步态时相对称性与假肢穿着者行走功能直观评价的相关分析

用步态时相对称性指数的计算方法与行走功能指数直观评价法对１５位不同残肢的假肢穿着者进行步态检查，得出两者之间的线性相关系数为０．８１７（Ｐ＜０．０１）。回归方程为：Ｙ_（对称性指数）＝４．２０６＋０．８８６Ｘ_（功能指数）。认为假肢穿着者的步态时相对称性指数能够反映其行走功能。

从非对称性相倚到彼此相倚互动模式的构建——基于亲师互动发起与回应的视角

彼此相倚型亲师互动模式的构建是亲子教育改革的方向及诉求。从亲师互动发起与回应的视角阐释亲子教育中亲师互动的类型及核心内涵，进而揭示亲师互动的典型特点及突出问题，从而提出在从非对称性相倚到彼此相倚的变革机制的建立和变革过程中对构建新型亲师互动模式的建议和设想，以期为亲子教育中亲师互动质量的提升在理论和实践层面提供有益探索。

彼此相倚:解决物业冲突的有效途径——以C市业主与物业冲突为例

社会心理学家巴克的"非对称性相倚"和"彼此相倚"理论是解释业主和物业冲突与合作的有效理论。由于信息、权力、收费服务和对利益理解等的不对称,使"非对称性相倚"成为业主与物业冲突的主要根源;而通过成立业主委员会,加快推进物业管理的社会化、市场化和专业化,明确双方定位、利益共享等"彼此相倚",则是解决业主与物业冲突的有效途径。

Etching Behavior of GaN/GaAs(001) Epilayers Grown by MOVPE

Wet etching characteristics of cubic GaN (c GaN) thin films grown on GaAs(001) by metalorganic vapor phase epitaxy (MOVPE) are investigated.The samples are etched in HCl,H 3PO 4,KOH aqueous solutions,and molten KOH at temperatures in the range of 90～300℃.It is found that different solution produces different etch figure on the surfaces of a sample.KOH based solutions produce rectangular pits rather than square pits.The etch pits elongate in 1 0] direction,indicating asymmetric etching behavior in the two orthogonal <110> directions.An explanation based on relative reactivity of the various crystallographic planes is employed to interpret qualitatively the asymmetric etching behavior.In addition,it is found that KOH aqueous solution would be more suitable than molten KOH and the two acids for the evaluation of stacking faults in c GaN epilayers. direction,indicating asymmetric etching behavior in the two orthogonal <110> directions.An explanation based on relative reactivity of the various crystallographic planes is employed to interpret qualitatively the asymmetric etching behavior.In addition,it is found that KOH aqueous solution would be more suitable than molten KOH and the two acids for the evaluation of stacking faults in c GaN epilayers.

Hidden Symmetries for Thermodynamics and Emergence of Relativity

Erik Verlinde recently proposed an idea about the thermodynamic origin of gravity.Though this is abeautiful idea, which may resolve many long standing problems in the theories of gravity, it also raises many otherproblems.In this article I will comment on some of the problems of Verlinde’s proposal with special emphasis on thethermodynamical origin of the principle of relativity.It is found that there is a large group of hidden symmetries ofthermodynamics, which contains the Poincare group of the spacetime for which space is emergent.This explains thethermodynamic origin of the principle of relativity.

Symmetries and Exact Solutions of the Breaking Soliton Equation

With the aid of the classical Lie group method and nonclassical Lie group method,we derive the classicalLie point symmetry and the nonclassical Lie point symmetry of (2+1)-dimensional breaking soliton (BS)equation.Usingthe symmetries,we find six classical similarity reductions and two nonclassical similarity reductions of the BS equation.Varieties of exact solutions of the BS equation are obtained by solving the reduced equations.

Nonclassical Symmetries for Nonlinear Partial Differential Equations via Compatibility

The determining equations for the nonclassical symmetry reductions of nonlinear partial differential equations with arbitrary order can be obtained by requiring the compatibility between the original equations and the invariant surface conditions. The （2＋1）-dimensional shallow water wave equation, Boussinesq equation, and the dispersive wave equations in shallow water serve as examples i11ustrating how compatibility leads quickly and easily to the determining equations for their nonclassical symmetries.

Perturbation to Unified Symmetry and Adiabatic Invariants for Relativistic Hamilton Systems

Based on the concept of adiabatic invariant, the perturbation to unified symmetry and adiabatic invariants for relativistic Hamilton systems are studied. The definition of the perturbation to unified symmetry for the system is presented, and the criterion of the perturbation to unified symmetry is given. Meanwhile, the Noether adiabatic invariants, the generalized Hojman adiabatic invariants, and the Mei adiabatic invariants for the perturbed system are obtained.

Some Similarity Reduction Solutions to Two-Dimensional Incompressible Navier-Stokes Equation

We investigate the symmetry reduction for the two-dimensional incompressible Navier-Stokes equationin conventional stream function form through Lie symmetry method and construct some similarity reduction solutions.Two special cases in [D.K.Ludlow,P.A.Clarkson,and A.P.Bassom,Stud.Appl.Math.103 (1999) 183] and a theoremin [S.Y.Lou,M.Jia,X.Y.Tang,and F.Huang,Phys.Rev.E 75 (2007) 056318] are retrieved.

Conformal Ricci Collineations of Static Spherically Symmetric Spacetimes

Conformal Ricei collineations of static spherically symmetric spacetimes are studied. The general form of the vector fields generating eonformal Rieei eollineations is found when the Rieei tensor is non-degenerate, in which ease the number of independent eonformal Rieei eollineations is 15, the maximum number for four-dimensional manifolds. In the degenerate ease it is found that the static spherically symmetric spaeetimes always have an infinite number of eonformal Rieei eollineations. Some examples are provided which admit non-trivial eonformal Rieei eollineations, and perfect fluid source of the matter.

Mei Symmetries and Lie Symmetries for Nonholonomic Controllable Mechanical Systems with Relativistic Rotational Variable Mass

The Mei symmetries and the Lie symmetries for nonholonomic controllable mechanical systems with relativistic rotational variable mass are studied. The differential equations of motion of the systems are established. The definition and criterion of the Mei symmetries and the Lie symmetries of the system are studied respectively. The necessary and sufficient condition under which the Mei symmetry is Lie symmetry is given. The condition under which the Mei symmetries can be led to a new kind of conserved quantity and the form of the conserved quantity are obtained. An example is given to illustrate the application of the results.

Porous Rh/BINAP polymers as efficient heterogeneous catalysts for asymmetric hydroformylation of styrene:Enhanced enantioselectivity realized by flexible chiral nanopockets

A new chiral monomer,(S)‐5,5′‐divinyl‐BINAP,was successfully synthesized and embedded intotwo different porous organic polymers(Poly‐1and Poly‐2).After loading a Rh species,the catalystswere applied for the heterogeneous asymmetric hydroformylation of styrene.Compared with thehomogeneous BINAP analogue,the enantioselectivity of Rh/Poly‐1catalyst was drastically increasedby approximately70%.The improved enantioselectivity of the porous Rh/BINAP polymerswas attributed to the presence of flexible chiral nanopockets resulting from the increased bulk ofthe R groups near the catalytic center.

Neutron Stars in the Model of Non—linear Realization of SU（2） Chiral Symmetry Spontaneous Breaking

The properties of neutron stars are studied in a relativistic mean-field model with SU(2) chiral symmetry spontaneous breaking being considered. The calculation results indicate that the effects of the chiral symmetry spontaneous breaking are not negligible.

Symmetry Reductions of a 1.5-Layer Ocean Circulation Model

The （2＋1）-dimensional nonlinear 1.5-layer ocean circulation model without external wind stress forcing is analyzed by using the classical Lie group approach. Some Lie point symmetries and their corresponding two-dimensional reduction equations are obtained.

Symmetry and Similarity Solutions of a （2＋1）-Dimensional Generalized Broer-Kaup System

We study the symmetries of a （2＋1）-dimensional generalized Broer-Kaup system by means of the classical Lie group theory. The corresponding group algebra is constructed. Based on the symmetries, severaJ types of similarity solutions are obtained.

A Note on Similarity Reductions of Barotropic and Quasi-geostrophic Potential Vorticity Equation

Applying the classical Lie symmetry approach to the barotropic and quasi-geostrophic potential vorticity equation without forcing and dissipation on a β-plane channel, we find a new symmetry, which is not presented in a previous work [F. Huang, Commun. Theor. Phys. （Beijing, China） 42 （2004） 903]. A general finite transformation group is obtained based on the full Lie point symmetry, Furthermore, two new types of similarity reduction solutions are obtained.

Peculiar Quantum Phase Transitions and Hidden Supersymmetry in a Lipkin-Meshkov-Glick Model

In this paper we theoretically report an unconventional quantum phase transition of a simple Lipkin- Meshkow-Glick model： an interacting collective spin system without external magnetic field. It is shown that this model with integer-spin can exhibit a flrst-order quantum phase transition between different disordered phases, and more intriguingly, possesses a hidden supersymmetry at the critical point. However, for half-integer spin we predict another flrst-order quantum phase transition between two different long-range-ordered phases with a vanishing energy gap, which is induced by the destructive topological quantum interference between the intanton and anti-instanton tunneling paths and accompanies spontaneously breaking of supersymmetry at the same critical point. We also show that, when the total spin-value varies from half-integer to integer this model can exhibit an abrupt variation of Berry phase from π to zero.

A Limit Symmetry of Modified KdV Equation and Its Applications

In this letter we consider a limit symmetry of the modified KdV equation and its application. The similarity reduction leads to limit solutions of the modified KdV equation. Besides, a modified KdV equation with new self-consistent sources is obtained and its solutions are derived.

Conformal Invariance and a New Type of Conserved Quantities of Mechanical Systems with Variable Mass in Phase Space

Conformal invariance and a new type of conserved quantities of mechanical systems with variable mass in phase space are studied. Firstly, the definition and determining equation of conformal invariance are presented. The relationship between the conformal invariance and the Lie symmetry is given, and the necessary and sufficient condition that the conformal invarianee would be the Lie symmetry under the infinitesimal transformations is provided. Secondly, a new type of conserved quantities of the conformal invariance are obtained by using the Lie symmetry of the system. Lastly, an example is given to illustrate the application of the results.

Symmetry Reductions of a Lax Pair for(2+1)-Dimensional Differential Sawada-Kotera Equation

Based on the symbolic computational system Maple, the similarity reductions of a Lax pair for the （2＋1 ）-dimensional differential Sawada Kotera （SK） equation by the classical Lie point group method, are presented. We obtain several interesting reductions. Comparing the reduced Lax pair＇s compatibility with the reduced SK equation under the same symmetry group, we find that the reduced Lax pairs do not always lead to the reduced SK equation. In general, the reduced equations are the subsets of the compatibility conditions of the reduced Lax pair.