具有整体代对称性的左右对称模型中的中微子质量

本文基于具有整体U(1)代对称性的SU(2)L×SU(2)R×U(1)模型推导了轻子的味混合矩阵,对中微子的质量问题进行了研究.在本文的模型中,产生轻子Dirac质量的汤川耦合拉格朗日密度具有整体U(1)代对称性,所以,模型中的带电轻子质量矩阵和中微子Dirac质量矩阵是Fritzsch形式的.但是,中微子除了具有Dirac质量,一般还具有Majorana质量,在这种一般情况下,轻中微子的有效质量矩阵就不再是Fritzsch形式的.为了不去处理非厄米矩阵的对角化问题,我们假设中微子Majorana质量矩阵的相位满足一定的关系,从而把问题简化为对一个实对称矩阵的对角化.然后,得到了轻子的味混合矩阵,并且结合中微子混合的实验数据,对本文中得到的一系列关系式进行了数值计算,结果显示,本文中考虑的模型可能无法与现在的中微子混合实验数据相符合.

SU(3)_g代规范群

本文讨论了粒子的代对称性,提出了选择代规范群的三个条件.详细讨论并计算了W~±和Z^0衰变实验结果和代规范作用的渐近自由条件对代规范群选取的限制.取到了满足三个条件的唯一选择:SU(3)■代规范群和相应的非平凡的代多重态分配.

N = 4 Supersymmetric Morse Oscillator and Its Spectrum-Generating Algebra

In this paper N = 4 supersymmetry of generalized Morse oscillators in one dimension is studied. Both bound states and scattering states of its four superpartner Hamiltonians are analyzed by using unitary irreducible representations of the noncompact Lie algebra su(1,1). The spectrum-generating algebra governing the Hamiltonian of the N = 4 supersymmetric Morse oscillator is shown to be connected with the realization of Lie superalgebra osp(1,2)or B(0,1) in terms of the variables of a supersymmetric two-dimensional harmonic oscillator.

Lie Reduction and Conditional Symmetries of Some Variable Coefficient Nonlinear Wave Equations

Lie symmetry reduction of some truly ＂variable coefficient＂ wave equations which are singled out from a class of （1 ＋ 1）-dimensional variable coefficient nonlinear wave equations with respect to one and two-dimensional algebras is carried out. Some classes of exact solutions of the investigated equations are found by means of both the reductions and some modern techniques such as additional equivalent transformations and hidden symmetries and so on. Conditional symmetries are also discussed.

Symmetries and Algebras of a (2+1)-Dimensional MKdV-Type System

In this paper, a （2＋1）-dimensional MKdV-type system is considered. By applying the formal series symmetry approach, a set of infinitely many generalized symmetries is obtained. These symmetries constitute a closed infinite-dimensional Lie algebra which is a generalization of w∞ type algebra. Thus the complete integrability of this system is confirmed.

sl(1|2)Super-Toda Fields

Explicit exact solution of supersymmetric Toda fields associated with the Lie superalgebra s/（2｜ 1） is constructed. The approach used is a super extension of Leznov-Saveliev algebraic analysis, which is based on a pair of chiral and antichiral Drienfeld-Sokolov systems. Though such approach is well understood for Toda field theories associated with ordinary Lie algebras, its super analogue was only successful in the super Liouville case with the underlying Lie superalgebra osp（1｜2）. The problem lies in that a key step in the construction makes use of the tensor product decom- position of the highest weight representations of the underlying Lie superalgebra, which is not clear until recently. So our construction made in this paper presents a first explicit example of Leznov-Saveliev analysis for super Toda systems associated with underlying Lie superalgebras of the rank higher than 1.

Lie Point Symmetry Algebras and Finite Transformation Groups of Baroclinic Mode for Rotating Stratified Flows

The transformation groups and symmetries of the baroclinic mode for rotating stratified flow can be obtained via the standard approach. Applying the symmetry group on some special solutions, the newly obtained results disprove a known conjecture.

A Classical Toda Family with a Common Virasoro Symmetry Algebra

By means of a simple ideal, which is firstly proposed for the continuous system, we present an arbitrary order classical Toda family invariant under common Virasoro-type symmetry algebra.

Symmetry Reduction of Two-Dimensional Damped Kuramoto-Sivashinsky Equation

In this paper, the problem of determining the largest possible set of symmetries for an important nonlinear dynamical system： the two-dimensional damped Kuramoto-Sivashinsky （（21）） DKS ） equation is studied. By applying the basic Lie symmetry method for the （217）） DKS equation, the classical Lie point symmetry operators are obtained. Also, the optimal system of one-dimensional subalgebras of the equation is constructed. The Lie invariants as well as similarity reduced equations corresponding to infinitesimal symmetries are obtained. The nonclassicaJ symmetries of the （2D） DKS equation are also investigated.

Cloning and stage-specific expression of CK-M1 gene during metamorphosis of Japanese flounder,Paralichthys olivaceus

The symmetrical body of flatfish larvae changes dramatically into an asymmetrical form after metamorphosis. The molecular mechanisms responsible for this change are poorly understood. As an initial step to clarify these mechanisms, we used representational difference analysis of cDNA for the identification of genes active during metamorphosis in the Japanese flounder, Paralichthys olicaceus. One of the up-regulated genes was identified as creatine kinase muscle type 1 (CK-M1). Sequence analysis of CK-M1 revealed that it spanned 1 708 bp and encoded a protein of 382 amino acids. The overall amino acid sequence of the CK-M1 was highly conserved with those of other organisms. CK-M1 was expressed in adult fish tissues, including skeletal muscle, intestine and gill. Whole mount in-situ hybridization showed that the enhanced expression of CK-M1 expanded from the head to the whole body of larvae as metamorphosis progressed. Quantitative analysis revealed stage-specific high expression of CK-M1 during metamorphosis. The expression level of CK-M1 increased initially and peaked at metamorphosis, decreased afterward, and finally returned to the pre-metamorphosis level. This stage-specific expression pattern suggested strongly that CK-M1 was related to metamorphosis in the Japanese flounder. Its specific role in metamorphosis requires further study.

THE BLOWUP OF RADIALLY SYMMETRIC SOLUTIONS FOR 2-D QUASILINEAR WAVEEQUATIONS WITH CUBIC NONLINEARITY

For a special class of quasilinear wave equations with small initial data which satisfy the nondegenerate assumption, the authors prove that the radially symmetric solution develops singularities in the second order derivatives in finite time while the first order derivatives and the solution itself remain continuous and small. More precisely, it turns out that this solution is a "geometric blowup solution of cusp type", according to the terminology posed by S. Alinhac[2].

Generating a New Higher-Dimensional Coupled Integrable Dispersionless System:Algebraic Structures,Bcklund Transformation and Hidden Structural Symmetries

The prolongation structure methodologies of Wahlquist-Estabrook [H.D. Wahlquist and F.B. Estabrook, J. Math. Phys. 16 （1975） 1] for nonlinear differential equations are applied to a more general set of coupled integrable dispersionless system. Based on the obtained prolongation structure, a Lie-Algebra valued connection of a closed ideal of exterior differential forms related to the above system is constructed. A Lie-Algebra representation of some hidden structural symmetries of the previous system, its Biicklund transformation using the Riccati form of the linear eigenvalue problem and their general corresponding Lax-representation are derived. In the wake of the previous results, we extend the above prolongation scheme to higher-dimensional systems from which a new （2 ＋ 1）-dimensional coupled integrable dispersionless system is unveiled along with its inverse scattering formulation, which applications are straightforward in nonlinear optics where additional propagating dimension deserves some attention.

The Elements in Crystal Bases Corresponding to Exceptional Modules

According to the Ringel-Green theorem,the generic composition algebra of the Hall algebra provides a realization of the positive part of the quantum group.Furthermore,its Drinfeld double can be identified with the whole quantum group,in which the BGP-reflection functors coincide with Lusztig's symmetries.It is first asserted that the elements corresponding to exceptional modules lie in the integral generic composition algebra,hence in the integral form of the quantum group.Then it is proved that these elements lie in the crystal basis up to a sign.Eventually,it is shown that the sign can be removed by the geometric method.The results hold for any type of Cartan datum.

Symmetries and Their Lie Algebra of a Variable Coefficient Korteweg-de Vries Hierarchy

IsospectrM and non-isospectral hierarchies related to a variable coefficient Painlev6 integrable Korteweg-de Vries （KdV for short） equation are derived. The hier- archies share a formal recursion operator which is not a rigorous recursion operator and contains t explicitly. By the hereditary strong symmetry property of the formal recur- sion operator, the authors construct two sets of symmetries and their Lie algebra for the isospectral variable coefficient Korteweg-de Vries （vcKdV for short） hierarchy.

Relation between the E(5) symmetry and the interacting boson model beyond the mean-field approximation

In a unified algebraic scheme,we investigate the relation between the E(5) symmetry and the interacting boson model beyond the mean-field level.The results indicate that the E(5) symmetry is actually in between the critical point of the U(5)-O(6) transition and the O(6) limit but it is fairly close to the former based on the phase diagram of the interacting boson model at the large boson number limit.In addition,an algebraic Hamiltonian of the E(5)-β2n model is proposed.

Algebraic Structure of Discrete Zero Curvature Equations and Master Symmetries of Discrete Evolution Equations

In this paper, based on a discrete spectral problem and the corresponding zero curvature representation,the isospectral and nonisospectral lattice hierarchies are proposed. An algebraic structure of discrete zero curvature equations is then established for such integrable systems. the commutation relations of Lax operators corresponding to the isospectral and non-isospectral lattice flows are worked out, the master symmetries of each lattice equation in the isospectral hierarchyand are generated, thus a τ-symmetry algebra for the lattice integrable systems is engendered from this theory.

Higgs Algebraic Symmetry of Screened System in a Spherical Geometry

The orbits and the dynamical symmetries for the screened Coulomb potentials and isotropic harmonic oscillators have been studied by Wu and Zeng [Z.B. Wund J.Y. Zeng, Phys. Rev. A 62 （2000） 032509]. We find similar properties in the corresponding systems in a sphericM space, whose dynamical symmetries are described by Higgs algebra. There exist extended Runge-Lenz vector for screened Coulomb potentials and extended quadruple tensor for screened harmonic oscillators. They, together with angular momentum, constitute the generators of the geometrical symmetry group. Moreover, there exist an infinite number of dosed orbits for suitable angular momentum values, and we give the equations of the classical orbits. The eigenenergy spectrum and corresponding eigenstates in these systems are derived.