Related papers: Some application of difference equations in Crypto…
Integrable difference equations commonly have more low-order conservation laws than occur for nonintegrable difference equations of similar complexity. We use this empirical observation to sift a large class of difference equations, in…
This paper presents a new Lie theoretic approach to fractal calculus, which in turn yields such new results as a Fractal Noether's Theorem, a setting for fractal differential forms, for vector fields, and Lie derivatives, as well as…
We present a quantum algorithm solving the $k$-distinctness problem in $O(n^{1-2^{k-2}/(2^k-1)})$ queries with a bounded error. This improves the previous $O(n^{k/(k+1)})$-query algorithm by Ambainis. The construction uses a modified…
Inverse spectral problems are studied for first-order integro-differential operators on a finite interval. These problems consist in recovering some components of the kernel from one or multiple spectra. Uniqueness theorems are proved for…
We give some basics about homological algebra of difference representations. We consider both the difference-discrete and the difference-rational case. We define the corresponding cohomology theories and show the existence of spectral…
We discuss the use of inequalities to obtain the solution of certain variational problems on time scales.
The methods of quantum cryptography enable one to have perfectly secure communication lines, whereby the laws of quantum physics protect the privacy of the data exchanged. Each quantum-cryptography scheme has its own security criteria that…
Fractional diffusion equations replace the integer-order derivatives in space and time by their fractional-order analogues. They are used in physics to model anomalous diffusion. This paper develops strong solutions of space-time fractional…
A regular way to define an additive coproduct (or ``coaddition'') on the q-deformed differential complexes is proposed for quantum groups and quantum spaces related to the Hecke-type R-matrices. Several examples of braided coadditive…
We introduce the concept of degree to classify the periods in the sense of Kontsevich. Using this notion we give some new understanding of some problems in transcendental number theory.
Stochastic differential equations for processes with values in Hilbert spaces are now largely used in the quantum theory of open systems. In this work we present a class of such equations and discuss their main properties; moreover, we…
In this paper, we develop discrete versions of Darboux transformations and Crum's theorems for two second order difference equations. The difference equations are discretised versions (using Darboux transformations) of the spectral problems…
In this study, a new sort of transform known as (Kuffi- Abbas- Jawad transform) or KAJ- integral transformation is introduced. We introduce and explore important KAJ- transformation features and applications in cryptography. KAJ-…
This thesis discusses recent advances in precision calculations of quantum chromodynamics and their application to the Large Hadron Collider (LHC) physics program and beyond.
In this introductory review, we focus on applications of quantum computation to problems of interest in physics and chemistry. We describe quantum simulation algorithms that have been developed for electronic-structure problems,…
In these lecture notes some applications of Monte Carlo integration methods in Quantum Field Theory - in particular in Quantum Chromodynamics - are introduced and discussed.
We show a degree formula for a type of orthogonal Deligne--Lusztig varieties and their Pl\"ucker embeddings. This is an analog of work of Li on a unitary case.
We investigate a fundamental property of device independent security in quantum cryptography by characterizing probability distributions which are necessarily independent of the measurement results of any eavesdropper. We show that…
Results of research of possibility of transformation of a difference equation into a system of the first-order difference equation are presented. In contrast to the method used previously, an unknown grid function is split into two new…
The geometric theory of Lie systems will be used to establish integrability conditions for several systems of differential equations, in particular Riccati equations and Ermakov systems. Many different integrability criteria in the…