In this paper, we propose a 2-parameter family of coupled Painlevé II systems in dimension four with affine Weyl group symmetry of type D (2) 3. We also propose a 4-parameter family of 2-coupled D (2) 3-systems in dimension eight with affine Weyl group symmetry of type D In this paper, we present a 2-parameter family of 2-coupled Painlevé II systems with affine Weyl group symmetry of type D

Design of Weyl-Heisenberg sets of waveforms for robust orthogonal frequency division multiplexing (OFDM) has been the subject of a considerable volume of work. In this paper, a complete parameterization of orthogonal Weyl-Heisenberg sets and their corresponding biorthogonal sets is given. Several examples of Weyl-Heisenberg sets designed using this parameterization are presented, which in simul...

The Besicovitch and Weyl pseudometrics on the space AŸ of biinfinite sequences measure the density of differences in either the central or arbitrary segments of given sequences. The Besicovitch and Weyl spaces are obtained from A by factoring through the equivalence of zero distance. Cellular automata are considered as dynamical systems on the Besicovitch and Weyl spaces and their topological a...

The fractal Weyl law connects the asymptotic level number with the fractal dimension of the chaotic repeller. We provide the first test for the fractal Weyl law for a three-dimensional open scattering system. For the four-sphere billiard, we investigate the chaotic repeller and discuss the semiclassical quantization of the system by the method of cycle expansion with symmetry decomposition. We ...

A Weyl structure on a compact conformal manifold is not complete in general. If, however, the life-time of incomplete geodesics can be controlled on compact subsets of the tangent bundle, the Weyl connection is called tame. We prove that every closed, non-exact, tame Weyl structure on a compact conformal manifold is either flat, or has irreducible holonomy, generalizing an analogous statement f...

Hadronic flux-tube solutions describing the mesonic and the baryonic states within the dual Ginzburg-Landau (DGL) theory are investigated by using the dual lattice formulation in the Weyl-symmetric approach. The shape of the flux tubes is determined by placement of the colorelectric Dirac-string singularity treated as a connected stack of quantized plaquettes in the dual lattice formulation. Th...

Recently, new spreading sequences have been proposed to multiplex the capacity of users. In particular, Weyl spreading sequences have the larger capacity of users than the Gold code. This paper shows that Weyl spreading sequences appear in bit recovering model and they are orthogonal basis. This result shows the reason why they have the large capacity and that any spreading sequence is expresse...

Probabilistic Weyl laws for quantized tori MACIEJ ZWORSKI UC Berkeley Abstract For the Toeplitz quantization of complex-valued functions on a 2n-dimensional torus we prove that the expected number of eigenvalues of small random perturbations of a quantized observable satisfies a natural Weyl law. In numerical experiments the same Weyl law also holds for “false” eigenvalues created by pseudospec...

Weyl and Dirac semimetals recently stimulate intense research activities due to their novel properties. Combining first-principles calculations and effective model analysis, we predict that nonmagnetic compounds BaYBi (Y = Au, Ag and Cu) are Dirac semimetals. As for the magnetic compound EuYBi, although the time reversal symmetry is broken, their long-range magnetic ordering cannot split the Di...

The discovery of Weyl semimetals (WSM) has brought forth the condensed matter realization of Weyl fermions, which were previously theorized as low energy excitations in high energy particle physics. Recently, transition metal mono-pnictides are under intense investigation for understanding properties of inversion-symmetry broken Weyl semimetals. Non-trivial Berry phase and chirality are importa...