# All Questions

**-1**

votes

**0**answers

15 views

### probability distribution [on hold]

X is a continous random variable of normal distribution for the length of the rulers produced in a factory. Given X has mode of 15 cm and standard deviation of 1 cm. A ruler is randomly selected from ...

**-1**

votes

**0**answers

34 views

### How to show Well Founded Induction false? [on hold]

The abstract reduction system ({a,b,c,d},→) where the → is defined as:
http://i.stack.imgur.com/TS0Ud.png
Let Q be a monadic predicate on {a,b,c,d} such that Q(a) = Q(b) = false and Q(c) = Q(d) = ...

**3**

votes

**2**answers

234 views

### If d(“G/H”) < d(G) = 2, must H contain a primitive element?

Let $G$ be a finite group that can be generated by $2$ elements, and let $H \leq G$ be a (not necessarily normal) subgroup for which there exists some $g \in G$ such that $H \langle g\rangle = G$. ...

**-2**

votes

**0**answers

30 views

### Underlying Set in Model Theory [migrated]

In model theory a structure has an underlying set.
In addition to the interpreted relations, are there
(implicit) assumptions made about possible
operations on this set? For example, is it assumed to ...

**3**

votes

**0**answers

111 views

### Blowig-up a point in the singular locus

Let $X\subset\mathbb{P}^n$ be a variety singular along a smooth subvariety $Z\subset X$ of positive dimension. Let us assume that $X$ has ordinary singularities along $Z$. Now, let $\pi:Y\rightarrow ...

**0**

votes

**0**answers

19 views

### Practical Way to Detect a Markov Chain is Regular Given the Transition Matrix [migrated]

I understand that a Markov Chain is reducible if, given its transition matrix $P$, there exists $n$ such that every element of $P^n$ is greater than 0.
However, I am wondering that if there is an ...

**6**

votes

**2**answers

182 views

### Homological criterion for $A(B \cap C) = AB \cap AC$?

Is there a homological criterion for the condition $A(B \cap C) = AB \cap AC$ for ideals in a ring $R$? I mean a statement such as "the given equation holds if and only if (some $\operatorname{Tor}$, ...

**10**

votes

**1**answer

218 views

### When is $X \rightarrow \text{Spec}(C(X))$ a homeomorphism?

Let $X$ be compact Hausdorff topological space. Consider the ring $C(X)$ of continuous functions $X \rightarrow \mathbb C$ (we do not consider the C* algebra structure, just consider $C(X)$ as a ring) ...

**-2**

votes

**0**answers

31 views

### Backpropagation KL-divergence for training “one level neural network” [on hold]

Hi I hope that some one could help me.
I have a L matrix (25x1000) (I have 10000 works each work is represent by 25 bits)
I map each word to one of 5 classes {vary negative,negative, ...

**-3**

votes

**0**answers

51 views

### Strict partition of size n [on hold]

I want to know how to calculate how many strict partitions of X are with size n.
For example there are 22 partitions of number 8, and there are 6 strict partitions of 8 (partitions with distinct ...

**-2**

votes

**0**answers

72 views

### Analytic formula to evaluate the exact value of solid angle subtended by an ellipse at any arbitrary point lying on the vertical axis [on hold]

`Question: How to evaluate the exact value of solid angle subtended by an ellipse (or elliptical plane) at any arbitrary point lying on the vertical axis passing through the center.
Standard equation ...

**0**

votes

**0**answers

69 views

### Relating overlapping simplicial complexes

Let $X$ be a simplicial complex and let $A,B\subset X$ be
subcomplexes such that $C=A\cap B$ is a non-empty simplicial
complex. Finally, let $C_{\cdot}(X)$, $C_{\cdot}(A)$, $C_{\cdot}(B)$,
...

**1**

vote

**1**answer

100 views

### Is there a formula for the intersection of projectivized lines inside a projectivized vector bundle?

Let $E\rightarrow D$ be a complex rank two vector bundle over a compact complex
one dimensional manifold $D$. Let $L_1, L_2 \subset E$ be rank one subbundles of E
(i.e. line bundles). Let
$$ n_1:= ...

**0**

votes

**0**answers

61 views

### Integral geometry and curvature of surfaces

I'll stick to 2-surfaces in $\mathbb{R}^3$ for simplicity. Higher dimensions generalizations welcome.
In classical integral geometry, we may obtain up to a scaling factor, for example, the surface ...

**0**

votes

**0**answers

29 views

### Find all integers x, y, and z such that 1/x + 1/y = 1/z [migrated]

Characterize all positive integers x, y, and z such that $\frac{1}{x} + \frac{1}{y} = \frac{1}{z}$. For example, $\frac{1}{x+1} + \frac{1}{x(x+1)} = \frac{1}{x}$

**0**

votes

**0**answers

23 views

### contiguity and infinite complexes

Two simplicial maps $f: K^{(n)}\to L$, $g: K\to L$ are called contiguous if for every simplex $\tau\in K^{(n)}$ and it carrier $\sigma$ we have that $f(\tau)\cup g(\sigma)$ is a simplex in $L$.
It ...

**0**

votes

**1**answer

126 views

### A question about open subsets of Hilbert space whose complements are compact sets

Let $H$ be an infinite-dimensional separable Hilbert space. Let $C$ be the intersection of a denumerably infinite sequence of sets, each of which is the complement of a compact subset of $H$. In other ...

**17**

votes

**4**answers

878 views

### Residual finiteness: why do we care?

Residually finite groups have been studied for a long time. However, I am struggling to work out why we care, or perhaps, why they continue to be of interest. Let me explain.
Magnus, in his 1968 ...

**5**

votes

**1**answer

131 views

### Comparing cardinalities of the spectrum of two masas in $B(H)$

If I imagine that (the self-adjoint part of) a C*-algebra $A$ represents the algebra of observables of some quantum system, then certain perspectives on algebraic quantum theory would ask me to ...

**6**

votes

**0**answers

152 views

### Polynomial growth without Gromov's theorem

It is a consequence of the theorem of M. Gromov on groups with polynomial growth and a result of P. Pansu(*) that if a finitely generated group $\Gamma = \langle S\rangle,\, S=S^{-1}$ satisfies ...

**5**

votes

**1**answer

108 views

### Foliations of Lorentzian manifolds by Spacelike Hypersurfaces

Suppose that $M$ is a Lorentzian manifold (not necessarily satisfying Einstein's equations). What conditions do we need in order to guarantee that $M$ admits a foliation by codimension-$1$ spacelike ...

**1**

vote

**1**answer

126 views

### Symplectic (contact) structure on $M_{n}(\mathbb{R})$

Assume that $n$ is an even number. What is a natural symplectic structure on $M_{n}(\mathbb{R})$, such that for every $1\leq k \leq n$ the manifold of $k$-rank matrices would be invariant under ...

**1**

vote

**1**answer

165 views

### How does one compute the first Chern class of a Line bundle defined as the Kernel of a linear map?

Let $M$ and $N$ be compact complex manifolds of the same dimension ($m$) and
$\mu: M \rightarrow N$ a holomorphic map. Let $D \subset M$ be the subset of
points of $M$, where $d\mu|_p$ fails to be ...

**0**

votes

**1**answer

136 views

### Function field of the Jacobian of genus 2 curve over $\mathbb{F}_q$

I have been trying to build the function field of the jacobian of a genus 2 smooth curve over a finite field, but I am having problems making it explicit, I need to work with another curve with points ...

**5**

votes

**3**answers

121 views

### Product of binary Boolean operators

I asked this question a day ago on math.stackoverflow but figured it could have an interest here.
I'm interested in the set $\mathcal{P}_N$ of boolean functions of boolean variables $p_1, p_2, ...

**0**

votes

**0**answers

63 views

### Pro-constructible subset of scheme intersects very dense subsets?

Let $X$ be a scheme, let $D$ be a very dense subset of $X$ and let $Y$ be a pro-constructible subset of $X$. Is it true that $Y \cap D \neq \emptyset$?
If $Y$ is just constructible, this is true.
...

**0**

votes

**0**answers

55 views

### Characterization of the stable manifold [on hold]

Assume we study a (finite dimensional) differential system
$$
x'(t)=f(x(t)), \quad x(t) \in \mathbb R^n,
$$
for a smooth function $f$ and such that $0$ is an equilibrium point. Thus, we have existence ...

**-1**

votes

**0**answers

33 views

### Combinatorial optimization problem [on hold]

Suppose I have a population, divided into 6 known classes. I get a feasible solution when I select 2 elements from each class (so, 12 in total). For every feasible solution, I can compute a "cost". ...

**-2**

votes

**0**answers

51 views

### Good upper bound for an alternanting series [on hold]

Someone know a good upper bound for the partial sums of $S=\sum(-1)^{n+1}\sqrt{n}$?
I mean how fast is the growth of this sum?

**-4**

votes

**0**answers

57 views

### Can a non-compact manifold be embedded? [on hold]

Can a non-compact smooth manifold be embedded into another smooth manifold? Moreover, Can we get a diffeomorphism between tow non-compact manifolds ?
The first part of the question is about smooth ...

**0**

votes

**0**answers

67 views

### Rolling map as a diffeomorphism?

Let $M$ be a (compact) Riemannian manifold and $x \in M$. For a piecewise smooth path $\gamma: [0, T] \longrightarrow M$, we can define Cartan's development map (or rolling map)
$$(\Phi\gamma)(t) = ...

**0**

votes

**0**answers

75 views

### When an integral with respect to a Poisson point process is finite?

Let $N(ds,dv)$ be a Poisson measure on $\mathbb{R} _+ \times \mathbb{R} _+$ with intensity $dsdv$. Let $N = \sum\limits \delta_{(s_i,v_i)}$. Assume that $N$ is compatible with a filtration $\{ ...

**0**

votes

**0**answers

157 views

### Multiplication Map, Is it invariant?

Let $\pi:X\rightarrow Z$ a double cover of an elliptic curve with genus $g\geq 3$. Choose a general rank 2 and degree -1 vector bundle $F$ on $Z$, let $E=\pi^*F$ and fix $x\in X$. The involution $i$ ...

**3**

votes

**1**answer

77 views

### Upper bounds on elements of a matrix

During my research I have come across matrices this type
$$C=B\left(B^T B\right)^{-1}B^T\ ,$$
where $B$ is an $m\times n$ real matrix. If $B^TB$ is not invertible, then $\left(B^T B\right)^{-1}$ ...

**-5**

votes

**0**answers

28 views

### what is the computational complexity for finding SVD and pseudo inverse? [on hold]

For a given MxN matrix A and A is full rank matrix (rank=N and M>N),what is the computational complexity for finding SVD and pseudo inverse ?Which one will be having low complexity?

**0**

votes

**0**answers

18 views

### Deriving inequalities from a polynomially-bounded derivative

In this paper (p. 2, definition/remark) the following notion of ‘polynomial growth’ is defined for a non-negative real function $g(x)$ and a real constant $b\in(0;1)$:
There exist positive ...

**10**

votes

**1**answer

205 views

### Piecewise linear (PL) structures on $\mathbf R^4$

One can read in Wikipedia that the 4-dimensional affine space $\mathbf R^4$ has uncountably many piecewise linear structures (in contrast with other dimensions, where it has exactly one). A reference ...

**3**

votes

**1**answer

796 views

### Who coined “mob” and “clan” and why these words?

A mob is a word used for a topological semigroup which is a Hausdorff space. A clan is a compact connected mob with a two-sided identity element.
Who used these words with these meanings first and ...

**-1**

votes

**0**answers

43 views

### Hyperbolic paraboloid, Analytic Geometry [on hold]

Please don't ban this question, I just need some advice on how to find the equation of the tangent plane on a point of the hyperbolic paraboloid which is perpendicular to a certain plane say ...

**1**

vote

**1**answer

164 views

### Relation between intersection and product of ideals

Let $C$ be a smooth projective (irreducible) curve in $\mathbb{P}^n$ for some $n$. Denote by $I_C$ the ideal of $C$. Let $g \in I_C\backslash I_{C}^2$, an irreducible element. Is it true that for any ...

**1**

vote

**1**answer

53 views

### An example of a non-(locally cyclic) Abelian group whose automorphism group is cyclic not of order $2$

In the wake of my curiosity on this kind of things, I was thinking if there is an example of a non-(locally cyclic) Abelian group whose automorphism group is cyclic not of order $2$. Every example I ...

**-1**

votes

**0**answers

75 views

### Represention of the element of a group: A Confusion [on hold]

I am reading a paper "FAST ALGORITHMS FOR CALCULATION OF GIBBS DERIVATIVES ON FINITE GROUPS" by R. S. Stankovic (Approx. Theory & its AppL 7:2, June 1991). In Section 2, following is written about ...

**1**

vote

**0**answers

95 views

### Averages of $L(s,\chi)$

Let $(\frac{m}{n})$ denote the usual quadratic Jacobi symbol.
What is the
abscissa of convergence
of the double Dirichlet series ?
$$
\sum_{\substack{m,n \in \mathbb{N} \\ \gcd(m,n)=1 \\m,n\equiv 1 ...

**-4**

votes

**0**answers

20 views

### Expression in theta notation [on hold]

Am I right that the theta notation for the following expression is: $n^2+(n^3/2)$ = theta ($gn^3$) as $n^2/2$ is the low order term

**0**

votes

**0**answers

109 views

### On Gromov's Theorem on Symplectic Homotopy

I want to understand the proof of the following theorem due to Gromov which I'll state in the context of Euclidean spaces. While I tried to read the proof from Macduff-Salamon, it turned out that my ...

**0**

votes

**0**answers

61 views

### A simple question about a resolution of a conifers singularity

Let $X$ be a conifold defined by the equation $xy-zw=0$ in $\mathbb{C}^4$ and $\tilde{X}$ its crepant resolution, which is isomorphic to $\mathcal{O}_{\mathbb{P^1}}(-1)^{\oplus 2}$. Then there is a ...

**7**

votes

**1**answer

130 views

### When is the tensor product of two graphs planar?

Given two graphs $G=(V_1,E_1)$ and $H=(V_2,E_2)$, the tensor product of $G$ and $H$ is the graph $G \times H = (V,E)$, where $V=V_1 \times V_2$ is the Cartesian product of the $V_i$ and
$ (u,v) \ E \ ...

**1**

vote

**1**answer

91 views

### configuration spaces of real projective space

Let $F(\mathbb{R}P^n,k)$ be the $k$-th ordered configuration space on $\mathbb{R}P^n$. In http://arxiv.org/abs/1502.04258, the cohomology ring
$$
H^*(F(\mathbb{R}P^n,k);R)$$
is obtained for any ...

**0**

votes

**0**answers

42 views

### To prove ideals are coprime [closed]

Let $K=\mathbb Q(\sqrt{-m}) $ be a quadratic field. Let $ O_K$ be ring of algebraic integers. Let $\alpha=a+b\sqrt{-m}\in O_{K} $ with gcd$(a,b)=1 .$ Then how to show that $\langle \alpha \rangle $ ...

**0**

votes

**1**answer

61 views

### Obstruction to the existence of global isometries on a constant-curvature Riemannian manifold

Let $M$ be an $m$-dimensional simply connected Riemannian manifold that is not geodesically complete. Suppose $M$ has constant sectional curvature.
Because the curvature is constant, locally $M$ ...