Analytical approach for the fractional differential equations by using the extended tanh method

In this study, we consider analytical solutions of space–time fractional derivative foam drainage equation, the nonlinear Korteweg–de Vries equation with time and space-fractional derivatives and time-fractional reaction–diffusion equation by using the extended tanh method. The fractional derivatives are defined in the modified Riemann–Liouville context. As a result, various exact analytical solutions consisting of trigonometric function solutions, kink-shaped soliton solutions and new exact solitary wave solutions are obtained.     

Biosynthesis of Cu/KF/Clinoptilolite@MWCNTs nanocomposite and its application as a recyclable nanocatalyst for the synthesis of new Schiff base of benzoxazine derivatives and reduction of organic pollutants

Molecular Diversity - In this work, we synthesized new Schiff base of benzoxazine derivatives in excellent yields using multicomponent reactions of phthalaldehyde or its derivatives, primary...     

The Nambu mechanics as a class of singular generalized dynamical formalisms

In a recent work Nambu has proposed ac-number dynamical formalism which can allow an odd numbern of canonical variables. Naturally associated to this new mechanics there exists ann-linear bracket whose study opens interesting possibilities. The purpose of this work is to show that besides this bracket another one which is bilinear and in fact a Lie bracket can also be associated with the Nambu mechanics. For anyn, however, this bracket is singular. In a sense previously used by the present author, this result exhibits the Nambu mechanics as an interesting class of singular generalized dynamical formalisms irrespective of the number of phase space variables. Reasons are given suggesting that such singular formalisms would be, within our context, the only ones capable of describing classical analogues of generalized quantum systems.     

斯特林制冷机薄壁气缸加工工艺研究

主要叙述斯特林制冷机中薄壁气缸的加工的工艺方法,加工过程的关键参数、刀具的选择、热处理的方法。提出薄壁件加工精度的技术途径。     

碳水混合物冲击压缩特性研究

 利用二级轻气炮加载技术研究了碳水混合物的冲击压缩特性。研究发现：冲击压力p低于19.0 GPa时，石墨与水混合物冲击压缩特性明显不同于金刚石与水混合物的冲击压缩；p大于23.0 GPa后，它们的特性十分接近，这说明有较多的石墨转变为金刚石；当p为52.9 GPa时石墨与水混合物的冲击压缩特性出现明显偏离，这和高压下碳水混合物产生气体成份有关。     

转镜式高速扫描相机时间分辨率的测定

 介绍了产生时间分辨率的原因，测量时间分辨率在高速摄影中的作用，前人曾做过的工作，时间分辨率测定的难点；着重介绍了新的测量方法，给出了实际测定的结果。结果表明，对于GSJ型相机，时间分辨率可达8.6 ns，测量的均方根误差为1.1 ns。     

Gauge theory of the star product

The choice of a star product realization for non-commutative field theory can be regarded as a gauge choice in the space of all equivalent star products. With the goal of having a gauge invariant treatment, we develop tools, such as integration measures and covariant derivatives on this space. The covariant derivative can be expressed in terms of connections in the usual way giving rise to new degrees of freedom for non-commutative theories.     

Free Energy as a Geometric Invariant

The free energy plays a fundamental role in statistical and condensed matter physics. A related notion of free energy plays an important role in the study of hyperbolic dynamical systems. In this paper we introduce and study a natural notion of free energy for surfaces with variable negative curvature. This geometric free energy encodes a new type of marked length spectrum of closed geodesics, which lies between the well-known marked length spectrum (marked by the corresponding element of the fundamental group) and the unmarked length spectrum. We prove that the free energy parametrizes the boundary of the domain of convergence of a Poincaré series which also encodes this spectrum. We also show that this new length spectrum, or equivalently the geometric free energy, is not an isometry invariant. In the final section we use tools from multifractal analysis to effect a fine asymptotic comparison of word length and geodesic length of closed geodesics. We hope that our geometric understanding of free energy will provide new insight into this fundamental physical and dynamical quantity. The work of the second author was partially supported by a National Science Foundation grant DMS-0355180. This work was completed during a visit by the first author to Penn State as a Shapiro Fellow.     

A new efficient synthetic methodology for tetrahydroisoquinoline and tetrahydro-β-carboline derivatives using the Pictet–Spengler reaction

A new solution-phase methodology microwave-assisted for improving the Pictet-Spengler reaction in the synthesis of the tetrahydroisoquinoline and beta-carboline derivatives has been reported. This methodology was applied to obtain a small library of tetrahydroisoquinoline and beta-carboline derivatives using L-Dopa, dopamine, and tryptophan, as well as a variety of commercially available aldehydes as starting material. The use of such nonconventional reaction conditions reveals several features like a short reaction time compared to conventional eating, ease of isolation of the products after work-up, and improvement of the yields. This new one-pot protocol would be an ideal and rapid method to synthesize compounds in a combinatorial context.     

含有高次微商的量子理论

这篇短文比较了两种含有高次微商的量子理论。一个是在某些情形下可用的,它将变数q表为许多适合二阶方程的Q的线性组合,而在量子化时,各个Q分别地被量子化。另一个是先将q的运动方程正则化,再引入量子条件。我们证明了两个理论,无论就各种量的对易关系而言,或就总哈密顿而言,是等效的。     

Mixture of outgoing and incoming electromagnetic radiation. Change of mass of the source of radiation

In a previous paper the author, using a method of successive approximations, verified by means of the Einstein-Maxwell equations of general relativity the well-known result that outgoing electromagnetic radiation from a source conveys energy, so that the source loses gravitational mass corresponding to this energy. The purpose of this work is to show a similar result for the general case of any mixture of outgoing and incoming radiation.This work is included in a thesis submitted by the author (1964) to the University of London for the degree of Ph.D.     

A general three-step one-pot synthesis of novel (<Emphasis Type="Italic">E</Emphasis>)-6-chloro-2-(aryl/hetarylvinyl)quinoline-3-carboxylic acids

In this work, a facile and general three-step one-pot synthesis of structurally new (E)-6-chloro-2-(aryl/hetarylvinyl)quinoline-3-carboxylic acid derivatives has been achieved from easily available ethyl 6-chloro-2-(chloromethyl) quinoline-3-carboxylate and aromatic or heteroaromatic aldehydes. This strategy features simple one-pot operation, tolerance of a wide range of substituents, and good yields. Moreover, these newly synthesized compounds belong to a new class of quinoline derivatives and could be good candidates for the development of more complex quinoline compounds for use in medicinal chemistry.     

On the choice of evolutional parameter within a framework of four-dimensional symmetry

Within the context of the variational principle, there is the freedom to choose specific evolutional parameters. Different parameters can be associated with physical time, while allowing the physical laws to preserve the property of four-dimensional symmetry. In this sense, the concept of time has flexibility. Besides proper time and relativistic time, another natural choice emerges, which is called the generalized Galilean time. We study the impact of this choice here. This approach provides a deeper understanding of the theory of special relativity, and it also provides a new basis to study other space-time theories.On leave from Shanghai University of Science and Technology, Shanghai, China.     

A generalization of variable phase equation

This paper describes a new formulation of phase equation based on a decomposition of wave function into two parts. An equation closely related to the WKB approximation is derived and solved numerically with exponential and Wood-Saxons potential.The author is indebted very much to Doc. J.Kvasnica CSc for the valuable discussions and interest in this work.     

新型抗肿瘤卡铂类衍生物的氢谱特征

卡铂是第二代铂类金属抗癌药物最重要的药物之一,广泛应用于临床. 为发现抗肿瘤活性更强的卡铂类药物,我们合成了6个新的卡铂类衍生物. 本文详细报道4个合成的新型卡铂衍生物的氢谱特征和归属.      

Linear alternative to the Boltzmann equation without linearization: II. Electron-electron scattering

A new form of projector suggested in the previous paper of the series is applied to Time-Convolutionless Generalized Master Equations (TCL-GME) and the problem of spinless interacting electron gas with finite concentration. As a result, a closedlinear kinetic equation for the single-electron density matrix (Wigner distribution function) is obtained. In the second order in the short range interaction and after a short period of forgetting details of initial conditions, a new linear equation with time-independent coefficients results providing a linear alternative to the famous Boltzmann-Uehling-Uhlenbeck equation for quantum gases.The author is really grateful to the International Centre for Theoretical Physics, Trieste for invitation to the Research Workshop on Condensed Matter Physics 1993 where a greater part of this work was completed.     

Bianchi Cosmologies with Particle Creation and Bulk Viscosity

In the context of open thermodynamic systems, we study in this paper the evolution of Bianchi cosmologies with time-dependent bulk viscosity and particle production. The possibility of an initial non-singularity occurs with a suitable choice of parameters as seen in the case of FRW models [Desikan, K. (1997). Gen. Rel. Grav. 29, 435.].     

Numerical Studies of a Two-dimensional Navier-Stokes System with New Boundary Conditions

In this paper we describe the results of numerical studies of solutions of the Navier-Stokes System (NSS) under the boundary conditions introduced recently in the paper by Dinaburg et al. (A new boundary problem for the two-dimensional Navier-Stokes system, see this issue of this journal). First, we investigate the decay of Fourier modes, confirming the results and conjectures made in Dinaburg et al. (A new boundary problem for the two-dimensional Navier-Stokes system, see this issue of this journal). Second, we explore the growth of the total energy and enstrophy, which is possible under the adopted boundary conditions. We show that the solutions of the finite-dimensional Galerkin approximations to the NSS may diverge to infinity in finite time, i.e. their energy may blow up. The author thanks Ya. Sinai and D. Li for involving him in this interesting work, N. Simanyi for help in the analysis of eigensolutions, and A. Korepanov for assistance with Mathematica-based computations. The author was partially supported by NSF grant DMS-0652896.