POSITIVE PERIODIC SOLUTION TO SECOND-ORDER NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATION WITH MIXED DELAY

We discuss two types of second-order neutral functional differential equations with mixed delay in this paper. By applying Krasnoselskii's fixed-point theorem, some results about the existence of positive periodic solution to the systems are obtained, which complement the previous known results.     

ON CERTAIN CLASS OF ANALYTIC FUNCTIONS DEFINED BY DIFFERENTIAL SUBORDINATION

In this paper, the new subclass Bn( ,a,A,B) of analytic functions is introduced. Its subordination relations, inclusion relations, the inequality properties and convering theorem are discussed. The results obtained in this paper are sharp, which generalize the related works of some authors and some other new results are obtained.     

Multiplication formulas for Kubert functions

The aim of this paper is two folds. First, we shall prove a general reduction theorem to the Spannenintegral of products of （generalized） Kubert functions. Second, we apply the special case of Carlitz＇s theorem to the elaboration of earlier results on the mean values of the product of Dirichlet L-functions at integer arguments. Carlitz＇s theorem is a generalization of a classical result of Nielsen in 1923. Regarding the reduction theorem, we shall unify both the results of Carlitz （for sums） and Mordell （for integrals）, both of which are generalizations of preceding results by Frasnel, Landau, Mikolas, and Romanoff et al. These not only generalize earlier results but also cover some recent results. For example, Beck＇s lamma is the same as Carlitz＇s result, while some results of Maier may be deduced from those of Romanoff. To this end, we shall consider the Stiletjes integral which incorporates both sums and integrals. Now, we have an expansion of the sum of products of Bernoulli polynomials that we may apply it to elaborate on the results of afore-mentioned papers and can supplement them by related results.     

一类具多个偏差变元混合型p-Laplacian周期解(英文)

Based on Mansevich-Mawhin continuation theorem and some analysis skill,some sufficient conditions for the existence of periodic solutions for mixed type p-Laplacian equation with deviating arguments are established,which are complement of previously known results.     

Harmonic L~p-functions on Complete Riemannian Manifolds

This survey paper concerns some existence theorems of harmonic functions belonging to LP (M), M being a complete Riemannian manifold. It is well known that a function which is analytic and bounded on the whole complex plane must reduce to a constant.This classical result, known as Liouville's theorem, is also true on a higher-dimensional Euclidean spaces. The generalization of this theorem to other Riemannian manifolds is very interesting. Besides its beauty, the proof usally requires sharp estimates which provide deeper understanding of the Laplacian and hence give broad applications to problems in global analysis.The basic problem in this paper is to study how the geometric conditions of a complete Riemannian manifold affect the validity of the Liouville theorem. The paper consists of two parts. Part I describes the results systematically and Part I will be more technical and will contain the detailed proofs of the results given in the first part.     

Global positive periodic solutions of age-dependent competing systems

This paper is to investigate positive periodic solutions of a biological system composed of two competing species. The existence and uniqueness of nonnegative solutions to the model for a set of given vital rates and initial distribution are treated and the contractive property of the solutions explored. Based on these results, some simple conditions for the global existence of positive periodic orbits are established by means of Horn’s asymptotic fixed point theorem.     

Trigonometric series with a generalized monotonicity condition

In this paper,we consider numerical and trigonometric series with a very general monotonicity condition.First,a fundamental decomposition is established from which the sufficient parts of many classical results in Fourier analysis can be derived in this general setting.In the second part of the paper a necessary and sufficient condition for the uniform convergence of sine series is proved generalizing a classical theorem of Chaundy and Jolliffe.     

Geometric meanings of the parameters on rational conic segments

Using algebraic and geometric methods,functional relationships between a point on a conic segment and its corresponding parameter are derived when the conic segment is presented by a rational quadratic or cubic Bézier curve.That is,the inverse mappings of the mappings represented by the expressions of rational conic segments are given.These formulae relate some triangular areas or some angles,determined by the selected point on the curve and the control points of the curve,as well as by the weights of the rational Bézier curve.Also,the relationship can be expressed by the corresponding parametric angles of the selected point and two endpoints on the conic segment,as well as by the weights of the rational Bézier curve.These results are greatly useful for optimal parametrization,reparametrization,etc.,of rational Bézier curves and surfaces.     

Orthogonality of Generalized (θ,φ)-Derivations on Ideals

In this paper,necessary and sufficient conditions concerning the orthogonality and the composition of a couple of generalized (θ,φ)-derivations on a nonzero ideal of a semiprime ring are presented.These results are generalizations of several results of Breˇsar and Vukman,which are related to a theorem of Posner on the product of two derivations on a prime ring.     

On an extension of the H k mean curvature flow

In this note,we generalize an extension theorem in [Le-Sesum] and [Xu-Ye-Zhao] of the mean curvature flow to the Hk mean curvature flow under some extra conditions.The main difficulty in proving the extension theorem is to find a suitable version of Michael-Simon inequality for the Hk mean curvature flow,and to do a suitable Moser iteration process.These two problems are overcome by imposing some extra conditions which may be weakened or removed in our forthcoming paper.On the other hand,we derive some estimates for the generalized mean curvature flow,which have their own interesting.     

理想上的广义$(\theta,\phi)$-导子的正交性

In this paper,necessary and sufficient conditions concerning the orthogonality and the composition of a couple of generalized （θ,φ）-derivations on a nonzero ideal of a semiprime ring are presented.These results are generalizations of several results of Breˇsar and Vukman,which are related to a theorem of Posner on the product of two derivations on a prime ring.     

ON NOETHER'S THEOREM AND CONSERVATION LAWS IN THERMO-ELASTICITY

Noether's theorem is generalized to the theory of coupled fields with parameters in this paper. Considering that many problems in continuum mechanics have Lagrange densities which are linear combinations of convolution integrals on a parameter of their arguments, the condition of stationary value of these functionals is discussed. Following the thought of Noether's theorem, the author reveals some relations among the invariants of the functionals mentioned above under a family of infinitesimal transformations, variational principles and conservation laws. In addition, two conservation laws for thermo-elasticity are established.     

ESTIMATES OF THE DOUBLE DETERMINANTS OF QUATERNION MATRICES

An estimate of the upper bound is given for the double determinant of the sum of two arbitrary quaternion matrices, and meanwhile the lower bound on the double determinant is established especially for the sum of two quaternion matrices which form an assortive pair. As applications, some known results are obtained as corollaries and a question in the matrix determinant theory is answered completely.     

OBLIQUE DERIVATIVE BOUNDARY VALUE PROBLEMS OF MIXED TYPE EQUATION

In this article, the oblique derivative boundary value problems for the mixed type equation uxx sgny uyy = aux buy cu d in another more general domain are discussed and by using the method of complex analysis, a series of solvability results is obtained, which generalizes some recent results.     

A Survey of the Whittaker-Shannon Sampling Theorem and Some of its Extensions

The aim of this paper is to present a survey of results concerning the WhittakerKotel′nikov-Raabe-Shannon-Someya sampling theorem and its various extensions obtained at Aachen since 1977. This theorem, basic in communication engineering, is often called the cardinal interpolation series theorem in mathematical circles. The interconnections of the sampling theorem (in the setting of Paley-Wiener space) with the theory of Fourier series and integrals are examined. Emphasis is placed upon error analysis, including the aliasing, round-off (or quantization), and time jitter errors. Some new error estimates are given, others are improved: many of the proofs are reduced to a common structure. Both deterministic and probabilistic methods are employed, whereas these results are worked out in detail, the paper also contains a brief discussion of some of the various generalizations.     

INVARIANCE PRINCIPLE FOR THE INTEGRAL PERIODOGRAM OF A MULTIPLE TIME SERIES

Many authers have studied the asymptotic behavior of the integral periodogram of a Gaussian stationary series. In this paper, the invariance principle for the integral periodogram of a multiple time series is investigated. We have obtained the following theorem:Let X, be a real M -dimensional stationary time series with spectral density matrix f(λ) which satis-fies the conditions:M,and X, can be represented in theform: Xn =whereξ, is the M-dimensional fourth order moment existedstationary martingale series, thenweakly converges to a Gauss process η(λ) withEη(λ) = 0,where V and Q are the second and fourth moment of the martingale seriesξ , respectively.From this theorem, two corollaries have been given, which cover some results of [2][5][6].     

对称Z-矩阵的惯量以及其Schur补的若干交错性质

In this Paper,the inertia of a symmetric Z-matrix is studied,and bounds of the number of its positive eigenvalues are obtained.Also the interlacing theorem for Schur complement of a symmetric Z-matrix is established,which can be considered as a generalization Cauchy interlacing theorem in some extent.     

A NEW CLASS OF BILEVEL GENERALIZED MIXED EQUILIBRIUM PROBLEMS IN BANACH SPACES

A new class of bilevel generalized mixed equilibrium problems involving setvalued mappings is introduced and studied in a real Banach space. By using the auxiliary principle technique, new iterative algorithms for solving the generalized mixed equilibrium problems and bilevel generalized mixed equilibrium problems involving set-valued mappings are suggested and analyzed. Existence of solutions and strong convergence of the iterative sequences generated by the algorithms are proved under quite mild conditions. The behavior of the solution set of the generalized mixed equilibrium problems and bilevel generalized mixed equilibrium problems is also discussed. These results are new and generalize some recent results in this field.     

Ambarzumyan Theorems for Dirac Operators

We consider the inverse eigenvalue problems for stationary Dirac systems with differentiable selfadjoint matrix potential.The theorem of Ambarzumyan for a Sturm-Liouville problem is extended to Dirac operators,which are subject to separation boundary conditions or periodic(semi-periodic)boundary conditions,and some analogs of Ambarzumyan's theorem are obtained.The proof is based on the existence and extremal properties of the smallest eigenvalue of corresponding vectorial Sturm-Liouville operators,which are the second power of Dirac operators.     

Semi-uniform Sub-additive Ergodic Theorems for Skew-product Quasi-flows

The aim of this paper is to extend the semi-uniform ergodic theorem and semi-uniform sub-additive ergodic theorem to skew-product quasi-flows. Furthermore, more strict inequalities about these two theorems are established. By making use of these results, it is feasible to get uniform estimation of the Lyapunov exponent of some special systems even under non-uniform hypotheses