# All Questions

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### How does Binary system work in computers

So, this was the closest place I could find, where this was relevant enough to ask it. I'll say up front that I'm not a math guy and I have never been great in it. Yet I've been trying to find answers ...
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Consider a real-valued radom variable X with EX^4=1,we know that EX^3<=1. If also EX<=0,find an constant c<1 such that EX^3<=c and find the smallest constant c for which this inequality ...
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### Two questions about proof in Hilbert Space [on hold]

I am currently studying Hilbert Space in Real analysis, and I have a part not understandable. This is a theorem for Hilbert Space $H$. $Theorem$ : If $L$ is a bounded linear functional on $H$, then ...
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### On the job market and and preparation for a career in applied cryptography [on hold]

I am currently an undergraduate mathematics major at UCLA and have come across a problem: It seems that the field of cryptography, outside of academia, is reserved for those who have studied computer ...
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### Small fractional part of powers of a real number

Let $p$ be a positive real number. For any fixed $\epsilon>0$ does there exist a positive integer $n$ such that fractional part of $p^n$ is less than $\epsilon$? Add-on: $p$ is rational. ...
30 views

### A question about PSL(2，8) [migrated]

Can anybody tell me how to construct the character table of $PSL(2，8)$? I need a specific method.
26 views

### Non-normal subgroup of finite group [on hold]

Is it possible for a group of order 150 to have a non-normal subgroup of order 25? Thanks.
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### Equichordal bodies in $\mathbb{R}^d$

There was quite a bit of work on the so-called equichordal problem throughout the 20th century, to decide if some plane convex curve could have two equichordal points. A point is equichordal if every ...
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### How to firgure out if a set of vectors represent lines, planes or hyperplanes? [on hold]

if i am given a span of, let's say 3 vectors, what would be a way to determine if they represented a line, plane or a hyperplane? i have reduced siad vectors to reduced row echelon form, but don't see ...
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### A calculation over product of Grassmannians

Let $c,d<N$ be integers and consider the product of two Grassmannians $M=Gr(c,N)\times Gr(d,N)$. Define $S\subset M$ to be the set of the pairs $([A_{c\times N}],[B_{d\times N}])$ such that ...
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### Is every symplectic manifold a Hamiltonian reduction of a cotangent bundle?

Today I heard the claim that in practice, all symplectic manifolds that people care about arise as the Hamiltonian reduction of a cotangent bundle $T^{\ast}(M)$ under the action of a Lie group $G$ ...
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### Random circle rotations

Weyl's equidistribution theorem states that the orbit of a point on the circle under rotation by $\alpha$ becomes asymptotically equidistributed with respect to Lebesgue (Haar) measure whenever ...
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### Algorithm proofs [on hold]

so I've got 2 algorithms in pseudocode: ...
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### How do ideal sheaves behave on the special fibers of the projective line over the integers?

Let $X=\mathbb{P}^1_{\mathbb{Z}}$ and $Y\subset X$ be a local complete intersection of codimension two with Ideal sheaf $I_Y$. (I'm mostly interested in the case where $Y$ is a single point $x$ ...
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### dual space of the subspace of the space of probability measures

I have a question which maybe so naive but I want to know the result about it. Let $\mathcal{M}=\mathcal{M}(\mathbb{R})$ be the space of bounded measures. Then by some materiau such as ...
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### $a_{0}$ such that $0<\lim\sup_{n\to\infty}\frac{p_{n+k}-p_{n}}{H_{k}\log^{a_{0}}(\frac{p_{n+k}+p_{n}}{2})}<\infty$

This question is somehow a follow-up from Would the following conjectures imply Cramer's conjecture? Let $g_{n,k}$ denote the quantity $p_{n+k}-p_{n}$, $s_{n,k}$ denote the quantity ...
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### Menon's identity basics [on hold]

this is the problem I'm having. It's pretty basic as you will see but still I hope you can clear this momentary confusion for me seeing that I'm stuck on this for a few hours. Menon's identity says ...
849 views

### Is it worthwhile to give off-topic talks?

I am a graduate student. Occasionally for some reason I am asked to give a talk on my research at a conference whose stated purpose is almost completely unrelated to my research. To preserve my ...
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### Spectrum of Laplacian in non-compact manifolds

What can be said about the spectrum of the Laplace-Beltrami operator on a non-compact, complete Riemannian manifold of finite volume? For example, is the point spectrum non-empty? What would be a ...
29 views

### differentiation of matrix norm [on hold]

Could you please help me how to derive differentiation of the following: d/dW |W - (1/K)a|^2 where || denotes frobenius norm, W denotes M-by-K (nonnegative real) matrix, a = w_1 + ... + w_K (w_k ...
231 views

### In any Lie group with finitely many connected components, does there exist a finite subgroup which meets every component?

This question concerns a statement in a short paper by S. P. Wang titled “A note on free subgroups in linear groups" from 1981. The main result of this paper is the following theorem. Theorem (Wang, ...
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### Strength of claims about extensions of partial preorders and orders to linear ones

Consider these two axioms: Every partial order extends to a linear order. Every partial preorder (reflexive and transitive relation) extends to a linear preorder while preserving strict orderings: ...
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### Measurability of a 'cone'

Let A be a (Lebesgue) measurable set in $\mathbb{R}^n$. Consider the 'cone with base A' $A(1) = \{\alpha x \in \mathbb{R}^n : x \in A, \alpha \in (0,1] \}$. Is B Lebesgue measurable? I assume it is, ...
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### Problem from math logic [on hold]

Is there any idea how this problem can be solved? ∀t,r Ⱶ t < r ∨ t = r ∨ t > r The main method, as far as I know, is to deny two of three unequatations and show the remaining one, but I'm getting ...
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### efficient arithmetic with (short) Conway games?

We consider "games" in the sense of ONAG. Conway's definition of a game $G$ as a pair $G = \{L \mid R \}$ of sets of games, together with the definitions of inequality and the arithmetic operations ...
94 views

### Regular lattice polygons

Suppose I want to construct an $N$-gon in the plane whose vertices are integer lattice points, and which is close to a regular $N$-gon (which means, the ratio of longest to the shortest side is within ...
44 views

### Difference in vector V and V*? [on hold]

I'm stuck on a question regarding two linear maps, one from U to V and the other from V to W. I have to show that something is equal to the map of W* -> U*, but I don't know what the difference ...
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### Fourier Transform of compactly supported $L^1$ functions

Background Given a (translation bounded) positive definite measure $\gamma$ lets say on $\mathbb R^d$, its Fourier transform as a tempered distribution is a positive measure $\widehat{\gamma}$. I am ...
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### how many graphs can be drawn if n vertices ara given [on hold]

If there are n vertices then number of undirected graphs can be defined as nc0+nc1+nc2........ncn. i.e combination of one vertex + combination of two vertices . Can anybody please help me in making ...
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### Inequality involving the side lengths of a quadrilateral

If $a$, $b$, $c$ and $d$ are the four sides of a quadrilateral, the problem is to show that $ab^2(b-c)+bc^2(c-d)+cd^2(d-a)+da^2(a-b)\ge 0$. I've verified it to be true for quite a large number of ...
144 views

### About the trace class operators and their motivation

What is the motivation for trace class operators? Can any body suggest the most general and standard reference that includes Schatten p class operators as well. I have following references ...
97 views

### Spectral measure and Stone's theorem

Let $T$ be an unbounded self-adjoint operator on a Hilbert space and let $E(\lambda )$ be the associated spectral measure and $R(\lambda ) = (T-\lambda )^{-1}$ the resolvent. By Stone's theorem we ...
118 views

### Iwasawa algebra

Suppose $M$ is a finitely generated torsion $Z_p[[T]]$-module; the torsion comes from the $\mu$-invariant part and the $Z_p$-part (the $\lambda$-invariant). Now consider $M/(p)$ and $M[p]$ ...
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### Smooth structures on quotient space

Suppose $G$ be a discreat group acting on $\mathbb R^n$ freely via two different actions $\rho_1$ and $\rho_2$. Suppose that $\mathbb R^n/\rho_1$ is homeomorphic to $\mathbb R^n/\rho_2$. However the ...
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### Problem with understanding an equation

I have read the article Short-wavelength Spectral Properties of the Gravity Field from a Range of Regional Data Sets and I don't know how to interpret Equation (10) on page 630, because this equation ...