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1.
61.IntroductionWeconsiderthefourthorderdifferentialequationx(`)(t)-p(t)lx(t)I'sgnx(t)=O,(1.l)wherea>l,isconstant,andp(t)ispositivecontinuousfunctionon[t,,oo),to>o.Werestrictourattentiontothosenontrivialsolutionsx(t)of(1.1)whichexistonsomehalf-[ine[T:,co)cy[t,,oo),suchasolutioniscalledapropersolutionof(1.l).ApropersolutioniscalledoscillatoryifithasarbitrarilylargezerosFotherwiseitiscallednonoscillatory.Wecon-sidertheoscillationandnonoscillationofpropersolutionsof(l,l).WeletEdenotethesetofall… 相似文献
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ZHENGHAI HUANG YUDA HU 《运筹学学报》1997,(2)
1.IntroductionTheclassicalworkOiltheoremsofthealternativeforsingle-valuedfunctionbyG..d..II]andMotzkin[2]wereextendbymanyresearchersinvariousways(suchasJeyakumar['l'],Lily],andTamminen[6]),whereconditionsofconvexityaremoreorlessrelaxed.Met's..rk[:]givesemphasistotheoremsofthealternativeinthesettingofset-valuedfunctionwhereconditionofconvexityissettobecone-convex.Thispaperaimsatprovidinganunifiedextensionoftheabove-mentionedtheorems,andgivesoutageneraltheoremofthealternativeinthecontextofset… 相似文献
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51.IntroductionLethbeahomeomorphismontherealaxisR,andsatisfyh(lco)=loo.Wecallaquasisymmetricfunction.lfthereexistsa'constantMsuchthatM-1Sp(x,t)SM,x,teR,(l.2)then(1.2)iscalledtheM-condition-Byvirtueoftheclassicresultofpaper[lj,ifp(x,t)sat-isfiestheM-condition,thenthereexistsaK(M')-quasiconformaIextensiononthel1alfplaneH,whichisthewell-knownBeurling-Ahlfors'extension:ytz)=u(x,y) iv(x,y),whereAfterpaper[lj,manyworkshavebeendoneforestimatingK-Particularly,itshouldbere-markedheretl1atM.Leht… 相似文献
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In[1],the Kothe nuclear sequence spaces are described and in[2]the characte-rization of the semi-nuclear and the barreled locally convex spaces by the boundedvariation of functions respectively.In this paper several kinds of bounded variationof operator-valued functions are studied. Let X and Y are Banach spaces,T(t):[0,1]→L(X,Y)be a operator-valued fun-ction.We called T(t)be uniformly bounded variation,if there exist a constantM>0,such that for any partition △:0=t_0相似文献
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On the k—smoothness and k—strong smoothness 总被引:5,自引:0,他引:5
5l.IntroductionFrompal,er[11,L2],to[3j,tI1efol1owingresultsareobtained:1)LetXbeaBanachspace,thenxes(X)={xeX;llxIl=1}isG-differetiableifandonIyif,foreachyeX,letXI=span(x,y).2)LetXbeaBanachspace,thenxeS(X)isF-differetiableifandonlyifIn[4j,NanchaoxunandWangjianhuaintroducedk-smoothnessandk-strongsmooth-ness.lnthisPaPer,wegive:Theorem1LetXbeaBanachspace,thcnthefollowingstatementsareequivalent.(i)xo6S(X)isk-smooth.(ii)IfX*cyXisk-dimensionalsubspaceandx,eX*,thenwhereU(x,,r)={xeX;l1x-xo… 相似文献
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Inbiology,itisveryimportanttoinvestigatethemovementofsomecellsororganismsinsomegivenbiologica1system(cf.[1,2]).Inordertounderstandhowthemovementrulesareaffectedbytheeffectofthechemo-attractant,OthmerandStevensintroducedin[1]severalgeneralclassesofpartialdifferentialequations.Inoneoftheirmodels,theyconsideredamasterequation,i.e.barrierandnearestneighborlatticemodel.Followingalimitingprocessthemodelisdescribedbythefollowingsystemofpartialdifferentialequations:wherep(x,t)istheparticledensityofap… 相似文献
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Thegracefulgraphswaspresentedinl966.Sincethattime,manyresultshavebeenobtainedongacefulgraphsandit'smanyapplicationsappear(see[2j,L4j).Thegraceful-nessofP.XP.andC.XP,areprovedbythepaper[1],[3j,[5j,[6]-Followingthis,inthispaper,itisobtainedthatthegracefu1nessofthefamiliesofthehexagonalgraphsG,(n)andG2(n).Fornotationsandteminologiesonthegracelulgraphnotdefinedhere,wefollowthereference[3j-NowletG(V,E)beagraph,6bethelabelingoftheverticesofG,andforanyedgeuv,define6(uv)=lo(u)-o(v)Iitistheedge's… 相似文献
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R.A.Gordon[1]generalizedthedefinitionoftheMcShaneintegralforrealvaluedfunctionstotheabstractfunctionsfromR1toBanachspaces.Inthispaper,wedefinetheMcShaneintegralforabstractfunctionsfromRntoBanachspacesandprovethatifeveryfunctionffromIoinRntoBanachspacesisMcShaneintegrablethenfisPettisintegrable,andiftheunitballB(X)inX*isrelativelyweaklycompact,fisPetitsintegrablethenfisMcShaneintegrableonIo.ThisgivesapositiveanswertoanopenproblemleftbyR.A.Gordonin[1].ThroughoutthispaperXwilldenoteare… 相似文献
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In1969,Sweedler[1]giventhedecompositiontheoreyofcoalgebraswhicharecocommu-tative.In1975,Kaplansky[2]showedthatanycoalgebracanbeuniquelydecomposedintoadirectsumofitsindecomposablesubcoalgebras.From1978to1992,Shudo[3]andXu[4]consructuredtheindecomposabledirectsumcomponentsofacoalggebra,viadefineequivalenceralationforthesetofsimplesubcoalgebras.Asweknow,themodolecoalgebraisthennaturalgeneralizationofcoalgebra.AndittakesplayanimportentroleintheDrinfelddouble.Inthispaper,wediscussthedecompositio… 相似文献
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1 IntroductionIn recent years, fractals have shown important applications in many fields. [1,2] and [3] have done some excellent initial and conclusion work on fractal and it's mathematical foundations. However, a fractal function: a type of Weierstrass functions defined byW(t) = (?), 0 < a < 1, A > 1, (1)because of it's special fractal properties, [1, 2, 4, 5] have given some detailed discussion about it's graph, fractal dimension, etc.Fractional calculus attract more and more attention recently. In this field, [6, 7] have done some important and detailed work. The fundamental conception is 相似文献
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本文证明了格的极小生成元集一定是最小生成元集且只能是非零完全并既约元全体,证明了分配格具有最小生成元集的必要条件是它满足并无限分配律.本文还证明了完全Heyting代数具有最小生成元集当且仅当它是强代数格,证明了完备格是强代数格当且仅当它和它的对偶格均是具有最小生成元集的分配格. 相似文献
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TheExistenceoftheCompleteandCompletelyDistributiveLatticesBatRuipu(白瑞蒲)(DepartmentofMathematics,HebeiUniversity,Baoding,07100... 相似文献
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讨论对于拓扑空间子集A是否存在包含A的最小开集和是否存在包含于A的最大闭集问题,证明了拓扑空间X是一个T1空间之充分且必要条件是,对于X的每一个子集A,X中存在包含A的最小开集(存在包含于A的最大闭集)当且仅当A是X的开集(闭集),同时给出几个例子说明了定理的条件. 相似文献
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The concept of locally strong compactness on domains is generalized to general topological spaces. It is proved that for each distributive hypercontinuous lattice L, the space SpecL of nonunit prime elements endowed with the hull-kernel topology is locally strongly compact, and for each locally strongly compact space X, the complete lattice of all open sets O(X) is distributive hypercontinuous. For the case of distributive hyperalgebraic lattices, the similar result is given. For a sober space X, it is shown that there is an order reversing isomorphism between the set of upper-open filters of the lattice O(X) of open subsets of X and the set of strongly compact saturated subsets of X, which is analogous to the well-known Hofmann-Mislove Theorem. 相似文献
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A permutation is simsun if for all k, the subword of the one-line notation consisting of the k smallest entries does not have three consecutive decreasing elements. Simsun permutations were introduced by Simion and Sundaram, who showed that they are counted by the Euler numbers. In this paper we enumerate simsun permutations avoiding a pattern or a set of patterns of length 3. The results involve Motkzin, Fibonacci, and secondary structure numbers. The techniques in the proofs include generating functions, bijections into lattice paths and generating trees. 相似文献
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Bill Sands 《Discrete Mathematics》1980,29(3):287-292
The dimension of a partially ordered set P is the smallest integer n (if it exists) such that the partial order on P is the intersection of n linear orders. It is shown that if L is a lattice of dimension two containing a sublattice isomorphic to the modular lattice M2n+1, then every generating set of L has at least n+2 elements. A consequence is that every finitely generated lattice of dimension two and with no infinite chains is finite. 相似文献
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集对Fuzzy格及其在格表示论中的应用 总被引:1,自引:0,他引:1
用幂集格构造了集对 Fuzzy 格(这与用整数对构造有理数集有相似之处),并用它证明了完整的软代数表示定理,即定义了到自身的映射且有最大元和最小元的格为软代数的充要条件是它与某个集对 Fuzzy 格的子格同构.这样,与分配格在幂集 Boole 格中表示相对应,软代数在集对 Fuzzy 格中有表示,在理论上是很完美的 相似文献
18.
SEMIGROUPS CHARACTERIZED BY THEIR FUZZY IDEALS 总被引:5,自引:2,他引:3
SEMIGROUPSCHARACTERIZEDBYTHEIRFUZZYIDEALSJ.AhsanandK.Saifullah(DepartmentofMathematicalSciencesKingFahdUniversityofPetroleuma... 相似文献
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The main results obtained are:– A Dedekind complete Banach lattice Y has a Fatou norm if and only if, for any Banach lattice X, the regular-norm unit ball Ur = {T Lr(X,Y): ||T||r 1} is closed in the strong operator topology on the space of all regular operators, Lr(X,Y).– A Dedekind complete Banach lattice Y has a norm which is both Fatou and Levi if and only if, for any Banach lattice X, the regular-norm unit ball Ur is closed in the strong operator topology on the space of all bounded operators, L(X,Y).– A Banach lattice Y has a Fatou–Levi norm if and only if for every L-space X the space L(X,Y) is a Banach lattice under the operator norm.– A Banach lattice Y is isometrically order isomorphic to C(S) with the supremum norm, for some Stonean space S, if and only if, for every Banach lattice X, L(X,Y) is a Banach lattice under the operator norm.Several examples demonstrating that the hypotheses may not be removed, as well as some applications of the results obtained to the spaces of operators are also given. For instance:– If X = Lp() and Y = Lq(), where 1 < p,q < , then Lr(X,Y) is a first category subset of L(X,Y). 相似文献