Well-posedness and stability of the repairable system with N failure modes and one standby unit

The well-posedness and stability of the repairable system with N failure modes and one standby unit were discussed by applying the c₀ semigroups theory of function analysis. Firstly, the integro-differential equations described the system were transformed into some abstract Cauchy problem of Banach space. Secondly, the system operator generates positive contractive c₀ semigroups T(t) and so the well-posedness of the system was obtained. Finally, the spectral distribution of the system operator was analyzed. It was proven that 0 is strictly dominant eigenvalue of the system operator and the dynamic solution of the system converges to the steady-state solution. The steady-state solution was shown to be the eigenvector of the system operator corresponding to the eigenvalue 0. At the same time the dynamic solution exponentially converges to the steady-state solution.     

The ideal property, the projection property, continuous fields and crossed products

Let A be the C^∗-algebra associated to an arbitrary continuous field of C^∗-algebras. We give a necessary and sufficient condition for A to have the ideal property and, if moreover A is separable, we give a necessary and sufficient condition for A to have the projection property. Some applications of these results are given. We also prove that “many” crossed products of commutative C^∗-algebras by discrete, amenable groups have the projection property, generalizing some of our previous results.     

Upper triangular operator matrices with the single-valued extension property

If A=(Aij)_1?i,j?n∈B(X) is an upper triangular Banach space operator such that AiiAij=AijAjj for all 1?i?j?n, then A has SVEP or satisfies (Dunford's) condition (C) or (Bishop's) property (β) or (the decomposition) property (δ) if and only if Aii, 1?i?n, has the corresponding property.     

A note on ball-covering property of Banach spaces

By a ball-covering B of a Banach space X, we mean that B is a collection of open (or closed) balls off the origin whose union contains the unit sphere SX of X; and X is said to have the ball-covering property (BCP) provided it admits a ball-covering by countably many balls. In this note we give a natural example showing that the ball-covering property of a Banach space is not inherited by its subspaces; and we present a sharp quantitative version of the recent Fonf and Zanco renorming result saying that if the dual X^∗ of X is w^∗ separable, then for every ε>0 there exist a (1+ε)-equivalent norm on X, and an R>0 such that in this new norm SX admits a ball-covering by countably many balls of radius R. Namely, we show that R=R(ε) can be taken arbitrarily close to (1+ε)/ε, and that for X=?₁[0,1] the corresponding R cannot be equal to 1/ε. This gives the sharp order of magnitude for R(ε) as ε→0.     

Stabilization of a coupled transport-diffusion system with boundary input

We consider the problem of stabilizing a coupled transport-diffusion system with boundary input. The system is described by two linear transport-diffusion equations and is not asymptotically stable. In order to stabilize the system with boundary input, sensor influence functions are assumed to be located at interior of the domain. First, we formulate the system as an evolution equation with unbounded output operators in a Hilbert space, using variable transformation. Next, we derive a reduced-order model with a finite-dimensional state variable for the infinite-dimensional system. Then, a stabilizing controller is constructed for the reduced-order model under an additional assumption. It is shown that the finite-dimensional controller together with a residual mode filter plays a role of a finite-dimensional stabilizing controller for the original infinite-dimensional system, if the order of the residual mode filter is chosen sufficiently large. Finally, the validity of the design method is demonstrated through a numerical simulation.     

Differentiability of the age-dependent population system with time delay in the birth process

In this paper, by using semigroup approach, we concerned with the regularity of the age-dependent population system with instantaneous time delay in the birth process. We prove that, under some additional condition, the solution semigroup of the population evolution equation is eventually differentiable, i.e., there exists t₀>0 such that T(t) is differentiable for t>t₀.     

On the weak-approximate fixed point property

Let X be a Banach space and C a bounded, closed, convex subset of X. C is said to have the weak-approximate fixed point property if for any norm-continuous mapping , there exists a sequence {xn} in C such that (xn−fn(xn)) converges to 0 weakly. It is known that every infinite-dimensional Banach space with the Schur property does not have the weak-approximate fixed point property. In this article, we show that every Asplund space has the weak-approximate fixed point property. Applications to the asymptotic fixed point theory are given.     

On a deterministic linear partial differential system

We develop an Lp theory for the Cauchy problem of linear partial differential systems of the form

     

Global bifurcation for a class of degenerate elliptic equations with variable exponents

We are concerned with the following nonlinear problem

     

The well-posedness and stability of a repairable standby human–machine system

In this paper, the solution of a standby human–machine system is investigated. By using the method of functional analysis, especially, the linear operator theory and the C₀ semigroup theory on Banach space, we prove the well-posedness and the existence of a positive solution of the system. And under some appropriate hypotheses, we study the asymptotic stability of solution of the system.     

Multiple solutions for some nonlinear Schrödinger equations with indefinite linear part

We consider a class of nonlinear Schrödinger equation with indefinite linear part in RN. We prove that the problem has at least three nontrivial solutions by means of Linking Theorem and (∇)-Theorem.     

On certain spaces of vector measures of bounded variation

If (Σ,X) is a measurable space and X a Banach space we investigate the X-inheritance of copies of ?_∞ in certain subspaces Δ(Σ,X) of bvca(Σ,X), the Banach space of all X-valued countable additive measures of bounded variation equipped with the variation norm. Among the consequences of our main theorem we get a theorem of J. Mendoza on the X-inheritance of copies of ?_∞ in the Bochner space L₁(μ,X) and other of the author on the X-inheritance of copies of ?_∞ in bvca(Σ,X).     

The Cauchy problem for the elliptic-hyperbolic Davey-Stewartson system in Sobolev space

We study the initial value problem for the elliptic-hyperbolic Davey-Stewartson systems

(0.1)     

Local regularity theorems for the stationary thermistor problem with oscillating degeneracy

In this paper we present some regularity results for solutions to the system −Δu=σ(u)²|∇φ|, div(σ(u)∇φ)=0 in the case where σ(u) is allowed to oscillate between 0 and a positive number as u→∞. In particular, we show that u is locally bounded if σ(u) is bounded below by a suitable exponential function.     

Asymptotic behavior of solutions to a hyperbolic-elliptic coupled system in multi-dimensional radiating gas

This paper is concerned with the asymptotic behavior of solutions to the Cauchy problem of a hyperbolic-elliptic coupled system in the multi-dimensional radiating gas

     

On the nonidentifiability property of Archimedean copula models under dependent censoring

In this paper, we prove a peculiar property shared by the Archimedean copula models, that is, different Archimedean copula models with distinct dependent levels can have the same crude survival functions for dependent censored data. This property directly shows the nonidentifiability property of the Archimedean copula models. The proposed procedure is then demonstrated by two examples.     

Riesz means associated with certain product type convex domain

In this paper we study the maximal operators and the convolution operators Tδ associated with multipliers of the form

     

On a generalization of the Evans Conjecture

The Evans Conjecture states that a partial Latin square of order n with at most n-1 entries can be completed. In this paper we generalize the Evans Conjecture by showing that a partial r-multi Latin square of order n with at most n-1 entries can be completed. Using this generalization, we confirm a case of a conjecture of Häggkvist.     

Large time behavior of solutions to a nonlinear integro-differential system

Asymptotic behavior of solutions as t→∞ to the nonlinear integro-differential system associated with the penetration of a magnetic field into a substance is studied. Initial-boundary value problems with two kinds of boundary data are considered. The first with homogeneous conditions on whole boundary and the second with non-homogeneous boundary data on one side of lateral boundary. The rates of convergence are given too.     

Colorings of k-balanced matrices and integer decomposition property of related polyhedra

We show that a class of polyhedra, arising from certain 0,1 matrices introduced by Truemper and Chandrasekaran, has the integer decomposition property. This is accomplished by proving certain coloring properties of these matrices.