Highest scored questions
159,041 questions
-2
votes
1
answer
230
views
Special value of Hecke $L$ function
Let $E:y^2＝x^3-x/ \Bbb{Q}(i)$ be elliptic curve and $L(E,1)$ be a special value of $L$ function of $E$ at $1$.
Let $L(ψ,1)$ be value at $1$ of Hecke $L$ function with respect to Hecke character $ψ$, ...
- 1,541
-2
votes
1
answer
201
views
Tricky (for me) limit
I've been trying to compute the following limit for a few hours. Let $f(\gamma, \beta)$ be defined as follows:
$$f(\gamma, \beta)=\lim_{x \rightarrow \infty} (1-\gamma^{1/x})(\log(x))^{\beta}.$$
I am ...
- 143
-2
votes
1
answer
262
views
Proving 2 matrices have the same trace [closed]
I found a problem in my textbook and I have tried solving it, but I had no succes. The problem is:
Let $A$ and $B$ be $n \times n$ matrices with complex number entries. Given that $AB−BA$ is ...
- 331
-2
votes
1
answer
430
views
Soft Question: Asking for advice: how to study math? [closed]
(I am aware that some people might frown on this question, but I had no place to ask; this will definitely be voted to be closed in SE. I apologize in advance.)
I am currently a 1st year grad student ...
- 105
-2
votes
1
answer
654
views
Definition and properties of the inverse of the flow of an ODE [closed]
At lesson, the teacher considers a flow $\Phi$ given by the solutions of the ode system for $t\in[0, T]$ and $x\in\mathbb R^d$,
$$
\begin{cases}
y'(s)=b(y(s), s),&s\leq T\\
y(t)=x
\end{cases},\...
- 171
-2
votes
1
answer
180
views
Is there a function $f$ that is a finite sum of functions with finite products of the inputs of $f$ as inputs with this property?
Note: This question aims to be a generalization of Is it possible to create a polynomial $p(x)$ with this relation between $p(0)$ and $p(c)$? and Is it possible to create a polynomial $p(x)$ with this ...
- 265
-2
votes
1
answer
72
views
Extend sum function for not integers [closed]
Is it possible to extend function for any not integer y ?
-2
votes
1
answer
708
views
Prove or disprove this integral of a function, defined on a countable set with infinite limit points, converges to zero [closed]
Edit: I got rid of my old definitions. Everything should be clear now
Since no one has answered my question on MSE, I’m hoping to get an answer here. I apologize if you dislike my writing. I am an ...
- 63
-2
votes
1
answer
168
views
Diophantine equation $10^n-a^3-b^3=c^2$
Consider the Diophantine equation:
$10^n-a^3-b^3=c^2$, for $a$, $b$, $c$, and $n$ positive.
Has this equation infinitely many solutions?
-2
votes
1
answer
286
views
Why this function is monotonic?
Let $a> 0, \alpha<0$ and $\beta>0$. How to prove that the function:
$$f(x)=\frac{(\Gamma(a)-\Gamma(a,\alpha \ln(\beta x))) (\alpha\ln(x))^a}{(\alpha\ln(\beta x))^a (\Gamma(a)-\Gamma(a,\alpha \...
- 395
-2
votes
1
answer
517
views
Local isometry implies covering map: nonempty boundary case [closed]
The following theorem is well known in the literature:
Let $M$ and $N$ be riemannian manifolds and let $f : M \to N$ be a local isometry. If $M$ is complete and $N$ is connected, then $f$ is a ...
- 2,095
-2
votes
1
answer
321
views
Is projective closure of a regular affine algebraic set also regular?
Now to specifics:
Let $V \subset \mathbb{A}^3$ be a reducible affine algebraic set defined by two irreducible polynomials $f,g \in K[X,Y, Z]$ of degree $d$ ($K$ algebraically closed). So, if $V$ is ...
-2
votes
1
answer
282
views
Existence of divisor in the Jacobian of smooth curve of genus two whose intersection with theta divisor is 1
Let $C$ be a smooth projective curve of genus $2$ and $J$ denotes the Jacobian of $C$. Let $\theta$ be the image of $C$ under the abel Jacobi map.
Is there exist a divisor $D$ in $J$ such that $D.\...
- 137
-2
votes
2
answers
477
views
Lower bound of q pochhammer symbol [closed]
How one could prove, that q pochhammer symbol $(1,1/n) = \prod_{k = 1}^{\infty}(1-\frac{1}{n^k}) \geq 1 - \frac{1}{n-1}$
-2
votes
1
answer
214
views
About infinite products and Euler Gamma functions [closed]
I am interested in knowing how to calculate infinite products like (or reading any reference about it):
$$\prod_{j=1}^{\infty}\left( 1-\left( \frac{x}{a+j\pi} \right) ^2 \right)$$
Inserting it into ...
-2
votes
1
answer
173
views
About intersections of two totally isotropic subspaces fo a quadratic form [closed]
Let $Q$ be a quadratic form on $\mathbb R^{2m}$ with the signature $(m,m)$. The maximal totally isotropic subspaces in $(\mathbb R^{2m},Q)$ have then dimensions $m$.
What dimensions $1,...,m-1$ of ...
- 11
-2
votes
1
answer
964
views
On the Cauchy-Schwarz Inequality for trace function of random matrices
In the deterministic case, for two matrices $A$ and $B$ with appropriate matrices, we know that
$$tr((A^{T}B)^{2})\leq tr(A^{T}A)tr(B^{T}B)$$
which is the trace form of Cauchy-Schwarz-Inequality (CSI)....
- 77
-2
votes
1
answer
577
views
Can this criterion to indicate the randomness some numbers? [closed]
John Derbyshire in his book PRIME OBSESSION says on page 366:
CHAPTER 3
10.
"Here is an example of e turning up unexpectedly. Select a random number
between 0 and 1. Now select another and add ...
- 1,305
-2
votes
1
answer
131
views
Prove or disprove Any subgroup of differentiable lie group is analytic submanifold? [closed]
I have made a research in the web to know more about analyticity of of lie group and to give a convinced answer to this question which i have accrossed it in my research which is stated the following :...
-2
votes
1
answer
180
views
When is the following fraction an integer $\frac{3^a}{2^b-3}[(\frac{2^b}{3})^c - 1]$ where $a,b,c \in \mathbb{Z}$? [closed]
I'm trying to evaluate the following fraction $\frac{3^a}{2^b-3}[(\frac{2^b}{3})^c - 1]$, but I'm getting stuck using gcd arguments or divisibility arguments. This is part of an ongoing research I'm ...
- 109
-2
votes
1
answer
339
views
Representing logic formulae in manifolds [closed]
Is there a meaningful way to transform logical equations (for instance $a \implies b$; $b \land a \implies c$ etc.) into geometrical representation in spaces such $\mathbb R^n$, $\mathbb C^n$ or ...
- 17
-2
votes
1
answer
138
views
Identifying two non-adjacent vertices and the effect on the Hadwiger number [closed]
Suppose $G$ is a finite simple graph. Let $h(G)$ denote the Hadwiger number of $G$; that is, the maximum $n\in\mathbb{N}$ such that $K_n$ is a minor of $G$.
What is an example of a graph $G_0=(V_0, ...
- 48.9k
-2
votes
1
answer
74
views
Matching and minimal degree
Let $n\in\mathbb{N}$ be a positive integer and let $G =(V,E)$ be a connected simple undirected graph with $|V| = 2n$. Is it true that if for the minimal degree $\delta(G)$ we have $\delta(G) \geq n$, ...
- 48.9k
-2
votes
1
answer
73
views
Edge covers of graphs with $\chi(G) \geq \aleph_0$
If $G=(V,E)$ is a simple, undirected graph, then $C\subseteq V$ is an edge cover if $C\cap e \neq \emptyset$ for all $e\in E$.
Let $G=(V,E) $ be a graph with infinite chromatic number. Is every edge ...
- 48.9k
-2
votes
1
answer
107
views
Does Maurer-Cartan form define surjection from Lie Group to Algebra-valued forms?
Let $G$ be a connected Lie Group of dimesion $m<\infty$ and let $g\in G$. The Maurer-Cartan form allows us to define a map from $G$ to the space of $\mathfrak{g}$-valued forms, via
$$g\rightarrow ...
- 99
-2
votes
1
answer
169
views
If the set of the output of a computable function is finite, is the sequence periodic eventually? [closed]
$$f:N \rightarrow B,\space B\subset N $$ and $B$ is finite, $S$ is the sequence constructed by $f(1),f(2)\cdots f(i)\cdots $.
Now, if $f$ is a computable function,is $S$ eventually periodic?
Update: ...
- 3,104
-2
votes
1
answer
277
views
Cramer's conjecture and Jacobsthal function
This question is a follow-up to my comment to the answer to this question. Writing $g_{n}:=p_{n+1}-p_{n}$, and as all numbers between $p_{n}$ and $p_{n+1}$ are composite, one has $j(p_{n})=O(\log^{2}...
- 6,982
-2
votes
1
answer
83
views
Splitting the vertices of undirected graphs into 2 sparse sets
(A version of this question for undirected graphs.)
Let $G=(V,E)$ be a finite, simple, undirected graph. For $v\in V$ set
$$
N(v) := \{x\in V: \{x,v\}\in E\}.
$$
Is it possible to find a ...
- 48.9k
-2
votes
4
answers
230
views
Finding integer zeroes for a particular family of equations [closed]
Given $p,q\in\mathbb Z^+$, and a vector $v=(x_1,\dots,x_{p+q})$ we consider the function $\chi(v)$:
$$\chi(v)=x_1^2+\dots+x_p^2-x_{p+1}^2-\dots-x_{p+q}^2$$
We wish to find solutions to $\chi(v)=0$ ...
- 1,226
-2
votes
1
answer
5k
views
Looking for the name of a mathematical symbol that looks remotely like 1 (answer: indicator function) [closed]
Original question:
The symbol looks like a numeral 1 written like an R in $\mathbb{R}$. It has a double vertical line and a serif at the bottom. It represents a function of a parameter: $1_{\{0,1\}}(x)...
- 121
-2
votes
1
answer
156
views
Recursion, Common Term, Combinatorics [closed]
May we find the common term for recursive sequence? if yes that how to find the common term of recursive sequence such: 1 2 1 3 1 2 1 4 1 2 1 3 1 2 1 5 1 2 1 3 1 2 1 4 1 2 1 3 1 2 1 6 ...
in a ...
- 13
-2
votes
1
answer
201
views
A question about the maximal subgroup of SO(n+1)? [closed]
Is SO(n) a maximal subgroup of SO(n+1)?
- 71
-2
votes
1
answer
137
views
Two graph structures on $\text{Hom}(G,H)$
By a graph I mean a pair $G = (V, E)$ where $V$ is a set and $E \subseteq [V]^2 := \{\{a,b\}: a\neq b \in V\}$. A graph homomorphism between graphs $G, H$ is a map $f:V(G)\to V(H)$ such that $\{v, w\}\...
- 48.9k
-2
votes
1
answer
291
views
stable splitting into a wedge sum [closed]
Suppose $X$ is a CW-complex such that there is a stable splitting of $X$ into wedge sum
$$
\Sigma^t X\cong \bigvee _{k=1}^\infty Y_k.
$$
(1). Does this imply
$$
X\to \Sigma^tX\to \bigvee _{k=1}^\...
- 1,990
-2
votes
1
answer
844
views
How can we solve the TSP problem using game theory? [closed]
Is there a known way to model the traveling salesman problem (TSP) using non-cooperative game theory?
I only found in the internet cooperative game theory. Why there is no work that solves the TSP ...
- 97
-2
votes
1
answer
259
views
Reductive space & Reductive Lie algebra
If $M=G/H$ is a reductive space and $\mathfrak{g}=\mathfrak{h}+\mathfrak{m}$ be the canonical decomposition, then are $\mathfrak{g}$ or $\mathfrak{h}$ or both reductive lie algebras? (in this case, ...
- 55
-2
votes
1
answer
328
views
Is there any Lefschetz-like principle for representations of finite groups?
Representation theory (at least the origin of this terminology) aims to exhibit a model (a represetative) in the group of matrices for an abstract group which is known by only its group law. So ...
- 2,583
-2
votes
2
answers
389
views
Equality of two conditional expectations
I would like to show that for any random variable $X$ and $Z$ such that $X$ and $Z$ are independent and for any measurable functions $f$ and $g$,
$$ \mathbb E \left[ f(g(X),Z) | g(X) \right] = \...
- 19
-2
votes
1
answer
248
views
Upper and lower limits [closed]
Find the following limits:
(1) $\limsup_{n\to\infty } \sin (n!) $
(2) $\liminf_{n\to\infty } \sin (n!) $
(3) $\limsup_{n\to\infty } \cos (n!) $
(4) $\liminf_{n\to\infty } \cos (n!) .$
- 469
-2
votes
1
answer
151
views
Is there some lattice not rigid
I heard that in complex hyperbolic space setting for example CH2, there is some deformation of lattice nontrivial. What confused me is it seems contradicting Mostow Rigidity. Could someone explain ...
- 1,121
-2
votes
1
answer
212
views
This theorem is true or false in infinite dimensions?
Consider a vector space $E$ with finite dimension and linear map $A: E \rightarrow E$. The following statements are equivalent:
$x'(t)=A \circ x(t)$ defines an attractor.
All eigenvalues of $A$ have ...
- 279
-2
votes
1
answer
289
views
Giuga and Carmichael numbers [closed]
If $p$ is both Giuga and Carmichael number
then its known that
$1^{p-1}+2^{p-1}+3^{p-1}+\cdots+(p-1)^{p-1} \equiv -1\pmod{p}$
is it true that
if $p$ is both Giuga and Carmichael number then
$1^{...
- 103
-2
votes
1
answer
788
views
Hilbert polynomials on a scheme
For a scheme $X$ of finite type over $k$, and a coherent sheaf $\mathcal{F}$ on $X$, the Hilbert polynomial of $\mathcal{F}$ is defined by $\Phi(n)=\chi(\mathcal{F}(n))$.
And for a scheme $X$ over $S$...
- 1
-2
votes
1
answer
427
views
Is the Chow ring's push forward of inclusion map a ring homomorphism?
Given a nonsingular projective variety $X$ with a close subvariety $Y \subset X$, let the inclusion map be $i : Y \rightarrow X$. Let $A(X)$ and $A(Y)$ be the Chow ring of $X$ and $Y$ respectively, is ...
-2
votes
1
answer
2k
views
sections of tensor product bundle ( tensor product of two vector bundles ) [closed]
Suppose we have a smooth manifold M and E--->M is a vector bundle. A connection on E is a linear map from the set of all smooth section on E into the set of smooth sections of the tensor product of E ...
- 165
-2
votes
1
answer
283
views
How to work with infinite random graph(s) ?
Hi,
In the case where we are dealing with an infinite random graph (RG with infinite nodes).
How do we model/work with notions like degrees, degree distribution ? How are they defined ?
Thanks!
- 167
-2
votes
1
answer
578
views
Simply-Connected Regions and Phragmen-Lindelöf Theorem
It's easy to see that the Phargmen-Lindelöf theorem from complex analysis can be generalized to non-simply-connected regions. Namely to regions $G$ with the property that for each $z \in \partial_\...
- 253
-2
votes
1
answer
103
views
Effectiveness of a wedged bundle
Let $X$ be a smooth projective variety, and let $E=\mathcal{O}\oplus \mathcal{O}(1)$ be a vector bundle of rank $2$. Then $L=\wedge ^{2} E $ is a line bundle on $X$. Is $L(-2)$ $\mathbb{Q}$-linear to ...
- 393
-2
votes
2
answers
167
views
Multiple Linear Regression Estimation without full recalc [closed]
Ok, so I am running a classic linear regression where betahat = (X'X)^-1X'y
Due to performance issues, I would like to estimate betahat with an additional data point (x1,x2,x3,x4,...,y) without ...
- 1
-2
votes
1
answer
947
views
Holonomy group of calabi yau manifold
Let $(M,J,\omega, \Omega)$ be a calabi-yau manifold (not necessary compact). Does it follow that the holonomy group of $M$ is $SU_{n}$, where $n$ is the complex dimension of $M$ ?
- 89