UPPER AND LOWER SOLUTIONS METHODS FOR EXISTENCE OF PERIODIC SOLUTIONS OF DUFFING EQUATION

1.IntroductionandNotationsInthispapertwestudytheexistenceofsolutionstothefollowingperiodicboundaryvalueproblemforthesecondorderDuffingequationwheresisarealparameter,g:[0,TIxR~RisaCarath6odoryfunctionandkER\{0}.Werecall(forexample,see[1])thatg:[0,TIxR~RiscalledaCarath6odoryfunctionifg(.,x)ismeasurableforallxERandg(t,.)iscontinuousfora.e.tE[0,TI.Theexistenceproblemfor(1.1)--(1.2)byusingtheupperandlowersolutionsmethodhasbeenstudiedbyFabryetal.in[2]foramoregeneralcasewhereacontinuousdampin…     

f-heredity knowledge and f-heredity mining

1. INTRODUCTION Professor Z.Pawlak, a Poland mathematician, putforward rough sets theory in 1982[1] and gave aprimary discussion about it. Ref. [2] developed roughsets into S-rough sets and gave a further discussion; Refs[3~5] put forward the heredity characteristics (F-heredity, F -heredity, F-heredity)of S-roughsets.There exists such a phenomena in S-rough sets:Suppose U={x1,x2,x3,x4,x5} is an element universe,α={α1,α2} is the attributes in U,[x]α is the knowledgewith attribute…     

Optimal deterministic disturbances rejection for singularly perturbed linear systems

1. INTRODUCTION It is well known that external disturbances exist in almost all practical systems, such as wind or ocean wave forces in active control systems for offshore structures[1], harmonic oscillations in flight control systems through wind shear[2] , and periodic disturb- ance in the disk drive[3]. In recent years, various reliable approaches with regard to the disturbance rejection and cancellation have been well documented in many literatures. Lee et al. [4] proposed the model-ba…     

THREE-POINT BOUNDARY VALUE PROBLEMSFOR A CLASS OF THREE ORDER DIFFERENTIAL INCLUSIONS

1.IntroductionandLemmasThree-pointboundaryvalueproblems(BVPforshort)forthreeorderdifferentialequationsareveryusefulincertainpracticalworkandattractcloseattentionextensively,see[l--41.Recently,in[11,GuptaandLakshmikanthamstudiedthefollowingthree-pointBVP:U"'(x)=f(x,ulU',U")--e(x),(l)u(0)=u(n)=u(1)~0,(2)wheref:[0,1]xR3-RdoesnothavetobecontinuousandnE(0,1).ThemainresultisthefollowingTheoremLetfsatisfyCarntheodory'sc.nditions[1]andthefollowingconditions:i)3a,b,cER,or(x)ELI[0,1],suchthatfo…     

A Regression Analysis Model Based on Wavelet Networks

1　 IntroductionWavelet analysis is one of the newestsubjects developing quickly in the pastfew decades,with theoretical significance and a wide range of application.Wavelet analysis was notused in the study of statistics until a few years ago.And discussions of nonlinear waveletestimating are focused mainly on two kinds of models. The first one is the modelconsidered by Donoho and his coauthors[1— 3] :yi =f( xi) εi,i =1 ,… ,n =2 J 1 ( 1 )wherexi=in∈ [0 ,1 ] ,ε1 ,… ,εnare independente…     

Linguistic Valued Association Rules

1　IntroductionData mining is the process of discovering interesting knowledge from large amounts of datastored either in database,data warehouses,or information repositories. The mining ofassociation rules is one of the most important topics in the field of data mining. Variousmining algorithms about association rules have been discussed in many literatures such as[1]and[2 ].The linguistic valued association rules are discussed in this paper.In Section2 ,the FCM algorithm in [3]is adopted t…     

Function S-rough sets and mining-discovery of rough law in systems

1. INTRODUCTION S-rough sets (singular rough sets) was presented in Ref. [3] in 2002, and defined on α -element equival- ence class [x] with dynamic characteristic. S-rough sets has more advantages than Z.Pawlak’s rough sets[24]. S-rough sets has been applied in dynamic object recognition[21], mechanical engineering[22] and information science[8-13]. In 2005, function S-rough sets was put forward in Refs. [1,2], and is defined on α -function equivalence class [u] with dynamic charact…     

Fuzzy Rough Relation and Its Properties

1　IntroductionThe notion of rough sets has been introduced by Pawlak[1 ] .The conceptof fuzzy sets wasintroduced by Zadeh in his classic paper[2 ] .A comparisons between fuzzy sets and roughsets have been given in Pawlak[3 ] ,where itis shown thatthese concepts are different. Thecombine study of fuzzy set and rough setis important. Then fuzzy rough setis introducedby S. Nanda and S. Majumder in 1992 [4] . In this paper,the concept of fuzzy rough rela-tion and the max- min composition of F…     

Grey Connection Analysis on Countryside Society ＆ Economy Sustainable Development Based—on Per Capita Net Income of Peasants

1　 IntroductionMeadows D.L.published″The Limits to Growth″ in 1 972 [1 ] .WCED published″OurCommon Future″in1 987[2 ] .Since1 960 s,the sustainable development has become oneimportanttopic worldwide.We reaped rich fruits aboutsustainable development[3～ 6] .TheGrey connection analysis is a systems analysis method[7] .By the method we can researchbetween social and economic indexes.By the method,we research the effect of society,economy and ecology environment on per capita net incom…     

Alternative Theorems and Sufficient Conditions of Global Convergence for a Class of Feasible Direction Algorithms

In this paper,two alternative theorems which differ from Theorem 10.2.6 in [1] andTheorem 1 in [3] are presented for a class of feasible direction algorithms.On the basis of alternativetheorems,furthermore,two sufficient conditions of global convergence of this class of algorithms areobtained.     

Analysis and optimization of delays in networked control systems

1 .INTRODUCTIONFeedback control systems wherein the control loopsare closed through networks are called networkedcontrol systems ( NCSs) . (See Fig.1) . Differenttypes of network systems are promoted in terms ofvarious network architectures embedded in controlsystems . There are approxi mately two kinds of NC-Ss :specific NCSs and generalized NCSs . The formerare based on common bus technology (e .g. De-viceNet ,ControlNet and LonWorks[1]) and the laterare constructed through comm…     

FEEDBACK REALIZATION OF HAMILTONIAN SYSTEMS

1 IntroductionIn the last few decades, symplectic geometry becomes a lbcus fOr multi-disciplines. Aspointed out in [1l: '"' cIassical mechanics, statistical mechanics, and quantum mechanics aretreated from the same perspective, that ofsylllplectic geornetry thus showing the unifying powerof the symp1ectic geometric approach." Particularly it becomes a new frame fOr Hamiltoniansystems[2--5]. Symp1ectic a1gorithm, [6] etc., provides a numerical method fOr solving the relatedproblems.In contr…     

Dissipative Control of the State Delayed Systems

1　 IntroductionSince the notion of dissipative system was introduced by Willems ( 1 972 a) [1 ] ,andsubsequently generalized by Hill and Moylan( 1 980 ) [2 ] ,it has played an important role insystems,circuits,and control.Dissipativeness is a generalization of the concept ofpassivity in electrical network and otherdynamical systems which dissipate energy in someabstract sense.Applications of dissipativeness in the stability analysis of linear systemswith certain nonlinear feedback were first…     

Contour representation based on wedgelet

1 .INTRODUCTIONRecently ,visual data has acquired a predominantrole in the exchange of information in many fieldsof communications . However , because of the in-convenience in the storage and distribution of thelarge amount of data ,i mage compression begins toplay ani mportant role . Althoughit has emerged asone of the preeminent tool for i mage compressionat present ,yet wavelets[1]still have obvious short-ages .In general ,a natural i mage contains edges ,smooth regions andtextures[2].…     

Enhanced ants system and its application

1 .INTRODUCTIONAnts system(AS) is one newtype of si mulative evo-lution algorithmfirst developed by Italian scholar M.Dorigo[1 ~5]et al . in recent years . Based on AS,there exist versatile types ,such as ant colonysystem,Max-Min ants system,ants algorithm[ 1 ,2] , which isone bionic algorithm originating from the biologyworld and achieves pronounced effect in a series ofdifficult combinational opti mization problem, espe-cially TSP problem[ 5 ,8 ~1 0].AS has made full development si…     

Color-texture segmentation using JSEG based on Gaussian mixture modeling

1.INTRODUCTIONColor i mage segmentation is useful in many applica-tions.Fromthe segmentationresults,it is possible toidentify regions of interest and objectsinthe scene.Avariety of techniques have been proposed,for exam-ple:stochastic model based approaches[1,4,9],mor-phological watershed based region growing[11],energydiffusion[10],and graph partitioning[7].However,due tothe difficult nature of the problem,there are few auto-matic algorithms that can work well on alarge variety ofdata.Th…     

A NOTE ON COMPLETELY POSITIVE GRAPHS

1. IlltroductionPioneered by M. Hall Jr. in 195811] and investigated by A. Berman [2--4] and J. H. Drew, C.R. Johnson and Loewy[5] et al., completely positive matrices have been shown their importancenot only in the study of block designs in combinatorial analysis[6], but also in establishingeconomic model.[7].Recall that an n x n matrix A is said to be completely positive, denoted by A E CPu, ifthere edest m nonnegative column vectors hi,'', ba such thatwhere I denotes transpose. The …     

State Estimation of Discrete Stochastic Singular System

1　 IntroductionIn the area of singular systems control much work has been done recently. The basictheory of singular systems has been proposed. A lot of results are obtained fordeterministic singluar systems[1～ 2 ] . However,only a few results are from stochasticsingular systems[3～ 5] ,in which attention is paid to time-invariant stochastic singularsystems. The state estimation and observation problems of time-invariant stochasticsingular systems have been discussed in[3 ] .The state estim…     

Family genetic algorithms based on gene exchange and its application

1. INTRODUCTION Genetic algorithms (GA) are a search techniques bas-ed on mechanics of nature selection and were initiallyproposed by Holland[1]. GA have already beensuccessfully applied in many diverse areas, such asfunction optimization, the traveling salesman proble-ms, multiobje-ctive optimization problems, schedulingneural network design, system identification, visioncontrol and machine learning. A detailed review ofthese applications is provided in Refs. [2] and [3]. The strength …     

mproving the Input of Classified Neural Networks Through Feature Construction

SOFTWARE,ALGORITHM AND SIMULATION1. Pas~EClassification, as an important program of data mining, is to build a classified function or model that is able tomap the item Of database to one of given classes. The classification algorithm in common use mainly includebayesian, decision trees, mule induction and neural networks [1].The classification algorithm based on decision trees has been in maturity earlier in 1980s', typical of whichis ID3 by J. R. Quinlan [21, it introduced the …