从自然科学到工程科学的对称性本体论研究

研究对称性在自然科学和工程科学中的共性,有助于工程师借鉴自然系统,优化工程系统.以生物学和物理学为例,建立了对称性在自然科学中的本体论框架,在此基础上提出一般系统的对称性本体框架.接着对比研究了对称性在机械工程科学中的本体体系,并发现自然科学与工程科学的对称性本体论具有基本一致性.在这一本体论中,提出自然和工程系统中普遍存在功能对称性、原理对称性及时间对称性,同时对空间对称性给出了比较系统完整的分类.进而指出:对称性在自然和工程系统中的存在模式具有层次结构性、相关性、多体性、多元性、多维性和组合性等共性特征.最后简要论及在自然和工程系统中对称性缺失的普遍存在及其与对称性存在的互补作用,并展望了研究前景.

药型罩材料技术基本要素探讨

总结了药型罩材料技术的四个基本要素,即密度、声速、物理对称性和几何对称性。对四个基本要素进行了理论分析,论述了四个基本要素对使用性能的影响,阐述了在选择药型罩材料及其制作工艺时应遵循的原则。

Properties of a Bound Polaron under a Perpendicular Magnetic Field

We investigate the influence of a perpendicular magnetic field on a bound polaron near the interface of a polar-polar semiconductor with Rashba effect. The external magnetic field strongly changes the ground state binding energy of the polaron and the Rashba spin-orbit （SO） interaction originating from the inversion asymmetry in the heterostructure splits the ground state binding energy of the bound polaron. In this paper, we have shown how the ground state binding energy will be with the change of the external magnetic field, the location of a single impurity, the wave vector of the electron and the electron areal density, taking into account the SO coupling. Due to the presence of the phonons, whose energy gives negative contribution to the polaron＇s, the spin-splitting states of the bound polaron are more stable, and we find that in the condition of week magnetic field, the Zeeaman effect can be neglected.

New Conserved Quantities of Noether-Mei Symmetry for Nonholonomic Mechanical System

Two new types of conserved quantities deduced by Noether-Mei symmetry of nonholonomic mechanicalsystem are studied.The definition and criterion of Noether-Mei symmetry for the system are given.A coordinationfunction is introduced,and the conditions under which the Noether-Mei symmetry leads to the two types of conservedquantities and the forms of the two types of conserved quantities are obtained.An illustrative example is given.Thecoordination function can be selected according to the demand for finding the gauge function,and the choice of thecoordination function has multiformity,so more conserved quantities deduced from Noether-Mei symmetry of mechanicalsystem can be obtained.

Chiral SU(3) Quark Model Study of Tetraquark States: cn■/cs

The new members of the charm-strange family Dsj^＊（2317）, Dsj（2460）, and Ds（2632）, which have the surprising properties, are challenging the present models. Many theoretical interpretations have been devoted to this issue. Most authors suggest that they are not the conventional cs^- quark model states, but possibly are four-quark states, molecule states, or mixtures of a P-wave cs^- and a four-quark state. In this work, we follow the four-quark-state picture, and study the masses of cnn^-s^-/css^-s^- states （n is u or d quark） in the chiral SU（3） quark model. The numerical results show that the mass of the mixed four-quark state （cnn^-s^-/css^-s^-） with spin parity j^P ： 0^＋ might not be Ds （2632）. At the same time, we also conclude that Dsj^＊（2317） and Dsj（2460） cannot be explained as the pure four-quark state.

Solution of ODE u″+p(u)(u′)2+q(u)=0 and Applications to Classifications of All Single Travelling Wave Solutions to Some Nonlinear Mathematical Physics Equations

Under the travelling wave transformation, some nonlinear partial differential equations such as Camassa-Holm equation, High-order KdV equation, etc., are reduced to an integrable ODE expressed by u＂ ＋p（u）（u＇）^2 ＋ q（u） = 0 whose generai solution can be given. Furthermore, combining complete discrimination system for polynomiai, the classifications of all single travelling wave solutions to these equations are obtained. The equation u＂＋p（u）（u＇）^2＋q（u） = 0 includes the equation （u＇）^2 = f（u） as a special case, so the proposed method can be also applied to a large number of nonlinear equations. These complete results cannot be obtained by any indirect method.

Nonlocal Symmetries to Systems of Nonlinear Diffusion Equations

In this paper, we study potential symmetries to certain systems of nonlinear diffusion equations. Thosesystems have physical applications in soil science, mathematical biology, and invariant curve flows in R^3. Lie point symmetries of the potential system, which cannot be projected to vector fields of the given dependent and independent variables, yield potential symmetries. The class of the system that admits potential symmetries is expanded.

Ωω States in a Chiral Quark Model

The structures of Ωω states with spin-parity JP= 5/2^-, 3/2^-, and 1/2^- are dynamically studied in both the chlral SU（3） quark model and the extended chiral SU（3） quark model by solving a resonating group method （RGM） equation. The model parameters are taken from our previous work, which gave a satisfactory description of the energies of the baryon ground states, the binding energy of the deuteron, the nucleon-nucleon （NN） scattering phase shifts, and the hyperon-nucleon （YN） cross sections. The calculated results show that the Ωω state has an attractive interaction, and in the extended chiral SU（3） quark model such attraction can make for a Ωω quasi-bound state with spin-parity JP = 3/2^- or 5/2^- and the binding energy of about several MeV.

Muon g - 2 in the Littlest Higgs Model

In this paper the anomalous magnetic dipole moment ofmuon in the littlest Higgs （LH） model is studied at one-loop level. We discuss the dependence of the contributions on the global symmetry breaking scale f, mizing angles c` and , and the Higgs triplet vacuum expectation value v＇ in the electroweak precision data preferring ranges. We find that the LH model can give a relatively small, but non-negligible extra weak contribution to the muon anomalous magnetic moment and can reduce the deviation of △aμ from 2.6σ for the SM to 2.5σ for the LH model.

Symmetry theories of Hamiltonian systems with fractional derivatives

The Noether and Lie symmetries as well as the conserved quantities of Hamiltonian system with fractional derivatives are es-tablished. The definitions and criteria for the fractional symmetrical transformations and quasi-symmetrical transformations inthe Noether sense of Hamiltonian system are first discussed. Then, using the invariance of Hamiltonian action under the infini-tesimal transformations with respect to time, generalized coordinates and generalized momentums, the fractional Noethertheorem of the system is obtained. Further, the Lie symmetry and conserved quantity of the system are acquired. Two exam-ples are presented to illustrate the application of the results.

Selection rules of electromagnetic transitions for chirality-parity violation in atomic nuclei

The nuclear Chirality-Parity(ChP) violation, a simultaneous breaking of chiral and reflection symmetries in the intrinsic frame, is investigated with a reflection-asymmetric triaxial particle rotor model. A new symmetry for an ideal ChP violation system is found and the corresponding selection rules of the electromagnetic transitions are derived. The fingerprints for the ChP violation including the nearly degenerate quartet bands and the selection rules of the electromagnetic transitions are provided. These fingerprints are examined for ChP quartet bands by taking a two-j shell h11/2 and d5/2 with typical energy spacing for A = 130 nuclei.

Electronic physics and possible superconductivity in layered orthorhombic cobalt oxychalcogenides

We suggest that cobalt-oxychalcogenide layers constructed by vertex sharing CoA_2O_2(A = S, Se, Te) tetrahedra, such as BaCoAO, are strongly correlated multi-orbitals electron systems that can provide important clues on the cause of unconventional superconductivity. Differing from cuprates and iron-based superconductors, these systems lack of the D_(4h) symmetry classification. However, their parental compounds possess antiferromagnetic(AFM) Mott insulating states through pure superexchange interactions and the low energy physics near Fermi surfaces upon doping is mainly attributed to the three t_(2g) orbitals that dominate the AFM interactions. We derive a low energy effective model for these systems and predict that a d-wave-like superconducting state with reasonable high transition temperature can emerge by suppressing the AFM ordering even if the pairing symmetry can not be classified by the rotational symmetry any more.

On New Similarity Solutions of the Boiti–Leon–Pempinelli System

In the present work, the new exact solutions of the Boiti-Leon-Pempinelli system have been found. The system has extensive physical background. The exact solutions of the Boiti-Leon-Pempinelli system are investigated using similarity transformation method via Lie group theory. Lie symmetry generators are used for constructing similarity variables for the given system of partial differential equations, which lead to the new system of partial differentiaJ equations with one variable less at each step and eventually to a system of ordinary differential equations （ODEs）. Finally, these ODEs are solved exactly. The exact solutions are obtained under some parametric restrictions. The elastic behavior of the soliton solutions is shown graphically by taking some appropriate choices of the arbitrary functions involved in the solutions.

Symmetry Analysis and Conservation Laws for the Hunter-Saxton Equation

In this paper, the problem of determining the most general Lie point symmetries group and conservation laws of a well known nonlinear hyperbolic PDE in mathematical physics called the Hunter-Saxton equation （HSE） is anaiyzed. By applying the basic Lie symmetry method for the HSE, the classical Lie point symmetry operators are obtained. Also, the algebraic structure of the Lie algebra of symmetries is discussed and an optimal system of one- dimensional subalgebras of the HSE symmetry algebra which creates the preliminary classification of group invariant solutions is constructed. Particularly, the Lie invariants as well as similarity reduced equations corresponding to in- finitesimal symmetries are obtained. Mainly, the conservation laws of the HSE are computed via three different methods including Boyer＇s generalization of Noether＇s theorem, first homotopy method and second homotopy method.

Physical origins of ruled surfaces on the reduced density matrices geometry

The reduced density matrices （RDMs） of many-body quantum states form a convex set. The boundary of low dimensional projections of this convex set may exhibit nontrivial geometry such as ruled surfaces. In this paper, we study the physical origins of these ruled surfaces for bosonic systems. The emergence of ruled surfaces was recently proposed as signatures of symmetry- breaking phase. We show that, apart from being signatures of symmetry-brealdng, ruled surfaces can also be the consequence of gapless quantum systems by demonstrating an explicit example in terms of a two-mode Ising model. Our analysis was largely simplified by the quantum de Finetti＇s theorem--in the limit of large system size, these RDMs are the convex set of all the symmetric separable states. To distinguish ruled surfaces originated from gapless systems from those caused by symmetry- breaking, we propose to use the finite size scaling method for the corresponding geometry. This method is then applied to the two-mode XY model, successfully identifying a ruled surface as the consequence of gapless systems.