id
stringlengths
27
136
text
stringlengths
4
1.05M
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_3176
GMAT Data Sufficiency (DS) - Page 165 Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack It is currently 24 Jan 2017, 04:32 # Events & Promotions ###### Events & Promotions in June Open Detailed Calendar # GMAT Data Sufficiency (DS) new topic Question banks Down...
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_3169
# Solving trig equations with involving aperiodic functions • July 13th 2014, 09:21 AM maxpancho Solving trig equations with involving aperiodic functions Attachment 31263 C) Principal domain: $-\dfrac{\pi}{2}\leq 2x^2+x-1\leq \dfrac{\pi}{2}$ $-1.41099 \leq x \leq 0.91099$ Next: $\sin(2x^2+x-1)=\dfrac{2}{5}$ $2...
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_3182
# Pavement Design Questions and Answers – Highway Materials – Subgrade Soil Properties – 2 « » 1. Which of the below is the correct formula to find group index (GI) of soil? a) GI =0.1a+0.0025ac+0.005bd b) GI =0.2a+0.005ac+0.01bd c) GI =0.01a+0.025ac+0.05bd d) GI =0.02a+0.05ac+0.001bd Explanation: GI =0.2a+0.005ac+0...
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_11744
New Titles  |  FAQ  |  Keep Informed  |  Review Cart  |  Contact Us Quick Search (Advanced Search ) Browse by Subject General Interest Logic & Foundations Number Theory Algebra & Algebraic Geometry Discrete Math & Combinatorics Analysis Differential Equations Geometry & Topology Probability & Statistics Applications Ma...
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_11745
Prove that the centralizer $C_K(H)$ has finite index in $K$ Let $H,K$ be subgroups of a group $G$. If $[H,K]$ is finite and $H$ is finitely generated, then the centralizer $C_K(H)$ has finite index in $K$. More precisely, if $[H,K]$ has order $n$ and $H$ is $m$-generated, then $|K : C_K(H)| \leq n^m$. - Hint 1: If $...
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_11746
# Tag Info 5 Hint: For a function $f : A \to 2$ and an element $a \in A$, either $f(a) = 0$ or $f(a) = 1$. For a subset $B \subseteq X$ and an element $a \in A$, either $a \in B$ or $a \not \in B$. How might you match up functions $A \to 2$ with subsets of $A$? Bigger hint: (hover mouse over grey box to see) 5 Note...
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_11748
# Linear Algebra: Find all axioms that fail k(a,b)=(ak^2,bk^2). ## Homework Statement If we define V as the set of vectors in R^2 with vector addition defined as it normally is, but scalar multiplication defined to be k(a,b)=(k2a,k2b), then V is not a vector space. Find all axioms that fail (and explain why they fail...
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_11749
Browse Questions Home  >>  CBSE XII  >>  Math  >>  Matrices # Construct $a_{2\times 2}$ matrix where $a_{ij} =\frac{(i + 2j)^2}{2}$ Toolbox: • In general $a_{2\times 2}$ matrix is given by $A=\begin{bmatrix}a_{11} & a_{12}\\a_{21} &a_{22}\end{bmatrix}$ Step1: Elements are given by $a_{ij}=\frac{(i+2j)^2}{2}$ Replace ...
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_11750
Category Theory I realize that we might be getting away from programming and diving into hard-core math. But you never know what the next big revolution in programming might bring and what kind of math might be necessary to understand it. There are some very interesting ideas going around, like functional reactive pro...
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_11751
# An object's velocity is given by v(t) = (t^2 -t +1 , t^3- 3t ). What is the object's rate and direction of acceleration at t=6 ? May 6, 2016 $a \left(6\right) = 105.57$ $\theta = {84.02}^{o}$ #### Explanation: ${a}_{x} \left(t\right) = \frac{d}{d t} = \left({t}^{2} - t + 1\right)$ ${a}_{x} \left(t\right) = 2 t -...
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_11752
# Difference between revisions of "2019 AMC 10B Problems/Problem 15" ## Problem Right triangles $T_1$ and $T_2$, have areas of 1 and 2, respectively. A side of $T_1$ is congruent to a side of $T_2$, and a different side of $T_1$ is congruent to a different side of $T_2$. What is the square of the product of the lengt...
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_11753
GMAT Question of the Day - Daily to your Mailbox; hard ones only It is currently 20 Oct 2018, 02:20 ### GMAT Club Daily Prep #### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email. Customize...
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_11754
1. Math 2. Trigonometry 3. hi im nearly there i think but can you please... # Question: hi im nearly there i think but can you please... ###### Question details hi, i'm nearly there i think but can you please show me the working that factorises / simplifies the answer given - i think it needs to be like the TI Inspi...
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_11756
# Failure rate (Redirected from Hazard function) Failure rate is the frequency with which an engineered system or component fails, expressed, for example, in failures per hour. It is often denoted by the Greek letter λ (lambda) and is important in reliability engineering. The failure rate of a system usually depends...
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_11757
# The continuous dual is Banach 1. Jan 18, 2008 ### quasar987 [SOLVED] The continuous dual is Banach 1. The problem statement, all variables and given/known data I'm trying to show that the continuous dual X' of a normed space X over K = R or C is complete. 3. The attempt at a solution I have shown that if f_n is...
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_11758
# Is there a more efficient way to calculate the determinant of this matrix? I used Gaussian Elimination to calculate $$\det\begin{pmatrix}1&4&9&16&25&36\\4&9&16&25&36&49\\9&16&25&36&49&64\\16&25&36&49&64&81\\25&36&49&64&81&100\\36&49&64&81&100&121\end{pmatrix}$$ and found the answer to be $$0$$. It took a lot of time...
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_11747
Module 7: The Central Limit Theorem # The Central Limit Theorem for Sums Barbara Illowsky & OpenStax et al. ### Learning Objectives Suppose X is a random variable with a distribution that may be known or unknown (it can be any distribution) and suppose: 1. μX = the mean of Χ 2. σΧ = the standard deviation of X If...
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_11755
# Is there a countable discrete infinite group $G$ over which the group algebra $\mathbb{C} G$ is semisimple? I am seeking for an Artin $$k$$-algebra (especially for group algebra) which is infinite-dimensional over some field $$k$$. It's known that any complex group algebra has trivial Jacobson radical. So I have the...
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_11759
# Rational and Irrational Numbers 1. Jan 25, 2005 ### lokisapocalypse I need to show that a rational + irrational number is irrational. I am trying to do a proof by contradiction. So far I have: Suppose a rational, b irrational. Then a = p/q for p, q in Z. Then a + b = p/q + b = (p + qb) / q But I don't know where...
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_15361
Number Theory and Combinatorics Seminar Fall 2007Spring 2008Fall 2008, Spring 2009, Fall 2009, Spring 2010, Fall 2010 Wednesday,  September 30, 2009 Room: TH204 Time: 12:00-12:50 PM Speaker: Dragos Ghioca (University of Lethbridge) Title: Arithmetic Dynamics Abstract :  Starting from a fundamental question regardin...
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_15363
# In a spherically symmetric central potential why do we look for eigenfunctions of the angular momentum operator? In finding the solutions to the wave equation for a spherically symmetric potential $$V(r)$$, we look for the eigenfunctions of $$\hat L^2$$ and $$\hat L_z$$ operators. However, what is the reasoning behi...
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_15365
#P1391E. Pairs of Pairs ID: 807 Type: RemoteJudge 3000ms 256MiB 尝试: 5 已通过: 3 难度: 10 上传者: 标签>constructive algorithmsdfs and similargraphsgreedytrees*2600 Pairs of Pairs Description You have a simple and connected undirected graph consisting of $n$ nodes and $m$ edges. Consider any way to pair some subset of these $...
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_15366
# real matrix fails to have an eigenvalue Wikipedia says: Having an eigenvalue is an accidental property of a real matrix (since it may fail to have an eigenvalue), but every complex matrix has an eigenvalue. Yet, IMO, real matrices are subclass of complex ones. So, even without having any mathematical degree I see ...
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_15367
# area of a trapezium • ## Area of a trapezium Area KS3 Maths Revision BBC Area of a trapezium. The area of a trapezium is given by $${A}=\frac{(a+b)}{2}\times{h}$$.. You can see that this is true by taking two identical trapezia (or trapeziums) to make a parallelogram. • Rectangles Area KS3 Maths Revision BBC Bites...
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_15368
GMAT Question of the Day - Daily to your Mailbox; hard ones only It is currently 20 Jun 2018, 20:05 ### GMAT Club Daily Prep #### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email. Customize...
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_15370
Part A: Each correct answer is worth 5 points Problem 1 The value of $\frac{1998 - 998}{1000}$ is $\text{(A)}\ 1 \qquad \text{(B)}\ 1000 \qquad \text{(C)}\ 0.1 \qquad \text{(D)}\ 10 \qquad \text{(E)}\ 0.001$ Problem 2 The number $4567$ is tripled. The ones digit (units digit) in the resulting number is $\text{(A)...
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_15372
Lemma 63.11.2. Let $P \in \text{Fil}^ f(\text{Mod}_\Lambda )$ be filtered finite projective, and $f : P \to P$ an endomorphism in $\text{Fil}^ f(\text{Mod}_\Lambda )$. Then $\text{Tr}(f|_ P) = \sum \nolimits _ p \text{Tr}(f|_{\text{gr}^ p(P)}).$ Proof. Omitted. $\square$ In your comment you can use Markdown and LaTe...
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_15373
Algebra Level 3 Find the sum: $$1$$ + $$2$$ + $$3$$ + $$4$$ + ... + $$999999998$$ + $$999999999$$ + $$1000000000$$ = $$?$$ ×
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_15374
# Frobenius Method to solve $x(1 - x)y'' - 3xy' - y = 0$ So, Im trying to self-learn method of frobenius, and I would like to ask if someone can explain to me how can we solve the following DE about $x = 0$ using this method. $$x(1 - x)y'' - 3xy' - y = 0$$ - ## 1 Answer The motivation behind Frobenius method is to...
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_15375
# The figure shows △ABC.¯¯BD¯ is the angle bisector of ∠ABC. What is AD ? Jan 10, 2017 2.67 #### Explanation: In triangle ABC Tan B= $\frac{6}{8}$ Therefore angle B = $36.87 \mathrm{de} g r e e s$ So angle ABD =$\frac{36.87}{2} = 18.43 \mathrm{de} g r e e s$ Looking at triangle ABD Tan 18.43=$\frac{A D}{8}$ Jan ...
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_15362
# A Visual Proof of a Remarkable Trig Identity Strange but true (try it on a calculator): $\displaystyle \cos \left( \frac{\pi}{9} \right) \cos \left( \frac{2\pi}{9} \right) \cos \left( \frac{4\pi}{9} \right) = \displaystyle \frac{1}{8}$. Richard Feynman learned this from a friend when he was young, and it stuck wit...
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_15364
# Proving statements true or false. • Sep 17th 2009, 02:40 PM GreenDay14 Proving statements true or false. I am having an absurd amount of trouble with what seems to be very easy questions. The question asks: Answer true or false and supply a direct proof or a counterexample to each of the following assertions. (a) T...
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_15369
how to find/define eigenvectors as a continuous function of matrix? - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-25T11:08:25Z http://mathoverflow.net/feeds/question/116123 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/116123/how-to-find-define-eigenvectors...
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_15371
## Precalculus (6th Edition) $12(m+5)$ Note that $60=12(5)$. Since $12$ is a factor of $60$, then $12$ is the greatest common factor (GCF) of $12$ and $60$. Factor out the GCF to obtain: $12m+60=12(m+5)$
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_15360
시간 제한메모리 제한제출정답맞힌 사람정답 비율 1 초 128 MB74231729.310% ## 문제 Bored with horse racing, Farmer John decides to investigate the feasibility of cow racing as a sport. He sets up his N cows (1 <= N <= 100,000) to run a race of L laps around a circular track of length C. The cows all start at the same point on the track and run...
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_19458
# Semicircle Calculate the length of a semicircle with a radius of 6cm. Correct result: x =  18.8496 cm #### Solution: We would be pleased if you find an error in the word problem, spelling mistakes, or inaccuracies and send it to us. Thank you! Tips to related online calculators Need help calculate sum, simplify...
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_19459
Open access peer-reviewed chapter # Interview of Natural Hazards and Seismic Catastrophe Insurance Research in China Written By Jian Zhu Submitted: September 28th, 2018 Reviewed: January 4th, 2019 Published: February 9th, 2019 DOI: 10.5772/intechopen.84159 From the Edited Volume ## Natural Hazards Edited by Joh...
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_19460
## Proceedings of the International Conference on Geometry, Integrability and Quantization ### f-biharmonic Maps Between Riemannian Manifolds Yuan-Jen Chiang #### Abstract We show that if $\psi$ is an $f$-biharmonic map from a compact Riemannian manifold into a Riemannian manifold with non-positive curvature satisf...
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_19463
# Inequality for the modulus of Riemann zeta on horizontal lines and alleged partial result of Maple According to a conjecture p.4 $|\zeta(\frac12 -\Delta + it))| > |\zeta(\frac12 + \Delta + i t|$ for $0 < \Delta < \frac12$ and $|t| > 2 \pi +1$. Since $\zeta(\overline{s}) = \overline{\zeta(s)}$, this is equvalent to $...
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_19464
Question #2b5ce Jan 1, 2018 $6.0 \cdot {10}^{23}$ Explanation: The thing to remember about an element's molar mass, which you'll find listed in the Periodic Table, is that it tells you the mass of $6.022 \cdot {10}^{23}$ atoms of that element. This is the case because the molar mass of an element represents the ma...
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_19465
# Class 11 Physics Chapter 14 Important Questions Oscillations Q. 1. What is a periodic motion? Which trigonometrical functions are suitable for expressing periodic motion? Ans. A periodic motion is that motion Science is a complex and challenging subject, as it involves so many principles and concepts that are diffi...
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_19466
RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB General information Latest issue Archive Impact factor Journal history Search papers Search references RSS Latest issue Current issues Archive issues What is RSS Fundam. Prikl. Mat.: Year: Volume: Issue: Page: Find ...
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_19467
Formal Methods in Computing(Most of the papers antecedent to 1995are not included in the list) FRAMES  NO FRAME Pravato-Roversi:1995-ICTCS (In proceedings) Author(s) Alberto Pravato and Luca Roversi Title « $\Lambda$! considered both as a paradigmatic language and as a meta-language » In Fifth Italian Conference on T...
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_19468
1. # Equivalent definitions for $BMO$ The space of functions of bounded mean oscillation $BMO$ is defined by the BMO norm $$\label{norm} ||f||_{BMO} = \sup_{\text{cubes }Q} \frac{1}{|Q|} \int_Q |u(y) - u_Q| dy$$ But an equivalent definition is to take the sup over balls instead of cubes ... 2. # The space $BMO$ ## I...
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_19469
# Lucas Numbers? Algebra Level 4 The expression : $$\sqrt[8]{2207-\dfrac{1}{2207-\dfrac{1}{2207-\cdots}}}$$ can be expressed as $$\dfrac{a+b\sqrt{c}}{d}$$ where $$a,b,c,d\in \Bbb{Z}$$. Find the value of $$a + b + c + d$$. $$c$$ is a square free integer, $$\gcd(a, b, d) = 1$$. ×
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_19471
## Pages News: Currently the LaTeX and hidden solutions on this blog do not work on Google Reader. Email me if you have suggestions on how to improve this blog! ## Sunday, 28 August 2011 ### Math GRE - #27 Which of the following is the best approximation of $\sqrt{1.5}(266)^{3/2}$? 1. 1000 2. 2700 3. 3200 4. 4100 ...
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_19457
# Tag Info ## Hot answers tagged convergence 12 Yes, this is the standard Aubin-Nitsche (or duality) trick. The idea is to use the fact that $L^2$ is its own dual space to write the $L^2$-norm as an operator norm $$\|u\|_{L^2} = \sup_{\phi\in L^2\setminus\{0\}} \frac{(u,\phi)}{\|\phi\|_{L^2}}.$$ We thus have to esti...
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_19461
# Euler-Lagrange equation Jump to: navigation, search for a minimal surface $z=z(x,y)$ The equation $$\left(1+\left(\frac{\partial z}{\partial x}\right)^2\right)\frac{\partial^2z}{\partial y^2}-2\frac{\partial z}{\partial x}\frac{\partial z}{\partial y}\frac{\partial^2z}{\partial x\partial y}+\left(1+\left(\frac{\p...
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_19462
# Orientation of manifold in topological sense What do we mean by orientability of a topological manifold? How do we orient two dimensional Euclidean space and why is Moebius band non-orientable? And it would be a great favour to me if you can tell me a good book that explains this idea. I read "Algebraic topology: An...
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_19470
# proof of basic criterion for self-adjointness 1. 1. $(1\implies 2)$ If $A$ is self-adjoint and $Ax=ix$, then $i\|x\|^{2}=(ix,x)=(Ax,x)=(x,A^{*}x)=(x,Ax)=(x,ix)=\overline{(ix,x)}=-i\|x\|^{2},$ so $x=0$. Similarly we prove that $Ax=-ix$ implies $x=0$. That $A$ is closed follows from the fact that the adjoint of an...
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_19456
# Eigenvalues and Domain of the Laplace-Beltrami Operator Assume $$(M,g)$$ is a compact Riemannian manifold without boundary, where $$g$$ is the Riemannian metric. Let $$L:=-\Delta$$ be the Laplace-Beltrami operator on $$M$$ defined by $$\Delta \cdot = \text{div}(\nabla \cdot)$$. I am reading in a lot of books/papers ...
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_4625
Apr 29th 2011, 02:42 PM #11 Member   Join Date: Nov 2010 Posts: 40 Let me work out this and see whether I am correct: $\int_{-b}^{-a}\frac {dx}{|x|} = sgn(-a)ln|-a|-sgn(-b)ln|-b| = -ln|-a|-(-ln|-b|) = ln\left | \frac {-b}{-a}\right | = ln\left | \frac {b}{a}\right |$ And $\int_{-b}^{a}\frac {dx}{|x|} = sgn(a)ln|a|-sgn(...
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_4628
# Sum of independent Binomial random variables with different probabilities? suppose I have independent random variables $X_i$ which are distributed binomially via $$X_i \sim \mathrm{Bin}(n_i, p_i)$$. Are there relatively simple formulae or at least bounds for the distribution $$S = \sum_i X_i$$ avaialble? - See th...
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_4629
# Math Help - explain how it is the asymptote plz 1. ## explain how it is the asymptote plz Hello. Can someone explain to me how the Horizontal Asymptote for this function is -1 (or the y-int. in an exponential function)? so the question is ... y= 2^x - 1 I graphed it, and the asymptote is one, I just would appre...
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_4630
# Number of right angled triangles formed by vertices of a 14-gon Here's a question that I found on the website of International Kangaroo Maths Contest. The question goes like this: What is the total number of right angled triangles that can be formed by joining the vertices of a regular 14-gon? Correct Answer: The ...
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_4631
## Thursday, July 19, 2012 ### On modal logic and rights There's been a lively discussion up on my Facebook wall for a while now. For those of you not in that loop, I've got an old friend, Joe, who holds and brandishes a clear and pure stripe of libertarian political and moral thinking, and will on occasion brandish ...
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_4632
# During very vigorous exercise, the body's temperature can go as high as 40°C. What would this temperature read on the Kelvin scale? The temperature would be $\text{313 K}$. In order to convert the Celsius temperature to Kelvins, add $273.15$ to the Celsius temperature. The Kelvin scale does not use a degree symbol. ...
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_4633
# General solution for absolute electric potential 0 pts ended Use the hyperbolic sin inverse in part 1 Image text transcribed for accessibility: Use dV =kdq/r to derive a general expression for the absolute electric potential at point P due to a line charge as shown below: Use Ex = ED = -dv/dD to find the x compone...
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_4634
# The Perfect Square Syndrome [closed] Using the numbers 1,2,3,4,5,6,7,8,9 only once in the complete set, Give me a set of perfect squares. Once you have found the set, you have the liberty to use all these numbers without a comma and give me a nine digit perfect square featuring all of the nine digits...JUST ONCE! ...
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_4636
# Tag Info Accepted ### The Likelihood Approach a.k.a. the 'third way' versus Bayesian How is the 'Likelihood Approach' different from the Bayesian approach? It's very different. Bayesians interpret probabilities in subjectivist terms as the measure of belief. They also use priors, so ... • 115k Accepted ### Bayesi...
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_4637
Where results make sense About us   |   Why use us?   |   Reviews   |   PR   |   Contact us # Topic: Eigenstates ###### In the News (Sat 25 May 19) Perturbation theory (quantum mechanics) - Wikipedia, the free encyclopedia An example of this phenomenon may be found in conventional superconductivity, in which the p...
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_4638
# LLN and CLT¶ Contents ## Overview¶ This lecture illustrates two of the most important theorems of probability and statistics: The law of large numbers (LLN) and the central limit theorem (CLT) These beautiful theorems lie behind many of the most fundamental results in econometrics and quantitative economic modeli...
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_4639
## Electronic Journal of Statistics ### Adaptive estimation of linear functionals by model selection #### Abstract We propose an estimation procedure for linear functionals based on Gaussian model selection techniques. We show that the procedure is adaptive, and we give a non asymptotic oracle inequality for the ris...
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_4624
Pełnotekstowe zasoby PLDML oraz innych baz dziedzinowych są już dostępne w nowej Bibliotece Nauki. Zapraszamy na https://bibliotekanauki.pl PL EN Preferencje Język Widoczny [Schowaj] Abstrakt Liczba wyników • # Artykuł - szczegóły ## Fundamenta Mathematicae 2011 | 213 | 3 | 255-270 ## A Hanf number for saturation ...
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_4626
# Deriving Dirac matrices 1. May 4, 2006 ### gulsen I'm trying to linearize Klein-Gordon equation, following Dirac's nobel lecture: $$(E^2 - (pc)^2 - (mc^2)^2) \psi = 0$$ $$(E + \alpha pc + \beta mc^2) (E + \alpha pc - \beta mc^2) \psi = 0$$ Expanding the equations yields: -$$\alpha$$ and $$\beta$$ commutes with E a...
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_4627
# A step towards defining the path of electron Hi learners, As the famous Heisenberg's uncertainty principle declares the inability of accurately measuring the properties of a quantum system, hence we can not determine the path of electron in the atom. The main aim of my discussion is to present you guys, a hypothesi...
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_4635
# 3.1 Exponents and roots  (Page 2/2) Page 2 / 2 We can continue this way to see such roots as fourth roots, fifth roots, sixth roots, and so on. There is a symbol used to indicate roots of a number. It is called the radical sign $\sqrt[n]{\phantom{\rule{16px}{0ex}}}$ ## The radical sign $\sqrt[n]{\phantom{\rule{1...
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_21536
## FANDOM 1,025 Pages The outer product (denoted as ⊗) of two vectors is a special form of the tensor product or Kronecker product where $\mathbf{u} \otimes \mathbf{v} = \mathbf{u} \mathbf{v}^\mathrm{H} = \begin{bmatrix}u_1 \\ \vdots \\ u_i\end{bmatrix} \begin{bmatrix} \overline{v_1} & \cdots & \overline{v_j} \end{b...
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_21537
# Equal Roots ! Level pending If two of the roots of the equation $$(a-2)(x^2+x+1)^2 - (a+2)(x^4+x^2+1) = 0$$ are equal, then the value(s) of $$a$$ are ×
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_21538
• mathslover If $$z_1$$ and $$z_2$$ are two complex numbers such that $$|\frac{z_1 - z_2}{z_1 + z_2}| =1$$ , prove that, $$\frac{iz_1}{z_2}=k$$ is a real number. Find the angle between the lines from the origin to the points $$z_1 + z_2$$ and $$z_1 - z_2$$ in terms of k. Mathematics Looking for something else? Not th...
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_21540
# Derivative of rectified linear unit in Mathematica? I am following the artificial neural networks literature and apparently the latest trend is to use the rectified linear units (ReLU) as the activation functions for each neuron. I tried to take the derivative of this function in Mathematica but it gives indetermina...
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_21541
Download Soccer 4Th Edition Steps To Success Download Soccer 4Th Edition Steps To Success by Katharine 4.4 1998) for algorithms of some of these natural download soccer 4th edition steps sequences. good chances are taken repeated up to be this with independent pairs. Hegyi( 1998) FEMS Microbiol. This is a some of th...
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_21543
# Linearly independent function sets • A Gold Member It is well known that the set of exponential functions ##f:\mathbb{R}\rightarrow \mathbb{R}_+ : f(x)=e^{-kx}##, with ##k\in\mathbb{R}## is linearly independent. So is the set of sine functions ##f:\mathbb{R}\rightarrow [-1,1]: f(x) = \sin kx##, with ##k\in\mathb...
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_21544
Thursday, November 29, 2012 Find the lowest common ancestor For a binary tree for a binary search tree Wednesday, November 28, 2012 Serialize and deserialize a generic tree File * serialize (node * n); node * deserialize (File * f); Monday, November 26, 2012 Isomorphic trees Two trees can be called isomorphic i...
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_21545
Near-field imaging of an unbounded elastic rough surface with a direct imaging method Near-field imaging of an unbounded elastic rough surface with a direct imaging method Xiaoli Liu Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China and School of Mathematical Sciences, Uni...
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_21546
Under the auspices of the Computational Complexity Foundation (CCF) REPORTS > DETAIL: ### Paper: TR07-127 | 22nd November 2007 00:00 #### Sound 3-query PCPPs are Long TR07-127 Authors: Arie Matsliah, Eli Ben-Sasson, Prahladh Harsha, Oded Lachish Publication: 7th December 2007 12:31 Keywords: Abstract: We initiat...
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_21548
# First Principles Example 3: square root of x ## Key Questions $f ' \left(x\right) = \frac{1}{2 \sqrt{x + 3}}$ #### Explanation: $f ' \left(x\right) = {\lim}_{h \to 0} \frac{f \left(x + h\right) - f \left(x\right)}{h}$ $f \left(x\right) = \sqrt{x + 3} , f \left(x + h\right) = \sqrt{x + h + 3}$, then $f ' \left(x...
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_21550
# Derivative of rotation matrix in a form skew-symmetric matrix I am working on an application of CV, in which a way to calculate the derivative of rotation matrix is involved. $$R$$ is the rotation matrix and $$R \in SO(3)$$ Also, $$R$$ is changing with $$t$$ giving $$R(t)$$. $$R(t)R(t)^\mathrm{T} = I$$ is known. W...
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_21551
Solving for optimal consumption bundle Consider a consumer who can consume either A or B, with the quantities being denoted by $a$ and $b$ respectively. If the utility function of the consumer is given by $$-[(10-a)^2+(10-b)^2]$$(suppose prices of both goods are equal to $1$), then solve for optimal consumption of the...
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_21539
## Lie Groups and Representation Theory Date, time & place Tuesday 16:30 - 18:00 126Room #126 (Graduate School of Math. Sci. Bldg.) Seminar information archive ### 2015/11/24 17:00-18:45   Room # (Graduate School of Math. Sci. Bldg.) Birgit Speh (Cornell University) Introduction to the cohomology of discrete groups...
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_21542
Is C^l closed in C^0? 1. Apr 12, 2012 SP90 1. The problem statement, all variables and given/known data Is $C^{k}[a,b]$ closed in $C^{0}[a,b]?$ 3. The attempt at a solution $C^{k}[a,b]$ is obviously a subset of $C^{0}[a,b]$. My gut feeling says no. I thought the best way would be to construct a function $f_{n}(x...
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_21547
# Making a matrix positive definite Suppose $$p \times p$$ matrix $$X$$ is symmetric and not positive definite (PD). I want to find the minimum value for $$\mu$$ such that $$X + \mu I_p$$ is positive definite. To this end, I suppose we can solve a semidefinite program (SDP) of the form $$\begin{array}{ll} \text{minim...
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_21549
## Differential Logic • Comment 1 Just a tangential association with respect to logical influence and pivotability.  I have been exploring questions related to pivotal variables (“Differences that Make a Difference” or “Difference In ⟹ Difference Out”) via logical analogues of partial and total differentials. For exa...
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_17488
# Math Help - F'(x) 1. ## F'(x) Find f'(x) e) f(x) 2^(log(3)x) The 3 is subscript Guys this is the last problem for my homework help me through this 2. Hi, $2^{\log_3x}=\exp\left(\frac{\ln x}{\ln 3}\cdot \ln 2\right)$ and this function can be differentiated using the chain rule.
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_17489
zbMATH — the first resource for mathematics Examples Geometry Search for the term Geometry in any field. Queries are case-independent. Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact. "Topological group" Phrases (multi-words) should be set in "straight quot...
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_17492
# Joint Probability 1. Jun 3, 2009 ### sauravrt If A and B are two events and I want to look at their joint probability P(A.B) do I have to be concerned with the order in with A and B occur? Saurav 2. Jun 3, 2009 ### EnumaElish No, in general. However, consider: A = {accumulation > x} B = {accumulation < x}. ...
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_17493
### Temperature (4597 views - Physics) Temperature is a physical quantity expressing hot and cold. It is measured with a thermometer calibrated in one or more temperature scales. The most commonly used scales are the Celsius scale (formerly called centigrade) (denoted °C), Fahrenheit scale (denoted °F), and Kelvin sca...
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_17494
# How do you find the asymptotes for f(x)=(3x^4 + 2x^2 + 1 )/ (5x^4 + x -1)? Jan 1, 2017 Horizontal: $\leftarrow y = \frac{3}{5} \rightarrow$. Vertical: $\uparrow x = - 0.7715135 \mathmr{and} x = 0.5482532 \downarrow$, nearly. #### Explanation: graph{5x^4+x-1 [-0.884, 0.8805, -0.443, 0.439]} By actual division, $f...
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_17496
# 0.2 Practice tests (1-4) and final exams  (Page 36/36) Page 36 / 36 26 . In a survey of 80 males, 45 had played an organized sport growing up. Of the 70 females surveyed, 25 had played an organized sport growing up. We are interested in whether the proportion for males is higher than the proportion for females. Th...
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_17497
# Recent questions tagged tifr2018 1 How many ways are there to assign colours from range $\left\{1,2,\ldots,r\right\}$ to vertices of the following graph so that adjacent vertices receive distinct colours? $r^{4}$ $r^{4} - 4r^{3}$ $r^{4}-5r^{3}+8r^{2}-4r$ $r^{4}-4r^{3}+9r^{2}-3r$ $r^{4}-5r^{3}+10r^{2}-15r$ 2 Let $A$ ...
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_17498
3 Q: # How many A's are there in the following sequence which are immediately followed by B as well as immediately preceded by Z?A M B Z A N A A B Z A B A Z B A P Z A B A Z A B A) Three B) Two C) One D) More than three Explanation: The letter A satisfying the following Structure ZAB A M B Z A N A A B Z $\inline&s...
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_17499
# Chapter 3 - Statistics for Describing, Exploring, and Comparing Data - 3-2 Measures of Center - Basic Skills and Concepts: 23 The contributions seem to favor Obama. #### Work Step by Step The mean can be counted by summing all the data and dividing it by the number of data: Obama: $\frac{275+452+...+250}{15}=653.8...
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_17502
# Graphs of Linear Systems ## Key Questions • It is possible for a system of equations to have no solution because a point on a coordinate graph to solve the equation may not exist. This concept may seem hard to understand at first, but if you think about it, it comes easily! The only way this can happen is if ther...
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_17503
Review question # What is the stopping distance for this car? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource Ref: R6841 ## Question A car is travelling at $\quantity{30}{mph}$ when the driver needs to make an emergency stop. It takes...
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_17490
## Thursday, March 13, 2014 ### How to Fix Issues with MathJax and Blogger Preview If you used MathJax on blogger you may have noticed that the preview  does not render the LaTex    output.  At the link below  you can find a simple way to fix it. Clueless Fundatma: Issues with MathJax and Blogger Preview ## Wednesd...
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_17495
# Cox Proportional Hazard ## Survival regression with covariates The Cox Proprtional hazard model is perhaps the most common survival model. In a number of ways it has similarities to traditional linear regression. There are two main differences: 1 - We are regressing against hazard rate (probability of dying condit...
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_17500
Please use this identifier to cite or link to this item: http://hdl.handle.net/10525/433 Title: Relative Compactness for Hyperspaces Authors: Sianesi, Francesca Keywords: Hyperspaces TopologiesRelative CompactnessSup MeasuresGap Functional Issue Date: 1999 Publisher: Institute of Mathematics and Informatics Bulgarian...
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_17501
# Direct comparison test – Serlo Zur Navigation springen Zur Suche springen In this chapter we will study an important convergence criterion called the direct comparison test. This criterion allows us to deduce the convergence behavior of a series by comparing it to that of another series. That way we can answer ques...
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_17491
437 views Answer the question on the basis on the basis of the information given below. Consider three circular parks of equal size with centres at $A_1,\:\: A_2,\:\:$ and $A_3$ respectively. The parks touch each other at the edge as shown in the figure (not drawn to scale). There are three paths formed by the triangl...
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_4753
# The Carter Catastrophe I’ve been reading Manifold: Time by Stephen Baxter. The book is quite good so far, and it presents a fascinating probabilistic argument that humans will go extinct in the near future. It is sometimes called the Carter Catastrophe, because Brandon Carter first proposed it in 1983. I’ll use Bay...