# All Questions

37 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 ...
63 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 ...
42 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 ...
72 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. ...
75 views

### First order pde with characteristics [on hold]

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 ...
32 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 ...
57 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 ...
24 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 ...
72 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 ...
71 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 ...
95 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 ...
25 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 ?
56 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 ...
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 ...
128 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 ...
68 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 ...
136 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 ...
61 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 ...
53 views

25 views

### IVP accuracy - scheme accuracy Vs. derivative accuracy?

General Question: If I have an IVP with periodic and continuous initial condition, which rules the accuracy of the scheme - the manner in which we approximate spatial derivative or the acuuracy of the ...
### Reference needed for Hilbert-Schmidt result regarding basis of $V \subset H$
I am seeking a reference that says: If $V \subset H \subset V^*$ is a Gelfand triple with all spaces Hilbert spaces and if $V \subset H$ is a compact embedding, then there is a basis of $V$ which ...