GLOBAL STABILITY OF SIRS EPIDEMIC MODELS WITH A CLASS OF NONLINEAR INCIDENCE RATES AND DISTRIBUTED DELAYS＊

In this article,we establish the global asymptotic stability of a disease-free equilibrium and an endemic equilibrium of an SIRS epidemic model with a class of nonlinear incidence rates and distributed...     

Variable selection in multivariate methods using global score estimation

A variable selection method using global score estimation is proposed, which is applicable as a selection criterion in any multivariate method without external variables such as principal component analysis, factor analysis and correspondence analysis. This method selects a subset of variables by which we approximate the original global scores as much as possible in the context of least squares, where the global scores, e.g. principal component scores, factor scores and individual scores, are computed based on the selected variables. Global scores are usually orthogonal. Therefore, the estimated global scores should be restricted to being mutually orthogonal. According to how to satisfy that restriction, we propose three computational steps to estimate the scores. Example data is analyzed to demonstrate the performance and usefulness of the proposed method, in which the proposed algorithm is evaluated and the results obtained using four cost-saving selection procedures are compared. This example shows that combining these steps and procedures yields more accurate results quickly.     

Large-scale semidefinite programs in electronic structure calculation

It has been a long-time dream in electronic structure theory in physical chemistry/chemical physics to compute ground state energies of atomic and molecular systems by employing a variational approach in which the two-body reduced density matrix (RDM) is the unknown variable. Realization of the RDM approach has benefited greatly from recent developments in semidefinite programming (SDP). We present the actual state of this new application of SDP as well as the formulation of these SDPs, which can be arbitrarily large. Numerical results using parallel computation on high performance computers are given. The RDM method has several advantages including robustness and provision of high accuracy compared to traditional electronic structure methods, although its computational time and memory consumption are still extremely large. The work of Mituhiro Fukuda was primarily conducted at the Courant Institute of Mathematical Sciences, New York University.     

On a New Fluctuation–Dissipation Theorem for Degenerate Stationary Flows

The theory of KM₂O-Langevin equations for stochastic processes (or more generally, flows in inner product spaces) have been developed in view of applications to time series analysis (e.g., Okabe and Nakano, 1991; Okabe, 1999, 2000; Okabe and Matsuura, 2000). In Klimek et al. (2002) and Matsuura and Okabe (2001, 2003), we have investigated degenerate flows, which is important in the analysis of time series obtained from deterministic dynamical systems. As a continuation, we shall in this paper derive an efficient algorithm by which the minimum norm coefficients of KM₂O-Langevin equations are explicitly obtained in degenerate cases. The obtained results have close relations to the calculations of conditional expectations such as nonlinear predictors of stochastic processes (Matsuura and Okabe, 2001). The method has also potential applications to financial mathematics.     

Blends of some non-flexible and flexible polymers: Routes to molecular composites?

The definition of a molecular composite is a blend of a rigid rod polymer and a flexible coil polymer that is miscible at the molecular level. This concept has been tested using systems in which the chain flexibilities differ as widely as possible as judged by the difference in glass transition temperatures (δTg). The biggest variation (δT ∼360°C) was obtained by mixing poly benzimidazole with copolymers of poly(vinyl acetate-ran-vinyl alcohol). It was observed that the blends were distinctly two phase when the hydroxyl content was less than 50 mol %. Above this value clear blends were obtained with finely dispersed phases although it is doubtful if mixing at the molecular level takes place. Miscible blends could be obtained from combinations of the sodium salt of poly(phenylene terephthalamide) with poly(4-vinylpyridine) and mixtures of poly(phenyl imino-1,4-phenyleneoxyterephthalate) with poly(styrene-stat-hydroxylstyrene) where coulombic interactions and hydrogen bonding respectively promoted the miscibility.