Quantitative estimates for a new complex Durrmeyer operator in compact disks

In the recent years the extension of linear positive operators from real to complex domain is one of the interesting area of research. In this context, we present the exact order of simultaneous approximation and Voronovskaja kind results with quantitative estimate for a new type of complex Durrmeyer operator (different from those previously studied), attached to analytic functions in compact disks. In this way, we put in evidence the overconvergence phenomenon for this kind of Durrmeyer operator, namely the extensions of approximation properties with exact quantitative estimates, from the real interval [1/3, 2/3] to compact disks in the complex plane.     

Tunneling of the hard‐core model on finite triangular lattices

We consider the hard‐core model on finite triangular lattices with Metropolis dynamics. Under suitable conditions on the triangular lattice sizes, this interacting particle system has 3 maximum‐occupancy configurations and we investigate its high‐fugacity behavior by studying tunneling times, that is, the first hitting times between these maximum‐occupancy configurations, and the mixing time. The proof method relies on the analysis of the corresponding state space using geometrical and combinatorial properties of the hard‐core configurations on finite triangular lattices, in combination with known results for first hitting times of Metropolis Markov chains in the equivalent zero‐temperature limit. In particular, we show how the order of magnitude of the expected tunneling times depends on the triangular lattice sizes in the low‐temperature regime and prove the asymptotic exponentiality of the rescaled tunneling time leveraging the intrinsic symmetry of the state space.     

A companion matrix approach to the study of zeros and critical points of a polynomial

In this paper, we introduce a new type of companion matrices, namely, D-companion matrices. By using these D-companion matrices, we are able to apply matrix theory directly to study the geometrical relation between the zeros and critical points of a polynomial. In fact, this new approach will allow us to prove quite a number of new as well as known results on this topic. For example, we prove some results on the majorization of the critical points of a polynomial by its zeros. In particular, we give a different proof of a recent result of Gerhard Schmeisser on this topic. The same method allows us to prove a higher order Schoenberg-type conjecture proposed by M.G. de Bruin and A. Sharma.     

Perturbation theory of polar hard Gaussian overlap fluid mixtures

A perturbation theory of polar hard Gaussian overlap fluid mixture is discussed. Explicit analytic expressions for the second and third varial coefficients are given. Numerical results are estimated for the thermodynamic properties of quadrupolar hard Gaussian overlap fluid and fluid mixture. It is found that the excess free energy and internal energy depend on concentrationsc ₁,c ₂, molecular diameter ratioR, shape parameterK and the quadrupole momentsQ*₁,Q*₂.     

Hard chaos and adiabatic quantization: The wedge billiard

We present a study of a series of eigenstates occurring in the wedge billiard which may be quantized about tori by sejiclassical adiabatic quantization, even though the underlying classical system exhibits hard chaos and strictly possesses no tori. We also show that adiabatic eigenstates should be common in many chaotic systems, especially among the lower eigenstates, and present a heuristic argument as to why this should be so.     

s~(1/2)=630GeV pp碰撞中微喷注的新分析

根据喷注判定的圆锥法来判断喷注，重新分析了ＵＡ１－１９８５年的６３０ＧｅＶ非单衍ｐｐ碰撞实验数据。分析发现对事件样本，单事件平均横动量ｐ与多重数ｎ是正关联的，而对喷注事件子样本则是负关联的；分析了微喷注产生嵉墓亓屯斯亓砻魑⑴缱⒉丛从诜侨砉毯透呓仔вΓ徊⑹状未邮笛樯瞎鄄獾轿⑴缱⒓浯嬖诖罂於燃涓裟谖蘖Ｗ拥氖吕治隽宋⑴缱⒉贝嬖诖罂於龋纾幔鸬募Ｏ蟆     

Solution of approximate gluon evolution equation for small-x at fixed ‘ρ’

A simple method has been applied to solve the approximate gluon evolution equation for small-x at fixedρ(≡√ln(x ₀/x)/ln[ln(Q ²/Λ²)/ln(Q ₀ ² /Λ²)]. Numerical comparison is made with the predictions from ‘double asymptotic scaling’ and fit. Better agreement is found between our solution and fit nearρ=1. The solution gives approximate double scaling in this region having ‘hard’ pomeron with small contamination.     

Approximate fixed-ρ solution of ‘sea-quark’ evolution equation at small-x and HERA

We found an approximate simple solution of sea-quark evolution equation in terms ofρ(=√ln(x ₀/x)/ln[ln(Q ²/Λ²)/(Q ₀ ² /Λ²)]) andζ(≡ln[ln(Q ²Λ²)/ln(Q ₀ ² /Λ²)]) in the small-x region whenρ is fixed and compared with HERA data. Agreement with data is found for largeQ ² and smallρ. Comparison with double asymptotic scaling prediction is made. We found a critical value ofρ. More data are needed to confirm this point.     

高能p+p(p)碰撞中J/ψ和γ的硬衍射产生

讨论从ISR到SSC能区p+p(p)→p+J/ψ(Υ)+X过程.假定Pomeron(p)的结构以胶子为主且在小x处有的行为后,在QCD最低阶计算了两个主要子过程的硬衍射截面和作为背景项的Drell-Yan模式的相应截面.与背景项在高能时随Ins增加不同,硬衍射项基本上随(InS)²增加,因而在TeV能区以上时后者将大大超过前者.这种性质对其它硬衍射过程具有普适性.因此如果关于P的上述假定正确,在准确地测定P的结构后,选择适当的硬衍射过程,可能在超高能时提供探测物理粒子的新实验方法.     

Derivation of macroscopic equations for individual cell‐based models: a formal approach

In this paper we review the theory of cells (particles) that evolve according to a dynamics determined by friction and that interact between themselves by means of suitable potentials. We derive by means of elementary arguments several macroscopic equations that describe the evolution of cell density. Some new results are also obtained—a formal derivation of a limit equation in the case of attractive potential as well as in the case of repulsive potential with a hard‐core part are presented. Finally we discuss the possible relevance of those results within the framework of individual cell‐based models. Several classes of potentials, including hard‐core, repulsive and potentials with attractive parts are discussed. The effect of noise terms in the equation is also considered. Copyright © 2005 John Wiley & Sons, Ltd.