Padé-type approximants with orthogonal generating polynomials

The interpolation of the function x → 1/(1 ? xt) generating the series f(t) = ∑^∞_{i = 0}c_itⁱ at the zeros of an orthogonal polynomial with respect to a distribution d α satisfying some conditions will give us a process for accelerating the convergence of f_n(t) = ∑ⁿ_{i = 0}c_itⁱ. Then, we shall see that the polynomial of best approximation of x → 1/(1 ? xt) over some interval or its development in Chebyshev polynomials T_n or U_n are only particular cases of the main theorem.At last, we shall show that all these processes accelerate linear combinations with positive coefficients of totally monotonic and oscillating sequences.     

Generalized Padé-Type Approximation and Integral Representations

In several complex variables, the multivariate Padé-type approximation theory is based on the polynomial interpolation of the multidimensional Cauchy kernel and leads to complicated computations. In this paper, we replace the multidimensional Cauchy kernel by the Bergman kernel function K (z,x) into an open bounded subset of C ⁿ and, by using interpolating generalized polynomials for K (z,x), we define generalized Padé-type approximants to any f in the space OL ²() of all analytic functions on which are of class L ². The characteristic property of such an approximant is that its Fourier series representation with respect to an orthonormal basis for OL ²() matches the Fourier series expansion of f as far as possible. After studying the error formula and the convergence problem, we show that the generalized Padé-type approximants have integral representations which give rise to the consideration of an integral operator – the so-called generalized Padé-type operator – which maps every f OL ²() to a generalized Padé-type approximant to f. By the continuity of this operator, we obtain some convergence results about series of analytic functions of class L ². Our study concludes with the extension of these ideas into every functional Hilbert space H and also with the definition and properties of the generalized Padé-type approximants to a linear operator of H into itself. As an application we prove a Painlevé-type theorem in C ⁿ and we give two examples making use of generalized Padé-type approximants.     

ON MULTILINEAR COMMUTATORS OF Θ-TYPE CALDERóN-ZYGMUND OPERATORS

In this paper, we discuss the multilinear commutator of θ-type Calderón- Zygmund operators, and obtain that this kind of multilinear commutators is bounded from Lp(Rn) to Lq(Rn), from Lp(Rn) to Triebel-Lizorkin spaces and on certain Hardy type spaces.     

A two-dimensional matrix Padé-type approximation in the inner product space

By introducing a bivariate matrix-valued linear functional on the scalar polynomial space, a general two-dimensional (2-D) matrix Padé-type approximant (BMPTA) in the inner product space is defined in this paper. The coefficients of its denominator polynomials are determined by taking the direct inner product of matrices. The remainder formula is developed and an algorithm for the numerator polynomials is presented when the generating polynomials are given in advance. By means of the Hankel-like coefficient matrix, a determinantal expression of BMPTA is presented. Moreover, to avoid the computation of the determinants, two efficient recursive algorithms are proposed. At the end the method of BMPTA is applied to partial realization problems of 2-D linear systems.     

Quantum steganography with large payload based on entanglement swapping of χ-type entangled states

In this paper, we firstly propose a new simple method to calculate entanglement swapping of χ-type entangled states, and then present a novel quantum steganography protocol with large payload. The new protocol adopts entanglement swapping to build up the hidden channel within quantum secure direct communication with χ-type entangled states for securely transmitting secret messages. Comparing with the previous quantum steganographies, the capacity of the hidden channel is much higher, which is increased to eight bits. Meanwhile, due to the quantum uncertainty theorem and the no-cloning theorem its imperceptibility is proved to be great in the analysis, and its security is also analyzed in detail, which is proved that intercept-resend attack, measurement-resend attack, ancilla attack, man-in-the-middle attack or even Dos(Denial of Service) attack couldn't threaten it. As a result, the protocol can be applied in various fields of quantum communication.     

Impedance spectroscopy and investigation of conduction mechanism in BaMnO3 nanorods

BaMnO₃ nanorods were synthesized at 200 °C and atmospheric pressure using the composite-hydroxide mediated method. X-ray diffraction, scanning electron microscopy and energy dispersive X-ray spectroscopy were used to investigate the structure, size, morphology, phase purity and elemental composition of BaMnO₃ nanorods. Electrical characterization of BaMnO₃ pellet was performed at 300-400 K and in the frequency range 200 Hz-2 MHz. Temperature dependence of AC conductivity suggests that the BaMnO₃ pellet behaves as a semiconducting material and conduction across the pellet can be explained by the correlated barrier hopping model. Impedance analysis was performed using the equivalent circuit model (R₁Q₁C₁)(R₂C₂) and it suggests a single relaxation process in the BaMnO₃ pellet at a particular temperature. The analysis reveals that the BaMnO₃ pellet behaves like an n-type semiconductor material due to the presence of oxygen vacancies and some disorder. Modulus spectroscopy also supports the impedance results.     

Syntheses,structures, and luminescence of three anion-dependent cadmium coordination polymers

Self-assembly of the flexible ligand 1,3,5-tri(1,2,4-triazol-1-ylmethyl)-2,4,6-trimethylbenzene (ttmb) with Cd(II) salts gave three coordination polymers {[Cd(ttmb)₂](SO₄)(H₂O)₁₆} _n (1), {[Cd(ttmb)₂(H₂O)₂](NO₃)₂(H₂O)₆} _n (2), and {[Cd(ttmb)₂(H₂O)₂](ClO₄)₂(H₂O)₇} _n (3). Complex 1 has a (3,6)-connected CdCl₂-type 2-D network. However, 2 and 3 show the 2-D (4,4) network and 1-D double chain, respectively. Complexes 1, 2, and 3 exhibit luminescent emission maxima at 306, 339, and 298?nm, respectively, in the solid state at room temperature.     

La-Sr-Ni-O系复合氧化物的合成及La_(2-x)Sr_xNiO_4体系催化性能研究

用硝酸盐分解法(N-法)和柠檬酸络合法(L-法)合成了La-Sr-Ni-O系复合氧化物.用XRD技术考察了样品组成、制备条件及灼烧气氛等对产物结构的影响.结果表明:按La_(1-x)Sr_xNiO_3计量比,用N-法合成只能形成四方体心K_2NiF_4结构的A_2BO_4型复合氧化物.而采用L-法,通过改变条件,在0.0≤x≤0.2范围内可形成菱形晶系钙钛矿结构的复合氧化物.另外,用L-法合成La_(2-x)Sr_xNiO_4系列样时发现,制备条件及灼烧温度、气氛对样品结晶态存在较大的影响,高温、空气氛下可形成高结晶态的K_2NiF_4结构复合氧化物.La_(2-x)Sr_xNiO_4体系CO催化氧化活性研究表明,随x(Sr~(2+)取代量)增加,CO的转化率增加.     

一类不可分解Banach空间上线性算子的谱性质

给出一类不可分解的∑_e~1型Banach空间上线性算子(不一定有界)的谱结构,并讨论这种空间上生成C_0群或C_0半群的线性算子的有界性、特殊的谱性质和谱结构,还给出这种空间上闭算子是有界算子的一个充分条件。