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A chain rule formula in BV and applications to conservation laws
chain rule formula BV conservation laws
2010/11/9
In this paper we prove a new chain rule formula for the distributional derivative of the composite function $v(x)=B(x,u(x))$, where $u:]a,b[\to\R^d$ has bounded variation, $B(x,\cdot)$ is continuousl...
On The Characteristic Polynomial of Frobenius of Supersingular Abelian Varieties Of Dimension up to 7 over Finite Fields
The Characteristic Polynomial Frobenius Supersingular Abelian
2010/11/15
In this article, we derive the list of the characteristic polynomials of the Frobenius endomorphism of simple supersingular abelian varieties of dimension $1,~2,~3,~4,~5,~6,~7$ over $\mathbb{F}_q$ whe...
On Quantum Markov Chains on Cayley tree II: Phase transitions for the associated chain with XY-model on the Cayley tree of order three
On Quantum Markov Chains Cayley tree II
2010/11/15
In the present paper we study forward Quantum Markov Chains (QMC) defined on a Cayley tree. Using the tree structure of graphs, we give a construction of quantum Markov chains on a Cayley tree. By me...
We consider extensions of the Rattray theorem and two Makeev's theorems, showing that they hold true for several maps, measures, or functions simultaneously, if we consider orthonormal $k$-frames in $...
On uniqueness of semi-wavefronts (Diekmann-Kaper theory of a nonlinear convolution equation re-visited)
semi-wavefronts Diekmann-Kaper theory
2010/11/22
Motivated by the uniqueness problem for monostable semi-wavefronts, we propose a revised version of the Diekmann and Kaper theory of a nonlinear convolution equation. Our version of the Diekmann-Kape...
The Yao-Yao partition theorem states that given a probability measure on an affine space of dimension n having a density which is continuous and bounded away from 0, it is possible to partition the sp...
Our main result is that if A is a finite subset of an abelian group with |A+A| < K|A|, then 2A-2A contains an O( log^{O(1)} K)-dimensional coset progression M of size at least exp(-O( log^{O(1)} K))|A...
Let $G$ be an arbitrary group. Let $\Z(G)$, $\Z_2(G)$, $\gamma_2(G)$ denote the center, the second center and the commutator subgroup of $G$. In this short note we prove that if $\gamma_2(G)$ is fini...
In 1962, H. de Vries proved a duality theorem for the category {\bf HC} of compact Hausdorff spaces and continuous maps. The composition of the morphisms of the dual category obtained by him differs ...
Many different programs are the implementation of the same algorithm. This makes the collection of algorithms a quotient of the collection of programs. Similarly, there are many different algorithms ...
On the volume formulas for a spherical tetrahedron
the volume formulas spherical tetrahedron
2010/11/18
The present paper gives two concrete formulas for the volume of an arbitrary spherical tetrahedron, which is in a 3-dimensional spherical space of constant curvature $+1$. One formula is given in term...
The goal of this paper is to show that there are strong relations between certain Monge-Amp\`ere integrals appearing in holomorphic Morse inequalities, and asymptotic cohomology estimates for tensor p...
A probabilistic approach to local limit theorems with applications to random graphs
local limit theorems applications to random graphs
2010/11/19
In this article, we develop a general method to obtain local limit theorems from distributional limit theorems. Our results use probabilistic arguments and yield explicit bounds on the quality of app...
A stationary random graph is a random rooted graph whose distribution is invariant under re-rooting along the simple random walk. We adapt the entropy technique developed for Cayley graphs and show i...
Abelian Yang-Mills theory on Real tori and Theta divisors of Klein surfaces
Abelian Yang-Mills theory Real tori Theta divisors
2010/11/11
The purpose of this paper is to determine natural theta line bundles of Klein surfaces as elements in the Grothendieck cohomology group which classifies Real line bundles in the sense of Atiyah. Thes...