High-Order Hamilton＇s Principle and the Hamilton＇s Principle of High-Order Lagrangian Function

In this paper, based on the theorem of the high-order velocity energy, integration and variation principle, the high-order Hamilton＇s principle of general holonomic systems is given. Then, three-order Lagrangian equations and four-order Lagrangian equations are obtained from the high-order Hamilton＇s principle. Finally, the Hamilton＇s principle of high-order Lagrangian function is given.     

Study on‘soft＇ and ‘hard＇ interactions in ^-pp （pp） collisions using HIJING and PYTHIA

This paper presents a study on ＇hard＇ and ＇soft＇ interactions in ^-pp （pp） collisions using a phenomenological model of HIJING, the jet-cone reconstruction method is employed to select the ＇hard＇ and ＇soft＇ event sub-samples from minimum bias events. It is found that the HIJING model can reproduce the energy scaling behaviour of mean transverse momentum （〈PT〉） distributions of charged hadrons versus multiplicity （Nch） in ＇soft＇ events. From the PYTHIA simulation comparing with the HIJING model, the enhancement of the kaon and proton yields from ＇hard＇ interactions comparing with ＇soft＇ interactions is observed to be due to the mini-jets effect. These mechanisms responsible for the increase of charged hadron＇s （PT） are different in ＇soft＇ and ＇hard＇ interactions.     

Synthesis,Characterization of 9, 9＇-Bianthracene and Fabrication of 9, 9＇-Bianthracene Field-Effect Transistors

We synthesize and purify 9, 9＇-bianthracene with the purity up to 96.4%. The electronic and crystallographic structures of 9, 9＇-bianthracene are studied. The results of a joint experimental investigation based on a combination of x-ray diffraction （XRD） spectra, hydrogen nuclear magnetic （HNMR） spectra, infrared absorption （FT-IR） spectra, and mass spectra （MS） of 9, 9＇-bianthracene are obtained. The uniform compact film is observed by an atomic-force microscope （AFM）. Organic field effect transistors （OFETs） with an active layer based on the synthesized 9, 9＇-bianthracene are fabricated for the first time. Its field-effect mobility is as large as 0.067 cm^2 /（V·s） and the on/off ratio is above 5 ×10^4. The result demonstrates that the oligomerization of a small semiconductor molecule is an effective method to develop high-mobility organic semiconductors.     

Macro-Behaviour of Agents＇ Opinion under Influence of an External Field

We propose a model to study the evolution of opinion under the influence of all external field on small world network. The maero-behaviour of agents＇ opinion and the relative change rate as time elapses are studied. The external field is found to play an important role in making the opinion s（t） balance or increase, and without the influence of the external field, the relative change rate γ（t） shows nonlinear increasing behaviour as time runs. What is more, this nonlinear increasing behaviour is independent of the initial condition, the strength of the external field and the time that we cancel the external field. The results may reflect some phenomena in our society, such as the function of the macro-control in China or the mass media in our society.     

The relation between and violation of Hardy＇s non-locality Bell inequality

We give an analytic quantitative relation between Hardy＇s non-locality and Bell operator. We find that Hardy＇s non-locality is a sufficient condition for the violation of Bell inequality, the upper bound of Hardy＇s non-locality allowed by information causality just corresponds to Tsirelson bound of Bell inequality and the upper bound of Hardy＇s non- locality allowed by the principle of no-signaling just corresponds to the algebraic maximum of Bell operator. Then we study the CabeUo＇s argument of Hardy＇s non-locality （a generalization of Hardy＇s argument） and find a similar relation between it and violation of Bell inequality. Finally, we give a simple derivation of the bound of Hardy＇s non-locality under the constraint of information causality with the aid of the above derived relation between Hardy＇s non-locality and Bell operator.     

Long-time limit behavior of the solution to an atom＇s master equation

We study the long-time limit behavior of the solution to an atom＇s master equation. For the first time we derive that the probability of the atom being in the α-th （α = j ＋ 1 -jz, j is the angular momentum quantum number, jz is the z-component of angular momentum） state is {（1 - K/G）/[1 - （K/G）2j＋1]}（K/G）^α-1 as t → ＋∞, which coincides with the fact that when K/G 〉 1, the larger the a is, the larger the probability of the atom being in the α-th state （the lower excited state） is. We also consider the case for some possible generaizations of the atomic master equation.     

Mei Symmetry and Conserved Quantity of Tzenoff Equations for Nonholonomic Systems of Non-Chetaev＇s Type

Mei symmetry of Tzenoff equations for nonholonomic systems of non-Chetaev＇s type under the infinitesimal transformations of groups is studied. Its definitions and discriminant equations of Mei symmetry are given. Sufficient and necessary condition of Lie symmetry deduced by the Mei symmetry is also given. Hojman conserved quantity of Tzenoff equations for the systems through Lie symmetry in the condition of special Mei symmetry is obtained.     

Thermal transport property of investigated by molecular Ge34 and d-Ge dynamics and the Slack＇s equation

In this study, we evaluate the values of lattice thermal conductivity κL of type Ⅱ Ge clathrate （Ge34） and diamond phase Ge crystal （d-Ce） with the equilibrium molecular dynamics （EMD） method and the Slack＇s equation. The key parameters of the Slack＇s equation are derived from the thermodynamic properties obtained from the lattice dynamics （LD） calculations. The empirical Tersoff＇s potential is used in both EMD and LD simulations. The thermal conductivities of d-Ge calculated by both methods are in accordance with the experimental values. The predictions of the Slack＇s equation are consistent with the EMD results above 250 K for both Ge34 and d-Ge. In a temperature range of 200-1000 K, the κL value of d-Ge is about several times larger than that of Ge34.     

Dust Lattice Waves of Dusty Plasma Chain with an External Magnetic Field

Dust lattice waves of a one-dimensional plasma crystal chain with an external magnetic field are investigated. When the magnetic field is in the vertical direction （θ- 0）, perpendicular to the chain, the vertical transverse mode is not affected, while the horizontal transverse mode is coupled with the longitudinal mode. In the high frequency range, we obtain an ‘upper-hybrid＇ dust lattice mode and in the low frequency range, we obtain a ＇lower-hybrid＇ dust lattice mode. Between the two modes, a ＇gap＇ is formed. When the magnetic field is oriented to the chain （0 = π/2）, the longitudinal mode is not affected while both the horizontal and vertical transverse modes are shifted due to the effect of the magnetic field.     

On Kaup and Newell＇s Method for Solving DNLS Equation

Kaup and Newell＇s revised inverse scattering transform for the derivative nonlinear Schrodinger （DNLS） equation is investigated. We compared it with a more reasonable approach proposed recently, which is rigorously proven by the Liouville theorem. It is conduded that Kanp and Newell＇s revision is only suitable for giving single-soliton solution and can not be generalized to multi-soliton case.     

A Criterion for Stability of Synchronization and Application to Coupled Chua＇s Systems

We investigate synchronization in an array network of nearest-neighbor coupled chaotic oscillators. By using of the Lyapunov stability theory and matrix theory, a criterion for stability of complete synchronization is deduced. Meanwhile, an estimate of the critical coupling strength is obtained to ensure achieving chaos synchronization. As an example application, a model of coupled Chua＇s circuits with linearly bidirectional coupling is studied to verify the validity of the criterion.     

Observation of Influence of Nucleons＇ Motion on Kaons Collective Flow in Dense Medium

In order to extract the information of the momentum-dependent interaction of kaons under the extreme condition, the properties of the positively charged kaons produced in a heavy ion collision are studied via a simple model which has an invariable nucleon＇s velocity. Our special attention is focused on the observation of the dependence of the kaon＇s properties on the motion of nucleons in a hot and dense nuclear environment. Starting from two kinds of kaon quasiparticle models defined in transport theories for simulating heavy ion collisions, we calculate the effective mass and potential of the K＋＇s produced in the collisions and find that these properties not only depend closely on the velocity of nucleons but the dependence varies with kaon＇s quasiparticle model. It is clearly shown that the motion of nucleons reduces the momentum of K＋＇s at a given rapidity and thus weakens the rapidity distribution of K＋＇s directed flow in realistic nuclear collisions.     

A New Approach for Impulsive Stabilization of Liu＇s System

An impulsive control scheme of Liu＇s system is presented in this paper. Some less conservative conditions with impulses at fixed times are provided, which can guarantee the global asymptotical stability and global exponential stability for the impulsive control of Liu＇s systems. We also present the estimate of the stable region for the equidistance impulsive interval. Furthermore, an illustrative example is given to show the effectiveness of the proposed results.     

Variational regularization method of solving the Cauchy problem for Laplace＇s equation： Innovation of the Grad-Shafranov （GS） reconstruction

The simplified linear model of Grad-Shafranov （GS） reconstruction can be reformulated into an inverse boundary value problem of Laplace＇s equation. Therefore, in this paper we focus on the method of solving the inverse boundary value problem of Laplace＇s equation. In the first place, the variational regularization method is used to deal with the ill- posedness of the Cauchy problem for Laplace＇s equation. Then, the ＇L-Curve＇ principle is suggested to be adopted in choosing the optimal regularization parameter. Finally, a numerical experiment is implemented with a section of Neumann and Dirichlet boundary conditions with observation errors. The results well converge to the exact solution of the problem, which proves the efficiency and robustness of the proposed method. When the order of observation error δ is 10-1, the order of the approximate result error can reach 10-3.     

Study of η and η＇ physics at BES-III

Decays of both η and η＇ provide very useful information in our understanding of low-energy QCD, and experimental signatures for these decays would be extremely helpful at BES-III. The rare decays of the η and η＇ mesons could serve as a low-energy test of the Standard Model and its beyond. The sensitivities of the measurements of η and η＇ decays are discussed at BES-III, in which the η and η＇ mesons are produced in the ψ decays.     

Benford＇s Law and β-Decay Half-Lives

The experimental values of 2059 β-decay half-lives are systematically analyzed and investigated. We have found that they are in satisfactory agreement with Benford＇s law, which states that the frequency of occurrence of each figure, 1-9, as the first significant digit in a surprisingly large number of different data sets follows a logarithmic distribution favoring the smaller ones. Benford＇s logarithmic distribution of β-deeay half-lives can be explained in terms of Neweomb＇s justification of Benford＇s law and empirical exponential law of β-decay half-lives. Moreover, we test the calculated values of 6721 β-decay half-lives with the aid of Benford＇s law. This indicates that Benford＇s law is useful for theoretical physicists to test their methods for calculating β-decay half-lives.     

Comment on ’The scale-transformation of electromagnetic theory and its applications’,’Distribution characteristic of scattering field for an ellipsoidal target irradiated by an electromagnetic wave from an arbitrary direction’ and ’Electric fields inside a

It is shown that the ’scale-transformation’ method proposed by Li Ying-Le et al.is not applicable to the Maxwell theory.     

MΦller＇s Energy of Kerr-NUT Metric

The energy distribution of the Kerr-NUT （Newman-Unti-Tamburino） spacetime is calculated using MΦller＇s energy-momentum complex within the framework of the Riemannian geometry.     

Numerical study of the coupling between F0 with varied numbers of c-subunits and F1 in an ATP synthase

ATP synthase is a rotary motor which is composed of two portions： the ‘rotor＇ Fo, consisting of a c-ring, and the ‘stator＇ F1, consisting of an a3/33 hexamer. In different species, the number of c-subunits which form the c-ring is varied from 10 to 14, whereas the a3/33 hexamer is fixed to be 3-fold symmetrical. We have numerically studied the rotational coupling between Fo with varied number of c-subunits and F1. It is found that, for any number of c-subunits, the rotor Fo advances 3 steps per revolution on average, which is determined by the period of F1, whereas the exact angular pausing positions are determined by the period of Fo. When the symmetry of the c-ring of Fo is matched with the 3-fold symmetry of F1, the three steps have equivalent sizes. If not matched, the three steps become nonequivalent： both the step size and average dwell time are different for these steps.     

Hofstadter＇s Butterfly and Phase Transition of Checkerboard Superconducting Network in a Magnetic Field

We study the magnetic effect of the checkerboard superconducting wire network. Based on the de Gennes- Alexader theory, we obtain difference equations for superconducting order parameter in the wire network. Through solving these difference equations, we obtain the eigenvalues, linked to the coherence length, as a function of magnetic field. The diagram of eigenvalues shows a fractal structure, being so-called Hofstadter＇s butterfly. We also calculate and discuss the dependence of the transition temperature of the checkerboard superconducting wire network on the applied magnetic field, which is related to up-edge of the Hofstadter＇s butterfly spectrum.