2
votes
0answers
23 views

Which journals publish short communications?

Perhaps, somebody asked this already, excuse me in this case. Can anybody advise mathematical journals that publish short communications? (I mean little papers without proofs.) I am working in ...
1
vote
0answers
13 views

Semigroup solution via Lumer-Phillips

Let $a$ be a coercive, bounded bilinear form on $H^1(\Omega)$, where $\Omega$ is some sufficiently "nice" region. I defined an operator $A:H^1(\Omega)\mapsto H^1(\Omega)^*$ by: $$ ...
0
votes
0answers
9 views

void probability for Poisson point process

Assume we have a Poisson point process (PPP) on 2D space with density $\lambda$. Let $d_i$ be the distance of each node respect to the origin. Assume that we mark each point $i$, independent of other ...
0
votes
0answers
21 views

Distance between point and plane [on hold]

So according to this, the signed distance between a point will be the dot product of the plane's normal vector (does it have to be a unit vector?) and the point-in-plane minus the point vector. I ...
0
votes
0answers
14 views

Construction of a path of quadratic variation

This question has been posted to Stack Exchange earlier, and no answer is available yet. Consider a path $x: [0,1] \to \mathbb R$. it's $p$-variation on an interval is defined by $$V_{p}(x, [a, b]) ...
0
votes
0answers
13 views

schatten 1-norm of rank $k$ matrix

I am looking for a high-probability lower bound for the following rank-$k$ matrix $$ X = u_1 v_1^T + u_2 v_2^T + \cdots + u_k v_k^T, $$ where $u_1,\dots,u_k,v_1,\dots,v_k$ are independent $N(0,I_n)$ ...
2
votes
0answers
47 views

Geometric generic fibre

This is a pretty elementary question about schemes, but it came up in the course of research, so let's try it here rather than MSE. Question: Are all but countably many fibres of a family of ...
5
votes
0answers
65 views

Counter examples for strengthening Whitehead's theorem?

Let $f:X\to Y$ be a pointed map of pointed connected $n$-dimensional CW complexes. Whitehead's theorem says that if $f_*:\pi_qX\to \pi_qY$ is an isomorphism for $q\le n$ and a surjection for $q=n+1$, ...
7
votes
2answers
180 views

A question of Erdos on entire functions

At the end of the following paper, Erdos asked if there is a family $F$ of entire functions of size continuum such that for every $z \in \mathbb{C}$, $\{f(z) : f \in F\}$ has size less than continuum. ...
1
vote
0answers
26 views

The representation theory for the fake Heisenberg groups over non-perfect local field

Let $K$ be a local field of characteristic $p$, where $p$ is a prime number greater than 2. In particular, $(x+y)^p=x^p+y^p$ for $x,y\in K$. The fake Heisenberg group is defined to be $$ ...
0
votes
0answers
40 views

What are constructions for induced $C_5$-free graphs?

During a recent workshop, the question came up whether there are some constructions for graphs that are induced $C_5$-free, but they contain "everything else," so we don't want to forbid $C_5$'s, ...
3
votes
0answers
100 views

homology fibrations induced by actions of topological monoids

In the paper Homology fibrations and group completion theorem, McDuff-Segal, page 280, lines from bottom 3-6, Proposition 2: If $M$ is a topological monoid which acts on a space $X$, and for each ...
0
votes
2answers
89 views

Worst case difference in rank by column-row swapping

Given a matrix $m\in\{-1,+1\}^{n\times n}$. Consider $m^\sigma$ to be collection of all matrices obtained from $m$ by permuting rows and columns. Consider $\mathscr{M}[m^\sigma]$ to be collection of ...
2
votes
0answers
78 views

Does the following $ C^{*} $-algebraic result have a purely algebraic proof?

While studying the proof of Bott periodicity for operator $ K $-theory in this set of notes, I learned this fact: Theorem. Let $ A $ and $ B $ be $ C^{*} $-algebras. Let $ f,g: A \to B $ be $ * ...
0
votes
0answers
27 views

Tomita Takesaki theory and boundeness of $S$

Let $M$ be a von Neumann algebra, $\xi$-separating and cyclic vector for $M$. Let $S$ be antilinear operator acting as $x \xi \mapsto x^* \xi$ where $x \in M$. Then one can show that $S$ is closable ...
1
vote
0answers
74 views

Compact finite dimensional group

Suppose that $G$ is a compact, finite dimensional topological group (finite dimensional as a topological space). Does it follows that $G$ can be faithfully represented on some $U(n)$ (in other words, ...
1
vote
0answers
42 views

a topos without an underlying boolean topos

I remember an example of a topos that does not have an underlying Boolean topos. My problem is, I cannot find where I saw it. The solution is supposed to have Setf and Set, and the objects of the ...
1
vote
1answer
79 views

Does the forgetful functor from presentable $\infty$-categories to $\infty$-categories preserve filtered colimits?

Marc's answer to my previous question gives a way to compute colimits in the category of presentable $\infty$-categories and continuous functors, using the (discontinuous) right adjoints to those ...
0
votes
0answers
26 views

To fast invert a real symmetric positive definite matrix that is almost similar to Toeplitz [migrated]

It is well known how to solve a Toeplitz system Ax = b, of a matrix A, n x n elements, ...
5
votes
0answers
164 views

Uniformly small sums of roots of unity

I have considerable numerical evidence that for all $0\leq k\leq{{n-1}\over 2}$ ($n$ odd) there exists a subset $ S_k$ of {1,2,...,n} of cardinality $k$ such that the modulus square of ...
2
votes
1answer
27 views

Fixed point iteration on symmetric biconvex function

Suppose $X\subseteq\mathbb{R}^n$ is a convex set and that a function $g(x,y):X\times X\rightarrow\mathbb{R}_+$ is smooth, "strictly biconvex" (strictly convex in $x$ and $y$ independently but not ...
-4
votes
0answers
39 views

Gamma Functions [on hold]

Writing the Integral Equation of the gamma function I(n)=n-1*I(n) is there a way to prove, if possible, that there exists only one gamma function? Please Help!
0
votes
0answers
42 views

Detailed example of a skew field different from Hamilton quaternion [migrated]

Do you have a reference of a detailed construction of a skew field different from the quaternions from Hamilton? I would appreciate if that would be accessible from the Internet.
0
votes
0answers
64 views

A question about a specific inverse proposition of Combinatorial Nullstellensatz

From the Hilbert's Nullstellensatz, we have the following consequence which is usually called Combinatorial Nullstellensatz: Let $F$ be an arbitrary field, and let $f = f(x_1,x_2,\cdots,x_n)$ be a ...
5
votes
0answers
87 views

Radical of a polynomial values

It has been observed by Langevin and Elkies that the following holds: Assume that the $ABC$- conjecture is true. Suppose that $f(x)\in\mathbb{Z}[x]$ has no repeated roots. Fix $\varepsilon >0.$ ...
9
votes
0answers
132 views

Minimum value of $|p(1)|^2+|p(2)|^2 +…+ |p(n+3)|^2$ over all monic polynomials $p$

Let $n$ be a positive integer. Determine the smallest possible value of $|p(1)|^2+|p(2)|^2 +...+ |p(n+3)|^2$ over all monic polynomials $p$ of degree $n$. This question was proposed (problem ...
5
votes
0answers
74 views

Does the critical sequence for subalgebras of elementary embeddings with finitely many generators have order type $\omega$?

Suppose that $\lambda$ is a cardinal. Let $\mathcal{E}_{\lambda}$ be the set of all elementary embeddings from $V_{\lambda}$ to $V_{\lambda}$. If $j,k\in\mathcal{E}_{\lambda}$, then define ...
-14
votes
0answers
93 views

HISTORY OF MATHEMATICS [on hold]

WHAT TYPE OF MATHEMATICS ARE THE GREEKS KNOWN FOR? history of mathematics WHICH GREEK MATHEMATICIAN IS KNOWN FOR HIS WORK ON CONIC SECTIONS? WHAT ARE THE CONIC SECTIONS? WHAT INFLUENTIAL BOOK DID ...
3
votes
1answer
76 views

What is the cokernel of a map of presentable stable $\infty$-categories?

Let $C$ and $D$ be presentable stable $\infty$-categories, and let $f:C \to D$ be a continuous functor between them. Let $0$ be the trivial stable $\infty$-category. What is the colimit of the ...
1
vote
0answers
52 views

Generalization of Pitt's theorem

Pitt's theorem (Pitt 1937), states that the one-dimensional Fourier tranform is well defined and continuous between the weighted spaces $L^p(\mathbb{R},|x|^{bp}dx)$ and $L^q(\mathbb{R},|x|^{\beta ...
4
votes
2answers
162 views

Is the $\infty$-category of presentable $\infty$-categories presentable?

Let $\mathit{Pr}^L$ be the $\infty$-category of presentable $\infty$-categories and continuous functors in some universe. Is it presentable itself a larger universe?
0
votes
1answer
140 views

Is the Gysin morphism equivariant?

Let $X$ be a smooth, projective complex variety and $j \colon D \hookrightarrow X$ a smooth divisor. Then we have a Gysin morphism in singular cohomology $$ j_\ast \colon H^{\bullet}(D) \to ...
0
votes
0answers
20 views

Ergodicity property for continuous-time Harris positive Markov process

I have posted this question on there, but got no answer. The following theorem is Theorem 13.3.3 of Meyn and Tweedie's Markov Chains and Stochastic Stability on page 328: Theorem 13.3.3. If ...
1
vote
0answers
18 views

Small degree vertices in an epsilon-tough graph

We say that a graph is t-tough if by deleting a set if vertices $S$, the resulting graph will have at most $|S|/t$ connected components. We say that a graph is minimally t-tough if the deletion of an ...
0
votes
0answers
116 views

How to prepare a radical change of research field after the PhD [duplicate]

I am in the middle of my PhD in functional analysis. My undergraduate studies were focused on pure theory and so it was logical to continue in this direction. However, recently I got into contact with ...
-1
votes
0answers
21 views

Freedom of speech in scientific discussions - An invitation to more tolerance in Scientific debates [migrated]

I hope this post enjoys some tolerance, and don't get closed or put on hold immediately. I believe that freedom of speech in scientific discussions is one of the key values which enriches the debates ...
2
votes
2answers
127 views

Lower bound for $ \sum_{i=1}^n x_i f(x_i)$ when $\sum_{i=1}^{n}x_i = K$

Considering, the set of all n dim. vectors $\{x_i\}_{i=1,...,n} $ such that $x_i \geq 0 $ and $\sum_{i=1}^{n}x_i = K$ Any continuous and strictly increasing function $f^+(x)$ : $ \mathbb R^+ \to ...
-1
votes
0answers
82 views

picard group of a cyclic cover

I want to find any result about the picard group of a ramified double cover of a projective plane. Isn't there any general result about this case unlike ruled surface? Can you recommend any good ...
5
votes
0answers
123 views

Log smooth models for abelian varieties

Let $K$ be a field which is complete for a discrete valuation. Assume that the residue field has characteristic $p > 0$. Let $A$ be an abelian variety over $K$ having the property that (for some ...
-1
votes
1answer
86 views

Bijection between dominant rational maps and morphisms of function fields?

Let $X$ and $Y$ be two integral schemes of finite type over a field $k$. Consider the function fields $K(X)$ and $K(Y)$. Do we have a bijection between: (a) Dominant rational maps $X \rightarrow Y$ ...
-1
votes
0answers
62 views

lie derivative on complex manifold

Let $M$ be a complex manifold with complex structure $J$. Then for any smooth vector field $X$ on $M$ can be splited into its holomorphic and anti-holomorphic components $X=Z+\overline{Z}$. For any ...
3
votes
0answers
61 views

Rectifying the definition of a closed category

The definition of a closed category I'm using is here. Suppose $V$ is a closed category and that for each object $b\in V$, $[b,-]$ has a left adjoint $- \otimes b$. The result is nearly a monoidal ...
2
votes
2answers
62 views

Integrals involving the Tricomi hypergeometric function

I am looking for a reference for the two following equalities involving the Tricomi function $U$ and the Meijer function $G$. I have found these formulas on the website http://functions.wolfram.com/, ...
3
votes
0answers
48 views

How small can the Mumford-Tate group of hypersurface be?

Is there some way of giving a lower bound on the dimension of the Mumford-Tate group of a hypersurface? Let's say it's of general type, say, of degree $10$ inside $ \mathbb{P}^3$. I would expect the ...
-2
votes
0answers
32 views

line complex in projective space [on hold]

In a paper of "R.H.Dye", which you can find here: http://link.springer.com/article/10.1007%2FBF02413785#page-1, I face with a mathematical object "line complex in projective space $PG(2n-1,q)$, I need ...
2
votes
0answers
64 views

Rank of a particular matrix

Denote $P_{2n}$ to be collection of homogeneous total degree $2$ real polynomials in exactly $2n$ variables such that coefficient of every monomial is either $1$ or $-1$. Split variable set into ...
1
vote
0answers
70 views

Orientation form on the blow up of a Kaehler manifold

Let $(X,\omega)$ be a complex Kaehler manifold of (complex) dimension $d$, and let $Y\subset X$ a complex submanifold of dimension $k$. Evidently $[\omega]^d\in H^{2d}(X,{\mathbb{R}})$ is always ...
6
votes
1answer
85 views

Counting equivalence relations with marked classes

The number of equivalence relations on a set of $n$ elements is the Bell number $B_n$. If we wish to count the number of equivalence classes on a set of $n$ elements where one of the classes is ...
2
votes
1answer
145 views

Existence of Hecke operators with distinct eigenvalues?

Consider the space of modular forms $M_k(N)$. Any modular form $f \in M_k(N)$ is determined by a finite number of Fourier coefficients (e.g., Sturm's bound), thus there is a finite set of Hecke ...
4
votes
0answers
77 views

Visibility in a prime orchard

This suggests a variant on Polya's orchard problem. That problem asks1 for which radius $\epsilon$ of trees at each lattice point within a distance $R$ of the origin block all lines of sight to the ...

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