N[a,b]类中边界Nevanlinna-Pick插值(I)

用所谓的Hankel向量方法求解N[a,b]函数类中带边界插值数据的Nevanlina-Pick插值(BNP(N[a,b]))问题,并建立BNP(N[a,b])问题与[a,b]上的某种带约束条件的Hausdorff矩量问题之间等价的可解条件以及解之间明确的一一对应关系.这使得当BNP(N[a,b])问题有多解时,能通过带约束条件的矩量问题的可解性准则和解获得BNP(N[a,b])问题的可解性准则和解的参数化描述,而在唯一解的情况下,通过BNP(N[a,b])问题解的存在唯一性准则和唯一解来获得带约束条件的     

On the Similarity between Volterra Operators and Transformation Operators for Integro-Differential Operators of Fractional Order

We establish the similarity between certain Volterra integral operators and the Riemann--Liouville fractional integration operator as well as the existence of a triangular transformation operator for integro-differential equations of fractional order. The results obtained are consistent with similar results for the case of integer order.     

THE SCHWARZIAN DERIVATIVE IN SEVERAL COMPLEX VARIABLES(II)

ＴＨＥＳＣＨＷＡＲＺＩＡＮＤＥＲＩＶＡＴＩＶＥＩＮＳＥＶＥＲＡＬＣＯＭＰＬＥＸＶＡＲＩＡＢＬＥＳ（ＩＩ）ＧＯＮＧＳＨＥＮＧＹＵＱＩＨＵＡＮＧＺＨＥＮＧＸＵＥＡＮＭａｎｕｓｃｒｉｐｔｒｅｃｅｉｖｅｄＡｕｇｕｓｔ３０，１９９６．Ｄｅ...     

Solving Nonlinear Programming Problems with Noisy Function Values and Noisy Gradients

An efficient algorithm for solving nonlinear programs with noisy equality constraints is introduced and analyzed. The unknown exact constraints are replaced by surrogates based on the bundle idea, a well-known strategy from nonsmooth optimization. This concept allows us to perform a fast computation of the surrogates by solving simple quadratic optimization problems, control the memory needed by the algorithm, and prove the differentiability properties of the surrogate functions. The latter aspect allows us to invoke a sequential quadratic programming method. The overall algorithm is of the quasi-Newton type. Besides convergence theorems, qualification results are given and numerical test runs are discussed.     

CONE-DIRECTED CONTINGENT DERIVATIVES AND GENERALIZED PREINVEX SET-VALUED OPTIMIZATION

By using cone-directed contingent derivatives, the unified necessary and suffi-cient optimality conditions are given for weakly and strongly minimal elements respectively in generalized preinvex set valued optimization.     

Dimensional Properties of Fractional Brownian Motion

Let B^α = {B^α（t）,t E R^N} be an （N,d）-fractional Brownian motion with Hurst index α∈ （0, 1）. By applying the strong local nondeterminism of B^α, we prove certain forms of uniform Hausdorff dimension results for the images of B^α when N 〉 αd. Our results extend those of Kaufman for one-dimensional Brownian motion.     

Synthesis, Crystal Structure and Electrochemical Properties of a Novel Phenothiazine Derivative

A new compound 1,1‘-bis(3-pyridyl)-propylene(3,7-diformyl-N-ethylphenothiazinyl)ketone (C30H23N3O2S, Mr = 489.4) has been synthesized, and its crystal structure was determined by single-crystal X-ray diffraction method. The crystal is of orthorhombic, space group Ima2 with a = 27.491 (5), b = 11.942(2), c = 7.389(2) A, V = 2425.8(7) A^3, Z = 8, Dc =1.340 g/cm^3,μ = 0,167 mm ^1, F(000) = 1024, the final R = 0.0363 and wR = 0.0869 for 2054 unique reflections with Rint = 0.0254. The structural determination shows that the molecule assumes a butterfly configuration with nearly planar wings. In addition, the electrochemical study indicates that there is a high electronic delocalization in the molecule.     

Ratio of Protein Fractions in Cereal Grains Cultivated in Uzbekistan

The glutelin fraction was used as the food value index of local corn. The base-soluble fraction was used as a test of the glassiness of local strains of rice grain. The content of gliadins and glutelins did not change over 24 h after wheat grain cultivated in Uzbekistan was moistened.     

Geometric Algebra in Linear Algebra and Geometry

This article explores the use of geometric algebra in linear and multilinear algebra, and in affine, projective and conformal geometries. Our principal objective is to show how the rich algebraic tools of geometric algebra are fully compatible with and augment the more traditional tools of matrix algebra. The novel concept of an h-twistor makes possible a simple new proof of the striking relationship between conformal transformations in a pseudo-Euclidean space to isometries in a pseudo-Euclidean space of two higher dimensions. The utility of the h-twistor concept, which is a generalization of the idea of a Penrose twistor to a pseudo-Euclidean space of arbitrary signature, is amply demonstrated in a new treatment of the Schwarzian derivative.     

Fractional extensions of some boundary value problems in oil strata

In the present paper, we solve three boundary value problems related to the temperature field in oil strata — the fractional extensions of the incomplete lumped formulation and lumped formulation in the linear case and the fractional generalization of the incomplete lumped formulation in the radial case. By using the Caputo differintegral operator and the Laplace transform, the solutions are obtained in integral forms where the integrand is expressed in terms of the convolution of some auxiliary functions of Wright function type. A generalization of the Laplace transform convolution theorem, known as Efros’ theorem is widely used.