Approximation Properties of a Class of Extremal Polynomials over Smooth Jordan Curves

There have been many elegant results discussing the approximation proper- ties of the Bieberbach polynomials. However, very few papers investigated the approxi- mation properties of the extremal polynomials over Jordan curves. In the present paper, some results on a class of extremal polynomials over C1+αsmooth Jordan curves are obtained.

The Approximation Properties Determined by Operator Ideals

We introduce the notion of the right approximation property with respect to an operator ideal A and solve the duality problem for the approximation property with respect to an operator ideal ,4, that is, a Banach space X has the approximation property with respect to Ad whenever X＊ has the right approximation property with respect to an operator ideal A. The notions of the left bounded approximation property and the left weak bounded approximation property for a Banach operator ideal are introduced and new symmetric results are obtained. Finally, the notions of the p-compact sets and the p-approximation property are extended to arbitrary Banach operator ideals. Known results of the approximation property with respect to an operator ideal and the p-approximation property are generalized.

Electronic and Optical Properties of TiS2 Determined from Generalized Gradient Approximation Study

The electronic and optical properties of TiS2 are studied of density functional theory. A linearized and augmented by using an ab-initio calculation within the frame plane wave basis set with the generalized gradient approximation as proposed by Perdew et al. is used for the energy exchange-correlation determination. The results show a metallic character of TiS2, and the plots of total and partial densities of states of TiS2 show the metallic character of the bonds and a strong hybridization between the states d of Ti and p of S below the Fermi energy. The optical properties of the material such as real and imaginary parts of dielectric constant （ε（w） = ε1（w） ＋ iε2（w））, refractive index n（w）, optical reflectivity R（w）, for E / /x and E / /z are performed for the energy range of 0-.14 eV.

First-principles calculations of structural and thermodynamic properties of β-PbO

We employed ab-initio calculations to investigate the structural and thermodynamic properties of Massicot or orthorhombic phase of PbO named β-PbO using the projector augmented-wave（PAW） method within the generalized gradient approximation（GGA）. The temperature and pressure dependence of bulk modulus, heat capacity at constant pressure and constant volume, entropy, thermal expansion coefficient and Grüneisen parameter were discussed. Accuracy of two different models, the Debye and Debye-Grüneisen which are based on the quasi-harmonic approximation（QHA） for producing thermodynamic properties of material were compared. According to calculation results, these two models can be used to designate thermodynamic properties for β-PbO with sensible accuracy over a wide range of temperatures and pressures, and our work on the properties of this structure will be useful for more deeply understanding various properties of this structure.

Weighted Approximation of Kantorovich-Type Operator of Butzer-Hahn

A kind of Kantorovich-type operator of Butzer-Hahn B*_n(f; x) on the bounded and integrable function space was introduced, and the properties of B*_n(f; x) were studied. Positive theorem, converse theorem, and the order of weighted ~approximation of B*_n(f; x) were obtained.

On Chlodowsky Variant of Baskakov Type Operators

In the present paper, we deal with Chlodowsky type generalization of the Baskakov operators, special case of these operators includes Chlodowsky type Meyer–K?nig and Zeller operators(see [21]). With the help of Bohman-Korovkin theorem,we obtain some approximation properties for these operators. We give a modification of the operators in the space of differentiable functions and we also present examples of graphs for approximation. Finally, we apply these operators to the solution of the differential equation.

Operators with the Lipschitz bounded approximation property

We show that if a bounded linear operator can be approximated by a net(or sequence)of uniformly bounded finite rank Lipschitz mappings pointwisely,then it can be approximated by a net(or sequence)of uniformly bounded finite rank linear operators under the strong operator topology.As an application,we deduce that a Banach space has an(unconditional)Lipschitz frame if and only if it has an(unconditional)Schauder frame.Another immediate consequence of our result recovers the famous Godefroy-Kalton theorem(Godefroy and Kalton(2003))which says that the Lipschitz bounded approximation property and the bounded approximation property are equivalent for every Banach space.

Estimates of Central Moments for One Kind of Exponential-Type Operators

In this paper,the explicit estimates of central moments for one kind of exponential-type operators are derived.The estimates play an essential role in studying the explicit approximation properties of this family of operators.Using the proposed method,the results of Ditzian and Totik in 1987,Guo and Qi in 2007,and Mahmudov in 2010 can be improved respectively.

SEEMINGLY INJECTIVE VON NEUMANN ALGEBRAS

We show that a QWEP von Neumann algebra has the weak* positive approximation property if and only if it is seemingly injective in the following sense: there is a factorization of the identity of Id_(M)= vu : M→uB(H)→vM with u normal, unital, positive and v completely contractive. As a corollary, if M has a separable predual, M is isomorphic(as a Banach space) to B(l2). For instance this applies(rather surprisingly) to the von Neumann algebra of any free group. Nevertheless, since B(H) fails the approximation property(due to Szankowski) there are M ’s(namely B(H)^(**) and certain finite examples defined using ultraproducts) that are not seemingly injective.Moreover, for M to be seemingly injective it suffices to have the above factorization of I dM through B(H) with u, v positive(and u still normal).

Fixed Point Curve for Weakly Inward Contractions and Approximate Fixed Point Property

In this paper, we discuss the concept of fixed point curve for linear interpolations of weakly inward contractions and establish necessary condition for a nonex- pansive mapping to have approximate fixed point property.

Quantitative Characterizations of Bounded Compact Approximation Property by Semi-Fredholm Operators

Based on a characterization of upper semi-Fredholm operators due to A.Lebow and M.Schechter,we introduce and investigate a new quantity characterizing upper semi-Fredholm operators.This quantity and several well-known quantities are used to characterize bounded compact approximation property.Similarly,a new quantity characterizing lower semi-Fredholm operators is introduced,investigated and used to characterize the bounded compact approximation property for dual spaces.

Homogeneous Approximation Property for Wavelet Frames with Matrix Dilations,Ⅱ

The homogeneous approximation property （HAP） states that the number of building blocks involved in a reconstruction of a function up to some error is essentially invariant under time-scale shifts. In this paper, we show that every wavelet frame with nice wavelet function and arbitrary expansive dilation matrix possesses the HAP. Our results improve some known ones.

Three-space Problems for the Bounded Compact Approximation Property

In this paper, the notion of the bounded compact approximation property （BCAP） of a pair [Banach space and its subspace] is used to prove that if X is a closed subspace of Eoo with the BCAP, then L∞/X has the BCAP. We also show that X＊ has the A-BCAP with conjugate operators if and only if the pair （X, Y） has the A-BCAP for each finite codimensional subspace Y C X. Let M be a closed subspace of X such that M~ is complemented in X＊. If X has the （bounded） approximation property of order p, then M has the （bounded） approximation property of order p.

Descriptors for DNA Sequences Based on Joint Diagonalization of Their Feature Matrices from Dinucleotide Physicochemical Properties

Numerical characterizations of DNA sequence can facilitate analysis of similar sequences. To visualize and compare different DNA sequences in less space, a novel descriptors extraction approach was proposed for numerical characterizations and similarity analysis of sequences. Initially, a transformation method was introduced to represent each DNA sequence with dinucleotide physicochemical property matrix. Then, based on the approximate joint diagonalization theory, an eigenvalue vector was extracted from each DNA sequence,which could be considered as descriptor of the DNA sequence. Moreover, similarity analyses were performed by calculating the pair-wise distances among the obtained eigenvalue vectors. The results show that the proposed approach can capture more sequence information, and can jointly analyze the information contained in all involved multiple sequences, rather than separately, whose effectiveness was demonstrated intuitively by constructing a dendrogram for the 15 beta-globin gene sequences.

Unique Ergodicity for Zero-entropy Dynamical Systems with the Approximate Product Property

We show that for every topological dynamical system with the approximate product property, zero topological entropy is equivalent to unique ergodicity. Equivalence of minimality is also proved under a slightly stronger condition. Moreover, we show that unique ergodicity implies the approximate product property if the system has periodic points.

Normal Systems over ANR's, Rigid Embeddings and Nonseparable Absorbing Sets

Most of results of Bestvina and Mogilski [Characterizing certain incomplete infinite-di- mensional absolute retracts. Michigan Math. J., 33, 291-313 （1986）] on strong Z-sets in ANR＇s and absorbing sets is generalized to nonseparable case. It is shown that if an ANR X is locally homotopy dense embeddable in infinite-dimensional Hilbert manifolds and w（U） ---- w（X） （where ＂w＂is the topological weight） for each open nonempty subset U of X, then X itself i,~ homotopy dense embeddable in a Hilbert manifold. It is also demonstrated that whenever X is an AR, its weak product W（X, ＊） ---- {（xn）=l C X ： x~ = ＊ for almost all n} is homeomorphic to a pre-Hilbert space E with E EE. An intrinsic characterization of manifolds modelled on such pre-Hilbert spaces is given.