Traveling waves for a reaction–diffusion–advection predator–prey model

In this paper we study a reaction–diffusion–advection predator–prey model in a river. The existence of predator-invasion traveling wave solutions and prey-spread traveling wave solutions in the upstream and downstream directions is established and the corresponding minimal wave speeds are obtained. While some crucial improvements in theoretical methods have been established, the proofs of the existence and nonexistence of such traveling waves are based on Schauder’s fixed-point theorem, LaSalle’s invariance principle and Laplace transform. Based on theoretical results, we investigate the effect of the hydrological and biological factors on minimal wave speeds and hence on the spread of the prey and the invasion of the predator in the river. The linear determinacy of the predator–prey Lotka–Volterra system is compared with nonlinear determinacy of the competitive Lotka–Volterra system to investigate the mechanics of linear and nonlinear determinacy.     

(ω,c)-asymptotically periodic functions,first-order Cauchy problem,and Lasota-Wazewska model with unbounded oscillating production of red cells

In this paper, we study a new class of functions, which we call (ω,c)-asymptotically periodic functions. This collection includes asymptotically periodic, asymptotically antiperiodic, asymptotically Bloch-periodic, and unbounded functions. We prove that the set conformed by these functions is a Banach space with a suitable norm. Furthermore, we show several properties of this class of functions as the convolution invariance. We present some examples and a composition result. As an application, we prove the existence and uniqueness of (ω,c)-asymptotically periodic mild solutions to the first-order abstract Cauchy problem on the real line. Also, we establish some sufficient conditions for the existence of positive (ω,c)-asymptotically periodic solutions to the Lasota-Wazewska equation with unbounded oscillating production of red cells.     

CPT violation does not lead to violation of Lorentz invariance and vice versa

We present a class of interacting nonlocal quantum field theories, in which the CPT invariance is violated while the Lorentz invariance is present. This result rules out a previous claim in the literature that the CPT violation implies the violation of Lorentz invariance. Furthermore, there exists the reciprocal of this theorem, namely that the violation of Lorentz invariance does not lead to the CPT violation, provided that the residual symmetry of Lorentz invariance admits the proper representation theory for the particles. The latter occurs in the case of quantum field theories on a noncommutative space–time, which in place of the broken Lorentz symmetry possesses the twisted Poincaré invariance. With such a CPT-violating interaction and the addition of a C-violating (e.g., electroweak) interaction, the quantum corrections due to the combined interactions could lead to different properties for the particle and antiparticle, including their masses.     

Experimental test of special relativity by laser spectroscopy

The Doppler-free laser-spectroscopic frequency measurement of Doppler-shifted optical lines in forward and backward direction of a fast ion beam permits a sensitive test of the relativistic Doppler-formula and, hence, the relativistic time dilation factor . An experiment on metastable ⁷Li⁺, stored at a velocity of v = 0.064c in the Heidelberg heavy-ion storage ring TSR, has confirmed time dilation with unprecedented accuracy. Latest tests at two different ion-velocities (v = 0.03c and v = 0.064c) will enhance these measurements. An improved version of this experiment will be carried out at the experimental storage ring (ESR) at the Gesellschaft für Schwerionenforschung (GSI) in Darmstadt. The ESR permits ⁷Li⁺ to be stored at v = 0.33c which promises an improvement of the sensitivity to deviations from γ _SR by an order of magnitude. A first test at the ESR has shown the feasibility for this kind of experiment.     

Scale invariance rule in electromagnetic scattering

The volume integral equation formalism is used to prove the scale invariance rule for an arbitrarily sized scatterer with an arbitrary shape, morphology, and orientation. The only assumptions are that the scatterer is made of optically isotropic linear materials and is embedded in a homogeneous, linear, isotropic, and nonabsorbing infinite medium.     

Fulop-Tsutsui interactions on quantum graphs

We examine scale invariant Fulop-Tsutsui couplings in a quantum vertex of a general degree n. We demonstrate that essentially same scattering amplitudes as for the free coupling can be achieved for two (n−1)-parameter Fulop-Tsutsui subfamilies if n is odd, and for three (n−1)-parameter Fulop-Tsutsui subfamilies if n is even. We also work up an approximation scheme for a general Fulop-Tsutsui vertex, using only n δ function potentials.