THE EQUILIBRIA OF THE SIZE STRUCTURED POPULATION MODEL

In this paper the existence and stability of the positive equilibrium of the size-structured population model are proved by Rabinowitz‘s theorem and the local linearization method.The result here shows that near the bifurcation point where a branch of positive equilibria appears,the stability of the positive equilibrium on the branch is dcpendent on the direction of the bifurcation.The argument for the model of age-structured population is generalized in this paper.     

A Parallel Algorithm for Corner Detection on Object Contour

; A new parallel algorithm for corner detection on object contour is presented in the paper. In this algorithm whenever a point (pixel) is scanned, the k direction codes between the two sides of the point, which is on the edge of an object, are obtained by k-step forward and backward boundary tracking. A comer is determined by the sum of the difference between the two weighted code chains. Note that the whole chain code sequence or boundary of an object is not necessary to be extracted at all in this algorithm, and the corners are obtained immediately once the image is scanned, furthermore, what humans perceive as corners can be detected and localized by this algorithm.     

Degradation algorithm of compressive sensing

The compressive sensing(CS) theory allows people to obtain signal in the frequency much lower than the requested one of sampling theorem.Because the theory is based on the assumption of that the location of sparse values is unknown,it has many constraints in practical applications.In fact,in many cases such as image processing,the location of sparse values is knowable,and CS can degrade to a linear process.In order to take full advantage of the visual information of images,this paper proposes the concept of dimensionality reduction transform matrix and then selects sparse values by constructing an accuracy control matrix,so on this basis,a degradation algorithm is designed that the signal can be obtained by the measurements as many as sparse values and reconstructed through a linear process.In comparison with similar methods,the degradation algorithm is effective in reducing the number of sensors and improving operational efficiency.The algorithm is also used to achieve the CS process with the same amount of data as joint photographic exports group(JPEG) compression and acquires the same display effect.     

COMPATIBLE EXTENSIONS OF FUZZY RELATIONS

In 1930 Szpilrajn proved that any strict partial order can be embedded in a strict linear order.This theorem was later refined by Dushnik and Miller(1941),Hansson(1968), Suzumura(1976),Donaldson and Weymark(1998), Bossert(1999). Particularly Suzumura introduced the important concept of compatible extension of a(crisp)relation.These extension theorems have an important role in welfare economics. In particularSzpilrajn theorem is the main tool for proving a known theorem of Richter that establishes theequivalence between rational and congruous consumers. In 1999 Duggan proved a general extensiontheorem that contains all these results. In this paper we introduce the notion of compatible extension of a fuzzy relation and we provean extension theorem for fuzzy relations. Our result generalizes to fuzzy set theory the main part ofDuggan's theorem. As applications we obtain fuzzy versions of the theorems of Szpilrajn, Hanssonand Suzumura. We also prove that an asymmetric and transitive fuzzy relation has a com     

EXISTENCE AND ANALYTICAL APPROXIMATIONS OF LIMIT CYCLES IN A THREE-DIMENSIONAL NONLINEAR AUTONOMOUS FEEDBACK CONTROL SYSTEM

This paper is concerned with the existence and the analytical approximations of limit cycles in a three-dimensional nonlinear autonomous feedback control system. Based on three-dimensional Hopf bifurcation theorem, the existence of limit cycles is first proved. Then the homotopy analysis method （HAM） is applied to obtain the analytical approximations of the limit cycle and its frequency. In deriving the higher-order approximations, the authors utilized the idea of a perturbation procedure proposed for limit cycles＇ approximation in van der Pol equation. By comparing with the numerical integration solutions, it is shown that the accuracy of the analytical results obtained in this paper is very high, even when the amplitude of the limit cycle is large.     

A NEW CHARACTERIZATION OF FIXED MODES FOR DECENTRALIZED CONTROL SYSTEMS

In this paper,a study of the characterization of fixed modes in decentralized control ismade.A new sufficient and necessary condition for the existence of fixed modes is obtained by meansof the generalized eigenvalue theory of matrix pairs,and the computability of the new condition ispresented.The results show that fixed modes can be computed in a reliable and efficient manner.     

A NEW PROOF OF THE HADAMARD MONODROMY THEOREM AND THE PERIODIC SOLUTION FOR A CLASS OF O.D.E.SYSTEMS AT RESONANCE

Early in 1904,Hadamard[1]showed the scale implicit function theorem of finitedimensions.Then it was generalized to infinite dimensions.In this paper a new proof of this theoremis given and the unique existence of the periodic solution for a class of ordinary differential equationsystems at resonance is obtained.     

A MULTI-ATTRIBUTE LARGE GROUP EMERGENCY DECISION MAKING METHOD BASED ON GROUP PREFERENCE CONSISTENCY OF GENERALIZED INTERVAL-VALUED TRAPEZOIDAL FUZZY NUMBERS

In this paper,a new decision making approach is proposed for the multi-attribute large group emergency decision-making problem that attribute weights are unknown and expert preference information is expressed by generalized interval-valued trapezoidal fuzzy numbers(GITFNs).Firstly,a degree of similarity formula between GITFNs is presented.Secondly,expert preference information on different alternatives is clustered into several aggregations via the fuzzy clustering method.As the clustering proceeds,an index of group preference consistency is introduced to ensure the clustering effect,and then the group preference information on different alternatives is obtained.Thirdly,the TOPSIS method is used to rank the alternatives.Finally,an example is taken to show the feasibility and effectiveness of this approach.These method can ensure the consistency degree of group preference,thus decision efficiency of emergency response activities can be improved.     

New delay-dependent stability criteria and robust control of nonlinear time-delay systems

This paper investigates the stability analysis and H_∞ control for a class of nonlinear timedelay systems,and proposes a number of new results.Firstly,an equivalent form is given for this class of systems by means of coordinate transformation and orthogonal decomposition of vector fields.Then,based on the equivalent form,some delay-dependent results are derived for the stability analysis of the systems by constructing a novel Lyapunov functional.Thirdly,the authors use the equivalent form and the obtained stability results to investigate the H_∞ control problem for a class of nonhnear time-delay control systems,and present a control design procedure.Finally,an illustrative example is given to show the effectiveness of the results obtained in this paper.It is shown that the main results of this paper are easier to check than some existing ones,and have less conservatism.     

Model and Algorithm of Transportation Problem on Network

Transportation problem on network needs to determine the freight quantity and the transportation route between supply point and demand point. Therefore, taken the uncertainty of freight supply and demand into account, a collaborative optimization model is formulated with transportation capacity constraint. In addition, a two-stage genetic algorithm （GA） is put forward. Herein, the first stage of this GA is adopted a priority-based encoding method for determining the supply and demand relationship between different points. Then supply and demand relationship which the supply and the demand are both greater than zero is a minimum cost flow （MCF） problem on network in the second stage. Aim at the purpose to solve MCF problem, a GA is employed. Moreover, this algorithm is suitable for balance and unbalance transportation on directed network or undirected network. At last, the model and algorithm are verified to be efficient by a numerical example.     

CONVERGENCE OF A CLASS OF MULTI-AGENT SYSTEMS IN PROBABILISTIC FRAMEWORK

Multi-agent systems arise from diverse fields in natural and artificial systems, and a basic problem is to understand how locally interacting agents lead to collective behaviors （e.g., synchronization） of the overall system. In this paper, we will consider a basic class of multi-agent systems that are described by a simplification of the well-known Vicsek model. This model looks simple, but the rigorous theoretical analysis is quite complicated, because there are strong nonlinear interactions among the agents in the model. In fact, most of the existing results on synchronization need to impose a certain connectivity condition on the global behaviors of the agents＇ trajectories （or on the closed-loop dynamic neighborhood graphs）, which are quite hard to verify in general. In this paper, by introducing a probabilistic framework to this problem, we will provide a complete and rigorous proof for the fact that the overall multi-agent system will synchronize with large probability as long as the number of agents is large enough. The proof is based on a detailed analysis of both the dynamical properties of the nonlinear system evolution and the asymptotic properties of the spectrum of random geometric graphs.     

Semi-algebraically connected components of minimum points of a polynomial function

In a recent article, the authors provided an effective algorithm for both computing the global infimum of f and deciding whether or not the infimum of f is attained, where f is a multivariate polynomial over the field R of real numbers. As a complement, the authors investigate the semi- algebraically connected components of minimum points of a polynomial function in this paper. For a given multivariate polynomial f over R, it is shown that the above-mentioned algorithm can find at least one point in each semi-algebraically connected component of minimum points of f whenever f has its global minimum.     

A line search filter secant method for nonlinear equality constrained optimization

<正> This paper formulates and analyzes a line search method for general nonlinear equalityconstrained optimization based on filter methods for step acceptance and secant methods for searchdirection.The feature of the new algorithm is that the secant algorithm is used to produce a searchdirection,a backtracking line search procedure is used to generate step size,some filtered rules areused to determine step acceptance,second order correction technique is used to reduce infeasibility andovercome the Maratos effect.Global convergence properties of this method are analyzed:under mildassumptions it is showed that every limit point of the sequence of iterates generated by the algorithmis feasible,and that there exists at least one limit point that is a stationary point for the problem.Moreover,it is also established that the Maratos effect can be overcome in our new approach by addingsecond order correction steps so that fast local superlinear convergence to a second order sufficient localsolution is achieved.Finally,the results of numerical experiments are reported to show the effectivenessof the line search filter secant method.     

Coopetition Games and Its Application in Cournot Model

Coopetition has become the current strategic trend of the economic development. In this paper, coopetition game and the equi‘ibrium have been developed through comparing the characteristics of cooperation game with those of competition game. Furthmore, an algorithm using one kind of minimax theorem proposed by Dingzhu-Du in 1990 is put forward to solve coopetitior game. The algorithm has great advantages over other methods, which can solve irregular and non-differential concave or convex function of the games.A coopetition game of cournot model with asymmetric oligarchs is advanced and the coopetition equilibriums have been obtained by simulation. The simulation results are compared with that of Nash equilibrium. Conclusions can be made that more members in a coalition could get higher satisfaction degrees at coopetition equilibriums, which is dependent on cost and potential market demands.     

Modelling of a Class of Nonstationary Time Series with Kalman Filter Using Moving Window

In this paper a method for modelling and forecasting of a class of nonstationary time series with Kalmnan filter using moving window is proposed. The procedure of the method is as follows: in terms of parameter estimation during recursive process by using LSM, the state space equation is constructed, then the Kahnan filter using moving window is made to get the data with reduced level of observation noise. Finally, the precise parameter estimation can be obtained by using the LSM again. The algorithm is carried on recursively. Good results for estimating and forecasting are shown by simulation, examples. The algorithm of Kalman filter using moving window proposed by us is introduced in this paper, which can guarantee the precision and convergence of Kalman filter.     

Necessary conditions for efficient solution of vector optimization problems

In this paper,by using Ljusternik’s theorem and the open mapping theorem of convex process,the author gives necessary conditions for the efficient solution to the vector optimization problems without requiring that the ordering cone in the objective space has a nonempty interior.     

HOW ARE PRODUCT-SERVICE COMBINED OFFERS PROVIDED IN GERMANY AND ITALY？ ANALYSIS WITH COMPANY SIZES AND COUNTRIES

A new business concept that offers products and services in a different way of traditional product-sales businesses is getting more attention especially in manufacturing industries. This paper investigates how this new business by means of integration of products and services is achieved in Germany and Italy. In addition, it analyzes the differences according to the company sizes. The results include that this type of business is in many cases motivated by their focus on customers and often consists of physical products and their maintenance. The Italian companies, as opposed to the German ones, often design their physical products specifically for this type of offers. From the analysis based on the size difference, small companies are found to achieve specific design for this type of offers while owning physical products. There do not seem to be any established methods or tools developed to support the development of such offers and within such methods/tools there would be room for more adaptation in form of physical product design.     

Finite-time tracking control for motor servo systems with unknown dead-zones

A finite-time tracking control scheme is proposed in this paper based on the terminal slid- ing mode principle for motor servo systems with unknown nonlinear dead-zone inputs. By using the differential mean value theorem, the dead-zone is represented as a time-varying system and thus the inverse compensation approach is avoided. Then, an indirect terminal sliding mode control （ITSMC） is developed to guarantee the finite-time convergence of the tracking error and to overcome the singu- larity problem in the traditional terminal sliding mode control. In the proposed controller design, the unknown nonlinearity of the system is approximated by a simple sigmoid neural network, and the ap- proximation error is diminished by employing a robust term. Comparative experiments on a turntable servo system are conducted to show the superior performance of the proposed method.     

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.