0
votes
0answers
1 view

Business Managment

Fhyzics is a leader in business analysis and business analytics. We help companies to solve complex business problems and to put their data to strategic advantage. Since inception, we are serving ...
0
votes
0answers
3 views

More precise statement about lower bounds on the cover time of general graphs

Uriel Feige has shown in 1995 in his paper "A Tight Lower Bound on the Cover Time for Random Walks on Graphs", the following result: For any graph $G$ on $n$ vertices, and any starting vertex $u$ ...
0
votes
0answers
5 views

Nonnegativity of matrix powers

Consider a matrix $A\in SL_2(\mathbb R)$, and let $\Gamma\begin{pmatrix}+&-\\+&-\end{pmatrix}\subset M_{2\times 2}(\mathbb R)$ denote the set of matrices whose coefficients have the indicated ...
1
vote
0answers
31 views

How do we respond to the question, “What is mathematics?”? [on hold]

The mathematical community has offered various responses, depending on who was asking, and depending on what century it was, and other variables. The Wikipedia article "Definitions of mathematics" ...
5
votes
0answers
63 views

Why is there a $\sqrt{5}$ in Hurwitz's Theorem?

Hurwitz's theorem is an extension of Minkowski's Theorem and deals with rational approximations to irrational numbers. The theorem states: For every irrational number $\alpha$, there are infinitely ...
0
votes
0answers
6 views

lattice basis reduction of the orbit of a rational vector on the torus

LEt $v=(p_1/q,...,p_n/q)$ be a vector of the torus $\mathbb{T}^n$, such that for any $i$, $p_i$ and $q$ are relatively prime. Let $L= \{ kv \mod \mathbb{T}^n , k=0,...,q-1 \}$. What is the lattice ...
0
votes
0answers
18 views

Period of closed phase curve [on hold]

I'm currently reading Arnolds "Mathematical Methods of Classical Mechanics" and I'm having a hard time solving some of the problems in Chapter 2. I think that the following problem is fairly simple ...
1
vote
0answers
43 views

Actions of the unit circle on complex matrices

Let $M_2(\mathbb{C})$ be the algebra of $2\times 2$ complex matrices and $\mathbb{S}^1$ the unit circle. How many actions of $\mathbb{S}^1$ on $M_2(\mathbb{C})$ exist (up to isomorphism)? And on ...
1
vote
0answers
43 views

Diagonalizing against a non stationary set of functions

Suppose $\kappa$ is regular uncountable (assume $2^{< \kappa} = \kappa$ and $\kappa$ is weakly Mahlo if needed). Is the following true? For every sequence $\langle f_i: i \to 2 \mid i \in A ...
0
votes
0answers
21 views

Enumeration of simple graphs with given degree distribution/sequence

Is there any exact formula for asymptotic/exact enumeration of simple graphs with given degree sequence? I just found some results about it, but the formula is hold on for some conditions, for example ...
0
votes
2answers
48 views

Operator on a Sobolev space

I'm studying Sobolev spaces using Evans' PDE book. I can't figure out this simple fact. Let $L$ be an operator in this form: $$Lu= \sum{D_i(a_{ij}D_j(u))+\sum{b_iD_i(u)+cu}}.$$ I can't understand why ...
0
votes
0answers
34 views

Least prime for which a square-free integer is a non-residue

Suppose $a$ is a square-free integer and $\left(\frac{a}{p}\right)=1$ for the primes $p\leq k$. I'll call $a$ a quasi-square of order $k$. What I am interested in is the maximum value of $k$ in terms ...
0
votes
0answers
37 views

What does the Plancherel theorem say about positive-definite distributions?

I'm trying to understand the answer to this MO question: Bochner's theorem for measures of positive type, which suggests a relationship between Bochner's theorem and the Plancherel theorem. The ...
0
votes
0answers
13 views

Distortion of the Hausdorff dimension of sums of Cantor sets under local scaling

The following question deals with possible distortion of the Hausdorff dimension of sums of Cantor sets as one "zooms in" on the sum around any given point. Let us assume that $C_1$ and $C_2$ are two ...
0
votes
0answers
16 views

Motion tracking formula by tracking information [on hold]

I have tracking information of a short clip that demonstrates a first person view flight. The red dot is a x,y tracking information of a specific point in the clip. Additionally, we have the angle, ...
0
votes
0answers
42 views

Well-ordered reference

I'm wondering if there is a standard reference for the following straightforward facts about well-orderings. (They are quite easy to prove, I just need a handy/standard reference.) Let $(S,<)$ ...
2
votes
0answers
12 views

Is there a perfect integral fusion category with PFdim = 2 mod 4?

A finite group $G$ is perfect if $G = G^{(1)} := \langle [G,G] \rangle$. Proposition: A finite group $G$ is perfect iff any $1$-dimensional complex representation of $G$ is trivial. proof: First if ...
3
votes
2answers
84 views

Infinitesimal deformations of a fibration

Let $f:X\rightarrow Y$ be a morphism of normal projective varieties over an algebraically closed field with connected fibers. Assume that both $Y$ and the general fiber of $f$ admit a non-trivial ...
0
votes
0answers
9 views

An algebraics Hamiltonian vector field with a finite number of periodic orbits(2)

Is there a polynomial Hamiltonian $H:\mathbb{R}^{4}\to \mathbb{R}$ such that the number of nontrivial periodic orbits of the corresponding Hamiltonian vector field $X_{H}$ is finite but different ...
-1
votes
0answers
36 views

examples of manifolds having two ends with $Ric \geqslant -(n-1)$ but not split

Let $M$ be an $n$-dim complete, non-compact Riemannian manifold with two ends. Then we can construct a line on $M$. If we assume that $Ric \geqslant 0$, by Cheeger-Gromoll's splitting theorem, the ...
2
votes
0answers
58 views

Representations of $\mathbb{H}^{\times}$ and $\mathbb{H}^{\times}/\mathbb{R}^{\times}$

In an attempt to recapture Eichler's theta correspondence I have hit a stumbling block. Let $D$ be a quaternion algebra over $\mathbb{Q}$, ramified at $p,\infty$. Also let $V_j = ...
-1
votes
0answers
19 views

Solve Higher ODE with boundary condition at infinity [on hold]

Given below is a second-order linear differential, $y''+Ay'+By=0$ The boundary conditions are: (a) $y(t=0)=1+H\frac{dy}{dt}$ (b) $y(t=\inf)=0$ Does a solution exist for this problem?
0
votes
0answers
48 views

Intersections of ideals and nilpotence

Let $R$ be a polynomial ring over a field $k$, $R = k[x_1, \dots, x_n]$. Suppose $R'$ is an associative $R$-algebra and it has the property that there exists a degree $m<n$ monomial in the $x_i$'s ...
2
votes
0answers
62 views

Infinite-dimensional admissible representations of SL(2,C)

I'm working in my research with the infinite dimensional (admissible) irreducible representations of $\mathrm{SL}(2,\mathbb{C})$ introduced by Harish-Chandra in his paper "Infinite Irreducible ...
0
votes
0answers
50 views

Reduced products of (abelian and triangulated) categories: references?

For a filter $U$ on a set $X$ and for a family of categories $C_x$ indexed by $X$ I would like to consider the (corresponding categorical version of) reduced product of $C_x$ (for $x\in X$) with ...
1
vote
2answers
88 views

Embedding finite lattices into the lattice of partitions of a finite set

For any set $X$ we denote by $\text{Part}(X)$ the set of all partitions of $X$, ordered by the refinement ordering. It is well known that this is a complete lattice for all sets $X$. Let $L$ be a ...
0
votes
0answers
8 views

Open Volumetric Time series data set

Does anyone know where I can find a good open volumetric time series data set? I had a look at some of Stanford's open data sets (https://graphics.stanford.edu/data/voldata/ ) But these do not seem ...
0
votes
0answers
34 views

Vector Valued Modular Forms with Monodromy

Is there a theory of vector valued modular objects with given weight, which represent the modular group further by permuting the entries (i.e. vector valued modular forms), but, which have a point of ...
3
votes
1answer
336 views

Is a non-trivial finite perfect group of order 4n?

A finite group $G$ is perfect if $G = G^{(1)} := \langle [G,G] \rangle$, or equivalently, if any $1$-dimensional complex representation is trivial. Question: Is a non-trivial finite perfect group of ...
-5
votes
0answers
32 views

profit and loss related aptitude qustion? [on hold]

A sold a watch to B at a gain of 5% and B sold it to C at a gain of 4%. If C paid Rs. 1902 for it, the price paid by A is?
-1
votes
0answers
27 views

Stochastic integration with respect to Fractional Brownian Motion

I would like to know what can be said about integral process $X_t = \int_0^t e^{-sr} dB_s^H,t\in[0,\infty)$, where $B^H_t$ is Fractional Brownian Motion with Hurst parameter $H>\frac{1}{2}$, ...
3
votes
0answers
53 views

Relations between modular functions of certain $q$-continued fractions

Given the j-function $j:=j(\tau)$, and $q=e^{2\pi i\tau} = \exp(2\pi i\tau)$ where, for convenience, we set $\tau=\sqrt{-n}$. I. $\frac{A_2(q)}{A_1(q)} = \text{q-cfrac}:\;$ Icosahedral group ...
6
votes
2answers
87 views

Moments of a random variable and of its conditional expectation

Let $X$ be a bounded random variable with $\mathbb{E}X=0$. Since $X$ is bounded, all its moments exist. Let $\mathcal{G}$ be any $\sigma$-field and let $Y:=\mathbb{E}[X|\mathcal{G}].$ I am interested ...
-4
votes
0answers
66 views

Is Zsigmondy's Theorem utilized in Sociology to the extent that a lay person might be familiar with its use? [on hold]

Is Zsigmondy's theorem somehow useful in sociological studies? Has it in some way been co-opted as a sociological term with a corresponding sociological theory, no matter how far off base from the ...
5
votes
2answers
67 views

Differential operators between modules, $\mathcal{D}_A(M, M)$ necessarily a filtered, almost commutative ring?

See here. Does it follow immediately that $\mathcal{D}_A(M, M)$ as defined in the link is a filtered, almost commutative ring? How can I visualize this geometrically?
8
votes
1answer
154 views

Is an explicit $c$ known to lead to a noncomputable Julia set?

Braverman & Yampolsky have shown that there exist noncomputable Julia sets, i.e., there exist $c \in \mathbb{C}$ such that the Julia set of $f(z) = c + z^2$ is not computable. "A set is ...
-3
votes
0answers
76 views

Non-flat $R \subseteq S$, which is integral, separable, $R$ is a noetherian (not integrally closed) integral domain

On ramification theory in noetherian rings, of Auslander and Buchsbaum say: "Chapter 4 is devoted to showing that under various conditions if $S$ is unramified over $R$, then $S$ is $R$-projective. ...
2
votes
1answer
104 views

Proving inequation with ceilings in Finite Field of characteristic $p$

Take $ui = pt_i +j_i$ where $p$ is a prime number and $u(p-r) \equiv 1 $ $(\mbox{mod p})$ for positive integers $1 \le i, r, j_i\le p-1$ and $t_i \ge 0$. How can I prove that: \begin{equation} ...
2
votes
1answer
53 views

A quasicompact space with a net that contains no convergent strict subnet

If $x:\Lambda \rightarrow X$ is a net in a topological space $X$ and $\Lambda '\subseteq \Lambda$ is a cofinal subset of the directed set $\Lambda$, then $x|_{\Lambda '}$ is a subnet of $x$. We call ...
0
votes
0answers
46 views

higher direct images of relative canonical sheaf plus a fractional divisor

For a map $f: Y \rightarrow X$ branched over simple normal crossing divisor $B=\sum_iB_i$, do we know of similar local freeness property for higher direct image of relative canonical sheaf plus a ...
3
votes
0answers
86 views

Thom Class of tensor bundles

Suppose $\xi$ and $\eta$ are oriented vector bundles over a CW-complex $B$. Is it possible to express the Thom class (with ${\mathbb Z}$ coefficients) of $\xi\otimes \eta$ or even ${\rm Sym}^2(\xi)$ ...
0
votes
0answers
78 views

Higher algebra and terminology about 2-objects

It is well known that one way to build higher category theory is to use some induction process, where an $n$-category has as $0$-cells some $n-1$ categories, such that for two $0$-cells $\mathcal{A}$ ...
2
votes
0answers
23 views

Nemytskii/superposition operator without separability of Banach space?

Let $T:[0,1] \times X \to \mathbb{R}$ be a nonlinear map where $X$ is a Banach space. Suppose that $T$ is a Caratheodory map, so that $t \mapsto F(t,x)$ is measurable and $x \mapsto F(t,x)$ is ...
1
vote
0answers
101 views

Riemann-Roch formula for nodal curves

Let $X$ be an irreducible, reduced, projective curve over an algebraically closed field, with at worst nodes as singularities. Let $\mathcal{F}$ be a trivial vector bundle on $X$ of rank $r$. Consider ...
-1
votes
1answer
144 views

On Cantor sets every map is $C^{\infty}$

For a fixed Cantor set $K\subset [0,1]$ and a continuous function $g:[0,1]\to \mathbb R.$ Is it always possible to find a $C^{\infty}$ map $f:[0,1]\to \mathbb R$ such that $g$ and $f$ coincide in $K?$ ...
0
votes
0answers
41 views

How to obtain a permutation of a tensor product? [on hold]

I am looking for a way to efficiently compute a re-ordered kronecker product from the result of another kronecker product. For example, consider $$F=A\otimes B\otimes C\otimes D\otimes E$$ from the ...
0
votes
0answers
12 views

Asymptotic behavior of the minimum eigenvalue of a certain Gram matrix with linear independence

Consider the density matrices with the following spectral decompositions: $$\rho=\lambda_1|\nu_1\rangle+\lambda_{2}|\nu_2\rangle$$ and $$\sigma=\gamma_1|\omega_1\rangle+\gamma_2|\omega_2\rangle$$ such ...
2
votes
0answers
88 views

Are these two $q$-continued fractions equivalent?

In this MSE post, Nicco Mnisi defined a particular $q$-continued fraction of order $12$. More generally, define the cfrac found in Ramanujan's Notebooks, Vol III, Chap. 16, page 24, $$U(q) = ...
7
votes
2answers
382 views

What is descent data (of higher categories), conceptually?

First consider a scheme $X$ with an open cover $\mathcal{U}=\{U_i\}$. An object with descent data on $\mathcal{U}$ is a collection $(\mathcal{E}_i,\phi_{ij})$ where $\mathcal{E}_i$ is a ...
3
votes
1answer
112 views

Number of non-isomorphic models

I had this question up on Math stackexchange: http://math.stackexchange.com/questions/1349247/number-of-non-isomorphic-models/1350763#1350763 . While it was answered partially there, I'm posting here ...

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