Equations of convolution type with monotone coefficients

This paper studies convolution type linear difference equations with coefficients satisfying some monotonicity properties. Methods from renewal theory are employed to obtain easily verified conditions for asymptotic stability of the zero solution, in terms of the coefficient sequence. Explicit bounds and rates of convergence are also considered, and an application to norms of matrix inverses is included.     

Involutions of \operatorname{{SL}} (nk), (n>2)

A first characterization of the isomorphism classes of -involutions for any reductive algebraic group defined over a perfect field was given in [7] using three invariants. In this paper we give a simple characterization of the isomorphism classes of involutions of with any field of characteristic not equal to . We classify the isomorphism classes of involutions for algebraically closed, the real numbers, the -adic numbers and finite fields. We also determine in which cases the corresponding fixed point group is -anisotropic. In those cases the corresponding symmetric -variety consists of semisimple elements.Aloysius G. Helminck was partially supported by N.S.F. Grant DMS-9977392.     

Prism-pattern design of an LCD light guide plate using a neural-network optical model

This paper proposes a neural-network optical model for a backlight module of a liquid crystal display (LCD) to expedite the design of the light-scattering prism-pattern of its light guide plate (LGP). First, the prism surface of a light guide plate is divided into several equal regions. Then the neural-network optical model is implemented using a back-propagation neural network to establish the relationship between the distribution density of the prism pattern and the exiting-light luminance of the LGP at each region. The input–output patterns for the neural network training and verification are generated using orthogonal arrays and ASAP simulation. Then a for-loop computational algorithm is executed to search an approximately optimal distribution density of the prism pattern using the neural-network optical model such that high luminance uniformity is achieved. It is demonstrated by the case study of a 13 in. LCD backlight module that luminance uniformity could reach 93.1%. Thus it can be concluded that the developed neural-network optical model effectively expedites the LGP prism-pattern design.     

Minimization of Linear Functionals Defined on Solutions of Large-Scale Discrete Ill-Posed Problems

The minimization of linear functionals defined on the solutions of discrete ill-posed problems arises, e.g., in the computation of confidence intervals for these solutions. In 1990, Eldén proposed an algorithm for this minimization problem based on a parametric programming reformulation involving the solution of a sequence of trust-region problems, and using matrix factorizations. In this paper, we describe MLFIP, a large-scale version of this algorithm where a limited-memory trust-region solver is used on the subproblems. We illustrate the use of our algorithm in connection with an inverse heat conduction problem. AMS subject classification (2000) 65F22     

Sign-changing critical points via Sandwich Pair theorems

The Sandwich Pair theorems have presented very efficient ways to determine the existence of critical points or critical sequences for nonlinear differentiable functionals. In this paper, under rather weak hypotheses new relationships are established between sign-changing critical points and Sandwich Pairs or Linking Sandwich Pairs. The abstract results are demonstrated by applications on semi-linear elliptic equations.     

Linear Response Function for Coupled Hyperbolic Attractors

The SRB measures of a hyperbolic system are widely accepted as the measures that are physically relevant. It has been shown by Ruelle that they depend smoothly on the system. Furthermore, Ruelle showed by a separate argument that the first derivative, i.e., the linear response function, admits a geometric interpretation. In this paper, we consider thermodynamic limits of SRB measures in lattices of coupled hyperbolic attractors. In a previous paper, using Markov partitions and thermodynamic formalism, we had established the smooth dependence of thermodynamic limits of SRB measures. Here, we establish that the linear response function admits a geometric interpretation. The formula is analogous to the one found by Ruelle for finite dimensional systems if one term is reinterpreted appropriately. We show that the limiting derivative is the thermodynamic limit of the derivatives in finite volume. We also obtain similar results for the derivatives of the entropy. Supported in part by NSF grants.     

Brønsted acid promoted imino-ene reactions

A series of all-carbon olefins react with glyoxylate derived imines in the presence of a phosphonic acid through an ene reaction. The isolation of the α-aminoester products is a clear indication that Brønsted acids efficiently promote the imino-ene reaction with hydrocarbon nucleophiles to deliver functionalized α-aminoesters in good yield. The reaction scope and preliminary mechanistic investigations are discussed.     

Optimal product design using a colony of virtual ants

The optimal product design problem, where the “best” mix of product features are formulated into an ideal offering, is formulated using ant colony optimization (ACO). Here, algorithms based on the behavior of social insects are applied to a consumer decision model designed to guide new product decisions and to allow planning and evaluation of product offering scenarios.