# All Questions

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5 views

### The coproduct on the 2-boxes space of the goup-subgroup subfactor planar algebras

Let $(H \subset G)$ be an inclusion of finite groups.
Let the subfactor $(\mathcal{R} \rtimes H \subset \mathcal{R} \rtimes G)$ with $\mathcal{R}$ the hyperfinite ${\rm II}_1$ factor, and its planar ...

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14 views

### How do you do e^x*lnx and why?

i was wondering is there an answer for e^x*lnx ? Is there is, how do you do it and what are the steps? Hope you somebody could help me! thank you in advance

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18 views

### Are infinite groups “locally topologizable”?

Does every infinite group admit a Hausdorff topology such that the multiplication and inverse are continuous at $1$ but $1$ is not an isolated point?
The question is inspired by and related to ...

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11 views

### $I$ is principal if and only if $ID_M$ is principal for all $M \in Max(D)$

In a semmi-quasi local domain $D$ ( i.e. $D$ has finitely many maximal ideals),
an ideal $I$ is principal if and only if $ID_M$ is principal for all $M \in Max(D)$.
[See Comm. Rings by Kaplansky, ...

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68 views

### Why calculus textbooks do not include the natural integration constants in the tables of integrals?

The formulas for integrals in the textbooks usually define indefinite integral up to a constant term. Yet the natural integration constant for antiderivative can be fixed from the following formula ...

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23 views

### Proof that $G(3)\le 7$ [migrated]

Let $G(k)$ be the minimal $n$ s.t. every sufficiently large integer is the sum of $n$ nonnegative $k$th powers.
Does anybody know where I can find Vaughan's proof that $G(3)\le 7$? I can't find a ...

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14 views

### An ideal that contained in finitely many maximal ideals but all of its elements contained in infinitely many maximal ideals [migrated]

Is it possible that an ideal I in an integral domain D is contained in only finitely many maximal ideals but each element of I is contained in infinitely many maximal ideals?
I am quit sure that it is ...

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22 views

### Arthur's refinement of parameters for unitary automorphic representations

In his work on the classification of automorphic representations of a group $G$, Arthur has conjectured that the parameterization of such representations involves a homomorphism $\rho : SL_2 \times ...

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53 views

### Is there a hyperplane avoiding two independent sets?

Let $V$ be a vector space over a field with $5$ elements, $A,B \subseteq V$ independent subsets. Must there be a subspace of $V$ of codimension 1 disjoint from $A \cup B$?

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19 views

### Is it possible to use multiple time scale algorithm here?

Suppose a random sequence is being generated (the next term generated depends on the previous term, but we don't know any distribution) until we hit some specific number. We want to calculate the ...

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69 views

### Homology theory represented by Madsen-Tillman spectra

The generalized homology theory of the Thom spectrum $MO=\varinjlim\Sigma^nMTO_n$ is bordism theory:\begin{equation*}\pi_k(MO\wedge X)=\Omega^O_k(X)\end{equation*}is the ring of $X$-cobordism classes ...

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19 views

### The Cayley tranform of a Closed Operator [on hold]

How does cayley transform of a closed operator on a banach space differs from that on a hilbert space?

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19 views

### Orthogonality of the point-wise product of sign-vectors

Consider the mutually orthogonal rows of the row-orthogonal rectangular matrix which is just a collection of +1s and -1s such that there are more +1s than -1s (column-wise). For size=5, we have,
S=
...

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votes

**1**answer

91 views

### An algorithm and symbolic manipulation for IF-THEN-ELSE [on hold]

Q1 Does there exists an algorithm similar to the theorem about parentheses? Or else, could you provide one (make it neat :-) ? (A possible mixture of both IF-THEN and IF-THEN-ELSE constructions ...

**3**

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48 views

### Separation of lattice points on the Mordell elliptic curve

Consider the Mordell equation x^3 – y^2 = k, where x is a non-square positive integer and y^2 is the perfect square nearest to x^3. Noam Elkies (see http://www.math.harvard.edu/~elkies/hall.html) ...

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90 views

### Standard conjectures on positive characteristic

In this MO answer of M. Bondarko, he says:
"the Hodge conjecture implies all the Grothendieck's standard conjectures over base fields of characteristic 0..."
and in Remarks on Grothendieck's ...

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35 views

### target category of extended field theory

An A-S TFT is a functor from $\text{Bord}_{<n−1,n>}(\mathcal{F})$ to $\text{Vect}$ where $\mathcal{F}$ denotes a set of background fields, eg a spin structure. An extended theory is a functor ...

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45 views

### Game on the tree

There's a problem from programming competition which already finished:
http://codeforces.com/contest/458/problem/F
Two weeks already passed but still nobody solved it yet - in fact you can see here ...

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vote

**1**answer

30 views

### When does a hypergraph represent maximal independent sets?

Let $G = (V,E)$ be a simple graph. Then, we can view the set of maximal independent sets (or the set of maximal cliques) as a hypergraph $H = (V, E')$. This is quite a useful device when connecting ...

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**1**answer

239 views

### Who defined and who coined “module”?

The title of my Q. says it all:
QUESTION: Who defined and who coined: module?
Would it be Emmy Noether?
EDIT In view of @anon's and KConrad's answers, and as it could have been ...

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votes

**1**answer

115 views

### How do I find coefficients of a product expansion

Any power series $f(t) = 1 + t \mathbb{Z}[[t]]$ can be uniquely expanded in the following two ways:
$$1 + \sum_{i=1}^\infty f_i t^i =
\prod_{i=1}^\infty (1-t^i)^{-n_i}$$
Here, the $f_i$ and $n_i$ ...

**5**

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93 views

### Who originated the standard symbols for Lie groups GL, SL, SU, etc.?

Who was first to use symbols GL, SL, O, SO, U, SU, Sp and their projective versions, and how did this notation become standard?
The notation appears in fairly modern form in Weyl's "The Classical ...

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**1**answer

28 views

### A possible minimal aperiodic set of corner Wang Tile

From one of my previous question Aperiodic set of corner Wang Tile (although it is put on hold), I realize there is a systematic way to construct aperiodic corner type of Wang tile from edge type ...

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87 views

### Higher Degree Data in a Cosimplicial Quasicategory and Delooping

If there is a short answer to this question and someone can write it here that'd be wonderful, but if it's longer, I'm also perfectly happy with a reference.
My question is regarding accessing data ...

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74 views

### A System of Diophantine Equations [on hold]

$p^2+1=2y^2$
$p+1=2x^2$
$p$ is prime and $x,y$ are integers. I conjecture that this only has solution for $p=7$

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28 views

### Extension of the product formula for valuations to a simultaneous completion

It is well known that $\mathbb{C}$ and $\mathbb{C}_p$ are "algebraically" isomorphic (that is, ignoring the topology), but an isomorphism depends on the axiom of choice and there is no canonical way ...

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29 views

### Toda Flow Embeddings

What are strategies for generating the following types of picture:
Here's what's going on here. Take a toda flow in 3 variables. The equations of motion are:
$$\frac{d}{dt}a_k=2(b_k^2-b_{k-1}^2),$$
...

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vote

**1**answer

127 views

### For a defined set $M$ (see problem) do there exist $a,b$ natural numbers so that $a,ab+1 \in M$

Let $\rho \in \mathbb{R}\setminus \mathbb{Q}$ be a irrational nuber, and
let $\varepsilon>0$ be arbitrarily small. Define $M=\{m \in \mathbb{N}: \exists k \in \mathbb{N}\hbox{ so that} |\rho m -k ...

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153 views

### Continuous relations? [on hold]

What might it mean for a relation $R\subset X\times Y$ to be continuous? In topology, category theory or in analysis? Is it possible, canonical, useful?
I have a vague idea of the possibility of ...

**4**

votes

**1**answer

66 views

### Behavior of the spectrum of the Laplacian under pointed smooth convergence

The Laplacian on a compact Riemannian manifold has a discrete spectrum. For example on a circle of perimeter $L$ the $n$-th eigenvalue starting at $0$ is $-\lambda_n = -(2\pi/L)^2 n^2$.
On the other ...

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**4**answers

131 views

### Approaching convex and discrete geometry from other disciplines

I would like to learn some convex and discrete geometry (number 52 in MSC2010). I thought that it would be interesting to approach it from some other parts of mathematics - either by learning ...

**2**

votes

**1**answer

86 views

### Nearby cycles and specialisation - properties

I am looking for reference for properties of nearby cycles - specifically, commutation with non-characteristic pull-back (good enough - commutation with pull-back to closed subvariety which is ...

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vote

**2**answers

121 views

### Plucker embedding and tautological/universal quotient bundle

Let $G$ be a Grassmannian and $Q$ the tautological/universal quotient bundle of $G$. As far as I understand, the associated tautological quotient line bundle for the Plucker embedding of the ...

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110 views

### A lifting problem

Let $E\overset{\pi'}{\longrightarrow} B'$ and $E\overset{\pi}{\longrightarrow} B$ be vector bundles.
For $i=0,1$, let $f_i$ be a fiber-preserving open embeddings of $\pi'$ into $\pi$, with $g_i$ the ...

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votes

**1**answer

93 views

### Torsion-free group that is not of type F but is virtually of type F

Recall that a group $G$ is of type F if there exists a compact $K(G,1)$.
There are many examples of groups which are not of type F but which are virtually of type F, that is, they have finite-index ...

**3**

votes

**1**answer

49 views

### Reference for Elliptic PDE on $\mathbb{R}^d$

Could anyone suggest a textbook, article, or lecture notes that covers elliptic PDE theory (existence, uniqueness, regularity) on all of $\mathbb{R}^d$, as opposed to the Dirichlet or Neumann problem ...

**3**

votes

**1**answer

27 views

### Eigendecomposition of analytic Hermitian matrix-valued functions of several variables

If $A(t)$ is an analytic, Hermitian matrix-valued function of a real variable $t$, then it is known that there are analytic functions $\lambda_i(t)$ and $x_i(t)$ corresponding to the eigenvalues and ...

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55 views

### Quantifier problem of equations in physics [on hold]

Equations in physics are often written without quantifiers. For instance, from time to time we can see the equation
$$E = mc^2$$
is casually written down.
To assert that static energy equals mass ...

**5**

votes

**1**answer

126 views

### Is the sequence of Apéry numbers a Stieltjes moment sequence?

Consider the sequence of Apéry numbers
$$
A_n = \sum_{k=0}^n \binom{n}{k}\binom{n+k}{k}\sum_{j=0}^k \binom{k}{j}^3
= \sum_{k=0}^n \binom{n}{k}^2\binom{n+k}{k}^2 .
$$
In an email, physicist Alan Sokal ...

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70 views

### Group action induced on homology under change of coefficients

Let $M$ be a closed manifold equipped with a (continuous or smooth) $\mathbb{Z}_2$-action such that - for simplicity - both $H_{k-1}(M;\mathbb{Z})$ and $H_{k+1}(M;\mathbb{Z})$ are zero for some ...

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28 views

### Maximizing the “uniformity” of a probability measure, with constraints, via path length minimization

I want to find a probability measure for a continuous random variable, subject to moment constraints, that is maximally "uniform", as defined below:
Definition: Maximally Uniform Probability ...

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102 views

### Operator norm vs spectral radius for positive matrices

I believe the following statement should be true but somehow I don't see an argument:
For every integer $d>1$ there exists a constant $C=C(d)>1$ such that whenever $A$ is a $d \times d$ matrix ...

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57 views

### Semidirect products with braid groups and type $F_\infty$

Let $F$ be a group which is strongly type $F_\infty$ in the sense that every subgroup is of type $F_\infty$. Here, type $F_\infty$ means that the group admits a classifying space with compact skeleta.
...

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93 views

### Without Skolem–Mahler–Lech Theorem? [on hold]

Using Skolem–Mahler–Lech theorem one can easily prove the $\displaystyle \lim_{n\to +\infty}\left|\Re\left(\frac{1+i\sqrt{7}}{2} \right)^n\right| =+\infty$.
Is there a "simple way" to prove this ...

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16 views

### Mixed Integer Quadratic Programming using Opti Toolbox in MATLAB [on hold]

I wish to solve a mixed integer quadratic program with linear constraints using OPTI toolbox in MATLAB. I want some of my decision variables to be continuous and some decision variables to be binary. ...

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vote

**1**answer

32 views

### Converting Dirichlet boundary conditions for E-L equations on a Lie group into an equivilent condition for EP equaiton

I need to find a specific geodesic of a right invariant Finsler geodesic on a Lie group ($SU(n)$) that connects $I$ to some desired $O$. These are Dirichlet boundary conditions for the E-L equations ...

**2**

votes

**1**answer

48 views

### Find base of kernel with as many 0 as possible

I have a 400x132 rectangular matrix with only 0 and 1.
I am looking for the linear combinations of the columns of the matrix that sum to 0.
For example C1 + C2 - C3 = 0.
I want to find the linear ...

**2**

votes

**2**answers

47 views

### Proof the solution of von Neumann equation will fluctuate forever if Hamiltonian and initial density matrix does not commute

Given von Neumann equation
$$\frac{d}{dt} \rho(t) = -i [H, \rho(t)] = -i e^{-iHt}[H, \rho(0)]e^{iHt}.$$
If we know that $[H, \rho(0)] \neq 0$, how do we prove that the solution will fluctuate ...

**2**

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37 views

### Linear transformation of a polyhedral cone

Let $C$ be a polyhedral cone in $\mathbb{R}^m$ with H- and V-representations
$C = \{x : A x \le 0 \} = \{R y : y \ge 0\}.$
The pair $(A,R)$ is referred to as a double description (DD) pair of the ...

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124 views

### concepts in fields other than physics and computer science which touch on concepts that are fundamental in pure mathematics [on hold]

[ Contextual Information:
Is mathematics held back by it's relative lack of ties to disciplines other than physics and computer science? Are there areas of mathematics which have gone underexplored ...