EXISTENCE THEOREMS OF SOLUTIONS FOR TWO－POINT BOUNDARY VALUE PROBLEM OF SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS IN BANACH SPACES

ＥＸＩＳＴＥＮＣＥＴＨＥＯＲＥＭＳＯＦＳＯＬＵＴＩＯＮＳＦＯＲＴＷＯ－ＰＯＩＮＴＢＯＵＮＤＡＲＹＶＡＬＵＥＰＲＯＢＬＥＭＯＦＳＥＣＯＮＤＯＲＤＥＲＯＲＤＩＮＡＲＹＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳＩＮＢＡＮＡＣＨＳＰＡＣＥＳＺｈａｎｇＳｈｉｓ...     

THE BOUNDED EXTERMINATION AND STABILITY OF MUTUAL INTERFERENCE SYSTEM OF FOUR－DIMENSIONAL SPECIES

ＴＨＥＢＯＵＮＤＥＤＥＸＴＥＲＭＩＮＡＴＩＯＮＡＮＤＳＴＡＢＩＬＩＴＹＯＦＭＵＴＵＡＬＩＮＴＥＲＦＥＲＥＮＣＥＳＹＳＴＥＭＯＦＦＯＵＲ－ＤＩＭＥＮＳＩＯＮＡＬＳＰＥＣＩＥＳＨｏｕＧａｎ－ｓｈｅｎｇ（侯赣生）（Ｄｅｐｌ．ｏｆＰｈｙｓｉｃｓ,Ｊｉａｎｇｘ...     

Mixed compatible element and mixed hybrid incompatible element variational methods in dynamics of viscous barotropic fluids

ＭＩＸＥＤＣＯＭＰＡＴＩＢＬＥＥＬＥＭＥＮＴＡＮＤＭＩＸＥＤＨＹＢＲＩＤＩＮＣＯＭＰＡＴＩＢＬＥＥＬＥＭＥＮＴＶＡＲＩＡＴＩＯＮＡＬＭＥＴＨＯＤＳＩＮＤＹＮＡＭＩＣＳＯＦＶＩＳＣＯＵＳＢＡＲＯＴＲＯＰＩＣＦＬＵＩＤＳＳｈｅｎＸｉａｏ－ｍｉｎｇ（沈孝明...     

EIGENFREQUENCIES OF THE THREE DIMENSIONAL EULER－BERNOULLI BEAM SYSTEM WITH DISSIPATIVE JOJNTS

ＥＩＧＥＮＦＲＥＱＵＥＮＣＩＥＳＯＦＴＨＥＴＨＲＥＥＤＩＭＥＮＳＩＯＮＡＬＥＵＬＥＲ－ＢＥＲＮＯＵＬＬＩＢＥＡＭＳＹＳＴＥＭＷＩＴＨＤＩＳＳＩＰＡＴＩＶＥＪＯＪＮＴＳＷｉｌｌｉａｍＨ．Ｐａｕｌｓｅｎ（ＤｅｐａｒｔｍｅｎｔｏｆＣｏｍｐｕｔｅｒＳｃｉｅｎ...     

CONSTRUCTION OF MODIFIED TAYLOR－GALERKIN FINITE ELEMENTS AND ITS APPLICATION IN COMPRESSIBLE FLOW COMPUTATION

ＣＯＮＳＴＲＵＣＴＩＯＮＯＦＭＯＤＩＦＩＥＤＴＡＹＬＯＲ－ＧＡＬＥＲＫＩＮＦＩＮＩＴＥＥＬＥＭＥＮＴＳＡＮＤＩＴＳＡＰＰＬＩＣＡＴＩＯＮＩＮＣＯＭＰＲＥＳＳＩＢＬＥＦＬＯＷＣＯＭＰＵＴＡＴＩＯＮＣＯＮＳＴＲＵＣＴＩＯＮＯＦＭＯＤＩＦＩＥＤＴＡＹＬＯＲ...     

UNCONDITIONAL STABLE SOLUTIONS OF THE EULER EQUATIONS FOR TWO－AND THREE－D WINGS IN ARBITRARY MOTION

ＵＮＣＯＮＤＩＴＩＯＮＡＬＳＴＡＢＬＥＳＯＬＵＴＩＯＮＳＯＦＴＨＥＥＵＬＥＲＥＱＵＡＴＩＯＮＳＦＯＲＴＷＯ－ＡＮＤＴＨＲＥＥ－ＤＷＩＮＧＳＩＮＡＲＢＩＴＲＡＲＹＭＯＴＩＯＮＧａｏＺｈｅｎｇｈｏｎｇ（高正红）（ＲｅｃｅｉｖｅｄＪａｎ．１２,１９９５,Ｃ...     

FORCED OSCILLATIONS OF BOUNDARY VALUE PROBLEMS OF HIGHER ORDER FUNCTIONAL PARTIAL DIFFERENTIAL EQUATIONS

ＦＯＲＣＥＤＯＳＣＩＬＬＡＴＩＯＮＳＯＦＢＯＵＮＤＡＲＹＶＡＬＵＥＰＲＯＢＬＥＭＳＯＦＨＩＧＨＥＲＯＲＤＥＲＦＵＮＣＴＩＯＮＡＬＰＡＲＴＩＡＬＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳＪｉｎＭｉｎｇＺｈｏｎｇ（靳明忠），ＤｏｎｇＹｉｎｇ（董莹），Ｌｉ...     

SPATIAL－TEMPORAL DISCRETE COORDINATION OF FEM AND DIRECT INTEGRAL METHOD FOR TRANSIENT DYNAMIC PROBLEMS

ＳＰＡＴＩＡＬ－ＴＥＭＰＯＲＡＬＤＩＳＣＲＥＴＥＣＯＯＲＤＩＮＡＴＩＯＮＯＦＦＥＭＡＮＤＤＩＲＥＣＴＩＮＴＥＧＲＡＬＭＥＴＨＯＤＦＯＲＴＲＡＮＳＩＥＮＴＤＹＮＡＭＩＣＰＲＯＢＬＥＭＳＷａｎｇＨｕａｉ－ｚｈｏｎｇ（王怀忠）（ＳｈａｎｇｈａｉＵｎｉｖｅｒ...     

NUMERICAL SIMULATION OF THREE DIMENSIONAL TURBULENT FLOW IN SUDDENLY EXPANDED RECTANGULAR DUCT

ＮＵＭＥＲＩＣＡＬＳＩＭＵＬＡＴＩＯＮＯＦＴＨＲＥＥＤＩＭＥＮＳＩＯＮＡＬＴＵＲＢＵＬＥＮＴＦＬＯＷＩＮＳＵＤＤＥＮＬＹＥＸＰＡＮＤＥＤＲＥＣＴＡＮＧＵＬＡＲＤＵＣＴＮＵＭＥＲＩＣＡＬＳＩＭＵＬＡＴＩＯＮＯＦＴＨＲＥＥＤＩＭＥＮＳＩＯＮＡＬＴＵＲＢＵ...     

ON THE EXISTENCE AND STABILITY OF SOLUTION FOR SEMI－HOMOGENEOUS BOUNDARY VALUE PROBLEM

ＯＮＴＨＥＥＸＩＳＴＥＮＣＥＡＮＤＳＴＡＢＩＬＩＴＹＯＦＳＯＬＵＴＩＯＮＦＯＲＳＥＭＩ－ＨＯＭＯＧＥＮＥＯＵＳＢＯＵＮＤＡＲＹＶＡＬＵＥＰＲＯＢＬＥＭＤｏｎｇＱｉｎｘｉ（董勤喜）;ＨｕａｎｇＸｉａｎｋａｉ（黄先开）（ＲｅｃｅｉｖｅｄＪｕｌｙ．４．１９...     

ON SINGULAR PERTURBATION FOR A NONLINEAR INITIAL-BOUNDARY VALUE PROBLEM (Ⅱ)

In this paper, we consider a singularly perturbed problem of a kind of quasilinear hyperbolic-parabolic equations, subject to initial-boundary value conditions with moving boundary: When certain assumptions are satisfied and ε is sufficiently small, the solution of this problem has a generalized asymptotic expansion (in the Van der Corput sense), which takes the sufficiently smooth solution of the reduced problem as the first term, and is uniformly valid in domain Q where the sufficiently smooth solution exists. The layer exists in the neighborhood of t=0. This paper is the development of references [3–5]. The Project supported by the National Natural Science Foundation of China.     

The Steiner problem on a surface

In this paper we generalize the Steiner problem on planes to general regular surfaces. The main result isTheorem 1 If A, B,C are three points on a regular surface Σ and if another point P on Σ such that the sum of the lengths of the smooth arcs AP+ BP + CP reaches the minimum, then the angles formed by every two arcs at P are all 120°.     

A complete expression of the asymptotic solution of differential equation with three-turning points

Ｗｅｈａｖｅｄｉｓｃｕｓｓｅｄｃｏｎｃｅｐｔｏｆｅｑｕａｔｉｏｎｗｉｔｈｎ＿ｔｕｒｎｉｎｇｐｏｉｎｔｓｉｎｍｙｐａｐｅｒ［１］,ｉ．ｅ．,ａｓｅｃｏｎｄｏｒｄｅｒｌｉｎｅａｒｏｒｄｉｎａｒｙｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｄ２ｙｄｘ２＋［λ２ｑ１（ｘ）＋λｑ２（ｘ,λ）］ｙ＝０,ｗｈｅｒｅｑ１（ｘ）＝（ｘ－μ１）（ｘ－μ２）…（ｘ－μｎ）ｆ（ｘ）,ｆ（ｘ）≠０,ａｎｄλｉｓａｌａｒｇｅｐａｒａｍｅｔｅｒ．Ａｌｔｈｒｏｕｇｈｔｈｅｆｉｒｓｔｔｅｒｍｏｆｔｈｅａｓｙｍｐｔｏｔｉｃｅｘｐａｎ…     

On the structure of continua and the mathematical properties of algebraic elastodynamic of a triclinic structural system

This paper is neither laudatory nor derogatory but it simply contrasts with what might be called elastostatic (or static topology), a proposition of the famous six equations. The extension strains and the shearing strains which were derived by A.L. Cauchy, are linearly expressed in terms of nine partial derivatives of the displacement function (u _i ,u _j ,u _h )=u(x ⁱ ,x ^j ,x ^k ) and it is impossible for the inverse proposition to sep up a system of the above six equations in expressing the nine components of matrix (∂(u _i ,u _j ,u _h )/∂(x ⁱ ,x ^j ,x ^k )). This is due to the fact that our geometrical representations of deformation at a given point are as yet incomplete^[1]. On the other hand, in more geometrical language this theorem is not true to any triangle, except orthogonal, for “squared length” in space^[2]. The purpose of this paper is to describe some mathematic laws of algebraic elastodynamics and the relationships between the above-mentioned important questions.     

About a condition for blow up of solutions of cauchy problem for a wave equation

ＣｏｎｓｉｄｅｒｔｈｅＣａｕｃｈｙｐｒｏｂｌｅｍｆｏｒｔｈｅｗａｖｅｅｑｕａｔｉｏｎｉｎＲＮ×Ｒ＋（Ｎ≥２）：２ｕ（ｘ,ｔ）ｔ２－ｘｉａｉｊ（ｘ）ｘｊｕ＝｜ｕ｜ｐ－１·ｕ　　（（ｘ,ｔ）∈ＲＮ×（０,Ｔ））,ｕ（ｘ,０）＝ｇ（ｘ）　（ｘ∈ＲＮ）,ｕｔ（ｘ,０）＝ｈ（ｘ）　（ｘ∈ＲＮ）,（１）ｗｈｅｒｅｕ（ｘ,ｔ）ｉｓｎｏｎｔｒｉｖｉａｌｓｏｌｕｔｉｏｎｗｉｔｈｆｉｎｉｔｅｓｐｅｅｄｏｆｐｒｏｐａｇａｔｉｏｎａｎｄｉｓｓｕｐｐｏｒｔｅｄｏｎａｆｏｒｗａｒｄｃｏｎｅ（ｘ,ｔ）·ｔ≥０,｜…     

The numerical stabilities of multiderivative block method

In [1], a class of multiderivative block methods (MDBM) was studied for the numerical solutions of stiff ordinary differential equations. This paper is aimed at solving the problem proposed in [1] that what conditions should be fulfilled for MDBMs in order to guarantee the A-stabilities. The explicit expressions of the polynomials and in the stability functions are given. Furthermore, we prove . With the aid of symbolic computations and the expressions of diagonal Pade' approximations, we obtained the biggest block size k of the A-stable MDBM for any given l (the order of the highest derivatives used in MDBM, l≥1)     

Generalized diagonalization of matrices over quaternion field

Ｉｎｒｅｃｅｎｔｙｅａｒｓ,ａｐｐｌｉｃａｔｉｏｎｓｏｆｑｕａｔｅｒｎｉｏｎｍａｔｒｉｃｅｓａｒｅｂｅｃｏｍｉｎｇｍｏｒｅａｎｄｍｏｒｅｉｍｐｏｒｔａｎｔａｎｄｅｘｔｅｎｓｉｖｅｉｎｒｉｇｉｄｍｅｃｈａｎｉｃｓ,ｑｕａｎｔｕｍｍｅｃｈａｎｉｃｓ,ｃｏｎｔｒｏｌｔｈｅｏｒｙａｎｄｈｅｌｉｃａｌｔｅｃｈｎｏｌｏｇｙ［１～３］．Ｗｉｔｈｔｈｅｒａｐｉｄｄｅｖｅｌｏｐｍｅｎｔｏｆｔｈｅａｂｏｖｅｄｉｓｃｉｐｌｉｎｅｓ,ｉｔｉｓｇｅｔｔｉｎｇｍｏｒｅａｎｄｍｏｒｅｎｅｃｅｓｓａｒｙｆｏｒｕｓｔｏｆｕｒｔｈ…     

Homogenization of the nonlinear Kelvin–Voigt model of viscoelasticity and of the Prager model of plasticity

Denoting by the stress tensor, by the linearized strain tensor, by A the elasticity tensor, and assuming that is a convex potential, the inclusion accounts for nonlinear viscoelasticity, and encompasses both the linear Kelvin–Voigt model of solid-type viscoelasticity and the Prager model of rigid plasticity with linear kinematic strain-hardening. This relation is assumed to represent the constitutive behavior of a space-distributed system, and is here coupled with the dynamical equation. An initial- and boundary-value problem is formulated, and the existence and uniqueness of the solution are proved via classical techniques based on compactness and monotonicity. A composite material is then considered, in which the function and the tensor A rapidly oscillate in space. A two-scale model is derived via Nguetseng’s notion of two-scale convergence. This provides a detailed account of the mesoscopic state of the system. Any dependence on the fine-scale variable is then eliminated, and the existence of a solution of a new single-scale macroscopic model is proved. The final outcome is at variance with the nonlinear extension of the generalized Kelvin–Voigt model, which is based on an apparently unjustified mean-field-type hypothesis.     

Boundary value problem for a singularly perturbed nonlinear system

I.Intr0ducti0n'Manyresultshavebeeng0tinstudyingthesingu1arperturbation0fboundaryvalueproblemfornonlinearsystemeg#=j(t,g,y',8)(l.l)bythemethodandthetechniqueofdiagonalizationl'~'l.Thepapersarebasedonsucha.conditionthattheeigenvaluesofJacobimatrixlu'offwit…     

Analysis and control of a class of uncertain linear periodic discrete-time systems

Feedback control problems for linear periodic systems （LPSs） with interval- type parameter uncertainties are studied in the discrete-time domain. First, the stability analysis and stabilization problems are addressed. Conditions based on the linear matrices inequality （LMI） for the asymptotical stability and state feedback stabilization, respec-tively, are given. Problems of L2-gain analysis and control synthesis are studied. For the L2-gain analysis problem, we obtain an LMI-based condition such that the autonomous uncertain LPS is asymptotically stable and has an L2-gain smaller than a positive scalar γ. For the control synthesis problem, we derive an LMI-based condition to build a state feedback controller ensuring that the closed-loop system is asymptotically stable and has an L2-gain smaller than the positive scalar γ. All the conditions are necessary and sufficient.