The solution to the problem of optical or electromagnetic-wave scattering from perfectly conducting rough surfaces modeled by a multiscale fractal function is generalized to the case of relative uniform translating motion with respect to the observer. The presence of motion can be treated by the relativistic frame hopping method by means of plane-wave simplification techniques, since the soluti...

A generalized central trinomial coefficient Tn(b, c) is the coefficient of x in the expansion of (x+bx+c) with b, c ∈ Z. In this paper we investigate congruences and series for sums of terms related to central binomial coefficients and generalized central trinomial coefficients. The paper contains many conjectures on congruences related to representations of primes by certain binary quadratic f...

In this paper, using similar symbolical method of Burchnall and Chaundy formulas of expansion for the generalized hypergeometric function were constructed. By means of the found formulas of expansion the formulas of an analytic continuation for hypergeometric function of Clausen is defined. The obtained formulas of an analytic continuation express known hypergeometric Appell function F2 (a; b1,...

We compute connected Green’s functions of a Bosonic field theory with cutoffs by means of a “minimal” expansion which in a single move, interpolating a generalized propagator, performs the usual tasks of the cluster and Mayer expansion. In this way it allows a direct construction of the infinite volume or thermodynamic limit and it brings constructive Bosonic expansions closer to constructive F...

We generalized the nonparaxial field components of Laguerre-Gaussian and flattened Gaussian beams obtained using the angular spectrum method to include symmetric radial and angular expansions and simplified them using an approximate evaluation of the integral equations for the field components. These field components possess series expressions in orders of a natural expansion parameter, which c...

We study a semiparametric generalized additive coefficient model, in which linear predictors in the conventional generalized linear models is generalized to unknown functions depending on certain covariates, and approximate the nonparametric functions by using polynomial spline. The asymptotic expansion with optimal rates of convergence for the estimators of the nonparametric part is establishe...

We derive the first three terms of the ε− expansion of the scalar one-loop Bhabha box function from a representation in terms of three generalized hypergeometric functions, which is valid in arbitrary dimensions.

A series of study to design guaranteed quality-of-service wireless access to broadband networks has been presented in this paper, based on randomly addressed polling and its generalized expansion multiple access protocol.

JAPAN In this paper, we consider Bogoliubov automorphisms of CAR algebra and we give imple-menters as continuous linear operators on the white noise (test or generalized) functionals for the Fermion system with the help of the Fock expansion.

We study the near diagonal asymptotic expansion of the generalized Bergman kernel of the renormalized Bochner-Laplacian on high tensor powers of a positive line bundle over a compact symplectic manifold. We show how to compute the coefficients of the expansion by recurrence and give a closed formula for the first two of them. As consequence, we calculate the density of states function of the Bo...