险自留——风险转移\n\n• A\n• B\n• C\n• D\n\n8\n(单项选择题)\n\n• A.\n\n加强施工调度\n\n• B.\n\n优化材料配合比\n\n• C.\n\n加强施工定额管理\n\n• D.\n\n及时落实设计变更签证\n\n• A\n• B\n• C\n• D\n\n9\n(单项选择题)\n\n• A.\n\n分别调整单价和总价\n\n• B.\n\n以单价为准调整总价\n\n• C.\n\n按市场价调整单价\n\n• D.\n\n以总价为准调整单价\n\n• A\n• B\n• C\n• D\n\n10\n(单项选择题)\n\n• A.\n\n测量控制网\n\n• B.\n\n原始坐标点\n\n• C.\n\n基准线\n\n• D.\n\n标高基准点\n\n• A\n• B\n• C\n• D\n\n11\n(单项选择题)", null, "• A.\n\n50.0\n\n• B.\n\n47.6\n\n• C.\n\n48.3\n\n• D.\n\n50.7\n\n• A\n• B\n• C\n• D\n\n12\n(单项选择题)\n\n• A.\n\n导致索赔的事件必须是对方的过错，索赔才能成立\n\n• B.\n\n只要对方存在过错，不管是否造成损失，索赔都能成立\n\n• C.\n\n未按照合同规定的程序提交索赔报告，索赔不能成立\n\n• D.\n\n只要索赔事件的事实存在，在合同有效期内任何时候提出索赔都能成立\n\n• A\n• B\n• C\n• D\n\n13\n(单项选择题)", null, "• A.\n\nA\n\n• B.\n\nB\n\n• C.\n\nC\n\n• D.\n\nD\n\n• A\n• B\n• C\n• D\n\n14\n(单项选择题)\n\n• A.\n\n定额机械费＋定额人工费\n\n• B.\n\n企业管理费\n\n• C.\n\n定额人工费\n\n• D.\n\n实际人工费\n\n• A\n• B\n• C\n• D\n\n15\n(单项选择题)\n\n• A.\n\n旁站、验收和平行检验\n\n• B.\n\n旁站、验收和专检\n\n• C.\n\n旁站、抽检和专检\n\n• D.\n\n旁站、巡视和平行检验\n\n• A\n• B\n• C\n• D\n\n16\n(单项选择题)\n\n• A.\n\n10%\n\n• B.\n\n15%\n\n• C.\n\n20%\n\n• D.\n\n30%\n\n• A\n• B\n• C\n• D\n\n17\n(单项选择题)\n\n• A.\n\n总承包管理单位的招标依赖于完整的施工图\n\n• B.\n\n业主负责项目总进度计划的编制、控制和协调\n\n• C.\n\n业主负责所有分包合同交界面的定义\n\n• D.\n\n各分包单位的各种款项必须通过总承包管理单位支付\n\n• A\n• B\n• C\n• D\n\n18\n(单项选择题)\n\n• A.\n\n提出索赔意向通知\n\n• B.\n\n提交索赔证据\n\n• C.\n\n提交索赔报告\n\n• D.\n\n与监理人进行谈判\n\n• A\n• B\n• C\n• D\n\n19\n(单项选择题)\n\n• A.\n\n质量记录\n\n• B.\n\n质量手册\n\n• C.\n\n程序文件\n\n• D.\n\n质量计划\n\n• A\n• B\n• C\n• D\n\n20\n(单项选择题)\n\n• A.\n\n监理人\n\n• B.\n\n承包人\n\n• C.\n\n发包人\n\n• D.\n\n项目管理公司\n\n• A\n• B\n• C\n• D\n\n21\n(单项选择题)\n\n• A.\n\n项目经理\n\n• B.\n\n建设单位负责人\n\n• C.\n\n施工单位负责人\n\n• D.\n\n项目专职安全员\n\n• A\n• B\n• C\n• D\n\n22\n(单项选择题)\n\n• A.\n\n信息储存数字化和集中化\n\n• B.\n\n信息传输的数字化和电子化\n\n• C.\n\n信息处理和变换的程序化\n\n• D.\n\n信息获取的便捷性和信息流扁平化\n\n• A\n• B\n• C\n• D\n\n23\n(单项选择题)\n\n• A.\n\n施工进度计划\n\n• B.\n\n施工平面图\n\n• C.\n\n施工部署和施工方案\n\n• D.\n\n工程概况\n\n• A\n• B\n• C\n• D\n\n24\n(单项选择题)\n\n• A.\n\n建设单位负责人\n\n• B.\n\n事故现场管理人员\n\n• C.\n\n施工单位负责人\n\n• D.\n\n监理单位负责人\n\n• A\n• B\n• C\n• D\n\n25\n(单项选择题)\n\n• A.\n\n组织结构图\n\n• B.\n\n项目结构图\n\n• C.\n\n工作流程图\n\n• D.\n\n合同结构图\n\n• A\n• B\n• C\n• D\n\n26\n(单项选择题)\n\n• A.\n\n概算指标\n\n• B.\n\n预算定额\n\n• C.\n\n劳动定额\n\n• D.\n\n投资估算指标\n\n• A\n• B\n• C\n• D\n\n27\n(单项选择题)\n\n• A.\n\n主要原材料的质量\n\n• B.\n\n施工作业面的施工质量\n\n• C.\n\n参与工程建设各方主体的质量行为\n\n• D.\n\n重要部位和关键工序的施工质量\n\n• A\n• B\n• C\n• D\n\n28\n(单项选择题)\n\n• A.\n\n合同主体的资信和能力风险\n\n• B.\n\n对现场环境调查和预测的风险\n\n• C.\n\n项目周边居民或单位的干预、抗议风险\n\n• D.\n\n合同依据的法律环境变化的风险\n\n• A\n• B\n• C\n• D\n\n29\n(单项选择题)\n\n• A.\n\n项目各参与方应编制统一的项目管理任务分工表\n\n• B.\n\n首先要明确项目经理的工作任务\n\n• C.\n\n已经确定的工作任务表在项目实施过程中不能调整\n\n• D.\n\n需要明确各工作部门的工作任务\n\n• A\n• B\n• C\n• D\n\n30\n(单项选择题)\n\n• A.\n\n14\n\n• B.\n\n5\n\n• C.\n\n7\n\n• D.\n\n28\n\n• A\n• B\n• C\n• D\n\n31\n(单项选择题)\n\n• A.\n\n费用节约，进度延误\n\n• B.\n\n费用节约，进度提前\n\n• C.\n\n费用超支，进度延误\n\n• D.\n\n费用超支，进度提前\n\n• A\n• B\n• C\n• D\n\n32\n(单项选择题)\n\n• A.\n\n职能组织结构\n\n• B.\n\n矩阵组织结构\n\n• C.\n\n网络组织结构\n\n• D.\n\n线性组织结构\n\n• A\n• B\n• C\n• D\n\n33\n(单项选择题)\n\n• A.\n\n施工现场管理人员工资\n\n• B.\n\n组织施工生产必要的差旅交通费\n\n• C.\n\n构成工程实体的材料费用\n\n• D.\n\n施工过程中发生的贷款利息\n\n• A\n• B\n• C\n• D\n\n34\n(单项选择题)\n\n• A.\n\n取得安全生产许可证的施工企业，需设立安全生产管理机构，但不需配备专职安全生产管理人员\n\n• B.\n\n建设工程项目中防治污染的设施必须经监理单位验收合格后方可投入使用\n\n• C.\n\n建设工程实行总承包的，因分包合同中已明确各自安全生产的权利和义务，分包单位发生安全生产事故时，总承包单位不承担连带责任\n\n• D.\n\n施工企业法定代表人是安全生产的第一负责人，项目经理是施工项目生产的主要负责人\n\n• A\n• B\n• C\n• D\n\n35\n(单项选择题)\n\n• A.\n\n编制施工质量计划\n\n• B.\n\n约束质量活动的行为\n\n• C.\n\n监督质量活动过程\n\n• D.\n\n处理施工质量的缺陷\n\n• A\n• B\n• C\n• D\n\n36\n(单项选择题)\n\n• A.\n\n投标担保\n\n• B.\n\n履约担保\n\n• C.\n\n预付款担保\n\n• D.\n\n支付担保\n\n• A\n• B\n• C\n• D\n\n37\n(单项选择题)\n\n• A.\n\n施工安全管理责任书\n\n• B.\n\n项目管理目标责任书\n\n• C.\n\n项目管理实施计划\n\n• D.\n\n工程质量责任承诺书\n\n• A\n• B\n• C\n• D\n\n38\n(单项选择题)\n\n• A.\n\n某构件制作计划\n\n• B.\n\n单项工程施工进度计划\n\n• C.\n\n项目年度施工进度计划\n\n• D.\n\n企业旬生产计划\n\n• A\n• B\n• C\n• D\n\n39\n(单项选择题)\n\n• A.\n\n竣工图不能委托设计单位编制\n\n• B.\n\n一般性图纸变更及符合杠改或划改要求的，可不编制竣工图\n\n• C.\n\n同一建筑物重复的标准图也必须编入竣工图中\n\n• D.\n\n重大变更及图面变更面积超过35%的，应当重新绘制竣工图\n\n• A\n• B\n• C\n• D\n\n40\n(单项选择题)\n\n• A.\n\n计划\n\n• B.\n\n检查\n\n• C.\n\n实施\n\n• D.\n\n处理\n\n• A\n• B\n• C\n• D\n\n41\n(单项选择题)\n\n• A.\n\n240.0\n\n• B.\n\n252.0\n\n• C.\n\n279.6\n\n• D.\n\n276.0\n\n• A\n• B\n• C\n• D\n\n42\n(单项选择题)\n\n• A.\n\n1\n\n• B.\n\n3\n\n• C.\n\n2\n\n• D.\n\n4\n\n• A\n• B\n• C\n• D\n\n43\n(单项选择题)\n\n• A.\n\n分部工程\n\n• B.\n\n工序\n\n• C.\n\n检验批\n\n• D.\n\n分项工程\n\n• A\n• B\n• C\n• D\n\n44\n(单项选择题)\n\n• A.\n\n25\n\n• B.\n\n50\n\n• C.\n\n100\n\n• D.\n\n200\n\n• A\n• B\n• C\n• D\n\n45\n(单项选择题)\n\n• A.\n\n技术原因引发的质量事故\n\n• B.\n\n管理原因引发的质量事故\n\n• C.\n\n操作责任事故\n\n• D.\n\n指导责任事故\n\n• A\n• B\n• C\n• D\n\n46\n(单项选择题)\n\n• A.\n\n进度计划系统是指组成进度计划的各项内容，包括执行时需要的资源和措施等\n\n• B.\n\n为便于协调各项目参与方，计划系统应由业主负责建立，各参与方协助完善\n\n• C.\n\n同一进度计划系统中，各计划的工作结构分解（项目分解）一定相同\n\n• D.\n\n同一进度计划系统中，各进度计划之间必须相互协调\n\n• A\n• B\n• C\n• D\n\n47\n(单项选择题)\n\n• A.\n\n1\n\n• B.\n\n3\n\n• C.\n\n2\n\n• D.\n\n5\n\n• A\n• B\n• C\n• D\n\n48\n(单项选择题)\n\n• A.\n\n自由时差一定不超过其与紧后工作的间隔时间\n\n• B.\n\n与其紧后工作间隔时间均为0的工作，总时差一定是0\n\n• C.\n\n工作的自由时差是0，总时差一定是0\n\n• D.\n\n关键节点间的工作，总时差和自由时差不一定相等\n\n• A\n• B\n• C\n• D\n\n49\n(单项选择题)\n\n• A.\n\n1－2－4－5－3\n\n• B.\n\n2－1－4－3－5\n\n• C.\n\n2－3－1－5－4\n\n• D.\n\n1－3－2－4－5\n\n• A\n• B\n• C\n• D\n\n50\n(单项选择题)\n\n• A.\n\n28\n\n• B.\n\n7\n\n• C.\n\n14\n\n• D.\n\n56\n\n• A\n• B\n• C\n• D\n\n51\n(单项选择题)\n\n• A.\n\n9\n\n• B.\n\n11\n\n• C.\n\n10\n\n• D.\n\n12\n\n• A\n• B\n• C\n• D\n\n52\n(单项选择题)\n\n• A.\n\n计算索赔款的时段可以是整个施工期\n\n• B.\n\n索赔金额为受影响工作调整后的实际总费用减去该项工作的报价费用\n\n• C.\n\n索赔款应包括受到影响时段内所有工作所受的损失\n\n• D.\n\n索赔款只包括受到影响时段内关键工作所受的损失\n\n• A\n• B\n• C\n• D\n\n53\n(单项选择题)\n\n• A.\n\n参建施工单位之间的协调程度\n\n• B.\n\n项目部质量管理制度\n\n• C.\n\n项目工程地质情况\n\n• D.\n\n各种能源介质的供应保障程度\n\n• A\n• B\n• C\n• D\n\n54\n(单项选择题)\n\n• A.\n\n施工定额\n\n• B.\n\n预算定额\n\n• C.\n\n概算定额\n\n• D.\n\n概算指标\n\n• A\n• B\n• C\n• D\n\n55\n(单项选择题)\n\n• A.\n\n暂估价\n\n• B.\n\n暂列金额\n\n• C.\n\n总承包服务费\n\n• D.\n\n增值税销项税额\n\n• A\n• B\n• C\n• D\n\n56\n(单项选择题)\n\n• A.\n\n以招标文件为准\n\n• B.\n\n要求中标人进行适当修正\n\n• C.\n\n以投标文件为准\n\n• D.\n\n要求发包人进行适当修正\n\n• A\n• B\n• C\n• D\n\n57\n(单项选择题)\n\n• A.\n\n质量监督文件\n\n• B.\n\n施工许可证\n\n• C.\n\n质量监督报告\n\n• D.\n\n监督计划方案\n\n• A\n• B\n• C\n• D\n\n58\n(单项选择题)\n\n• A.\n\n因基准日期后合同适用的法律发生变化，增加的安全文明施工费由发包人承担\n\n• B.\n\n发包人可以根据施工项目环境和安全情况酌情扣减部分安全文明施工费\n\n• C.\n\n承包人经发包人同意采取合同约定以外的安全措施所产生的费用，由承包人承担\n\n• D.\n\n承包人对安全文明施工费应专款专用，在财务账目中与管理费合并列项备查\n\n• A\n• B\n• C\n• D\n\n59\n(单项选择题)\n\n• A.\n\n业主方\n\n• B.\n\n工程监理方\n\n• C.\n\n施工总承包管理方\n\n• D.\n\n分包方\n\n• A\n• B\n• C\n• D\n\n60\n(单项选择题)\n\n• A.\n\n22\n\n• B.\n\n23\n\n• C.\n\n24\n\n• D.\n\n25\n\n• A\n• B\n• C\n• D\n\n61\n(单项选择题)\n\n• A.\n\n与招标文件内容不一致时，以补充文件为准\n\n• B.\n\n不能作为招标文件的组成部分\n\n• C.\n\n其法律效力仅次于招标文件\n\n• D.\n\n与招标文件内容不一致时，以招标文件为准\n\n• A\n• B\n• C\n• D\n\n62\n(单项选择题)\n\n• A.\n\n非关键线路上的工作都按最迟时间开始\n\n• B.\n\n所有工作都按最早开始时间开始\n\n• C.\n\n施工成本大的工作按最迟时间开始\n\n• D.\n\n人工消耗量大的工作按最早时间开始\n\n• A\n• B\n• C\n• D\n\n63\n(单项选择题)\n\n（缺图）\n\n• A.\n\n22\n\n• B.\n\n12\n\n• C.\n\n18\n\n• D.\n\n24\n\n• A\n• B\n• C\n• D\n\n64\n(单项选择题)\n\n（缺图）\n\n• A.\n\n109.83\n\n• B.\n\n115.13\n\n• C.\n\n122.48\n\n• D.\n\n141.01\n\n• A\n• B\n• C\n• D\n\n65\n(单项选择题)\n\n• A.\n\n施工现场的主要道路进行硬化处理\n\n• B.\n\n施工污水有组织地直接排入市政污水管网\n\n• C.\n\n采取防火措施后在现场焚烧包装废弃物\n\n• D.\n\n废弃的降水并及时用建筑废弃物回填\n\n• A\n• B\n• C\n• D\n\n66\n(单项选择题)\n\n• A.\n\n共同性依据\n\n• B.\n\n专业技术性依据\n\n• C.\n\n项目专用性依据\n\n• D.\n\n施工管理依据\n\n• A\n• B\n• C\n• D\n\n67\n(单项选择题)\n\n• A.\n\n提高各类设施的可靠性\n\n• B.\n\n限制能量和隔离危险物质\n\n• C.\n\n设置安全监控系统\n\n• D.\n\n加强员工的安全意识教育\n\n• A\n• B\n• C\n• D\n\n68\n(单项选择题)\n\n• A.\n\n工程承包人为提供给劳务分包人使用的机械办理保险，劳务分包人承担保险费\n\n• B.\n\n运至现场用于劳务施工的材料，由承包人办理保险，劳务分包人承担保险费\n\n• C.\n\n劳务分包人必须为从事危险作业的职工办理意外伤害保险，并承担保险费\n\n• D.\n\n施工开始前，工程承包人应获得发包人为施工现场内第三方人员生命财产办理的\n\n• A\n• B\n• C\n• D\n\n69\n(单项选择题)\n\n• A.\n\n制定高于国家标准的控制准则\n\n• B.\n\n执行《建筑工程施工质量验收统一标准》\n\n• C.\n\n按照相关专业验收规范组织检查验收\n\n• D.\n\n强化管理人员和操作员人员的质量意识\n\n• A\n• B\n• C\n• D\n\n70\n(单项选择题)", null, "• A.\n\n工作G的紧前工作有工作C和工作D\n\n• B.\n\n工作B的紧后工作有工作C和工作D\n\n• C.\n\n工作D的紧后工作有工作E和工作G\n\n• D.\n\n工作C的紧前工作有工作A和工作B\n\n• A\n• B\n• C\n• D", null, "", null, "" ]
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https://cs.stackexchange.com/questions/80570/do-most-bitstrings-expand-if-they-halt-when-executed-by-a-universal-turing-machi
[ "# Do most bitstrings expand if they halt when executed by a Universal Turing machine?\n\nAccording to the counting argument, most bitstrings are incompressible or only slightly compressible. However, the counting argument does not work in the opposite direction, since there are an infinite number of bitstrings that are longer. So, the counting argument does not tell us whether most bitstrings will or will not expand when run on a universal Turing machine and halt.\n\nIs it known whether most halting bitstrings will expand?\n\nBy 'expand' I mean that a bitstring $b_1$ generates a bitstring $b_2$ when run on a universal Turing machine, \\begin{align*} \\mathcal{U}(b_1)=b_2, \\end{align*} such that the length of $b_2$ is greater than $b_1$ \\begin{align*} \\ell(b_2) > \\ell(b_1). \\end{align*}\n\n• It's not quite clear to me what you mean with \"bitstrings expand when run on a TM and halt\". – adrianN Aug 29 '17 at 4:51\n• @adrianN The edit helps, doesn't it? – Raphael Sep 2 '17 at 8:26\n\nBoth can happen.\n\nThe counting argument applies to all TMs that always halt.\n\nIn the partial world, you can construct Turing machines for both extreme cases (and everything in between) like so. Assume $T$ is a Turing machine. Construct\n\nT<(x) = if |T(x)| < |x| then return T(x) else loop\n\n\nand\n\nT>(x) = if |T(x)| > |x| then return T(x) else loop\n\n\nNote that if T(x) loops, both T<(x) and T>(x) loop; that's not a problem. It's easy so see that for T<, all halting inputs contract, and for T> all expand.\n\nRice's theorem immediately shows that these expansion/contraction properties (and related ones) are undecidable, by the way.\n\nWell, ... several (different!) scenarios:\n\nI assume that U is a (fixed) UTM, you give it a string s = (TM,input), U(s) = TM(input) = either a finite output \"f\" or else DIS, the TM does not halt. Additional difficulty: \"DIS\" vs. \"f requires enormous time\" can not be resolved by just looking while waiting (in many cases).\n\nYour question then might be: How often do we have |s| < |f| (expansion), how often is |s| >= |f| in the non-DIS cases.\n\n1A. \"Often\" as a counter is void: Both cases appear (countably) infinitely often,namely:\n\nLarge s, short f: just stop the (short) TM, regardless of the (arbitrarily large) input, put f = empty word;\n\nShort s, large f: TM consists of $(i)$ copy input to output to make for infinitely many cases, then $(ii)$ run BusyBeaver(7), producing a lot more output, in general run BB(7+log(log(|s|))).\n\n1B. \"Often\" as a measure is more useful: Count each case with measure $2^{-|s|}$ ($s$ should be self-delimiting), throw away those DIS cases.\n\nCompare $\\mu(\\le) = \\sum_{U(s)\\ stops, |f| \\le|s|} 2^{-s}$ with $\\mu(>) = \\sum_{U(s)\\ stops, |f| > |s|} 2^{-s}$.\n\nMy feeling is that a considerable fraction of machines just produces nothing or a short output, for any, even quite large, input, so probably $\\mu(\\le) > \\mu(<)$ (no proof yet).\n\nThis might actually be decidable in finite time: If the difference between the two measures is larger than the measure of the unchecked cases, we are done.\n\n2A/B. You include DIS in one of the cases (since nothing definite happens, the output is neither larger nor shorter than the input, a very large current tape contents might be blanked out later).\n\nI guess that the side with DIS wins. Again, this might be (even easier) decidable by knowledge of finitely many cases.\n\n1. You separate output and working tape and count DIS cases according to the actual output (which will not be allowed to shrink ... but still might grow). Very unclear situation for the $\\mu(\\le)$ part, while a DIS with current output longer than $|s|$ certainly goes into $\\mu(>)$.\n\nSummarizing:\n\nInteresting question,\n\npotential of completely answering it with finite effort (unlike, e.g. the halting probability $\\Omega$ in all its precision);\n\nI do not know this answer.\n\n• That's a lot of words for saying \"I have no idea\". o.o – Raphael Sep 2 '17 at 12:20\n\nThere are a finite number of bitstrings with a length less than the output, but an infinite number with greater length. Therefore, it is much more likely a halting bitstring will produce a shorter bitstring than a longer bitstring.\n\n• This statement is false in general, as my answer shows. That is to say, I'm sure you can find a random model for which it is true (\"X is more likely than Y\") but you should specify what you have in mind. – Raphael Sep 4 '17 at 15:03\n• I'm unclear why being able to construct a TM for a particular purpose invalidates the statement. If we pick a universal TM without reference to a particular output, then for any output, it will only map a finite number of shorter inputs to that output, but it will map an infinite number of longer inputs to that output. If we restrict the TM to only halt with shorter inputs, then it is no longer a UTM as it can no longer compute everything a UTM can. – yters Sep 4 '17 at 18:20\n• Neither your question nor your answer mention that they are about universal TMs. Even so, note that I construct partially computable functions for the extreme cases, which means that any UTM has infinitely many (!) indices for each of them, and myriads of other, similar functions. There are so many infinite quantities here that there is no simple conclusion about what is \"more likely\". You'll need a random model to make such a statement. – Raphael Sep 4 '17 at 18:40" ]
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