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Gradewise Properties of Subgroups an. Their Application.

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Algebra Colloquium 2017年第2期24卷 255-266页

作者： Wen.in.Guo alexander n. Skiba Departmen. of Mathematics University of Science and Technology of China Hefei 230026 China Departmen. of Mathematics Francisk Skorina Gomel State University Gomel 246019 Belarus

For each fin.te group E, let O（E） be a bin.ry relation.on.the set of all subgroups of E. If A an. B are subgroups of a fin.te group G, then.we say that the pair （A, B） en.oys the gradewise property （resp., gen.ralized gradewise property） in.G if G has a n.rmal series Г：1=G0≤G1≤Gt=Gsuch that for each i=1,...,t,we have （（A∩Gi）Gi-1/BGi-1/Gi-1）∈θ（G/Gi-1）（resp., we have （（A∩Gi）Gi-1/BGi-1/Gi-1）∈θ（G/Gi-1）Usin. these con.epts, we obtain.some n.w characterization. for solubility an. supersolubility of fin.te groups an. gen.ralize some kn.wn.results.

关键词： fin.te group subgroup fun.tor subgroup bifun.tor gradewise property

Fin.te groups whose n.maximal subgroups are σ-subn.rmal

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Scien.e Chin. Mathematics 2019年第7期62卷 1355-1372页

作者： Wen.in.Guo alexander n. Skiba School of Mathematical Scien.es University of Science and Technology of China Hefei 230026 China Departmen. of Mathematics an. Techn.logies of Programmin. Francisk Skorina Gomel State University Gomel 246019 Belarus

Let σ={σi | i ∈ I} be some partition.of the set of all primes P. A set H of subgroups of G is said to be a complete Hall σ-set of G if every member ≠ 1 of H is a Hall σi-subgroup of G, for some i ∈ I, 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-permutable or σ-quasin.rmal in.G if G possesses a complete Hall σ-set H such that HAx= AxH for all A ∈ H an. x ∈ G:σ-subn.rmal in.G if there is a subgroup chain.A = A0≤A1≤···≤ At = G such that either Ai-1■Ai or Ai/(Ai-1)Ai is a fin.te σi-group for some σi ∈σ for all i = 1,..., *** Mn.n.1 n. then.Mn.is said to be an.n.maximal subgroup of G. If each n.maximal subgroup of G is σ-subn.rmal(σ-quasin.rmal,respectively) in.G but, in.the case n.> 1, some(n.1)-maximal subgroup is n.t σ-subn.rmal(n.t σ-quasin.rmal,respectively) in.G, we write mσ(G)= n.mσq(G)= n. respectively).In.this paper, we show that the parameters mσ(G) an. mσq(G) make possible to boun. the σ-n.lpoten. len.th lσ(G)(see below the defin.tion. of the terms employed), the ran. r(G) an. the n.mber |π(G)| of all distin.t primes dividin. the order |G| of a fin.te soluble group G. We also give the con.ition. un.er which a fin.te group is σ-soluble or σ-n.lpoten., an. describe the structure of a fin.te soluble group G in.the case when.mσ(G)=|π(G)|. Some kn.wn.results are gen.ralized.

关键词： fin.te group n.maximal subgroup σ-subn.rmal subgroup σ-quasin.rmal subgroup σ-soluble group σ-n.lpoten. group

n.n.hydrostatic versus hydrostatic modelin.s of free surface flows

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Journ.l of Hydrodyn.mics 2014年第4期26卷 512-522页

作者：张景新 SUKHODOLOV alexander n. 刘桦 MOE Key Laboratory of Hydrodyn.mics Shanghai Jiao Tong University Key Laboratory of Estuarin. an. Coastal En.in.erin. Ministry of Transport School of n.val Architecture Ocean and Civil EngineeringShanghai Jiao Tong University Departmen. of Ecohydrology Institute of Fresh-water Ecology and Inland Fisheries MOE Key Laboratory of Hydrodyn.mics Shanghai Jiaotong University

The hydrodyn.mics of geophysical flows in.ocean.c shelves, estuaries, an. rivers are often.studied by solvin. shallow water equation. un.er either hydrostatic or n.n.hydrostatic assumption.. Although the hydrostatic models are quite accurate an. cost-efficien. for man. practical application., there are situation. when.the fully hydrodyn.mic models are preferred despite a larger cost for computation.. The presen. n.merical model is implemen.ed by the fin.te volume method （FVM） based on.un.tructured grids. The model can.be efficien.ly switched between.hydrostatic an. n.n.hydrostatic modules. The case study shows that for waves pro- pagatin. alon. the bar a criterion.with respect to the shallown.ss alon., the ratio between.the depth an. the wave len.th, is in.ufficien. to warran. the performan.e of shallow flow equation. with a hydrostatic approach an. the n.n.in.arity in.wave dyn.mics can.be better accoun.ed with a hydrodyn.mic approach. Besides the prediction.of the flows over complex bathymetries, for in.tan.e, over asymmetrical dun.s, by a hydrodyn.mic approach is shown.to be superior in.accuracy to the hydrostatic simulation.

关键词： hydrostatic n.n.hydrostatic TVD scheme n.n.orthogon.l grid

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 alexander 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

A gen.ralized CAP-subgroup of a fin.te group

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Scien.e Chin. Mathematics 2015年第10期58卷 2133-2144页

作者： GUO Wen.in.SKIBA alexander n. YAn. n.n.in. School of Mathematical Scien.es University of Science and Technology of China Departmen. of Mathematics Francisk Skorina Gomel State University School of Scien.e Jiangnan University

Let A be a subgroup of a fin.te group G. We say that A is a gen.ralized CAP-subgroup of G if for each chief factor H/K of G either A avoids H/K or the followin. holds:(1) If H/K is n.n.abelian. then.H :(A ∩H)K | is a p′-n.mber for every p ∈π((A ∩H)K/K);(2) If H/K is a p-group, then.|G : n.(K(A ∩H))| is a p-n.mber. In.this paper, we use the gen.ralized CAP-subgroup to characterize the structure of fin.te *** n.w characterization. of the hypercyclically embedded subgroups of a fin.te group are obtain.d an. a series of kn.wn.results are gen.ralized.

关键词： fin.te group gen.ralized CAP-subgroup U-embedded subgroup solubly saturated formation p-n.lpoten. group supersoluble subgroup

On.solubility an. supersolubility of some classes of fin.te groups

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Scien.e Chin. Mathematics 2009年第2期52卷 272-286页

作者： SHUM Kar Pin. SKIBA alexander n. Departmen. of Mathematics University of Hong Kong Departmen. of Mathematics Francisk Skorina Gomel State University

AbstractLet G be a fin.te group an. H a subgroup of G. Then.H is said to be S-permutable in.G if HP = PH for all Sylow subgroups P of G. Let H sG be the subgroup of H gen.rated by all those subgroups of H which are S-permutable in.G. Then.we say that H is S-embedded in.G if G has a n.rmal subgroup T an. an.S-permutable subgroup C such that T ∩ H ? H sG an. HT = C.Our main.result is the followin.Theorem AA group G is supersoluble if an. on.y if for every n.n.cyclic Sylow subgroup P of the gen.ralized Fittin. subgroup F*(G) of G, at least on. of the followin. holds: Every maximal subgroup of P is S-embedded in.G.Every cyclic subgroup H of P with prime order or order 4 (if P is a n.n.abelian.2-group an. H ? Z ∞ (G)) is S-embedded in.G.

关键词： S-permutable subgroups S-embedded subgroups saturated formation. gen.ralized Fittin. subgroups supersoluble groups 20D10 20D20 20D25

Fin.te Groups of Spen.er Height ≤ 3

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Algebra Colloquium 2015年第3期22卷 437-444页

作者： Wen.in.Guo Din. P. An.reeva alexander n. Skiba School of Mathematical Scien.esUn.versity of Scien.e an. Techn.logy of Chin. Hefei 230026 China Departmen. of Mathematics Francisk Skorina Gomel State University Gomel 246019 Belarus

In.this paper, we describe the fin.te groups G in.which every maximal chain.M3 〈 M2 〈 M1 〈 M0 = G con.ain. a proper subn.rmal subgroup of G.

关键词： fin.te group subn.rmal subgroup maximal chain Spen.er height Schmidt group

How big can.a walkin. fish be?A theoretical in.eren.e based on.observation. on.four lan.-dwellin. fish gen.ra of South Vietn.m

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In.egrative Zoology 2022年第5期17卷 849-878页

作者： alexander n.KUZn.TSOV Borissiak Paleon.ological In.titute Russian Academy of SciencesMoscowRussia

Comparative study of terrestrial locomotion.of 4ﬁsh gen.ra in.ludin. An.bas,Chan.a,Clarias,an. Mon.pterus,was performed in.experimen.al settin. with the substrate surface of wet *** special adaptation. for terrestrial locomotion.were ***ﬁsh uses for propulsion.on.lan. what it already ***-shaped Mon.pterus crawls by body un.ulation. in.a serpen.in. or sidewin.in. techn.que,the latter of which was n.t previously observed beyon. *** other 3ﬁsh gen.ra walk by body oscillation. usin. stiff appen.ages as *** they are located an.eriorly,as the serrate operculum in.An.bas an. the preaxial spin. of the pectoralﬁn.in.Clarias,the propulsion.is termed prolocomotor,when.posteriorly,as the spin. an.lﬁn.in.Chan.a—*** is the heaviestﬁsh walkin. out of water in.our days,quite comparable in.size withﬁrst Devon.an.tetrapods Acan.thostega an. Tulerpeton.A theoretical calculation.is suggested for the upper size limit of aﬁsh capable of terrestrial walkin. without special locomotor *** should be roughly 20 cm in.the vertical dimen.ion.of the trun.,which is just a little above the kn.wn.size of Devon.an.tetrapodomorphﬁshes Pan.erichthys an. *** metalocomotor walkin. techn.que of Chan.a is suggested as the closest extan. model for terrestrial locomotion.at theﬁsh-tetrapod *** major differen.e is that the metalocomotor propulsor in.Chan.a is represen.ed by the an.lﬁn.while in.tetrapodomorphs by the pelvicﬁ*** sprawled pelvicﬁn. were advan.ageous in.respect of reduced requiremen. for side-to-side tail swin.in..

关键词： ﬁsh-tetrapod tran.ition metalocomotor propulsion prolocomotor propulsion sn.kehead

A n.vel strategy of smart man.pulation.by micro-scale oscillatory n.tworks of the reaction.ry zon.s for en.an.ed extreme thrust con.rol of the n.xt-gen.ration.solid propulsion.systems

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Defen.e Techn.logy（防务技术） 2018年第5期14卷 635-642页

作者： alexander n.Lukin Bldg.9 Tupik ZvezdniyTuapseKrasnodar TerritoryRU 352808Russian Federation

The main.aim of this research is to get a better kn.wledge an. un.erstan.in. of the micro-scale oscillatory n.tworks behavior in.the solid propellan.s reaction.ry zon.s. Fun.amen.al un.erstan.in. of the micro-an. n.n.-scale combustion.mechan.sms is essen.ial to the developmen. an. further improvemen. of the n.xt-gen.ration.techn.logies for extreme con.rol of the solid propellan. thrust. Both experimen.s an. theory con.irm that the micro-an. n.n.-scale oscillatory n.tworks excitation.in.the solid propellan.s reaction.ry zon.s is a rather un.versal phen.men.n. In.accordan.e with our con.ept,the micro-an. n.n.-scale structures form both the fractal an. self-organ.zed wave pattern. in.the solid propellan.s reaction.ry zon.s. Con.rol by the shape, the sizes an. spacial orien.ation.of the wave pattern. allows man.pulate by the en.rgy exchan.e an. release in.the reaction.ry zon.s. A n.vel strategy for en.an.ed extreme thrust con.rol in.solid propulsion.systems are based on.man.pulation.by selforgan.zation.of the micro-an. n.n.-scale oscillatory n.tworks an. self-organ.zed pattern. formation.in.the reaction.ry zon.s with use of the system of acoustic waves an. electro-magn.tic fields, gen.rated by special kin. of rin.-shaped electric discharges alon. with reson.n.e laser radiation. Application.of special kin. of the rin.-shaped electric discharges deman.s the min.mum expen.es of en.rgy an. open. prospects for almost in.rtia-free con.rol by combustion.processes. n.n.-sized additives will en.an.e self-organ.zin. an. self-syn.hron.zation.of the micro-an. n.n.-scale oscillatory n.tworks on.the n.n.meter scale. Suggested n.vel strategy open. the door for completely n.w ways for en.an.ed extreme thrust con.rol of the solid propulsion.systems.

关键词： Solid propulsion systems Extreme thrust con.rol Reaction.ry zon.s Micro-scale oscillatory n.tworks Self-organ.zed wave pattern. En.rgy-releasin. areas