Related papers: Pseudorandom Numbers and Hash Functions from Itera…
In the present paper we generate binary pseudorandom sequences using generalized polynomials. A generalized polynomial is a function in whose description we not only allow addition and product (as it is the case in usual polynomials) but…
We estimate the frequency of polynomial iterations which falls in a given multiplicative subgroup of a finite field of $p$ elements. We also give a lower bound on the size of the subgroup which is multiplicatively generated by the first $N$…
We give a method of solution to the problem of iterating holomorphic functions to fractional or complex heights. We construct an auxiliary function from natural iterates of a holomorphic function; the auxiliary function will be…
We consider the hashing mechanism for constructing binary embeddings, that involves pseudo-random projections followed by nonlinear (sign function) mappings. The pseudo-random projection is described by a matrix, where not all entries are…
Many mathematicians have been studying various degenerate versions of special polynomials and numbers in some arithmetic and combinatorial aspects. Our main focus here is a new type of degenerate poly-Euler polynomials and numbers. This…
Studying degenerate versions of various special polynomials have become an active area of research and yielded many interesting arithmetic and combinatorial results. Here we introduce a degenerate version of polylogarithm function, called…
Idempotent Boolean functions form a highly structured subclass of Boolean functions that is closely related to rotation symmetry under a normal-basis representation and to invariance under a fixed linear map in a polynomial basis. These…
In this paper, we construct families of polynomials defined by recurrence relations related to mean-zero random walks. We show these families of polynomials can be used to approximate $z^n$ by a polynomial of degree $\sim \sqrt{n}$ in…
The analysis of observable phenomena (for instance, in biology or physics) allows the detection of dynamical behaviors and, conversely, starting from a desired behavior allows the design of objects exhibiting that behavior in engineering.…
The study of iterations of functions over a finite field and the corresponding functional graphs is a growing area of research with connections to cryptography. The behaviour of such iterations is frequently approximated by what is know as…
Loop invariants are properties of a program loop that hold before and after each iteration of the loop. They are often employed to verify programs and ensure that algorithms consistently produce correct results during execution.…
Consider the representations of an algebraic group G. In general, polynomial invariant functions may fail to separate orbits. The invariant subring may not be finitely generated, or the number and complexity of the generators may grow…
We study orthogonal polynomials for a weight function defined over a domain of revolution, where the domain is formed from rotating a two-dimensional region and goes beyond the quadratic domains. Explicit constructions of orthogonal bases…
We enhance the approximation capabilities of algebraic polynomials by composing them with homeomorphisms. This composition yields families of functions that remain dense in the space of continuous functions, while enabling more accurate…
The origin of this study is based on not only explicit formulas of finite sums involving higher powers of binomial coefficients, but also explicit evaluations of generating functions for this sums. It should be emphasized that this study…
The concepts of evaluation and interpolation are extended from univariate skew polynomials to multivariate skew polynomials, with coefficients over division rings. Iterated skew polynomial rings are in general not suitable for this purpose.…
In combinatorics, the probabilistic method is a very powerful tool to prove the existence of combinatorial objects with interesting and useful properties. Explicit constructions of objects with such properties are often very difficult, or…
The double-direction orthogonalization algorithm is applied to construct sequences of polynomials, which are orthogonal over the interval [0,1]with the weighting function 1. Functional and recurrent relations are derived for the sequences…
Necessary and sufficient conditions under which two real functions defined on the real interval can be separated by a polynomial are given. An immediate consequence of the main result is the existence of the polynomial separation of convex…
Empirical evidence suggests that hashing is an effective strategy for dimensionality reduction and practical nonparametric estimation. In this paper we provide exponential tail bounds for feature hashing and show that the interaction…