On a Finite Branch and Bound Algorithm for the Global Minimization of a Concave Power Law Over a Polytope

In this paper, a finite branch-and-bound algorithm is developed for the minimization of a concave power law over a polytope. Linear terms are also included in the objective function. Using the first order necessary conditions of optimality, the optimization problem is transformed into an equivalent problem consisting of a linear objective function, a set of linear constraints, a set of convex constraints, and a set of bilinear complementary constraints. The transformed problem is then solved using a finite branch-and-bound algorithm that solves two convex problems at each of its nodes. The method is illustrated by means of an example from the literature.     

Some Siegel modular standard L-values, and Shafarevich-Tate groups

We explain how the Bloch-Kato conjecture leads us to the following conclusion: a large prime dividing a critical value of the L-function of a classical Hecke eigenform f of level 1, should often also divide certain ratios of critical values for the standard L-function of a related genus two (and in general vector-valued) Hecke eigenform F. The relation between f and F (Harder?s conjecture in the vector-valued case) is a congruence involving Hecke eigenvalues, modulo the large prime. In the scalar-valued case we prove the divisibility, subject to weak conditions. In two instances in the vector-valued case, we confirm the divisibility using elaborate computations involving special differential operators. These computations do not depend for their validity on any unproved conjecture.     

Capillary electrophoresis methods for the determination of covalent polyphenol–protein complexes

The bioactivities and bioavailability of plant polyphenols including proanthocyanidins and other catechin derivatives may be affected by covalent reaction between polyphenol and proteins. Both processing conditions and gastrointestinal conditions may promote formation of covalent complexes for polyphenol-rich foods and beverages such as wine. Little is known about covalent reactions between proteins and tannin, because suitable methods for quantitating covalent complexes have not been developed. We established capillary electrophoresis methods that can be used to distinguish free protein from covalently bound protein–polyphenol complexes and to monitor polyphenol oxidation products. The methods are developed using the model protein bovine serum albumin and the representative polyphenol (−)epigallocatechin gallate. By pairing capillaries with different diameters with appropriate alkaline borate buffers, we are able to optimize resolution of either the protein–polyphenol complexes or the polyphenol oxidation products. This analytical method, coupled with purification of the covalent complexes by diethylaminoethyl cellulose chromatography, should facilitate characterization of covalent complexes in polyphenol-rich foods and beverages such as wine.     

Cellular integration and vascularisation promoted by a resorbable, particulate-leached, cross-linked poly(ε-caprolactone) scaffold

Flexible, strong scaffolds were created by crosslinking PCL with 1,6‐hexamethylenediisocyanate, using paraffin beads as a porogen. Particulate leaching generated homogeneous scaffolds with interconnected spherical pores of 5–200 µm. Subcutaneous implantation in rats for 3 months resulted in minimal scaffold resorption and a non‐inflammatory regenerative host response, with complete infiltration by alternatively‐activated CD68⁺ macrophages. In addition, scaffolds were populated extensively along microfractures by a stromal matrix, which was highly vascularised and contained a subset of stromal cells that expressed the anti‐inflammatory CD163 antigen. Such microfractures may be an important physical feature for directing stromal integration and vascularisation events.

     

Note on similarity solutions for viscous flow over an impermeable and non-linearly (quadratic) stretching sheet

Similarity solutions for flow over an impermeable, non-linearly (quadratic) stretching sheet were studied recently by Raptis and Perdikis (Int. J. Non-linear Mech. 41 (2006) 527-529) using a stream function of the form ψ=αxf(η)+βx²g(η). A fundamental error in their problem formulation is pointed out. On correction, it is shown that similarity solutions do not exist for this choice of ψ.     

Dark forces at the Tevatron

A simple explanation of the W+dijet excess recently reported by the CDF collaboration involves the introduction of a new gauge boson with sizable couplings to quarks, but with no or highly suppressed couplings to leptons. Anomaly-free theories which include such a leptophobic gauge boson must also include additional particle content, which may include a stable and otherwise viable candidate for dark matter. Based on the couplings and mass of the Z^′ required to generate the CDF excess, we predict such a dark matter candidate to possess an elastic scattering cross section with nucleons on the order of σ∼¹⁰−40 cm², providing a natural explanation for the signals reported by the CoGeNT and DAMA/LIBRA collaborations. In this light, CDF may be observing the gauge boson responsible for the force which mediates the interactions between the dark and visible matter of our universe.     

A new formulation of the initial value problem for nonlocal theories

There are a number of reasons to entertain the possibility that locality is violated on microscopic scales, for example through the presence of an infinite series of higher derivatives in the fundamental equations of motion. This type of nonlocality leads to improved UV behavior, novel cosmological dynamics and is a generic prediction of string theory. On the other hand, fundamentally nonlocal models are fraught with complications, including instabilities and complications in setting up the initial value problem. We study the structure of the initial value problem in an interesting class of nonlocal models. We advocate a novel new formulation wherein the Cauchy surface is “smeared out” over the underlying scale of nonlocality, so that the usual notion of initial data at t=0$t=0$ is replaced with an “initial function” defined over −M−1?t?0$-M^{-1}?t?0$ where M is the underlying scale of nonlocality. Focusing on some specific examples from string theory and cosmology, we show that this mathematical re-formulation has surprising implications for the well-known stability problem. For D-brane decay in a linear dilaton background, we are able to show that the unstable directions in phase space cannot be accessed starting from a physically sensible initial function. Previous examples of unstable solutions in this model therefore correspond to unphysical initial conditions, an observation which is obfuscated in the old formulation of the initial value problem. We also discuss implication of this approach for nonlocal cosmological models.     

Redox-switchable chromophores based on metal (Ni, Pd, Pt) mixed-ligand dithiolene complexes showing molecular second-order nonlinear-optical activity

The synthesis and full characterization of the redox-active nickel triad mixed-ligand dithiolene complexes based on Bz(2)pipdt = 1,4-dibenzylpiperazine-3,2-dithione and dmit = 2-thioxo-1,3-dithiole-4,5-dithiolate ligands are reported. These complexes show a reversibly bleacheable solvatochromic peak and a remarkably high negative molecular first hyperpolarizability, whose values depend on the metal being highest for the platinum(II) compound.     

31P NMR studies demonstrating the assembly of catena-phosphorus frameworks from chlorophosphinochlorophosphonium cations

New examples of chlorophosphinochlorophosphonium (4) and chlorophosphinodichlorophosphonium (5) cations have been prepared and spectroscopically characterized. These bifunctional phosphinophosphonium cations offer a new approach to the development of phosphinophosphonium frameworks using reductive coupling reactions and have been exploited as synthons to assemble larger catena-phosphorus cations. The reactions of 4 and 5 with stibine reducing agents have been studied using (31)P NMR spectroscopy and have been shown to produce a variety of new and known frameworks in a facile manner, depending on the reducing agent selection and the stoichiometry of the reaction. New derivatives of frameworks containing three, four, and five phosphorus atoms have been identified by (31)P NMR spectroscopy. Crystals of the [GaCl(4)](-) salt of the five-membered dication 11((i)Pr) have been isolated from the reaction of [4((i)Pr)][GaCl(4)] with SbBu(3), and the solid state structural features and solution state dynamics are comprehensively described in the context of (31)P{(1)H} NMR spectroscopic observations.