A fourth-order parabolic equation modeling epitaxial thin film growth

We study the continuum model for epitaxial thin film growth from Phys. D 132 (1999) 520-542, which is known to simulate experimentally observed dynamics very well. We show existence, uniqueness and regularity of solutions in an appropriate function space, and we characterize the existence of nontrivial equilibria in terms of the size of the underlying domain. In an investigation of asymptotical behavior, we give a weak assumption under which the ω-limit set of the dynamical system consists only of steady states. In the one-dimensional setting we can characterize the set of steady states and determine its unique asymptotically stable element. The article closes with some illustrative numerical examples.     

Nondensely defined evolution impulsive differential inclusions with nonlocal conditions

In this paper, we shall establish sufficient conditions for the existence of integral solutions for some nondensely defined evolution impulsive differential inclusions in Banach spaces with nonlocal conditions.     

Boundary conditions of Sturm-Liouville operators with mixed spectra

We study bounds on averages of spectral functions corresponding to Sturm-Liouville operators on the half line for different boundary conditions. As a consequence constraints are obtained which imply existence of singular spectrum embedded in a.c. spectrum for sets of boundary conditions with positive measure and potentials vanishing in an interval [0,N]. These constraints are related to estimates on the measure of sets where the spectral density is positive.     

A real options approach for entering the Internet securities trading businesses with start‐up time

This paper uses a real options approach to establish a new evaluation model under uncertainty of both the volume of Internet securities transactions and the total transaction volume of a securities firm. The proposed approach can assist securities firms in evaluating the optimal thresholds for entering the Internet securities trading business and withdrawing from the conventional securities trading business. This paper assumes that the annual number of Internet securities transactions and the total annual number of securities transactions both follow a geometric Brownian motion. Besides, this model considers a start‐up time to complete the entry project's procedure. Accordingly, a decision model based on the real options approach is introduced, and the closed form solutions for the optimal threshold values of the entry or withdrawal models are determined. The conclusions provide some valuable references to help strategic managers of securities firms in making decisions on entering the Internet securities trading business or withdrawing from the conventional trading business. Copyright © 2003 John Wiley & Sons, Ltd.     

A time domain analysis of wave motions in chiral materials

A time domain analysis of the equations governing wave propagation in an unbounded chiral medium is presented by a spectral family approach and by a direct eigenfunction expansion using Beltrami–Moses fields.     

Operator–valued Fourier multiplier theorems on Besov spaces

We investigate analytical properties of a measure geometric Laplacian which is given as the second derivative w.r.t. two atomless finite Borel measures μ and ν with compact supports supp μ ? supp ν on the real line. This class of operators includes a generalization of the well‐known Sturm‐Liouville operator as well as of the measure geometric Laplacian given by . We obtain for this differential operator under both Dirichlet and Neumann boundary conditions similar properties as known in the classical Lebesgue case for the euclidean Laplacian like Gauß‐Green‐formula, inversion formula, compactness of the resolvent and its kernel representation w.r.t. the corresponding Green function. Finally we prove nuclearity of the resolvent and give two representations of its trace.     

Lipschitz estimates for generalized commutators of fractional integrals with rough kernel

Let (0 < α < n) be the generalized commutator generated by fractional integral with rough kernel and the m–th order remainder of the Taylor formula of a function A. In this paper, the (L^p, L^r) (r > 1) boundedness, the weak (L¹, L^{n/(n–α–β)}) boundedness and the (L^p, ?^{β, ∞}_p) boundedness of are discussed, when D^γA belongs to the Lipschitz function spaces.     

Rational Approximation of Analytic Functions Having Generalized Orders of Rate of Growth

Let f be holomorphic on a domain G C¯ and _n be the error in best approximation of f in the supremum norm on a compact set E G by rational functions of order n. We obtain results characterizing the degree of decrease of the best approximation _n in terms connected with the condenser (E,F), F=C¯ \ G¯, and the rate of growth of the maximum modulus of f(z). In particular, if f has a generalized order (, , f) in the domain G, thenlim sup_n (n)/ (log (1/log⁺((_{0 1} ....... _n)^1/n(n+1) ))) (, , f),where = exp (1/C(E,F)), C(E,F) is the capacity of the condenser (E,F).     

Vessel Arrival Process and Queueing in Marine Ports Handling Bulk Materials

We study the vessel arrival process in bulk ports handling either cargo containers or minerals. Then we introduce the SHIP/G/1 queue to be able to study the queueing behavior at the port. We present approximations for the asymptotic probabilities of delay and the number of vessels at the port. Numerical examples show the accuracy of the approximations. In appendices, we provide details of the analysis of the number of vessels at the port and the correlation properties of the vessel arrival process.     

An Epidemic Model with a Time Delay in Transmission

We study a mathematical model which was originally suggested by Greenhalgh and Das and takes into account the delay in the recruitment of infected persons. The stability of the equilibria are also discussed. In addition, we show that the introduction of a time delay in the transmission term can destabilize the system and periodic solutions can arise by Hopf bifurcation.