0
votes
0answers
3 views

An inequality in positive reals.

Prove that $a^ab^bc^c\ge{(abc)^\frac{a+b+c}{3}}$ where $a,b,c\in\mathbb{R^+}$ I tried using powered AM-GM but didn't get anything. please give me a hint to solve it.
0
votes
1answer
3 views

How to show a Fejér kernel is a good kernal??

I can prove the other two properties,but I cant show that the integration of the modulus of Fejér kernel is bdd,that is $\int$ |$K_n$|$\leq $ $M$ $for$ $all$ $n$ $\geq$$1$
0
votes
0answers
4 views

function 3 digit arithmetic

I want ask this question correct? If wrong, please show the way to calculate. I am some confusion the 3 digit arithmetic, can explain it to me?
0
votes
0answers
6 views

changing forms of constant of integration

In solving O.D.E in my book sometimes he changes the constant of integration in the form for example C=Sin(A) where C & A are constants obtain the general solution in an explicit form but how ...
0
votes
0answers
4 views

Help solving ODE using Laplace Transform

The problem: y '' +4y ' + 40x = 0, seems unfamiliar to me because of the x variable. I don't know if this is a typo or not. Can you please assist?
0
votes
0answers
3 views

(Affine) Tensor Field

There are several equivalent definitions of tensor. The same goes with tensor fields. In the one defined by the property under coordinate transformation, say: \begin{equation} {\bar{T}}^{ij} = ...
0
votes
0answers
4 views

uniform convergence of characteristic functions

Assume that a sequence of probability measures $\mu_n$ converges weakly to $\mu$. Let $\phi_n$ and $\phi$ denote respetively the characteristic function of $\mu_n$ and $\mu$. Prove that $\phi_n$ ...
0
votes
1answer
12 views

Can we prove the Riemann-Lebesgue lemma by using the Weierstrass approximation theorem?

I'd like to prove the following version of the Riemann-Lebesgue lemma: Let $f: [0,1] \to \mathbb R$ be continuous. Then $$\int_0^1 f(x)\sin(nx) \, dx \xrightarrow{n \to \infty} 0$$ It's quite ...
0
votes
2answers
15 views

Is multiplication normally/binomially distributed?

I was thinking about the binomial formula in the context of coin flips and got to thinking about the reason that even though HHHHHHHHHH is just as likely to occur as a sequence as HHHHHTTTTT, 5 heads ...
2
votes
0answers
23 views

The number of the solutions of $‎ x^{10}=‎ ‎ ‎\begin{bmatrix}1&0\\‎ ‎0&1‎ ‎\end{bmatrix}‎$

How many solutions does the following equation have in $ M_{2}(\mathbb R)$ and why? $$‎ x^{10}=‎ ‎\begin{bmatrix}1&0\\‎ ‎0&1‎ ‎\end{bmatrix}‎$$ Every hint is appreciated.
0
votes
2answers
13 views

How to show that $at^2+bt+c$ can be written as $\displaystyle \begin{equation} a \left( t+\frac{b}{2a}\right) ^2-\frac{1}{4a}(b^2-4ac)\end{equation}$?

I've just expanded $$\displaystyle \begin{equation} a \left( t+\frac{b}{2a}\right) ^2-\frac{1}{4a}(b^2-4ac)\end{equation}\tag{1}$$ to $$at^2+bt+c\tag{2}$$ but I guess that perhaps showing it ...
1
vote
0answers
4 views

Pure Cubic Fields

Let $K=\mathbb Q(\sqrt[3]m) $, $m $ cube free is a pure cubic field. Then are we able to get number of unramified quadratic extensions of this field? Any help in this direction is useful. Thank you ...
0
votes
1answer
8 views

verifying whether a conditional density function is valid

I want to verify whether a given conditional probability function is valid or not. $\mathsf P(y\mid x)=\begin{cases}c\, e^{(-y/x)} & : y\geqslant 0, x>0;\\ 0 & ...
0
votes
2answers
9 views

Iteration of derived sets

Let $A$ be a set in the real line $\Bbb R$, and $A'$ the derived set of $A$, and $A''$ the derived set of $A'$, and so on. Is it possible to get an infinitively many distinct subsets of $\Bbb R$? ...
0
votes
1answer
21 views

Given $f(x)=x+\int_{0}^1 t(t+x)f(t) dt $ , what is $f(0) $?

Let $f:\mathbb R \to \mathbb R$ be such that $f(x)=x+\int_{0}^1 t(t+x)f(t) dt $ , then how do we find $f(0) $ ?
0
votes
1answer
8 views

solving equations with log and polynomials.

I need to solve/estimate for x in the following equation - $Klnx + x^\beta = r$. $K,r > 0.$ An estimate for large r(fixed K) is what I am looking for.
0
votes
0answers
4 views

convert the constrained optimization problem into unconstrained optimization using penalty parameter?

how we can convert the constrained optimization problem into unconstrained optimization using penalty parameter? and what the best method to find min if the derivatives are very difficult to ...
1
vote
4answers
32 views

What would be an example of a magma such that $x\cdot(x\cdot x)\neq (x\cdot x)\cdot x$?

Let $(M,\cdot)$ be a non-associative magma. What would be an example of $M$ such that there exists $x\in M$ such that $x\cdot(x\cdot x)\neq (x\cdot x)\cdot x$?
0
votes
3answers
8 views

Examples of automorphisms on structures

For some structure $(M,I)$ with $M$ a set and $I$ the interpretation of the constants, functions, and predicates, what is an example of a such a structure such that for each $a$ of $M$ there are only ...
2
votes
0answers
13 views

Prove $\lnot \lnot B$

Prove: $\lnot \lnot B$ from $\lnot \lnot A \implies \lnot \lnot B, \lnot(A \implies B) $ I cant use excluded middle: $B \lor \lnot B$ So I choose $\lnot B$ as hypothesis and will try to get $B$ ...
0
votes
0answers
11 views

Complex function, analyticity

Consider a function from $\mathbf{C}^2$ to $\mathbf{C}$ is defined as $$ f(z,w)=\frac{\alpha}{z} + \frac{\beta}{w} $$ where the parameters $\alpha, \beta$ are complex numbers. Is it analytic in ...
0
votes
0answers
9 views

help me with this question anyone?

Let{An}n=1,2...be a sequence of countable sets. Show that X=UAn is uncountable.
0
votes
0answers
12 views

I'm confused in the definition of derivative could someone help me?

A function's rate of change may change or not change or may have no rate of change at all.The way I see it is their are three possible way a function may change its rate. Case 1: It change ...
0
votes
1answer
15 views

A closed set is a derived set, true or false?

My question is on the title : true or false : a closed set is a derived set ? Thank you very much.
-2
votes
0answers
14 views

pROBABILITY USING DICES

When dice are irregular so that the sides of the dice are not equal in size or weight, then the most accurate way to determine the probability that they will land with a certain side (such as 5) up is ...
1
vote
1answer
24 views

straightforward calculus problem

Find the arc length of the graph of $\displaystyle \large x^{\frac{2}{3}}+y^{\frac{2}{3}}=1$. Hint: Use symmetry with respect to the line $y=x$. Let $y=x$ intersect at $a$. So, $\displaystyle ...
2
votes
0answers
10 views

Characterizing $\text{PGL}_2(\mathbb F_p)$

Where can I find a description and proof of the basic structure of $\operatorname{PGL}_2(\mathbb{F}_p)$ (Number of elements with each order, conjugacy classes, etc.) which is understandable by an ...
0
votes
1answer
18 views

Automorphisms of $(\mathbb{R}, +)$

Does the structure $(\mathbb{R}, +)$ have infinitely many automorphisms?
0
votes
1answer
9 views

How to directly show that $\mathbb{Z}_{(p)}$ is a local ring with the unique maximal ideal $p \mathbb{Z}_{(p)}$?

I know that $\mathbb{Z}_{(p)}$ is a local ring because it's the localization of $\mathbb{Z}$ over $p$, but is there a direct way to prove that and find its unique maximal ideal? I've been ...
2
votes
1answer
15 views

How prove this Ratio Test and Its Generalizations problem?

Question: let $\alpha\in (0,1)$,and the postive sequence $\{a_{n}\}$ such $$\lim_{n\to\infty}\inf \left(n^{\alpha}\left(\dfrac{a_{n}}{a_{n+1}}-1\right)\right) =\lambda\in (0,+\infty)$$ show ...
0
votes
1answer
12 views

A concrete example of a unital noncommutative ring without maximal two-sided ideals

Whenever I say ideal in this question I'm talking about two sided-ideals. Does there exist a concrete example of a non-commutative ring with $1$ without maximal ideals? We know that if $R$ is a ...
0
votes
1answer
13 views

Introduction to Measure-theoretic Probability George Roussas. example 4 page 1

I am reading Introduction to measure-theoretic Probability George Roussas. example 4 page 1 says: Let $\Omega$ be infinite (countably or not) and let $\mathcal{C}= \lbrace A \subseteq \Omega;A$ is ...
0
votes
0answers
10 views

Assume that A is a subset of some underlying universal set U.

Prove the domination laws in Table 1 by showing that a) A ∪ U = U. here is the answer but i have no idea how to come up with this answer and where does T come from?:O A ∪ U = {x | x ∈ A ∨ x ∈ ...
0
votes
0answers
12 views

Centralizer of element in group PSL(2,F_p)

Is it true, that $\forall g\in PSL(2,F_p)\setminus\{e\}$, $Z(g)$ is Abelian? I think that this is true, but i can't find simple prove.
0
votes
0answers
13 views

Can books be arranged into bags?

I'm trying to find an algorithm (sub exponential) to answer the following question (informal): given a (finite) set of distinct books of different (positive integer) sizes and a (finite) set of bags ...
0
votes
0answers
3 views

Biostatistics book

Do you know a book in biostatistics that fits very well to these topics: Analysis of counts: estimating probabilities, re-expression probabilities as ratios, odds, logits, probits, etc., comparing ...
0
votes
0answers
3 views

inter-event time distribution

We have a counting process N(t) and two processes X(t) and Y(t) where each renewal point of N(t) is a renewal point of X(t) with probability q or Y(t) with probability 1-q. If Fn(t) is the ...
0
votes
0answers
11 views

Evaluate the line integral with Euler.

Need some help evaluating this line Intergral. $\int$$_c$ xy${e^y}$$^z$ dy Where C: x = 4t ; y = 3t$^2$ ; z = 3t$^3$ ; 0$\le$t$\le$1 Any help would be great. Thanks.
0
votes
0answers
7 views

Singular Jacobian in Newton's method

How can we prove that Newton's method for a non-linear system converges linearly (as opposed to quadratically) if the Jacobian is singular at the root? Is this related to being multiple roots at that ...
0
votes
1answer
14 views

Subspace not open of a differentiable manifold

Suppose $M$ is an orientable differentiable manifold with dimension $n$. $U$ is a subspace of $M$. If $U$ is not open, is it true that $U$ also is an orientable differentiable manifold ? I need a ...
0
votes
0answers
7 views

A Extended Euclidean Algorithm related problem

I want to solved the problem in the link : http://uva.onlinejudge.org/external/100/10090.html Someone Solved this in the following way. but I can't understand how he fixed up the value of t. My ...
1
vote
0answers
18 views

Does there exist a positive integer which is a power of two, such that by rearranging it's digits we can get another power of two?

Does there exist a positive integer which is a power of two, such that by rearranging it's digits we can get another power of two? I know a quite good solution, that involves working with sum of ...
2
votes
2answers
34 views

Can the zero vector be an eigenvector for a matrix?

I was checking over my work on WolfRamAlpha, and it says one of my eigenvalues (this one with multiplicity 2), has an eigenvector of (0,0,0). How can the zero vector be an eigenvector?
0
votes
0answers
10 views

When the fibers of a flat morphism are varieties.

Notations: As in Hatshorne's book. Suppose that $f:X\longrightarrow Y$ is a flat morphism between two non-singular projective varieties over an algebraically closed field. Are the fibers of $f$ ...
0
votes
1answer
19 views

Real Analysis Cardinality Proof

I am trying to prove that given a finite set A and an uncountable set B, A and A union B have the same cardinality. I looks to me like I need to show that there is are injective functions from A to A ...
0
votes
0answers
15 views

If the variance is $0$ is it constant?

We know that the variance of a constant is $0$. Is the converse also true? Can we say that if the variance of some random variable is $0$ it is a constant?
0
votes
0answers
6 views

Expected Return, Expected Value, and an Ito Process

I am reading John Hull's "Options, Futures, and Other Derivatives". I am currently in Ch. 31 on the HJM Model. Hull makes a statement which a need an explanation for. First, some notation. Let ...
0
votes
0answers
27 views

Generalizing Mathematical Proof [on hold]

I recently spoke with one of my professors about his method of proofs. He insisted that there is no "for all" algorithm to follow as far as formulating a proof goes, but it seemed to me as though he ...
0
votes
1answer
24 views

A problem related to combinatorics and number theory

$n$ and $m$ are two numbers. We have to make $n$ with $m$ numbers (only taking their sum). For example, if $n=6$, $m=3$, $6$ is formed with $3$ numbers in the following way: $$ 1+1+4=6 \\ 2+2+2=6 \\ ...
1
vote
0answers
14 views

Proper and free action of a discrete group

In Gallot, Hulin, Lafontaine's Riemannian Geometry: Definition Let $G$ be a discrete group, acting continuously on the left on a locally compact topological space $E$. One says that $G$ acts ...

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