An Algorithm for the Problem of Minimal Number-Grouped Partitions of Random Permutations

Iu this paper,it is shown that the problem of finding minimal number-grou-ped partitions(MNGP)of random permutations can be solved with an algorithmwhose time complexity is O(n~32~(n-2)),and the open problem in [1] is solved. Definition 1.Let T_n be a rooted tree with its root v_0. If it satisfies the fol-lowing condition that     

Duality Theorems of Multiobjective Programming for a Class of Generalized Convex Functions

1.DefinitionsDefinition1.AfunctionalF(x)inthespaceVCE"issaidtobeasublinearfunctionalifforx,yeV,andor20,Inparticular,F(0)=0.Letop(x)beadifferentiablerealfunctiononasetCCEd.ForagivensublinearfunctionFandafunctionp:CxC-EIIp(x,u)/0(x/u),themoregeneralgeneralizedconvexfunctioncanbedefinedasthefollwing:Definition2.op(x)issaidtobe(F,p)--invarialltconvexfunctiononCifforxl,xZECDefinition3.op(x)issaidtobe(F,P)--invariantquasiconvexfunctiononCifforal,xZECthatis,Definition4.op(x)issaidtobe(F,…     

HOMOTOPY FORMULA FOR A LOCAL q-CONCAVE WEDGE IN STEIN MANIFOLDS AND IT'S APPLICATIONS

1IntroductionTheauthorhasobtainedaKoppelman-Leray-Norguetformulaforaiccafq-coneavewedgeinndimensionalSteinmanifoldsX[11,inthispaperbasedonthisformulaweobtainahomotopyformulaforalocalq-concavewedge,byusingthisformulaweobtainthesolutionformulafor0-equationonlocalq-concavewedges,anddiscussanextensionproblemonlocalq-concavewedges.Inviewofsavespareweusethenotationsdefinitionsandresultsdirectlywithoutspreadout.airlateruseweonlyintroducetwonewdefinitions[2]:Definition1.1Acolloction(U,pl,''tPN)wi…     

On Weak Riemann-Stieltjes Integration of Abstract Function Valued in Locally Convex Topological Algebra

Let A be a locally convex topological algebra.We denote by F the set of allnon-zero multiplicative linear continuous functionals on A and WF the weak topologyon A determined by F. Definition 1 Let x(t),y,(t)be abstract functions mapping closed interval[a,b]to A.Given a severation λ:Let     

＊ Exact Sequence and Commutative Diagrams of Semimodule Homomorphism

61.FundamentalConceptsDefinitionlSupposef:A-Bisamapping,defineKer.f={(x,y)Ix,yeA,f(x)=f(y)}Im'f=lBU(ImfXImf)Lemma1lff:A-Bisamappingg,tl1enKer'fisA)secluivalencerelation,In1'j.isB,sequivalencerelation.Theproofiseasy,weomitithere.Definition2ThelimitedsequenceofR-semimoduleI1omomorphism-flf2f3f.-lf"A.-A,-A=-.-'-A"-,-A"iscalled*exact,ifIm.f=Ker'f-,(1相似文献   

The Minimun -Bases for Partially Order Sets

Asetofgeneratingelements(see[1,2J)anditsdualconcept,anordergeneratingset(seeL3]),areimportantconceptsinlatticetheory.Theconceptofasetofgeneratingelementforcontlnuouspartiallyordersetswasalsoproposedin[2J-Inthispaper,theconceptofageneratingsystemisintroducedatfirst-ThentheconceptofpbaseforthegeneratingsystemFofapartiallyorderset(P0Sforshort)isprop0sed-Finally,theminimumpbasesf0rPOSarestudied.Definition1LetTbeasetofsubsetsofaPOSL.Iff0ranyaeL,thereexistsAep,suchthata=supA,then9iscalledage…     

RESEARCH ANNOUNCEMENTS Morrey Regularity of the Solutionto the Dirichlet Problem

To study the local regularity of solutions to second order elliptic partial differential equations, Morrey in [1] introduced some function spaces, which are called the Morrey spaces todaySince then, many mathematicians have studied regularities of solutions to some kinds of secondorder elliptic equations in Morrey spaces.We give the deceptions of Morrey space and weak Morrey space first.Definition 1 Let TheThesubset of those functions of Lp for which will be called the Morrey space LpDefi…     

RESEARCH ANNOUNCEMENTS── On Unique Decomposition Pseudo-EuclideanRing

Throughoutthispaper,Rdenotesaringwithanidentity.Weusenotationsfrom[1],weneedsomeresultsofordinalarithmetic,see[3]fordetails.Euclideanringisakindofimportantintegraldomains,andDivisionAlgorithmandEuclideanAlgorithmaretwoelementarytoolsforstudyingEuclideanring.Forusingthesetwotoolsonmorekindsofimportalsrings,weintroducepseudO-Euclideanringasfonowing:Definition1LetAbeanordinalnumber,ifthereisafunction6:R-^suchthatforanya,bERthereedestq,rERwithb=qa r,r~0or8(r)<6(a),thenwesayRisa(left)pseudry…     

有限域上二次型序列与几何序列的互相关性

§1Introduction Letpbeaprimenumber,q=pm,andFqdenotethefinitefieldwithqelements.Fo anyn≥1,Trmnm(·)isthetracefunctionfromFqntoFq.LetαbeaprimitiveelementofFq and{α1,α2,...,αn}beabasisofFqnoverFq.Definition1.ForanonlinearfunctionffromFqtoFp,thesequenceS={Si}qn-1i=1withit termdefinedby Si=f(Trmnm(αi))(1iscalledageometricsequence.SuchageometricsequenceShasperioddividingqn-1.Geometricsequences includingm-sequence[1],GMWsequence[2,3],cascadedGMWsequence[4,5]andman others[6],mayhavelar…     

TIGHT PERFORMANCE BOUND OF AFB_k BIN PACKING

1.IntroductionIntheone-dimensionalbinpackingproblem,itemsinalistL,i.e.numbersal(i=1,…,n)intherange(0,1],aretobepackedintobins,eachofwhichhasacapacity1,andthegoalistominimizethenumberofbinsused.SincetheproblemoffindinganoptimalpackingisNP-hard,researchhasfocusedonfindingnear-optimalapproximationalgorithms.CsirikandJohnson[1]directedattentiontoaspeciallyrestrictedclassofsuchalgorithms:algorithmsthatare"on-line"anduse"boundedspace".Thedefinitionsareasfollows.Definition1.Abinpackingalgorithmis…     

A Graceful Algorithm of a Class of Trees

Let T be a tree with v vertices. It is said to be graceful if we can label the vertices with numbers 1,2,……,v in such a manner that the differences of any two adjacent vertices will again form the set {1,2,…,v-1}.Ringel conjectured, in1963, that every tree has a such labelling [1]. Ringel's conjecture remains unsettled. In this article, we shall investigate a class of graceful trees. Definition The,T_λ~((n)) is a tree with v_n vertices. Its vertices are v_i(j=0,1,…,n+1);v_(?)(j_o=1,2,…,n;j_1=1,2,…,k_1;……; j=1,2,…,k,≤λ), where λ,n,k_1,     

On Some Total Chromatic Number ofOuterplanar Graphs with Δ(G) = 6(English)

AMS(1991)SubjectClassifiction:05C15Definition1Aplanargraphissaidtobeanouterplanarifitsvenicescanbeplacedontheboundaryofaparticularface,calledtheouterface.Definition2Aplanaredge-face--colouringofaplanargraphG(V,E,F)isanassignmentofkcolourstoalledgesandfacesinEUFsuchthatnotwoadjacentorincidentelementsreceivethesamecolour.Theminimumnumberkforwhichaproperdege-facek-colouringofGexistsiscalledtheedge--facetotalchromaticnumberofG,denotedbyX.(G).similarly,wecandefinethevertex-edge--facetotalchr…     

ON NUMBER OF LEAVES ANDBANDWIDTH OF TREES

1.IntroductionFOragraphG=(V,E)oforderp,aonetoonemappingfromVinto{l,2,',p}iscalledanumberingofG.Definition1.1.SupposefisanumberingofG.LetBj(G)=(u57teif(u)--f(v)l.ThebandwidthofG,denotedbyB(G),isdefinedbyB(G)=min{Bf(G)IfisanumberingofG}.Thebandwidthproblemofgraphshasbecomeveryimportantsincethemid-sixties(see[21or[4]).Itisverydifficulttodeterminethebandwidthofagraph.GareyetallllshowedthatthebandwidthproblemisNP-completeevenifitisrestrictedtotreeswithmaximumdegree3.Soitisinterestingtoe…     

Structure of a Class of Integrable Lie Algebras

In , for any complex n×n matrix A, we have a Lie algebra g(A). Ifthe Chevalley generators e_i, f_i=(i = 1,…,n) of g(A) are locally nilpotent, theng(A) is integrable. The central object of our study is this class of integrableLie algebras.Definition 1 A matrix A is said to be equivalent to a matrix B if there ex-ists a non-degenerate diagonal matrix D such thatDB=A(by reordering the indices)     

A Class of Singular Integral Operators

Our main tool is the block decomposition of functions defined on∑_(n-1). Definition 1 A function b(x')defined on ∑_(n-1) is called a q-block,1相似文献   

C_(αβ) Classification of Analytic Toeplitz Operators

Let H be a separable Hilbert space and L(H) the set of all bounded linear operatorson H .A∈ L (H ) is said to be a contraction if‖ A‖≤ 1 .In [1 ] Sz-Nagy and Foiasintroduced the notion of the class Cαβ of contractions on H as follows:　Definition1　 Let T∈L(H) be a contraction.WriteT∈C0 .,　　 if h∈H,‖Tnh‖→ 0 ,as n→∞ ;T∈C1· ,　　if h∈H,h≠ 0 ,‖ Tnh‖\→ 0 ,as n→∞ ;T∈C· 0 ,　　if h∈H,‖ T* nh‖→ 0 ,as n→∞ ;T∈C· 1 ,　　if h∈H,h≠ 0 ,‖ T* nh‖\→ 0 …     

A Generalization of Algebraic Lattices

In this paper,we prove two theorems on lattices and operators.Definition Let L be a complete lattice.An element a in L is(＊)-compact if and only 1if whenever a≤VA for A(?)L then a≤VB for some B(?)Awith B is at most countable.L is called(＊)—algebraic lattice if every element in L is a supremum of(＊)—compactelements.(＊)—algebraic lattice is a generalization of algebraic lattice.     

A CHARACTERIZATION OF THE GENERAL DEN JOY INTEGRAL

We give a necessary and sufficient condition for an abstract integration (Definition 1) to be the general Denjoy integral (D-integral). This is a revised version of the author‘ s paper[2].     

EQUIVALENCE BETWEEN EXACT INTERNAL CONTROLLABILITY OF THE KIRCHHOFF PLATE-LIKE EQUATION AND THEWAVE EQUATION

1.IntroductionConsiderthefollowingillitial-boundaryvalueproblemLetD(A)={vEHI(fl)ItvEL'(fl)},V~Ha(~~),H~L'(fl).Thenthefiniteenergystatespacesofthesystems(1.1),(1.2)are,respectively,uk~D(A)xV,U.~VxH.ConsiderthegeneralizedfunctionspaceH-1~V'DHDV.ForbEC'(fl)anduEH-',wedefinebaEH-1by(bu)(()~u(bo,V(6HJ(n).(1.3)WehaveusedtheSobolevspaces.Wereferthereadersto[1]fortheknowledgeofthosespaces.Definition1.1.Thesystem(1.1)issaidtobeexactlycontrollableinukbyH-1-controlsifforevery(yo,yi)6uk,th…     

A Claas of Generalized Stirling Transforms

Here announced is an extension of the basic result presented in my fomernote (cf. The Fibonacci Quarterly,4 (1987),346-351). Denote by Г the ring of formal power series. Two elements φ and ψ are calledreciprocal elements if φ (ψ(t))=t With φ(0)=ψ(0)=0. Definition 1 A sequence of polynomials {P_n(t)} is said to be normal ifdeg p_n(t)=n, p_0(t)=1 and p_n(0)=0, (n1).