Related papers: Linear Relation on General Ergodic T-Function
We study correlations of multiplicative functions taken along deterministic sequences and sequences that satisfy certain linear independence assumptions. The results obtained extend recent results of Tao and Ter\"av\"ainen and results of…
We formulate and prove a general recurrence relation that applies to integrals involving orthogonal polynomials and similar functions. A special case are connection coefficients between two sets of orthonormal polynomials, another example…
We consider the scenario in which a set of sources generate messages in a network and a receiver node demands an arbitrary linear function of these messages. We formulate an algebraic test to determine whether an arbitrary network can…
New properties of the quark correlator are found via equations of motion. As a first result, approximate relations can be established among the "soft" functions; one such relation may help in determining the quark transversity in a nucleon.…
This paper is concerned with the concept of linear repetitivity in the theory of tilings. We prove a general uniform subadditive ergodic theorem for linearly repetitive tilings. This theorem unifies and extends various known (sub)additive…
By making use of the generalized concept of orthogonality in Latin squares, certain t-partite graphs have been constructed and a suggestion for a net work system and some applications have been made.
It is well known, due to Lindstr\"om, that the minors of a (real or complex) matrix can be expressed in terms of weights of flows in a planar directed graph. Another classical fact is that there are plenty of homogeneous quadratic relations…
Tasks that model the relation between pairs of tokens in a string are a vital part of understanding natural language. Such tasks, in general, require exhaustive pair-wise comparisons of tokens, thus having a quadratic runtime complexity in…
We introduce sequences of functions orthogonal on a finite interval: proper orthogonal rational functions, orthogonal exponential functions, orthogonal logarithmic functions, and transmuted orthogonal polynomials
We investigate the relationship between (countable) transfinite iteration and ordinal arithmetic. The nice connection between finite iteration and addition, multiplication, and exponentiation is lost when passing to the transfinite. In this…
We prove some interesting multiplicative relations which hold between the coefficients of the logarithmic derivatives obtained in a few simple ways from $\mathbb{F}_q$-linear formal power series. Since the logarithmic derivatives connect…
The author introduced models of linear logic known as ''Interaction Graphs'' which generalise Girard's various geometry of interaction constructions. In this work, we establish how these models essentially rely on a deep connection between…
The canonical k-tangent structure on $T^1_kQ=TQ\oplus\stackrel{k}...\oplus TQ$ allows us to characterize nonlinear connections on $T^1_kQ$ and to develop G\"unther's (k-symplectic) Lagrangian formalism. We study the relationship between…
The central idea of this article is to present a systematic approach to construct some recurrence relations for the solutions of the second-order linear difference equation of hypergeometric-type defined on the quadratic-type lattices. We…
Rational relations are binary relations of finite words that are realised by non-deterministic finite state transducers (NFT). A particular kind of rational relations is the sequential functions. Sequential functions are the functions that…
We show that the imaginary part of the embedding potential, a generalised logarithmic derivative, defined over the interface between an electrical lead and some conductor, has orthogonal eigenfunctions which define conduction channels into…
A result for subadditive ergodic cocycles is proved that provides more delicate information than Kingman's subadditive ergodic theorem. As an application we deduce a multiplicative ergodic theorem generalizing an earlier result of…
We study a new flexible method to extend linearly the graph of a non-linear, and usually not bijective, function so that the resulting extension is a bijection. Our motivation comes from cryptography. Examples from symmetric cryptography…
We prove orthogonality relations for some analogs of trigonometric functions on a $q$-quadratic grid and introduce the corresponding $q$-Fourier series. We also discuss several other properties of this basic trigonometric system and the…
We develop the general theory of Jack-Laurent symmetric functions, which are certain generalisations of the Jack symmetric functions, depending on an additional parameter p_0.