0
votes
0answers
3 views

Numerical Laplace Transform

I want to compute the Laplace transform of data vectors. I have tried the usual numerical software and I'm surprised to see that does not have this operation available. I wonder if there is a straight ...
0
votes
0answers
5 views

Does this density limit exist?

Suppose that $T:\mathbb{R}^k\rightarrow\mathbb{R}^k$ is a transformation which is differentiable at a point $x\in\mathbb{R}^k$. Let $\lambda$ be the Lebesgue measure on $\mathbb{R}^k$. Denote by ...
0
votes
0answers
5 views

Regularization of a (divergent) cosine series

What would be a suitable regularized value for the following divergent series: $$ S(y) = \sum_{k=1}^{\infty} \cos(k y) \quad y \in R\\ $$ By way of added context, this series arises from a formal ...
0
votes
0answers
3 views

Spherically wrapped gaussian distribution

I want to rotate a 3D vector by a random angle from a spherically wrapped gaussian distribution, but i dont know what exactly this distribution is?
-2
votes
0answers
10 views

How to derive Int f'(x)[f(x)]dx

Using clear explanations in the form of words and diagrams, explain how the formula for Int f'(x)[f(x)]dx is derived.
0
votes
0answers
4 views

Intersection product of line bundles with $\mathcal{F}$.

I am having trouble with computing the intersection number using the following definition [Ref Vakil Chapter 20]: Suppose $\mathcal{F}$ is a coherent sheaf on $X$ with proper support of ...
0
votes
1answer
8 views

I'm searching cutting points of a central angle of a circumference.

I'm working in a 2D drawing software and I need draw points of the cutting central angle to the circumference. I have a circumference, I know how its center point (2D coordinates), I know the radius, ...
1
vote
2answers
17 views

If $G$ is abelian, it has a subgroup in every order of $|G|'s$ divisors?

Assume that $G$ is an abelian group, I read somewhere that it can be derived from Lagrange's theorem that it has a number of subgroups that is equal to the number of $G$'s divisors. Why does it hold? ...
0
votes
0answers
13 views

Basis of (first de Rham) cohomology: $y^n=f(x)$

Let $K$ be a field, $f(x) \in K[x]$ be a monic polynomial with distinct roots, $\deg(f)=d$. Let $R=K[x,y]/(y^n-f(x))$ and $C=Spec(R)$. $\:\:\;\:\:\:\:\quad$ ($n>1$ integer) What is the basis ...
1
vote
0answers
26 views

Transfering to function when power of the x in power series is odd

Just a little question. When i have even power, it is obvious, for example: $$\sum _{n=0}^{\infty }\:x^{2n}\:=\:\frac{1}{1-x^2}$$ Is it correct to say that (when the power is odd): $$\sum ...
0
votes
1answer
8 views

principal arguement of a complex number. principal argZ1 = a and principal argZ2=b . what will be arguement of (Z1.Z2) when a+b is greater than pi.

principal argZ1 = a and principal argZ2=b . what will be arguement of (Z1.Z2) when a+b is greater than pi.According to me it should be a+b-pi but its given a+b-2 pi .
0
votes
0answers
15 views

Question about the solution to Unexpected hanging paradox

The following is the unexpected hanging paradox: A judge tells a condemned prisoner that he will be hanged at noon on one weekday in the following week but that the execution will be a surprise to ...
2
votes
0answers
8 views

Irreducible components of scheme over the 2-adic integers

Let $X=\mathrm{Spec}\,\mathbb{Z}_2[x]/\langle x^2-1\rangle$, where $\mathbb{Z}_2$ are the $2$-adic integers. What are (the coordinate rings of) the irreducible components of $X$? Here is what I've ...
1
vote
0answers
9 views

Induced representation from subgroup to subgroup

I wonder why the third of the properties of the induced representation here (http://mathworld.wolfram.com/InducedRepresentation.html) holds. Does it follow from the universal property? I could not ...
0
votes
0answers
7 views

Determine probability of better player given indirect measurements

Say you have a two-player game and three, fixed-but-different skill players: A, B and C. Player A only plays against C and player B also only plays against C. You want to to determine if player A is ...
0
votes
2answers
14 views

how do they calculate these following columns

I have these data: I am sorry the data is in Portuguese, and it is an image so I can't convert it to a table but the translate "probably" ( i am not a native speakers for Portuguese language) is: ...
0
votes
1answer
30 views

Closed form for an integral

I am trying to find a closed form for this integral: $\int\limits_{a}^{\infty} \exp(-\frac{b}{x})\exp(-cx)dx$ where a,b,c, are positive constants. Does anyone have any suggestions or can advise? ...
-1
votes
1answer
21 views

$ \frac{\left(\begin{matrix}n \\ r\end{matrix}\right)}{k^n}$

How to calculate large $ \frac{\left(\begin{matrix}n \\ r\end{matrix}\right)}{k^n}$ ,given very large n. Since n is large enough normal methods of calculating $ \left(\begin{matrix}n \\ ...
0
votes
0answers
7 views

Cumulant-Legendre

I have a short question: So suppose $b=\text{ess sup} X<\infty$, where $X$ is a random variable on $\mathbb{R}$. Now take $\Lambda (u)=\ln \mathbb{E}[e^{uX}]$, the cumulant, and ...
2
votes
1answer
18 views

Are there some theorems about the structure of a finitely generated $\mathbb Z[x]$-module?

There is a very clear picture about the structure of any finitely generated abelian groups. Are there some theorems about the structure of a finitely generated $\mathbb Z[x]$-module?
1
vote
2answers
35 views

Indeterminate form $0^0$ using L'hospitals rule when calculating $\lim_{x\to0^+} x^{\sin(x)}$

Given the question $$\lim_{x\to0^+} x^{\sin(x)}$$ I have deducted so far that this has the indeterminate form $0^0$ so I have taken the natural logarithm of both sides to give me: $$\lim_{x\to0^+} ...
2
votes
2answers
29 views

Finding subgroups of $\mathbb{Z}_{13}^*$

I need to find all nontrivial subgroups of $G:=\mathbb{Z}_{13}^*$ (with multiplication without zero) My attempt: $G$ is cyclic so the order of subgroup of $G$ must be $2,3,4,6$ Now to look for ...
0
votes
0answers
8 views

Doubt about about claim about complexity of edge coloring powers of the line graph

Likely I am misunderstanding/missing something, but a claim in a paper appears wrong to me. According to Coloring Graph Powers: Graph Product Bounds and Hardness of Approximation p. 2 Unless ...
6
votes
0answers
13 views

Nodes of the Dynkin diagram for even-dimensional orthogonal groups

I'm reading Wilson's book "The Finite Simple Groups", specifically the sections on the orthogonal groups. In section 3.7.4, he discusses subgroups of the orthogonal groups. The Dynkin diagram for the ...
0
votes
0answers
9 views

Quasi-Banach algebras

We know that the space $Lp(0, 1)$, when $0<p<1$ is quasi-Banach spaces and has a trivial dual; $L_{p}(0,1)^{*}=\{0\}. $But its not algebra. Is there any quasi-Banach algebra with trivial dual? ...
1
vote
0answers
23 views

What is the difference between the slope and the angular coefficient?

What is the difference between the slope and the angular coefficient?
2
votes
1answer
31 views

Proof for the upper bound and lower bound for binomial coefficients.

I have seen the bounds $\left(\frac{n}{k}\right)^k \leq {n \choose k} \leq \left( \frac{en}{k}\right)^k$ for integers $n \geq k >0$ for the binomial coefficient. I can prove the upper bound in this ...
0
votes
1answer
34 views

Inverse function simple question

Please explain question no. c in detail
1
vote
1answer
23 views

Area of “Scalene” rectangles

My friend told me that from antiquity land revenue officials compute area of "reasonably" rectangular ( diagonal no matter) fields to assess tax taking the opposite sides average as .. $$ A = ...
2
votes
1answer
53 views

How do I show $(a, b)$ is incomplete?

If I take the sequence $\{a + 1/n\}$, then it's Cauchy and the limit as $n$ goes to infinity is $a$, which completes the proof. Is this correct? Edit: I doubt this is the right approach because the ...
0
votes
1answer
23 views

Hitting all bins at least once

$m$ balls are thrown at a total of $n$ bins. Each ball will fall into exactly one randomly chosen bin with each throw. What is the probability that each bin is hit at least once (contains at least one ...
0
votes
1answer
13 views

Reversing Rotation + XOR

I have this cypher which is as follows : Take 2 numbers : A=1011 and B=1010 if the ith bit of X is 1 then shift Y* i times to the left. So in the end you will get ...
1
vote
4answers
48 views

A combinatorial proof for $\binom mk$+$\binom m{k-1}$=$\binom {m+1}k$

I do realize that there is a elementary proof of this result which follows from applying the formula $$\binom mk=\frac{m \cdot (m-1) \cdot \ldots \cdot (m-k+1)}{k!}.$$ I do wonder if there is an ...
0
votes
0answers
8 views

Product of a Householder transformation and reflection through the origin in 3 dimensions

This came up doing some research in quantum information. Let us consider two orthogonal three-dimensional unit vectors $v$ and $w$ $v^T\cdot w=0$, and the Householder transformation ...
-1
votes
0answers
15 views

What are principal eigenvectors?

I came across the term principal eigenvectors - what are these? Presumably, they are the largest eigenvectors of a matrix, but I would like to be sure.
6
votes
1answer
38 views

What is the importance of modules in algebraic geometry?

I have been trying to teach myself the basics of algebraic geometry. I understand the basic premise, how we define geometry spaces (algebraic sets and schemes) in terms of commutative rings. And I ...
0
votes
3answers
26 views

Open intervals in $R^1$ is open

I know this question would seem like a duplicate, but I here I provided a proof of the statement I just don't know how to justify certain thing in my proof. Proof: Suppose y is an arbitrarily ...
0
votes
1answer
28 views

Prove that multiplying an elementary matrix to a matrix can produce the same effect as an elementary row operation.

Elementary row operations: 1) Interchange any two rows of the matrix 2) Multiply every entry of some row of the matrix by the same nonzero scalar 3) Add a multiple of one row of the matrix to ...
0
votes
1answer
32 views

performing a power operation ($a^n$) in a ring

In a ring - when performing a power operation, i.e $a^n$, to which operation is it related to? $+$ or $*$? On one hand - I know that a power is defined on multiplication - in "regular" numbers, but ...
1
vote
0answers
18 views

Book similar to Milnor's book

I just finished to read "Topology from the differentiable viewpoint" of Milnor, and for me this was the perfect mathematic book : short, clear with really beautiful results proved at the end. (I'm ...
-4
votes
1answer
36 views

Is every continuous 1-1 function onto? [on hold]

Is it true that every continuous 1-1 function on the interval [0,1] to [0,1] onto?
1
vote
1answer
25 views

Uniform convergency of a two sequence of functions

For, $n\ge 1$ let, $g_n(x)=\sin^2(x+1/n)$ , $x\in [0,\infty)$ and $f_n(x)=\int_0^xg_n(t)\,dt.$ Then, which is(/are) correct ? (A) $\{f_n(x)\} $ converges pointwise to a function $f$ on $[0,\infty)$ ...
1
vote
0answers
12 views

largest distance between vertices on a polyhedron

I have a polyhedron defined by m inequations and n unknowns. I am interested in the largest distance between two vertices (the number of edges I have to follow from one vertex to another). I am ...
1
vote
3answers
38 views

Calculate Infinite Limit

I'm trying to calculate the limit and when I get to the last step I plug in infinity for $\frac 8x$ and that divided by -4 I get - infinity for my answer but the book says 0. Where did I go wrong? $$ ...
0
votes
0answers
10 views

Convergence of Laplace transform and its inverse

There is a sequence of functions $F^{\epsilon}(\lambda)$ which converges to 0 as $\epsilon \rightarrow 0$. Assume that each $F^{\epsilon}(\lambda)$ has a inverse Laplace transform f(s) such that ...
1
vote
0answers
11 views

Conditional probability of a zero inner product

Consider a random $n$ by $n$ matrix $M$ chosen uniformly over all $n$ by $n$ $(0,1)$ matrices and a random vector $v \in \{-1,0,1\}^n$ chosen uniformly as well. Let $X = Mv$. What is $$P(X_i = 0 ...
2
votes
3answers
49 views

$0,1,0,1,0,1$… has only $2$ limit points

Prove that the sequence $0,1,0,1,0,1$... has only $2$ limit points : $0$ and $1$. To be frank, I know the solution to the above particular problem. What I am interested is in knowing a general ...
0
votes
1answer
25 views

Power series representation of gamma function?

I am looking for a power-series expression of the form $\Gamma(z)=b+\sum_{k=0}^\infty a_kz^k$ where the $a_k$ can be calculated as some function of k.
0
votes
1answer
37 views

Solving an exponential function

I have the below exponential function which I wish to solve it for $b$. Other than resorting to the Lambert W function, is there alternative way of representing the solution? $$ \frac{(1+a)(1-b)}{ab ...
0
votes
0answers
11 views

Parameterization of a “concurrent line”

What is a valid parameterization for a general, real intersection of two surfaces: $$ f(x,y,z) = 0, \, g(x,y,z) =0 ? $$ For particular cases we eliminate a coordinate if possible and use the form ...

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