Related papers: New Combinatorial Complete One-Way Functions
We say that a function $f \in L^1(\mathbb{R})$ tiles at level $w$ by a discrete translation set $\Lambda \subset \mathbb{R}$, if we have $\sum_{\lambda \in \Lambda} f(x-\lambda)=w$ a.e. In this paper we survey the main results, and prove…
The main goal in this manuscript is to present a class of functions satisfying a certain orthogonality property for which there also exists a three term recurrence formula. This class of functions, which can be considered as an extension to…
Various threshold effects are investigated on a discrete quasi-1D scattering system. In particular, one of these effects is to add corrections to Levinson's theorem. We explain how these corrections are due to the opening or to the closing…
We study reduction schemes for functions of "many" variables into system of functions in one variable. Our setting includes infinite-dimensions. Following Cybenko-Kolmogorov, the outline for our results is as follows: We present explicit…
Robin Milner (1984) gave a sound proof system for bisimilarity of regular expressions interpreted as processes: Basic Process Algebra with unary Kleene star iteration, deadlock 0, successful termination 1, and a fixed-point rule. He asked…
In this paper, we almost completely solve the existence of an almost resolvable cycle system with odd cycle length. We also use almost resolvable cycle systems as well as other combinatorial structures to give some new solutions to the…
In \cite{HRW15}, Haglund, Remmel, Wilson state a conjecture which predicts a purely combinatorial way of obtaining the symmetric function $\Delta_{e_k}e_n$. It is called the Delta Conjecture. It was recently proved in \cite{GHRY} that the…
In recent years L-functions and their analytic properties have assumed a central role in number theory and automorphic forms. In this expository article, we describe the two major methods for proving the analytic continuation and functional…
In 2005, building on his own recent work and that of F. Zanello, A. Iarrobino discovered some constructions that, he conjectured, would yield level algebras with non-unimodal Hilbert functions. This thesis provides proofs of non-unimodality…
In this paper, we prove a Logarithmic Conjugation Theorem on finitely-connected tori. The theorem states that a harmonic function can be written as the real part of a function whose derivative is analytic and a finite sum of terms involving…
We provide a new universal real flow of the Hilbert-cubical type. We prove that any real flow can be equivariantly embedded in the translation on $L(\mathbb{R})^\mathbb{N}$, where $L(\mathbb{R})$ denotes the space of $1$-Lipschitz functions…
A possible method to solve the sign problem is developed by modifying the original theory. Considering several modifications of the partition function, the observable in the original theory is reconstructed from the identity connecting the…
Symmetric functions show up in several areas of mathematics including enumerative combinatorics and representation theory. Tewodros Amdeberhan conjectures equalities of $\Sigma_n$ characters sums over a new set called $Ev(\lambda)$. When…
A physically more adequate definition of a quaternionic holomorphic (H-holomorphic) function of one quaternionic variable compared to known ones and a quaternionic generalization of Cauchy-Riemann's equations are presented. At that a class…
While there is a long tradition of reasoning about (non)termination in program analysis, specialized logics are typically needed to give different termination criteria. This includes partial correctness, where termination is not guaranteed,…
A new type of combinations of Bernstein operators is given in [1]. Here, we introduce another one, which can be used to approximate the functions with singularities. The direct and inverse results of the weighted approximation of this new…
For the first time, we develop a convergent numerical method for the llinear integral equation derived by M.M. Lavrent'ev in 1964 with the goal to solve a coefficient inverse problem for a wave-like equation in 3D. The data are non…
The classical technique for proving termination of a generic sequential computer program involves the synthesis of a ranking function for each loop of the program. Linear ranking functions are particularly interesting because many…
We study Translation functors and Wall-Crossing functors on infinite dimensional representations of a complex semisimple Lie algebra using D-modules. This functorial machinery is then used to prove the Endomorphism-theorem and the…
The present work determines the exact nature of {\em linear time computable} notions which characterise automatic functions (those whose graphs are recognised by a finite automaton). The paper also determines which type of linear time…