Codes from curves with total inflection points

The concept of pure gaps of a Weierstrass semigroup at several points of an algebraic curve has been used lately to obtain codes that have a lower bound for the minimum distance which is greater than the Goppa bound. In this work, we show that the existence of total inflection points on a smooth plane curve determines the existence of pure gaps in certain Weierstrass semigroups. We then apply our results to the Hermitian curve and construct codes supported on several points that compare better to one-point codes from that same curve.      

Gaussian bounds for propagators perturbed by potentials

We develop the perturbation theory for propagators, with the objective to prove Gaussian bounds. Let U be a strongly continuous propagator, i.e., a family of operators describing the solutions of a non-autonomous evolution equation, on an Lp-space, and assume that U is positive and satisfies Gaussian upper and lower bounds. Let V be a (time-dependent) potential satisfying certain Miyadera conditions with respect to U. We show that then the perturbed propagator enjoys Gaussian upper and lower bounds as well. To prepare the necessary tools, we extend the perturbation theory of strongly continuous propagators and the theory of absorption propagators.     

Existence for neutral impulsive differential inclusions with nonlocal conditions

In this paper, by using a fixed point theorem for condensing multi-valued maps, we have investigated the existence of mild solutions for a class of semilinear impulsive neutral functional differential inclusions with nonlocal conditions. As an application, an example has been presented to illustrate the results obtained.     

WEAK REGULARIZATION FOR A CLASS OF ILL-POSED CAUCHY PROBLEMS

This article is concerned with the ill-posed Cauchy problem associated with a densely defined linear operator A in a Banach space. A family of weak regularizing operators is introduced. If the spectrum of A is contained in a sector of right-half complex plane and its resolvent is polynomially bounded, the weak regularization for such ill-posed Cauchy problem can be shown by using the quasi-reversibility method and regularized semigroups. Finally, an example is given.     

ASYMPTOTIC BEHAVIOR FOR COMMUTATIVE SEMIGROUPS OF ALMOST ASYMPTOTICALLY NONEXPANSIVE TYPE MAPPINGS

This article introduces the concept of commutative semigroups of almost asymptotically nonexpansive-type mappings in a Banach space X which has the Opial property and whose norm is UKK, and establishes the weak convergence theorems for almost-orbits of this class of commutative semigroups. The author improves, extends and develops some recent and earlier results.     

Identification of the unknown diffusion coefficient in a quasi‐linear parabolic equation by semigroup approach with mixed boundary conditions

In this article, a semigroup approach is presented for the mathematical analysis of the inverse coefficient problems of identifying the unknown diffusion coefficient k(u(x, t)) in the quasi‐linear parabolic equation u_t(x, t)=(k(u(x, t))u_x(x, t))_x, with Dirichlet boundary conditions u_x(0, t)=ψ₀, u(1, t)=ψ₁. The main purpose of this work is to analyze the distinguishability of the input–output mappings Φ[·] : ??→C¹[0, T], Ψ[·] : ??→C¹[0, T] using semigroup theory. In this article, it is shown that if the null space of semigroups T(t) and S(t) consists of only a zero function, then the input–output mappings Φ[·] and Ψ[·] have the distinguishability property. Copyright © 2008 John Wiley & Sons, Ltd.     

The Perron-Frobenius Theorem Revisited

An extension of the Perron-Frobenius Theorem is presented in the much more general setting of indecomposable semigroups of nonnegative matrices. Many features of the original theorem including the existence of a fixed positive vector, a block-monomial form, and spectral stability properties hold simultaneously for these semigroups. The paper is largely self-contained and the proofs are elementary. The classical theorem and some related results follow as corollaries.     

Almost Periodic Solutions of Abstract Retarded Functional Differential Equations with Unbounded Delay

We establish the existence of bounded, almost periodic and asymptotically almost periodic mild solutions for first- and second-order abstract-retarded functional differential equations with unbounded delay.     

Construction of some quantum stochastic operator cocycles by the semigroup method

A new method for the construction of Fock-adapted quantum stochastic operator cocycles is outlined, and its use is illustrated by application to a number of examples arising in physics and probability. The construction uses the Trotter-Kato theorem and a recent characterisation of such cocycles in terms of an associated family of contraction semigroups. In celebration of Kalyan Sinha’s sixtieth birthday     

Windowing Waveform Relaxation of Initial Value Problems

We present a windowing technique of waveform relaxation for dynamic systems.An effectiveestimation on window length is derived by an iterative error expression provided here.Relaxation processes canbe speeded up if one takes the windowing technique in advance.Numerical experiments are given to furtherillustrate the theoretical analysis.