An example of three-dimensional differential system is constructed such that it has infinitely many distinct knotted periodic orbits. By using a perturbation method we show thae the perturbed system has an attractive-invariant two-dimensional torus depending on one parameter λ. As λ varies, infinitely many bifurcation sequences of (m, n)-torus knots of periodic orbits can be created.

This paper presetits a new O(Xlog X) algorithm for finding all periodic subwords in a given string X. We show how subword-tree and linear algorithm for lowest common ancester can be used to spot all such periodic subwords.

In this paper we deal with the queueing system GI/M/I with bulk arrival and bulk service as a semi-Markov sequence. We obtain its distributions of busy cycles and the number of customers served in a busy cycle (period). The limiting behavior of the embedded Markov Chain of this system in also considered.

This paper has constructed a class of explicit linear:4-step methods of order 3, and proved their absolute stable range theoretically. In an eigenvalue system withquite large variation. in range of a real-time simulation, the integration speed of this class of methods, is 3 to 7 times faster than that of the practical methods of Adams of order 3.

In this paper, the variational inequalities and complementary problem for a class of multivalued mappings are discussed in the framework of a locally convex Hausdorff topological linear space. Our results extend and improve the recent results of [2, 5, 6].As applications, we utilize our results to study the nonlinear programming and saddle point problems in infinite dimensional spaces, and some interesting results are obtained.

A set of necessary conditions for the existence of designs of Latin square type with given parameters is obtained. Soiree applications of these conditions to the case of lower orders are also given.

A strongly independent set of a graph G is an independent set S which intersects every maximal clique of G. This paper gives a linear time algorithm of finding a strongly independent set with maximum weight of a chordal graph.

In this paper, we investigate the degree of approximation by Feller operators for functions which have only discontinuity points of the first kind on [0, ∞) with exponential growth. Our estimates are essentially the best possible. The results here include the results or partial results of the references [2, 3, 6, 7, 9].

A state space approach to. the finite automata was proposed by Tony T. Lee in 1983[1].He introduced the ψ-representation of Languages and gave the state equation of he finite automata under the condition of Σ={0, 1}.This paper extends it to Σ={δ₀, δ₁, …, δ_2^m-1} and discusses some properties of the ψ-representation, associates it with Kleene's equation and gives a numerical example of recognizabel languages of incompletely specified finite automata.

The existence of periodic solutions for delay partial differential equations is investigated Our first objective is to give the, exist<:nce theorem of solutions of abstract delay differential equations, and then prove the existence of periodic solutions in suitable spaces by Schauder fixed point theorem. Finally, we use the abstract results obtained above to prove the existence of periodic solutions for delay semilinear partial differential equations.

In this paper, we introduce a class of new positive definite functions.

It is shown in this paper that the decision of the existence of (v, k, λ)-near difference sets of type 2 is equivalent to that of (v, k, λ)-cyclic sequences., Thereof it's proved that any (v, k, λ)-near difference sets of type 2 for v≥9 must satisfy the condition that k≥3 (or equivalently, k≤v/3) and the equality holds if and only if λ=1.Subsequently some results with respect to the parameters(v, k, λ) for an odd v are derived.

In this paper, we study the existence and stability of a competitive diffusion system with homogenous Dirichlet boundary condition, obtain some critical condition of the existence of a coexistence solution, and discuss its stability by bifurcation method. Finally, we give a more detailed analysis for a special case by asymptotic method and obtain the same results which describe the stability of a coexistence solution under the Neumann boundary condition.

In this paper, it is proved that each of a class of KdV=type equations has only two-soliton solutions. The process of proof provides a simple approach to negating the Hirota condition.

Continuous time first, arrival target discounted moment optimal models with countable state and action spaces are invest}igatedl. A general formula of the k-th moment of total discounted return is given. A relation between the continuous and associated discrete time quasi-discounted return is established. It is shown that there exists a unique bounded solution for the moment optimal equation under a rather weak condition. Some properties of optimal policies are discussed.

In 1979, A. Kotzig [1] presented the following open problem:"Is it true that, for every regular self-complementary graph G, there is at least one isomorphism permutation p such that, except for the cycle of length one, every cycle of p is of length exactly four?" The problem has not been settled until now. In this note, w e construct a counterexample to show the answer is negative.

In this paper, two new dual types of multiobjective fractional programming are given. Their weak dual theorem and strong dual theorem are established, respectively. Furthermore, we discuss the relation between these two types of dual programming.

The main aim in this paper is to establis-h the representation formula of periodic solutions of the following Volterra equations of the form

As the corollaries to our results, the corresponding results in [1]-[5] are included.

This paper deals with the matrix equation A^m=λJ,where A is an n×n integer matrix and J is an n×n matrix with all the entries being one.

Accidents caused by one phase breakdown often happens in power systems In these cases, the manner of working has its intrinsic features, In this paper we make an exclusive study of its features. At first, a mathematical model illustrating this type of functioning is established. Then the boundedness of solutions and the existence of periodic solutions are given. The existence of large harmonic solutions provides the probable overvoltage phenomenon in the system with a theoretical basis, while the existence of small harmonic solution predicts such a manner of working will eventually be set up, Finally, a few numerical results are given to demonsCrate the theoretical results.

In this paper we reduce the initial-boundary problem for the pseudo-parabolic equation to Cauchy problem of nonlinear evolution equation. Using the semigroup method we establish the existence and uniqueness of the solution of the inverse problem for the evolution equation and apply this result to the pseudo-parabolic equation.

The connections among symmetries; the Backlund transformation and the Painleve preperty for Burgers hierarchies are discussed. Firstly, the Backlund transformation is constructed by means of the symmetries; then according to the symmetries and Backlund transformation, the Painleve property for Burgers hierarchies can be analysed.

This paper studies the existence, the uniqueness and the asymptotic behaviour of the solutions of boundary value problems for a class of third-order nonlinear ordinary differential equations.

By using the method of Dulac function we investigate the uniqueness of limit cycles surrounding multiple singular points for a type of planar differential systems, and obtain a simple sufficient condition for the uniqueness. In particular, we give a condition for Lienard equation which guarantees the existence of exactly one limit cycle surrounding the multiple singular points. Moreover, we also discuss the examples of cubic systems etc.

In this paper, we consider the oscillations for some higher-order neutral functional differential equations with several deviating arguments, thus improving the work of G.Ladas and Y. G. Sficas in essence. We also get a series of oscillation criteria for the equations. Lastly we give a new oscillation criterion on the boundless solutions for the equations, which is not obtained in G. Ladas and Y. G. Sficas paper.

Let be an LSE of parameter,β in a linear model. This paper proves that the distribution of statistic f()-Ef()/{Varf()}^1/2 converges to the standard normal distribution with ideal rate O(1/n^1/2) under certain conditions with e_k independent but non-identically distributed.

Three dimensions transient elastrodynamic equation is given through the Laplace integral transform and its fundamental solution have been derived in more detail. According to Beth's reciprocal theorem the boundary integral equation of transient elastrodynamic problem appropriate to the tranformed space is established and solvability of boundary-value problem is also studied.

For the nonlinear periodic large-scale system

we first derive the sufficient conditions to guarantee that (A) has unique and asymptotically stable periodic solution (namly, stationary oscillation), using the character of a matrix measure. Then we obtain the sufficient conditions of stationary oscillation for large-scale systems with structural perturbations,

These conditions are simple and easily verifiable.

In this paper, we have improved the Hoff's results^[1] and proved the existence of globally smooth solutions of system (1), (2) under large initial data by using a new, simple method.

The complexity of group testing is an unsolved hard problem. Recently, Du and Ko discussed some problems related to it, which explained the intractability of group testing. One of the problems is the determincy of test-sequences, on which they left several open problems. In this paper, we resolve some of them.

The doubly stochastic time series models are the general nonlinear time series models which include many known nonlinear models such as the time-varying coefficient, exponentially autoregressive and bilinear models. The general stationary conditions of these models will be given in this paper, especially when the coefficients are MA(1).

The complexity of group testing is a long-standing open problem. Recently, Du and Ko studied some related problems which can explain the difficulty of group testing indirectly.One of such problems is called the determinacy problem on which they Left some open problem.In this paper,we resolve one of these problems.

One period of an M-sequence is an important finite sequence. In this paper, we discuss its complexity from three aspects——upper and lower bounds, ergodicity and distribution.

In this paper, we apply the method of Majorants to give some existence theorems of analyric solution for the two classes linear functional differential equations (1.1) and (1.2).

The valve-placement problem is a combinatorial optimization problem with strong background. In this paper,we study an important special case. We show the NP-completeness of the problem in this special case and also present some results concerning the existence of polynomial time heuristics for the problem.

The population evolution system is treally a nonlinear system. In this paper,a age-ependent logistic nonlinear population model has been studied. The model is described by the first order nonlinear partial differential equation. The existence and uniqueness of the equation have been proved. The asymptotity of the equation has been discussed.