# All Questions

**2**

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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

**0**answers

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**

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**0**answers

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**

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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**

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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

**0**answers

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

**0**answers

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

**0**answers

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

**2**answers

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

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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

**0**answers

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

**0**answers

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

**2**answers

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

**0**answers

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**

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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

**0**answers

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

**0**answers

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

**1**answer

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

**0**answers

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

**0**answers

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

**1**answer

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**

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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

**0**answers

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

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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

**0**answers

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

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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

**0**answers

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**

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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

**1**answer

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

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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

**2**answers

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

**1**answer

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

**0**answers

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

**0**answers

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

**0**answers

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

**0**answers

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

**2**answers

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

**0**answers

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

**0**answers

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

**1**answer

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

**0**answers

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

**0**answers

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

**2**answers

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

**0**answers

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

**0**answers

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

**0**answers

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

**0**answers

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

**1**answer

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

**1**answer

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

**0**answers

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 ...