On hermitian polynomial optimization

We compare three levels of algebraic certificates for evaluating the maximum modulus of a complex analytic polynomial, on a compact semi-algebraic set. They are obtained as translations of some recently discovered inequalities in operator theory. Although they can be stated in purely algebraic terms, the only known proofs for these decompositions have a transcendental character. Received: 27 June 2005     

Conjugate points and Maslov index in locally symmetric semi-Riemannian manifolds

We study the singularities of the exponential map in semi Riemannian locally symmetric manifolds. Conjugate points along geodesics depend only on real negative eigenvalues of the curvature tensor, and their contribution to the Maslov index of the geodesic is computed explicitly. We prove that degeneracy of conjugate points, which is a phenomenon that can only occur in semi-Riemannian geometry, is caused in the locally symmetric case by the lack of diagonalizability of the curvature tensor. The case of Lie groups endowed with a bi-invariant metric is studied in some detail, and conditions are given for the lack of local injectivity of the exponential map around its singularities.     

Gating processes in Na-channel of biological membrane from the standpoint of superionic phase transition

The method of condensed matter physics is applied to reason out the problem of Na transport through a biological membrane. A similiarity of gating process in Na ion channel to the superionic phase transition is discussed. A possible microscopic mechanism is suggested.     

Dimensional reduction for Helmholtz's equation on a bounded domain

Summary. The dimensional reduction method for solving boundary value problems of Helmholtz's equation in domain by replacing them with systems of equations in dimensional space are investigated. It is proved that the existence and uniqueness for the exact solution and the dimensionally reduced solution of the boundary value problem if the input data on the faces are in some class of functions. In addition, the difference between and in is estimated as and are fixed. Finally, some numerical experiments in a domain are given in order to compare theretical results. Received April 2, 1996 / Revised version received July 30, 1990     

A shape-optimization technique for the capillary surface problem

Summary The problem of the construction of an equilibrium surface taking the surface tension into account leads to Laplace-Young equation which is a nonlinear elliptic free-boundary problem. In contrast to Orr et al. where an iterative technique is used for direct solution of the equation for problems with simple geometry, we propose here an alternative approach based on shape optimization techniques. The shape of the domain of the liquid is varied to attain the optimality condition. Using optimal control theory to derive expressions for the gradient, a numerical scheme is proposed and simple model problems are solved to validate the scheme.     

Symmetric bi-derivations on prime and semi-prime rings

Summary LetR be a ring. A bi-additive symmetric mappingD(.,.): R × R R is called a symmetric bi-derivation if, for any fixedy R, a mappingx D(x, y) is a derivation. The purpose of this paper is to prove some results concerning symmetric bi-derivations on prime and semi-prime rings. We prove that the existence of a nonzero symmetric bi-derivationD(.,.): R × R R, whereR is a prime ring of characteristic not two, with the propertyD(x, x)x = xD(x, x), x R, forcesR to be commutative. A theorem in the spirit of a classical result first proved by E. Posner, which states that, ifR is a prime ring of characteristic not two andD ₁,D ₂ are nonzero derivations onR, then the mappingx D ₁(D ₂ (x)) cannot be a derivation, is also presented.     

A method for computing the tension parameters in convexity-preserving spline-in-tension interpolation

Summary This paper is concerned with the problem of convexity-preservng (orc-preserving) interpolation by using Exponential Splines in Tension (or EST's). For this purpose the notion of ac-preserving interpolant, which is usually employed in spline-in-tension interpolation, is refined and the existence ofc-preserving EST's is established for the so-calledc-admissible data sets. The problem of constructing ac-preserving and visually pleasing EST is then treated by combining a generalized Newton-Raphson method, due to Ben-Israel, with a step-length technique which serves the need for visual pleasantness. The numerical performance of the so formed iterative scheme is discussed for several examples.     

同多酸和杂多酸修饰微电极的电化学研究——Ⅳ.1:2-磷钼杂多酸薄膜修饰碳纤维微电极的制备和电化性质

本文报道了1:12-磷铜杂多酸(PMo_(12)薄膜修饰碳纤维(CF)微电极的制备及其电化学性质。采用简单,快速的浸渍吸附制备的PMo_(12)薄膜修饰CF电极在酸性介质中具有很高的稳定性和氧化还原活性,电解质溶液的pH值和扫描电位范围对PMo_(12)膜的稳定性和电化学性质产生较大的影响。另一方面,PMo_(12)薄膜修饰CF微电极对酸性水溶液中的PMo_(12)和氯酸根离子(ClO)_3~-)的电催化还原作用也进行了描述。     

The study of the partitioning mechanism of methyl orange in an aqueous two-phase system

An aqueous two-phase system of dodecyl triethylammonium bromide (C₁₂NE, cationic surfactant) and sodium dodecyl sulfate (SDS, anionic surfactant) mixture is proposed for the extraction of some dyes and porphyrin compounds. Transparent two phase-systems are formed when the surfactant concentrations and C₁₂NE/SDS ratios are in certain regions. In this study, the aqueous two phase-systems were prepared by mixing 0.1 mol l⁻¹ C₁₂NE and SDS with a molar ratio of 1.7:1.0. The results showed that negatively charged chlorophyll (sodium copper chlorophyllin) and positively charged dye (methyl violet) were efficiently extracted into the upper phase. The negatively charged methyl orange (pH>7) was moved into the upper phase mostly while amphoteric methyl orange (pH<3) was distributed in the two phases uniformly. Except for hydrophobic force, charge interaction between solute and surfactant also play an important role in the extraction process.