Quantitative estimations of bivariate summation‐integral–type operators

In this paper, we study the approximation properties of bivariate summation‐integral–type operators with two parameters . The present work deals within the polynomial weight space. The rate of convergence is obtained while the function belonging to the set of all continuous and bounded function defined on ([0],∞)(×[0],∞) and function belonging to the polynomial weight space with two parameters, also convergence properties, are studied. To know the asymptotic behavior of the proposed bivariate operators, we prove the Voronovskaya type theorem and show the graphical representation for the convergence of the bivariate operators, which is illustrated by graphics using Mathematica. Also with the help of Mathematica, we discuss the comparison by means of the convergence of the proposed bivariate summation‐integral–type operators and Szász‐Mirakjan‐Kantorovich operators for function of two variables with two parameters to the function. In the same direction, we compute the absolute numerical error for the bivariate operators by using Mathematica and is illustrated by tables and also the comparison takes place of the proposed bivariate operators with the bivariate Szász‐Mirakjan operators in the sense of absolute error, which is represented by table. At last, we study the simultaneous approximation for the first‐order partial derivative of the function.     

一类非局部Cahn-Hilliard方程弱解的存在唯一性

研究一类对流非局部Cahn-Hilliard方程的Neumann问题.通过一致Schauder估计和Leray-Schauder不动点定理,得到了该问题经典解的存在唯一性.进而,利用弱收敛方法得到了该问题弱解的存在唯一性.     

基于跟踪度的Gabor小波特征跟踪方法的研究

图像的边缘包含了目标的大量特征信息。利用Gabor小波可以从目标图像中提取具有特征位置、角度和尺度的参数。利用这些参数可以重建除均值以外的所有图像信息。图像边缘与均值无关。根据重建图像边缘线段的长度和边缘拟和度以及特征点的个数,提出了跟踪度的概念,分析了跟踪度的性质,并在跟踪度准则指导下确定了跟踪的特征点个数。仿真实验证明,跟踪度反映了目标特征跟踪的可靠程度,提供了跟踪精度的客观标准,为选择特征点个数、平衡计算复杂度和跟踪精度提供了客观的依据。通过对目标进行姿态变换和大面积遮挡的跟踪实验证明,当跟踪度达到0 95以上时就可以稳定地跟踪目标。     

Can a Circulating Light Beam Produce a Time Machine

In a recent paper, Mallett found a solution of the Einstein equations in which closed timelike curves (CTC’s) are present in the empty space outside an infinitely long cylinder of light moving in circular paths around an axis. Here we show that, for physically realistic energy densities, the CTC’s occur at distances from the axis greater than the radius of the visible universe by an immense factor. We then show that Mallett’s solution has a curvature singularity on the axis, even in the case where the intensity of the light vanishes. Thus it is not the solution one would get by starting with Minkowski space and establishing a cylinder of light.     

On the origin of Kaluza’s idea of unification and its relation to earlier work by Thirring

We argue that the starting point of Kaluzas idea of unifying electrodynamics and gravity was the analogy between gravitation and electromagnetism which was pointed out by Einstein and Thirring. It seems that Kaluzas attention was turned to this point by the three papers on the Lense–Thirring effect and the analogy between gravitation and electromagnetism which were published a short time before Kaluzas paper was submitted. We provide here also an English translation of the third of these papers (Phys. Zeits. 19: 204, 1918).     

Unitarily Inequivalent Representations in Algebraic Quantum Theory

It has been maintained that the physical content of a model of a system is completely contained in the C∗-algebra of quasi-local observables that is associated with the system. The reason given for this is that the unitarily inequivalent representations of are physically equivalent. But, this view is dubious for at least two reasons. First, it is not clear why the physical content does not extend to the elements of the von Neumann algebras that are generated by representations of . It is shown here that although the unitarily inequivalent representations of are physically equivalent, the extended representations are not. Second, this view detracts from special global features of physical systems such as temperature and chemical potential by effectively relegating them to the status of fixed parameters. It is desirable to characterize such observables theoretically as elements of the algebra that is associated with a system rather than as parameters, and thereby give a uniform treatment to all observables. This can be accomplished by going to larger algebras. One such algebra is the universal enveloping von Neumann algebra, which is generated by the universal representation of ; another is the direct integral of factor representations that are associated with the set of values of the global features. Placing interpretive significance on the von Neumann algebras mentioned earlier sheds light on the significance of unitarily inequivalent representations of , and it serves to show the limitations of the notion of physical equivalence.     

Modulation Characteristics of Tunable Quantum-Well Heterolasers at the Radiation Frequency Tuning

The influence of the tuning of the radiation frequency of quantum-well heterolasers within the limits of their amplification band on the output laser radiation parameters at different frequencies of pump-current modulation has been numerically simulated using two optical models of an active medium under the assumption that the excess of the invariable component of the pump current over its threshold value at any point of the amplification band is constant. It has been established that the amplitude-detuning characteristics of the lasers studied are linear at high current-modulation frequencies and nonlinear at medium ones. The behavior of the nonlinear spectral response of a laser diode is explained by its multiresonance structure and is mainly determined by the ratio between the pump-current modulation frequency and the maximum resonance frequency of the laser. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 72, No. 4, pp. 473–478, July–August, 2005.     

Nonlinear Double-well Schrödinger Equations in the Semiclassical Limit

We consider time-dependent Schrödinger equations with a double well potential and an external nonlinear, both local and non-local, perturbation. In the semiclassical limit, the finite dimensional eigenspace associated to the lowest eigenvalues of the linear operator is almost invariant for times of the order of the beating period and the dominant term of the wavefunction is given by means of the solutions of a finite dimensional dynamical system. In the case of local nonlinear perturbation, we assume the spatial dimension d=1 or d=2.     

Effect of spermine and DNase on DNA release from bacteriophage T5

Bacterial viruses (bacteriophages) consist of nucleic acid protected by a protein envelope called capsid. At the start of infection, the phage genome is translocated into the bacterial cytoplasm. In vitro (and also in vivo), this DNA release can be triggered by binding a specific receptor protein to the phage tail. The force responsible for the release arises from energy stored in the capsid due to strong confinement of the DNA. We show that this force can be modified by adding molecules like spermine that affect DNA conformation. The tetravalent cation spermine can reduce the pressure inside the capsid and induce condensation of the released DNA. We examine the effect of spermine on DNA ejection from phage T5 by using light scattering and gel electrophoresis to measure the amount of DNA remaining in the capsid at the end of ejection. We discuss the results in terms of free energy minimization and we demonstrate that the presence of a DNA condensate outside the phage generates an additional force pulling passively on the DNA remaining inside the capsid.     

B-值随机变量序列大数定律的收敛速度

设{X_n:n≥1}是在某可分Banach空间B上取值的独立随机变量序列,S_n=X_1+…+X_n,n≥1,对某00和>1,定义P_n(ε)=P(‖S_n‖/n~(1/p)≥ε)。本文的目的是研究当n→+∞时,P(ε)→0的速度,在Banach空间上推广了Heyde和Rohatgi的结果;同时,本文还讨论了P_n(ε)→0的速度与S_n/n~(1/p)→0 a.s.的关系问题。