In this paper, we present the sufficient and necessary condition of unique decodability of block codes for multiple-access adder channels and relevant criterions. The decoding algorithms are investigated for the uniquely decodable block codes.

This paper presents analytical solutions to the partial differential equation for unsteady rotatory flow of viscoelastic fluid in annular pipes by using the integral transform method. The results can be used to analyse the behavior of rotatory velocity and shear stress unsteady flow of non-Newtonian fluids in annular pipes and to provide a theoretical base for drilling engineering design.

As a new phase transition model, the phase field model is expected to be an approximation for stefan-type problems, In present paper, error estimates are derived for a FEM with nonsmooth initial data. Some exact solutions of the stefan-type problems are given. And the numerical results demonstrate that the phase field model is an efficient approximation at least in one-dimension case and three-dimension spherical symmetric case.

In this paper the relationship between homotopy algorithms and penalty function methods for nonlinear programming problems is brought to light and the convergency of the former is discussed. Some computational results are presented to show that the piecewise-linear homotopy algorithms exploiting structure are efficient for nonlinear programming problems with special structure.

In this paper, we present a new polynomial-time algorithm for linear programming, which has a family of feasible directions at each iteration step. Meanwhile, the switch strategy is used. By all these means, it is possible to reduce the amount of inverse matrix calculations greatly. Finally, it is proved that the algorithm can be stopped in O(nL) iterations.

In this paper, we gave complete discriptions. And we discussed the ultraproduct of divisible closed semirings envelope of an element and an embedding theorem. These results provided a theoretical basis to the further study of closed Bemiring and their application.

In this paper, a new variant of the interior ellipsoid method for convex quadratic programming is developed. Compared to the algorithm proposed by Ye and Tse^[5],the sub-problem of new algorithm is a linear programming which is easy to solve, although both have the same complexity.

In this paper, the recurrence formula of the transmission and reflection amplitudes is established of a plane wave, e^-ikx, (with wave number k>0) through N→+∞;A essential and sufficient condition when the system is insulator is obtained; Last, the method of determining whether the system is an insulator is found,of some one-dimensional sequences generated by substitutive sequences.

This paper Discusses the BVP of the semilinear elliptic equation △u=f(u) in R^N with f∈C(R), uf(u)>0, f(0)=0, it gives properties of the classic radial solution, and proves existence and nonexistence, and uniqueness, further the estimations of the radial solution are also given, these properties better describe the behaviour of the radial solution as well.

Let (T,Σ,μ) be a finite measure space and (X,‖·‖) be a Banach space. let L_p(T < X)(1≤p<∞) denote the spaces of p-power Bochner integrable functions defined on T with its range in the X. In this paper, we mainly prove the characteristic theorems that general subset G and subset L_p(T,Y) (Y∈X) of particular type in L_p (T,X) are suns; for real Hilbert space X, we also get the characterization that subset L_p(T,Y) in L_p(T,X) is a semi-Chebyshev sun, and give the condition that subset L_p(N,Y(in L_p(N,X) is a strongly Chebyshev subspace. (T,X), and get the theorems of unicity and strong unicity for a sort of suns.

In this paper, we investigated Hopf bifurcation of the sunflower equation

where a was regarded as bifurcation parameter. We obtained the conditions for Hopf bifurcanon of the equation and gave the direction of bifurcation, the expression of the bifurcating periodic solutions as well as their stability.

Sufficient conditions are established for the oscillation of solutions of delay by perbolic equations of the form
,
where Ω is a bounded domain in Rⁿ with a piecewise smooth boundary ∂Ω.

In this paper, a smooth nonparametric estimator for quantile function is proposed in the censorship model. Under some conditions, we obtain the strong and weak Bahadur representations. From these results we derive the asymptotic normal distribution and the law of the iterated logarithm of the estimator.

Consider the independent variables a_it,…,a_pt satisfying m(≥1) linear regression relationships,i.e. i=1,…,m.Some of these independent variables,Say a_it=(i=r+1,…,p) can be observed without errors in them, while the observations of other variables can be obtained with errors, i.e.

On the basis of Bézier curve/surface^[1],this paper defines the generalized Bézier cure/surface. With their property of high order smooth interpolation at the curve segment's ends and surface patch's boundary, we can construct the GC^r transitional curve segment/surface patch between two parametric curve segment/surface patches more freely.

In this paper, we first use a new method to obtain some new results concerning the uniform boundedness, uniformly ultimate boundedness and extreme stability of solutions of higher dimensional systems. And then using these results we study the existence and uniqueness of periodic solutions of higher dimensional systems. On the other hand, we also introduce the concept of "ladderlike system" and present an approach to study the existence of periodic solutions for such system.

In this paper, we consider the dynamics behavior of Ginzburg-Landau-Newell model, we obtain the existence of the global attractors for this model, meanwhile, we get the lower bounds on the dimension of the global attractor, and get an upper bounds on the dimension of the global attractor in terms of physical quantities.

The stopping probability p^*, a measure of the continuous sampling plan CSP-1, is discussed in this paper. Methods of transition probability generating function and power series are introduced to develop some theoretical results on p^*. It is showed that the Dodge-type CSP-1 and the CSP-1 with stopping rule(n^*-i) have the identical AOQ, AFI and OC. Numerical results are illustrated in the last section.

In this paper, a integral estimation and inverse theorem of week type are obtained for Bernstein-Sikkema operators.

Let A be a singular M-matrix, and A=M-N a graph compatible weak regular splitting.In the paper, we study the spectral property of the iteration matrix and obtain a theorem associated the index of the iteration matrix, which generalizes the corresponding results of [3, 4].

Solving characteristics matrix equations (CME) of linear retarded systems is the key problem for stabilizing the system using reduction technique. This paper gives the solution of CME under the general condition that the eigenvalues occur in the spectrum of the system with algebraic and geometric multiplicities being greater than or equal to one. The main idea is to transform the CME into a group of linear algebraic equations (LAE). The sufficient conditions for the existence of the solution of the LAE and for the independence of the solution vectors of the LAE corresponding to a given eigenvalue are established. An algorithm for dealing with the stabilization problem in the case that the left eigenvectors of the system corresponding to different eigenvalues are linearly dependent is presented. An illustrative example is given to show the design procedure.

A constant, Lip, which quantitatively characterizes the least Lipschitz constant of nonlinear Lipschitz operators under all strong equivalent metrics, is introduced for nonlinear Lipschitz operators in metric spaces. Two useful evaluation theorems on Lip are presented. By using Lip, nonlinear generalizations on Nemann Lemma and Perturbation Lemma in linear operator theory are obtained.

This paper deals with the initial boundary value problem of the generalized Fitz-Hugh-Nagumo equations. Without the restriction that the initial data contain in some invariant set, we prove the existence of global attractor of the abqve system in l, and give upper bounds of the attractor. Moreover, we construct the inertial manifold for the above system as the space dimension is less than or equal to 2. Gur approach simplifies the work of P. Constantin, C. Foias, B. Nicolaenko, and R. Temam.

Abstract Suppose Y₁,Y₂,…,Y_n, i.i.d., EY=β, CovY₁=Σ, where both β∈R^m and Σ:m×m>0 are unknown. Let L₁(d,β)=(d-β)'(d-β),L₂=(d,β)(d-β)' and L={L₁Y₁+L₂Y₂+…+L_nY_n:L_i is an m×m real matrix, i=1, 2…,n}. In this paper, we give the necessary and sufficient conditions that a linear estimator of β is admissible among L under L₁ and L₂, respectively.

We introduction random topological degree theory and proved some new random fixed point theorems^[1]. The purpose of this paper is to introduce the random fixed point index theory of random 1-set-constraction operator and use it to prove some new random fixed point theorems. We offered one of the fundamental methods for studying the existence of,the random solution of random equations and also showed the application to the random Hammerstein type nonlinear integral equations.

In this paper, we first introduce the concept of admissible pair and obtain space-time estimates for linear Schrodinger equation of higher order. By use of space-time estimates and nonlinear function estimates, we obtain the existence and uniqueness of global strong solution for Schödinger equation of higher order.

In this paper we consider the neutral differential equations with positive and negative coefficients. Sufficient conditions for the existence and nonexistence of positive solutions are obtained respectively. Some comparison theorems also have been established.

This paper presents a set of methods for constructing the orthogonal latin squares and the magic square by using the linear congruent transformation. These meth- ods are wider than the method for constructing odd order orthogonal latin squares (Tao Zhaomin^[1]), the method for constructing the pandiagonal magic square (Zheng Geyu^[2]), and the methods for constructing the odd order magic square (De la Loubère^[1],Bachet de Méziriac^[1], Chen Hao^[3] and Xiao Zhengang^[4], etc.).

In this paper we consider the weak convergence of probability measures convolution prwer on some compact semigroups. The Kawada-Itô type result on a kind of compact semigroups is obtained.

This paper investigates further degree raising properties of generalized Ball-Spline curve and surface on a triangle. Arbitrary degree raising formula is given. Also,conversion algorithm between generalized Ball-Spline basis and Bernstein basis is provided,too.

Although much attention have been paid to the total least squares problem (TLS for short), the suf&cient and necessary condition on the solvability still remains to be investigated. Following the author's approach described in [7], this paper presents a complete analysis of the solvability for TLS. And more, a perturbation theorem is also proved.

In this note we generalize the technique in [1],[3] and obtain the exact integral expressions of nth-order stress intensity factor at a notch tip in antiplane shear for bimaterials in the general case.

In this paper, some necessary and sufficient conditions are first proposed which ensure the convergence of solutions of second-order evolution equations and related difference approximation equations in Banach spaces.

The aim of this paper is to study wellposedness and numerical method for a class of nonlocal parabolic boundary value problems. First the existence, uniqueness and continuous dependence of the solution upon the data are demonstrated, and then a fully discretized Galerkin approximation scheme is established. It is proved that both numerical solutions are stable and convergent. The efficiency of the numerical method is testified by numerical examples.

Let {X (t), t > 0} be a p-dimensional Gaussian Process, under some conditions, we get the asymptotic distributions of point process formed饰the numbers of {X(t), 0 < t < T} ε-upcrossing level {U_T(> 0)} as T→∞, and prove the asymptotic independence of the p component point processes. Meanwhile we get the asymptotic distribution of M(T)=sup {X(t), 0 < t < T} as T→∞.

In this paper, we investigate the relationship between the shadowing property for continuous semi-flows on a compact metric space and that for the continuous flows on the inverse limit spaces. As applications, we show that the restriction to the nonwandering set of a semi-flow with the strong shadowing property has the strong shadowing property, and give the spectral decomposition theorem for semi-flows.