Orientation dependence in high harmonics of ZnO with polarization corrections to counteract the birefringent effect

We investigate the influence of the birefringence on the high-order harmonics in an a-cut Zn O crystal with midinfrared laser pulses. The high harmonics exhibit strong dependence on the alignment of the crystal with respect to the laser polarization. We introduce the Jones calculus to counteract the birefringent effect and obtain the harmonics with polarization corrections in Zn O. We show that the birefringent effect plays an important role in the orientation dependence of HHG.     

Numerical solution of random differential initial value problems: Multistep methods

This paper deals with the construction of numerical methods of random initial value problems. Random linear multistep methods are presented and sufficient conditions for their mean square convergence are established. Main statistical properties of the approximations processes are computed in several illustrative examples. Copyright © 2010 John Wiley & Sons, Ltd.     

Modeling and character analyzing of multiple fractional-order memcapacitors in parallel connection

Recently,the memory elements-based circuits have been addressed frequently in the nonlinear circuit theory due to their unique behaviors.Thus,the modeling and characterizing of the mem-elements become essential.In this paper,the analysis of the multiple fractional-order voltage-controlled memcapacitors model in parallel connection is studied.Firstly,two fractional-order memcapacitors are connected in parallel,the equivalent model is derived,and the characteristic of the equivalent memcapacitor is analyzed in positive or negative connection.Then a new understanding manner according to different rate factor K and fractional orderαis derived to explain the equivalent modeling structure conveniently.Additionally,the negative order appears,which is a consequence of the combination of memcapacitors in different directions.Meanwhile,the equivalent parallel memcapacitance has been drawn to determine that multiple fractional-order memcapacitors could be calculated as one composite memcapacitor.Thus,an arbitrary fractional-order equivalent memcapacitor could be constructed by multiple fractional-order memcapacitors.     

Theoretical analysis of the velocity field, stress field and vortex sheet of generalized second order fluid with fractional anomalous diffusion

The velocity field of generalized second order fluid with fractional anomalous diiusion caused by a plate moving impulsively in its own plane is investigated and the anomalous diffusion problems of the stress field and vortex sheet caused by this process are studied. Many previous and classical results can be considered as particular cases of this paper, such as the solutions of the fractional diffusion equations obtained by Wyss; the classical Rayleigh’s time-space similarity solution; the relationship between stress field and velocity field obtained by Bagley and co-worker and Podlubny’s results on the fractional motion equation of a plate. In addition, a lot of significant results also are obtained. For example, the necessary condition for causing the vortex sheet is that the time fractional diffusion index β must be greater than that of generalized second order fluid α; the establiihment of the vorticity distribution function depends on the time history of the velocity profile at a given point, and the time history can be described by the fractional calculus.     

Analytic models for commuting operator tuples on bounded symmetric domains

For a domain in and a Hilbert space of analytic functions on which satisfies certain conditions, we characterize the commuting -tuples of operators on a separable Hilbert space  such that is unitarily equivalent to the restriction of to an invariant subspace, where is the operator -tuple on the Hilbert space tensor product  . For the unit disc and the Hardy space , this reduces to a well-known theorem of Sz.-Nagy and Foias; for a reproducing kernel Hilbert space on such that the reciprocal of its reproducing kernel is a polynomial in and  , this is a recent result of Ambrozie, Müller and the second author. In this paper, we extend the latter result by treating spaces for which ceases to be a polynomial, or even has a pole: namely, the standard weighted Bergman spaces (or, rather, their analytic continuation) on a Cartan domain corresponding to the parameter in the continuous Wallach set, and reproducing kernel Hilbert spaces for which is a rational function. Further, we treat also the more general problem when the operator is replaced by ,  being a certain generalization of a unitary operator tuple. For the case of the spaces on Cartan domains, our results are based on an analysis of the homogeneous multiplication operators on , which seems to be of an independent interest.

     

On the inversion of the convolution and Laplace transform

We present a new inversion formula for the classical, finite, and asymptotic Laplace transform of continuous or generalized functions . The inversion is given as a limit of a sequence of finite linear combinations of exponential functions whose construction requires only the values of evaluated on a Müntz set of real numbers. The inversion sequence converges in the strongest possible sense. The limit is uniform if is continuous, it is in if , and converges in an appropriate norm or Fréchet topology for generalized functions . As a corollary we obtain a new constructive inversion procedure for the convolution transform ; i.e., for given and we construct a sequence of continuous functions such that .

     

异硫氰酸荧光素标记抗体的固体基质室温磷光性质研究

研究了异硫氰酸荧光素（FITC）标记的羊抗人抗体（GAHAb-FITC)和兔抗羊抗体9RAGAb-FITC)，及其以三种免疫方式与人免疫球蛋白（IgG)反应所得免疫复合物在多种固体薄膜基质上发射室温磷光（RTP）的适宜条件及其光谱，强度和寿命等性质。研究发现，标记抗体及其免疫复合物保留了FITC优良的固体基质室温磷光性质，λ m0643em^(max)=525/650nm，其RTP强度与其浓度线性相关，并有很高的灵敏度，更为重要的是，免疫反应及其RTP检测能结合于同一基质，方便地相继完成，在聚酰胺膜（PM）上，以Pb(Ac)2为重原子微扰剂，稀释比为1：10（ψ）的GAHAb-FITC,RAGAb-FITC及其与人IgG形成的免疫复合物均能发射较强制 RTP信号并有较长的RTP寿命，本结果为建立相应的固体基质室温磷光免疫分析（SS-RTP-IA）新方法奠定了相应的实验基础。     

Fractional-order optimal fuzzy control for network delay

Fuzzy logic control has been used frequently in tuning network control system (NCS) due to its on-line dynamic static non-linear match and several remarkable fractional-order controllers have achieved satisfactory control performance when applied to NCS in present years, therefore, in this paper, a novel fractional fuzzy logic controller which combined the fractional algorithm and fuzzy logic control together has been proposed to deal with fixed and random network induced delays in closed-loop feedback systems. The comparisons of set-point tracking performances of fractional fuzzy logic PID controller (FFuzzyPID), conventional fuzzy logic PID controller(FuzzyPID), fractional optimal PID controller (FOPID), and optimal PID controller(OPID) on a representative plant with fixed and random network delays have been shown with simulations. The simulation results indicate that fractional fuzzy logic controller has higher capability to handle network delays compared with other controllers in most cases.     

Examples of Twisted Cyclic Cocycles from Covariant Differential Calculi

For two covariant differential *-calculi, the twisted cyclic cocycle associated with the volume form is represented in terms of commutators for some self-adjoint operator and some *-representation of the underlying *-algebra.     

LITTLEWOOD-PALEY THEOREM FOR SCHR DINGER OPERATORS

Let H be a Schrodinger operator on Rn. Under a polynomial decay condition for the kernel of its spectral operator, we show that the Besov spaces and Triebel-Lizorkin spaces associated with H are well defined. We further give a Littlewood-Paley characterization of Lp spaces in terms of dyadic functions of H. This generalizes and strengthens the previous result when the heat kernel of H satisfies certain upper Gaussian bound.