Integral-type operators from iterated logarithmic Bloch spaces to Zygmund-type spaces

Let denote the space of all holomorphic functions on the unit ball of and the radial derivative of h. In this paper we study the boundedness and compactness of the following integral operator:, from iterated logarithmic Bloch spaces to Zygmund-type spaces.     

强收敛于Banach空间中非扩张映象的切萨罗平均

设f是一个压缩常数为h的压缩映象,T是一个非扩张映象使得F(T)≠Φ。{xn}是由下式xn+1=αnf(xn)+(1-αn)1/n+1 sum Tjxn from j=0 to n,n∈N,定义的迭代序列,其中{αn}(0,1)且满足lim αn=0 n→∞和sum αn=∞ from n=1 to ∞。证明{xn}强收敛于F(T)中某个变分不等式的唯一     

单位球上μ-Bloch空间之间的广义Cesàro算子

Let μ,ν ∈ [0,1) be normal functions and g be holomorphic function on the unit ball.In thispaper,we prove that the generalized Cesaro operator Tg:βμ→βν is bounded and compact.     

On the partial sums,Cesáro and de la Valleé Poussin means of convex and starlike functions of order 1/2

In this paper we study certain properties of partial sums, cesáro and de la valleé Poussin means of convex and starlike functions.     

Cesàro function spaces fail the fixed point property

The Cesàro sequence spaces , are reflexive but they have the fixed point property. In this paper we prove that in contrast to these sequence spaces the corresponding Cesàro function spaces on both and for are not reflexive and they fail to have the fixed point property.

     

Mean Convergence Theorems for Weighted Sums of Arrays of Residually <Emphasis Type="Italic">h</Emphasis>-integrable Random Variables Concerning the Weights under Dependence Assumptions

From the classical notion of uniform integrability of a sequence of random variables, a new concept called residual h-integrability is introduced for an array of random variables, concerning an array of constants, which is weaker than other previous related notions of integrability. Martingale difference, pairwise negative quadrant dependence, tail φ-mixing property and L _p -mixingale are four special kinds of dependence structures, where 1≤p≤2. By relating the residual h-integrability with such these dependence assumptions, some conditions are formulated under which mean convergence theorems for weighted sums of arrays of random variables are established, and many earlier results are explained as the special cases of the ones appearing in our present work.      

SOME NEW TYPE OF DIFFERENCE SEQUENCE SPACES DEFINED BY MODULUS FUNCTION AND STATISTICAL CONVERGENCE

In this article we introduce the difference sequence spaces W 0 [f,Δm ],W 1 [f,Δm ],W∞[f,Δm ] and S[f,Δm ],defined by a modulus function f.We obtain a relation between W 1 [f,Δm ] ∩l∞[f,Δm ] and S[f,Δm ] ∩l∞[f,Δm ] and prove some inclusion results.     

Ergodic properties of operators in some semi-Hilbertian spaces

This article deals with linear operators T on a complex Hilbert space ?, which are bounded with respect to the seminorm induced by a positive operator A on ?. The A-adjoint and A ^1/2-adjoint of T are considered to obtain some ergodic conditions for T with respect to A. These operators are also employed to investigate the class of orthogonally mean ergodic operators as well as that of A-power bounded operators. Some classes of orthogonally mean ergodic or A-ergodic operators, which come from the theory of generalized Toeplitz operators are considered. In particular, we give an example of an A-ergodic operator (with an injective A) which is not Cesàro ergodic, such that T ^?* is not a quasiaffine transform of an orthogonally mean ergodic operator.     

Best molecular multiple quantum bit for the diatomic molecular quantum computer using potassium nitride and calcium nitride through vibrational progression

In this article, based on the former accurate and precise ab initio calculation results for potassium nitride (KN) and calcium nitride (CaN), I revisit the possibilities and potentials of KN and CaN as the best candidate for molecular multiple quantum bit (MMQB) for the diatomic molecular quantum computer (DMQC), and would like to propose the two molecules as CPUs of the DMQC. Lowest lying four electronic states of CaN are energetically located within 1800 cm^?1. These four states form the good molecular electronic two quantum bits through the dipole and weak spin–orbit interactions. ³Π state of KN is calculated to lie above ground ³Σ^? state by 177 cm^?1. KN is a promising candidate for an electronic one quantum bit. When vibrational progression is considered to be accompanied by the electronic transition, CaN and KN are good candidates for larger MMQBs up to a thousand even in the single molecule because the concrete quantum state bearing the quantum bit is each molecular ro‐vibronic state, that is, the specific rotational state on each vibronic level. When CaN and KN work in assemblies as quantum bit, those assemblies become larger MMQBs, the number of which might reach the Avogadro number because the molecular spectra appearing in the molecular spectroscopy are the results from the observation by the photon‐exchange among intramolecular quantum states made up of 10¹⁵ to the Avogadro (6.02 × 10²³ mol^?1) number of molecules interacting with radiation. Even without the vibrational progression, in the case of the lowest two quantum bit of KN, which is a stable vibronic two quantum bit, a thousand of KN molecules provide a thousand of MMQBs. That is the same situation as that for CaN. Using KN and CaN as MMQBs (playing the triple roles of CPU, RAMs (memory), and storages) ultra‐fast “in core” quantum computation can be done. An application of the full‐CI quantum chemistry calculation results for the demonstration of the DMQC is discussed. I strongly hope that the MMQB will “oscillate” and that the DMQC will be realized in the near future for the welfare of human being and the further development of modern material civilization. © 2014 Wiley Periodicals, Inc.