Related papers: On flexible sequences
Fluctuation relations are powerful equalities that hold far from equilibrium. However, the standard approach to include measurement and feedback schemes may become inapplicable in certain situations, including continuous measurements,…
We study the concept of density for sets of natural numbers in some lacunary $A$-convergent sequence spaces. Also we are trying to investigate some relation between the ordinary convergence and module statistical convergence for evey…
The consideration of nonstandard models of the real numbers and the definition of a qualitative ordering on those models provides a generalization of the principle of maximization of expected utility. It enables the decider to assign…
Sequences are often conveniently encoded in the form of a generating function depending on a formal variable. This note presents two observations that allow one to draw conclusions about the generated sequence from the generating function.…
Recently, a classical approach to continuous structures has been proposed in [ABBMZ] and [Z] that extends the class of structures falling under the scope of [HI] or [BBHU]. These articles introduce the notion of structures with a standard…
This note examines the infinite divisibility of density-based transformations of normal random variables. We characterize a class of density-based transformations of normal variables which produces non-infinitely divisible distributions. We…
We derive theorems which outline explicit mechanisms by which anomalous scaling for the probability density function of the sum of many correlated random variables asymptotically prevails. The results characterize general anomalous scaling…
The survey is devoted to the combinatorial and metric theory of filtrations, i.\,e., decreasing sequences of $\sigma$-algebras in measure spaces or decreasing sequences of subalgebras of certain algebras. One of the key notions, that of…
In this work we provide alternative formulations of the concepts of lambda theory and extensional theory without introducing the notion of substitution and the sets of all, free and bound variables occurring in a term. We also clarify the…
We study here a sequence of secondary measures, so called because the set of secondary polynomials on a given term become orthogonal for the next measure. The main result is a formula making explicit the density of any term of the sequence,…
We study the convergence of certain subseries of the harmonic series corresponding to increasing sequences of integers whose digits in a certain base are not uniformly distributed. We also discuss the case of irregular sequences, where the…
We suggest an extension of the standard concept of statistical ensembles. Namely, we introduce a class of ensembles with extensive quantities fluctuating according to an externally given distribution. As an example the influence of energy…
We extend the close interplay between continued fractions, orthogonal polynomials, and Gaussian quadrature rules to several variables in a special but natural setting which we characterize in terms of moment sequences. The crucial condition…
We define a bi-directional embedding between hypersequent calculi and a subclass of systems of rules (2-systems). In addition to showing that the two proof frameworks have the same expressive power, the embedding allows for the recovery of…
Nominal algebra includes $\alpha$-equality and freshness constraints on nominal terms endowed with a nominal set semantics that facilitates reasoning about languages with binders. Nominal unification is decidable and unitary, however, its…
The linear complexity is a measure for the unpredictability of a sequence over a finite field and thus for its suitability in cryptography. In 2012, Diem introduced a new figure of merit for cryptographic sequences called expansion…
In this work we extend our study on a link between automaticity and certain algebraic power series over finite fields. Our starting point is a family of sequences in a finite field of characteristic $2$, recently introduced by the first…
Labeled infinite trees provide combinatorial interpretations for many integer sequences generated by nested recurrence relations. Typically, such sequences are monotone increasing. Several of these sequences also have straightforward…
``Fusion rules'' are laws of multiplication among eigenspaces of an idempotent. We establish fusion rules for flexible power-associative algebras, following Albert. We define the notion of an axis in the noncommutative setting (compare with…
The set A = {a_n} of nonnegative integers is an asymptotic basis of order h if every sufficiently large integer can be represented as the sum of h elements of A. If a_n ~ alpha n^h for some real number alpha > 0, then alpha is called an…