半单Malcev代数上不变双线性型的自对称性

介绍Malcev代数的定义 ,并在特征为零的数域上讨论Malcev代数的理想 ,单性 ,半单性 ;利用不变性及Jacobian证明单Malcev代数上不变双线性型的自对称性 。

Exact Solutions of a Generalized Multi-Fractional Nonlinear Diffusion Equation in Radical Symmetry

This paper is devoted to investigating exact solutions of a generalized fractional nonlinear anomalousdiffusion equation in radical symmetry.The presence of external force and absorption is also considered.We firstinvestigate the nonlinear anomalous diffusion equations with one-fractional derivative and then multi-fractional ones.Inboth situations,we obtain the corresponding exact solutions,and the solutions found here can have a compact behavioror a long tailed behavior.

A Coupled Hybrid Lattice: Its Related Continuous Equation and Symmetries

The hybrid lattice, known as a discrete Korteweg-de Vries (KdV) equation, is found to be a discrete modified Korteweg-de Vries (mKdV) equation in this paper. The coupled hybrid lattice, which is pointed to be a discrete coupled KdV system, is also found to be discrete form of a coupled mKdV systems. Delayed differential reduction system and pure difference systems are derived from the coupled hybrid system by means of the symmetry reduction approach. Cnoidal wave, positon and negaton solutions for the coupled hybrid system are proposed.

Two New Multi-component BKP Hierarchies

We firstly propose two kinds of new multi-component BKP （mcBKP） hierarchy based on the eigenfunction symmetry reduction and nonstandard reduction, respectively. The first one contains two types of BKP equation with self-consistent sources whose Lax representations are presented. The two mcBKP hierarchies both admit reductions to the k-constrained BKP hierarchy and to integrable （1＋1）-dimensional hierarchy with self-consistent sources, which include two types of SK equation with self-consistent sources and of hi-directional SK equations with self-consistent

INSTABILITY OF SYMMETRIC TYPHOON CIRCULATION AND ADAPTIVE OBSERVATION

This study presents a new way to identify the sensitive areas,which are determined by invoking the negative anomalies of moist potential vorticity (MPV) for typhoon adaptive observations. It is found that the areas of negative MPV are the symmetric instability areas and can be taken as sensitive areas for typhoon adaptive observations. Three typhoons in 2008,Nuri,Fung-wong,and Fengshen,were simulated with the help of MM5 model. It is shown that these typhoons are well simulated in the first 12 hours. Based on these investigations,the calculations of MPV are carried out sequentially. The result shows that the negative maxima of MPV are always around the typhoon eyes for all the cases,which means that the sensitive areas are also near them all the time.

Two-Photon Exchange Corrections to Single Spin Asymmetry of Neutron and 3He

In a simple hadronie model, the two-photon exchange contributions to the single spin asymmetries for the nucleon and the 3He are estimated. The results show that the elastic contributions of two-photon exchange to the single spin asymmetries for the nucleon are rather small while those for the 3He are relatively large. Besides the strong angular dependence, the two-photon contributions to the single transfer. spin asymmetry for the 3He are very sensitive to the momentum

Solution of Dirac Equation with Killingbeck Potential by Using Wave Function Ansatz Method under Spin Symmetry Limit

The Dirac equation is solved for Killingbeck potential. Under spin symmetry limit, the energy eigenvalues and the corresponding wave functions are obtained by using wave function ansatz method.

Distinct patterns of monthly Southern Annular Mode events

The Southern Annular Mode(SAM)is the leading mode of atmospheric variability in the mid–high latitudes of the Southern Hemisphere,representing large-scale variations in pressure and the polar front jet(PFJ).In SAM events,the combination of the SAM and other modes may result in different atmospheric patterns.In this study,a neural-network-based cluster technique,the self-organizing map,was applied to extract the distinct patterns of SAM events on the monthly time scale based on geopotential height anomalies at 500 hPa.Four pairs of distinguishable patterns of positive and negative SAM events were identified,representing the diversity in spatial distribution,especially the zonal symmetry of the center of action at high latitudes—that is,symmetric patterns,split-center patterns,West Antarctica patterns,and a tripole pattern.Although the SAM is well known to be beltshaped,within the selected SAM events,the occurrence frequency of symmetric patterns is only 23.8%—less than that of West Antarctica patterns.Diverse PFJ variations were found in the symmetric and asymmetric patterns of SAM events.The more asymmetric the spatial distribution of the pressure anomaly,the more localized the adjusted zonal wind anomaly.The adjusted PFJ varied in meridional displacement and strength in different patterns of SAM events.In addition,the entrance and exit of the jet changed in most of the patterns,especially in the asymmetric patterns,which might result in different climate impacts of the SAM.

Invariant Functions, Symmetries and Primary Branch Solutions of First Order Autonomous Systems

An invariant function （IF） is defined as a multiplier of a symmetry that means a symmetry multiplied by an IF is still a symmetry. Primary branch solutions of arbitrary first order scalar systems can be obtained by means of the IF and its related symmetry approach. Especially, one recursion operator and some sets of infinitely many high order symmetries are also explicitly given for arbitrary （l q-1）-dimensional first order autonomous systems. Because of the intrusion of the arbitrary function, various implicit special exact solutions can be found by fixing the arbitrary functions and selecting different seed solutions.

Spin and Pseudospin Symmetries of Dirac Equation and the Yukawa Potential as the Tensor Interaction

Considering of a tensor interaction in Dirac equation removes the degeneracy in spin and pseudospin doublets and consequently leads to results consistent with the experimental data. Here, instead of the commonly used Coulomb or linear terms, we investigate a tensor interaction of Yukawa form. We obtain arbitrary state solutions of Dirac equation under vector, scalar and tensor Yukawa potentials via a physical approximation and the Nikiforov-Uvarov methodology. The solutions are discussed in detail.

Exploitation of symmetry in periodic Self-Consistent-Field ab initio calculations: application to large three-dimensional compounds

Symmetry can dramatically reduce the computational cost （running time and memory allocation） of Self-Consistent-Field ab initio calculations for crystalline systems. Crucial for running time is use of symmetry in the evaluation of one- and two-electron integrals, diagonalization of the Fock matrix at selected points in reciprocal space, reconstruction of the density matrix. As regards memory allocation, full square matrices （overlap, Fock and density） in the Atomic Orbital （AO） basis are avoided and a direct transformation from the packed AO to the SACO （Symmetry Adapted Crystalline Orbital） basis is per- formed, so that the largest matrix to be handled has the size of the largest sub-block in the latter basis. We here illustrate the effectiveness of this scheme, following recent advancements in the CRYSTAL code, concerning memory allocation and direct basis set transformation. Quantitative examples are given for large unit cell systems, such as zeolites （all-silica faujasite and silicalite MF1） and garnets （pyrope）. It is shown that the full SCF of 3D systems containing up to 576 atoms and 11136 Atomic Orbitals in the cell can be run with a hybrid functional on a single core PC with 500 MB RAM in about 8 h.

Quantifying Spontaneously Symmetry Breaking of Quantum Many-Body Systems

Spontaneous symmetry breaking is related to the appearance of emergent phenomena, while a non-vanishing order parameter has been viewed as the sign of turning into such symmetry-breaking phase. We study the spontaneous symmetry breaking in the conventional superconductor and Bose–Einstein condensation with a continuous measure of symmetry by showing that both the many-body systems can be mapped into the many spin model. We also formulate the underlying relation between the spontaneous symmetry breaking and the order parameter quantitatively. The degree of symmetry stays unity in the absence of the two emergent phenomena, while decreases exponentially at the appearance of the order parameter which indicates the inextricable relation between the spontaneous symmetry and the order parameter.

(n+1)-Dimensional Gravity Duals to Quantum Criticalities with Spontaneous Symmetry Breaking

We reexamine the charged AdS domain wall solution to the Einstein-Abelian-Higgs model proposed by Gubser et al. as holographic superconductors at quantum critical points and comment on their statement about the uniqueness of gravity solutions. We generalize their explorations from （3 ＋ 1）-dimensions to arbitrary n -b 1Ds and find that the n ＋1≥5D charged AdS domain walls are unstable against electric perturbations.

Detection of topological symmetry in the one-dimensional Afeck-Kennedy-Lieb-Tasaki model of integer spin with ultracold spinor atoms in optical lattices

A scheme is proposed for detection of the topology in the one-dimensional Afeck-Kennedy-Lieb-Tasaki model,based on ultracold spinor atomic gas in an optical lattice.For this purpose,a global operation O(θ)is introduced with respect to the breaking of spinrotational symmetry.Consequently,the topology can be manifested unambiguously by identifying the special values ofθwhere the expectation value of the global operator with degenerate ground states is vanishing.Furthermore,experimentallyθcan be detected readily by the interference of ultracold atomic gases.This scheme can be implemented readily in experiment since it does not need the addressing of individual atoms or the probing of a boundary.

Tests of gravitational symmetries with radio pulsars

Symmetries play important roles in modern theories of physical laws. In this paper, we review several experimental tests of important symmetries associated with the gravitational interaction, including the universality of free fall for self-gravitating bodies,time-shift symmetry in the gravitational constant, local position invariance and local Lorentz invariance of gravity, and spacetime translational symmetries. Recent experimental explorations for post-Newtonian gravity are discussed, of which, those from pulsar astronomy are highlighted. All of these tests, of very different aspects of gravity theories, at very different length scales, favor to very high precision the predictions of the strong equivalence principle(SEP) and, in particular, general relativity which embodies SEP completely. As the founding principles of gravity, these symmetries are motivated to be promoted to even stricter tests in future.

No Spin-Localization Phase Transition in the Spin-Boson Model without Local Field

We explore the spin-boson model in a special case, i.e., with zero local field. In contrast to previous studies, we find no possibility for quantum phase transition （QPT） happening between the localized and delocalized phases, and the behavior of the model can be fully characterized by the even or odd parity as well as the parity breaking, instead of the QPT, owned by the ground state of the system. The parity breaking mentioned in our case is completely different from the spontaneously broken symmetry relevant to the conventionally defined QPT in previous studies. Our analytical treatment about the eigensolution of the ground state of the model presents for the first time a rigorous proof of no- degeneracy for the ground state of the model, which is independent of the bath type, the degrees of freedom of the bath and the calculation precision. We argue that the QPT mentioned previously appears due to incorrect employment of the ground state of the model and/or unreasonable treatment of the infrared divergence existing in the spectral functions for Ohmic and sub-Ohmic dissipations.

SU(2) symmetry in a Hubbard model with spin-orbit coupling

We study the underlying symmetry in a spin-orbit coupled tight-binding model with Hubbard interaction.It is shown that,in the absence of the on-site interaction,the system possesses the SU(2)symmetry arising from the time reversal symmetry.The influence of the on-site interaction on the symmetry depends on the topology of the networks:The SU(2)symmetry is shown to be the spin rotation symmetry of a simply-connected lattice even in the presence of the Hubbard interaction.On the contrary,the on-site interaction breaks the SU(2)symmetry of a multi-connected lattice.This fact indicates that a discrete spin-orbit coupled system has exclusive features from its counterpart in a continuous system.The obtained rigorous result is illustrated by a simple ring system.