Slater Sum in Cylindrically Symmetric Inhomogeneous Electron Liquids: Towards A Differential Equation for the Stark Effect in Hydrogen Atom

Abstract

Attention is focussed here on a variety of cylindrically symmetric inhomogeneous electron liquids. These include separable potentials in which a general variation along the (z) axis of cylindrical symmetry is combined with isotropic harmonic confinement in the (x, y) plane. in this case, an explicit differential equation is derived for the Slater sum along the z axis by projecting out of the (off-diagonal) canonical density matrix the states with zero angular momentum about the axis of symmetry. Some attention is then given to the calculation of the Slater sum for a hydrogen-like atom in a uniform electric field of arbitrary strength. the model of a separable potential with harmonic confinement, though no longer exact, is shown to lead directly to a (now approximate) equation for the Slater sum along the z axis for the Stark effect in hydrogen. Finally some further progress is shown to be possible in the extreme high field limit.     

Heavy flavor baryon spectra via QCD sum rules

In this talk, we give a short review of our recent works on studying the singly heavy baryon, doubly heavy baryon, and triply heavy baryon spectra from QCD sum rules.     

Strong coupling constants of light pseudoscalar mesons with heavy baryons in QCD

We calculate the strong coupling constants of light pseudoscalar mesons with heavy baryons within the light cone QCD sum rules method. It is shown that sextet–sextet, sextet–antitriplet and antitriplet–antitriplet transitions are described by one universal invariant function for each class. A comparison of our results on the coupling constants with the predictions existing in literature is also presented.     

Spectrum is periodic for n-intervals

In this paper we study spectral sets which are unions of finitely many intervals in R. We show that any spectrum associated with such a spectral set Ω is periodic, with the period an integral multiple of the measure of Ω. As a consequence we get a structure theorem for such spectral sets and observe that the generic case is that of the equal interval case.     

Progress in DNA Aptamers as Recognition Components for Protein Functional Regulation

Proteins play a central role in all domains of life, and precise regulation of their activity is essential for understanding the related biological processes and therapeutic functions. Nucleic acid aptamers, the molecular recognition components derived from systematic evolution of ligands by exponential enrichment(SELEX), can specifically identify proteins with antibody-like recognition characteristics and help to regulate their activity. This minireview covers the SELEX-based selection of protein-binding aptamers, membrane protein analytical techniques based on aptamer-mediated target recognition, aptamer-mediated functional regulation of proteins, including membrane receptors and non-membrane proteins(thrombin as a model), as well as the potential challenges and prospects regarding aptamer-mediated protein manipulation, aiming to supply some useful information for researchers in this field.     

自然数幂方和用二项系数表示的系数公式

得到了自然数幂方和由二项系数表示的系数a_i~(k)的公式,和由排列数表示的系数b_i~(k)的公式,证明了系数存在唯一性及系数间的若干重要性质,给出了计算系数的C-语言程序.     

具交叉感染的流行病模型的数学分析

In this paper,an initial boundary value problem with homogeneous Neumann boundary condition is studied for a reaction-diffusion system which models the spread of infectious diseases within two population groups by means of self and criss-cross infection mechanism. Existence,uniqueness and boundedness of the nonnegative global solution (u1,u2,u3,u4),existence of the limit of the solution as t→+∞,namely,(u1,u2,u3,u4)→(u*1,0,u*3,0),are proved.     

Exponential stability of Takagi-Sugeno fuzzy systems with impulsive effects and small delays

This paper deals with the exponential stability of impulsive Takagi-Sugeno fuzzy systems with delay. Impulsive control and delayed fuzzy control are applied to the system, and the criterion on exponential stability expressed in terms of linear matrix inequalities （LMIs） is presented.     

New robust chaotic system with exponential quadratic term

This paper proposes a new robust chaotic system of three-dimensional quadratic autonomous ordinary differential equations by introducing an exponential quadratic term. This system can display a double-scroll chaotic attractor with only two equilibria, and can be found to be robust chaotic in a very wide parameter domain with positive maximum Lyapunov exponent. Some basic dynamical properties and chaotic behaviour of novel attractor are studied. By numerical simulation, this paper verifies that the three-dimensional system can also evolve into periodic and chaotic behaviours by a constant controller.