# All Questions

**0**

votes

**0**answers

3 views

### A property of minimal prime ideals

Let $R$ be a commutative ring with $1$, and let $\frak{p}$ be a minimal prime ideal of $R$. If $\frak{p}\subseteq I_1\cap I_2$, where $I_1$ and $I_2$ are two ideals of $R$, can we deduce that $ \...

**0**

votes

**0**answers

6 views

### Exact formula for computing n-step transition probability of random walks with self-transitions

Consider a semi-infinite random walks $X_n$, $n=0,1,2,\ldots$, whose state space is a set of consecutive integers and whose one-step transition probabilities are $P_{ij}=\mathrm{Pr}\{X_{n+1}=j|X_n=i\}$...

**0**

votes

**0**answers

21 views

### Bijection modeling isomorphism of infinite-dimensional vector spaces

Let $T : V \to W$ be an isomorphism of vector spaces with bases $B_V$ and $B_W$, which may be of any cardinality.
Does there exist a bijection $f : B_V \to B_W$ such that, for each
$b_V \in B_V$,...

**1**

vote

**1**answer

38 views

### Cambridge Mathematical Tripos papers from late 19th century

Are the scanned images of Cambridge Mathematical Tripos papers from late 19th century available anywhere on Internet?

**0**

votes

**0**answers

11 views

### Variation of Radon transform for probability measures on $\mathbb C$

Let $\mu$ be a probability measure on $\mathbb C$. For $z \in \mathbb C$, let $$f^z \colon \mathbb C \to \mathbb R_{\geq 0}$$ be the function $f^z(\lambda) = |\lambda - z|$. Consider now the family $(\...

**1**

vote

**1**answer

66 views

### Could I affirm that $f$ is not identically 0?

Consider the following situation: Let $\Omega =l^{\infty}(\mathbb{R})$ be the
space of all bounded sequences of real numbers. We will consider in $\Omega$ the metric:
$
d(x,y)=\sum_{i\geq 1}\frac{|...

**3**

votes

**0**answers

18 views

### When is a functorial coverage a sheaf, and what universal property does it have?

In The Elephant (A.2.1.9), Johnstone defines the notion of a coverage on a category $\mathcal{C}$. Quoting verbatim, a coverage on $\mathcal{C}$ is
a function assigning to each object $A$ of $\...

**2**

votes

**0**answers

32 views

### Measures on a unit sphere of a Hilbert space

Consider a real separable infinite-dimensional Hilbert space $H$. Let $S=\{h\in H\mid \|h\|=1\}$ be a unit sphere in $H$. What are the most natural measures on $S$? Is there a (Borel) measure $\mu$ on ...

**1**

vote

**0**answers

29 views

### Reference quest: variety of lines and variety of planes

Let $X\subset \mathbb P_{\mathbb C}^n$ be a smooth projective variety, $F(X)\subset G(2,n+1)$ its Fano variety of lines and $$I_F=\left\{([l],[l'])\in F(X)\times F(X), l\cap l'\neq \emptyset\right\}$$ ...

**1**

vote

**0**answers

25 views

### Ellipticity of Bott-Chern Laplacian

I want to prove that Bott-Chern Laplacian
$$\tilde{\Delta}_{BC}^{p,q}=(\partial\bar\partial)(\partial\bar\partial)^*+(\partial\bar\partial)^*(\partial\bar\partial)+(\bar\partial^*\partial)(\bar\...

**0**

votes

**0**answers

43 views

### graduate study in graph theory and combinatorics in canada [on hold]

I'm looking for any graduate programs related to graph theory or combinatorics in canada like in waterloo or simon fraser universities. any other suggestions?

**6**

votes

**0**answers

127 views

### getting papers published when you're not affiliated to a university

I graduated in Maths 20 years ago, spent a long time away from the subject and recently returned to it. I work entirely alone right now but after a refresher phase, I'm starting to look at some very ...

**3**

votes

**2**answers

358 views

### Unreasonable application of mathematics in the other areas

What are some papers or talks on the philosophy of mathematics which contains some statements about the unnecessary and unreasonable application of mathematics in other areas of science?
I found ...

**-4**

votes

**0**answers

25 views

### Better tuition for 10th grade math [on hold]

Which is better, online tuition or private tuition for 10th grade math?

**0**

votes

**1**answer

54 views

### Exterior derivative on principal bundle [on hold]

In Nakahara's Geometry, Topology and Physics on page 375, he constructs a Lie-algebra-valued one-form $\omega$ on a principal bundle $P$ by "lifting" a Lie-algebra-valued one-form $\mathcal A_i$ on an ...

**-5**

votes

**0**answers

25 views

### Cardinality of infinite sets' subtraction [on hold]

$A = \mathbb{N}$; $B = \{\frac{p}{q} : p, q \in \mathbb{Z}\setminus\{0\}\}$. Find the cardinality of $P(A\setminus B)$.
We know that the cardinality of $\mathbb{N}$ is $\aleph_0$, so as the ...

**1**

vote

**0**answers

61 views

### Description of connecting maps of Derived functors

Let $C$ be an abelian category with enough injectives and $F$ be a left exact additive functor. Consider the short exact sequence $0 \to A' \to A \to A ''\to 0$. Therefore, we have connecting maps $\...

**2**

votes

**1**answer

40 views

### Have semigroups with actions on themselves that have a dual to the compatibility axiom ever been studied?

For a semigroup $G$ with a left action on itself, the axiom for compatibility becomes:
$$
\forall f,g,h\in G:hg(f)=h(g(f))
$$
Now suppose there is additional axiom, or constraint if you prefer, ...

**0**

votes

**0**answers

41 views

### is it possible to solve this nonlinear differential equation analytically? [on hold]

I have a hard time trying to solve a first order nonlinear equation, I posted it in math.stackexchange but I did not get any answer.
I have the following first order differential equation:
$$y^2\...

**0**

votes

**0**answers

20 views

### optimize a Quadratic Matrix Programming with multi-spherical constraints

I have got the following quadratic problem restricted on the Cartesian product of Euclidean spheres.
$\underset{X \in \mathbb{R}^{n\times 3}}{\text{min}}$ $Q(X) = \frac{1}{2} Tr(X^TA X) + Tr(B^T X)$
...

**8**

votes

**0**answers

46 views

### On spatial tensor products of von Neumann algebras

Let $H$ be a Hilbert space, and let $A_1,A_2,A_3\subset B(H)$ be three commuting von Neumann algebras.
We write $\odot$ for the algebraic tensor product,
and $\bar\otimes$ for the spatial tensor ...

**0**

votes

**0**answers

32 views

### Relative Leopoldt defect

Let F be a totally real field such that the Leopoldt conjecture holds at a prime number $p$ and $M$ be a quadratic totally real extension of $F$.
Is there a bound of the Leopoldt defect of $M$ ?

**0**

votes

**0**answers

28 views

### $nD$ rotation around a general $(n-2)$-dimensional subspace [on hold]

According the Rodrigues' Rotation Formula $3D$ rotation matrix $\in$ $SO(3)$
corresponding to a rotation by an angle $\theta$ about a fixed axis specified by the unit vector $\hat{\omega}=(\omega_x,\...

**9**

votes

**0**answers

277 views

### Why should Algebraic Geometers and Representation Theorists care about Geometric Complexity Theory?

Geometric Complexity Theory has demonstrated that Complexity Theorists should care about Algebraic Geometry and Representation Theory, but, why should Algebraic Geometers and Representation Theorists ...

**-4**

votes

**0**answers

30 views

### A number divided by 2 n times and sum each division [on hold]

Is there a function that can complete n number of divisions by 2 and sum?
If your base is 400 for example and n=5:
answer ...

**3**

votes

**0**answers

42 views

### commutativity of a diagram in cohomology of $C^*$-algebras

The setting is the same as in my last question commutative diagram with $K_{i+1}(A)\to K_i(A\rtimes_{\rho} \mathbb{R})$ (for $C^*$-algebras) :
Let $A$ be in the bootstrap category (=N in the other ...

**1**

vote

**1**answer

69 views

### Some integrals with respect to a Gaussian measure on a Hilbert space

Assume that $(H,\langle\cdot,\cdot\rangle)$ is a real separable Hilbert space equipped with a Gaussian measure $\mu$ with a mean $m$ and a covariance operator $C$. Let $x\in H$ be a fixed vector. What ...

**2**

votes

**1**answer

71 views

### Number of vectors of fixed norm

Let $P$ and $Q$ be two even, unimodular, positive definite quadratic forms of rank $n$. Let $r_{k}(P)$ be the number of vectors of norm $k$, in symbols:
$$
r_k(P)=\textrm{cardinality of }\{v\in \...

**0**

votes

**0**answers

63 views

### some strange sums ramanujan type

i found sum as
$$\sum _{k=0}^{\infty } \frac{e^{k x} \left(-\frac{1}{y}\right)^k}{p-e^{k x}}=\sum _{n=1}^{\infty } \left(\frac{-1+\, _2F_1\left(1,\frac{2 i n \pi -\log \left(-\frac{1}{y}\right)}{x};\...

**-1**

votes

**0**answers

25 views

### product distinct prime factors of prime(n)-1 and prime(n)+1 [on hold]

The prime 127 has 127-1=126 with distinct prime factors 2,3,7 and 127+1=128 with
distinct prime factors of only 2; hence 2*3*7=42<127. Log 127/42=q=1.296. Are
such primes common? Can a value of ...

**1**

vote

**0**answers

57 views

### The Linnik problem for dimension $2$

For $N$ an integer, let
$$\Omega_N:=\left\{\frac{\alpha}{\|\alpha\|}|\alpha \in\textbf{Z}^n~\text{and}~\|\alpha\|^2=N\right\}.$$
For $n=3$, Linnik asked if the set $\Omega_N$ was uniformly distributed ...

**0**

votes

**0**answers

58 views

### Finding the unique Nash equilibrium [on hold]

$$
m^2(1-m)[(1+m)^2 - R] x^3 + [6m^2R + 12mR - 2m(1-m^2)(6+2m) - 4tm^2(1+m)^2] x^2 + [(1-m)(6+2m)^2 + 8tm(1+m)(6+2m)] x - 4t(6+2m)^2=0
$$
where:
m ∈ (0, 0.5), R ∈ [0, 0.25], t ∈ [0, 1], x ∈ [0, 2]...

**2**

votes

**0**answers

47 views

### On the size of residue class

Let $n \in \mathbb{N}$ be a odd number. Let $S \subseteq \{1,3,5,7,...,n-2,n\}$ and $|S|$ is even number. Let $R_i^k=\{a \mid a \in S \text{ } \&\text{ } a\equiv i \text{ }(mod \text{ } k)\}$ ...

**-1**

votes

**0**answers

10 views

### Markov Chain: Number of communicating classes of a power of the irreducible transition matrix [on hold]

Suppose $P$ is an irreducible transition matrix, with period $d$. Consider the transition matrix $P_k$. In terms of $d$ and $k$, how many communicating classes does $P_k$ have, and what is the period ...

**5**

votes

**0**answers

96 views

### Why is every object cofibrant in an excellent model category?

In Appendix A.3 of the book higher topos theory appears the notion of an excellent model category (see Definition A.3.2.16). The main feature of this notion is that when $\mathbf{S}$ is an excellent ...

**4**

votes

**0**answers

36 views

### Examples of maps with nontrivial Hopf invariant but Lusternik-Schnirelmann category of the cofiber doesn't increase?

Let $A$ be a suspension and $X$ be a space with Lusternik-Schnirelmann category $n$ and let $\alpha: A\to X$. It is easy to see that the cofiber $C_\alpha$ has $\mathrm{cat}(C_\alpha) \leq n+1$. One ...

**0**

votes

**0**answers

53 views

### Application(s) of complex dynamical system into some other areas of mathematics [on hold]

Complex dynamical system is a very active branch in mathematics. I wondered are there some nice applications of complex dynamical system into the some other areas of mathematics.

**1**

vote

**0**answers

49 views

### relative chernoff bound

Is the following true? Is there a contradicting example?
Let $x_1,\ldots,x_n$ be independent random "bits", with $\forall u:\Pr[x_i=u]\in\{0,\frac{1}{2}\}$. Denote $x=\sum_i x_i$, and assume $\mathrm{...

**-1**

votes

**0**answers

66 views

### Are the theorems of Ergodic Theory valid for non-probability spaces?

The theorems in Ergodic Theory have assumed a probability measure, always. I am interested to know if they hold even when the space is not equipped with a probability measure. In other words, if my ...

**-5**

votes

**0**answers

20 views

### How can you prove that f(x) DNE when f(x)+f(2-x)=3x^2+4x+2? [on hold]

How can you prove that f(x) DNE when f(x)+f(2-x)=3x^2+4x+2?

**1**

vote

**0**answers

123 views

### Computational number theory

Suppose that $p$ is prime and $q$ is an even number divides $p-1$, such that $q<\frac{p-1}{q}$ and $u$ has order $q$ modulo $p$. Let $S$ be the subgroup of $Z^*_p$ consisting of the powers of $u$. ...

**0**

votes

**0**answers

57 views

### Boundary conditions for Klein-Gordon equation [on hold]

Let us consider the Klein-Gordon equation
$$(\Box +m^2)u=0,$$
where $u$ is a scalar valued function, $m\geq 0$, $\Box=\frac{\partial^2}{\partial x_0^2}-\sum_{i=1}^d\frac{\partial^2}{\partial x_i^2}$.
...

**5**

votes

**2**answers

464 views

### Can a Morse function define a unique structure on a closed manifold?

I was thinking about the doubt that if $M$ and $N$ are closed manifold and if there exists two Morse function $f$ and $g$ respectively on $M$ and $N$ with the following property that they both have ...

**-2**

votes

**0**answers

62 views

### topology- Compute π1(M3) when M3 be the 3-manifold [on hold]

Let M3 be the 3-manifold obtained by gluing two handlebodies of genus g by
the identity map. To be precise: Let H1, H2 be two copies of a “standard” genus
g handlebody in S
3
. If we denote Σ1 = ∂H1, ...

**2**

votes

**1**answer

195 views

### What's $H^*(X - \{x_1,\ldots,x_n\},\mathcal{O})$, when $X$ is a projective smooth surface?

Let $X$ be a smooth projective surface over a field $k$. Is there a way to compute $H^1(X - \{x\},\mathcal{O}_{X-\{x\}})$ in terms of similar invariants for $X$? Actually I'd like to remove even ...