In the framework of toroidal Pseudodifferential operators on the flat torus Tn := (R/2πZ)n we begin by proving the closure under composition for the class of Weyl operators Opw ~ (b) with simbols b ∈ Sm(Tn × Rn). Subsequently, we consider Opw ~ (H) when H = 1 2 |η| + V (x) where V ∈ C(T;R) and we exhibit the toroidal version of the equation for the Wigner transform of the solution of the Schröd...

It is important to seek for more explicit exact solutions of nonlinear partial differential equations (NLPDEs) in mathematical physics. With the help of symbolic computation software like Maple or Mathematica, much work has been focused on the various extensions and applications of the known methods to construct exact solutions of NLPDEs. Mathematical modelling of physical systems often leads t...

We use elementary facts about quadratic forms in characteristic 2 to evaluate the sign of some Walsh transforms in terms of a Jacobi symbol. These results are applied to the Walsh transforms of the Gold and KasamiWelch functions. We prove that the Gold functions yield bent functions when restricted to certain hyperplanes. We also use the sign information to determine the dual bent function.

Long binary sequences related to cyclic difference sets are investigated. Among all known constructions of cyclic difference sets we show that only sequences constructed from Hadamard difference sets can have an asymptotic nonzero merit factor. Maximal length shift register sequences, Legendre, and twin-prime sequences are all constructed from Hadamard difference sets. We prove that the asympto...

We describe a method for numerical construction of a symplectic map for particle propagation in a general accelerator lattice. The generating function of the map is obtained by integrating the Hamilton-Jacobi equation as an initial-value problem on a finite time interval. Given the generating function, the map is put in explicit form by means of a Fourier inversion technique. We give an example...

We prove general lower bounds on the maximal determinant of n× n {+1,−1}matrices, both with and without the assumption of the Hadamard conjecture. Our bounds improve on earlier results of de Launey and Levin (2010) and, for certain congruence classes of n mod 4, the results of Koukouvinos, Mitrouli and Seberry (2000). In an Appendix we give a new proof, using Jacobi’s determinant identity, of a...

In a deformation quantization of R, the Jacobi identity is automatically satisfied. This article poses the contrary question: Given a set of commutators which satisfies the Jacobi identity, is the resulting associative algebra a deformation quantization of R? It is shown that the result is true. However care must taken when stating precisely how and in which algebra the Jacobi identity is satis...

In this article, the anti-plane deformation of an orthotropic sector with multiple defects is studied analytically. The solution of a Volterra-type screw dislocation problem in a sector is first obtained by means of a finite Fourier cosine transform. The closed form solution is then derived for displacement and stress fields over the sector domain. Next, the distributed dislocation method is em...

formulae expressing explicitly the coefficients of an expansion of double jacobi polynomials which has been partially differentiated an arbitrary number of times with respect to its variables in terms of the coefficients of the original expansion are stated and proved. extension to expansion of triple jacobi polynomials is given. the results for the special cases of double and triple ultraspher...