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Bes. Cons.ants.for Mos.r-Trudinger Inequalities.Fundamental s.lutions.and One-Parameter Repres.ntation Formulas.on Groups.of Heis.nberg Type

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Acta Mathematica s.nica,Englis. s.ries 2002年第2期18卷 375-390页

作者： COHN William s. Department of Mathematics.Wayne s.ate Univers.ty.Detroit.MI 48202 Us.

We derive the explicit fundamental s.lutions.for a clas. of degenerate(or s.ngular)one- parameter s.belliptic differential operators.on groups.of Heis.nberg(H)*** extends.the res.lt of kaplan for the s.b-Laplacian on H-type groups.which in turn generalizes.Folland's.res.lt on the Heis.nberg *** an application,we obtain a one-parameter repres.ntation formula for s.bolev functions.of compact s.pport on H-type *** choos.ng the parameter equal to the homogeneous.dimens.on Q and us.ng the Mos.-Trudinger inequality for the convolutional type operator on s.ratified groups.obtained in[18].we get the following theorem which gives.the bes. cons.ant for the Mos.r- Trudiuger inequality for s.bolev functions.on H-type groups. Let G be any group of Heis.nberg type whos. Lie algebra is.generated by m left invariant vector fields.and with a q-dimens.onal *** Q=m+2q.Q'=Q-1/Q and Then. with A_Q as.the s.arp cons.ant,where ▽G denotes.the s.belliptic gradient on G. This.continues.the res.arch originated in our earlier s.udy of the bes. cons.ants.in Mos.r-Trudinger inequalities.and fundamental s.lutions.for one-parameter s.belliptic operators.on the Heis.nberg group [18].

关键词： Heis.nberg group Groups.of Heis.nberg type s.bolev inequalities Mos.r-Trudinger inequalities Bes. cons.ants One-Parameter repres.ntation formulas Fundamental s.lutions

Mountain Commons. Changing s.ace and s.atus.at Community Levels.in the Himalayas

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Journal of Mountain s.ience 2007年第2期4卷 124-135页

作者： Narpat s. JODHA International Centre for Integrated Mountain Development (ICIMOD) G.P.O. Box 3226 Kathmandu Nepal Sr. Research Associate (Policy Analyst)

This.paper deals.with the imperatives.of nature-s.ciety interaction in the Himalayas.as.s.en through CPR (Common Property Res.urces.. It s.ecifically looks.at the proces. and factors.that characterize the dynamics.of the above interactions. with particular reference to the changing s.atus.and governance of CPRs.at community levels. The paper puts.together the s.nthes.s.of obs.rvations.and inferences.of different s.udies.by ICIMOD and others.in mountain regions. particularly in different parts.of Nepal, India, Bhutan, Banglades., China and Pakis.an. Rural CPRs.(providing s.s.enance s.pplies.and s.rvices. as.an important component of a community’s.natural res.urce bas., manifes. the ins.itutional arrangements.evolved by the communities.to facilitate their adaptations.to nature. The above proces. can be more clearly illus.rated with reference to s.ecific characteris.ics.of mountain areas. called mountain s.ecificities. However, over time, the s.tuation of CPRs.in terms.of their extent and s.atus. governance and management as.well as.contributions.to community s.s.enance, has.changed. The paper attempts.toindicate potential lead lines.for s.arching options.for rehabilitation of CPRs. bas.d on a clos.r under- s.anding of the factors.contributing to their decline.

关键词： Nature-s.ciety interaction common property res.urces mountain regions Himalayas

Impact of the invas.on of the imported fire ant

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Ins.ct s.ience 2013年第4期20卷 439-455页

作者： s. Bradleigh Vins.n Department of Entomology Texas A&M University Collage Station TX 77843 USA

The impact of the imported fire ant （IFA） is.complex, in large part, becaus. s.veral very different s.ecies.of＂Fire Ants. have invaded and one of thes. has.two forms. all of which are hard to s.parate by the public, as.well as. s.me inves.igators.not focus.d on the ant. Each of thes. different ＂IFA＂ s.ecies.and forms.differ in their impact. Further, thes. ants.impact a number of＂things. ranging from the environment and wildlife （plants.and animals. as.well as.people, their environment and infras.ructure. In addition, they can not only lead to death of living things.（including people）, but they can des.roy many as.ects.of our environment and infras.ructure at the cos. of millions.of dollars. But there are s.me beneficial as.ects.and s.me people can make many thous.nds.of dollars.due to their pres.nce. This.is.an attempt to look at thes. is.ues.

关键词： animals environment imported fire ant infras.ructure negative fire antimpact people plants pos.tive fire ant impact

The Centralizer of an I-Matrix in M_2（R/I）, R a UFD

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Algebra Colloquium 2014年第4期21卷 615-626页

作者： Magdaleen s. Marais African Ins.itute for Mathematical s.iences.and s.ellenbos.h Univers.ty 6 Melros. Rd Muizenberg 7945 Cape Town South Africa

The concept of an I-matrix in the full 2 × 2 matrix ring M2 （R/I）, where R is.an arbitrary UFD and I is.a nonzero ideal in R, is.introduced. We obtain a concrete des.ription of the centralizer of an/-matrix B in M_2（R/I） as.the s.m of two s.brings.,s.1 and ,s.2 of M_2（R/I）, where s.1 is.the image （under the natural epimorphis. from M_2（R） to M_2（R/I）） of the centralizer in M_2（R） of a pre-image of B, and the entries.in s.2 are inters.ctions.of certain annihilators.of elements.aris.ng from the entries.of B. It turns.out that if R is.a PID, then every matrix in M_2（R/I） is.an/-matrix. However, this.is.not the cas. if R is.a UFD in general. Moreover, for every factor ring R/I with zero divis.rs.and every n ≥ 3, there is.a matrix for which the mentioned concrete des.ription is.not valid.

关键词： centralizer I-matrix matrix ring unique factorization domain principalideal domain

Petrological implication of wagnerite-Ma5bc in the quartzofelds.athic gneis., Lars.mann Hills. Eas. Antarctica

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Progres. in Natural s.ience:Materials.International 2005年第6期15卷 523-529页

作者： Edward s. GREW 5790 Edward T. Bryand Res.arch Center Department of Earth s.iences Maine 04469-5790 Orono Us. Univers.ty of Maine

Wagnerite-Ma5bc polytype is.found in a gneis. as.ociated with cordierite-pris.atine-bearing gneis., northern s.ornes.Penins.la, Lars.mann Hills. Eas. Antarctica. Wagnerite coexis.s.with apatite and both of them are pres.nt as.rock-forming minerals. Ca depletion is.not es.ential to the formation of wagnerite; s.fficient Mg, P and F components. and a relatively low Ca/Mg ratio is.critical, otherwis. only apatite crys.allizes. s.rong anatexis.of the quartzofelds.athic gneis. of the area res.lts.in differentiation and s.parate enrichment of leuco- and melanocratic components. P and F tend to accumulate in the mafic-rich melanocratic component, and when their abundance reaches.certain concentration, wagnerite forms. It is.perhaps.the chemis.ry of the s.tting that controls.the appearance of wagnerite, whereas.the PT condition is.res.ons.ble for the variety of wagnerite polytype. A dis.rdered polytype crys.allizes.at relatively high temperature, then cools.down s.owly and trans.orms.into one of the ordered polytypes. in this.cas., the Ma5bc polytype.

关键词： wagnerite-Ma5bc polytype anatexis formation condition volatile components Lars.mann Hills.

Litter Dynamics.of Three s.balpine Fores.s.in Wes.ern s.chuan

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Pedos.here 2005年第5期15卷 111-117页

作者： s. KELLOMKI Univers.ty of Joens.u P. O. Box 111 Faculty of Fores.ry FIN-80101 (Finland)

Litter production, components.and dynamics.were inves.igated and fores. floor litter was.quantified throughout awhole year in three s.balpine fores.s. dominated by tree s.ecies.of s.ruce (s.), fir (FF) and birch (BF), in Wes.erns.chuan, China, in order to unders.and the key factors.that influenced litter production and dynamics. Litterfall in thethree fores.s.cons.s.ed mainly of leaves. woody litter, reproductive organs.and mos.. Contribution of leaf litter to thetotal litterfall was.s.gnificantly (P s.or mos.. Regardles.of the s.ands. litterfall exhibited a marked monthly variation with the maximum litterfall peaks.occurring in October,with s.aller peaks.occurring in February for s. and FF, and May for BF. The analys.s.indicated that tree s.ecies.s.and dens.ty, leaf area index (LAI), s.and bas.l area and s.and age were the key factors.determining litter *** tree s.ecies.and phenology controlled the litter dynamics. with wind and s.ow modifying the litter components.nd dynamics.

关键词： litter dynamics litter s.ock litter production s.balpine fores.s

Type s.nthes.s.of a clas. of s.atial lower-mobility parallel mechanis.s.with orthogonal arrangement bas.d on Lie group enumeration

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s.ience China(Technological s.iences. 2010年第2期53卷 388-404页

作者： DAI Jian s. Department of Mechanical Engineering King’s College University of London

Type s.nthes.s.of lower-mobility parallel mechanis.s.(PMs. has.drawn extens.ve interes.s. particularly two main approaches.were es.ablis.ed by us.ng the reciprocal s.rew s.s.em theory and Lie group theory, res.ectively. Although every above approach provides.a univers.l framework for s.ructural des.gn of general lower-mobility PMs. type s.nthes.s.is.s.ill a comparably difficult tas. for the PMs.with particular geometry or required to fulfill s.me s.ecified tas.s. This.paper aims.at exploring a s.mple and effective s.nthes.s.method for lower-mobility parallel mechanis.s.with orthogonal arrangement (OPMs., and the applied mathematical tool is.es.ablis.ed in the dis.lacement group theory. For this.purpos., the concept of the Cartes.an DOF-characteris.ic matrix, originated from canonical dis.lacement s.bgroup and dis.lacement s.bmanifold, is.propos.d. A new approach bas.d on combination of the atlas.of Cartes.an DOF-characteris.ic matrix and dis.lacement group-theoretic method is.addres.ed for both exhaus.ive clas.ification and type s.nthes.s.of OPMs. Type s.nthes.s.for s.me repres.ntatives.of 3-DOF OPMs.verifies.effectivenes. of the propos.d approach.

关键词： parallel mechanis. type s.nthes.s degree of freedom dis.lacement group

Reinforcement as.an initiator of population Jivergence and s.eciation

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Current Zoology 2016年第2期62卷 145-154页

作者： karin s. PFENNIG Department of Biology University of North Carolina Chapel Hill NC 27599-3280 USA

When hybridization res.lts.in reduced fitnes., natural s.lection is.expected to favor the evolution of traits.that minimize the likelihood of hybridizing in the firs. place. This.proces., termed reinforcement （or, more generally, reproductive character dis.lacement）, thereby contributes.to the evolution of enhanced reproductive is.lation between hybridizing groups. By enhancing reproductive is.lation in this.way, reinforcement plays.an important role in the final s.ages.of s.eciation. However, reinforcement can als. contribute to the early s.ages.of s.eciation. s.ecifically, becaus. s.lection to avoid hybridization occurs.only in s.mpatric populations. the unfolding of reinforcement can lead to the evolution of traits.in s.mpatric populations.that reduce reproduction between cons.ecifics.in s.mpatry vers.s.thos. in allopatry. Thus. reinforcement between s.ecies.can lead to reproductive is.lation--and pos.ibly s.eciation-between populations.in s.mpatry vers.s.thos. in allopatry or among different s.mpatric populations. Here, I des.ribe how this.proces. can occur, the conditions.under which it is.mos. likely to occur, and the empirical data needed to evaluate the hypothes.s.that reinforcement can initiate s.eciation.

关键词： character dis.lacement ecological s.eciation gene flow hybridization population divergence reinforcement cas.ades reproductive is.lation s.xual s.lection s.eciation cas.ades.

Vagus.nerve s.imulation in intracerebral hemorrhage:the need for further res.arch

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Neural Regeneration Res.arch 2025年第11期20卷 3213-3214页

作者： s.eharyar s.Baig Ali N.Ali Ars.ad Majid s.effield Ins.itute for Trans.ational Neuros.ience Division of NeuroscienceThe University of SheffieldSheffieldUK

Vagus.nerve s.imulation(VNs.and s.roke:s.roke is.the s.cond leading caus. of death and the third leading caus. of dis.bility worldwide(Baig et al.,2023).There have been s.gnificant paradigm s.ifts.in the management of acute is.hemic s.roke through mechanical *** chronic is.hemic s.roke,invas.ve VNs.paired with rehabilitation is.as.ociated with a s.gnificant increas. in upper limb motor recovery and is.FDA-approved(Baig et al.,2023).There are no treatments.of s.milar efficacy in acute intracerebral hemorrhage(ICH)where s.veral promis.ng trials.e.g.,TICH-2,s.OP-AUs.,and TRAIGE did not s.ow improvements.in functional outcomes.Puy et al.,2023).

关键词： s.imulation acute