There are several important questions on the coupling between properties of the protein shape and the rate of protein folding. We have studied a series of structural descriptors intended for describing protein shapes (the radius of gyration, the radius of cross-section, and the coefficient of compactness) and their possible connection with folding behavior, either rates of folding or the emerge...

under favorable soil conditions such as existence of easily destructible organic compounds, balanced heat and moisture, adequate ventilation and abundant nutrients, organic materials are mineralized. once mineralizing occurs, mineral elements like p, s, ca, mg, k and other cations are released. a related study was conducted to determine the effect of seven organic fertilizers (leaf mold (lm), r...

This paper addresses a multi-scale finite element method for second order linear elliptic equations with arbitrarily rough coefficient. We propose a local oversampling method to construct basis functions that have optimal local approximation property. Our methodology is based on the compactness of the solution operator restricted on local regions of the spatial domain, and does not depend on an...

We introduce and investigate classes of (p,q)-starlike harmonic univalent functions defined by subordination. first obtained a coefficient characterization these functions. give necessary sufficient convolution conditions, distortion bounds, compactness extreme points for the with negative coefficients.

A new and simpler proof is given of the result of P. Rabinowitz for nontrivial time periodic solutions of a vibrating string equation utt-ux, + g(u) = 0 and Dirichlet boundary conditions on a finite interval. We assume essentially that g is nondecreasing, and g(u)/u+m as Iu(+w. The proof uses a modified form (PS), of the Palais-Smale condition (PS). Let g : R-+R be a continuous nondecreasing fu...

Let f be a positive smooth function on a close Riemann surface (M,g). The f − energy of a map u from M to a Riemannian manifold (N, h) is defined as E f (u) = M f |∇u| 2 dV g. In this paper, we will study the blow-up properties of Palais-Smale sequences for E f. We will show that, if a Palais-Smale sequence is not compact, then it must blows up at some critical points of f. As a sequence, if an...

In this paper, the concept of countably near PS-compactness inL-topological spaces is introduced, where L is a completely distributive latticewith an order-reversing involution. Countably near PS-compactness is definedfor arbitrary L-subsets and some of its fundamental properties are studied.