The (singular) orthogonal graph O(2ν + δ, q) over a field with q elements and of characteristic 2 (where ν ⩾ 1, and δ = 0, 1 or 2) is introduced. When ν = 1, O(2 · 1, q), O(2 · 1 + 1, q) and O(2 · 1 + 2, q) are complete graphs with 2, q + 1 and q² + 1 vertices, respectively. When ν ⩾ 2, O(2ν + δ, q) is strongly regular and its parameters are computed. O(2ν + 1, q) is isomorphic to the symplectic graph Sp(2ν, q). The chromatic number of O(2ν + ν, q) except when δ = 0 and ν is odd is computed and the group of graph automorphisms of O(2ν + δ, q) is determined.

This paper considers the Kipriyanov–Radon transform constructed as a special Radon transform adopted for dealing with singular Bessel differential operators of the corresponding indices acting on a part of the variables. The authors obtain inversion formulas generalizing the classical formulas for the Radon transform of axially-symmetric functions and relating to the integro-differentiation of fractional order in a one-dimensional parameter.

In the applications it may occur that our initial pseudorandom binary sequence turns out to be not long enough, thus we have to take the concatenation or merging of it with other pseudorandom binary sequences. Here our goal is study when we can form the concatenation of several pseudorandom binary sequences belonging to a given family? We introduce and study new measures which can be used for answering this question.

Résumé

Ce chapitre présente les principaux résultats de physique statistique et leurs liens avec la théorie des probabilités. Les grandeurs physiques sont introduites à partir des mesures de Gibbs qui déterminent la fonction de partition. Cette fonction est centrale dans le calcul des autres grandeurs et en particulier dans les transitions de phases. Elle se généralise au cas quantique.

The airport pavement system is a complicated mechanical system, which is composed of the airplane load, pavement and foundation. The research on the parameter identification method for the system is an important category in the aeronautic and transport engineering. Although such topic has already been reported in the literature [1 –3], there are still some dissatisfied respects for the practical applications. In this paper, a numerical method is presented in order to identify the parameters of the airport system.

Firstly, based on the solution of infinite plate under concentrated load, an analytical solution of infinite plate on elastic foundation under multiple wheel load is obtained. Several numerical examples are presented to illustrate the effectiveness of the analytical solution. A series of boundary adjust parameter are introduced to deal with the problems of finite plate, in which the load transform capability among different plates and the size of each plate bring obvious effect. By using these boundary adjust parameters, these method can solve the problems of arbitrary finite-size plates such as rectangle or hexagonal plate. Furthermore, these method can be used to evaluate strength of the double-layer pavement by using the equivalent stiffness relation or the approximate formula prevailed in American military engineering.

Secondary, a general method is established to identify the correlative parameters. An optimization algorithm is employed to identify the objective function that is constructed by comparing with the measure displacement curve and computing displacement curve. According this optimization algorithm, we can obtain the thickness, bending rigidity and foundation response modulus conveniently. These parameter will play an important role in evaluating strength of the old pavement.

In order to show the application of the method developed in this paper, an actual airport is investigated. By using this software, the foundation response modulus can be identified convenienttely, and the results show a good agreement with experimental results.

A geometric conservation law should be considered on moving boundary problems in body-fitted coordinated grid system. In this paper, as moving grid problem, threedimensional unstructured mesh with add and eliminated grid system is dealt with. In using add and eliminated grid method, the unstructured moving grid finite volume method is adopted. In this case, a control volume is treated as four-dimensional spacetime unified domain. So, a procedure of calculation is relatively complicatedly, espacially, in the case of parallel computation. In this paper, parallelization with OpenMP of the computation is estimated.

For any n≥3, let V⊂ℙⁿ⁻¹ be an irreducible variety of degree d whose ideal is generated by forms defined over the rationals. In this degree of generality one might still ask whether anything meaningful can be said about the corresponding counting function N_v(B), as defined in (1.6). In contrast to the preceding chapter, where precise asymptotic formulae were sought for N_U(B) for suitable open subsets U⊆V, the aim of the present chapter is to seek general upper bounds for the full counting function N_V(B), making as few assumptions on V as possible.