Green’s function, an analytical approach in inhomogeneous linear differential equations, is the impulse response, which is applied for deriving the wave equation solution in composite materials mediums. This paper investigates the study of SH wave’s transmission influenced by concentrated point source disturbance in piezomagnetic material resting over heterogeneous half-space. Green function ap...

We prove a Paley-Wiener Theorem for a class of symmetric spaces of the compact type, in which all root multiplicities are even. This theorem characterizes functions of small support in terms of holomorphic extendability and exponential type of their (discrete) Fourier transforms. We also provide three independent new proofs of the strong Huygens’ principle for a suitable constant shift of the w...

We consider the symmetric Darlington synthesis of a p × p rational symmetric Schur function S with the constraint that the extension is of size 2p×2p. Under the assumption that S is strictly contractive in at least one point of the imaginary axis, we determine the minimal McMillan degree of the extension. In particular, we show that it is generically given by the number of zeros of odd multipli...

By using a complex eld with a symmetric combination of electric and magnetic elds, a rstorder covariant Lagrangian for Maxwell's equations is obtained, similar to the Lagrangian for the Dirac equation. This leads to a dual-symmetric quantum electrodynamic theory with an in nite set of local conservation laws. The dual symmetry is shown to correspond to a helical phase, conjugate to the conserve...

In this paper, we consider the D-brane, especially D−-brane, in the pp-wave background, which has the eight dynamical and the eight kinematical supercharges. Since the pp-wave background has not a SO(8) but a SO(4)× SO(4) symmetric group, the D-brane world-volume theory has a non-trivial symmetric group which depends on the configuration of D-brane. Here, we will analyze the open string spectru...

A classical theorem of MacMahon states that the number of lozenge tilings of any centrally symmetric hexagon drawn on the triangular lattice is given by a beautifully simple product formula. In this paper, we present a counterpart of this formula, corresponding to the exterior of a concave hexagon obtained by turning 120° after drawing each side (MacMahon’s hexagon is obtained by turning 60° af...

Algebraic immunity of Boolean function f is defined as the minimal degree of a nonzero g such that fg = 0 or (f + 1)g = 0. Given a positive even integer n, it is found that the weight distribution of any n-variable symmetric Boolean function with maximum algebraic immunity n 2 is determined by the binary expansion of n. Based on the foregoing, all n-variable symmetric Boolean functions with max...

We propose an anti-parity-time (anti-$\mathcal{PT}$) symmetric non-Hermitian Su-Schrieffer-Heeger (SSH) model, where the large non-Hermiticity constructively creates nontrivial topology and greatly expands topological phase. In anti-$\mathcal{PT}$-symmetric SSH gain loss are alternatively arranged in pairs under inversion symmetry. The appearance of degenerate point at center Brillouin zone det...

We prove that the subset of quasisymmetric polynomials conjectured by Bergeron and Reutenauer to be a basis for the coinvariant space of quasisymmetric polynomials is indeed a basis. This provides the first constructive proof of the Garsia–Wallach result stating that quasisymmetric polynomials form a free module over symmetric polynomials and that the dimension of this module is n!.