We propose a class of synthetic optical materials in which the refractive index satisfies n(−x) = −n∗(x). We term such systems antisymmetric parity-time (APT ) structures. Unlike PT -symmetric systems, which require balanced gain and loss, i.e., n(−x) = n∗(x), APT systems consist of balanced positiveand negative-index materials. Despite the seemingly PT -symmetric optical potential V (x) ≡ n(x)...

Let F∗ n be the set of Boolean functions depending on all n variables. We prove that for any f ∈ F∗ n, f |xi=0 or f |xi=1 depends on the remaining n − 1 variables, for some variable xi. This existent result suggests a possible way to deal with general Boolean functions via its subfunctions of some restrictions. As an application, we consider the degree lower bound of representing polynomials ov...

It has been conjectured that there are no homogeneous rotation symmetric bent Boolean functions of degree greater than two. In this paper we begin by proving that sums of short-cycle rotation symmetric bent Boolean functions must contain a specific degree two monomial rotation symmetric Boolean function. We then prove most cases of the conjecture in n=2p, p>2 prime, variables and extend this wo...

In this study, the boundary element method is formulated to evaluate hydrodynamic characteristics of bodies including free surface effect. The method is based on two equations, the perturbation potential boundary integral and the pressure Kutta condition, which are solved simultaneously. The method uses isoparametric elements for both quantity and geometric on the boundary. The method is first ...

Steep gravity-capillary waves are studied experimentally in a channel. The range of cyclic frequencies investigated is 6.94-9.80 Hz; namely, the high-frequency portion of the regime of internal resonances according to the weakly nonlinear theory (Wilton’s ripples). These wave trains are stable according to the nonlinear Schrodinger equation. The experimental wave trains are generated by large, ...

This paper has two main parts. First, we consider the Tutte symmetric function XB, a generalization of chromatic function. We introduce vertex-weighted version XB and show that this admits deletion-contraction relation. also demonstrate spanning-tree spanning-forest expansions generalizing those polynomial by connecting to other graph functions. Second, give several methods for constructing non...

in this paper energy bands and berry curvature of graphene was studied. desired hamiltonian regarding the next-nearest neighbors obtained by tight binding model. by using the second quantization approach, the transformation matrix is calculated and the hamiltonian of system is diagonalized. with this hamiltonian, the band structure and wave function can be calculated. by using calculated wave f...

A quantization of a breathing motion of a rotating chiral soliton on S 3 is performed in terms of a family of trial functions for a profile function of the hegdehog ansatz. We determine eigenenergies of the quantized S 3 skyrmion by solving the Schrödinger equation of the breathing mode for several lower spin and isospin states varying the Skyrme term constants e. When S 3 radius is smaller tha...