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简介：Bymeansofthegeneralizedvariableprincipleofmagnetoelectroelasticsolids,theplanemagnetoelectroelasticsolidsproblemwasderivedtoHamiltoniansystem.Insymplecticgeometryspace,whichconsistsoforiginalvariables,displacements,electricpotentialandmagneticpotential,andtheirdualityvariables,lengthwaysstress,electricdisplacementandmagneticinduction,theeffectivemethodsofseparationofvariablesandsymplecticeigenfunctionexpansionwereappliedtosolvetheproblem.Thenalltheeigen-solutionsandtheeigen-solutionsinJordanformoneigenvaluezerocanbegiven,andtheirspecificphysicalsignificationswereshownclearly.Atlast,thespecialsolutionswerepresentedwithuniformloader,constantelectricdisplacementandconstantmagneticinductionontwosidesoftherectangledomain.

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简介：Thispaperderivesfirstordernecessaryandsufficientconditionsforunconstrainedconed.c.Programmingproblemswheretheunderlinedspaceispartiallyorderedwithrespecttoacone.Theseconditionsaregivenintermsofdirectionalderivativesandsubdifferentialsofthecomponentfunctions.Moreover,conjugatedualityforconed.c.Optimizationisdiscussedandweakdualitytheoremisprovedinamoregeneralpartiallyorderedlineartopologicalvectorspace(generalizingtheresultsin[11]).

简介：Inthispaper,thenotionofL-Rcrossedcoproductisintroducedasaunifiedap-proachforsmashcoproducts,crossedcoproductsandL-RsmashcoproductsofHopfalgebras.AdualitytheoremforL-Rcrossedcoproductisproved.

简介：Thispapergivesthedefinitionsandsomepropertiesofε-directionalderivateandε-subgradientsofcone-convexfunction.Fromthem,theoptimalityconditionsoflocalandglobaloptimalpointofunconstrainedcone-d.c.programmingaregained.Atlast,thedualitytheoremsofthisprogrammingarepresented.

简介：Inthispaper,apairofMond-Weirtypehigher-ordersymmetricdualprogramsoverarbitraryconesisformulated.Theappropriatedualitytheorems,suchasweakdualitytheorem,strongdualitytheoremandconversedualitytheorem,areestablishedunderhigher-order(strongly)conepseudoinvexityassumptions.

简介：基于两重性的观点，这份报纸学习在弄弯的表面身体和里面之间的相互作用粒子。由有几何两重性的convex/concave身体，粒子的相互作用潜力定位了外面，在弄弯的表面内，身体被显示有两重性。与两重性，在弄弯的表面身体之间的基于弯曲的潜力和里面，粒子被导出。而且，在粒子上施加的正常、正切的驱动力被学习并且表示了为弯曲和弯曲坡度的功能。数字实验被设计测试基于弯曲的潜力的精确性。

简介：在这篇论文，二维的单个Roesser模型(2-DSRM)的双系统的性质和概念被学习。双系统的二个不同概念为2-DSRM被建议。一个人从为打电话给S双的系统的二维的单个一般模型(2-DSGM)定义的两重性被导出；另一个基于2-DSRM被定义在一传统叫感觉T双的系统。2-DSRM是否是免费的跳模式或跳模式，被看那可达到，然后，它能相等地被转变成2-DSRM，T两重性和S两重性为是相等的一种正规形式。这将具有在2-DSRM的柔韧的控制的一些观点应用。关键词2-D系统-单个系统-两重性-可控制性这个工作被中国的国家自然科学基金会部分地支持(号码60474078，60574015，60674014)，并且部分地为博士后的研究资金(0601010B)由江苏计划了工程。邹云从西北的大学在数学收到了学士学位，Xian，中国在1983，并且在从科技的南京大学设计的自动控制的硕士和博士学位，南京，中国，1987，和1990分别地。他当前是在科技的南京大学的电力工程的一个教授。他的当前的研究兴趣包括微分代数学的方程系统，二维的系统，单个不安，功率系统的短暂稳定性，和功率市场。邹博士是杂志的一个评论家美国数学社会的数学评论，和一个成员。徐惠玲在2005从科技的南京大学在控制科学和控制工程收到了博士学位。她兴趣的区域包括柔韧的过滤和控制，单个系统，二维的系统和非线性的系统。

简介：Usinggeneralizedunivexfunctions,anondifferentiablemultiple-objectiveoptimizationproblemisconsidered.Kuhn-Tuckertypesufficientoptimalityconditionsareobtainedforafeasiblepointtobeanefficientorproperlyefficientsolution.Mond-Weirtypedualityprogrammingisconstructed,theweakandstrongdualitytheoremsareproved.

简介：Thebundleofthe2-formson6-manifolddecomposesintothreesubbundlessuchthatΛ2（R6）=Λ21⊕Λ26⊕Λ28withdimensions1,6and8,respectively.Theselfandantiselfdualitysolutionsofthe2-forms,calledΦ-duality,arehandledandthesesolutionsshowthattheantiselfdualgaugefieldsliveonthesubbundlesΛ21andΛ26whiletheselfonesequationsonΛ28.AlsothesolutiononΛ21presentsaflatconnection.Inaddition,thecurvaturesoftheconnectionsonΛ26andΛ28haveTr[F3]=0,andsothetopologicalinvariantsdeterminedbytheChernclasses,i.e.topologicalcharge,consistonlyonthesecondChernclass.Intheresultofthiscase,theantiselfandselfΦ-dualgaugeinvariantLagrangiansofdefinedonbothsubbundlesareboundedbythesametopologicalcharge.Also,onegivesaquantizationcasetoberelatingtotheinstantonnumber.

简介：Softsettheoryhasarichpotentialapplicationinseveralfields.Asoftgroupisaparameterizedfamilyofsubgroupsandafuzzysoftgroupisaparameterizedfamilyoffuzzysubgroups.Theconceptoffuzzysoftgroupisthegeneralizationofsoftgroup.AbdulkadirAygunogluandHalisAygunintroducedthenotionoffuzzysoftgroupsin2009[1].Inthispaper,theconceptoflatticeorderedfuzzysoftgroupsanditsdualityhasbeenintroduced.Thendistributiveandmodularlatticeorderedfuzzysoftgroupsareanalysed.Theobjectiveofthispaperistostudythelatticetheoryoverthecollectionoffuzzysoftgroupinaparametricmanner.Somepertinentpropertieshavebeenanalysedandhenceestablisheddualityprinciple.

简介：Inthispaper,nonsmoothunivex,nonsmoothquasiunivex,andnonsmoothpseudounivexfunctionsareintroduced.Byutilizingthesenewconcepts,sufficientoptimalityconditionsforaweaklyefficientsolutionofthenonsmoothmultiobjectiveprogrammingproblemareestablished.WeakandstrongdualitytheoremsarealsoderivedforMond-Weirtypemultiobjectivedualprograms.

简介：AclassoffunctionscalledquasiB,-invexandpseudoB,-invexfunctionsareintroducedbyusingtheconceptofsymmetricgradient.TheexamplesofquasiB,-invexandpseudoB,-invexfunctionsaregiven.ThesufficientoptimalityconditionsandMond-Weirtypedualityresultsareobtainedforanondifferentioblenonlinearsemi-infiniteprogrammingprobleminvolvingquasiB,-invexandpseudoB,-invexfunctions.

简介：LetLbeanellipticoperator,wegiveargumentsaboutthedualityestimatebetweenMorreyspacesanditspre-dualspacescharacterizedbytheheatkernelassociatedtoLthatisgivenin[6],[8].

简介：为为秒的优化问题的适应有限元素方法命令到状态的坡度的2标准上的pointwise限制的线性椭圆形的部分微分方程题目被考虑。在一个弱两重性背景，即没有假定象Slater的存在那样的限制资格，指，剩余基于一个posteriori错误评估者被导出。在连续水平上在限制资格克服缺乏，弱Fenchel双被利用。几数字测试说明建议错误评估者的表演。