相关论文: A Few Surprising Integrals

A first-order theory is equational if every definable set is a Boolean combination of instances of equations, that is, of formulae such that the family of finite intersections of instances has the descending chain condition. Equationality…

The investigation of colour symmetries for periodic and aperiodic systems consists of two steps. The first concerns the computation of the possible numbers of colours and is mainly combinatorial in nature. The second is algebraic and…

In [Discrete Mathematics 306 (2005) 153-158], So proposed a conjecture saying that integral circulant graphs with different connection sets have different spectra. This conjecture is still open. We prove that this conjecture holds for…

The purpose of this paper is twofold. First, we provide a novel characterization of independence of random vectors based on the checkerboard approximation to a multivariate copula. Using this result, we then propose a new family of tests of…

Codifference is a commonly used measure of dependence for stable vectors and processes for which covariance is infinite. However, we argue that it can also be used for other heavy-tail distributions and it provides useful information for…

We present various results on multiplying cycles in the symmetric group. Our first result is a generalisation of the following theorem of Boccara (1980): the number of ways of writing an odd permutation in the symmetric group on $n$ symbols…

We prove a color-position symmetry for a class of ASEP-like interacting particle systems with discrete time on the one-dimensional lattice. The full space-time inhomogeneity of our systems allows to apply the result to colored (or…

We develop some aspects of the theory of derivators, pointed derivators, and stable derivators. As a main result, we show that the values of a stable derivator can be canonically endowed with the structure of a triangulated category.…

An acyclic edge coloring of a graph $G$ is a proper edge coloring such that no bichromatic cycles are produced. The acyclic edge coloring conjecture by Fiam{\v{c}}ik (1978) and Alon, Sudakov and Zaks (2001) states that every simple graph…

In this note we prove a large deviation bound on the sum of random variables with the following dependency structure: there is a dependency graph $G$ with a bounded chromatic number, in which each vertex represents a random variable.…

In this paper, we prove a new generalized Mikhlin multiplier theorem whose conditions are given with respect to fractional derivatives in integral forms with two different integration intervals. We also discuss the connection between…

We study two parameters obtained from the Euler characteristic by replacing the number of faces with that of induced and induced non-separating cycles. By establishing monotonicity of such parameters under certain homomorphism and edge…

In this paper we extend the classical Glivenko-Cantelli theorem to real-valued empirical functions under dependence structures characterised by $\alpha$-mixing and $\beta$-mixing conditions. We investigate sufficient conditions ensuring…

We prove some new degeneracy results for integral points and entire curves on surfaces; in particular, we provide the first example, to our knowledge, of a simply connected smooth variety whose sets of integral points are never…

Two new families of completely integrable perturbations of the N-dimensional isotropic harmonic oscillator Hamiltonian are presented. Such perturbations depend on arbitrary functions and N free parameters and their integrals of motion are…

Conditional independence and graphical models are well studied for probability distributions on product spaces. We propose a new notion of conditional independence for any measure $\Lambda$ on the punctured Euclidean space $\mathbb…

We consider a family of Markov chains whose transition dynamics are affected by model parameters. Understanding the parametric dependence of (complex) performance measures of such Markov chains is often of significant interest. The…

V. I. Arnold [Russian Math. Surveys 26, no. 2, 1971, 29-43] constructed smooth generic families of matrices with respect to similarity transformations depending smoothly on the entries of matrices and got bifurcation diagrams of such…

A vector composition of a vector $\mathbf{\ell}$ is a matrix $\mathbf{A}$ whose rows sum to $\mathbf{\ell}$. We define a weighted vector composition as a vector composition in which the column values of $\mathbf{A}$ may appear in different…

We develop some basic results about full amalgamation classes with intrinsic trascendentals. These classes have generics whose models may have finite subsets whose intrinsic closure is not contained in its algebraic closure. We will show…