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On.Existen.e of Hall Subgroups in.Fin.te Groups

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Algebra Colloquium 2017年第1期24卷 75-82页

作者： Yufen. Liu Wen.in.Guo n. Skiba School of Mathematics an. In.ormation.l Scien.eShan.on. In.titute of Busin.ss an. Techn.logy Yantai Shandong 264005 China School of Mathematical Scien.es University of Science and Technology of ChinaHefei 230026 China Departmen. of Mathematics Gomel State University of F. Skorina Gomel 246028 Belarus

In.this paper, we give some n.w con.ition. of the existen.e of Hall subgroups in.n.n.soluble fin.te groups, an. so the famous Hall theorem an. Schur-Zassen.aus theorem are gen.ralized.

关键词： fin.te groups n.n.soluble groups Hall subgroups

On.σ-semipermutable Subgroups of Fin.te Groups

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Acta Mathematica Sin.ca,En.lish Series 2018年第9期34卷 1379-1390页

作者： Wen.Bin.GUO Alexan.er n. SKIBA Departmen. of Mathematics University of Science and Technology of China Hefei 230026 P. R. China Departmen. of Mathematics an. Techn.logies of Programmin. Francisk Skorina Gomel State University Gomel 246019 Belarus

Let a = {σi｜ i ∈ I} be some partition.of the set of all primes P, G a fin.te group an. σ（G） = {σi｜σi ∩ π （G） ≠ Ф}. A set H of subgroups of G is said to be a complete Hall or-set of G if every member ≠ 1 of H is a Hall σi-subgroup of G for some σi ∈ σ an. H con.ain. exactly on. Hall σi-subgroup of G for every σi ∈ σ（G）. A subgroup H of G is said to be： σ-semipermutablc in.G with respect to H if HHi x = Hi x H for all x ∈ G an. all x ∈ G an. all Hi ∈H such that （｜H｜, ｜Hi｜） = 1; σ-semipermutable in.G if H is σ-semipermutable in.G with respect to some complete Hall σ-set of G. We study the structure of G bein. based on.the assumption.that some subgroups of G are σ-semipermutable in.G.

关键词： Fin.te group Hall subgroup p-soluble group p-supersoluble group σ-semipermutable subgroup

Metallurgical challen.es in.microelectron.c 3D IC packagin. techn.logy for future con.umer electron.c products

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Scien.e Chin.(Techn.logical Scien.es) 2013年第7期56卷 1740-1748页

作者： K. n. TU TIAn.Tian Departmen. of Mechan.cal an. Biomedical En.in.erin. City University of Hong Kong Departmen. of Materials Scien.e an. En.in.erin. University of California at Los Angeles

Metallurgical challen.es in.con.rollin. the microstructural stability of Cu an. solder microbumps in.3D IC packagin. techn.l-ogy are discussed. Usin. un.-direction.l orien.ed n.n.twin.ed Cu, the con.rolled growth of orien.ed Cu6Sn. on.the n.n.twin.ed Cu an. its tran.formation.to Cu3Sn.without Kirken.all voids have been.achieved. In.order to join.a stack of Si chips in.o a 3D device, multiple reflows of solder microbumps may be required; we con.ider localized heatin. to do so by the use of self-sustain.d explosive reaction.in.multi-layered Al/n. thin.films of n.n. thickn.ss. It avoids re-meltin. of those solder join.s which have been.formed already in.the 3D stackin. structure.

关键词： 3D IC packagin. microbump localized heatin.

Does defen.ive posture in.rease mimetic fidelity of caterpillars with eyespots to their putative sn.ke models？

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Curren. Zoology 2014年第1期60卷 76-89页

作者： Thomas John.HOSSIE Thomas n. SHERRATT Ottawa-Carleton.In.titute of Biology Carleton University 1125 Colonel By Drive Ottawa ON K1S 5B6 Canada Departmen. of Biology Carleton University 1125 Colonel By Drive Ottawa ON K1S 5B6 Canada

Organ.sms often.evolve behaviours that in.rease or rein.orce the protection.from predators afforded by their morpho- logical defen.es. For example, mimetic an.mals may adopt postures or locomotory behaviours that emulate a characteristic fea- ture of their model to in.rease predator deception. Caterpillars with eyespots are thought to mimic sn.kes, an. when.threaten.d man. of these caterpillars adopt a posture that appears to en.an.e this resemblan.e. Herein.we evaluate the quan.itative stren.th of eviden.e of behavioural mimicry in.the caterpillars of 14 species by comparin. how closely a series of putative sn.ke-mimickin. caterpillars resemble sn.kes while at rest an. when.threaten.d. Specifically, we quan.ified the head morphology an. eye position.of a ran.e of sn.ke species, as well as the shape of the apparen. head （i.e. an.erior body segmen.s） an. position.of eyespots in.caterpillars restin. or in.their defen.ive posture. This allowed us to objectively examin. eviden.e for an.in.reased resemblan.e to either sn.kes gen.rally, or to Viperidae sn.kes specifically, upon.adoptin. the defen.ive posture. Widen.n. the an.erior body segmen.s durin. the defen.ive posture typically made caterpillars appear more viper-like as opposed to more sn.ke-like in.gen.ral. En.an.ed resemblan.e to vipers upon.moun.in. the defen.ive posture was apparen. on.y from the dorsal view. Laterally, caterpillars more closely resembled sn.kes in.the restin. posture an. shiftin. to the defen.ive posture in.tead reduced mimetic fidelity, Overall we foun. eviden.e for behavioural mimicry in.all 14 species examin.d. We highlight that objectively quan.ifyin. mimetic fidelity can.help iden.ify key features in.olved in.deception..

关键词： Behaviour Geometr!c morphometrics Protective colouration Mimicry Morphology Vipers

Criteria of Existen.e of Hall Subgroups in.n.n.soluble Fin.te Groups

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Acta Mathematica Sin.ca,En.lish Series 2010年第2期26卷 295-304页

作者： Wen.Bin.GUO A. n. SKIBA Departmen. of Mathematics Xuzhou Normal University Xuzhou 221116 P. R. China Departmen. of Mathematics Francisk Skorina Gomel State University Gomel 246019 Belarus

In.this paper, the famous Hall theorem an. the famous Schur-Zassen.aus theorem are gen.ralized.

关键词： fin.te groups n.n.soluble groups Hall subgroups

DIFFUSIVE-DISPERSIVE TRAVELIn. WAVES An. KIn.TIC RELATIOn. IV. COMPRESSIBLE EULER EQUATIOn.

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Chin.se An.als of Mathematics,Series B 2003年第1期24卷 17-34页

作者： n. BEDJAOUI P.G.LEFLOCH Cen.re de Mathematiques Appliquees & Cen.re n.tion.l de la Recherche Scien.ifique UMR 7641 Ecole Polytechnique 91128 Palaiseau Cedex France. INSSET Universite de Picardie 48 rue Raspail 02109 Saint-Quentin France.Centre de Mathematiques Appliquees & Centre National de la Recherche Scientifique UMR 7641 Ecole Polytechnique 91128 Palaiseau Cedex France.

The authors con.ider the Euler equation. for a compressible fluid in.on. space dimen.ion.hen.the equation.of state of the fluid does n.t fulfill stan.ard con.exity assumption. an.viscosity an. capillarity effects are taken.in.o accoun.. A typical example of n.n.on.ex con.stitutive equation.for fluids is Van.der Waals' equation. The first order terms of these partialdifferen.ial equation. form a n.n.in.ar system of mixed (hyperbolic-elliptic) type. For a class ofn.n.on.ex equation. of state, an.existen.e theorem of travelin. waves solution. with arbitrarylarge amplitude is established here. The authors distin.uish between.classical (compressive) an.n.n.lassical (un.ercompressive) travelin. waves. The latter do n.t fulfill Lax shock in.quali-ties, an. are characterized by the so-called kin.tic relation. whose properties are in.estigatedin.this paper.

关键词： Elasto dyn.mics Phase tran.ition. Hyperbolic con.ervation.law Diffusion Dispersion Shock wave Un.ercompressive En.ropy in.quality Kin.tic relation

EXISTEn.E OF SOLUTIOn.An. APPROXIMATE COn.ROLLABILITY OF A SECOn.-ORDER n.UTRAL STOCHASTIC DIFFEREn.IAL EQUATIOn.WITH STATE DEPEn.En. DELAY

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Acta Mathematica Scien.ia 2016年第5期36卷 1509-1523页

作者： San.ukta DAS Dwijen.ra PAn.EY n. SUKAVAn.M Departmen. of Mathematics Indian Institution of Technology Roorkee

This paper has two section. which deals with a secon. order stochastic n.utral partial differen.ial equation.with state depen.en. delay. In.the first section.the existen.e an. un.quen.ss of mild solution.is obtain.d by use of measure of n.n.compactn.ss. In.the secon. section.the con.ition. for approximate con.rollability are in.estigated for the distributed secon. order n.utral stochastic differen.ial system with respect to the approximate con.rollability of the correspon.in. lin.ar system in.a Hilbert space. Our method is an.exten.ion.of co-author n. Sukavan.m’s n.vel approach in.[22]. Thereby, we remove the n.ed to assume the in.ertibility of a con.rollability operator used by authors in.[5], which fails to exist in.in.in.te dimen.ion.l spaces if the associated semigroup is compact. Our approach also removes the n.ed to check the in.ertibility of the con.rollability Gramian.operator an. associated limit con.ition.used by the authors in.[20], which are practically difficult to verify an. apply. An.example is provided to illustrate the presen.ed theory.

关键词： approximate con.rollability cosin. family state depen.en. delay n.utral stochastic differen.ial equation measure of n.n.ompactn.ss

EXISTEn.E An. Un.QUEn.SS RESULTS FOR BOUn.ARY VALUE PROBLEMS OF HIGHER ORDER FRACTIOn.L In.EGRO-DIFFEREn.IAL EQUATIOn. In.OLVIn. GROn.ALL'S In.QUALITY In.BAn.CH SPACES

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Acta Mathematica Scien.ia 2013年第3期33卷 758-772页

作者： Dimplekumar n. CHALISHAJAR K. KARTHIKEYAn Departmen. of Mathematics an. Computer Scien.e Virginia Military Institute (VMI) 417 Mallory HallLexington VA 24450 USA Departmen. of Mathematics KSR College of TechnologyTiruchengode-637 215 Tamilnadu India

We study boun.ary value problems for fraction.l in.egro-differen.ial equation. in.olvin. Caputo derivative of order α∈ （n.1, n. in.Ban.ch spaces. Existen.e an. un.quen.ss results of solution. are established by virtue of the Holder＇s in.quality, a suitable sin.ular Cron.all＇s in.quality an. fixed poin. theorem via a priori estimate method. At last, examples are given.to illustrate the results.

关键词： Boun.ary value problems fraction.l order in.egro-differen.ial equation. boun.-ary value problems existen.e an. un.quen.ss sin.ular gron.all in.quality fixed poin. theorem

THE DUAL OF n.n.OMMUTATIVE LOREn.Z SPACES

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Acta Mathematica Scien.ia 2011年第5期31卷 2067-2080页

作者：韩亚洲 Turdebek n. Bekjan College of Mathematics an. System Scien.es Xinjiang University

We prove some n.n.ommutative an.logues of the classical results about dual spaces of the classical Loren.z spaces.

关键词： dual spaces n.n.ommutayive Loren.z spaces operator algebras