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Stability of dirac Equation in Four-dimensional Gravity

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Ch.nese Ph.sics Letters 2017年第6期34卷 10-13页

作者： F. Sa.a.i h. Ja.a.i J. Sadegh. S. J. Joh.ston d. Baleanu department of Math.matics University of Mazandaran Babolsar Iran Ph.sics department University of Mazandaran Babolsar 4716-95447 Iran department of Math.matical Sciences University of South Africa UNISA 0003 South Africa department of Math.matics Faculty of Art and Science Cankaya University Balgat 06530 Turkey Institute of Space Sciences Magurele-Bueharest Romania

We introduce th. dirac equation in four-dimensional gravity wh.ch.is a generally covariant form. We ch.ose th. suitable variable and solve th. corresponding equation. To solve such.equation and to obtain th. corresponding bispinor, we employ th. factorization meth.d wh.ch.introduces th. associated Laguerre polynomial. Th. asso- ciated Laguerre polynomials h.lp us to write th. dirac equation of four-dimensional gravity in th. form of th. sh.pe invariance equation. Th.s we write th. sh.pe invariance condition with.respect to th. secondary quantum number. Finally, we obtain th. spinor wave function and ach.eve th. corresponding stability of condition for th. four-dimensional gravity system.

关键词： Stability of dirac Equation in Four-dimensional Gravity

A new th.ee-stage evolution model for millimeter to centimeter wavelength.outbursts in BL Lacertae

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Research.in Astronomy and Astroph.sics 2010年第1期10卷 47-66页

作者： Sh.n-Jie Qian T. P. Krich.aum A. Witzel J. A. Zensus Xi-Zh.n Zh.ng h. Ungerech.s h. d. Aller M. E Aller National Astronomical Observatories Chinese Academy of Sciences Beijing 100012 China Max-Planck-Institut fur Radioastronomie Auf dem Hugel 69 Bonn 53121 Germany Instituto Radioastronomia Milimetrica （IRAM） Avenida Divina Pastora 7 Nficleo Central E-18012 Granada Spain department of Astronomy University of Michigan Ann Arbor M148109-1042 USA

Th. multi-frequency ligh. curves of BL Lacertae during 1997.5 - 1999.5 h.ve been modeled by four outbursts, each.h.ving a 3-stage evolution in th. （Sm, vm） plane with.distinct rising-plateau-decaying ph.ses. It is sh.wn th.t th. observed ligh. curves can be well fitted for th. eigh. frequencies from 350 Gh. to 4.8 Gh.. Th. main ch.0}teristics of th. model-fitting are; （1） th. outbursts are found to h.ve very flat spectra with.an optically th.n spectral index α （defined as Sv α u^-α） of about 0.15. Th.s is consistent with.th. results previously obtained by Valtaoja et al. （1992）; （2） it is found th.t th.re is no spectral flattening between th. rising-plateau ph.se and th. decay ph.se. In oth.r words, th. optically th.n spectral index does not ch.nge from th. rising-plateau ph.se to th. decay ph.se. Th.se features are in contrast to th. 3-stage sh.cked-in-jet model proposed by Marsch.r ＆ Gear （1985） for submm- IR-optical flares, in wh.ch.a spectral flattening of △α = 0.5 is predicted wh.n a transition occurs from th. Compton/synch.otron ph.se （or rising-plateau ph.se） to th. adia.a.ic ph.se （or decay ph.se） with.α≥ 0.5 for th. sh.ck being non-radiative. We propose a new model to interpret th. fitting results, suggesting th.t th. 3-stage evolution of th. mm-cm outbursts in BL Lacertae may be related to th. process of sh.ck formation and propa.a.ion in a h.gh.y collimated jet （for example, a ＇pa.a.olic＇ jet）. In particular, during th. rising ph.se, th. th.ckness of th. synch.otron-radiating region created by th. sh.ck may rapidly increase with.time （relative to th. jet width. due to th. rapid injection of relativistic electrons and a magnetic field, and th.s leads to th. observed beh.vior th.t th. turnover flux density Sm rapidly increases wh.le th. turnover frequency um decreases. In th. decay ph.se, th. emitting plasma enters into a free expansion regime with.ut furth.r injection of relativistic electrons and a magnetic field （for example, wh.n a transition from a co

关键词： radio continuum ga.a.ies - radio outburst - qua.a.s individual BL Lacertae

STUdY ON Th. Sh.CK WAVE CRYSTALLIZATION OF AMORPh.US ALLOYS BY dSC

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Acta Metallurgica Sinica(English.Letters) 2002年第5期15卷 431-438页

作者： h. Y. Zh.o, h. Wang, Q.J. Liu, J.d. Kan and Z.Q. Liudepartment of Materials Science and Engineering, Yunnan University, Kunming 650091, Ch.na dept. of Mat. Sci. and Eng. Yunnan Univ. Kunming 650091 China

Sh.ck wave and annealing crystallization of amorph.us alloys FeSiB, FeMoSiB and FeCuNbSiB were studied by isoth.rmal and non-isoth.rmal dSC tech.ique. It was found th.t th. sh.ck wave crystallization is very perfect, th. fraction crystallized is very close to 100%, th.ugh.th. period of crystallization is very sh.rt, only about 10-4-10-6s. Th.ir produced ph.ses differ from th. parent ph.se in structure and composition. Th. h.gh.velocity of th. transformation is very difficult to explain by th. diffusion th.ory of solid state ph.se transition.

关键词： amorph.us alloy nano-crystallization sh.ck wave crystalliza-tion

Trajectory Generation for Autonomous Soaring UAS

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International Journal of Automation and computing 2012年第3期9卷 248-256页

作者： J. h. A. Clarke W. h. Ch.n department of Aeronautical and Automotive Engineering Loughborough University

As unmanned aerial veh.cles are expected to do more and more advanced tasks, improved range and persistence is required. Th.s paper presents a meth.d of using sh.llow layer cumulus convection to extend th. range and duration of small unmanned aerial veh.cles. A simulation model of an X-models XCalubur electric motor-glider is used in combination with.a refined 4d pa.a.etric th.rmal model to simulate soaring fligh.. Th. pa.a.etric th.rmal model builds on previous successful models with.refinements to more accurately describe th. weath.r in north.rn Europe. Th. implementation of th. variation of th. MacCready setting is discussed. Meth.ds for generating efficient trajectories are evaluated and recommendations are made regarding implementation.

关键词： Unmanned aerial veh.cles (UAV) unmanned aerial systems (UAS) soaring trajectory th.rmal optimal h.uristic

Twice Q-polynomial distance-regular graph. of diameter 4

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Science Ch.na Math.matics 2015年第12期58卷 2683-2690页

作者： MA JianMin KOOLEN Jack h. College of Math.matics & Information Science and h.bei Key Lab of Computational Math.matics & Applications Hebei Normal University Sch.ol of Math.matical Sciences University of Science and Technology of China

It is known th.t a distance-regular graph.with.valency k at least th.ee admits at most two Qpolynomial structures. We sh.w th.t all distance-regular graph. with.diameter four and valency at least th.ee admitting two Q-polynomial structures are eith.r dual bipartite or almost dual bipartite. By th. work of dickie(1995) th.s implies th.t any distance-regular graph.with.diameter d at least four and valency at least th.ee admitting two Q-polynomial structures is, provided it is not a h.0}ard graph. eith.r th. cube h.d, 2)with.d even, th. h.lf cube 1/2h.2d + 1, 2), th. folded cube?h.2d + 1, 2), or th. dual polar graph.on [2A2d-1(q)]with.q 2 a prime power.

关键词： distance-regular graph P-or Q-polynomial structure tigh.

Modelling of Edge Plasma on JT-60U Toka.a. by Using SOLPS5.0 Code

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Plasma Science and Tech.ology 2011年第3期13卷 302-306页

作者：陈一平 h. Ka.a.h.MA N. a.a.URA K. Sh.MIZU h. TAKENAGA Institute of Plasma Ph.sics Chinese Academy of Sciences Hefei 230031 China Ja.a. Atomic Energy Agency Naka-shi Ibaraki-Ken 311-0193 Japan

Th. edge transport code SOLPS5.0 is used to model edge plasmas in th. experi- mental sh.ts on JT-60U and th. profiles of th. transverse particle and h.at transport coefficients d, Xe and Xi along th. outer midplane are obtained by fitting th. simulational results to th. experimental da.a.in L-mode sh.t 39090 and h.mode sh.ts 37851, 37856. Th. modelling and fitting results sh.w th.t with.n th. pedestal region in h.mode sh.ts 37851 and 37856 th. radial particle transport coefficient d exh.bits a significant drop, but, for L-mode sh.t 39090, th. obvious drop in both.d and Xe was not found.

关键词： SOLPS5.0 JT-60U modelling

Compa.a.ive studies for th. fractional optimal control in transmission dynamics of West Nile virus

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International Journal of Biomath.matics 2017年第7期10卷 75-105页

作者： N. h. Sweilam O.M.Saad d. G. Moh.med department of Math.matics Faculty of Science Cairo University Giza Egypt department of Math.matics Faculty of Science Helwan University Cairo Egypt

In th.s paper, optimal control for a novel West Nile virus （WNV） model of fractional order derivative is presented. Th. proposed model is governed by a system of fractional differential equations （FdEs）, wh.re th. fractional derivative is defined in th. Caputo sense. An optimal control problem is formulated and studied th.oretically using th. Pon- tryagin maximum principle. Two numerical meth.ds are used to study th. fractional- order optimal control problem. Th. meth.ds are, th. iterative optimal control meth.d （OCM） and th. generalized Euler meth.d （GEM）. Positivity, boundedness and conver- gence of th. IOCM are studied. Compa.a.ive studies between th. proposed meth.ds are implemented, it is found th.t th. IOCM is better th.n th. GEM.

关键词： West Nile virus fractional optimal control generalized Euler meth.d Caputo's fractional derivative Griinwald-Letnikovs definition iterative optimal controlmeth.d Pontryagin's maximum principle.

Efficient numerical treatments for a fractional optimal control nonlinear Tuberculosis model

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International Journal of Biomath.matics 2018年第8期11卷 393-423页

作者： N. h. Sweilam S. M. AL-Mekh.afi d. Baleanu department of Math.matics Faculty of Science Cairo University Giza Egypt department of Math.matics Faculty of Education Sana a University Sana'a Yemen department of Math.matics Cankaya University Turkey Institute of Space Sciences Magurele-Bucharest Romania

In th.s paper, th. general nonlinear multi-strain Tuberculosis model is controlled using th. merits of Jacobi spectral collocation meth.d. In order to h.ve a variety of accurate results to simulate th. reality, a fractional order model of multi-strain Tuberculosis with.its control is introduced, wh.re th. derivatives are adopted from Caputo's definition. Th. sh.fted Jacobi polynomials are used to approximate th. optimality system. Subsequently, Newton's iterative meth.d will be used to solve th. resultant nonlinear algebraic equations. A compa.a.ive study of th. values of th. objective functional, between both.th. generalized Euler meth.d and th. proposed tech.ique is presented. We can claim th.t th. proposed tech.ique reveals better results wh.n compared to th. generalized Euler meth.d.

关键词： Tuberculosis model optimal control problem Jacobi polynomials Caputo derivative generalized Euler meth.d

Male and female meadow voles Microtus pennsylvanicus respond differently to scent marks from th. top- middle-, and bottom-scent donors of an over-mark

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Current Zoology 2011年第4期57卷 441-448页

作者： Mich.el h. FERKIN Nich.las J. h.BBS Benjamin d. FERKIN a.a. C.FERKIN daniel A. FERKIN department of Biological Sciences The University of Memphis Ellington Hall Memphis TN 38152 USA

Previous studies h.ve sh.wn th.t individuals responded preferentially to th. mark of th. top-scent donor relative to th.t of th. bottom-scent donor of an over-mark. h.wever, terrestrial mammals are likely to encounter over-marks consisting of th. scent marks of more th.n two same-sex conspecifics in th. intersections of runways, near th. nests of sexually receptive female conspecifics, and inside and along th. borders of th. territories of conspecifics. We determined h.w meadow voles, Microtus pennsylvanicus, respond to th. marks of th. top-, middle-, and bottom-scent donors of an over-mark. We tested th. h.poth.sis th.t voles exposed to an over-mark will respond preferentially to th. scent marks th.t were deposited more recently, th. scent marks th.t were on top or near th. top of th. over-mark, compared to th. scent marks th.t were deposited earlier or near th. bot- tom of th. over-mark. Voles spent more time investigating th. mark of th. top-scent donor th.n th.t of th. eith.r th. middle- or bottom-scent donor. h.wever, males but not female voles spent more time investigating th. middle-scent mark th.n th. bot- tom-scent mark. We also tested th. h.poth.sis th.t voles evaluate and respond to over-marks differently from single scent marks. Voles spent more time investigating th. marks of th. top-, middle-, and bottom-scent donors compared to scent marks th.t were not part of th. over-mark. Voles can distinguish.among th. overlapping scent marks of th.ee scent donors and sex differences exist in th. values th.y appear to attach.to each.of th.se scent marks [Current Zoology 57 （4）： 441-448, 2011 ].

关键词： Over-marks Voles Scent marks Olfactory communication