2008 OCT 20 - (VerticalNews.com) -- "In this paper, we describe the H-differentials of some well known NCP functions and their merit functions. We show how, under appropriate conditions on an H-differential of f, minimizing a merit function corresponding to f leads to a solution of the nonlinear complementarity problem," researchers in Kamloops, Canada report.

  "Our results give a unified treatment of such results for C-1-functions, semismooth-functions, and locally Lipschitzian functions. Illustrations are given to show the usefulness of our results," wrote M.A. Tawhid and colleagues, Thompson Rivers University ...read more

  2008 OCT 20 - (VerticalNews.com) -- According to recent research from the United States, "This paper continues a systematic theoretical analysis of electromagnetic scattering by a group of arbitrarily sized, shaped, and oriented particles embedded in an absorbing, homogeneous, isotropic, and unbounded medium."

  "The previously developed microphysical approach is used to derive the generalized form of the radiative transfer equation (RTE) applicable to a large group of sparsely, randomly, and uniformly distributed particles. The derivation of the RTE directly from the macroscopic Maxwell equations yields unambiguous and definitive analytical expressions for the participating quantities and thereby fully resolves the lasting Controversy Caused by the conflicting outcomes of several phenomenological approaches," wrote M.I. Mishchenko and colleagues, National Aeronautics and Space Administration ...read more

  2008 OCT 20 - (VerticalNews.com) -- "We propose two kinds of variational sets of any order for multivalued mappings and show that they are advantageous over many known generalized derivatives in the use for establishing optimality conditions," researchers in Vietnam report.

  "Applying these sets, we prove both necessary and sufficient optimality conditions of any order for efficiency and weak efficiency in a unified way. Many corollaries and examples are provided to show that our results include many recent existing ones," wrote P.Q. Khanh and colleagues ...read more