Time-Dependent Variational Approach to Ground-State Phase Transition and Phonon Dispersion Relation of the Quantum Double-Well Model

The ground-state phase transition and the phonon dispersion relation of the quantum double-well model are studied by means of the time-dependent variational approach combined with a Hartree-type many-body trial wavefunction. The single-particle state is taken to be a frozen Jackiw-Kerman wavefunction. Under the condition of minimum uncertainty relation, we obtain an effective classical Hamiltonian for the system and equations of motion for the particle＇s expectation values. It is shown that the effective substrate potential transits from a symmetric double-well potential to a symmetric single-well potential, and the ground state exhibits a transition from a broken symmetry phase to a restored symmetry phase as increasing the strength of quantum fluctuations. We also obtain the phonon dispersion relations and the phonon gaps at the two phases.

Commutators of Weighted Lipschitz Functions and Multilinear Singular Integrals with Non-Smooth Kernels

This paper is devoted to studying the commutators of the multilinear singular integral operators with the non-smooth kernels and the weighted Lipschitz functions. Some mapping properties for two types of commutators on the weighted Lebesgue spaces, which extend and generalize some previous results, are obtained.

Gluonic Origin and Glueball Nature of Pomeron

The Pomeron-nucleon coupling vertex is theoretically derived from the fundamental theory of strong interaction QCD. The empirical vertex βγ^μF1 （t） used commonly in diffractive processes with a coupling strength β = 6.0 GeV^-1 is initially obtained from QCD theoretically. Our study not only reproduces the Pomeron-nucleon coupling from QCD but also clearly shows the gluonlc origin and glueball nature of Pomeron, which is a longstanding puzzle. From this investigation, we claim that Pomeron can be regarded as a Reggeized tensor glueball ζ（2230） with quantum numbers of I^GJ^PC = 0＋2＋＋. Since the tensor glueball ζ（2230） lies on the Pomeron trajectory αp（t = Mζ^2） = 2, the longstanding puzzle that no physical particle lies on the Pomeron trajectory, αp（t） = 1.08 ＋ 0.20 GeV^-2 .t, seems to be solved.

ALL MEROMORPHIC SOLUTIONS OF AN AUXILIARY ORDINARY DIFFERENTIAL EQUATION AND ITS APPLICATIONS

In this paper, we first employ the complex method to deritive all meromorphic solutions of an auxiliary ordinary differential equation, and then find all meromorphic exact solutions of the modified ZK equation, modified KdV equation, nonlinear Klein-Gordon equation and modified BBM equation. Our work shows that there exist some classes of rational solutions wr,2 （z） and simple periodic solutions ws,1 （z） which are new and are not degenerated successively to by the elliptic function solutions.

Asymptotic behavior of 2D generalized stochastic Ginzburg-Landau equation with additive noise

The 2D generalized stochastic Ginzburg-Landau equation with additive noise is considered. The compactness of the random dynamical system is established with a priori estimate method, showing that the random dynamical system possesses a random attractor in H^1 0.

Quark Mass Dependence of Nucleon Magnetic Moment and Charge Radii

Understanding hadron structure within the framework of QCD is an extremely challenging problem. Our purpose here is to explain the model-independent consequences of the approximated chiral symmetry of QCD for two famous results concerning the quark structure of the nucleon. We show that both the apparent success of the constituent quark model in reproducing the ratio of proton to neutron magnetic moments and the apparent success of the Foldy term in reproducing the observed charge radius of the neutron are coincidental. That is, a relatively small change of the current quark mass would spoil both results.

BIFURCATION ANALYSIS AND COMPUTATION OF DOUBLE TAKENS-BOGDANOV POINT IN Z_2-EQUIVARIABLE NONLINEAR EQUATIONS

The paper deals with the computation and bifurcation analysis of double Takens-Bogdanov point (u0, ∧0) (in short, DTB point) in the Z2-equivariable nonlinear equation f(u, ∧) = 0, f: U × R4 → V , where U and V are Banach spaces, parameters ∧∈ R4. At (u0,∧0) , the null spaceof fu0 has geometric multiplicity 2 and algebraic multiplicity 4. Firstly a regular extended system for computing DTB point is proposed. Secondly, it is proved that there are four branches of singular points bifurcated from DTB point: two paths of STB points, two paths of TB-Hopfpoints. Finally,the numerical results of one dimensional Brusselator equations are given to show the effectiveness of our theory and method.

The improved ICA algorithm and its application in the seismic data denoising

The field seismic data is disturbed by the interferential information, which has low signal to noise ratio (SNR). That is disadvantage for seismic data interpretation. So it is important to remove the noise of seismic data. Independent component analysis (ICA) can remove most of the noise interference. However, ICA has some defects in noise reduction, because it needs some conditions that seismic data is independent reciprocally for denoising. To solve these defects, this paper proposes an improved ICA algorithm to noise reduction. Through simulation experiments, it can be obtained that the best decomposition levels of the new algorithm is 3. At last, the proposed improved ICA is applied to deal with the actual seismic data. The results show that it can effectively eliminate most of seismic noise such as random noise, linear interference, surface waves, and so on. The improved ICA is not only easy to denoising, but also has excellent mathematical theoretical properties.

Bitcoin price change and trend prediction through twitter sentiment and data volume

Twitter sentiment has been shown to be useful in predicting whether Bitcoin’s price will increase or decrease.Yet the state-of-the-art is limited to predicting the price direction and not the magnitude of increase/decrease.In this paper,we seek to build on the state-of-the-art to not only predict the direction yet to also predict the magnitude of increase/decrease.We utilise not only sentiment extracted from tweets,but also the volume of tweets.We present results from experiments exploring the relation between sentiment and future price at different temporal granularities,with the goal of discovering the optimal time interval at which the sentiment expressed becomes a reliable indicator of price change.Two different neural network models are explored and evaluated,one based on recurrent nets and one based on convolutional networks.An additional model is presented to predict the magnitude of change,which is framed as a multi-class classification problem.It is shown that this model yields more reliable predictions when used alongside a price trend prediction model.The main research contribution from this paper is that we demonstrate that not only can price direction prediction be made but the magnitude in price change can be predicted with relative accuracy(63%).

Riemann Boundary Value Problem of Non-Normal Type on the Infinite Straight Line

Various kinds of Riemann boundary value problems (BVPs) for analytic functions on closed curves or on open arc, doubly periodic Riemann BVPs, doubly quasi-periodic Riemann BVPs, and BVPs for polyanalytic functions have been widely investigated in [1-8]. The main ap- proach is to use the decomposition of polyanalytic functions and their generalization to transform the boundary value problems to their corresponding boundary value problems for analytic functions. Recently, inverse Riemann BVPs for generalized analytic functions or bianalytic functions have been investigated in [9-12]. In this paper, we consider a kind of Riemann BVP of non-normal type on the infinite straight line and discuss the solvable conditions and the general solution for it.

Dynamical Running Mass of Quark in the Dyson-Schwinger Equation Approach

Based on the Dyson-Schwinger equations of QCD in the "rainbow" approximation, the fully dressed quarkpropagator Sf(p) is investigated, and then an algebraic parametrization form of the propagator is obtained as a solutionof the equations. The dressed quark amplitudes Af and Bf built up the fully dressed quark propagator and the dynamicalrunning masses Mf defined by Af and Bf for light quarks u, d and s are calculated, respectively. Using the predictedrunning masses Mf, quark condensates <0|q(0)q(0)|0> = -(0.255 GeV)a for u, d quarks, and <0|s s|0> = 0.8<0|q(0)q(0)]0)for s quark, and experimental pion decay constant fπ = 0.093 GeV, the masses of Goldstone bosons K, π, and η are alsoevaluated. The numerical results show that the masses of quarks are dependent on their momentum p2. The fully dressedquark amplitudes Af and Bf have correct behaviors which can be used for many purposes in our future researches onnonperturbative QCD.

A fast direct point-by-point generating algorithm for B Spline curves and surfaces

Traditional generating algorithms for B Spline curves and surfaces require approximation methods where how to increment the parameter to get the best approximation is problematic; or they take the pixel-based method needing matrix trans- formation from B Spline representation to Bézier form. Here, a fast, direct point-by-point generating algorithm for B Spline curves and surfaces is presented. The algorithm does not need matrix transformation, can be used for uniform or nonuniform B Spline curves and surfaces of any degree, and has high generating speed and good rendering accuracy.

Periodic Bifurcation and Soliton Deflexion for Kadomtsev-Petviashvili Equation

The spatial-temporal bifurcation for Kadomtsev-Petviashvili （KP） equations is considered. Exact two-soliton solution and doubly periodic solution to the KP-I equation, and two classes of periodic soliton solutions in different directions to KP-Ⅱ are obtained using the bilinear form, homoclinic test technique and temporal and 1 spatial transformation method, respectively. The equilibrium solution uo =-1/6, a unique spatial-temporal bifurcation which is periodic bifurcation for KP-I and deflexion of soliton for KP-Ⅱ, is investigated.

Periodic Homoclinic Wave of （1＋1）-Dimensional Long-Short Wave Equation

The exact periodic homoclinic wave of （1＋1）D long-short wave equation is obtained using an extended homoclinic test technique. This result shows complexity and variety of dynamical behaviour for a （1＋1）-dimensional long-short wave equation.

J/ψ and φ Electro-production in Pomeron Exchange Model

Based on Pomeron exchange model, J/ψ and φ production in electro-proton interaction are investigated with both linear and non-linear Pomeron trajectory. The experimental differential cross sections measured as a function of the kinematic variable Q^2,W and t are reproduced successfully in the model. Our conclusions are that the Pomeron exchange model is a successful description of J/ψ and φ electro-productions on the proton, and that the linear trajectory is a good approximation to non-linearity of the Pomeron trajectory.

Uniqueness of Entire Functions Concerning Differential Polynomials

In this paper,we deal with the uniqueness problems on entire functions concerning differential polynomials that share one small function.Moreover,we improve some former results of M Fang and W Lin.

Some Properties of a Kind of Singular Integral Operator with Weierstrass Function Kernel

We considered a kind of singular integral operator with Weierstrass function kernel on a simple closed smooth curve in a fundamental period parallelogram. Using the method of complex functions, we established the Bertrand Poincaré formula for changing order of the corresponding integration, and some important properties for this kind of singular integral operator.

Coordinated Control of Traffic Signals for Multiple Intersections

The proper phase difference of traffic signals for adjacent intersections could decrease the time of operational delay. Some theorems show how to minimize the total average delay time for vehicle operating at adjacent intersections under given conditions. If the distance and signal cycles of adjacent intersections satisfy with specific conditions, the total average delay time would achieve zero. If the signal cycles of adjacent intersections and the phase difference of them are co-prime numbers, the total average delay time would be a constant. In general, if signal cycles of adjacent intersections and the phase difference of them are reducible numbers, the minimum total average delay time would be solved by the given algorithm. Numerical experiments have verified the rationality of these theorems.

Bounded Nonoscillatory Solutions of Nonlinear Functional Differential Equations

In this paper, we obtain some nonoscillatory theories of the functional differential equation (r(t)ψ(x(t))x (t)) + f(t, x(t), x(σ(t))) = 0, t ≥ t 0 , where r ∈ C 1 ([t 0 , ∞); (0, ∞)), ψ∈ C 1 (R, R) and f ∈ C([t 0 , ∞) × R × R, R).

Prediction of Cosmological Constant Λ in Veneziano Ghost Theory of QCD

Based on the Veneziano ghost theory of QCD, we estimate the cosmological constant Λ, which is related to the vacuum energy density, , by =8πG . In the recent Veneziano ghost theory is given by the absolute value of the product of the local quark condensate and quark current mass: =(2NfH/m)*c|mq<0|:qq:|0>|.By solving Dyson-Schwinger Equations for a dressed quark propagator, we found the local quark condensate;-(235 MeV)3, the generally accepted value. The quark current mass is mq 4.0 Mev. This gives the same result for as found by previous authors, which is somewhat larger than the observed value. However, when we make use of the nonlocal quark condensate, =g(x), with g(x) estimated from our previous work, we find Λ is in a good agreement with the observations.