Abstract: We apply the Izergin-Korepin analysis to the study of the projected wavefunctions of the generalized free-fermion model. We introduce a generalization of the -operator of the six-vertex model by Bump-Brubaker-Friedberg and Bump-McNamara-Nakasuji. We make the Izergin-Korepin analysis to characterize the projected wavefunctions and show that they can be expressed as a product of factors and certain symmetric functions which generalizes the factorial Schur functions. This result can be seen as a generalization of the Tokuyama formula for the factorial Schur functions. PubDate: Tue, 20 Jun 2017 00:00:00 +000

Abstract: We study the quantum cosmology of a quadratic theory with a FRW metric, via one of its equivalent Horndeski type actions, where the dynamic of the scalar field is induced. The classical equations of motion and the Wheeler-DeWitt equation, in their exact versions, are solved numerically. There is a free parameter in the action from which two cases follow: inflation + exit and inflation alone. The numerical solution of the Wheeler-DeWitt equation depends strongly on the boundary conditions, which can be chosen so that the resulting wave function of the universe is normalizable and consistent with Hermitian operators. PubDate: Sun, 18 Jun 2017 00:00:00 +000

Abstract: Based on the three-dimensional real special orthogonal Lie algebra , by zero curvature equation, we present bi-integrable and tri-integrable couplings associated with for a hierarchy from the enlarged matrix spectral problems and the enlarged zero curvature equations. Moreover, Hamiltonian structures of the obtained bi-integrable and tri-integrable couplings are constructed by applying the variational identities. PubDate: Sun, 04 Jun 2017 07:14:24 +000

Abstract: On the basis of fluid approximation, an improved version of the model for the description of dc glow discharge plasma in the axial magnetic field was successfully developed. The model has yielded a set of analytic formulas for the physical quantities concerned from the electron and ion fluids equations and Poisson equation. The calculated results satisfy the practical boundary conditions. Results obtained from the model reveal that although the differential equations under the condition of axial magnetic field are consistent with the differential equations without considering the magnetic field, the solution of the equations is not completely consistent. The results show that the stronger the magnetic field, the greater the plasma density. PubDate: Sun, 28 May 2017 00:00:00 +000

Abstract: The problem of guaranteed cost finite-time control of fractional-order positive switched systems (FOPSS) is considered in this paper. Firstly, a new cost function is defined. Then, by constructing linear copositive Lyapunov functions and using the average dwell time (ADT) approach, a state feedback controller and a static output feedback controller are constructed, respectively, and sufficient conditions are derived to guarantee that the corresponding closed-loop systems are guaranteed cost finite-time stable (GCFTS). Such conditions can be easily solved by linear programming. Finally, two examples are given to illustrate the effectiveness of the proposed method. PubDate: Wed, 24 May 2017 00:00:00 +000

Abstract: We investigate the 3D quasilinear hyperbolic equations with nonlinear damping which describes the propagation of heat wave for rigid solids at very low temperature, below about 20 K. The global existence and uniqueness of strong solutions are obtained when the initial data is near its equilibrium in the sense of -norm. Furthermore, if, additionally, -norm () of the initial perturbation is finite, we also prove the optimal decay rates for such a solution without the additional technical assumptions for the nonlinear damping given by Li and Saxton. PubDate: Tue, 23 May 2017 00:00:00 +000

Abstract: We study the translation invariant properties of the eigenvalues of scattering transmission problem. We examine the functional derivative of the eigenvalue density function to the defining index of refraction . By the limit behaviors in frequency sphere, we prove some results on the inverse uniqueness of index of refraction. In physics, Doppler’s effect connects the variation of the frequency/eigenvalue and the motion velocity/variation of position variable. In this paper, we proved the functional derivative PubDate: Sun, 21 May 2017 00:00:00 +000

Abstract: Globally, cyanobacteria blooms frequently occur, and effective prediction of cyanobacteria blooms in lakes and reservoirs could constitute an essential proactive strategy for water-resource protection. However, cyanobacteria blooms are very complicated because of the internal stochastic nature of the system evolution and the external uncertainty of the observation data. In this study, an adaptive-clustering algorithm is introduced to obtain some typical operating intervals. In addition, the number of nearest neighbors used for modeling was optimized by particle swarm optimization. Finally, a fuzzy linear regression method based on error-correction was used to revise the model dynamically near the operating point. We found that the combined method can characterize the evolutionary track of cyanobacteria blooms in lakes and reservoirs. The model constructed in this paper is compared to other cyanobacteria-bloom forecasting methods (e.g., phase space reconstruction and traditional-clustering linear regression), and, then, the average relative error and average absolute error are used to compare the accuracies of these models. The results suggest that the proposed model is superior. As such, the newly developed approach achieves more precise predictions, which can be used to prevent the further deterioration of the water environment. PubDate: Thu, 04 May 2017 00:00:00 +000

Abstract: HDG method has been widely used as an effective numerical technique to obtain physically relevant solutions for PDE. In a practical setting, PDE comes with nonlinear coefficients. Hence, it is inevitable to consider how to obtain an approximate solution for PDE with nonlinear coefficients. Research on using HDG method for PDE with nonlinear coefficients has been conducted along with results obtained from computer simulations. However, error analysis on HDG method for such settings has been limited. In this research, we give error estimations of the hybridizable discontinuous Galerkin (HDG) method for parabolic equations with nonlinear coefficients. We first review the classical HDG method and define notions that will be used throughout the paper. Then, we will give bounds for our estimates when nonlinear coefficients obey “Lipschitz” condition. We will then prove our main result that the errors for our estimations are bounded. PubDate: Wed, 03 May 2017 00:00:00 +000

Abstract: This study is focused on the pressure blow-up criterion for a smooth solution of three-dimensional zero-diffusion Boussinesq equations. With the aid of Littlewood-Paley decomposition together with the energy methods, it is proved that if the pressure satisfies the following condition on margin Besov spaces, for then the smooth solution can be continually extended to the interval for some . The findings extend largely the previous results. PubDate: Mon, 24 Apr 2017 06:02:54 +000

Abstract: The paper aims to apply the complex-sedenions to explore the wave functions and field equations of non-Abelian gauge fields, considering the spatial dimensions of a unit vector as the color degrees of freedom in the complex-quaternion wave functions, exploring the physical properties of the color confinement essentially. J. C. Maxwell was the first to employ the quaternions to study the electromagnetic fields. His method inspires subsequent scholars to introduce the quaternions, octonions, and sedenions to research the electromagnetic field, gravitational field, and nuclear field. The application of complex-sedenions is capable of depicting not only the field equations of classical mechanics, but also the field equations of quantum mechanics. The latter can be degenerated into the Dirac equation and Yang-Mills equation. In contrast to the complex-number wave function, the complex-quaternion wave function possesses three new degrees of freedom, that is, three color degrees of freedom. One complex-quaternion wave function is equivalent to three complex-number wave functions. It means that the three spatial dimensions of unit vector in the complex-quaternion wave function can be considered as the “three colors”; naturally the color confinement will be effective. In other words, in the complex-quaternion space, the “three colors” are only the spatial dimensions, rather than any property of physical substance. PubDate: Wed, 12 Apr 2017 00:00:00 +000

Abstract: We develop the price game model based on the entropy theory and chaos theory, considering the three enterprises are bounded rationality and using the cost function under the resource constraints; that is, the yield increase will bring increased costs. The enterprises of new model adopt the delay decision with the delay parameters and , respectively. According to the change of delay parameters and , the bifurcation, stability, and chaos of the system are discussed, and the change of entropy when the system is far away from equilibrium is considered. Prices and profits are found to lose stability and the evolution of the system tends to the equilibrium state of maximum entropy. And it has a big fluctuation with the increase of and . In the end, the chaos is controlled effectively. The entropy of the system decreases, and the interior reverts to order. The results of this study are of great significance for avoiding the chaos when the enterprises make price decisions. PubDate: Mon, 10 Apr 2017 00:00:00 +000

Abstract: The exact solutions of the nonlinear vibration systems are extremely complicated to be received, so it is crucial to analyze their approximate solutions. This paper employs the spreading residue harmonic balance method (SRHBM) to derive analytical approximate solutions for the fifth-order nonlinear problem, which corresponds to the strongly nonlinear vibration of an elastically restrained beam with a lumped mass. When the SRHBM is used, the residual terms are added to improve the accuracy of approximate solutions. Illustrative examples are provided along with verifying the accuracy of the present method and are compared with the HAM solutions, the EBM solutions, and exact solutions in tables. At the same time, the phase diagrams and time history curves are drawn by the mathematical software. Through analysis and discussion, the results obtained here demonstrate that the SRHBM is an effective and robust technique for nonlinear dynamical systems. In addition, the SRHBM can be widely applied to a variety of nonlinear dynamic systems. PubDate: Mon, 10 Apr 2017 00:00:00 +000

Abstract: This paper considers the problem of designing a genetic circuit which is robust to noise effect. To achieve this goal, a mixed and Integral Quadratic Constraints (IQC) approach is proposed. In order to minimize the effects of external noise on the genetic regulatory network in terms of norm, a design procedure of Hill coefficients in the promoters is presented. The IQC approach is introduced to analyze and guarantee the stability of the designed circuit. PubDate: Thu, 06 Apr 2017 00:00:00 +000

Abstract: Supercavity can increase speed of underwater vehicles greatly. However, external interferences always lead to instability of vehicles. This paper focuses on robustness of supercavitating vehicles. Based on a 4-dimensional dynamic model, the existence of multistability is verified in supercavitating system through simulation, and the robustness of vehicles varying with parameters is analyzed by basins of attraction. Results of the research disclose that the supercavitating system has three stable states in some regions of parameters space, namely, stable, periodic, and chaotic states, while in other regions it has various multistability, such as coexistence of two types of stable equilibrium points, coexistence of a limit cycle with a chaotic attractor, and coexistence of 1-periodic cycle with 2-periodic cycle. Provided that cavitation number varies within a small range, with increase of the feedback control gain of fin deflection angle, size of basin of attraction becomes smaller and robustness of the system becomes weaker. In practical application, robustness of supercavitating vehicles can be improved by setting parameters of system or adjusting initial launching conditions. PubDate: Wed, 05 Apr 2017 00:00:00 +000

Abstract: We consider a particular type of continuous time random walk where the jump lengths between subsequent waiting times are correlated. In a continuum limit, the process can be defined by an integrated Brownian motion subordinated by an inverse -stable subordinator. We compute the mean square displacement of the proposed process and show that the process exhibits subdiffusion when , normal diffusion when , and superdiffusion when . The time-averaged mean square displacement is also employed to show weak ergodicity breaking occurring in the proposed process. An extension to the fractional case is also considered. PubDate: Tue, 04 Apr 2017 06:45:08 +000

Abstract: We propose combining the adjoint assimilation method with characteristic finite difference scheme (CFD) to solve the aerosol transport problems, which can predict the distribution of atmospheric aerosols efficiently by using large time steps. Firstly, the characteristic finite difference scheme (CFD) is tested to compute the Gaussian hump using large time step sizes and is compared with the first-order upwind scheme (US1) using small time steps; the US1 method gets error of 0.2887 using , while CFD method gets a much smaller of 0.2280 using a much larger time step . Then, the initial distribution of concentration is inverted by the adjoint assimilation method with CFD and US1. The adjoint assimilation method with CFD gets better accuracy than adjoint assimilation method with US1 while adjoint assimilation method with CFD costs much less computational time. Further, a real case of concentration distribution in China during the APEC 2014 is simulated by using adjoint assimilation method with CFD. The simulation results are in good agreement with the observed values. The adjoint assimilation method with CFD can solve large scale aerosol transport problem efficiently. PubDate: Thu, 30 Mar 2017 06:17:05 +000

Abstract: The modified function projective lag synchronization of the memristor-based five-order chaotic circuit system with unknown bounded disturbances is investigated. Based on the LMI approach and Lyapunov stability theorem, an adaptive control law is established to make the states of two different memristor-based five-order chaotic circuit systems asymptotically synchronized up to a desired scaling function matrix, while the parameter controlling strength update law is designed to estimate the parameters well. Finally, the simulation is put forward to demonstrate the correctness and effectiveness of the proposed methods. The control method involved is simple and practical. PubDate: Thu, 23 Mar 2017 09:17:17 +000

Abstract: In this paper, numerical simulations are performed in a single and double lid driven square cavity to study the flow of a Bingham viscoplastic fluid. The governing equations are discretized with the help of finite element method in space and the nonconforming Stokes element is utilized which gives 2nd-order accuracy for velocity and 1st-order accuracy for pressure. The discretized systems of nonlinear equations are treated by using the Newton method and the inner linear subproablems are solved by the direct solver UMFPACK. A qualitative comparison is done with the results reported in the literature. In addition to these comparisons, some new reference data for the kinetic energy is generated. All these implementations are done in the open source software package FEATFLOW which is a general purpose finite element based solver package for solving partial differential equations. PubDate: Mon, 20 Mar 2017 08:56:53 +000

Abstract: The Korteweg-de Vries (KdV) equation, especially the fractional higher order one, provides a relatively accurate description of motions of long waves in shallow water under gravity and wave propagation in one-dimensional nonlinear lattice. In this article, the generalized -expansion method is proposed to construct exact solutions of space-time fractional generalized fifth-order KdV equation with Jumarie’s modified Riemann-Liouville derivatives. At the end, three types of exact traveling wave solutions are obtained which indicate that the method is very practical and suitable for solving nonlinear fractional partial differential equations. PubDate: Mon, 20 Mar 2017 07:45:46 +000

Abstract: We consider a kind of second-order neutral functional differential equation. On the basis of Mawhin’s coincidence degree, the existence and uniqueness of periodic solutions are proved. It is indicated that the result is related to the deviating arguments. Moreover, we present two simulations to demonstrate the validity of analytical conclusion. PubDate: Sun, 19 Mar 2017 00:00:00 +000

Abstract: Ground-supported cylindrical tanks are strategically very important structures used to store a variety of liquids. This paper presents the theoretical background of fluid effect on tank when a fluid container is subjected to horizontal acceleration. Fluid excites the hydrodynamic (impulsive and convective) pressures, impulsive and convective (sloshing) actions. Seismic response of cylindrical fluid filling tanks fixed to rigid foundations was calculated for variation of the tank slenderness parameter. The calculating procedure has been adopted in Eurocode 8. PubDate: Sun, 19 Mar 2017 00:00:00 +000

Abstract: We focus on developing the finite difference (i.e., backward Euler difference or second-order central difference)/local discontinuous Galerkin finite element mixed method to construct and analyze a kind of efficient, accurate, flexible, numerical schemes for approximately solving time-space fractional subdiffusion/superdiffusion equations. Discretizing the time Caputo fractional derivative by using the backward Euler difference for the derivative parameter () or second-order central difference method for (), combined with local discontinuous Galerkin method to approximate the spatial derivative which is defined by a fractional Laplacian operator, two high-accuracy fully discrete local discontinuous Galerkin (LDG) schemes of the time-space fractional subdiffusion/superdiffusion equations are proposed, respectively. Through the mathematical induction method, we show the concrete analysis for the stability and the convergence under the norm of the LDG schemes. Several numerical experiments are presented to validate the proposed model and demonstrate the convergence rate of numerical schemes. The numerical experiment results show that the fully discrete local discontinuous Galerkin (LDG) methods are efficient and powerful for solving fractional partial differential equations. PubDate: Thu, 16 Mar 2017 00:00:00 +000

Abstract: A relaxed secant method is proposed. Radius estimate of the convergence ball of the relaxed secant method is attained for the nonlinear equation systems with Lipschitz continuous divided differences of first order. The error estimate is also established with matched convergence order. From the radius and error estimate, the relation between the radius and the speed of convergence is discussed with parameter. At last, some numerical examples are given. PubDate: Wed, 08 Mar 2017 00:00:00 +000

Abstract: In this paper, we will focus on the dynamical behavior of a rigid body suspended on an elastic spring as a pendulum model with three degrees of freedom. It is assumed that the body moves in a rotating vertical plane uniformly with an arbitrary angular velocity. The relative periodic motions of this model are considered. The governing equations of motion are obtained using Lagrange’s equations and represent a nonlinear system of second-order differential equations that can be solved in terms of generalized coordinates. The numerical solutions are investigated using the fourth-order Runge-Kutta algorithms through Matlab packages. These solutions are represented graphically in order to describe and discuss the behavior of the body at any instant for different values of the physical parameters of the body. The obtained results have been discussed and compared with some previous published works. Some concluding remarks have been presented at the end of this work. The importance of this work is due to its numerous applications in life such as the vibrations that occur in buildings and structures. PubDate: Wed, 08 Mar 2017 00:00:00 +000

Abstract: We propose a new method applying matrix theory to analyse the instability conditions of unique homogeneous coexistent state of multispecies host-parasitoid systems. We consider the eigenvalues of linearized operator of systems, and by dimensionality reduction, this infinite dimensional eigenproblem will be reduced to a parametrized finite dimensional eigenproblem, thereby applying combinatorial matrix theory to analyse the linear instability of such constant steady-state. PubDate: Tue, 28 Feb 2017 14:20:05 +000

Abstract: For point charges of which are negative and equal quasi-exact periodic solutions of their Coulomb equation of motion are found. These solutions describe a motion of the negative charges around a coordinate axis in such a way that their coordinates coincide with vertices of a regular polygon in planes perpendicular to the axis along which the positive charge moves. The Weinstein and center Lyapunov theorems are utilized. PubDate: Tue, 28 Feb 2017 10:12:07 +000

Abstract: A numerical approach is proposed for solving multidimensional parabolic diffusion and hyperbolic wave equations subject to the appropriate initial and boundary conditions. The considered numerical solutions of the these equations are considered as linear combinations of the shifted Bernoulli polynomials with unknown coefficients. By collocating the main equations together with the initial and boundary conditions at some special points (i.e., CGL collocation points), equations will be transformed into the associated systems of linear algebraic equations which can be solved by robust Krylov subspace iterative methods such as GMRES. Operational matrices of differentiation are implemented for speeding up the operations. In both of the one-dimensional and two-dimensional diffusion and wave equations, the geometrical distributions of the collocation points are depicted for clarity of presentation. Several numerical examples are provided to show the efficiency and spectral (exponential) accuracy of the proposed method. PubDate: Wed, 22 Feb 2017 13:37:29 +000