A generating function for Rankin–Cohen brackets

We give a closed formula for the Rankin–Cohen formal covariant quantization in terms of generating functions of Jacobi polynomials.     

Generalized Transvectants-Rankin–Cohen Brackets

We introduce o(p+1q+1)-invariant bilinear differential operators on the space of tensor densities on Rⁿ generalizing the well-known bilinear sl₂-invariant differential operators in the one-dimensional case, called Transvectants or Rankin–Cohen brackets. We also consider already known linear o(p+1q+1)-invariant differential operators given by powers of the Laplacian.     

Rankin–Cohen Brackets and Associativity

Don Zagier introduced and discussed in Zagier [Proc Indian Acad Sci (Math Sci) 104(1) 57–75, 1994] a particular algebraic structure of the graded ring of modular forms. In this note we interpret it in terms of an associative deformation of this graded ring.     

Non-perturbative QEG corrections to the Yang–Mills beta function

We discuss the non-perturbative renormalization group evolution of the gauge coupling constant by using a truncated form of the functional flow equation for the effective average action of the Yang–Mills-gravity system. Our result is consistent with the conjecture that quantum Einstein gravity (QEG) is asymptotically safe and has a vanishing gauge coupling constant at the non-trivial fixed point.     

The Gallavotti–Cohen Fluctuation Theorem for a Nonchaotic Model

We test the applicability of the Gallavotti–Cohen fluctuation formula on a nonequilibrium version of the periodic Ehrenfest wind-tree model. This is an one-particle system whose dynamics is rather complex (e.g., it appears to be diffusive at equilibrium), but its Lyapunov exponents are nonpositive. For small applied field, the system exhibits a very long transient, during which the dynamics is roughly chaotic, followed by asymptotic collapse on a periodic orbit. During the transient, the dynamics is diffusive, and the fluctuations of the current are found to be in agreement with the fluctuation formula, despite the lack of real hyperbolicity. These results also constitute an example which manifests the difference between the fluctuation formula and the Evans–Searles identity.     

Gluon distribution function from the Berger–Block–Tan form of the structure function F 2

Physics of Atomic Nuclei - We present a set of formulas to extract the gluon distribution function from the Berger–Block–Tan form of the deep inelastic structure function F 2 and its...     

On Cohen–Macaulayness of Algebras Generated by Generalized Power Sums

Generalized power sums are linear combinations of ith powers of coordinates. We consider subalgebras of the polynomial algebra generated by generalized power sums, and study when such algebras are Cohen–Macaulay. It turns out that the Cohen–Macaulay property of such algebras is rare, and tends to be related to quantum integrability and representation theory of Cherednik algebras. Using representation theoretic results and deformation theory, we establish Cohen–Macaulayness of the algebra of q, t-deformed power sums defined by Sergeev and Veselov, and of some generalizations of this algebra, proving a conjecture of Brookner, Corwin, Etingof, and Sam. We also apply representation-theoretic techniques to studying m-quasi-invariants of deformed Calogero–Moser systems. In an appendix to this paper, M. Feigin uses representation theory of Cherednik algebras to compute Hilbert series for such quasi-invariants, and show that in the case of one light particle, the ring of quasi-invariants is Gorenstein.     

Periodic solutions for discrete-time Cohen–Grossberg neural networks with delays

In this paper, the existence of periodic solutions for general discrete-time Cohen–Grossberg neural networks with delays (DCGNND) is investigated. Based on graph theory, coincidence degree theory, and Lyapunov method, a sufficient criterion ensuring the existence of periodic solutions for DCGNND is established. In the end, an example and its numerical simulation are given to demonstrate the effectiveness of the theoretical result.     

The Green function for the Duffin–Kemmer–Petiau equation

We present a calculation of the Green function for the Duffin–Kemmer–Petiau equation in the case of scalar and vectorial particles interacting with a square barrier potential, and relate it to that of the Klein–Gordon equation. A formal Hamiltonian of the Duffin–Kemmer–Petiau theory is first developed using the Feshbach–Villars analogy and the Sakata and Taketani decomposition. The coefficients of reflection and transmission are deduced.     

Optical parameters and work function of Zn–In–Sn–O films

The work function behavior of Zn–In–Sn–O (ZITO) films with various Zn and Sn contents were studied. The work function increased with addition of Zn content. With further increase of Zn contents, the work function gradually decreased. The work function behavior can be investigated by (1) Fermi level position relative the carrier concentration, (2) ionization potential by the surface dipole change. The Fermi level position related the carrier concentration was calculated by Drude parameters, and ionization potential measured by UPS. As results, we confirmed that the work function of ZITO may be linked to changes in ionization potential, not carrier concentration.     

Performance comparison of various modulation schemes over free space optical (FSO) link employing Gamma–Gamma fading model

Free Space Optics (FSO) is an emerging line-of-sight technology intending to provide last-mile solution to the network problem where fiber technology is not feasible. The use of Wavelength Division Multiplexing (WDM) technology for FSO is inspired due to the demand for broadband communication. This technique has brought a revolution because the system data capacity is enhanced by simply adding more number of channels and reducing the channel spacing without having the need of more than one FSO link. By reducing the channel spacing to an appropriate level, Dense Wavelength Division Multiplexing (DWDM) based FSO systems are also be attained and are reported by various research works. FSO finds applications in vast areas like backhaul networks for cellular communication, disaster recovery, LAN–LAN connectivity, high-definition TV, MAN-extension, video transmission, medicine industry and surveillance. However, its usage is limited due to the serious challenges of link vulnerability to weather and atmospheric turbulence-induced fading. This paper is based on a WDM-FSO system. An 8-channel WDM based FSO system is proposed and performance is evaluated on widely accepted modulation schemes under weak, moderate and strong turbulence conditions. Gamma–Gamma fading model is employed for atmospheric turbulence modelling. The system is simulated on OptiSystem 14.0.     

Stochastic finite-time stability of reaction-diffusion Cohen–Grossberg neural networks with time-varying delays

This paper investigates the problem of the stochastic finite-time stability of reaction-diffusion Cohen-Grossberg neural networks with time varying delays using the Dirichlet boundary condition. The concept of finite-time stability for the system is first derived by using the stochastic conditions. By constructing a new Lyapunov–Krasovskii functional and utilizing Jensen’s inequality, Wirtinger’s type inequality technique, the Gronwall inequality and the linear matrix inequality (LMI) frame work, conditions are obtained which guarantee the stochastically finite-time stability of Cohen–Grossberg neural networks. Finally, two numerical examples are given to show the effectiveness of the proposed results.     

Gamma畸变的相位误差模型与Gamma标定技术

Gamma畸变是数字相移测量技术的主要误差源。以通用的均匀步长相移技术为对象,分析了Gamma畸变对相位计算的影响,建立了相位误差与谐波系数的关系模型,证明了各阶谐波系数在Gamma值影响下的递推公式,进而提出了基于离散傅里叶变换的Gamma标定技术。基于此Gamma标定值,通过Gamma预矫正降低相位误差。实验结果表明,标定的Gamma值在整个像平面具有较强的稳定性,Gamma矫正后使相位误差减小了77.5%,在曲面测量的结果中,水波纹明显得到抑制,曲面质量得以提高。     

Coulomb wave function corrections for n-particle Bose–Einstein correlations

The effect of multi-particle Coulomb final state interactions on higher-order intensity correlations is determined in general, based on a scattering wave function which is a solution of the n-body Coulomb Schr?dinger equation in (a large part of) the asymptotic region of n-body configuration space. In particular, we study Coulomb effects on the n-particle Bose–Einstein correlation functions of similarly charged particles and remove a systematic error as big as 100% from higher-order multi-particle Bose–Einstein correlation functions. Received: 24 November 1999 / Published online: 17 March 2000     

Multiple Lagrange stability and Lyapunov asymptotical stability of delayed fractional-order Cohen–Grossberg neural networks

This paper addresses the coexistence and local stability of multiple equilibrium points for fractional-order CohenGrossberg neural networks(FOCGNNs) with time delays.Based on Brouwer's fixed point theorem,sufficient conditions are established to ensure the existence of Π_(i=1)~n(2 K_i+1) equilibrium points for FOCGNNs.Through the use of Hardy inequality,fractional Halanay inequality,and Lyapunov theory,some criteria are established to ensure the local Lagrange stability and the local Lyapunov asymptotical stability of Π_(i=1)~n(K_i+1) equilibrium points for FOCGNNs·The obtained results encompass those of integer-order Hopfield neural networks with or without delay as special cases.The activation functions are nonlinear and nonmonotonic.There could be many corner points in this general class of activation functions.The structure of activation functions makes FOCGNNs could have a lot of stable equilibrium points.Coexistence of multiple stable equilibrium points is necessary when neural networks come to pattern recognition and associative memories.Finally,two numerical examples are provided to illustrate the effectiveness of the obtained results.     

Reduction of the Bethe–Salpeter wave function: Fermion–scalar case and scalar–scalar case

In this paper, the general forms of the nonrelativistic Bethe–Salpeter wave functions for fermion–scalar bound state and scalar–scalar bound state are presented. Using the obtained normalization conditions and the corresponding Schrödinger equations for these bound states, the nonrelativistic Bethe–Salpeter wave functions can be calculated and can be used to compute the amplitude for the process involving these bound states.     

Gamma射线与暗物质

德国的一位天体物理学家声称,通过使用新的统计技术分析美国国家航空和航天局（NASA）的Fermi空间望远镜公布的数据发现银河系中有奇异粒子湮灭的迹象．     

Contextualist viewpoint to Greenberger–Horne–Zeilinger paradox

We present probabilistic analysis of the Greenberger–Horne–Zeilinger (GHZ) scheme in the contextualist framework, namely under the assumption that distributions of hidden variables depend on settings of measurement devices. On one hand, we found classes of probability distributions of hidden variables for that the GHZ scheme does not imply a contradiction between the local realism and quantum formalism. On the other hand, we found classes of probability distributions of hidden variables for that the GHZ scheme still induce such a contradiction (despite variations of distributions). It is also demonstrated that (well known in probability theory) singularity/absolute continuity dichotomy for probability distributions is closely related to the GHZ paradox. Our conjecture is that this GHZ coupling between singularity/absolute continuity dichotomy and incompatible/compatible measurements might be a general feature of quantum theory.