A note on quasi-stationary distributions of birth-death processes and the SIS logistic epidemic

For Markov processes on the positive integers with the origin as an absorbing state, Ferrari, Kesten, Martinez and Picco studied the existence of quasi-stationary and limiting conditional distributions by characterizing quasi-stationary distributions as fixed points of a transformation Phi on the space of probability distributions on {1, 2,.. }. In the case of a birth-death process, the components of Phi(nu) can be written down explicitly for any given distribution nu. Using this explicit representation, we will show that Phi preserves likelihood ratio ordering between distributions. A conjecture of Kryscio and Lefevre concerning the quasi-stationary distribution of the SIS logistic epidemic follows as a corollary.

Valuing of firm's prior knowledge: A measure of knowledge distance

Knowledge, especially scientific and technological knowledge, grows according to knowledge trajectories and guideposts that make up the prior knowledge of an organization. We argue that these knowledge structures and their specific components lead to successful innovation. A firm's prior knowledge facilitates the absorption of new knowledge, thereby renewing a firm's systematic search, transfer and acquisition of knowledge and capabilities. In particular, the exponential growth in biotechnology is characterized by the convergence of disparate scientific and technological knowledge resources. This paper examines the shift from protein-based to DNA-based diagnostic technologies as an example, to quantify the value of a firm's prior knowledge using relative values of knowledge distance. The distance between core prior knowledge and the rate of transition from one knowledge system to another has been identified as a proxy for the value a firm's prior knowledge. The overall difficulty of transition from one technology paradigm to another is discussed. We argue this transition is possible when the knowledge distance is minimal and the transition process has a correspondingly high value of absorptive capacities. Our findings show knowledge distance is a determinant of the feasibility, continuity and capture of scientific and technological knowledge. Copyright © 2003 John Wiley & Sons, Ltd.

Implicit vector equilibrium problems with applications

Let X and Y be Hausdorff topological vector spaces, K a nonempty, closed, and convex subset of X, C: K--> 2(Y) a point-to-set mapping such that for any x is an element of K, C(x) is a pointed, closed, and convex cone in Y and int C(x) not equal 0. Given a mapping g : K --> K and a vector valued bifunction f : K x K - Y, we consider the implicit vector equilibrium problem (IVEP) of finding x* is an element of K such that f (g(x*), y) is not an element of - int C(x) for all y is an element of K. This problem generalizes the (scalar) implicit equilibrium problem and implicit variational inequality problem. We propose the dual of the implicit vector equilibrium problem (DIVEP) and establish the equivalence between (IVEP) and (DIVEP) under certain assumptions. Also, we give characterizations of the set of solutions for (IVP) in case of nonmonotonicity, weak C-pseudomonotonicity, C-pseudomonotonicity, and strict C-pseudomonotonicity, respectively. Under these assumptions, we conclude that the sets of solutions are nonempty, closed, and convex. Finally, we give some applications of (IVEP) to vector variational inequality problems and vector optimization problems. (C) 2003 Elsevier Science Ltd. All rights reserved.

Quasiequilibrium problem in H-spaces

In the present paper, we study the quasiequilibrium problem and generalized quasiequilibrium problem of generalized quasi-variational inequality in H-spaces by a new method. Some new equilibrium existence theorems are given. Our results are different from corresponding given results or contain some recent results as their special cases. (C) 2003 Elsevier Science Ltd. All rights reserved.

On continuous selection problems for multivalued mappings with the local intersection property in hyperconvex metric spaces

In the paper we present two continuous selection theorems in hyperconvex metric spaces and apply these to study xed point and coincidence point problems as well as variational inequality problems in hyperconvex metric spaces.

A comparative study of iterative Chebyshev and Lanczos implementations of the boundary inhomogeneity method for quantum scattering

We have recently developed a scaleable Artificial Boundary Inhomogeneity (ABI) method [Chem. Phys. Lett.366, 390–397 (2002)] based on the utilization of the Lanczos algorithm, and in this work explore an alternative iterative implementation based on the Chebyshev algorithm. Detailed comparisons between the two iterative methods have been made in terms of efficiency as well as convergence behavior. The Lanczos subspace ABI method was also further improved by the use of a simpler three-term backward recursion algorithm to solve the subspace linear system. The two different iterative methods are tested on the model collinear H+H2 reactive state-to-state scattering.

The uniqueness of solutions to discrete, victor, two-point boundary value problems

Difference equations which may arise as discrete approximations to two-point boundary value problems for systems of second-order, ordinary differential equations are investigated and conditions are formulated under which solutions to the discrete problem are unique. Some existence, uniqueness implies existence, and convergence theorems for solutions to the discrete problem are also presented.