Scaling properties of ℤ k- 1 actions on the circle

We derive universal scaling properties for ^k–1 actions on the circle whose generators have rotation numbers algebraic of degreek. As fork=2 these properties can be explained for arbitraryk in terms of a renormalization group transformation. It has at least one trivial fixed point corresponding to an action whose generators are pure rotations. The spectrum of the linearized transformation in this fixed point is analyzed completely. The fixed point is hyperbolic with a (k–1)-dimensional unstable manifold. In the casek=2 the known results are therefore recovered.     

Topological degree of a family of convex functions and localization of nash equilibrium points

We define the degree of a family of convex functionsf _x, wherex , and prove that, if this degree is different from zero, one has at least one Nash equilibrium point in . This is a criterion of localization of such equilibrium points.     

STUDY ON THE PROPERTIES OF BLEND OF NATURAL RUBBER LATEX/METHYL METHACRYLATE GRAFTED RUBBER LATEX BY GAMMA RADIATION

Natural rubber latex(NRL)and methyl methacrylate(MMA)grafted rubber latex were blended in different ratios and irradiated at various absorbed doses by gamma rays from Co-60 source at room temperature.The tensile properties, swelling ratio and permanent set were measured.The maximum tensile strength and modulus at 500% elongation were obtained at an absorbed dose of 8 kGy.Modulus increases from 6.99 MPa to 9.87 MPa for an increase in proportion of MMA grafted rubber from 40% to 60% in the blend at similar absorbed dose.Elongation at break and swelling ratio decrease with increasing absorbed dose as well as the MMA grafted rubber content in the blends.The decreasing trend of permanent set is high up to 5 kGy absorbed dose,and beyond that dose,it becomes almost flat.     

Bioactive steroidal glycosides from the marine sponge Erylus lendenfeldi

Bioassay-guided fractionation of the methanol extract of Erylus lendenfeldi using engineered strains of budding yeast (Saccharomyces cerevisiae) has resulted in the isolation of the known compound eryloside A (1) and two new compounds, erylosides K (2) and L (3). The structures were established based mainly on 1D and 2D NMR data. The absolute stereochemistry of eryloside A, which had never been fully characterized, was determined using the modified Mosher's method. The absolute stereochemistry of eryloside K was determined by comparison with tetrahydroeryloside A. Compounds 1-3 exhibited selective cytotoxicity against a yeast strain (Δrad50) deficient in double strand break (DSB) repair.     

Three‐dimensional wave impact on a rigid structure using smoothed particle hydrodynamics

Navier–Stokes computations of a wave–structure interaction are performed with the aim of assessing the potential of smoothed particle hydrodynamics to accurately estimate impact loading time history. A three‐dimensional dam‐break flow with a rectangular column located downstream is considered. The net force and impulse exerted on the column is monitored throughout the simulation with the results correlating well with existing experimental data. Initial and boundary conditions and numerical parameters are varied and their effect on the column load investigated. The column load is found to be most sensitive to the choice of boundary treatment. Copyright © 2011 John Wiley & Sons, Ltd.     

Extended radial epiderivatives of non-convex vector-valued maps and parametric quasiconvex programming

In this paper, we consider extended vector-valued mappings defined on a normed linear space. Based on the recent semicontinuous regularizations related to hypographical and/or epigraphical profile mappings of the considered function introduced, we define semicontinuous radial epiderivatives. We, then, demonstrate that the properties of these epiderivatives amount to properties of hypographical and/or epigraphical profile mappings of the corresponding difference quotient of the underlying function, which simplify fairly well the proofs in the radial epiderivative formulaes. In particular, we stress the impact of semicontinuity, hence, we characterize with new arguments the radial epiderivatives in terms of the suprema and/or infima of the interiorly radial cone of the hypograph and/or epigraph of the considered function. Finally, we obtain optimality conditions for general non-convex constrained vector optimization problems. We apply thereafter the obtained pattern to a parametric quasiconvex programming problem for which we derive necessary and sufficient optimality conditions that are not sensitive to perturbation at the nominal level, yielding henceforth more – and strong at least under asymptotically regular constraints – information than the recent stability results obtained under additional conditions on the regularity of the normal cone to the adjusted sublevel sets of the underlying function.     

a-convex convergent alternating series

Teaching in a Mathematics Learning Centre requires special skills and knowledge of the theory of teaching and learning. This paper explores those skills and knowledge then considers how they can be applied to help students attain their full academic potential.     

On Convergence of Quasi ρ-preserving Locally Related Quasi-nonexpansive Mappings

The concept of quasi-nonexpansive mappings was initiated in Diaz and Metcalf (Bull. Amer. Math. Soc. 73 (1967), 516–519), further it was generalized by Petryshyn and Williamson (Journal of Mathematical Analysis and Applications 43, no. 2 (1973): 459-497). Further investigating the above work, in this article a Banach space with a relation ρ has been considered, the notion of ρ-preserving and quasi ρ-preserving locally related quasi-nonexpansive mappings has been introduced. It has been shown that every ρ-preserving mapping is a quasi ρ-preserving and every nonexpansive mapping is locally related quasi-nonexpansive but converse may not hold. The necessary and sufficient conditions for the convergence of Picard, Mann and Ishikawa iterations of ρ-preserving, quasi ρ-preserving locally related quasi-nonexpansive mappings are presented.     

On some Fermat rules for set-valued optimization problems

The aim of this article is to obtain necessary optimality conditions for Pareto minima in set-valued optimization problems. We employ a new method to derive generalized Fermat rules for set-valued optimization. This method is based on openness results for multifunctions and allows recovery of a large number of results and, at the same time, getting several new ones.