# All Questions

**0**

votes

**0**answers

61 views

### Becoming a Mature Mathematician

I am currently a sophomore in my undergraduate mathematics program. It has taken me a while to take school seriously; I was one of "those" students who just skated by without studying until Linear ...

**1**

vote

**0**answers

30 views

### Are these moduli problems of curves “well-behaved”?

Let X be a smooth projective surface over $\mathbb C$, and let $d\geq 3$ be an integer. Suppose that all smooth hypersurfaces of degree $d$ are of genus $g\geq 2$.
Let $H_{X,d}$ be the Hilbert scheme ...

**-4**

votes

**0**answers

11 views

### applications that involves the Legendre Polynomials [on hold]

i am requested to make a basic research about the applications that involve the Legendre Polynomials.. thanks in advance

**2**

votes

**1**answer

48 views

### harmonic analysis on $p$-adic $x^2 + y^2 + z^2 = 1$?

Are there p-adic analogues to spherical harmonics? In the case of $K = \mathbb{R}$, the spherical harmonics form a basis to $L^2 [SO(3)]$ where
What happens in the $p$-adic case? Is there sphere ...

**0**

votes

**0**answers

9 views

### History of the Vertex Disjoint Cycle Cover with Minimal Edgeweight Sum

Questions:
who first posed the problem of determining a collection of (directed) cycles, whose edgeweight sum is minimal and, for which each vertex belongs to exactly one of the cycles?
who came up ...

**0**

votes

**0**answers

10 views

### If $f$ is dynamically coherent, is there a unique invariant foliation tangent to $E^{c}$?

Let $f$ be a diffeomorphism of a closed manifold $M$ such that $f$ is partially hyperbolic if the tanget bundle of $M$, $TM$ splits into three invariant sub-bunbles
$$
TM = E^{s} \oplus E^{c} \oplus ...

**-6**

votes

**0**answers

36 views

**-3**

votes

**0**answers

25 views

### finding eigenvector [on hold]

I have
where λ1 = λ2 = 6 and λ2 = λ3 = 0.
I wish to find the eigenvectors for these eigenvalues above.
I've tried to turn it into equations and trying to solve them (this is for λ1 & λ2):
...

**0**

votes

**0**answers

9 views

### Stucture of inverse (MP) of totally positive rectangular matrix

The special structure of inverse of non-singular totally positive square matrix (whose all entries are positive) discussed in MO(see here). The inverse has a special structure (M-matrix).
With some ...

**0**

votes

**0**answers

27 views

### SVD alternatives for symmetric matrices

Given any symmetric real valued matrix $A \in \mathbb{R}^{n\times n}$, I can decompose $A$ as the product of two complex matrices
$$
A = E'E
$$
Practically this can be done easily using SVD ...

**0**

votes

**0**answers

33 views

### How to find a basis of weight vectors?

I have to following Lie Algebra $L=\{x\in End(\mathbb{C}^6)\colon x^tS+Sx=0\}$, where $S=[\begin{smallmatrix} 0&I_3 \\ I_3&0 \end{smallmatrix}]$, and the subalgebra $H$ given by the diagonal ...

**0**

votes

**0**answers

18 views

### Mixed PDE/finite difference equation

I have the following mixed pde/finite-difference equation for $f(t,x,y)$:
$a x^2 f_{xx} + bxf_x + f_t - bxy + c\sinh(d\delta) = 0$
subject to $f(T,x,y)=0$, $x>0,\ t\geq 0,\ y\in\mathbb Z$,
...

**5**

votes

**0**answers

40 views

### What are the indecomposable $U_q\mathfrak g$-modules?

Let $\mathfrak g=\mathfrak{sl}(2)$.
Let $\zeta$ be a primitive root of unity of even order. Say $\zeta=e^{2\pi i/6}$, for concreteness.
Let $U_q\mathfrak g$ be Lusztig's integral form of the ...

**1**

vote

**1**answer

87 views

### projectivity with assumption of big and semi-amplness

Let $X$ be a compact Kaehler manifold with $D$ be an effective divisor on $X$ such that $K_X+D$ is semi-ample and big then $X$ is projective?

**2**

votes

**0**answers

33 views

### Correspondence between dual center and linear characters of finite reductive group

Let $(G,F)$ be a connected reductive group defined over $\mathbb{F}_q$ via the Frobenius $F$ and let $(G^*,F^*)$ be a group in duality with $(G,F)$ with respect to rational maximal tori $T \subseteq ...

**1**

vote

**0**answers

21 views

### (quasi)metric on Riemannian manifolds via Brownian Motion?

Given points A and B on a Riemannian manifold, I would like a (quasi)metric that corresponds to the average commute time from A to B under Brownian Motion (or rather, to an $\epsilon$-ball around B).
...

**-2**

votes

**0**answers

18 views

### Cumulative distribution function and sum of random variables [on hold]

For two continuous (iid) random variables $X$ and $Y$, we have (ref): $$ \mathbb{P}(X+Y \le a) =\int_{-\infty}^\infty \int_{-\infty}^{c-x} \big ( f(x,y) dy \big ) dx$$ with $f$ being the joint density ...

**1**

vote

**0**answers

63 views

### Presentation of hyperbolic groups

Is it true that all hyperbolic groups are finitely presented? If yes, what is the right reference for that?

**3**

votes

**1**answer

58 views

### geodesics on $G/K$ which are not the orbits of a 1-parameter subgroup of $G$

Let $G$ be Lie group and $K \subset G$ a closed subgroup, such that there exists a $v \in T(G/K)$ whose isotropy-group $G_v$ is discrete (so iff $\dim G_v =0$). Lets assume $g$ acts properly on ...

**-1**

votes

**1**answer

31 views

### Hadwiger number of total graph

Let $G=(V,E)$ be a finite, simple, undirected graph, and let $T(G)$ be its total graph. The Hadwiger number $\eta(G)$ is the maximum $n\in\mathbb{N}$ such that $K_n$ is a minor of $G$.
Is there an ...

**9**

votes

**0**answers

200 views

### What's wrong with Advanced Studies in Contemporary Mathematics (Kyungshang)?

By some reason the Journal mentioned in the title is no longer covered by the AMS Math. Reviews. On the MathSciNet web page it says:
Last Issue: 24, no. 1 2014
Indexed cover-to-cover
Status: No ...

**2**

votes

**1**answer

118 views

### s(n) = kn or s(n) = n/k? [on hold]

This is not an important question, just for fun.
Definition:
$\sigma (n)$ = sum of the positive divisors of $n$.
$s(n)$ = sum of the proper positive divisors of $n$.
For $s(n) = kn$ , where $k$ ...

**-4**

votes

**0**answers

32 views

### Homomorphism, Group Theory [on hold]

Let G=Z4, the group of integers modulo 4, and let H be the Klein four group, let f: G->H be a homomorphism. Why does the kernel of f must contain the element of 2 of G?

**2**

votes

**0**answers

55 views

### Critical case of Sobolev Embedding

I got stuck in the following lemma:
Lemma: Let $B$ be the unit ball in the 4 dimensional Euclidean space. Suppose that $u\in W^{2,2}(B)$, then $e^{u}\in L^{q}$ for any $q>1$.
As we know this is ...

**4**

votes

**1**answer

43 views

### $G$-orbits in Springer resolution (or, stabilizer actions on Springer fibers)

This may be an elementary question, but I'm having trouble coming up with an answer: Let $\tilde{N} = T^*(G/B)$ be the Springer resolution of the nilpotent cone. Does it have finitely many ...

**20**

votes

**2**answers

2k views

### Why is this new result such a big deal?

This popular article reports a recent result in reverse mathematics, showing that a certain theorem in Ramsey theory is provable from RCA$_0$, the base theory in SOSOA. Then there are a bunch of ...

**0**

votes

**0**answers

78 views

### Density of Sophie Germain $3\bmod 4$ primes

Is there any reason to expect the density of primes $p$ such that $2p+1$ is also a prime where $p=3\bmod4$ holds would be different from case of $p=1\bmod4$?
What if $2p+1$ is replaced by $2p-1$ and ...

**0**

votes

**0**answers

63 views

### Divisibility of Dirichlet L-functions

let $k$ be an even integer and $p$ a prime number such that $p-1|k$. Suppose that $p$ does not divide $L(1-k,\chi)$ and $L(1-k,\psi)$, where $\chi$ and $\psi$ are quadratic characters. Can we deduce ...

**5**

votes

**1**answer

135 views

### Normal subgroups of Aut(M)

Let $S$ be the set of all finite permutations of $\mathbb{N}$, i.e. they fix all but a finite set, and $A\subset S$ the set of all even permutations.
Theorem The normal subgroups of $S_\infty$ are ...

**5**

votes

**3**answers

165 views

### Text for studying group representations in the context of (abstract) harmonic analysis

I would like to study elements of representation theory as I often encounter it when reading texts on harmonic analysis. I was therefore curious if someone could recommend a book for this.
When ...

**5**

votes

**0**answers

44 views

### Does the Hodge *-operator act on the tangent space at 0 to the space of integral (n-1)-cycles in a conformal manifold of dimension d=2n?

Suppose $M$ is a compact, oriented conformal manifold of even dimension $d=2n$.
Write ${\cal D}^{\mathit{int}}_{k}(M)$ for the space of integral
$k$-currents in $M$
and write ${\cal ...

**-1**

votes

**0**answers

33 views

### Floquet solution to Mathieu equation in terms of Mathieu sin and cos [on hold]

In wikipedia https://en.wikipedia.org/wiki/Mathieu_function#Floquet_solution
I want to know how the Floquet solution is plotted.
One way I am thinking is to write Floquet solution in terms of the ...

**2**

votes

**1**answer

52 views

### Choi type matrix condition for completely positivity on a certain operator system spanned by some unitaries

Let $B_1$ and $B_2$ be $C^*$-algebras. Let $U_1, \ldots, U_n$ be some unitaries in $B_1.$ We consider the operator system $S$ spanned by $U_iU_j^*.$
Let $\phi: S \rightarrow B_2.$
Given that the ...

**6**

votes

**0**answers

50 views

### Does the Turaev-Viro theory for the generalized $E_6$ subfactor for $\mathbb{Z}/7$ distinguish $L(7,1)$ and $L(7,2)$?

In the paper Sato-Wajui "COMPUTATIONS OF TURAEV-VIRO-OCNEANU INVARIANTS OF 3-MANIFOLDS FROM SUBFACTORS" they compute certain Turaev-Viro-Ocneanu invariants of certain lens spaces. One of the results ...

**6**

votes

**1**answer

112 views

### Density of prime divisors of $a^n + b$

Suppose $a > 1, b \neq 0$ be two rational numbers. Is it known in general that the set of prime divisors of (the numerator of) $a^n + b$ has a positive relative density?

**0**

votes

**0**answers

46 views

### which is the relationship between infinite set and the orbits of their points? [on hold]

I have been studying the proof of the following theorem:
Theorem: Let's suppose that $X$ is some metric space and $X$ is a infinite set. If $f:X\to X$ is transitive and has dense periodic points the ...

**1**

vote

**1**answer

50 views

### Asymptotic formula for average geodesic length on graph?

If $G$ is a finite, connected simple graph then is there an expression for the average geodesic length?
That is suppose I know two nodes $n_1$ and $n_2$, the number of edges in my graph and at those ...

**1**

vote

**0**answers

54 views

### When does effective descent of modules hold?

Let $A$ be a commutative ring with identity. I denote by $\Delta_{\leq 1}$ the full subcategory of the simplex category $\Delta$ with objects $[0]$ and $[1]$. Let $B_{\cdot} : \Delta_{\leq ...

**0**

votes

**0**answers

4 views

### Can I study a global stability of equilibrium point in a fractional order system?

I have a system of fractional-order differential equations in the sense of Caputo’s derivatives. For this model, I obtained the equilibrium points and proved that some equilibrium points are locally ...

**0**

votes

**0**answers

19 views

### diffusion and potentials in several dimensions

In a Lagrangian field theory there are conserved quantities, like total energy. This allows geometric arguments to be made about the behaviour of a system with known potential. (E.g. on asymptotic ...

**0**

votes

**0**answers

48 views

### Fourier analytic estimate

The following question arises naturally from applications to the image processing. Let $\alpha\in [0,1]$ and assume that for infinitely many $n\ge 1$ we have
$$\sum_{k=1}^n\frac{1-|\cos(2\pi ...

**0**

votes

**1**answer

100 views

### Is there any infinite set which is Dedekind finite and weakly Dedekind finite?

Is there any infinite set which is Dedekind finite and weakly Dedekind finite?
If $X$ is a weakly Dedekind finite amorphous set, can we show that $\mathcal P(X)$, the power set of $X$, is also weakly ...

**2**

votes

**0**answers

36 views

### How are $\alpha$ and $f(\alpha)$ obtained from the calculated values of $h(q)$ in the Multifractal analysis? [on hold]

In most papers they mention some kind of Legendre transform but I'm not entirely clear about the process, sine they don't mention enough details, at least for me, I tried reading the cited references ...

**2**

votes

**0**answers

22 views

### Points of continuity of a lower semicontinuous function have non empty interior

Let $X\subset \mathbb R^d$ having non empty interior and let $f:X\to\mathbb{R}$ be lower semicontinuous.
I know that the set of discontinuities of such a function is contained in a meager set, and ...

**5**

votes

**0**answers

126 views

### Solving polynomial equations modulo $1$

Let $P\in \mathbb{R}\lbrack x\rbrack$ be given. (In practice, the coefficients could be given as, say, decimals to sufficient precision.) Let $M\geq 1$, and let $I$ be an interval in ...

**1**

vote

**1**answer

168 views

### Closed subgroups of $\mathrm{SO}(4)$

My question is quite simple : we know all closed subgroups of $\mathrm{SO}(3)$; is it also known what are the closed subgroups of $\mathrm{SO}(4)$?

**0**

votes

**0**answers

46 views

### Let $f:R\to S$ be a local finite monomorphism .If $M$ is an Artinian $S$-module, is it an Artinian $R$-module?

Let $(R,m)$ and $(S,n)$ be local rings (commutative Noetherian with 1). Let $f:R\to S$ be a local homomorphism/monomorphism ($f(m)=n$), such that the natural induced homomorphism $R/m\to S/n$ is an ...

**5**

votes

**1**answer

198 views

### On property of monic polynomial with integer coefficients

For a monic polynomial with integer coefficients $f$ where $\partial f = 2$, we have
$$
\textrm{inf}(f(x)) > 0 \implies
\textrm{inf}(f(x)) \geq \frac{3}{4} .
$$
Could we generalize this (for ...

**-1**

votes

**1**answer

38 views

### Is every implicit function reparametrized? [on hold]

Consider a continously differentiable non-constant function $f:\mathbb{R}^2\to\mathbb{R}$. Define
$$
K=\{x\in\mathbb{R}^2|f(x)=0\}.
$$
I wish to know whether there is a continuously differentiable ...

**5**

votes

**1**answer

125 views

### Motivating the existence of Canonical Bases for Representations

In Representation Theory, the theme of the existence of a canonical basis has been explored quite a lot. I will limit myself in this question to the kind of canonical bases that arise from the ...