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

ＭＩＸＥＤＣＯＭＰＡＴＩＢＬＥＥＬＥＭＥＮＴＡＮＤＭＩＸＥＤＨＹＢＲＩＤＩＮＣＯＭＰＡＴＩＢＬＥＥＬＥＭＥＮＴＶＡＲＩＡＴＩＯＮＡＬＭＥＴＨＯＤＳＩＮＤＹＮＡＭＩＣＳＯＦＶＩＳＣＯＵＳＢＡＲＯＴＲＯＰＩＣＦＬＵＩＤＳＳｈｅｎＸｉａｏ－ｍｉｎｇ（沈孝明...     

A UNIFORMLY DIFFERENCE SCHEME OF SINGULAR PERTURBATION PROBLEM FOR A SEMILINEAR ORDINARY DIFFERENTIAL EQUATION WITH MIXED BOUNDARY VALUE CONDITION

ＡＵＮＩＦＯＲＭＬＹＤＩＦＦＥＲＥＮＣＥＳＣＨＥＭＥＯＦＳＩＮＧＵＬＡＲＰＥＲＴＵＲＢＡＴＩＯＮＰＲＯＢＬＥＭＦＯＲＡＳＥＭＩＬＩＮＥＡＲＯＲＤＩＮＡＲＹＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＷＩＴＨＭＩＸＥＤＢＯＵＮＤＡＲＹＶＡＬＵＥＣＯＮＤＩＴ...     

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

ＥＸＩＳＴＥＮＣＥＴＨＥＯＲＥＭＳＯＦＳＯＬＵＴＩＯＮＳＦＯＲＴＷＯ－ＰＯＩＮＴＢＯＵＮＤＡＲＹＶＡＬＵＥＰＲＯＢＬＥＭＯＦＳＥＣＯＮＤＯＲＤＥＲＯＲＤＩＮＡＲＹＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳＩＮＢＡＮＡＣＨＳＰＡＣＥＳＺｈａｎｇＳｈｉｓ...     

SINGULAR PERTURBATION OF INITIAL BOUNDARY VALUE FROBLEMS OF REACTION DIFFUSlON EQUATION WITH DELAY

ＳＩＮＧＵＬＡＲＰＥＲＴＵＲＢＡＴＩＯＮＯＦＩＮＩＴＩＡＬＢＯＵＮＤＡＲＹＶＡＬＵＥＦＲＯＢＬＥＭＳＯＦＲＥＡＣＴＩＯＮＤＩＦＦＵＳｌＯＮＥＱＵＡＴＩＯＮＷＩＴＨＤＥＬＡＹＺｈａｎｇＸｉａｎｇ（张祥）（ＡｎｈｕｉＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ）Ｗｕ...     

ANOTHER CLASS D＇ALEMBERT PRINCIPLE AND A NEW MAGGI EQUATION FOR ARBITRARY ORDER NONHOLONOMIC MECHANICAL SYSTEMS IN DERIVATIVE SPACE

ＡＮＯＴＨＥＲ　ＣＬＡＳＳ　Ｄ＇ＡＬＥＭＢＥＲＴ　ＰＲＩＮＣＩＰＬＥ　ＡＮＤ　Ａ　ＮＥＷ　ＭＡＧＧＩ　ＥＱＵＡＴＩＯＮ　ＦＯＲ　ＡＲＢＩＴＲＡＲＹ　ＯＲＤＥＲ　ＮＯＮＨＯＬＯＮＯＭＩＣ　ＭＥＣＨＡＮＩＣＡＬ　ＳＹＳＴＥＭＳ　ＩＮ　ＤＥＲＩＶＡＴＩＶＥ...     

SINGULAR PERTURBATIONS FOR A CLASS OF BOUNDARY VALUE PROBLEMS OF HIGHER ORDER NONLINEAR DIFFERENTIAL EQUATIONS

ＳＩＮＧＵＬＡＲ　ＰＥＲＴＵＲＢＡＴＩＯＮＳ　ＦＯＲ　Ａ　ＣＬＡＳＳ　ＯＦ　ＢＯＵＮＤＡＲＹ　ＶＡＬＵＥ　ＰＲＯＢＬＥＭＳ　ＯＦ　ＨＩＧＨＥＲ　ＯＲＤＥＲ　ＮＯＮＬＩＮＥＡＲ　ＤＩＦＦＥＲＥＮＴＩＡＬ　ＥＱＵＡＴＩＯＮＳＳｈｉＹｕａｎｉｎｇ（史玉明）...     

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

ＣＯＮＳＴＲＵＣＴＩＯＮＯＦＭＯＤＩＦＩＥＤＴＡＹＬＯＲ－ＧＡＬＥＲＫＩＮＦＩＮＩＴＥＥＬＥＭＥＮＴＳＡＮＤＩＴＳＡＰＰＬＩＣＡＴＩＯＮＩＮＣＯＭＰＲＥＳＳＩＢＬＥＦＬＯＷＣＯＭＰＵＴＡＴＩＯＮＣＯＮＳＴＲＵＣＴＩＯＮＯＦＭＯＤＩＦＩＥＤＴＡＹＬＯＲ...     

ACTUATION OF SLOSHING MODULATED FORCE AND MOMENT ON LIQUID CONTAINER DRIVEN BY JITTER ACCELERATIONS ASSOCIATED WITH SIEW MOTION IN MICROGRAVITY

ＡＣＴＵＡＴＩＯＮＯＦＳＬＯＳＨＩＮＧＭＯＤＵＬＡＴＥＤＦＯＲＣＥＡＮＤＭＯＭＥＮＴＯＮＬＩＱＵＩＤＣＯＮＴＡＩＮＥＲＤＲＩＶＥＮＢＹＪＩＴＴＥＲＡＣＣＥＬＥＲＡＴＩＯＮＳＡＳＳＯＣＩＡＴＥＤＷＩＴＨＳＩＥＷＭＯＴＩＯＮＩＮＭＩＣＲＯＧＲＡＶＩＴＹＲ...     

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...     

BENDING SOLUTION OF A RECTANGULAR PLATE WITH ONE EDGE BUILT－IN AND ONE CORNER POINT SUPPORTED SUBJECTED TO UNIFORM LOAD

ＢＥＮＤＩＮＧ　ＳＯＬＵＴＩＯＮ　ＯＦ　Ａ　ＲＥＣＴＡＮＧＵＬＡＲ　ＰＬＡＴＥ　ＷＩＴＨ　ＯＮＥ　ＥＤＧＥ　ＢＵＩＬＴ－ＩＮ　ＡＮＤ　ＯＮＥ　ＣＯＲＮＥＲ　ＰＯＩＮＴ　ＳＵＰＰＯＲＴＥＤ　ＳＵＢＪＥＣＴＥＤ　ＴＯ　ＵＮＩＦＯＲＭ　ＬＯＡＤＸｕＱｉｌｏ...     

Z n-equivariant singularity theory

The basic concepts, normal forms and universal unfoldings of Z_n-equivariant singularity are investigated in the present paper. As an example, the normal forms and universal unfoldings of Z_s-singularity are formulated. As a matter of fact, the theory provides a useful tool to study the subharmonic resonance bifurcation of the periodic parameter-excited system. Project supported by the National Natural Science Foundation of China     

An integration method for detecting chaotic responses of nonlinear systems subjected to double excitations

A methodology designed for identifying chaos of the nonlinear systems subjected to double excitations is proposed. Based on simulations in this study, it is shown by bifurcation diagram that method of Poincaré sections, the conventional chaos-observing method, fails to pinpoint the onset of chaotic motions with the nonlinear systems subjected to double excitations. To remedy this problem, “K_s integration method” is proposed, which integrates the distance between trajectories and origin in phase plane over an excitation period and designates the obtained integration values as K_s's to take the roles of the sampling points derived by Poincaré sections in constructing bifurcation diagram. This “K_s integration method” is shown capable of providing valuable information in bifurcation diagram such that the parameter range leading to chaos can be easily decided and the number of distinguishable time-domain responses can be determined.     

Multiplicity Results for Periodic Solutions to Second-Order Difference Equations

By using the Z _p geometrical index theory, some sufficient conditions on the multiplicity results of periodic solutions to the second-order difference equations

THE SOLUTION TO THE DESTABILIZING CRITICAL LOAD OF CIRCULAR DOUBLE ARTICULATED ARCH UNDER GOING VERTICAL DISTRIBUTIVE LOAD g0/cos2θ

In this paper, after taking the effect of axis force on bending into consideration, the general potential energy for the circular double articulated arch is established undergoing vertical distributive load g₀/cos²θ. With sufficient engineering precision, the fourth approximations to the destabilizing critical load of the arch under t his load are obtained by Ritz method. The approximations to the critical load ta ble are listed for various center angles of arch, and are contrasted with the critical load circular arch undergoing radial uniform load. Some reference results have been obtained.     

Contribution of point defects to the temperature anomaly of the yield stress in single crystals of the Ni<Subscript>3</Subscript>Ge alloy

The temperature dependence of the yield stress τ_* Ni ₃ Ge single crystals is studied. The temperature dependence τ_*(T) in the high-temperature region (above 420 K) is found to be conditioned by thermally activated accumulation of the density of non-screw components of superdislocations. Interaction of point defects with edge dislocations and its effect on the temperature anomaly of the yield stress in Ni ₃ Ge single crystals are analyzed. The calculated results are found to agree with experimental data. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 4, pp. 154–161, July–August, 2007.     

Robust H∝ filtering for discrete-time impulsive systems with uncertainty

This paper investigates robust filter design for linear discrete-time impulsive systems with uncertainty under H∞ performance. First, an impulsive linear filter and a robust H∞ filtering problem are introduced for a discrete-time impulsive systems. Then, a sufficient condition of asymptotical stability and H∞ performance for the filtering error systems are provided by the discrete-time Lyapunov function method. The filter gains can be obtained by solving a set of linear matrix inequalities （LMIs）. Finally, a numerical example is presented to show effectiveness of the obtained result.     

Degree of branching of polypropylene measured from Fourier-transform rheology

In this study, linear and branched polypropylenes (PP) were compared under medium strain amplitude oscillatory shear (usually strain amplitude range from 10 to 100%) with Fourier-transform rheology (FT rheology). On a log–log diagram, the third relative intensity (I ₃/I ₁), which is a parameter to represent nonlinearity, shows a linear relationship with the strain amplitude in the range of medium strain amplitude. The slope of I ₃/I ₁ of linear PP with various molecular weight and molecular weight distribution was 2 as most constitutive equations predict, while that of branched PP was 1.64, which is lower than that of linear PP. When the linear and branch PP were blended, the slope of I ₃/I ₁ was proportional to the composition of the branch PP. Therefore, it is suggested that the degree of branching can be defined in terms of the slope of I ₃/I ₁ under medium amplitude oscillatory shear.     

Green's function,continual weighted composition operators along trajectories,and hyperbolicity of linear extensions for dynamical systems

The hyperbolicity of linear skew-product flows with infinite-dimensional fibersE over a dynamical system on a compact metric spaceX is described in terms of the existence and uniqueness of Green's function and in terms of the spectra for family of the semigroups of weighted composition operators acting inL ₂(R;E) and parametrized by the points ofX.     

Maximal elements and generalized games involving condensing mappings in locally FC-uniform spaces and applications （II）

This paper is a continuum of the preceding paper of author. Some new systems of generalized vector quasi-equilibrium problems involving condensing mappings are introduced and studied in locally FC-uniform spaces. By applying the existence theorem of maximal elements of condensing set-valued mappings in locally FC-uniform spaces obtained by author in the preceding paper, some new existence theorems of solutions for the systems of generalized vector quasi-equilibrium problems are proved in locally FC-uniform spaces. These results improve and generalize some known results in literature to locally FC-uniform spaces. Project supported by the Natural Science Foundation of Sichuan Education Department of China (No. 2003A081 and SZD0406)     

<Emphasis Type="Italic">J</Emphasis><Subscript>2</Subscript> invariant relative orbits via differential correction algorithm

This paper describes a practical method for finding the invariant orbits in J ₂ relative dynamics. Working with the Hamiltonian model of the relative motion including the J ₂ perturbation, the effective differential correction algorithm for finding periodic orbits in three-body problem is extended to formation flying of Earth’s orbiters. Rather than using orbital elements, the analysis is done directly in physical space, which makes a direct connection with physical requirements. The asymptotic behavior of the invariant orbit is indicated by its stable and unstable manifolds. The period of the relative orbits is proved numerically to be slightly different from the ascending node period of the leader satellite, and a preliminary explanation for this phenomenon is presented. Then the compatibility between J ₂ invariant orbit and desired relative geometry is considered, and the design procedure for the initial values of the compatible configuration is proposed. The influences of measure errors on the invariant orbit are also investigated by the Monte–Carlo simulation. The project supported by the Innovation Foundation of Beihang University for Ph.D. Graduates, and the National Natural Science Foundation of China (60535010).