# All Questions

**0**

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3 views

### Which algorithm is most efficient for a specific QP problem

I have a QP problem of the following kind:
$\min_{\alpha\in\mathbb{R}^n}\frac{1}{2}\alpha^T M \alpha - p^T\alpha$
s.t. $l\leq \alpha \leq u$
The matrix $M$ is symmetric and positive definite and of ...

**0**

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8 views

### Does there exist an Affinization or Projectivization process for Varieties?

Let us consider the classical isomorphism of real manifolds between $S^2$ and ${\mathbb CP}^1$. First strange thing we have here is that both are varieties, but $S^2$ is an affine and ${\mathbb CP}^1$ ...

**1**

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12 views

### Find a subset such that its sum is divided by n

It is said that the following proposition is true.
$\forall S \subset \mathbb{Z}, |S| = 2n-1.\ \exists A \subset S, |A| = n$ which satisfies
$$
n \ | \ \sum_{a \in A}a.
$$
Could someone gives a ...

**1**

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**0**answers

29 views

### Why do we study symplectic geometry?

What is the motivation behind studying smooth manifolds with non-degenerate closed two-forms?
I am trying to learn the subject and find it hard to find motivation. Is there a reason that ...

**0**

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**0**answers

38 views

### Which varieties are flat degenerations of projective space?

Let $V$ be a vector space over a field with discrete valuation and let $R$ be its ring of integers.
Which varieties can be reached as the special fiber of a flat degeneration over $R$, when the ...

**-4**

votes

**0**answers

10 views

### Good estimates on the truncation of the exponential series. [on hold]

What are the good (analytic) upper bounds we have on the series $\sum_{k=D}^\infty \frac{a^k}{k!}$ in terms of $a$ and $D$?

**0**

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32 views

### Monodromy theorem of degeneration of smooth projective varieties to non-reduced central fiber

Given a family $\pi: \mathcal{X}\rightarrow\Delta$ smooth away from $0\in\Delta$, Where $\mathcal{X}$ is a smooth complex manifold, $\Delta$ is a small disk, the general fiber of $\pi$ is smooth ...

**2**

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26 views

### Norm vs A-norm in non-Archimedean Functional Analysis

Let $K =(K,| \cdot |)$ be a non-Archimedean valued field.
Let $E$ be a $K$-vector space. A norm on $E$ is a map $||\cdot||:E\to[0,\infty)$ such that:
$||x||=0$ if and only if $x=0$,
$||\lambda ...

**0**

votes

**0**answers

14 views

### Looking for examples of large hyperbolic two-generator knots or 3-manifolds

We say a knot $K$ in $S^3$ is small if its exterior contains no closed properly embedded incompressible surfaces and we say $K$ is large otherwise.
Does anyone know of an example of a large ...

**2**

votes

**1**answer

80 views

### Is there a bijection $f: N \times N \rightarrow U \subset N$ with $f(x,y)+f(u,v)=f(x+u,y+v)$ and $f(x,y) \cdot f(u,v)=f(x \cdot u, y \cdot v)$?

Is there a subset of natural numbers that has the same additive and multiplicative structure as the set of ordered pairs of natural numbers under the classical operations of addition and ...

**0**

votes

**0**answers

53 views

### Spectral theory of $\frac{\partial ^2}{\partial x^2} + \frac{\partial ^2}{\partial y^2}$ and $4 \frac{\partial ^2}{\partial z\partial \bar{z}}$ [on hold]

Since $\mathbb R^2 \simeq \mathbb C$ and $\frac{\partial ^2}{\partial x^2} + \frac{\partial ^2}{\partial y^2} =4 \frac{\partial ^2}{\partial z\partial \bar{z}}$, I like to know is that the spectral ...

**-3**

votes

**0**answers

18 views

### How to make Markov Chain model from sequence of data using MATLAB? [on hold]

I have a sequence and from that I have to make Markov Chain Model in MATLAB. Markov Chain model considers only 1-step transition probabilities i.e. probability distribution of next state depends only ...

**3**

votes

**1**answer

170 views

### what is the universal cover of GL(2,R)?

In the theory of Bridgeland stability conditions one has an action of the universal cover $G'$ of $G = GL^+(2,\mathbb R)$.
What is G'?
I know there is concrete description in terms of pairs ...

**0**

votes

**0**answers

70 views

### Canonical model on Kontsevich's moduli space

Motivation: Work of Eisenbud, Harris, and Mumford shows that
$M_g$ is of general type when $g≥24$. What about Kontsevich's moduli space?
Let $X$ be a smooth complex projective Calabi-Yau manifold, ...

**5**

votes

**2**answers

235 views

### Can the topological algebra of analytic functions be endowed with a norm that defines the natural topology?

Right, so in my research in complex analysis I was puzzled by this question which may have a simple approachable answer that eludes me, but I am truly itching to find out and in need of it so I am ...

**1**

vote

**0**answers

62 views

### More generalized RSA construction

Is there a way to construct RSA type cryptosystem over general number rings? Can Number Field Sieve technique be applied here?

**-5**

votes

**0**answers

72 views

### When and why did this happen: ${1,2,3} \neq {1,3,2}$? [on hold]

Formerly, there was a clear distinction between $(1,2,3)$ and $\{1,2,3\}$, and only the former indicated order. Now, in Mathematica and elsewhere, $\{1,2,3\} \neq \{1,3,2\}$. Also, a sequence was ...

**1**

vote

**0**answers

13 views

### Determine existence of matroid with some barrier given

Let $E$ be a finite ground set. Let $\mathcal{L}$ (as lower barrier) and $\mathcal{U}$ (upper) be subsets of $2^E$. How can we determine whether there is some matroid $\mathcal{M}=(E,\mathcal{I})$ ...

**1**

vote

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27 views

### Notation to denote substitution of vector elements [duplicate]

I'm looking for notation to denote vector substitution and elimination of elements. This is possible using set notation, but I am looking for shorthand notation that is perhaps already in use.
...

**-3**

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**0**answers

44 views

### Does it make sense to compare sets (polytopes) with different dimensions? [on hold]

In the context of integer programming, I am considering 3 different linear models for a given problem. The goal is to determine which formulation is the tightest, that is, the one whose polytope is ...

**1**

vote

**1**answer

42 views

### A question related to the semisimplification of a Weil-Deligne representation

I have been trying to find the answer to this question, I think it must not be hard but I don't get it.
I have a Weil-Deligne representation ($\rho,N$) of the Weil group $W$ of $Q_p$, that is $\rho$ ...

**-6**

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**0**answers

29 views

### Anyone else here believe entangled particles create mini wormholes? [on hold]

The properties of their interactions are a little too similar to ignore. Entangled objects ability to align regardless of distance. Their ability to align seemingly even before the other is viewed. ...

**4**

votes

**0**answers

134 views

### Deligne's theorem on the characterisation of Tannakian categories

I am trying to understand the proof of the Theorem 7.1 from Catégories Tannakiennes by Pierre Deligne https://publications.ias.edu/sites/default/files/60_categoriestanna.pdf.
Essentially, it is ...

**0**

votes

**2**answers

40 views

### Shortest path in a weighted graph with coloured edges

I have a weighted undirected graph with $N$ veritces and $M$ edges with 10 different colours in the whole graph. Each time I pass edges of different colour I have to pay additional fee equal to $K$. ...

**1**

vote

**0**answers

39 views

### Does a homotopy sphere that bounds a highly connected manifold also bound a parallelizable manifold?

Suppose that the homotopy sphere $\Sigma^{n}$ can be realized as the boundary of a smooth $(n+1)$-dimensional cobordism that is $(n-1)/2$-connected for $n$ odd (respectively, $(n-2)/2$-connected for ...

**3**

votes

**2**answers

157 views

### Equivalence of different cohomology groups

Let $X$ be a topological space (may be assumed to be locally compact). Let $A$ be either a field or $\mathbb{Z}$. One can consider various cohomology groups:
(1) singular cohomology ...

**3**

votes

**0**answers

43 views

### Two notions of bundle of C* algebras

One can find in the literature two notions of $C^*$-algebra over a topological space $X$.
The first is as the data of an open surjection $ \pi: B \rightarrow X$ together with the structure of a ...

**1**

vote

**0**answers

21 views

### The decay rate of the spectrum of the Gaussian kernel on compact manifolds

It seems that the $k^{th}$ largest eigenvalue of the intergral operator induced on $S^n$ by the Gaussian kernel, $e^{-\frac{\vert \vec{x} - \vec{y} \vert _2^2}{2\sigma^2}}$ decays as $k^{-k}$. This is ...

**0**

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**0**answers

12 views

### Equivalence classes on an ordered Bratteli diagram

Let $S$ be the adic transformation preserving a probability measure $\mu$ on the set $\Gamma$ of infinite paths of a $\mathbb{N}$-graded ordered Bratteli graph.
For every $n \geq 0$ define the ...

**10**

votes

**1**answer

242 views

### Banach-Mazur distance between the cube and the octahedron

The Banach-Mazur distance $d(X, Y)$ between two normed spaces $X, Y$ of the same dimension is defined as $d(X, Y) = \log\inf \|T\| \cdot \|T^{-1}\|$, where the $T:X \to Y$ is a linear and invertible ...

**5**

votes

**0**answers

32 views

### Which graphs embedded in surfaces have symmetries acting transitively on vertex-edge flags?

A vertex-edge flag in a graph is a vertex together with an edge incident to that vertex. Given a graph $\Gamma$ embedded in a compact oriented surface $S$, when does the group of homeomorphisms of ...

**1**

vote

**0**answers

33 views

### Lower bound for the $C^*$-unitisation norm?

Let $A$ be a $C^*$-algebra without unit. Its unitisation $A^+$ carries the $C^*$-norm
$$\|(a,\lambda)\|_{A^+} = \sup \{\|ax+\lambda x\|_A \;\big|\; \|x\|_A = 1 \},$$
which is the operator norm of ...

**2**

votes

**0**answers

49 views

### Sections of a linear system splitting as a product of degree one polynomials

Let $X\subset\mathbb{P}^n$ be a hypersurface of degree $d$ and with multiplicities $m_1,...,m_k$ at $p_1,...,p_k\in\mathbb{P}^n$ general points.
Let $S\subseteq |\mathcal{O}_{\mathbb{P}^n}(d)|$ be ...

**0**

votes

**0**answers

18 views

### Regularity of a Dirichlet form

I have a question about Dirichlet form.
Let $\Omega$ be an Euclidean domain of $\mathbb{R}^{N}$ and
$X=\bar{\Omega}$. The measure $m$ on the Borel
$\sigma$ algebra $\mathcal{B}(X)$ is given by ...

**4**

votes

**1**answer

122 views

### A finiteness property for semi-simple algebraic groups

Let $G$ be a semi-simple algebraic group over a field $K$, I am considering a question about whether there exists a finite set of semi-simple $K$-subgroups, say $H_1,...,H_r$, such that for any ...

**2**

votes

**0**answers

73 views

### Modified Jacobi’s theta function

Be $t\in\mathbb{R}_0^+$.
Jacobi’s theta function is $$\Theta(t):=\sum\limits_{k=-\infty}^{+\infty} e^{-\pi k^2 t}$$ with $$\Theta(\frac{1}{t})=\sqrt{t}\Theta(t)$$
Therefore $$\sum\limits_{k=1}^\infty ...

**2**

votes

**0**answers

445 views

### Is this group given presentation isomorphic to $\mathbb{Z}_2$, and why? [migrated]

We have the group $G = \langle a, \,b \; | \; a^2b^2ab^{-1}, \, a^3b^4a^{-2}b^{-3}\rangle$.
Obviously $G/G' = \mathbb{Z}_2$. Is it true that $G = \mathbb{Z}_2$ or equivalently that $G'=1$? It is ...

**0**

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50 views

### Weak formulation of a nonlinear problem with test functions in a dense subspace of $H_0^1$

Let $\Omega\subset \mathbb R^{d=3}$ is a bounded and Lipschitz domain. Let $u\in H_g^1(\Omega)$ satisfy the weak formulation
$$a(u,v)+\int\limits_{\Omega}{f(u)vdx}=0,\,\forall v\in H_0^1(\Omega)\cap ...

**2**

votes

**1**answer

52 views

### Injectivity/Surjectivity of $F_A :=\frac{d}{dt} +A(t) :H^1 (\mathbb{R},\mathbb{R}^m )\to L^2 (\mathbb{R},\mathbb{R}^m )$

I am looking for a reference to the following problem:
Given a hyperbolic (no purely imaginary eigenvalues), continuous path of matrices $A(t)$ in $\mathbb{R}$ with hyperolic limits at $\pm \infty $.
...

**0**

votes

**0**answers

16 views

### Complexity of counting the number of ways that a special rule coloring can occur in a simple graph

Given a set of vertices with a set of edges that can are yet to be "applied".
Say an edge can be colored red if when it is applied, it connects an empty vertex to a full vertex. Else it is colored ...

**1**

vote

**1**answer

40 views

### leray schauder fixed point and schauder fixed point

I have seen these 2 fixed point theorem and I think the condition of Leray Schauder fixed point theorem is very strong and we require to consider the fixed point of $u=\sigma Tu$ $\forall \sigma ...

**0**

votes

**0**answers

16 views

### Probability that one normal (uncorrelated) variable is greater than another if the latter is positive [on hold]

Assume that $X\sim N(0,\sigma_x^2)$, $Y\sim N(0,\sigma_y^2)$ and $X$ and $Y$ are uncorrelated. Can we solve analytically for $\mathbb P(X>Y |Y>0)$?

**1**

vote

**2**answers

79 views

### Invertibility of all left multiplication maps in non-unital rings

Suppose that $R$ is a ring, not necessarily commutative nor associative. Assume that for every non-zero $a \in R$, the left multiplication map
$$ \lambda_a \colon R \to R \colon x \mapsto ax $$
is ...

**1**

vote

**1**answer

138 views

### Non-regular languages fulfilling the Pumping Lemma

Some non-regular languages don't yield to the Pumping Lemma ($L_1=a^nb^mc^m$ should work). But now consider the set of non-regular languages L only over the alphabet {a}. (Like $L_2=a^{n^2}$ or ...

**3**

votes

**0**answers

52 views

### Number of linearly independent subsets in arbitrary set

Consider $n$-dimensional vector space $\mathbb{F}_p^n$ over finite field $\mathbb{F}_p$ and a function $a: \mathbb{F}_p^n\rightarrow\mathbb{C}$. Let
$$ F(a) = \sum_{\substack{S\subset \mathbb{F}_p^n ...

**4**

votes

**1**answer

154 views

### Weil's Haar measure construction from below

Weil's construction of a Haar measure on a locally compact group rests on approximating a function from above by sums of translates of another function.
I would need to know something similar for an ...

**2**

votes

**1**answer

42 views

### Topology with no direct lower neighbor

Given any poset $(P,\leq)$ and $x, y\in P$ we set $[x,y] = \{p\in P: x\leq p \leq y\}$. For any set $X$, let $\text{Top}(X)$ denote the set of topologies on $X$. The set $\text{Top}(X)$ is a complete ...

**5**

votes

**1**answer

144 views

### Arbitrarily many primes in a Fibonacci-type sequence

It is conjectured that the standard Fibonacci sequence contains infinitely many primes. While this is perhaps too difficult, I am wondering about the following simpler version:
Question. For any $K$, ...

**-4**

votes

**0**answers

43 views

### How to prove this complex inequality? [on hold]

Let $Z\in C,n\ge 2$,and show this complex inequality
$$|z^n-1|^2\le |z-1|^2\left(1+|z|^2+\dfrac{2}{n-1}\Re{(z)}\right|^{n-1}$$
for $n=2$the inequality os equivalent to
$$|z^2-1|^2\le ...

**8**

votes

**3**answers

264 views

### References for Yang-Mills Theory

We are looking to run a working seminar about the Yang-Mills story. We hope that our seminars is of interest to analysts (working with curvatures and Ricci flows on Riemannian manifolds), the ...