EXISTENCE AND UNIQUENESS FOR SECOND-ORDER VECTOR BOUNDARY VALUE PROBLEM OF NONLINEAR SYSTEMS

This paper is concerned with the following second-order vector boundary value problem ：x^R=f（t,Sx,x,x＇）,0〈t〈1,x（0）=A,g（x（1）,x＇（1））=B,where x,f,g,A and B are n-vectors. Under appropriate assumptions,existence and uniqueness of solutions are obtained by using upper and lower solutions method.

Vectorization and Parallel Computation of a CFD Code on YH－2 Parallel Supercomputer

MacCormack explicit scheme and Baldwin-Lomax algebraic turbulent model are employed to solve the axisymmetric compressible Navier-Stokes equations for the numerical simulation of the supersonic mustanl floats interacted with transverse injection at the base of a cone. A temperature switch function must be added to the artificial viscous model suggested by jameson etc to enhance the scheme's ability to eliminate oscillation for some injection case.The typical code optimization techniques about vectorization and some useful concepts and terminology about multiprocessing of YH-2 parallel supercmputer is given and explatined with some examples After reconstruction and optimization the code gets a spedup 5 .973 on pipeline computer YH- 1 and gets a speedup 1 886 for 2 processors and 3.545 for 4 processors on YH-2 parallel supeercomputer by using domain decomposition method..

SOLVABILITY OF THE FOURTH ORDER NONLINEAR SUBELLIPTIC EQUATIONS ON THE HEISENBERG GROUP

In this paper,some existence results for the fourth order nonlinear subelliptic equations on the Heisenberg group are given by means of variational methods.

Two-dimensional interactions due to moving load in generalized thermoelastic solid with diffusion

The present paper is concerned with the investigation of disturbances in＇a homogeneous, isotropic elastic medium with generalized thermoelastic diffusion, when a moving source is acting along one of the co-ordinate axis on the boundary of the medium. Eigen value approach is applied to study the disturbance in Laplace-Fourier transform domain for a two dimensional problem. The analytical expressions for displacement components, stresses, temperature field, concentration and chemical potential are obtained in the physical domain by using a numerical technique for the inversion of Laplace transform based on Fourier expansion techniques. These expressions are calculated numerically for a copper like material and depicted graphically. As special cases, the results in generalized thermoelastic and elastic media are obtained. Effect of presence of diffusion is analyzed theoretically and numerically.

UNSTABLE SOLUTIONS TO A CLASS OF VECTOR DIFFERENTIAL EQUATIONS OF SIXTH ORDER

In this paper, we consider a class of nonlinear vector differential equations of sixth order. By constructing appropriate Lyapunov functions, the non-existence of periodic solutions is established. Moreover, we provide an example to show the feasibility of our results. Our results extend and improve two related results in the previous literature from scalar cases to vectorial cases.

ON THE INSTABILITY OF SOLUTIONS TO A NONLINEAR VECTOR DIFFERENTIAL EQUATION OF FOURTH ORDER

This paper presents a new result related to the instability of the zero solution to a nonlinear vector differential equation of fourth order.Our result includes and improves an instability result in the previous literature,which is related to the instability of the zero solution to a nonlinear scalar differential equation of fourth order.

ON STABILITY OF SOLUTION OF A CERTAIN FOURTH ORDER VECTOR DIFFERENTIAL EQUATIONS

This paper gives sufficient conditions for the global asmptotic stability of the zero solution of the differential equation (1. 1). The result improves and generalizes the wellknown results.

ON THE STABILITY OF SOLUTIONS TO A CERTAIN FOURTH-ORDER VECTOR DELAY DIFFERENTIAL EQUATION

In this paper, by constructing a Lyapunov functional, sufficient conditions for the uniform stability of the zero solution to a fourth-order vector delay differential equation are given.

Verifiable Secret Sharing Scheme Based on Certain Projective Transformation

The main purpose of verifiable secret sharing scheme is to solve the honesty problem of participants. In this paper, the concept of nonzero k-submatrix and theresidual vector of system of hyperplane intersecting line equations is proposed. Based on certain projective transformations in projective space, a verifiable (t, n)-threshold secret sharing scheme is designed by using the structure of solutions of linear equations and the difficulty of solving discrete logarithm problems. The results show that this scheme can verify the correctness of the subkey provided by each participant before the reconstruction of the master key, and can effectively identify the fraudster. The fraudster can only cheat by guessing and the probability of success is only 1/p. The design of the scheme is exquisite and the calculation complexity is small. Each participant only needs to hold a subkey, which is convenient for management and use. The analysis shows that the scheme in this paper meets the security requirements and rules of secret sharing, and it is a computationally secure and effective scheme with good practical value.

Vector NLS solitons interacting with a boundary

We construct multi-soliton solutions of the n-component vector nonlinear Schrödinger equation on the half-line subject to two classes of integrable boundary conditions(BCs):the homogeneous Robin BCs and the mixed Neumann/Dirichlet BCs.The construction is based on the so-called dressing the boundary,which generates soliton solutions by preserving the integrable BCs at each step of the Darboux-dressing process.Under the Robin BCs,examples,including boundary-bound solitons,are explicitly derived;under the mixed Neumann/Dirichlet BCs,the boundary can act as a polarizer that tunes different components of the vector solitons.Connection of our construction to the inverse scattering transform is also provided.

Bending Prediction Method of Multi-Cavity Soft Actuator

The multi-cavity soft actuator is assembled from single-cavity soft actuator through a reasonable geometric distribution.It has the characteristic that the pneumatic soft actuator is driven by its own deformation and has more degrees of freedom.Pneumatic soft actuator is widely used as an emerging discipline and its strong compliance has been greatly developed and applied.However,as the most application potential type of soft actuators,there is still a lack of simple and effective deformation prediction methods for studying the spatial deformation of multi-cavity soft actuators.To solve this problem,a vector equation method is proposed based on the analysis of the principle of the space deformation of the two-cavity,three-cavity and four-cavity soft actuators.Furthermore,a nonlinear mathematical model of the air pressure,space position and deformation trajectory of the soft actuator end is established by combining the vector equation method.Finally,the three-channel soft actuator is verified through experiments.The results show that the mathematical model can better predict the space deformation trajectory of the soft actuator,which provides a new research method for studying the space deformation of the multi-channel soft actuator.