# All Questions

**-2**

votes

**0**answers

25 views

### mathematical modelling question [on hold]

You are asked to help with a sociological study on the survival of surnames.Consider a closed community with N individuals at time t=0 with K different surnames.Assume that all children of any ...

**0**

votes

**0**answers

17 views

### Solution to a system of linear equations containing some inequalities [on hold]

I have a system of equations as follows:
$a_{11}x_1 + a_{12}x_2 + a_{13}x_3 = b_1$
$a_{21}x_1 + a_{22}x_2 + a_{23}x_3 = b_1$
$a_{31}x_1 + a_{32}x_2 + a_{33}x_3 < b_1$
$a_{41}x_1 ...

**-1**

votes

**0**answers

78 views

### Fermat's little theorem question [on hold]

I'm studying Number theory (in my spare time) and I need to prove a lemma in order to prove the exercise. The topic is Fermat's little theorem.
Well the lemma goes like this:
Let's say we have ...

**2**

votes

**1**answer

157 views

### Simplicial version of the A-infinity operad

I am looking for a description of the $A_\infty$ operad in the category of simplicial sets. More specifically, I am looking for a formulation of the loop space recognition principle for simplicial ...

**-1**

votes

**0**answers

58 views

### A combinatorial and number theoretical problem [closed]

Given N positive integers, not necessarily distinct, how many ways you can take 4 integers from the N numbers such that their GCD is 1.
For example,N=10 and the positive integers are ...

**-2**

votes

**0**answers

116 views

### Does any one know what this problem is called? [on hold]

We are given finite sets A and B and a set S⊆P(A). The members of S may have arbitrary intersections with one another and their union is not necessarily A. We wish to determine whether there is a ...

**-2**

votes

**0**answers

30 views

### How to calculate a sequence in Maple [closed]

Please how can I using Maple obtain the following sequence defined successively
$$X_1=1,\quad X_k=\Big(\frac{1/k+\sum_{i+j=k}X_i X_j}{k^2}\Big)^{1/2}$$
here $i,j,k\in\mathbb {N}$
i wish to have ...

**-5**

votes

**0**answers

34 views

### Diffusion Equation [closed]

Kindly give me suggestions on my following assignment of Simulations in Fluid Flow:
Solve the following differential equation for transport of f(x,y,z,t) by MS Excel
∂f/∂t+Ux ∂f/∂x+Uy ∂f/∂z+Uz ...

**-4**

votes

**0**answers

28 views

### Find the vector component of vector u orthogonal to vector a [closed]

I have vector u = (-2, 3, 1) and vector a = (-2, 2, 2). How do I find the vector component of u orthogonal to a?
I've done the cross product and I get (-4,-2,-2), but I am assuming that this is also ...

**0**

votes

**0**answers

46 views

### Integrate Faddeeva function

I came across this integration in my studies.
$\int_{-\infty}^{\infty}|F((w_\textbf{_} - \hat{w_\textbf{_}})\tau) |^2 . d\tau$
It uses the Faddeeva function which is $F(z) = e^{-z^2}erfc(-iz)$. I ...

**2**

votes

**0**answers

57 views

### What is the computational complexity to compute the integral numerically?

Given $$\int_{\Delta}\frac{P_1(x_1,x_2,\dots,x_n)}{P_2(x_1,x_2,\dots,x_n)}$$ where $P_i$ is polynomial(that is $P_1(x_1,x_2,\dots,x_n), P_2(x_1,x_2,\dots,x_n)$ are polynomial) whose coefficients are ...

**2**

votes

**1**answer

117 views

### A perfect $(n,k)$ shuffle function

Suppose you have a deck of $n$ cards; e.g., $n{=}12$:
$$
(1,2,3,4,5,6,7,8,9,10,11,12) \;.
$$
Cut the deck into $k$ equal-sized pieces, where $k|n$;
e.g., for $k{=}4$, the $12$ cards are partitioned ...

**-2**

votes

**0**answers

124 views

### how to solve 3 6-degree polynomial equations for 3 variables? [on hold]

I am a physicist and need to solve three $6$-order polynomial equations for $3$ unknowns $(p, q, r)$. Here is the system of equations looks like:
$$\sum(A[n]*p^i*q^j*r^k) = 0,$$
...

**0**

votes

**0**answers

57 views

### Parallel topologies on a Prüfer group with the trivial group topology as the only group topology contained in both

Let $p$ be a prime number. A homomorphism $f:\Bbb Z_{p^\infty}\to \Bbb T$ induces a group topology $\mathcal T_f$ on $\Bbb Z_{p^\infty}$ with a base of neighborhoods $\mathcal N_f$ of $0$.
Are there ...

**5**

votes

**1**answer

272 views

### Groups with a unique composition series

Which finite groups $G$ have a unique composition series? I don't mean in the sense of the Jordan-Holder theorem, but rather actually unique.
Some examples are the cyclic groups $C_{p^n}$ and the ...

**6**

votes

**1**answer

88 views

### Injectivity of Rewrite Rule in a Free Lie Algebra

Let $L$ be a free Lie algebra (over $\mathbb{Q}$) on generators $x_1, x_2, \ldots, x_n$, and let $V_k$ be the subspace spanned by the $k$-fold brackets. Let $U_1 = \mathrm{span}\{ x_i | i< ...

**2**

votes

**0**answers

76 views

### Galois group for 0-dimensional motives

$\newcommand{\M}{\mathcal{M}_0}$$\newcommand{\Q}{\mathbb{Q}}$
It is my understanding that in dimension 0, the theory of motives should just be Galois theory for fields. I am hoping to find a reference ...

**4**

votes

**0**answers

214 views

### If 2-manifolds are homeomorphic and smooth, are they diffeomorphic? [closed]

Perhaps this question has already been asked on Mathoverflow. I mean this question in a global sense. A friend mentioned it to me today, and I started thinking about it. I'm not sure how to prove it. ...

**-1**

votes

**0**answers

40 views

### A fredholm index associated with two vector fields generating a 2 dimensional foliation

Let $M$ be a compact manifold and $X,Y$ be two independent vector fields on $M$ with $[X,Y]=0$. Let $\mathcal{F}$ be the 2 dimensional foliation associated with the distribution ...

**-7**

votes

**0**answers

90 views

### Does anyone want to see the critical figure for n= 7? [closed]

I watched Ronald Lewis Graham's youtube blurb for the "happy ending problem". it's about 5 minutes long. I was able to supply him with the positions of the points for the case: n=7. it looks like a ...

**4**

votes

**2**answers

158 views

### Relation between Turing degrees and functions computable with them

Suppose $A<_T B$ ($A$ is a set computable from $B$ but not vice versa). Is it always the case that there exists a $B$-computable function which eventually outgrows all $A$-computable functions?
Of ...

**4**

votes

**0**answers

78 views

### $A_\infty$ structure on sum of twists of structure sheaf

Fix $n$ and let $P^n$ be projective $n$-space. Let $S = k[x_0, \dots, x_n]$. Set $A^0 = \bigoplus_{d \ge 0} H^0(P^n, \mathcal{O}(d))$ and $A^n = \bigoplus_{d < -n} H^n(P^n, \mathcal{O}(d))$.
I ...

**4**

votes

**2**answers

233 views

### Powers of finite simple groups

I have heard about the following result: for each finite simple non-abelian group $S$ and each natural number $r\ge 2$ there exists a number $n=n(r,S)$ such that the power $S^n$ is $r$-generator but ...

**1**

vote

**0**answers

54 views

### Measurability of solution of diffusion equation in sub sigma algebra

I want to solve the following problem:
Get $\omega \in \Omega \subset \mathbb{R}$, $x \in D \subset \mathbb{R}^2$ and $0<a_i\leq a(.,.)\leq a_x<\infty$.
Let $a( x;. )$ and $f(x;.)$ be ...

**3**

votes

**0**answers

136 views

### Log schemes, differentials, Beilinson

Let $K$ be a $p$-adic field and $K'$ be a finite extension of $K$. Let $\Omega_{(K',\mathcal{O}_{K'})}$ be the sheaf of relative log differentials of the pair $(K',\mathcal{O}_{K'})$ over ...

**11**

votes

**2**answers

279 views

### Is the Amitsur-Levitzki identity essentially unique?

Let us consider the matrix algebra. $Mat_n(\mathbb{C})$. The Amitsur-Levitzki identity states that for any matrices $X_1, X_2, ..., X_{2n} \in Mat_n(\mathbb{C})$ the sum $\Sigma_{\sigma \in S_{2n}} ...

**-2**

votes

**0**answers

37 views

### Summation with 2 functions [closed]

Solve for $L$ if you can please. I want to know how to solve $G(x_i,y_j)$ with double integration, where $G=(x-y)$. The equation is below as follows:
$L=\sum\limits_{i=1}^2 $ $\sum\limits_{j=1}^2 ...

**-3**

votes

**0**answers

47 views

### Find a prime when some primitive roots are given [closed]

p is a prime. some primitive roots modulo p are 2, 3, 5, 7, 11. How can I find p?

**1**

vote

**2**answers

251 views

### Notion of manifold curvature?

Consider a particular embedding of a $C^2$ manifold $\mathcal{M}\subseteq\mathbb{R}^m$. Given $p\in\mathcal{M}$, suppose $\epsilon>0$ is small enough that the portion $U$ of $\mathcal{M}$ which is ...

**3**

votes

**4**answers

262 views

### Continuity in Banach space for non-linear maps

I want to find an example of a Banach space $X$ and a continuous map $f:X\rightarrow X$ such that $f$ is not bounded on the unit ball. I do not doubt that such an example exists, but I cannot make it ...

**-2**

votes

**1**answer

77 views

### how to reduce 3-colorable graph to this? [closed]

suppose we have a finite set X and a set S of subsets of X and we want to determine is there a subset S' of S such that all members of X belong to exactly one set in S' I think the best problem to ...

**2**

votes

**1**answer

95 views

### Norm of swapped power series in the unit disk

Suppose $f(z)=a_0+a_1z+\cdots+a_nz^n+\cdots$ is defined in the unit disk and $\|f\|_{\infty}\leq 1.$ Lets form another series $g$ by interchanging $a_1$ and $a_k$ i.e. ...

**1**

vote

**0**answers

259 views

### Testing the faithfulness of group homomorphisms by testing on the level of induced Lie Algebras

Let $G$ be a group and let $\Gamma_G(k)$ be the $k$th term of the
lower central series of $G$. For each $k\geq 1$, set
$\mathrm{gr}_k(G)=\Gamma_G(k)/\Gamma_G(k+1)$ and
...

**0**

votes

**0**answers

11 views

### matching Robinson-Foulds distance and way to compute RF dist in Phylip

In Comparison of Phylogenetic Trees, Robinson D.F. and Foulds L.R., didn't show how to compute the RF distance between trees, counting the different partition generated by the removing of an internal ...

**4**

votes

**0**answers

67 views

### Trying to understand straightening functor associated to a right fibration of simplicial sets

Let $p:X \to S$ be a right fibration of simplicial sets; one can roughly think of it as some sort of "functor" $S^{op} \to Set_\Delta$ (where $Set_\Delta$ denotes simplicial sets) sending $s \in S$ ...

**0**

votes

**0**answers

92 views

### E- and A-algorithms for finite arithmetic prime progressions and other sets

There is certain Eratosthenes spirit to my problem (See below). First of all I'd like to stress the mathematical aspect of my question. Also, my question does not amount to the divide and conquer ...

**2**

votes

**1**answer

56 views

### Calculating the “Belvedere Hull” of a Simple Planar Polygon

As an informal motivation the problem, imagine a tower with polygonal footprint, that is located in a beautiful landscape, the "Belvedere Hull" is then related to the directions, in which one would ...

**3**

votes

**0**answers

116 views

### Donsker's Theorem for triangular arrays

I should mention that I already posed this question on Math Stack Exchange, but didn't receive much feedback.
Assume we have a sequence of smooth i.i.d. random variables $(X_i)_{i=1}^{\infty}$. Given ...

**-5**

votes

**0**answers

34 views

### Help to write the generating function [closed]

How do I write the generating function and the closed for form the generating function
The sequence is
0 0 0 1 1 1 1 1 1
Is this correct?
A(x) = 0+0x+0x^2+1x^3+1x^4+1x^5+1x^6+1x^7+1x^8
This is ...

**2**

votes

**0**answers

64 views

### Restricted singular values of random matrix

Let $X \in \mathbb{R}^{p\times p}$ be a large square matrix, consisting of i.i.d. Gaussian entries. Then it is known that the singular values of $X$ follow the Marchenko-Pastur law.
Now let's ...

**1**

vote

**0**answers

121 views

### Finding an overgroup or a subgroup in PGL

Let k be a nonperfect field of characteristic $2$. Let $a\in k\backslash k^2$, $G=PGL_4(k)$ and and $$H= \left\{ \small\left[\begin{array}{cccc}
x ...

**3**

votes

**0**answers

77 views

### Partitions with each part dividing the original number

I have a question on partitions that I have not seen being discussed. It deals with those related to divisors.
My definition of partitions I am working with is as follow: a sequence of weakly ...

**4**

votes

**0**answers

162 views

### Unitary representations of Tarski Monsters and other beasts

Did people study the unitary representations of Tarsky Monsters, for example the ones constructed by Ol'shanskii? Are there any exotic representations, ie. except the ones related to the left regular, ...

**-2**

votes

**0**answers

43 views

### when a given graph is 3-colorable? [closed]

I want to use graph 3-colorability to prove a problem is NP-complete But I'm not sure when a given graph is 3-colorable.
I think if it doesn't have any node to be connected to all 3 vertices of a ...

**-1**

votes

**0**answers

19 views

### Calculate point P(x,y) in a circle given a radius and angle degree [closed]

I'm doing a program in Java to draw a PieChart based on given value as link below.
data for piechart
Given that the diameter, radius, angle degree, center point (150,150) and First Point A (150,0) ...

**2**

votes

**0**answers

75 views

### Is this a generic $L$-parameter?

I am wondering if some local $L$-parameter of the unitary group is generic or non-generic parameter. Let me introduce my $L$-parameter I have.
Let $E/F$ be a quadratic extension of number fields and ...

**0**

votes

**2**answers

160 views

### Computing the nonsingular projective model of a plane curve

Is there an implemented algorithm available in standard software systems (Sage, Magma, Macaulay, etc.) that will compute the nonsingular projective model of a plane curve over $\mathbb Q$?

**4**

votes

**1**answer

146 views

### When does $\mathbf{Top}/X$ embedd fully faithfully into $\mathbf{Top}$?

Under what conditions on the topological space $X$ is the overcategory $\mathbf{Top}/X$ of topological spaces over $X$ equivalent to a full subcategory of $\mathbf{Top}$? Surely if $X$ terminal i.e. a ...

**0**

votes

**0**answers

136 views

### Rational multiple of a line bundle

In the paper http://arxiv.org/pdf/1207.5011.pdf of Chi Li and Song Sun, they say that "$D$ is a smooth divisor which is $\mathbb{Q}$-linearly equivalent to $−\lambda K_X$ for some $λ \in \mathbb{Q}$", ...

**-1**

votes

**0**answers

39 views

### How can i simplify the sum of modified partial bell polynomials [closed]

I am trying to prove my conjecture that uses partial bell polynomials as well as modified partial bell polynomials. Putting these bell polynomials into a workable form is a huge problem for me. The ...