Spectral analysis of non‐compact symmetrizable operators on Hilbert spaces

This paper revisits and complement in different directions the classical work by W. T. Reid on symmetrizable completely continuous transformations in Hilbert spaces and a more recent paper by one of the authors. More precisely, we deal with spectral properties of % non‐compact operators G on a complex Hilbert space H such that SG is self‐adjoint where S is a (not necessarily injective) nonnegative operator. We study the isolated eigenvalues of G outside its essential spectral interval and provide variational characterization of them as well as stability estimates. We compare them also to spectral objects of SG. Finally, we characterize the Schechter essential spectrum of strongly symmetrizable operators in terms singular Weyl sequences; in particular, we complement J. I. Nieto's paper on the essential spectrum of symmetrizable. Copyright © 2014 John Wiley & Sons, Ltd.     

Global attractivity for a class of delayed discrete SIRS epidemic models with general nonlinear incidence

This paper deals with global dynamics of a class of delayed discrete susceptible‐infected‐recovered (SIR) compartmental epidemic models with general nonlinear incidence rate and disease‐induced mortality, which are proposed from the Mickens nonstandard discretization of the corresponding delayed continuous epidemic models. By constructing discrete Lyapunov functions, the sufficient conditions for the global attractivity of the disease‐free equilibrium and endemic equilibrium are established. Under some additional assumptions (see (H₃) in Section 3 and (H₄) in Section 4 ), it is shown that the disease‐free equilibrium is globally attractive when basic reproduction number , and when , there is a unique endemic equilibrium, which is globally attractive. Furthermore, some special cases are discussed, and as corollaries, several idiographic results are established. Copyright © 2015 John Wiley & Sons, Ltd.     

Multi‐component integrable couplings for the Ablowitz–Kaup–Newell–Segur and Volterra hierarchies

A kind of N × N non‐semisimple Lie algebra consisting of triangular block matrices is used to generate multi‐component integrable couplings of soliton hierarchies from zero curvature equations. Two illustrative examples are made for the continuous Ablowitz–Kaup–Newell–Segur hierarchy and the semi‐discrete Volterra hierarchy, together with recursion operators. Copyright © 2014 John Wiley & Sons, Ltd.     

Well‐posedness for the Cauchy problem of the modified Hunter–Saxton equation in the Besov spaces

This paper is concerned with the Cauchy problem of the modified Hunter‐Saxton equation. The local well‐posedness of the model equation is obtained in Besov spaces (which generalize the Sobolev spaces H^s) by using Littlewood‐Paley decomposition and transport equation theory. Moreover, the local well‐posedness in critical case (with ) is considered.     

Global stability and Hopf bifurcation of a delayed eco‐epidemiological model with Holling type II functional response

In this paper, a delayed eco‐epidemiological model with Holling type II functional response is investigated. By analyzing corresponding characteristic equations, the local stability of each of the feasible equilibria and the existence of Hopf bifurcations at the disease‐free equilibrium, the susceptible predator‐free equilibrium and the endemic‐coexistence equilibrium are established, respectively. By means of Lyapunov functionals and LaSalle's invariance principle, sufficient conditions are derived for the global stability of the endemic‐coexistence equilibrium, the disease‐free equilibrium, the susceptible predator‐free equilibrium and the predator‐extinction equilibrium of the system, respectively. Numerical simulations are carried out to illustrate the theoretical results. Copyright © 2014 John Wiley & Sons, Ltd.     

Design and Characterisation of Inhibitory Peptides against Bleg1_2478, an Evolutionary Divergent B3 Metallo-β-lactamase

Previously, a hypothetical protein (HP) termed Bleg1_2437 (currently named Bleg1_2478) from Bacillus lehensis G1 was discovered to be an evolutionary divergent B3 subclass metallo-β-lactamase (MBL). Due to the scarcity of clinical inhibitors for B3 MBLs and the divergent nature of Bleg1_2478, this study aimed to design and characterise peptides as inhibitors against Bleg1_2478. Through in silico docking, RSWPWH and SSWWDR peptides with comparable binding energy to ampicillin were obtained. In vitro assay results showed RSWPWH and SSWWDR inhibited the activity of Bleg1_2478 by 50% at concentrations as low as 0.90 µM and 0.50 µM, respectively. At 10 µM of RSWPWH and 20 µM of SSWWDR, the activity of Bleg1_2478 was almost completely inhibited. Isothermal titration calorimetry (ITC) analyses showed slightly improved binding properties of the peptides compared to ampicillin. Docked peptide–protein complexes revealed that RSWPWH bound near the vicinity of the Bleg1_2478 active site while SSWWDR bound at the center of the active site itself. We postulate that the peptides caused the inhibition of Bleg1_2478 by reducing or blocking the accessibility of its active site from ampicillin, thus hampering its catalytic function.     

Optimal decay rates and global existence for a semilinear Timoshenko system with two damping effects

In this paper, we study a semilinear Timoshenko system having two damping effects. The observation that two damping effects might lead to smaller decay rates for solutions in comparison with one damping effect is rigorously proved here in providing optimality results. Moreover, the global well‐posedness for small data in a low regularity class is presented for a larger class of nonlinearities than previously known and proved by a simpler approach. Copyright © 2016 John Wiley & Sons, Ltd.     

Effect of cold plasma permittivity on the radiation of the dominant TEM‐wave by an impedance loaded parallel‐plate waveguide radiator

The effects of wall impedances on the radiation of the dominant transverse electromagnetic wave by an impedance loaded parallel‐plate waveguide radiator immersed in a cold plasma have been analyzed. The solution to the governing mathematical model in cold plasma is determined while using the Wiener–Hopf technique. It is observed that the amplitude of the radiated field increases with increasing permittivity of the plasma. The work presented may be of great interest to quantify the effects of ionosphere plasma on the communicating signals between Earth station and an artificial satellite in the Earth's atmosphere. Copyright © 2015 John Wiley & Sons, Ltd.     

Numerical solution of the fractional Bagley‐Torvik equation by using hybrid functions approximation

In this paper, a new numerical method for solving the fractional Bagley‐Torvik equation is presented. The method is based upon hybrid functions approximation. The properties of hybrid functions consisting of block‐pulse functions and Bernoulli polynomials are presented. The Riemann‐Liouville fractional integral operator for hybrid functions is introduced. This operator is then utilized to reduce the solution of the initial and boundary value problems for the fractional Bagley‐Torvik differential equation to a system of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique. Copyright © 2015 John Wiley & Sons, Ltd.     

Algebro‐geometric constructions of the Wadati‐Konno‐Ichikawa flows and applications

With the aid of Lenard recursion equations, we derive the Wadati–Konno–Ichikawa hierarchy. Based on the Lax matrix, an algebraic curve of arithmetic genus n is introduced, from which Dubrovin‐type equations and meromorphic function φ are established. The explicit theta function representations of solutions for the entire WKI hierarchy are given according to asymptotic properties of φ and the algebro‐geometric characters of . Copyright © 2015 John Wiley & Sons, Ltd.