Isospin and symmetry structure in ^(34)S

The interacting boson model-3(IBM-3) has been used to study the energy levels and electromagnetic transitions for the nucleus 34 S.The main components of the wave function,isoscalar and isovector parts in the M1 and E2 transitions for low-lying states have been investigated.According to this study,the theoretical calculations are in agreement with experimental data,and the nucleus 34 S is in transition from U(5) to S U(3).

Structural Equation and Mei Conserved Quantity of Mei Symmetry for Appell Equations in Holonomic Systems with Unilateral Constraints

Structural equation and Mei conserved quantity of Mei symmetry for Appell equations in holonomic systems with unilateral constraints are investigated. Appell equations and differential equations of motion for holonomie mechanic systems with unilateral constraints axe established. The definition and the criterion of Mei symmetry for Appell equations in holonomic systems with unilateral constraints under the infinitesimal transformations of groups axe also given. The expressions of the structural equation and Mei conserved quantity of Mei symmetry for Appell equations in holonomic systems with unilateral constraints expressed by Appell functions are obtained. An example is given to illustrate the application of the results.

Shape-induced phase transition of vortex domain structures in ferroelectric nanodots and their controllability by electrical and mechanical loads

Shape-induced phase transition of vortex domain structures （VDSs） in BaTiO3 （BT） nanodots under open circuit boundary condition have been investigated using an effective Hamiltonian method. Our calculation indicates the tetragonal VDS missing in cubic BT nanodots can be induced by varying the shape of a nanodot from cube to platelet. Interestingly, a novel VDS is found in BT nanoplatelets in our simulations. Further investigation shows that it is a result of compromise between the ground state and the symmetry of the shape of the nanodot. Furthermore, based on the novel VDS, routes of controlling VDSs governed by homogeneous electric field and uniform stress are discussed. In particular, our results show the possibility of designing multi-states devices based on a single VDS. ~ 2017 The Authors. Published by Elsevier Ltd on behalf of The Chinese Society of Theoretical and Applied Mechanics.

Signature of symmetry of laterally coupled quantum dots in far-infrared spectrum

We study the effect of structure asymmetry on the energy spectrum and the far-infrared spectrum （FIR） of a lateral coupled quantum dot. The calculated spectrum shows that the parity break of coupled quantum dot results in more coherent superpositions in the low-lying states and exhibits unique anti-crossing in the two-electron FIR spectrum modulated by a magnetic field. We also find that the Coulomb correlation effect can make the FIR spectrum of coupled quantum dot without strict parity deviate greatly from Kohn theorem, which is just contrary to the symmetric case. Our results therefore suggest that FIR spectrum may be used to determine the symmetry of coupled quantum dot and to evaluate the degree of Coulomb interaction.

Synthesis,Crystal and Electronic Structure of Ba_3ZnSb_2O_9 with the 6H-perovskite-type Structure

Crystals of Ba3ZnSb2O9 have been grown by a high-temperature solid-state reaction and characterized by single-crystal X-ray diffraction.Ba3ZnSb2O9 crystallizes in the hexagonal P63/mmc space group with a = 5.8663（4）,c = 14.478（2） ,V = 431.49（8） 3,Z = 2 and R（all data） = 0.0167.The structure of Ba3ZnSb2O9 consists of pairs of face-sharing Sb2O9 bi-octahedra connected via corners with two single layers of mutually isolated ZnO6 octahedra.Each Ba2＋ ion is bonded to 12 oxygen atoms.The UV-vis absorption spectrum of the compound has been investigated.Additionally,the calculations of band structure and density of states have also been performed with density functional theory method.The obtained results tend to support the experimental data of the absorption spectrum.

Gait planning and intelligent control for a quadruped robot

We present a method for designing free gaits for a structurally symmetrical quadruped robot capable of performing statically stable, omnidirectional walking on irregular terrain. The robot＇s virtual model is constructed and a control algorithm is proposed by applying virtual components at some strategic locations. The deliberative-based controller can generate flexible sequences of leg transferences while maintaining walking speed, and choose optimum foothold for moving leg based on integration data of exteroceptive terrain profile. Simulation results are presented to show the gait＇s efficiency and system＇s stability in adapting to an uncertain terrain.

PRIMARY RESEARCH ON FRACTAL GEOMETRY OF MERIDIAN THEORY

In meridian theory of traditional Chinese medicine (TCM), the geometrical descriptions can be traced back to the remote ancient times in China, mainly in The Yellow Emperor’s Internal Classic (The Internal Classic in short). Euclid’s geometry, topology and other classic mathematics are all at their wit’s end to explain the high complexity and non clinear phenomenon of the meridian. In recent over 2000 years, the meridian phenomenon has been being the challenge to fundamental mathematics. Fractral geometry, founded by Mandelbrot (1975), is a branch of learning for investigating irregular geometrical curves. It has successfully solved some qualitative and quantitative problems about the topographical structure of molecular Brown’s movement curve and other irregular complicated curves and geometrical characters. The characteristics of geometrical topographical structure of meridian and its phenomenon belong to the research category of Fractal Geometry. The author of this paper believes that Fractal Geometry may provide a useful mathematical tool and a possible way for revealing the enigma of acup moxibustion meridian theory. The human body is of basic characters of Fractal Geometry in structure, while meridian is the expression form of Fractal structure of the human body. The basic Fractal geometrical characters of meridian are: self similarity, self affinity, symmetry, minute structure and self avoidance, which has been applied for thousands of years in clinic, such as “taking the acupoints on the right side of the body in cases of disorders appearing on the left side and vice versa". The basic characters of meridians are 1) symmetry of the 12 regular meridians on the bilateral sides of the body (symmetry); 2) similarity in characters and actions of acupoints of the same one meridian (self similarity); 3) taking acupoints on the lower part of the body when disorders occurring on the upper part of the body; and taking acupoints on the upper part of the body if disorders appearing on the lower part (self affinity); 4) micro acupuncture system including hand acupuncture, foot acupuncture, scalp acupuncture, auricular acupuncture and eye acupuncture (minute structure); and 5) systematical running of needling sensation (self avoidance).

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.