First principles calculations of oxygen adsorption on the UN (001) surface

Fabrication, handling and disposal of nuclear fuel materials require comprehensive knowledge of their surface morphology and reactivity. Due to unavoidable contact with air components (even at low partial pressures), UN samples contain considerable amount of oxygen impurities affecting fuel properties. The basic properties of O atoms adsorbed on the UN(001) surface are simulated here combining the two first principles calculation methods based on the plane wave basis set and that of the localized atomic orbitals.Comment: 9 page

Infinitely many local higher symmetries without recursion operator or master symmetry: integrability of the Foursov--Burgers system revisited

We consider the Burgers-type system studied by Foursov, w_t &=& w_{xx} + 8 w w_x + (2-4\alpha)z z_x, z_t &=& (1-2\alpha)z_{xx} - 4\alpha z w_x + (4-8\alpha)w z_x - (4+8\alpha)w^2 z + (-2+4\alpha)z^3, (*) for which no recursion operator or master symmetry was known so far, and prove that the system (*) admits infinitely many local generalized symmetries that are constructed using a nonlocal {\em two-term} recursion relation rather than from a recursion operator.Comment: 10 pages, LaTeX; minor changes in terminology; some references and definitions adde

Algebraic theories of brackets and related (co)homologies

A general theory of the Frolicher-Nijenhuis and Schouten-Nijenhuis brackets in the category of modules over a commutative algebra is described. Some related structures and (co)homology invariants are discussed, as well as applications to geometry.Comment: 14 pages; v2: minor correction

A Translation of the T. Levi-Civita paper: Interpretazione Gruppale degli Integrali di un Sistema Canonico Rend. Acc. Lincei, s. 3^a, vol. VII, 2^o sem. 1899, pp. 235--238

In this paper we provide a translation of a paper by T. Levi-Civita, published in 1899, about the correspondence between symmetries and conservation laws for Hamilton's equations. We discuss the results of this paper and their relationship with the more general classical results by E. Noether.Comment: 12 page

A unified approach to computation of integrable structures

We expose (without proofs) a unified computational approach to integrable structures (including recursion, Hamiltonian, and symplectic operators) based on geometrical theory of partial differential equations. We adopt a coordinate based approach and aim to provide a tutorial to the computations.Comment: 19 pages, based on a talk on the SPT 2011 conference, http://www.sptspt.it/spt2011/ ; v2, v3: minor correction

Exponential queuing network with dependent servicing, negative customers, and modification of the customer type

The open exponential queuing network with negative customers (G-network) was considered. For each arriving customer, given was a set of its random parameters such as the route defining the sequence of network nodes passed by the customer, route length, size, and servicing duration at each stage of the route. It was assumed that the negative customer arriving to the sth node with the probabilities ωs and ωs + either kills the positive customer in a randomly chosen server or does not affect it at all and with the probability ωs - = 1 - ωs - ωs + transforms it into a negative customer which after an exponentially distributed time arrives to the s′th node with the given probability. The multidimensional stationary probability distribution of the network states was proved to be representable in the multiplicative form

RESEARCH OF NTRU ENCRYPTION ALGORITHM

Об’єктом дослідження є алгоритм шифрування із відкритим ключем NTRU (Nth-degree TRUncated polynomial ring). Наводиться коротка історія розвитку алгоритму, опис його реалізації з точки зору виконуваних математичних операцій. Велика увага приділяється значимості алгоритму у сучасному комп’ютерному світі. Розглянуті найбільш відомі методи криптографічних атак. Сформульовані переваги алгоритму, що роблять його фаворитом серед асиметричних алгоритмів.Объектом исследования является алгоритм шифрования с открытым ключом NTRU (Nth-degree TRUncated polynomial ring). Приводится короткая история развития алгоритма, описание его реализации с точки зрения используемых математических операций. Большое внимание уделяется значимости алгоритма в современном компьютерном мире. Рассмотрены наиболее известные методы криптографических атак. Сформированы преимущества алгоритма, которые делают его фаворитом среди ассиметричных алгоритмов.The object of research is encryption algorithm with the public key called NTRU (Nth-degree TRUncated polynomial ring). Contains the briefly history of algorithm, description of implementation from the point of used mathematical operations. Big attention is dedicated to significance of the algorithm in the modern computer world. Possible methods of cryptographic attacks were reviewed. Benefits of the algorithm that make it better than the others were described

Exponential queueing network with dependent discipline, negative requests, and variable request types

An open exponential queueing network with negative requests (G-network) is considered. A set of random parameters is given for each request entering the network: its route along the network, governing the units sequence passed by the request, the route length, request body and its servicing duration of every route stage. The multidimensional stationary distribution of state probabilities of the considered network is represented in the multiplicative form