A New Method for Achieving an Initial Regular Solution of a Linear Programming

A method is provided for finding an initial regular solution of a linear programming in this paper. The key to this method is to solve an auxiliary linear programming instead of to introduce any artificial variable or constraint. Compared with the traditional method of achieving the regular solution by introducing an artificial constraint, it has advantages of saving the memories and little computational efforts.

Least Squares Solution for Discrete Time Nonlinear Stochastic Optimal Control Problem with Model-Reality Differences

In this paper, an efficient computational approach is proposed to solve the discrete time nonlinear stochastic optimal control problem. For this purpose, a linear quadratic regulator model, which is a linear dynamical system with the quadratic criterion cost function, is employed. In our approach, the model-based optimal control problem is reformulated into the input-output equations. In this way, the Hankel matrix and the observability matrix are constructed. Further, the sum squares of output error is defined. In these point of views, the least squares optimization problem is introduced, so as the differences between the real output and the model output could be calculated. Applying the first-order derivative to the sum squares of output error, the necessary condition is then derived. After some algebraic manipulations, the optimal control law is produced. By substituting this control policy into the input-output equations, the model output is updated iteratively. For illustration, an example of the direct current and alternating current converter problem is studied. As a result, the model output trajectory of the least squares solution is close to the real output with the smallest sum squares of output error. In conclusion, the efficiency and the accuracy of the approach proposed are highly presented.

GLOBAL EXISTENCE OF WEAKLY DISCONTINUOUS SOLUTIONS TO A KIND OF MIXED INITIAL-BOUNDARY VALUE PROBLEM FOR QUASILINEAR HYPERBOLIC SYSTEMS

In this paper, the mixed initial-boundary value problem for general first order quasi- linear hyperbolic systems with nonlinear boundary conditions in the domain D = {（t, x） ｜ t ≥ 0, x ≥0} is considered. A sufficient condition to guarantee the existence and uniqueness of global weakly discontinuous solution is given.

Exact solution of the one-dimensional Klein-Gordon equation with scalar and vector linear potentials in the presence of a minimal length

Using the momentum space representation, we solve the Klein--Gordon equation in one spatial dimension for the case of mixed scalar and vector linear potentials in the context of deformed quantum mechanics characterized by a finite minimal uncertainty in position. The expressions of bound state energies and the associated wave functions are exactly obtained.

Alternating segment explicit-implicit scheme for nonlinear third-order KdV equation

A group of asymmetric difference schemes to approach the Korteweg-de Vries （KdV） equation is given here. According to such schemes, the full explicit difference scheme and the full implicit one, an alternating segment explicit-implicit difference scheme for solving the KdV equation is constructed. The scheme is linear unconditionally stable by the analysis of linearization procedure, and is used directly on the parallel computer. The numerical experiments show that the method has high accuracy.

Statistical Thermodynamic Properties of Linear Protein Solutions

The thermodynamic properties of linear protein solutions are discussed by a statistical me-chanics theory with a lattice model. The numerical results show that the Gibbs function of the solution decreases, and the protein chemical potential is enhanced with increase of the protein concentration for dilute solutions. The influences of chain length and temperature on the Gibbs function of the solution as well as the protein chemical potential are analyzed.As an application of the theory, the chemical potentials of some mutants of type I antifreeze proteins are computed and discussed.

ON GLOBAL MEROMORPHIC SOLUTIONS OF SECOND-ORDER LINEAR DIFFERENTIAL EQUATIONS WITH MEROMORPHIC COEFFICIENTS

The main purpose of this article is to study the existence theories of global meromorphic solutions for some second-order linear differential equations with meromorphic coefficients, which perfect the solution theory of such equations.

POSITIVE PERIODIC SOLUTION FOR A NONAUTONOMOUS LOGISTIC MODEL WITH LINEAR FEEDBACK REGULATION

A nonautonomous delayed logistic model with linear feedback regulation is proposed in this paper. Sufficient conditions are derived for the existence, uniqueness and global asymptotic stability of positive periodic solution of the model

ON THE HOLOMORPHIC SOLUTION OF NON-LINEAR TOTALLY CHARACTERISTIC EQUATIONS WITH SEVERAL SPACE VARIABLES

In this paper the authors study a class of non-linear singular partial differential equation in complex domain C-t x C-x(n). Under certain assumptions, they prove the existence and uniqueness of holomorphic solution near origin of C-t x C-x(n).

MULTIPLE POSITIVE SOLUTIONS FOR A CLASS OF QUASI-LINEAR ELLIPTIC EQUATIONS INVOLVING CRITICAL SOBOLEV EXPONENT

In this paper, we study the multiplicity results of positive solutions for a class of quasi-linear elliptic equations involving critical Sobolev exponent. With the help of Nehari manifold and a mini-max principle, we prove that problem admits at least two or three positive solutions under different conditions.

On growth of meromorphic solutions of some kind of non-homogeneous linear difference equations

In this paper,we investigate the growth of meromorphic solutions of some kind of non-homogeneous linear difference equations with special meromorphic coefficients.When there are more than one coefficient having the same maximal order and the same maximal type,the estimates on the lower bound of the order of meromorphic solutions of the involved equations are obtained.Meanwhile,the above estimates are sharpened by combining the relative results of the corresponding homogeneous linear difference equations.

PCR ALGORITHM FOR PARALLEL COMPUTING MINIMUM-NORM LEAST-SQUARES SOLUTION OF INCONSISTENT LINEAR EQUATIONS

This paper presents a new highly parallel algorithm for computing the minimum-norm least-squares solution of inconsistent linear equations Ax = b(A∈Rm×n,b∈R (A)). By this algorithm the solution x = A + b is obtained in T = n(log2m + log2(n - r + 1) + 5) + log2m + 1 steps with P=mn processors when m × 2(n - 1) and with P = 2n(n - 1) processors otherwise.

DIFFERENTIATOR SERIES SOLUTION OF LINEAR DIFFERENTIAL ORDINARY EQUATION

In this paper, the principle techinique of the differentiator method, and some examples using the method to obtain the general solution and special solution of the differential equation are introduced. The essential difference between this method and the others is that by this method special and general solutions can be obtained directly with the operations of the differentor in the differential equation and without the enlightenment of other scientific knowledge.

Exact solution to the one-dimensional Dirac equation of linear potential

In this paper the one-dimensional Dirac equation with linear potential has been solved by the method of canonical transformation. The bound-state wavefunctions and the corresponding energy spectrum have been obtained for all bound states.

Exact solutions and linear stability analysis for two-dimensional Ablowitz Ladik equation

The Ablowitz-Ladik equation is a very important model in nonlinear mathematical physics. In this paper, the hyper- bolic function solitary wave solutions, the trigonometric function periodic wave solutions, and the rational wave solutions with more arbitrary parameters of two-dimensional Ablowitz-Ladik equation are derived by using the （GI/G）-expansion method, and the effects of the parameters （including the coupling constant and other parameters） on the linear stability of the exact solutions are analysed and numerically simulated.

Periodic solutions and flip bifurcation in a linear impulsive system

In this paper, the dynamical behaviour of a linear impulsive system is discussed both theoretically and numerically. The existence and the stability of period-one solution are discussed by using a discrete map. The conditions of existence for flip bifurcation are derived by using the centre manifold theorem and bifurcation theorem. The bifurcation analysis shows that chaotic solutions appear via a cascade of period-doubling in some interval of parameters. Moreover, the periodic solutions, the bifurcation diagram, and the chaotic attractor, which show their consistence with the theoretical analyses, are given in an example.

Linearization and analytic solution of fluid dynamics of cell two-phase flow

Linearized equations of fluid dynamics of cell two phase flow for one dimensional case are proposed. Based on the equations, an analytic solution is derived, in which the frequency of wave is observed. The frequency formula consists of all important parameters of the fluid dynamics. In our observation, the group velocity and phase velocity of the motion of wave propagation are explicitly exhibited as well.

A Way to Find All the Optimal Solutions in Linear Programming

With the expression theorem of convex polyhedron, this paper gives the general expression for the solutions in standard linear programming problems. And the calculation procedures in determining the optimal solutions are also given.

PERIODIC SOLUTIONS OF LINEAR NEUTRAL INTEGRO-DIFFERENTIAL EQUATIONS

Consider the linear neutral FDEd/dt[x(t) + Ax(t - r)] = R [dL(s)]x(t + s) + f(t)where x and / are ra-dimensional vectors; A is an n x n constant matrix and L(s) is an n x n matrix function with bounded total variation. Some necessary and sufficient conditions are given which guarantee the existence and uniqueness of periodic solutions to the above equation.

Exact Solution of a Linear Difference Equation in a Finite Number of Steps

An exact solution of a linear difference equation in a finite number of steps has been obtained. This refutes the conventional wisdom that a simple iterative method for solving a system of linear algebraic equations is approximate. The nilpotency of the iteration matrix is the necessary and sufficient condition for getting an exact solution. The examples of iterative equations providing an exact solution to the simplest algebraic system are presented.