# All Questions

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### Bound this expression

Here is a problem I have encountered in the course of trying to apply the Berry-Esseen theorem to a sum of random variables, and I would like a hint as to how to approach it, or a reference. I believe ...
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### Recursion and Time Complexity Concept

I have been solving this question which appeared in one of the entrance exam. The question is as follows: ...
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### extension of log concave functions

So I need to prove something or see if its true and I don't know how to write in nice math text because this is my first question, so please bear with me We have a CDF Fh[s] for 0<=s<=1. The ...
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### Matrices of rank 1

Let the n x n complex matrix A have rank 1. Prove: $A^2$ = c(A) for some scalar c. What I know is that all matrices having rank 1 have rows based on a scalar multiple of the other. This should ...
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### How do we find u(x)?

I want to know how to find u(x) in the below question: $$u''(x)+{e^u}^{(x)} = 0\\ x \in[0,1]\\u(0) = u(1) = 0$$ Please explain briefly how this was done?? Thanks!!
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A garden is in the shape of a rectangle, $20$m by $8$m. Around the outside is a border of uniform width and in the middle is a square pond. The area which is not occupied by either border or pond is ...
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### the partial derivative of poisson kernel w.r.t. theta tends to 0 as r tend to 1?

the partial derivative of poisson kernel w.r.t. theta tends to 0 as r tend to 1? how to show it ,thanks!!! seem it diverge,because we have a 'n' term after diff.?
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### Analytic Solution of Second Order Nonlinear odes

Any idea how to find analytic solution of the following ode. $y''+0.1 y'+y^{5} = sin (t)$ I will really appreciate your response! Shah
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### Design new data structure

Design a data structure and a search algorithm to solve the following problem. It should be able to answer the query in O(log2 n) time. A high-level description of your data structure, the search ...
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### Proving the inequality $x^2\sin{x}+x\cos{x}+x^2+\frac{1}{2}>{0}$ [on hold]

Prove the inequality for real number $x$ $x^2\sin{x}+x\cos{x}+x^2+\frac{1}{2}>{0}$
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### Ziploc Conjecture [on hold]

A flexible plastic bag width $w$ and height h is filled with a liquid of volume V almost fully to roundness, sealed at top and placed on a flat table with its height approximately vertical. Prove ...
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### Integer solutions of $a^3+2a+1=2^b$

What are the solutions in integers of $a^3+2a+1=2^b$? [Source: Serbian competition problem]
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### Prove that $S$ is a subring of $\mathbb{Z}_{28}$

Question: $S=\{0,4,8,12,16,20,24\}.$ Prove that $S$ is a subring of $\mathbb{Z}_{28}$ Confusion 1: This might be a dumb question, but when we refer to $[4]$ in $S$, for example, is that the congruent ...
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### Discriminant of $x^2+x-1$

I'm working on a homework problem, and am worried I'm going crazy. I believe $x^2+x-1$ is irreducible, but it's discriminant is $1^2-4(1)(-1)=5$ is positive, which would make it reducible (since ...
### A is a square matrix where $3A^9- 7A^4 + 4A = I$. Prove that A is invertible by finding $A^{-1}$
The question is: A is a square matrix where $3A^9- 7A^4 + 4A = I$. Prove that A is invertible by finding A^-1. I have looked at other similar questions on this site: 1. Here 2. and Here But they use ...
### Equation: $2\sqrt{1-x}-\sqrt{1+x}+\sqrt{1-x^2}=3-x$
$2\sqrt{1-x}-\sqrt{1+x}+\sqrt{1-x^2}=3-x$ Could someone help me solve this problem?