0
votes
0answers
1 views

irreducible affine scheme over Z has good reduction almost everywhere

Let $f(x_1,\ldots,x_n)\in\mathbf{Z}[x_1,\ldots,x_n]$ be a polynomial. Assume that $f$ is irreducible over $\overline{\mathbf{Q}}$. Where can I find a proof of the following classical result: for ...
0
votes
0answers
6 views

Reference or a short argument that a certain subset generates the ring of p-typical symmetric functions under plethysm

Let p be a prime and$\Lambda_p$ be the subring of the ring of symmetric functions $\Lambda$ (over $\mathbb{Z}$) such that $$x \in \Lambda_p$$ iff there is an $i \in \mathbb{N}$ such that $p^ix \in ...
1
vote
1answer
54 views

What kind of SAT am I dealing with here?

Problem set up: I have a long list of variables, $v_i$ (say about 200 total). I am given a bunch of Boolean statements as follows: $$\omega_1\land \omega_2\land \omega_3\land \omega_4\land \omega_5 ...
1
vote
1answer
23 views

Lower bound of Hecke eigenvalues of Maass form

If $f$ is a Maass form and $p$-Hecke eigenvalue (i.e. Hecke eigenvalue of usual Hecke operator $T_p$) of $f$ is $\lambda_f(p)$, do we know anything about lower bound of the sum$$S(x) = \sum_{x\le p\le ...
2
votes
1answer
31 views

scott continuity, sub additivity

Let $(X, \sqsubseteq_x)$ and $(Y, \sqsubseteq_y)$ be two posets and let $\delta_x:X \to X$ and $\delta_y:Y \to Y$ be two closure operators (monotone, inflationary, idempotent). Then, a monotone ...
0
votes
2answers
25 views

Solvability of quasilinear elliptic equations on closed manifolds

Is there any reference about solvability theory of quasilinear elliptic equations on closed manifolds? In particular, I am looking for solvability condition for function $f$ of following equation ...
-1
votes
0answers
35 views

What Lie groups have a discrete set of order two elements?

We know that the set of order two elements of $R^n$, tori and $S^3$ are discrete. Are there others examples of Lie groups with such property? Are there some characterization of such class?
0
votes
0answers
41 views

ellipsoids have spherical section

I want to prove that "For any $(2k-1)$-dimensional ellipsoid $E$ ,there is a $k$-flat $L$ passing through the center of $E$ such that $ E \cap L$ is a Euclidean ball. I see a proof for it in the book ...
-1
votes
0answers
26 views

Does the intersection of the curve $C$ with an other curve isomorphic to $\mathbb{P}^{1}$ is always transversal? [on hold]

Let $S$ be a nonsingular projective surface over an algebraically closed field $k$ and $C$ be a nonsingular curve in $S$. Suppose that $L$ is an other curve in $S$, which is isomorphic to ...
-1
votes
0answers
20 views

force singular value decomposition to use the solution with the biggest absolute value [on hold]

Well I'm writing a code to solve a positioning problem. given arrival times from multiple sources I want to invert and get the receiver position. obviously I have the xyz of each receiver. so I ...
2
votes
0answers
20 views

Expectation of ratio of functions of i.i.d. Bernoullis: a concentration question

Consider the following $n \times n$ symmetric matrix of i.i.d. Bernoulli random variables, $X_{ij}$. For $i=1,...,n$ and $i<j\le n$. Let $X_{ij} \sim \text{Bernoulli}(p)$ when $i \ne j$ ($p$ ...
0
votes
0answers
22 views

Expected number of times a specific pattern appears in a set of n Bernoulli trials

Let's consider a set of $n$ Bernoulli trials of parameter $p$ (call them $\text{(O1,...,On)}$). Let's name the two possible outcomes as $+$ and $-$. How do you calculate the expected number of times ...
-1
votes
0answers
16 views

PDE: determine particular solution by finding the coefficients of the general solution. [on hold]

Can anyone help me on how to find the particular solution and coefficients of the general solution of f(x)=3cos((5*pi/l)*x) - 7 cos ((2*pi/l)*x)+4 or f(x)=e^(l-x)-(l-x)e^l and g(x)=x We are ...
-2
votes
0answers
51 views

How to solve the differential equation $y'' = y^{-1/2}$? [on hold]

How to solve the differential equation $y'' = y^{-1/2}$ ?
-3
votes
0answers
32 views

Directsum of ideals and local ring [on hold]

Let $(R,m)$ be a local ring, are there two ideas $I$ and $J$ of $R$ such that $I \bigoplus J \unlhd R$?
2
votes
0answers
27 views

Pointwise a.e. formulation of parabolic PDE, what if null set depends on test function?

Let $u \in L^2(0,T;V)$ with $u_t \in L^2(0,T;V^*)$ be a solution of $$\langle u_t(t), v \rangle + a(t;u(t), v) = \langle f(t), v \rangle$$ where $f \in L^2(0,T;V^*)$ and we have the usual assumptions ...
4
votes
0answers
52 views

Fixed sets of orbit spaces

I've run across something that surprises me, so I'm wondering (1) Is it true? and (2) Is it well known? (And if the answers are affirmative, why didn't I know this already?) Let $G$ be a compact Lie ...
0
votes
0answers
35 views

Mapping class group and fundamental group of a 3 manifold

If the 3 manifold is Haken, then the natural homomorphism from the mapping class group of this 3 manifold to the outer automorphism of its fundamental group is an isomorphism. Any other kind of 3 ...
-4
votes
0answers
73 views

What did Sarnak mean? [on hold]

In that old article "Prime Time" they quote Peter Sarnak saying "Right now, when we tackle problems without knowing the truth of the Riemann hypothesis, it's as if we have a screwdriver. But when we ...
0
votes
0answers
31 views

A question on the minimum of a real-valued function? [on hold]

Define a real-valued function $f$ on $[0,1]^{n}$ by: $f(a_{1},...,a_{n})=\sum_{i=1}^{n}i^{2}a_{i}-(\sum_{i=1}^{n}ia_{i})^{2}$. Let $K:=\{(a_{1},...,a_{n})\in [0,1]^{n}:\sum_{i=1}^{n}a_{i}=1\}$. My ...
2
votes
1answer
48 views

Counterexample for the Generalized Associativity Equation

The Generalized Associativity Equation is given by $$ F(G(x,y),z)=K(x,H(y,z)),$$ where the functions $F,G,H$ and $K$ are all from $\mathbb{R}^2$ to $\mathbb{R}$. In his book "Lectures on Functional ...
1
vote
0answers
54 views

Gromov hausdorff convergence [on hold]

Is the Gromov-Hausdorff limit of a sequence of compact submanifolds of an Euclidean space also in the Euclidean space ?
0
votes
0answers
27 views

Is simultaneous diophantine approximation (in a weaker sense) NP hard?

The traditional approach to finding a good simultaneous diophantine approximation is the following: given a set of rational numbers $\alpha=(g_1,\ldots,g_d)$, an integer $N$, and a rational ...
2
votes
1answer
38 views

Equivalence classes of (2,3)-pairs in PSL(2,q)

This may not be a research-level question, which is why I submitted it to math.stackexchange first, but so far the question there has barely been viewed, let alone answered. Apologies if submitting it ...
1
vote
0answers
30 views

Number of cyclic difference sets

A subset $D=\{a_1,\ldots,a_k\}$ of $\mathbb{Z}/v\mathbb{Z}$ is said to be a $(v,k,\lambda)$-cycic difference set if for each nonzero $b\in\mathbb{Z}/v\mathbb{Z}$, there are exactly $\lambda$ ordered ...
1
vote
1answer
49 views

Rational mapping related to cubic surfaces

A theorem in Manin's book on cubic forms leads to the conclusion that the least degree of a rational mapping from $\mathbb{P}^2$ to general cubic surfaces(e.g. Picard rank=1) over $\mathbb{Q}$ is 6. ...
2
votes
2answers
48 views

First order pde with characteristics

Consider a first order pde of the type $$u_y+b(x)u_x=0$$ and suppose that the coefficient $b$ is not necessairly continuous (for instance with a jump in some point). Is it still possible to apply in ...
1
vote
0answers
23 views

Complexity of an algorithm to solve linear diophantine equations

A friend of mine ask me yesterday a problem, however, the interesting part for me it is not his problem, but what I will ask here. I want to know the optimal complexity of an algorithm (I mean the ...
2
votes
0answers
50 views

If matrices describe simplices, what do matrix operations describe?

Suppose we are given a $d \times d$ matrix $M$ with rows $m_1, \dots, m_d$. This matrix describes a simplex, namely the convex closure of the origin with the vectors $m_1, \dots, m_d$. Now, scaling ...
1
vote
0answers
15 views

Wide cylinders on half-translation surfaces

Take a collection of pairwise disjoint, simple polygons in the plane. Identify pairs of sides between polygons by either a translation in the plane, or, a translation composed with a rotation by ...
0
votes
0answers
33 views

Models of BL$\forall$

What results are known about the construction of models for a theory $T$ of the logic BL$\forall$ for languages of higher cardinality? The construction for the countable case relies on 1) The fact ...
0
votes
0answers
31 views

Extension of Radon measure

I will mention this specific case, Let $m_1$ be a (homogeneous) Radon probability measure on $X=\{0,1\}^\kappa$ of Maharam type $\kappa$. As $X$ is zero-dimensional space, so it has an algebra ...
2
votes
2answers
66 views

quotient of planar groups

If G is an infinite planar group (it means that it has a generating subset C such that Cay (S, C) is a planar graph) and H is a normal subgroup of it, I would be very grateful if somebody helps me and ...
1
vote
0answers
49 views

Which morphisms of varieties and motives induce surjections of their lower Chow groups?

This question is a contination of Varieties with Chow groups supported in positive codimension: examples and properties? What examples are known of morphisms of varieties and Chow motives (say, over ...
-6
votes
0answers
23 views

Borel function and random variable [on hold]

Positive part of a function X+ is borel function and will be a random variable if X is random variable. I know this things, but how should i prove it mathematically ?
4
votes
0answers
52 views

Bound on the number of lattice points in d-dimensional ball

The following paper states that the number of lattice points in a $d$-dimensional ball of radius $R$ is $V_d R^d + O(R^\alpha)$ where $\alpha = d - 2$ and $V_d$ is the volume of the unit ...
-3
votes
0answers
24 views

Breadth First Search and Depth First Search on Graphs [on hold]

What i would like to know is if it's possible to use these two algorithms on a directed or on a not directed graph and visit every node.From what i've seen it seems impossible to me to visit every ...
0
votes
0answers
83 views

Surjectivity of the algebraic K-functor

Let $R \to S$ be a surjective morphism of commutative rings. For a fixed integer $q$, is there any known condition under which the resulting morphism of the K-groups, $K_q(R) \to K_q(S)$ is ...
1
vote
0answers
43 views

Substitutions and Sturmian sequences

We know that any substitution can generate sequence, for example the Fibonacci substitution: $\sigma(0)=01, \sigma(1)=0$, then we can define a Sturmian sequence $\omega$, i.e., the fixed point of ...
2
votes
2answers
130 views

Standard homology result on double complexes

Suppose you have got a double complex in an abelian category with objects $(A_{rs},d_{rs})$ such that $A_{rs} = 0$ for $r < 0$ or $s < 0$. Suppose furthermore that the rows ...
7
votes
0answers
49 views

Detecting invertible elements in group rings by their images for finite quotients of the group

Let $G$ be a "nice" infinite group: at least finitely presented and residually finite, maybe also linear and right-orderable (or even bi-orderable, or residually free nilpotent). Consider an element ...
0
votes
2answers
39 views

Metric properties of a quadratic differential at an essential singularity

Let $f(z)dz^2$ be a holomorphic quadratic differential on the punctured disk $\{0<|z|<1\}$, which gives rise to a Riemannian metric $g=|f(z)|\,|dz|^2$ and hence a volume form $\nu=|f(z)| ...
1
vote
0answers
13 views

singularity of the solution to an integral equation

I consider a function $x\mapsto f(x)$ which is the positive solution to the integral equation $$\int_{f(x)}^\infty \frac{du}{u^\gamma-x}=1, \quad x\ge 0,$$ where $\gamma\in (1, 2]$ is some ...
-6
votes
0answers
22 views

Graph Theory - Adjacent certices in a simple graph [on hold]

Let u and v be adjacent vertices in a simple graph G. Prove that uv belongs to at least d(u) + d(v) - n(G) triangles in G.
-4
votes
0answers
22 views

Graph Theory - Question on hypercubes and cycles [on hold]

Prove that every cycle of length 2r in a hypercube is contained in a subcube of dimension at most r. Can a cycle of length 2r be contained in a subcube of dimension less than r?
4
votes
2answers
103 views

Why is the spectrum of this matrix product invariant with respect to order of the multiplicants?

I've been chewing on the following problem for some time and I just don't have any more ideas how to tackle it. I have matrices $A_1,...,A_k \in \mathbb R^{n\times n}$ and I'm observing that the ...
0
votes
0answers
18 views

Bounds on Product of CDF or Beta function

I have functions of the form \begin{align} I_i = \int_0^\infty F_0(x)^aF_1(x)^b(1-F_0(x))^c(1-F_1(x))^ddF_i(x)~~~~i = 0,1 \end{align} $F_0(x)$ and $F_1(x)$ are CDFs corresponding to the random ...
32
votes
11answers
3k views

Has philosophy ever clarified mathematics?

I've recently been reading some standard textbooks on the philosophy of mathematics, and I've become quite frustrated that (surely due to my own limitations) I don't seem to be gleaning any ...
-4
votes
0answers
42 views

Normal line, regular surface [on hold]

Let $\mathcal A$ be a regular surface in $\mathbb R^3$ and $P$ a point in $\mathbb R^3\setminus\mathcal A$. Suppose that $C$ is a point at minimum distance from $P$. Show that $P$ belongs to the ...
1
vote
1answer
70 views

Ricci flow and conformal classes

Is it true that the conformal class of the metric is preserved under Ricci flow? I have seen it mentioned in an answer on this site. Is there an easy argument? (This question was asked on MSE but it ...

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