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.

REGULAR SOLUTIONS FOR SCHRODINGER EQUATION ON UNBOUNDED DOMAINS

The authors study a class of solutions,namely, regular solutions of the Schrodinger equation (1/2 Delta + q)u = 0 on unbounded domains. They definite the regular solutions in terms of sample path properties of Brownian motion and then characterize them by analytic method. In Section 4, they discuss the regular solution to the stochastic Dirichlet problem for the equation (1/2 Delta + q)u = 0 having limit alpha at infinity.

Non-Global Existence of Regular Solution to Initial Value Problem of Relativistic Euler Equations in R^(N)

In fluid mechanics and astrophysics,relativistic Euler equations can be used to describe the effects of special relativity which are an extension of the classical Euler equations.In this paper,we will consider the initial value problem of relativistic Euler equations in an initial bounded region of R N.If the initial velocity satisfies max→x 0∈∂Ω(0)N∑i=1 v_(i)^(2)(0,→x 0)<c^(2)A_(1)/2,where A 1 is a positive constant depend on some sufficiently large T^(*),then we can get the non-global existence of the regular solution for the N-dimensional relativistic Euler equations.

The Regularity of Solutions to Mixed Boundary Value Problems of Second-Order Elliptic Equations with Small Angles

This paper considers the regularity of solutions to mixed boundary value problems in small-angle regions for elliptic equations. By constructing a specific barrier function, we proved that under the assumption of sufficient regularity of boundary conditions and coefficients, as long as the angle is sufficiently small, the regularity of the solution to the mixed boundary value problem of the second-order elliptic equation can reach any order.

THE REGULAR SOLUTIONS OF THE ISENTROPIC EULER EQUATIONS WITH DEGENERATE LINEAR DAMPING

The regular solutions of the isentropic Euler equations with degenerate linear damping for a perfect gas are studied in this paper. And a critical degenerate linear damping coefficient is found, such that if the degenerate linear damping coefficient is larger than it and the gas lies in a compact domain initially, then the regular solution will blow up in finite time; if the degenerate linear damping coefficient is less than it, then under some hvpotheses on the initial data. the regular solution exists globally.

Calculation of Activity Coefficient from Immiscible Binary Alloy Phase Diagram by Means of Modified Sub-regular Solution Model

The modified sub regular solution model was used for a calculation of the activity coefficient of immiscible binary alloy systems. The parameters needed for the calculation are the interaction parameters, λ 1 and λ 2, which are represented as a linear function of temperature, T . The molar excess Gibbs free energy, G m E, can be written in the form G m E= x A x B[( λ 11 + λ 12 T )+( λ 21 + λ 22 T ) x B ] The calculation is carried out numerically for three immiscible binary alloy systems, Al Pb, Cu Tl and In V. The agreement between the calculated and experimentally determined values of activity coefficient is excellent.

Regular Solution and Lattice Miura Transformation of Bigraded Toda Hierarchy

The authors give finite dimensional exponential solutions of the bigraded Toda hierarchy （BTH）. As a specific example of exponential solutions of the BTH, the authors consider a regular solution for the （1, 2）-BTH with a 3 × 3-sized Lax matrix, and discuss some geometric structures of the solution from which the difference between the （1, 2）- BTH and the original Toda hierarchy is shown. After this, the authors construct another kind of Lax representation of （N, 1）-BTH which does not use the fractional operator of Lax operator. Then the authors introduce the lattice Miura transformation of （N, 1）-BTH which leads to equations depending on one field, and meanwhile some specific examples which contain the Volterra lattice equation （a useful ecological competition model） are given.

On Blow-up of Regular Solutions to the Isentropic Euler and Euler-Boltzmann Equations with Vacuum

In this paper,the authors study the Cauchy problem of n-dimensional isentropic Euler equations and Euler-Boltzmann equations with vacuum in the whole space.They show that if the initial velocity satisfies some condition on the integral J in the"isolated mass group"(see(1.13)),then there will be finite time blow-up of regular solutions to the Euler system with J≤0(n≥1)and to the Euler-Boltzmann system with J<0(n≥1)and J=0(n≥2),no matter how small and smooth the initial data are.It is worth mentioning that these blow-up results imply the following:The radiation is not strong enough to prevent the formation of singularities caused by the appearance of vacuum,with the only possible exception in the case J=0 and n=1 since the radiation behaves differently on this occasion.

Activity Calculation in Complex Metallurgical Molten Slag Systems Based on Regular Solution Model

The activity of FetO is very important in ironmaking and steelmaking process. In order to predict the activ- ity of Fe, O and optimize the operation conditions in ironmaking and steelmaking process, by application of regular so lution model in molten slag systems, FeO-Fe2 O3-SIO2 ternary system, FeO-Fe2 O3-SiO2-CaO and FeO-Fe2 O3-SiO2-NiO quaternary systems have been studied by the chemical equilibrium between H2/H20 gas mixture and liquid slag con tained in solid iron. The values of interaction energy between cations concerning steelmaking slags have been deter- mined by application of ferric-ferrous iron equilibrium and iron-ferric iron equilibrium. And then the activity of Fe, O can be calculated. The results show that the relative error is 3.9% in FeO-Fe203-SiO2 system and 18% in FeO- Fe203-SiO2 CaO system. The prediction of activities of FetO in the systems are in good agreement with the measure- ments and the regular solution model is valid for predicting the activity of FetO in complex molten slags systems. The activity of Fe, O in FeO-Fe20a-NiO system have not been tested presently, and the calculated result can not be assessed.

Unbiased Estimation Formula of Unit Weight Standard Deviation in Regularization Solution

Regularization method is an effective method for solving ill\|posed equation. In this paper the unbiased estimation formula of unit weight standard deviation in the regularization solution is derived and the formula is verified with numerical case of 1 000 sample data by use of the typical ill\|posed equation, i.e. the Fredholm integration equation of the first kind.

THE REGULARIZED SOLUTION APPROXIMATION OF FORWARD/BACKWARD PROBLEMS FOR A FRACTIONAL PSEUDO-PARABOLIC EQUATION WITH RANDOM NOISE

This paper deals with the forward and backward problems for the nonlinear fractional pseudo-parabolic equation ut+(-Δ)^(s1)ut+β(-Δ)^(s2)u=F(u,x,t)subject o random Gaussian white noise for initial and final data.Under the suitable assumptions s1,s2andβ,we first show the ill-posedness of mild solutions for forward and backward problems in the sense of Hadamard,which are mainly driven by random noise.Moreover,we propose the Fourier truncation method for stabilizing the above ill-posed problems.We derive an error estimate between the exact solution and its regularized solution in an E‖·‖Hs22norm,and give some numerical examples illustrating the effect of above method.

ON THE REGULARITY OF THE MINIMUM SOLUTION OF THE RESTRAINED VARIATIONAL PROBLEMS

This paper is concerned with the regularity of minimum solution u of the following functional L(u) = integral(Omega) a alpha(beta)(x)g(ij)(u)D alpha u(i)D(beta)upsilon(i)dx on the restraint E = {u is an element of W-0(1,2) (Omega, R(N))\parallel to u parallel to L(D) = 1}. Under appropriate conditions, the bounded minimum solution u of the above functional is proved to be nothing but Holder continuous.

REGULARIZATION METHOD FOR IMPROVING OPTIMAL CONVERGENCE RATE OF THE REGULARIZED SOLUTION OF ILL-POSED PROBLEMS

This paper presents anew regularization method for solving operator equations of the first kind; the convergence rate of the regularized solution is improved, as compared with the ordinary Tikhonov regularization.

A FUNDAMENTAL SOLUTION FOR THE LAPLACE OPERATOR ON THE QUATERNIONIC HEISENBERG GROUP

In this paper, the author studies the Laplace operator on the quaternionic Heisenberg group, construct a fundamental solution for it and use this solution to prove the L-p-boundedness and the weak (1-1) boundedness of certain singular convolution operators on the quaternionic Heisenberg group.

Inversion and III-Posed Problem Solutions in Atmospheric Remote Sensing

With the swift advances in earth observation,satellite remote sensing and application of atmospheric radiation theory have been developed in the past decades,atmospheric sensing inversion with its algorithms is getting more and more importance.It is known that since a remote sensing equation falls into an integral equation of the first kind,thus leading to the fact that it is ill-posed and particularly the solution is unsteady,tremendous difficulties arise from the retrieval.This paper will present a simple review on the inversion techniques with some necessary remarks,before introducing the successful efforts with respect to such equations and the encouraging solutions achieved in recent decades by researchers of the world.

Thermodynamic analysis of β → α(α_2) phase transformation temperature in a Ti-Al-H alloy system

The T0 face equation of a Ti-Al-H alloy system was set up by the regular solution model,and the relationship between the β phase stabilizing parameter of hydrogen and the equilibrium phase compositions was attained.According to the T0 face equation and the thermodynamic parameters from literature,the effect of hydrogen on the β→α（α2） transformation temperature was evaluated.The calculated results were in a better consistence with the measured ones.

ON SPINODAL BOUNDARIES OF Al-Li ALLOYS

The spinodal decomposition can occur in Al-Li alloys containing 5.8-14.2 at.% Li at room temperature. The modutated structure wavelength is approximately 3.1 nm for com mercial Al-LI alloys. The limit composition of the miscibility gap is 3.66 -16.06 at.%Li at 298 K. The highest temperature of the miscibility gap is 377 K.

An extension result for the Landau-Lifshitz equation with Neumann boundary condition

We establish an extension result of existence and partial regularity for the nonzero Neumann initial-boundary value problem of the Landau-Lifshitz equation with nonpositive anisotropy constants in three or four dimension space. The partial regularity is proved up to the boundary and this result is an important supplement to those for the Dirichlet problem or the homogeneous Neumann problem.

Nested regular polygon solutions for planar 2N-body problems

In this paper we study the necessary conditions for the masses of the nested regular polygon solutions of the planar 2N-body problem.We prove that the masses at the vertices of each regular polygon must be equal to each other.

An iterative algorithm for solving ill-conditioned linear least squares problems

Linear Least Squares（LLS） problems are particularly difficult to solve because they are frequently ill-conditioned, and involve large quantities of data. Ill-conditioned LLS problems are commonly seen in mathematics and geosciences, where regularization algorithms are employed to seek optimal solutions. For many problems, even with the use of regularization algorithms it may be impossible to obtain an accurate solution. Riley and Golub suggested an iterative scheme for solving LLS problems. For the early iteration algorithm, it is difficult to improve the well-conditioned perturbed matrix and accelerate the convergence at the same time. Aiming at this problem, self-adaptive iteration algorithm（SAIA） is proposed in this paper for solving severe ill-conditioned LLS problems. The algorithm is different from other popular algorithms proposed in recent references. It avoids matrix inverse by using Cholesky decomposition, and tunes the perturbation parameter according to the rate of residual error decline in the iterative process. Example shows that the algorithm can greatly reduce iteration times, accelerate the convergence,and also greatly enhance the computation accuracy.