# All Questions

**0**

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8 views

### Counterexample for the Generalized Associativity Equation

The Generalized Associativity Equation is given by
$$ F(G(x,y),z)=K(x,H(y,z)),$$
where the functions $F,G,H$ and $K$ are all from $\mathbb{R}^2$ to $\mathbb{R}$. In his book "Lectures on Functional ...

**0**

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14 views

### Gromov hausdorff convergence

Is the Gromov-Hausdorff limit of a sequence of compact submanifolds of an Euclidean space also in the Euclidean space ?

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7 views

### Is simultaneous diophantine approximation (in a weaker sense) NP hard?

The traditional approach to finding a good simultaneous diophantine approximation is the following: given a set of real numbers $\alpha=(g_1,\ldots,g_d)$, an integer $N$, and a real $\gamma>0$ we ...

**0**

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7 views

### Equivalence classes of (2,3)-pairs in PSL(2,q)

This may not be a research-level question, which is why I submitted it to math.stackexchange first, but so far the question there has barely been viewed, let alone answered. Apologies if submitting it ...

**1**

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**0**answers

10 views

### Number of cyclic difference sets

A subset $D=\{a_1,\ldots,a_k\}$ of $\mathbb{Z}/v\mathbb{Z}$ is said to be a $(v,k,\lambda)$-cycic difference set if for each nonzero $b\in\mathbb{Z}/v\mathbb{Z}$, there are exactly $\lambda$ ordered ...

**0**

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10 views

### Rational mapping related to cubic surfaces

A theorem in Manin's book on cubic forms leads to the conclusion that the least degree of a rational mapping from $\mathbb{P}^2$ to general cubic surfaces(e.g. Picard rank=1) over $\mathbb{Q}$ is 6.
...

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10 views

### First order pde with characteristics

Consider a first order pde of the type $$u_y+b(x)u_x=0$$ and suppose that the coefficient $b$ is not necessairly continuous (for instance with a jump in some point).
Is it still possible to apply in ...

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8 views

### Complexity of an algorithm to solve linear diophantine equations

A friend of mine ask me yesterday a problem, however, the interesting part for me it is not his problem, but what I will ask here.
I want to know the optimal complexity of an algorithm (I mean the ...

**1**

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**0**answers

35 views

### If matrices describe simplices, what do matrix operations describe?

Suppose we are given a $d \times d$ matrix $M$ with rows $m_1, \dots, m_d$.
This matrix describes a simplex, namely the convex closure of the origin with the vectors $m_1, \dots, m_d$.
Now, scaling ...

**1**

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6 views

### Wide cylinders on half-translation surfaces

Take a collection of pairwise disjoint, simple polygons in the plane. Identify pairs of sides between polygons by either a translation in the plane, or, a translation composed with a rotation by ...

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23 views

### Models of BL$\forall$

What results are known about the construction of models for a theory $T$ of the logic BL$\forall$ for languages of higher cardinality? The construction for the countable case relies on
1) The fact ...

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21 views

### Extension of Radon measure

I will mention this specific case,
Let $m_1$ be a (homogeneous) Radon probability measure on $X=\{0,1\}^\kappa$ of Maharam type $\kappa$. As $X$ is zero-dimensional space, so it has an algebra ...

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votes

**2**answers

49 views

### quotient of planar groups

If G is an infinite planar group (it means that it has a generating subset C such that Cay (S, C) is a planar graph) and H is a normal subgroup of it, I would be very grateful if somebody helps me and ...

**0**

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35 views

### Which morphisms of varieties and motives yield isomorphisms of their lower Chow groups?

This question is a contination of Varieties with Chow groups supported in positive codimension: examples and properties?
What examples are known of morphisms of varieties and Chow motives (say, over ...

**-6**

votes

**0**answers

19 views

### Borel function and random variable [on hold]

Positive part of a function X+ is borel function and will be a random variable if X is random variable. I know this things, but how should i prove it mathematically ?

**4**

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**0**answers

39 views

### Bound on the number of lattice points in d-dimensional ball

The following paper states that the number of lattice points in a $d$-dimensional ball of radius $R$ is $V_d R^d + O(R^\alpha)$ where $\alpha = d - 2$ and $V_d$ is the volume of the unit ...

**-3**

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**0**answers

21 views

### Breadth First Search and Depth First Search on Graphs [on hold]

What i would like to know is if it's possible to use these two algorithms on a directed or on a not directed graph and visit every node.From what i've seen it seems impossible to me to visit every ...

**0**

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**0**answers

58 views

### Surjectivity of the algebraic K-functors

Let $R \to S$ be a surjective morphism of commutative rings. For a fixed integer $q$, is there any known condition under which the resulting morphism of the K-groups, $K_q(R) \to K_q(S)$ is ...

**1**

vote

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35 views

### Substitutions and Sturmian sequences

We know that any substitution can generate sequence, for example the Fibonacci substitution:
$\sigma(0)=01, \sigma(1)=0$, then we can define a Sturmian sequence $\omega$, i.e., the fixed point of ...

**2**

votes

**2**answers

122 views

### Standard homology result on double complexes

Suppose you have got a double complex in an abelian category with objects $(A_{rs},d_{rs})$ such that $A_{rs} = 0$ for $r < 0$ or $s < 0$. Suppose furthermore that the rows ...

**6**

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**0**answers

39 views

### Detecting invertible elements in group rings by their images for finite quotients of the group

Let $G$ be a "nice" infinite group: at least finitely presented and residually finite, maybe also linear and right-orderable (or even bi-orderable, or residually free nilpotent).
Consider an element ...

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**2**answers

26 views

### Metric properties of a quadratic differential at an essential singularity

Let $f(z)dz^2$ be a holomorphic quadratic differential on the punctured disk $\{0<|z|<1\}$, which gives rise to a Riemannian metric $g=|f(z)|\,|dz|^2$ and hence a volume form $\nu=|f(z)| ...

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10 views

### singularity of the solution to an integral equation

I consider a function $x\mapsto f(x)$ which is the positive solution to the integral equation
$$\int_{f(x)}^\infty \frac{du}{u^\gamma-x}=1, \quad x\ge 0,$$
where $\gamma\in (1, 2]$ is some ...

**-6**

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**0**answers

20 views

### Graph Theory - Adjacent certices in a simple graph [on hold]

Let u and v be adjacent vertices in a simple graph G. Prove that uv belongs to at least d(u) + d(v) - n(G) triangles in G.

**-4**

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**0**answers

21 views

### Graph Theory - Question on hypercubes and cycles [on hold]

Prove that every cycle of length 2r in a hypercube is contained in a subcube of dimension at most r. Can a cycle of length 2r be contained in a subcube of dimension less than r?

**4**

votes

**2**answers

68 views

### Why is the spectrum of this matrix product invariant with respect to order of the multiplicants?

I've been chewing on the following problem for some time and I just don't have any more ideas how to tackle it. I have matrices $A_1,...,A_k \in \mathbb R^{n\times n}$ and I'm observing that the ...

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16 views

### Bounds on Product of CDF or Beta function

I have functions of the form
\begin{align}
I_i = \int_0^\infty F_0(x)^aF_1(x)^b(1-F_0(x))^c(1-F_1(x))^ddF_i(x)~~~~i = 0,1
\end{align}
$F_0(x)$ and $F_1(x)$ are CDFs corresponding to the random ...

**24**

votes

**8**answers

2k views

### Has philosophy ever clarified mathematics?

I've recently been reading some standard textbooks on the philosophy of mathematics, and I've become quite frustrated that (surely due to my own limitations) I don't seem to be gleaning any ...

**-4**

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**0**answers

38 views

### Normal line, regular surface [on hold]

Let $\mathcal A$ be a regular surface in $\mathbb R^3$ and $P$ a point in $\mathbb R^3\setminus\mathcal A$. Suppose that $C$ is a point at minimum distance from $P$. Show that $P$ belongs to the ...

**1**

vote

**1**answer

67 views

### Ricci flow and conformal classes

Is it true that the conformal class of the metric is preserved under Ricci flow? I have seen it mentioned in an answer on this site. Is there an easy argument?
(This question was asked on MSE but it ...

**0**

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22 views

### computational question concerning singular integral theory

Let $m\in C^\infty(\mathbb{R}^d-\{0\})$ be homogeneous of degree zero and has mean zero on the sphere$(S^{d-1})$. Then $m$ defines a tempered distribution and $\partial_j^dm\in S'(\mathbb{R}^d)$ is ...

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**2**answers

36 views

### Summation mollifier to ensure a certain alternating series has the correct value

I would like the function $f(n,M)$, where $n$ and $M$ are integers and $n\le M$, so that $f$ satisfies the following two conditions:
(1) $\sum_{n=0}^M (-1)^n f(n,M) = \tfrac{1}{2}$
(2) $f(n,M) ...

**1**

vote

**0**answers

13 views

### IVP accuracy - scheme accuracy Vs. derivative accuracy?

General Question: If I have an IVP with periodic and continuous initial condition, which rules the accuracy of the scheme - the manner in which we approximate spatial derivative or the acuuracy of the ...

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38 views

### Reference needed for Hilbert-Schmidt result regarding basis of $V \subset H$

I am seeking a reference that says:
If $V \subset H \subset V^*$ is a Gelfand triple with all spaces Hilbert spaces and if $V \subset H$ is a compact embedding, then there is a basis of $V$ which ...

**2**

votes

**1**answer

34 views

### Bound the degree of the generator of polynomial ring

Suppose we are given two polynomial rings $R_1$ and $R_2$ by presenting their generators, $S_1$ and $S_2$, where $S_i$ are finite set of $m_i$ variables, $i.e.$, $S_i\subset ...

**4**

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**0**answers

109 views

### analogy between connections and $\ell$-adic sheaves: what happens with the residue?

There are many analogies between $\ell$-adic sheaves on varieties over finite fields and vector bundles with connections on varieties over fields of characteristic zero. I would like to know what is ...

**3**

votes

**1**answer

214 views

### Why $( \infty , n)$-categories are useful for?

I know that mathematicians are trying to construct adequate models for $( \infty, n)$-categories. Although, it seems to be an interesting task, I would like to know some explicity examples where this ...

**0**

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50 views

### Vanishing of the module of differentials of a extension of perfect fields

Let $L|F$ be a extension of perfect fields of characteristic $p$, $\phi_F:F \to F_{\phi}$, $\phi_L:L \to L_{\phi}$ the Frobenius isomorphisms ($F_{\phi}=F$ but considered as $F$-algebra via $\phi_F$). ...

**6**

votes

**1**answer

84 views

### Limiting probabilities for two-player game drawing random uniform numbers

Consider this simple 2-person game I just made up:
Player A goes gets to draw a uniform U[0,1] number up to X times. At any time, he may either keep his number, or draw a brand new uniform number. ...

**0**

votes

**1**answer

125 views

### Existence of a rational function on a nonsingular curve with a simple zero at P and order 0 at Q

Let $X$ be a nonsingular curve over an algebraically closed field $k$ (by curve over $k$, I mean an integral separated scheme of finite type over $k$ which has dimension 1). Let $P$ and $Q$ be ...

**-4**

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**0**answers

54 views

### 2d crank-nicolson [on hold]

I require your assistance in creating the system of equations for a 2-dimensional heat diffution equation, using a finite differences crank nicolson scheme. Can you direct me to a solved example, or ...

**9**

votes

**1**answer

112 views

### Hlawka inequality for determinants of positive definite matrices

It is mentioned here that if $A, B, C\in M_{n}(\mathbb C)$ are positive semidefinite, then $$\det (A+B+C)+\det C\ge \det (A+C)+\det (B+C)$$ (quoted from this article) and the special case ($C=\bf 0$) ...

**38**

votes

**2**answers

762 views

### Does one real radical root imply they all are?

Is there an example of an irreducible polynomial $f(x) \in \mathbb{Q}[x]$ with a real root expressible in terms of real radicals and another real root not expressible in terms of real radicals?

**2**

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**0**answers

55 views

### What is the (mixed strategies) equilibrium of this game?

Given a weight vector $w\in [0,1]^d$ such that $\sum w_i=1$, the game goes as follows:
Two players, $X,Y$ choose strategies $x,y\in [0,1]^d$ such that $\sum x_i = \sum y_i = 1$.
The utility (profit) ...

**0**

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**0**answers

32 views

### Is $[u_1,u_2]$ an edge of the polytope $conv(F)$? [on hold]

Here's the problem. I have a finite set of vectors $F \subset \mathbb{Z}_{\geq 0}^d$.
I define $P$ to be the convex polytope $conv(F)$ i.e. the convex hull of $F$.
Given $u_1, u_2 \in F$, is the ...

**5**

votes

**1**answer

94 views

### Modular polynomials for elliptic curves point counting

The Schoof-Elkies-Atkin (SEA) algorithm (for counting points on elliptic curves over a finite field) performs computations over polynomials modulo some modular polynomials. Originally the "classical" ...

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98 views

### On monotonicity of the roots of polynomials

I feel that the question that I am posting is not a general research level question but probably some special form of it where the behaviors of the roots of polynomials are studied.
Here is my ...

**-1**

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**0**answers

53 views

### Colon ideal and Artin-Rees lemma [on hold]

Let $a$ and $b$ be ideals of a Noetherian integral domain $R$. Prove that there exists a natural number $r$ such that $(a^n:b) = a^{n-r}(a^r:b)$ for $n > r$. (homework of nagata's local rings, page ...

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16 views

### Reference for holder estimate on parabolic equation with neumann boundary condition

I saw a type of holder estimate in Friedman's book: partial differential equations of parabolic type(page 200 3.24) as following:
Suppose we have a uniformly parabolic equation with holder ...

**-1**

votes

**0**answers

134 views

### Two Questions on $\pi(x)$ [on hold]

I have recently came to know about this conjecture.
The questions that naturally came to my mind are,
$\forall$ $x,y \geq2$ and $x,y \in \mathbb{N}$ prove that $\pi(x) \pi(y) \leq \pi(xy)$ ...