一类自伴随Lubrication方程的对称,守恒律,拉格朗日函数和精确解

本文借助李对称分析研究了一类自伴随的Lubrication方程,此类方程可用来描述液体薄膜动力学行为.基于非奇异的局域守恒律乘子和李对称方法,我们系统地推导出了此类方程的局域守恒律,非局域相关系统,李对称和一些有趣的精确解.此模型的非局域相关系统在本文中被首次研究,可用于寻找原方程更丰富的解空间.此外,基于局域守恒律和变分原则,我们推导出原方程的四类拉格朗日函数.     

Fredholm theory for pseudoholomorphic curves with brake symmetry

We study the pseudoholomorphic curves with brake symmetry in symplectization of a closed contact manifold. We introduce the pseudo-holomorphic curves with brake symmetry and the corresponding moduli space. Then we get the virtual dimension of the moduli space.     

Quantum mechanics versus realism

Quantum theory accepts the point-like indivisible (classical) character of a particle as a mere product of a measuring process, or what has become known as a collapse. Following the notion of empty waves, which accepts the particle as a real existent entity without regard to the measurement process, we propose an experiment that may shed some light on the reality of the particle and the consequences of that reality.     

A goldstone mode in the Kawasaki-Ising model

The hydrodynamic regime of superfluids is dominated by a Goldstone mode corresponding to a spontaneously brokenU(1) symmetry. In this article we map the Kawasaki-Ising model for a classical lattice gas into a quantum model for a superfluid and establish a connection between the normal density fluctuations of the first and the Goldstone mode of the second. The fact that the quantum model we obtain describes a superfluid derives from an inequality by Penrose and Onsager which gives a lower bound to the Bose-Einstein condensate density. Mathematically, the Goldstone mode can be described by means of a quantum extension of the local algebra of the Ising model. The classification of its irreducible representations requires an additionalU(1) phase factor and the correspondingU(1) gauge symmetry is spontaneously broken for all finite values of the temperature and of the density.     

Effect of heavy quark symmetry on the mass difference ofB-system in minimal left right symmetric model

An estimation of the mass difference of system with heavy quark symmetry formalism is presented. The effective Hamiltonian describing the transition (whereh=b forB _d ⁰ -system) is considered in a manifest left right symmetric (MLRS) model along with contribution from neutral Higgs boson. We use the spin and flavor symmetry for heavy quarks to obtain the transition matrix element 〈B _d ⁰ |ℋ_eff(x)| _d ⁰ 〉 in terms of Isgur-Wise function. Assuming thatB _d ⁰ and states are at rest, we find that Isgur-Wise function turns out to be unity. However using the experimental values of ΔM _K and as input, we find thatM _R=835 GeV andM _H⩾2·9 TeV.     

“Statistical” symmetry with applications to phase transitions

Hermann proposed that mesomorphic media should be classified by assigning certain statistical symmetry groups to each possible partially ordered array. Two translational groups introduced were called superordinate and subordinate. We find that the average density in such a partially ordered medium has the superordinate symmetry ₁, while the pair correlation function has the subordinate symmetry ₂. A complete listing is made of all compatible combinations of ₁ and ₂ in two and three dimensions. This leads to more possible symmetries than Hermann obtained, e.g., also to nonstoichiometric crystals. The order parameter space for the systems is found to be the quotient space ₁/₂. In most cases it is identical to the order parameter space of low-dimensionalXY spin systems. The Landau free energy is expanded as functional of the two-particle correlation functionK; the translation group is found to be ₁×₂. A Landau mean-field theory can then be carried out by expanding the system free energy into a series of invariants of the active irreducible representations ofK and mapping the free energy onto that for anXY planar spin system. We predict novel critical behavior for transitions between mesomorphic phases and go nogo selection rules for continuous transitions. We give the structure factors for X-ray scattering so changes in all such phase transitions are observable. The statistical symmetry groups, which describe point and translational symmetries of the mesophases, are classified. Proposals are made to include quasi-long-range or topological order in the classification scheme.This work supported in part by National Science Foundation (Division of International Programs), the PSC-BHE—Faculty Research Award CUNY and Deutsche Forschungsgemeinschaft.     

THE MORPHOLOGICAL SIMILARITY AND SYMMETRY OF NEURONES IN THE LEECH Whitmania pigra

Using the method of intracellular injection of horseradish peroxidase, the arborizations of several neurones with different functions in the segmental ganglia of the leech Whitmania pigra are investigated. Comparison is made in each kind of neurones in order to verify their typical pattern. Results show that the morphology of the axonal arbors of identified neurones has an accurate similarity within and among the individuals of the leech, and the axonal arborizations of the bilaterally identified neurones in the same ganglion have a stable symmetry. The possible reasons of the formation and its functional significance of the symmetrical nervous system are discussed.     

固体Hp[EuA_4]配合物异构体的研究

合成了化学式为Hp[EuA_4]的配合物(A=对甲氧基苯甲酰苯甲酰甲烷;Hp=六氢吡啶),用X-射线粉末衍射法,荧光光谱及热谱等方法研究了它们的性质,并发现由于合成条件(反应物的摩尔投量比,反应温度,所用溶剂)不同,在固体Hp[EuA_4]配合物中配体空间的排布不同,而有不同的异构体存在。     

ESR study of NiIII complexes with nitrosonaphthols and dithio acids

Mixed-ligand Ni^III complexes with -nitroso--naphthol, -nitroso--naphthol,o-ethylxanthate, andN,N-diethyldithiocarbamate as ligands have been studied by ESR in liquid and frozen solutions. The degrees of symmetry distortion for the first coordination sphere of these complexes have been determined. It is shown that the transition from planar square Ni^IIL₂ complexes to more stable octahedral Ni^IIIL₂L and Ni^IIILL₂ complexes occursvia the radical addition mechanism. A method for trapping short-lived radicals is suggested on the basis of the complex formation scheme.Translted fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 8, pp. 1513–1515, August, 1995.The work was financially supported by the Russian Foundation for Basic Research (Project No. 93-03-5050)     

Theory of helicenic hydrocarbons. Part 1: Invariants and symmetry

Helicenes form a subclass of polyhexes and correspond to hydrocarbons of considerable chemical interest. This paper is the first part of a general graph-theoretical treatment of helicenes. The invariants are studied: the relations between them, their possible values, and their upper and lower bounds in helicenes. Extremal helicenes and circular helicenes are useful definitions of subclasses of the systems under consideration. Finally an account of symmetry of helicenes is given.On leave from: Department of Mathematics, Xinjiang University, Wulumuqi Xinjiang 830046, People's Republic of China.