A CRITERION FOR DISCRETE SPECTRUM OF A CLASS OF DIFFERENTIAL OPERATORS

In this paper,a sufficient and necessary condition is obtained to ensure that the spectrum of a class of 2n-order weighted differential operators is discrete.The proof is based on the method of certain weighted Sobolev spaces to be compactly embedded in weighted L^2(R).     

ON APPROXIMATION BY REPRODUCING KERNEL SPACES IN WEIGHTED L^p SPACES

In this paper, we investigate the order of approximation by reproducing kernel spaces on （-1, 1） in weighted L^p spaces. We first restate the translation network from the view of reproducing kernel spaces and then construct a sequence of approximating operators with the help of Jacobi orthogonal polynomials, with which we establish a kind of Jackson inequality to describe the error estimate. Finally, The results are used to discuss an approximation problem arising from learning theory.     

Two-Weight Norm Inequality for Imaginary Powers of a Laplace Operator

We study two-weight norm inequality for imaginary powers of a Laplace operator in R^n, n ≥ 1, especially from weighted Lebesgue space Lv^p（R^n） to weighted Lebesgue space Lμ^p（R^n）, where 1 〈 p 〈 ∞. We prove that the two-weighted norm inequality holds whenever for some t 〉 1, （μ^t, v^t） ∈ Ap, or if （μ, v） ∈Ap, where μ and v^-1/（p-1） satisfy the growth condition and reverse doubling property.     

Interval-valued intuitionistic fuzzy aggregation operators

The notion of the interval-valued intuitionistic fuzzy set (IVIFS) is a generalization of that of the Atanassov’s intuitionistic fuzzy set. The fundamental characteristic of IVIFS is that the values of its membership function and non-membership function are intervals rather than exact numbers. There are various averaging operators defined for IVIFSs. These operators are not monotone with respect to the total order of IVIFS, which is undesirable. This paper shows how such averaging operators can be represented by using additive generators of the product triangular norm, which simplifies and extends the existing constructions. Moreover, two new aggregation operators based on the ukasiewicz triangular norm are proposed, which are monotone with respect to the total order of IVIFS. Finally, an application of the interval-valued intuitionistic fuzzy weighted averaging operator is given to multiple criteria decision making.     

Weighted Probability Density Estimator with Updated Bandwidths

In this paper, the authors study a class of weighted version of probability density estimator.It is shown that the weighted estimator contains some existing estimators of probability density, no matter they are recursive or non-recursive. Some statistical results including weak consistency, strong consistency, rate of strong consistency, and asymptotic normality are established under some mild conditions. Moreover, the random weighted estimator is also investigated. Some numerical simulations an...     

STRONG CONVERGENCE OF MONOTONE HYBRID METHOD FOR FIXED POINT ITERATION PROCESSES*

K. Nakajo and W. Takahashi in 2003 proved the strong convergence theorems for nonex-pansive mappings, nonexpansive semigroups, and proximal point algorithm for zero point of monotone operators in Hilbert spaces by using the hybrid method in mathematical programming. The purpose of this paper is to modify the hybrid iteration method of K. Nakajo and W. Takahashi through the monotone hybrid method, and to prove strong convergence theorems. The convergence rate of iteration process of the monotone hybrid method is faster than that of the iteration process of the hybrid method of K. Nakajo and W. Takahashi. In the proofs in this article, Cauchy sequence method is used to avoid the use of the demiclosedness principle and Opial＇s condition.     

THE WEAK BENSON PROPER EFFICIENT SUBGRADIENT AND THE OPTIMALITY CONDITIONS OF SET－VALUED OPTIMIZATION

The subgradient,under the weak Benson proper efficiency,of a set-valued mapping in ordere Banach space is developed.and the weak Benson proper efficient HahnBanach theorem of a set-valued mapping is established.with which the existence of the subgradient is proved and the characterizations of weak Benson proper efficient elements of constrained(unconstrained)vector set-valued optimization problems are presented.     

Some new similarity measures for intuitionistic fuzzy values and their application in group decision making

We first propose a series of similarity measures for intuitionistic fuzzy values (IFVs) based on the intuitionistic fuzzy operators (Atanassov 1995). The parameters in the proposed similarity measures can control the degree of membership and the degree of non-membership of an IFV, which can reflect the decision maker’s risk preference. Moreover, we can obtain some known similarity measures when some fixed values are assigned to the parameters. Furthermore, we apply the similarity measures to aggregate IFVs and develop some aggregation operators, such as the intuitionistic fuzzy dependent averaging operator and the intuitionistic fuzzy dependent geometric operator, whose prominent characteristic is that the associated weights only depend on the aggregated intuitionistic fuzzy arguments and can relieve the influence of unfair arguments on the aggregated results. Based on these aggregation operators, we develop some group decision making methods, and finally extend our results to interval-valued intuitionistic fuzzy environment.     

THE SPECTRAL COMPLETION OF A CLASS OF OPERATOR PARTIAL MATRICES

1. IntroductionLet Hi be complex Banach spaces, i = 1, 2,'' 5 n, and B(Hi, Hi) (B(Hi) if i = j) denotethe Banach space of all bounded linear operators from Hi to Hi. Let H ~ ffi:=IHi; thenA E B(H) may .be denoted by (Ail)... with Ail e B(Hj,Hi). Given a subset J C {(i,j)li,j = 1, 2,'',n} and Ail E B(Hj,Hi) for (i,i) e J, we get a partially specified n x n matriX(Xij)... with Xij ~ Ail if (i,i) e J and Xby (Ail)J If Q = (oil) E B(H) such that oil ~ Aijwhenever (i,i) e J, the…     

FINITE DIMENSIONAL BEHAVIOR FOR THE DISSIPATIVE GENERALIZED SYMMETRIC REGULARIZED LONG WAVE EQUATIONS

This paper deals with the asymptotic behaviour of solutions for the generalized symmetric regularized long wave equations with dissipation term. We first show the existence of global weak attractors for the periodic initial value problem of this equations in H2 x H1. And then by an energy equation and an idea of Ghidaglia and Guo, we conclude that the global weak attractor is actually the global strong attractor for S(t) in H2(2) x H1(M).The finite dimensionality of the global attractor is also established.     

APPLICATIONS OF THE DIVISION PROBLEM IN SPACES OF ENTIRE FUNCTIONS

Based on the results of (Wang 2001), we give some applications of division problem in spaces of entirefunctions of finite type. Especially, when ρ=1 and H is the support functions of a bounded convex domainof C~N, our theorems extend the results of(Krivosheev 1991)and(Lelong 1986).     

ANTI-PERIODIC SOLUTIONS FOR FIRST AND SECOND ORDER NONLINEAR EVOLUTION EQUATIONS IN BANACH SPACES

In this paper, a new existence theorem of anti-periodic solutions for a class ofstrongly nonlinear evolution equations in Banach spaces is presented. The equations con-tain nonlinear monotone operators and a nonmonotone perturbation. Moreover, throughan appropriate transformation, the existence of anti-periodic solutions for a class of second-order nonlinear evolution equations is verified. Our abstract results are illustrated by anexample from quasi-linear partial differential equations with time anti-periodic conditionsand an example from quasi-linear anti-periodic hyperbolic differential equations.     

Vector tracking loops in GNSS receivers for dynamic weak signals

Vehicle positioning with the global navigation satellite system(GNSS) in urban environments faces two problems which are attenuation and dynamic.For traditional GNSS receivers hardly able to track dynamic weak signals,the coupling between all visible satellite signals is ignored in the absence of navigation state feedback,and thermal noise error and dynamic stress threshold are contradictory due to non-coherent discriminators.The vector delay/frequency locked loop(VDFLL) with navigation state feedback and the joint vector tracking loop(JVTL) with coherent discriminator which is a synchronization parameter tracking loop based on maximum likelihood estimation(MLE) are proposed to improve the tracking sensitivity of GNSS receiver in dynamic weak signal environments.A joint vector position tracking loop(JVPTL) directly tracking user position and velocity is proposed to further improve tracking sensitivity.The coherent navigation parameter discriminator of JVPTL,being able to ease the contradiction between thermal noise error and dynamic stress threshold,is based on MLE according to the navigation parameter based linear model of received baseband signals.Simulation results show that JVPTL,which combines the advantages of both VDFLL and JVTL,performs better than both VDFLL and JVTL in dynamic weak signal environments.     

BASIC PROPERTIES OF K-SPACES

Every complete metric linear space is a K-space.A non-completenormed space can be a K-space.And non-metrizable K-spaces exist.A series ofbasic results on complete metric linear spaces Can be generalized to K-spaces.Forexample,every bounded linear operator from a K-space into a locally convex spaceis sequentially continuous;every bounded semi-norm on a K-space is sequentiallycontinuous and,therefore,piecewise separable;a.C-sequeatial K-space is both bar-relled and bornological;the family of sequentially continuous linear functionals ona K-space is weak sequentially complete.     

POINTWISE MULTIPLIERS OF DIRICHLET TYPE SPACES ON THE UNIT BALL OF C~n

1 IntroductionLet B be the uait ball of Cn with boundary S, u the Lebesgue measure on B normalized sothat u(B) = 1 and u the normalized rotation invarian measure on S, i.e. a(S) = 1. The classof all holomorphic functions will be denoted by H(B).Let f be i…     

Universality of Competitive Networks in Complex Networks

The paper proposes a model which helps to investigate the competitive aspect of real networks in quantitative terms. Through theoretical analysis and numerical simulations, it shows that the competitive model has the universality for a weighted network. The relation between parameters in the weighted network and the competitiveness in the competitive network is obtained by theoretical analysis. Based on the expression of the degree distribution of the competitive network, the strength and degree distributions of the weighted network can be calculated. The analytical solution reveals that the degree distribution of the weighted network is correlated with the increment and initial value of edge weights, which is verified by numerical simulations. Moreover, the evolving pattern of a clustering coefficient along with network parameters such as the size of a network, an updating coefficient, an initial weight and the competitiveness are obtained by further simulations.     

THE COMPLETENESS OF EIGENFUNCTIONS OF PERTURBATION CONNECTED WITH STURM-LIOUVILLE OPERATORS

In this paper, non-self-adjoint Sturm-Liuville operators in Weyl＇s limit-circle case are studied. We first determine all the non-self-adjoint boundary conditions yielding dissipative operators for each allowed Sturm-Liouville differential expression. Then, using the characteristic determinant, we prove the completeness of the system of eigenfunctions and associated functions for these dissipative operators.     

Approaches to Improving Consistency of Interval Fuzzy Preference Relations

This article introduces a consistency index for measuring the consistency level of an interval fuzzy preference relation（IFPR）.An approach is then proposed to construct an additive consistent IFPR from a given inconsistent IFPR.By using a weighted averaging method combining the original IFPR and the constructed consistent IFPR,a formula is put forward to repair an inconsistent IFPR to generate an IFPR with acceptable consistency.An iterative algorithm is subsequently developed to rectify an inconsistent IFPR and derive one with acceptable consistency and weak transitivity.The proposed approaches can not only improve consistency of IFPRs but also preserve the initial interval uncertainty information as much as possible.Numerical examples are presented to illustrate how to apply the proposed approaches.     

The Social Network Analysis of Techno-Economic Systems:Comparing Results Based on Binary and Weighted Networks

The network analysis of a technological system combines the interindustry transactions with a matrix of sectoral innovative efforts as measured by R&D investment intensity.The matrixes of interindustry transactions of R&D-embodied products(innovations)are weighted matrixes where the interindustry flows measure the intensity of the innovation diffusion.In the past,studies using this approach in innovation studies have transformed weighted matrixes into binary matrixes of zero and one element where the flows less than a selected threshold value were considered to be zero and the flows greater than the threshold value were counted as one.Such matrix transformation leads to the loss of a great deal of information.In the present study,using degree and clustering coefficients for both binary direct as well as weighted direct techno-economic networks of the manufacturing sector of the German economy,we show that the binary directed network analysis is incapable of refined ranking of interindustry innovation transactions.The total degree index based on the weighted network of the German techno-economic system assigns a unique ranking to each sector,and clustering coefficients show that at least 75%of sectors in the network of Germany have two links with the other industries.However,the same indices based on the binary network are incapable of such refined ranking.     

FEEDBACK CONTROL OF A CLASS OF FLEXIBLE SYSTEMS WITH COUPLED BENDING AND TORSIONAL VIBRATIONS

In this paper, a class of flexible systems of beams with coupled bending andtorsional vibrations, which has important applications in the dynamics of aircraft is dis-cussed. The existence and uniqueness of the solution for this class of systems are proved,where the spectral analysis method and the unconditional base theory are used, and asufficient condition for the asymptotic stability of the closed-loop system is obtained bymeans of the (D) class operators theory.