Correlation between the Soret coefficient and the static structure factor in a polymer blend

Mutual mass diffusion and thermal diffusion has been investigated in poly(dimethylsiloxane)/ poly(ethylmethylsiloxane) (PDMS/PEMS) polymer blends of equal weight fractions. Molar masses ranged from below 1 to over 20 kg/mol. Both the mutual mass (D) and the thermal diffusion (D_T) coefficient contain a thermally activated factor with an activation temperature of 1415 K. The molar mass dependence of D_T is due to an end-group effect of the local friction coefficient. The thermal diffusion coefficient in the limit of long chains and infinite temperature is D_T^0, = - 1.69×10^-7cm²(sK)^-1. The Soret coefficient S_T of blends far enough away from a critical point is proportional to the static structure factor S(q = 0).     

On optics of human meridians

A new concept and its methodology for studying human meridians are presented based on rigorous and scientific observation on the objective existence of human meridians in view of biomedical optics. According to this methodology, the infrared radiant characteristics of acupuncture meridians over human body and the optical transport properties of light propagating along the meridian are reported. This study, thus, confirms the existence of acupuncture meridians, sheds new light on an approach to investigation of human meridians and offers a new perspective in understanding the potential meridian functions such as energy and information transfer and physiological regulation. Supported by the National Key Basic Research Program of China (Grant No. 2006CB504505), the National Natural Science Foundation of China (Grant Nos. 60578056 and 30572309), the Science Research Foundation of Ministry of Health & United Fujian Provincial Health and Education Project for Tackling the Key Research of China (Grant No. WKJ2005-2-004), the Young Scientists and Technicians Innovation Project of Fujian Province (Grant No. 2007F3026), and the Fund from Fujian Normal University (Grant No. 2008100218)     

Linking-Preserving Perturbations of Symmetric Functionals

We consider paths of functionals starting with one which is invariant under the action of an arbitrary group of symmetries. We give conditions for the existence of an unbounded sequence of critical values of the non-symmetric functional at the end of the path in terms of the growth of the critical values of the symmetric one. We apply this to obtain a multiplicity result for a system of elliptic equations whose symmetries are perturbed by a linear term and a non-homogeneous boundary condition.     

Rotating an interval and a circle

We compare periodic orbits of circle rotations with their counterparts for interval maps. We prove that they are conjugate via a map of modality larger by at most 2 than the modality of the interval map. The proof is based on observation of trips of inhabitants of the Green Islands in the Black Sea.

     

Asymptotic Uniqueness of Best Rational Approximants of Given Degree to Markov Functions in L 2 of the Circle

We improve over a sufficient condition given in [8] for uniqueness of a nondegenerate critical point in best rational approximation of prescribed degree over the conjugate-symmetric Hardy space of the complement of the disk. The improved condition connects to error estimates in AAK approximation, and is necessary and sufficient when the function to be approximated is of Markov type. For Markov functions whose defining measure satisfies the Szego condition, we combine what precedes with sharp asymptotics in multipoint Padé approximation from [43], [40] in order to prove uniqueness of a critical point when the degree of the approximant goes large. This lends perspective to the uniqueness issue for more general classes of functions defined through Cauchy integrals.     

ON THE CONVERGENCE OF KING-WERNER ITERATION METHOD IN BANACH SPACE ON THE CONVERGENCE OF KING-WERNER ITERATION METHOD IN BANACH SPACE

1. IntroductionLetf(x) = 0 (1.1)where j: X - Y is a norilineax operator which maps Banach space X into Baaedspace Y. The well-known iteration methods for solving (1.1) are the Nixon methodaam very ldnds of its improvement methods. One of them is the so called King-Wernerm6thod denned bykw(p, x03 yo):which is established by King in [7], Werner in [12] in d~nt formulas, respectively.It is interesting that the method (1.2) is of order 1 fi with the same functioncompotatinn coSt and twO ti…     

Weakly <Emphasis Type="Italic">φ</Emphasis>-pairs and common fixed points in cone metric spaces

In this paper we introduce a weak contractive condition, called weakly φ-pair, for two mappings in the framework of cone metric spaces and we prove a theorem which ensures existence and uniqueness of common fixed points for such mappings. Also we obtain a result on points of coincidence. These results extend and generalize well-known comparable results in the literature. The authors are supported by Università degli Studi di Palermo, R. S. ex 60%.     

Symmetrized-lexicographic order and the method of points

A variant of lexicographic order called symmetrized-lexicographic order is defined. The symmetrized-lexicographic order finds its application in the goal programming procedure called the method of points. The symmetrized-lexicographic order is shown to be representable using linear algebra and, thus, the method of points can be implemented as a linear programming problem.     

Certain algebraic surfaces with Eisenbud‐Harris general fibration of genus 4

We classify the algebraic surfaces with Eisenbud‐Harris general fibration of genus 4 over a rational curve or an elliptic curve whose slope attains the lower bound. The classification of our surfaces is strongly related to the result of the classification for certain relative quadric hypersurfaces in 3‐dimensional projective space bundles over a rational curve and an elliptic curve. We further prove some results about the canonical maps, the quadric hulls of the canonical images and the deformation for these surfaces.