SELECTION OF STATE VARIABLES AND CONSTRUCTION OF STATE EQUATIONS

In modern control engineering and simulations,it is perferable to get the governing equationsby an easier way,so that state equations have been widely used.There are many rules to select statevariables,but the uses of these rules may have different forms of limitations and exceptions,yet afully argumented bond graph can be processed in proper way to select the state variables and toyield the state equations.The state variables are usually related to the energy-storing elements.State equations can easily be derived from bond graph by means of constitutive relations and struc-tural relations.     

THE EXISTENCE OF SOLUTIONS OF SYSTEMS OF NONLINEAR HAMMERSTEIN TYPE INTEGRAL EQUATIONS

This paper makes use of the theory of characteristic values and characteristic functions and the theoryof topological degree in studying the solutions of systems of Hammerstein-type equations;where G is a bounded closed set in R~ , and mes G ≠0.Equations (1) can be rewritten as the following operator equationSuppose that P is a cone in C~no:     

THE FREDHOLM THEOREM FOR SYSTEMS OF INTEGRO-FUNCTIONAL EQUATIONS

Some problems of hyperbolic systems of partial differential equations can be turned into systems of in-tegro-functional equations of the following form[1]here F(x) = (f_1(x),…,f_m(x))~T and H(x)=(h_1(x),…,t_m(x))~T both belong to (C~∞[-R,R])~m, are theunknown and know vector functions respectively; λis a parameter, 0相似文献   

SOME PROPERTIES OF SOLUTIONS OF ONE-DIMENSIONAL STOCHASTIC DIFFERENTIAL EQUATIONS WITH GENERAL COEFFICIENTS

In this paper, the one-dimensional time-homogenuous lto's stochastic differential equations, which have degenerate and discontinuous diffusion coefficients, are considered. The non-confluent property of solutions is showed under some local integrability condition on the diffusion and drift coefficients. The strong comparison theorem for solutions is also established.     

NONHOMOGENEOUS PROBLEM E FOR THE SYSTEMS OF PARTIAL DIFFERENTIAL EQUATIONS OF COMPOSITE TYPE

In this paper, we first consider the following problem;Problem Ewhere G is a simple connected domain, L~0 is an elliptic operator, a_(1、1)(z)and b_(2,0)(z) are real functions, u is required to satisfy the following conditions;S_ = {(t,z) |t> O,z ∈ G}. We suppose that the coefficient functions are all differentiable and integrable(belong to w_2~(2)( ) ).First, let f~* (t,z) ≠0, g_1(t,z) = g_2(t,z) 0. Assume that {v_k}, {w_k} are the system of eigenfunc-     

ON THE INITIAL-BOUNDARY VALUE PROBLEM FOR THE SYSTEM OF MULTI-DIMENSIONAL GENERSALIZED BBM EQUATIONS AND KdV EQUATIONS

The Benjamin-Bona-Mahony (BBM) equationu_1+UU_x-u_(xxt)=0and the Korteweg-de Vries (KdV) equationu_1+uu_z+u_(xxx)=0have both been proposed as models for long waves in nonlinear dispersive systems and the Cauchy's problemwas studied for the above equations.1 We consider the periodic boundary value problem for the system of n-dimensional generalized BBMequationswhere be a n-dimensional cube with21 in each direction,and _0(x) is a n-dimensional periodic functional     

THE CALCULATING EQUATIONS OF THE THERMOPHYSICAL PARAMETERS OF THE MOIST AIR AT HIGH TEMPERATURE

By using compression factors of real gas and the Vilia equations and considering the variation of the thermophysical parameters of the mois air with its temperature, this paper develops the calculating equations of the thermophysical para leters of the moist air at high temperature ranging from 100℃- 200℃. It is convenient to calculate the thermophysical parameters and the thermophysical processes of the moist air at high temperature.     

SINGULAR PERTURBATION PROBLEM FOR THE SYSTEM OF LINEAR INTEGRAL EQUATIONS

In the paper we use the boundary layer function method (cf,[1]) to consider the following problem;where y,f and z,g are m and r-dimensional vector value functions respectively; f,g are smooth enough on[0,1]×[O,ε_0] for some ε_0>0; k_(ij);, i, j=1,2, with the corresponding order for the system are smoothenough on [0,1]×[0, 1] except for the line x=s and there are jumps:J_(ij)(x) = K_(ij)(x,x~-) -K_(ij)(x,x~+), x∈[0, 1],i,j = 1,2.At the first, we make the hypothesis as follows(I) J_(22)(x)∈C([0,1]), and its all eigenvalues have nonzero real parts for x∈[0,1].By the condition we can take the kernel matrices and vector functions of (1) in following block forms:     

THE BASIC THEORY OF SOLUTIONS OF FUNCTIONAL DIFFERENTIAL EQUATIONS WITH BOUNDED DELAY IN THE SPACE OF INTEGRABLE FUNCTIONS

在可积函数空间中讨论有界滞量泛函微分方程，建立其解的基本理论，包括解的存在性，唯一性及延展性。     

BOUNDARY VALUE PROBLEMS OF QUASILINEAR ELLIPTIC SYSTEM OF FIRST ORDER EQUATIONS IN SEVERAL BICYLINDER DOMAIN

Suppose D=D_1x…x D_z,D_j={|z_j|p_j}, = x… _, _j={|t_j|=p_j},0相似文献   

EXISTENCE AND REGULARITY OF POSITIVE SOLUTIONS OF THE ELLIPTIC EQUATIONS INVOLVING CRITICAL NONLINEAR AND SUBLINEAR

0 IntroductionLet Ωbe a smooth bounded domain in R~n with n>3, consider the problem of finding a function u(x)which satisfieswhere 0<α<1, 1 1 there is asolution of (0. 1) for any λ>0.The principal tecncihique of argument in [1] is using positive radial solution (0. 3) of equation -△u=u~2~n-1 in R~*.     

MIXED BOUNDARY VALUE PROBLEM FOR SECOND ORDER SYSTEM OF DIFFERENTIAL EQUATIONS OF THE ELLIPTIC TYPE

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