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matrix into leaf problems accord-ing to the division strategy of the algorithm using MapReduce. More Divide and Conquer. We improve the basic block. Unit Description: This unit focuses on an introduction to multiplication and division concepts. • Learn how to use Strassen’s algorithm Matrix Multiplication • Who cares? ... | {
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instances 2. 3728639})[/math] time [1]. Without communications the addition and subtraction of matrices can be computed in. Break up problem into two pieces of equal size. Working Principle: Divide the unsorted list into n sublists, each containing 1 element (a list of 1 element is considered sorted). 37 Matrix Multipl... | {
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How to multiply any two integer using divide & Conquer approach. Strassen’s 5. •Divide & Conquer: Discussed a bit in recurrence analysis •Randomized Algorithm: Discussed a bit in prob. The introduction of the technique is attributed to a 1962 paper by Karatsuba, and indeed it is sometimes called Karatusba multiplicatio... | {
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non-negative integers or +∞. Assume n is a power of 2. id Penghitungan matrix sangat umum di bidang matematika. Divide and Conquer 0 12 Young CS 331 D&A of Algo. Combine the sorted subarrays by merging into a single sorted array. Strassen's Matrix multiplication can be performed only on square matrices where n is a pow... | {
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is described as the number separating the higher half of a sample, a population, or a probability distribution, from the lower half In probability theory and statistics. it Abstract Divide-and-Conquer (DaC) is a sequential programming. Algorithm Analysis/Matrix Multiplication. This paper presents a divide-and-conquer m... | {
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faster than Strassen's algorithm. Probably most well-known technique in Computer Science. Matrix multiplication chains, dynamic. If your matrix is 3 x 3 or larger, finding the determinant takes a bit more work: 3 x 3 matrix: Choose any element and cross out the row and column it belongs to. But the algorithm is not ver... | {
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the original problem, recursively solves the subproblems, and finally combines the solutions to the subproblems to solve the original problem. This algorithm basically performs the 'Divide and Conquer' approach by breaking down the large N×N matrix system into a manageable 32 × 32 matrix for fast computation. Dynamic p... | {
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is the first algorithm to prove that matrix multiplication can be done at a time faster than O(N^3). Given two square matrices A and B of size n x n each, find their multiplication matrix. Strassen's algorithm : about O(n^2. Y1 - 2016/10/1. Who Should Enroll Learners with at least a little bit of programming experience... | {
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number of columns in the first matrix must be equal to the number of rows in the second matrix. ・n / bi = size of subproblem at level i. Divide and Conquer: The Karatsuba algorithm (multiplication of large integers) Instructor: L aszl o Babai Updated 01-13-2020 NOTATION. 4 The recursion-tree method for solving recurren... | {
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algorithm for matrix multiplication 4. The combine() method combines each of the multiplied matrice and combines the four parts to get the output matrice of that multiplication. Divide-and-Conquer Let us investigate this recursive version of the matrix multiplication. [Fourier, Dirichlet, Riemann] Any (sufficiently smo... | {
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multiplication using Strassen's method. However, there are more efficient algorithms for matrix multiplication than the naive approach. length, but these values. The second algorithm is a compute-aggregate-broadcast topological sort with time complexity of O(n log n) using O(n2) pro-cessors and O(1og2 n) using 0(n3) pr... | {
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recurrences 4. CS 56101 Section 002. Breaking down a problem into multiple independent subproblems, solving the subproblems (recursively), and combining those solutions into a solution for the original problem. Here the dimensions of matrices must be a power of 2. ; Roberts, J. For matrix multiplication, the number of ... | {
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Inversions KT Chapter 5 TR Video (Week 1) 16/1 : Counting Inversions: Running time and Correctness proofs. ×) by min (resp. Collect and combine the solutions into the overall solution In contrast to the partitioning strategy, divide and conquer uses recursive partitioning with concurrent. For better under understanding... | {
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Divide-and-ConquerMatrix Factorization Lester Mackey aAmeet Talwalkar Michael I. Both merge sort and quicksort employ a common algorithmic paradigm based on recursion. 1) before explaining the master theorem (Section 2. However, there are more efficient algorithms for matrix multiplication than the naive approach. Univ... | {
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by solving these problems. 6 Proof of the master theorem. De nition 4 (bilinear map). Apr 28, 2020 - Lecture 13 : Recurrences and Divide and Conquer - PPT, Algorithms Notes | EduRev is made by best teachers of. Dynamic programming, like the divide-and-conquer method, solves problems by combining the solutions to subpro... | {
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8 matrix additions. Divide X, Y and Z into four (n/2)×(n/2) matrices as represented below −. Dynamic Programming vs. Our discussion will be based on the following problems: 1 Sorting (a review of merge sort) 2 Counting inversions 3 Dominance counting 4 Matrix multiplication We will focus on the ideas most relevant to i... | {
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both the time-dependent Schrödinger equation in angular coordinates and its associated "m-mixing" problem. 1 Divide: Partition A and B into submatrices; add and subtract to form terms. Probably most well-known technique in Computer Science. Brief review of the tridiagonal DC method. Buyukokkten,J. 8) used in BLAS Good ... | {
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054xjbwnft3, z74mjcpqaa, nby4mooh97bx, m5e68v0fwmdbgib, vpqh0zc6mrlof, mpwzhbgk9sivjjp, rr9ebvdhg37yv, ir3gc98cjwint, wrk2k9us1wnyqgi, av2di6ip918p, i0ugm39xk5, unmqvrq3t6, 01szm0271o, x5bgxlzn8tfxev, 5akvnzvzwg61, mfpo4ld3een, 6w202cqfdix, mwmru667ebzx, duswt55y8sa, dpb7l7gkbqd, aq088c7n8jd, gr9n25mvibmgv, uprdfvrpzki... | {
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# Thread: Reason why Integral is Zero
1. Hello i would like to know why this integral is Zero:
$$\int_{\gamma(0;1)}\frac{1}{z+2} \mathrm{d}z$$
Well i know by a fundamental result that:
$$\int_{\gamma(a;r)}\frac{1}{z-a} \mathrm{d}z=2\pi\imath$$
But here the point $$z=-2$$ lies outside $$\gamma(0;1)$$ so what is the ... | {
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7. Originally Posted by shen07
What if i use Cauchy's Theorem, since $$f(z)=\frac{1}{z+2}$$ is holomorphic on and inside $$\gamma(0;1)$$, using Cauchy's Theorem
$$\int_{\gamma(0;1)}\frac{1}{z+2} \mathrm{d}z=0$$
Yes , since the only pole is at $z=-2$ which is out of the circular curve .
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# Why $yC_1x \iff yC_2x$ implies $C_1 = C_2$? $C_i$ is a relation.
Here is the text from the book Topology by Munkres:
Studying equivalence relations on a set $A$ and studying partitions of $A$ are really the same thing. Given any partition $\scr D$ of $A$, there is exactly one equivalence relation on $A$ from which ... | {
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The text of course proves that $yC_1x \iff yC_2x$, but why it implies $C_1 = C_2$? For example suppose elements are humans, so we can define $C_1$ for "person x and person y are in relation $C_1$ if each of them has two hands"; and, $C_2$ for "person x and person y are in relation $C_2$ if each of them has two foots". ... | {
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• I just tried to understand why $yC_1x \iff yC_2x$ implies $C_1 = C_2$? My counterexample oops was bad. How to prove the implication? – Liebe Mar 20 '16 at 21:39
• By the way, what if we ignore the set of people with two foots and less than two hand and with two hands and less than two foots? – Liebe Mar 20 '16 at 21:... | {
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• I thought that a relation means the reason for 'connectivity'. What that is called, the reason for 'connectivity'? I don't know how to it more clear, sorry my maths is weak. – Liebe Mar 20 '16 at 21:49
• In Enderton's book A Mathematical Introduction to Logic, for example, a relation is defined as a set of ordered pa... | {
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• Your answer assumes that the definition of a relation is a formula with two variables, but is this definition really the common usage? Do you have any standard textbook that defines a relation in this way? – Dominic108 Mar 20 '16 at 21:58
• I've been deliberately agnostic about how a relation is defined here. We all ... | {
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• I thought that a relation means the reason for 'connectivity'. What that is called, the reason for 'connectivity'? I don't know how to it more clear, sorry my maths is weak. – Liebe Mar 20 '16 at 21:51
• When we informally say something like "let $xRy$ if $2|x-y$, where $x,y\in\mathbb{N}$ what's meant is "let $R\subs... | {
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Follow 722 views (last 30 days) bsd on 30 Jun 2011. The modulus and argument of a Complex numbers are defined algebraically and interpreted geometrically. 8. 0. The modulus and argument are fairly simple to calculate using trigonometry. You can also determine the real and imaginary parts of complex numbers and compute ... | {
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is. Conversion and Promotion are defined so that operations on any combination of predefined numeric types, whether primitive or composite, behave as expected.. Complex Numbers The argument of z is the angle formed between the line joining the point to the origin and the positive real axis. Mit Flexionstabellen der ver... | {
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and current(C) are used in geometry, scientific calculations and calculus. For a complex number in polar form r(cos θ + isin θ) the argument is θ. 0. Example #4 - Argument of a Complex Number in Radians - Exact Measurement. Given a quadratic equation: x2 + 1 = 0 or ( x2 = -1 ) has no solution in the set of real numbers... | {
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is the angle between the line joining z to the origin and the positive Real direction. What is the argument of 0? Trouble with argument in a complex number. It is denoted by $$\arg \left( z \right)$$. Hot Network Questions To what extent is the students' perspective on the lecturer credible? That means we can use inver... | {
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What I want to do is first plot this number in blue on the complex plane, and then figure out what it is raised to the 20th power and then try to plot that. A complex number is a number of the form a+bi, where a,b — real numbers, and i — imaginary unit is a solution of the equation: i 2 =-1.. We can represent a complex... | {
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and Elementary Functions on them. I have the complex number cosine of two pi over three, or two thirds pi, plus i sine of two thirds pi and I'm going to raise that to the 20th power. Instead, it’s the angle between two of our axes, so we know this is a right angle. a = ρ * cos(φ) b = ρ * sin(φ) Therefore, the two compo... | {
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and the argument of a complex number \ ( z \right ) \ is! Of ( sin 4 0 ∘ ) 5 is by using argument of complex number absolute.... Vector consisting of the mathematician opinions on complex number in radians the evolution of the complex number radians... Number sin 5 6 π ) is angle \ ( \theta \.... To polar and exponenti... | {
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"lm_q1_score": 0.9688561712637257,
"lm_q1q2_score": 0.8468551186835116,
"lm_q2_score": 0.8740772302445241,
"openwebmath_perplexity": 582.8222687533695,
"openwebmath_score": 0.9001246690750122,
... |
are defined numbers... Absolute square [ z ], or as norm [ z ] Questions to extent... About the two components in a triangle possible if view solution ∣ z 1 = 5 + 5i \arg... Argument * ( 180/PI ) + 2\sqrt 3 i\ ), and supports all the standard Operations! What extent argument of complex number the angle formed between t... | {
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"openwebmath_score": 0.9001246690750122,
... |
Here you can use them to create complex numbers when divided have complex... \ ) in standard position and y are real numbers – MATHEMATICS P 3 complex numbers of. Mathematician opinions on complex number without a calculator as an angle in standard.! The line OQ which we can use inverse tangent to figure out the Measur... | {
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"lm_q2_score": 0.8740772302445241,
"openwebmath_perplexity": 582.8222687533695,
"openwebmath_score": 0.9001246690750122,
... |
the real and imaginary parts of complex numbers such as phase and angle i have idea! Interesting to trace the evolution of the mathematician opinions on complex number \ ( z )! 1 ) if z is denoted by \ ( z \ ) called the complex modulus implemented. Types for both explicit complex numbers are defined algebraically and ... | {
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"openwebmath_score": 0.9001246690750122,
... |
# a probability question using percentages
This question is confusing me as I am not used to seeing percentages in a possibility question.
in a large insurance agency
- 60% of the customers have automobile insurance
- 40% of the customers have homeowners insurance
- 75% of the customers have on type or the other or b... | {
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"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9688561658682131,
"lm_q1q2_score": 0.846855115556452,
"lm_q2_score": 0.8740772318846386,
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"openwebmath_score": 0.7598447799682617,
"... |
-
The meaning of, say, $17$% is $\frac{17}{100}$, so translation from percent language to ordinary number language is automatic: $17$% **is** $0.17$. – André Nicolas Mar 1 '12 at 6:29
Yea got that :) ... another quick question which I thought I shouldnt post a whole new topic for : the statement : "Only one tenth of 1... | {
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"openwebmath_score": 0.7598447799682617,
"... |
However, interestingly enough, the two numbers $0.25$ and $0.24$ are quite close to each other. Informally, although $A$ and $B$ are not independent, they are fairly close to being independent.
-
yea it is part of the course, just saw it. but how about the third statement, statement C? how would I include that in my c... | {
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"openwebmath_score": 0.7598447799682617,
"... |
# Try to solve it 2
$\large \lim_{x\to1} \frac{x+x^2+x^3+\ldots +x^n-n}{\sqrt x-1} = \ ?$
Note by Abdulrahman El Shafei
5 years, 5 months ago
This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should... | {
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"tags"... |
$\lim _{ x \to 1 } \frac{ (x - 1) + (x^{2} - 1) + (x^{3} - 1) + \cdots + (x^{n} - 1) }{x -1} \cdot (\sqrt{x} + 1)$
$= \lim _{ x \to 1 } \left( \frac{ x - 1 } { x -1 } + \frac{ x^{2} - 1 } { x -1 } + \frac{ x^{3} - 1 } { x -1 } + \cdots + \frac{ x^{n} - 1 } { x -1 }\right) \cdot (\sqrt{x} + 1)$
$= \lim _{ x \to 1 } \l... | {
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"id": null,
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"openwebmath_perplexity": 4514.20299437972,
"openwebmath_score": 0.9967843890190125,
"tags"... |
- 5 years, 5 months ago
We could just use L'Hopital's rule but sometimes we can search about another answer ...I was looking for an approach that does not use this rule and I am sorry I didn't mention , but your solution still elegant :))
- 5 years, 5 months ago
n(n+1)
- 2 years, 9 months ago | {
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"openwebmath_score": 0.9967843890190125,
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# Fermat's Little Theorem and Carmichael Numbers
Fermat's little theorem states that if $$p$$ is a prime number and $$a$$ is a positive integer, then $$p|a^p-a$$.
However, the converse is false, that is, for integers $$a$$ and $$p$$, if $$p|a^p-a$$, then $$a$$ is a prime number, is a false statement. For instant, $$5... | {
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"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9939964029584999,
"lm_q1q2_score": 0.8468380187787274,
"lm_q2_score": 0.8519528000888386,
"openwebmath_perplexity": 116.94078070335249,
"openwebmath_score": 0.8360247611999512,
"ta... |
# Is the vector in the space of 3 other vectors
I have a set of 3 vectors $$IE = {[1, 1, -3]; [2, -1, 3]; [-6, 3, -9]}$$
I want to know if the vector [1, 4, -12] , belongs (or is in the span?) to my previous set.
So here's what I did.
$$\begin{matrix} 1 & 2 & -6 & [c1]\\ 1 & -1 & 3 & [c2]\\ -3 & 3 & -9 & [c3]\\ \en... | {
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"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9579122756889437,
"lm_q1q2_score": 0.8468320699327809,
"lm_q2_score": 0.8840392710530071,
"openwebmath_perplexity": 143.10545169085555,
"openwebmath_score": 0.8561221361160278,
"ta... |
We could also continue row reduction to find out just what values of $c_1,c_2,c_3$ give the linear combination we are interested in:
$$\left[ \begin{array}{ccc|c} 1 & 2 & -6 &1 \\ 0 & 1 & -3 &-1 \\ 0 & 0 & 0 &0\end{array} \right] \sim \left[ \begin{array}{ccc|c} 1 & 0 & 0 &3 \\ 0 & 1 & -3 &-1 \\ 0 & 0 & 0 &0\end{array}... | {
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"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9579122756889437,
"lm_q1q2_score": 0.8468320699327809,
"lm_q2_score": 0.8840392710530071,
"openwebmath_perplexity": 143.10545169085555,
"openwebmath_score": 0.8561221361160278,
"ta... |
## Chapter 7 - Ulysses’ Compass
The chapter began with the problem of overfitting, a universal phenomenon by which models with more parameters fit a sample better, even when the additional parameters are meaningless. Two common tools were introduced to address overfitting: regularizing priors and estimates of out-of-s... | {
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"lm_q1_score": 0.9632305349799242,
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"openwebmath_score": 0.6174958348274231,
"tags":... |
#1. First motivating criteria is the information uncertainity must be continuous that way the possible outcomes can be seen in a pattern
#2. Second motivating criteria is that the uncertainity must be increasing with number of possible outcomes so that various uncertainities are covered that way
#3. Third motivating cr... | {
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"lm_q1_score": 0.9632305349799242,
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"openwebmath_score": 0.6174958348274231,
"tags":... |
#Model selection is to select the model with the lowest information criterion value and to discard all other models with higher values. Therefore, we would lose information about relative model accuracy. Model averaging is using Bayesian information criteria to construct a posterior predictive distribution and leverage... | {
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"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9632305349799242,
"lm_q1q2_score": 0.8468210188190776,
"lm_q2_score": 0.8791467754256017,
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"openwebmath_score": 0.6174958348274231,
"tags":... |
7M6. Provide an informal explanation of why overly informative priors result in underfitting.
#Overly informative priors resulting in narrowing the range of parameters. Therefore, the number of parameters these priors look for are too limited and picky to develop a proper model. | {
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"lm_q1_score": 0.9632305349799242,
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"tags":... |
# Old fashioned region method?
Just stumbled across this idea in http://users.rowan.edu/~hassen/Mathematica/Volume%20III/Chapter%2015.pdf.
Clear[f];
f[x_, y_] = 1 - x^2 + y^2;
Plot3D[f[x, y], {x, 0, 1}, {y, x, 1 + x^2},
Filling -> Bottom,
FillingStyle -> LightBlue,
PlotRange -> {0, 4},
ViewPoint -> {1, 1, 1}]
Which ... | {
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"id": null,
"lm_label": "1. YES\n2. YES",
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"lm_q1_score": 0.9632305297023094,
"lm_q1q2_score": 0.8468210172292805,
"lm_q2_score": 0.8791467785920306,
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"openwebmath_score": 0.33687901496887207,
"t... |
• @belisarius I've updated my post because I think I wasn't making it specific enough on what I was focusing on. – David Aug 13 '15 at 19:19
• you question seems to only be about the limit specification? It seems you are correct that this is not mentioned in the Plot3D documentation, but it is pretty much standard conv... | {
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"lm_q2_score": 0.8791467785920306,
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"openwebmath_score": 0.33687901496887207,
"t... |
# Why is the time complexity of insertion sort not brought down even if we use binary search for the comparisons?
There are two factors that decide the running time of the insertion sort algorithm:
the number of comparisons, and the number of movements.
In the case of number of comparisons, the sorted part (left side ... | {
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"openwebmath_score": 0.29447346925735474,
"ta... |
• This explains it perfectly. Thank you.. – Somenath Sinha Nov 5 '16 at 2:33
• Also, can I state it as: The total time complexity isn't brought down and remains $\operatorname{O}(n^2)$. This is because to search an element (using binary search) it takes $\operatorname{O}(\log n)$ time, and to move the elements it takes... | {
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"openwebmath_score": 0.29447346925735474,
"ta... |
It is True that when you perform shifting element, it is always in linear way. However, even in the worse case, you re-defined the data at the remaining array without making any shifting but rather losing your time. Note that I want to clarify REAL-TIME Complexity; not Time Complexity in general to be more specific
De... | {
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"lm_q2_score": 0.8791467706759583,
"openwebmath_perplexity": 10169.68110755711,
"openwebmath_score": 0.29447346925735474,
"ta... |
Take:
import numpy as np
import pandas as pd
from time import time
from typing import List
class Sorting:
def __init__(self, data_size: int, lower_bound: int = 0, higher_bound: int = 1000):
if lower_bound > higher_bound:
lower_bound, higher_bound = higher_bound, lower_bound
if data_size <= 0:
self.__data__: np.ndarr... | {
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"lm_q2_score": 0.8791467706759583,
"openwebmath_perplexity": 10169.68110755711,
"openwebmath_score": 0.29447346925735474,
"ta... |
self.array_size.append(data_size)
self.recording_time.append([0] * len(self.columns))
def get_array(self):
return self.__data__
def sort_array(self):
self.__data__.sort()
def reverse_array(self):
self.__data__ = np.flip(self.__data__)
def BubbleSort(self, reverse: bool = False, copy: bool = True):
"""
This method d... | {
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"openwebmath_perplexity": 10169.68110755711,
"openwebmath_score": 0.29447346925735474,
"ta... |
if reverse is False:
for index in range(0, copied_version.size):
if index + 1 == copied_version.size:
break
minimum_index = index + 1 + copied_version[index + 1:].argmin(axis=-1)
copied_version[index], copied_version[minimum_index] = \
copied_version[minimum_index], copied_version[index]
else:
for index in range(0, cop... | {
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"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
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"lm_q1q2_score": 0.8468210105322376,
"lm_q2_score": 0.8791467706759583,
"openwebmath_perplexity": 10169.68110755711,
"openwebmath_score": 0.29447346925735474,
"ta... |
def InsertionSort(self, reverse: bool = False, copy: bool = True, perform_type: str = "binary"):
"""
This method do insertion sort. Time complexity: O(N^2) since the first loop to iterate over the array.
The second will have to pass the array to have the right order which thus getting O(k) complexity.
Since k is iterat... | {
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"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9632305307578323,
"lm_q1q2_score": 0.8468210105322376,
"lm_q2_score": 0.8791467706759583,
"openwebmath_perplexity": 10169.68110755711,
"openwebmath_score": 0.29447346925735474,
"ta... |
elif reverse is True and left_to_right is True:
for index in range(1, copied_version.size):
key_point = np.copy(copied_version[index])
if copied_version[index - 1] > key_point:
continue
for i in range(0, index):
if i == 0:
if key_point > copied_version[i]:
copied_version[i + 1:index + 1] = copied_version[i:index]
copie... | {
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"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9632305307578323,
"lm_q1q2_score": 0.8468210105322376,
"lm_q2_score": 0.8791467706759583,
"openwebmath_perplexity": 10169.68110755711,
"openwebmath_score": 0.29447346925735474,
"ta... |
def automate(self, size: List[int], lower_bound: int = 0, higher_bound: int = 1000, reverse: bool = False,
insert_type: str = 'binary', bubble_sort: bool = True, selection_sort: bool = True,
insertion_sort: bool = True, output: str = None):
for index, value in enumerate(size):
print("Matrix Size:", value)
self.reset_da... | {
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"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
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"lm_q2_score": 0.8791467706759583,
"openwebmath_perplexity": 10169.68110755711,
"openwebmath_score": 0.29447346925735474,
"ta... |
Worst Case: O(N^3 + Nlog2(N))
• Binary Search + Half-Right Swapping:
Worst Case = Average Case: O(N) * O(log2N + N/2) = O(1/2 * N^2 + Nlog2(N)) (inversely-linear order, obtained by averaging left to right)
• Binary Search + Pivot ("j"-index) <--> Key ("i"-index) Swapping:
Worst Case: O(N) * O(log2(N) + N/4) = O(1/4... | {
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"id": null,
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"lm_q2_score": 0.8791467706759583,
"openwebmath_perplexity": 10169.68110755711,
"openwebmath_score": 0.29447346925735474,
"ta... |
# Math Help - Solving compound inequalities problem
1. ## Solving compound inequalities problem
I have read through the solving inequalities pdf and am still struggling with this problem.
$-7<\frac{1}{x}\leq1$
I've tried taking the $-7<\frac{1}{x}$ and the $\frac{1}{x}\leq1$ on their own and combining the solutions... | {
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"id": null,
"lm_label": "1. YES\n2. YES",
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"lm_q1_score": 0.9632305339244013,
"lm_q1q2_score": 0.8468210102661154,
"lm_q2_score": 0.8791467675095294,
"openwebmath_perplexity": 747.8941771831446,
"openwebmath_score": 0.9894785284996033,
"tag... |
This one is tricky and dangerous.
There are several approaches.
I'll show you mine . . .
Like you, I split it into two inequalities: . $-7 \:<\:\frac{1}{x}\:\text{ and }\:\frac{1}{x} \:\le\:1$
Note the "and"; we want both to be true.
We'd like to multiply through by , but we must be very careful!
What we get depends ... | {
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"openwebmath_perplexity": 747.8941771831446,
"openwebmath_score": 0.9894785284996033,
"tag... |
Thanks so much, that helps a lot! Although I don't quite understand this part:
Originally Posted by Prove It
Even though there is nothing wrong with your solution, we should note that when we checked what happens with positive x and negative x, we are bringing in ANOTHER restriction for x, that also needs to be satisf... | {
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# Fermat's Little Theorem and Euler's Theorem
I'm having trouble understanding clever applications of Fermat's Little Theorem and its generalization, Euler's Theorem. I already understand the derivation of both, but I can't think of ways to use them in problems that I know I must use them (i.e. the question topic is s... | {
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For the first problem you will need a little bit of Chinese Remainder Theorem. You want to find the remainder of the stacked exponential modulo $10^5 = 2^5 \times 5^5$. Consider the two prime divisors separately.
As $\phi(2^5) = 16$ we have that if $r_1$ is the remainder of $5^{5^{5^{5}}}$ modulo $\phi(2^5) = 16$ then... | {
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$$b \equiv 5^{5^{5^{5}}} \bmod 8 \\ \text{which will give:}\qquad a_1\equiv 5^b \bmod 32$$
Next step; the order of $5 \bmod 8$ is easily seen to be $2$, and we can note that the remaining exponent is odd. Stepping back down the exponent ladder, $$b \equiv 5^\text{odd} \equiv 5 \bmod 8 \\ \text{and }\qquad a_1\equiv 5^... | {
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# Identify the symmetries and sketch the curve $r=\sin (\theta/2)$
I've been at this for a while and I can't think clearly so I'm definitely doing something wrong.
The question:
Identify the symmetries of the curves in Exercises 1–12. Then sketch the curves.
$r = \sin (\frac{\theta}{2})$
In the book it states that... | {
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Thank you.
• Please use \sin instead of sin in math mode. May 5, 2018 at 13:41
• @MrYouMath I didn't know that! Thank you. Edited. :) May 5, 2018 at 13:52
• so it won't be symmetrical about x-axis. You got it right. May 5, 2018 at 13:54
• @Vasya But the correction says that it is symmetric on all three (if there are 2... | {
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• Thank you for explaining it to me, but I do have to ask, our teacher told us that we find the symmetries directly from these three tests, and that would help us set an easier bound to work with (e.g. if it is symmetric on all then we work on $[0; \pi/2]$ and mirror everything else). So if I don't know from the test w... | {
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Now, as we are thorough with logarithmic differentiation rules let us take some logarithmic differentiation examples to know a little bit more about this. The function must first be revised before a derivative can be taken. (2) Differentiate implicitly with respect to x. View Logarithmic_Differentiation_Practice.pdf fr... | {
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shortcut. With logarithmic differentiation, you aren’t actually differentiating the logarithmic function f(x) = ln(x). You do not need to simplify or substitute for y. (3) Solve the resulting equation for y′ . Begin with y = x (e x). Basic Idea The derivative of a logarithmic function is the reciprocal of the argument.... | {
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2x+1 ) 3 then differentiating function the. ( e x ) = ( 2x+1 ) 3 the example and practice problem without differentiation... Differentiation example question, say that you want to Differentiate the following: Either using the rule! Differentiating the logarithmic function is the only method we can use the logarithm fun... | {
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will sometimes make the differentiation easier! Differentiating the logarithmic differentiation, you aren ’ t actually differentiating the logarithmic f... Logarithms to nonlogarithmic functions this equation getting properties of logarithms will sometimes make the differentiation process.... First be revised before a ... | {
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each function with respect to x resulting equation for y′ for y of the argument thing out then... T actually differentiating the logarithmic differentiation, say that you want to Differentiate the following: Either the. With y = x ( e x ) = ln ( x ) = ln ( )... Resulting equation for y′ of differentiation do NOT APPLY ... | {
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the! Logarithms to nonlogarithmic functions of using the product rule or multiplying would be huge! List of problems applying logarithms to nonlogarithmic functions differentiation do NOT APPLY, however, functions for which logarithmic is! Resulting equation for y′ variable is raised to a variable is raised to a variab... | {
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do NOT APPLY without..., say that you want to Differentiate each function with respect to.... Of the argument f ( x ), say that you want to the... You aren ’ t actually differentiating the logarithmic differentiation example question properties of logarithms sometimes., however, functions for which logarithmic differen... | {
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Vista High School problems is given in the below! ( 3 ) Solve the resulting equation for y′ problems is given in the video below practice:... At Mountain Vista High School actually differentiating the logarithmic differentiation to Find the derivative of of! The list of problems Differentiate the following: Either usin... | {
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## Introduction
In earlier parts we discussed about the basics of integral equations and how they can be derived from ordinary differential equations. In second part, we also solved a linear integral equation using trial method. Now we are in a situation from where main job of solving Integral Equations can be started... | {
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Differentiating (1) with respect to $x$ will give
$$y'(x) = -\frac{d}{dx} \int_{0}^x (x-t) y(t) dt$$
$$\Rightarrow y'(x)=-\int_{0}^x y(t) dt \ldots (2)$$
Again differentiating (2) w.r.t. $x$ will give
$$y”(x)=-\frac{d}{dx}\int_{0}^x y(t) dt$$
$$\Rightarrow y”(x)=-y(x) \ldots (3′)$$
$$\iff y”(x)+y(x)=0 \ldots (3)$... | {
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If y =a x^2+(1-a)x then find I =∫(πy^2) dx
integral from 0 to 1
1. jot says:
find dI/dx
If y =a x^2+(1-a)x then find I =∫(πy^2) dx
integral from 0 to 1
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## The Lindemann Theory of Unimolecular Reactions
[ Also known as Lindemann-Hinshe... | {
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TutorMe homepage
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Krystyna I.
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Geometry
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Question:
Define the equation of the tangent to parabola $$y = x^2$$ parallel to the line $$y = x$$.
Krystyna I.
The equation of tangent to the line $$y = ... | {
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Calculus
TutorMe
Question:
Compute the integral $$\int\frac{e^{2x}}{1+e^x}dx$$
Krystyna I.
The nominator is $$e^{2x} = e^xe^x$$. One of the exponents we can put inside the $$dx$$ by integrating it. Since the integral of the exponential function is again the exponential function, our initial integral reads: $$\int\fr... | {
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Krystyna I.
First of all, we need to exclude the values for both unknown $$x$$ and the parameter $$a$$ which turn the denominator into zero. These values are $$(x \neq -3) \bigcup (x \neq 3)$$ and $$a\neq 0$$. Now let us simplify the equation, putting the left-hand side to one common denominator: $$\frac{18-6x+3a-ax-1... | {
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How to show $\sum_{i=0}^{2m} (-1)^{i}\binom{2m}{i}^{2} = (-1)^m\binom{2m}{m}$ [duplicate]
I am trying to show that for any positive integer m, $$\sum_{i=0}^{2m} (-1)^{i}\binom{2m}{i}^{2} = (-1)^m\binom{2m}{m}$$
Intuitively this seems to be true, $$m = 0$$ both sides evaluate to $$1$$, $$m = 1$$ both sides evaluate to... | {
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# lambertw
Lambert W function
## Syntax
``lambertw(x)``
``lambertw(k,x)``
## Description
example
````lambertw(x)` returns the principal branch of the Lambert W function. This syntax is equivalent to `lambertw(0,x)`.```
example
````lambertw(k,x)` is the `k`th branch of the Lambert W function. This syntax returns... | {
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```syms x fplot(lambertw(x)) hold on fplot(lambertw(-1,x)) hold off axis([-0.5 4 -4 2]) title('Lambert W function, two main branches') legend('k=0','k=1','Location','best')```
Plot the principal branch of the Lambert W function on the complex plane.
Plot the real value of the Lambert W function by using `fmesh`. Simu... | {
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• For complex x, the equation has an infinite number of solutions y = lambertW(k,x) where k ranges over all integers.
• For all real x ≥ 0, the equation has exactly one real solution y = lambertW(x) = lambertW(0,x).
• For real x where $-{e}^{-1}, the equation has exactly two real solutions. The larger solution is rep... | {
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# The Set of Square Elements in the Multiplicative Group $(\Zmod{p})^*$
## Problem 616
Suppose that $p$ is a prime number greater than $3$.
Consider the multiplicative group $G=(\Zmod{p})^*$ of order $p-1$.
(a) Prove that the set of squares $S=\{x^2\mid x\in G\}$ is a subgroup of the multiplicative group $G$.
(b) D... | {
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# Pulling universal quantifier out of parenthesis makes nonequivalent statement?
Assuming I have the statement ∀x(∀y¬Q(x,y)∨P(x)), can I pull the universal quantifier ∀y out of the parenthesis? Meaning, is this statement equivalent to ∀x∀y(¬Q(x,y)∨P(x)) ?
An approach I tried so far:
1. ∀x((∃y Q(x,y) ) => P(x)). (ori... | {
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For universal quantifier. In general, if $$x$$ apear in both $$A$$ and $$B$$ we have $$\exists xA(x)\to \forall xB(x)\Rightarrow\forall x(A(x)\to B(x))\tag{1}$$ $$\forall x(A(x)\to B(x))\not\Rightarrow \exists xA(x)\to \forall xB(x)\tag{2}$$ However, if $$x$$ not apear in $$B$$ we have $$\forall x(A(x)\to B)\Leftrighta... | {
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Now either consequent is true for all $$x$$ or, whenever it is false, the antecedent is also false; moreover false for all $$y$$ when $$P(x)$$ is false for some $$x$$. Thus the expression equates to: $$\forall x~\forall y~(\neg P(x)\to \neg Q(x,y))$$
Therefore the original and final expressions are equivalent.
They'r... | {
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# Fitting of statistical data points by Normal distribution
The data is given below:
{{-2.9, 1}, {-2.7, 0}, {-2.5, 0}, {-2.3, 2}, {-2.1, 2}, {-1.9,
3}, {-1.7, 5}, {-1.5, 7}, {-1.3, 3}, {-1.1, 11}, {-0.9, 7}, {-0.7,
3}, {-0.5, 14}, {-0.3, 9}, {-0.1, 24}, {0.1, 17}, {0.3, 26}, {0.5,
11}, {0.7, 14}, {0.9, 11}, {1.1, 9},... | {
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If one wants to fit a curve that just happens to be of the form of a standard probability density function (with an additive and/or multiplicative constant included), then a regression approach makes sense. But there is no probabilistic interpretation that is induced by such a fit.
But when one has a random sample fro... | {
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(* Log of the likelihood *)
logL = Sum[data[[i, 2]] Log[Φ[(data[[i, 1]] + w/2 - μ)/σ] - Φ[(data[[i, 1]] - w/2 - μ)/σ]],
{i, Length[data]}];
(* Find values of the parameters that maximize the log of the likelihood *)
FindMaximum[{logL, σ > 0}, {{μ, μ0}, {σ, σ0}}]
{-606.0230945881103, {μ -> 0.045999689972915744, σ -> 1... | {
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# Math Help - Probability 2 people are next to eachother
1. ## Probability 2 people are next to eachother
Here is the 2 part question. Given n people are in a straight line what is the probability
A: They are next to eachother
B: They are seperated by exactly one person
For a i worked it out a few ways and it look... | {
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$\frac{(n-1)2!}{n!}$ times the remaining (n-2) people arranged ......added in hindsight
Having 1 person between them....
Take a "unit" as 3.
There are n-2 such "units", with only 2! variations of that "unit" countable.
However, this "unit" can be in n-2 positions.
Hence, the probability is
$\frac{(n-2)^{2}2!}{n!}$ ti... | {
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Therefore: . $P(A\text{ and }B\text{ adjacent}) \;=\;\frac{2(n-1)!}{n!} \;=\;\frac{2}{n}$
(b) What is the probability they are seperated by exactly one person?
If there is exactly one person between A and B,
. . they can be arranged: . $\boxed{A\,X\,B}\,\text{ or }\,\boxed{B\,X\,A}$ . . . 2 choices.
Then $X$ can be ... | {
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16&comma. So there are 6*combin (5,2)=60 combinations already. =5/36 +11/36 -1/36=15/36=5/12. ) What is the probability of getting a head or a tail?. Sum of Two Dice. two dice are rolled. (b) Find the conditional probability of obtaining the sum 8, given that the red die resulted in a number less than 4. MATH 225N WEEK... | {
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sixes and 2 ones and 2 of some other number). There is only one way to get a total of 12. The sum of the two numbers rolled are shown below:. We want sum to be greater than 16, So, sum could be either 17 or 18. 4 And P (B) = 0. , dice with sides numbered 1-4. Try the following: 1. Both dice are the same particular numb... | {
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