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m.ny Fam.lie. of e.act Solutions for Nonline.r Syste.0}of Partial Diffe.e.tial e.uations De.cribing the.Dynam.cs of DNA

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Journal of Partial Diffe.e.tial e.uations 2013年第4期26卷 373-384页

作者： zayed elsayed m. e. ARNOUS Ahm.d H. m.the.0}tics De.artm.nt Faculty of Science Zagazig University Zagazig Egypt. De.artm.nt of e.gine.ring m.the.0}tics and Physics Higher Institute of Engineering El Shorouk Egypt.

The.obje.tive.of this pape. is to apply the.im.rove. ge.e.alize. Riccati e.uation m.pping m.thod to find m.ny fam.lie. of e.act trave.ing wave.solutions for the.ge.e.al nonline.r dynam.c syste.0}in a ne. double.chain m.de. of DNA. This m.de. consists of two long e.astic hom.ge.e.us strands conne.te. with e.ch othe. by an e.astic m.m.rane. Hype.bolic and trigonom.tric function solutions of this m.de. are.obtaine.. Com.arison be.we.n our re.ults and the.we.l-known re.ults are.give..

关键词： Nonline.r dynam.cs of DNA m.de. e.act solutions im.rove. ge.e.alize. Riccatie.uation m.pping m.thod double.chain m.de. of DNA.

The.Asym.totics of the.He.t Se.0}group for a Ge.e.al Bounde. Dom.in with m.xe. Boundary Conditions

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Acta m.the.0}tica Sinica,e.glish Se.ie. 2000年第4期16卷 627-636页

作者： e. m. e. zayed m.the.0}tics De.artm.nt. Faculty of Scie.ce. Zagazig Unive.sity. Zagazig. e.ypt

Sm.ll-tim. asym.totics of the.trace.of the.he.t se.0}group θ（t）=Σv=1x e.p（-tμv）. whe.e.{μv} are.the.e.ge.value. of the.ue.ative.Laplacian -Δ= -Σβ=12（/xβ）2 in the.（x1, x2）-plane. is studie. for a ge.e.al bounde. dom.in Ω with a sm.oth boundary Ω. whe.e.a finite.num.e. of Dirichle.. Ne.m.nn and Robin boundary conditions, on the.pie.e.ise.sm.oth parts Γi（i=1, ..., n） of )Ω such that)Ω=∪i=1nΓ are.conside.e.. Som. ge.m.trical prope.tie. associate. with Ω are.de.e.m.ne.

关键词： He.t se.0}group Inve.se.proble. m.xe. boundary conditions e.ge.value.

On the.solutions and pe.iodic nature.of som. syste.0} of diffe.e.ce.e.uations

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Inte.national Journal of Biom.the.0}tics 2014年第6期7卷 121-146页

作者： e. m. elsayed m.the.0}tics De.artm.nt Faculty of ScienceKing Abdulaziz University P. O. Box 80203 Jeddah 21589 Saudi Arabia De.artm.nt of m.the.0}tics Faculty of ScienceMansoura University Mansoura 35516 Egypt

In this pape., we.conside. the.solution of the.following rational syste.0} of diffe.e.ce.e.uations：xn＋1=zn-1xn-2/xn-2±yn,yn＋1=xn-1yn-2/yn-2±zn,zn＋1=yn-1zn-2/zn-1±xn,whe.e.initial conditions are.nonze.o re.l num.... 详细信息

关键词： Diffe.e.ce.e.uations re.ursive.se.ue.ce. pe.iodic solutions syste.0}of diffe.-e.ce.e.uations stability.

The.m.difie. Sim.le.e.uation m.thod and the.m.ltiple.e.p-function m.thod for Solving Nonline.r Fractional Sharm.-Tasso-Olve. e.uation

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Acta m.the.0}ticae.Applicatae.Sinica 2016年第4期32卷 793-812页

作者： elsayed m.e.zayed Yase. A.Am.R Abdul-Ghani AL-NOWe.Y m.the.0}tics De.artm.nt Faculty of SciencesZagazig University m.the.0}tics De.artm.nt Faculty of EducationAin Shams University

In this article. the.fractional de.ivative. in the.se.se.of the.m.difie. Rie.0}nn-Liouville.de.ivative. toge.he. with the.m.difie. sim.le.e.uation m.thod and the.m.ltiple.e.p-function m.thod are.e.0}loye. for constructing the.e.act solutions and the.solitary wave.solutions for the.nonline.r tim. fractional Sharm.-Tasso- Olve. e.uation. With he.p of m.ple. we.can ge. e.act e.plicit l-wave. 2-wave.and 3-wave.solutions, which include.l-soliton, 2-soliton and 3-soliton type.solutions if we.use.the.m.ltiple.e.p-function m.thod while.we.can ge. only e.act e.plicit l-wave.solution including l-soliton type.solution if we.use.the.m.difie. sim.le.e.uation m.thod. Two case. with spe.ific value. of the.involve. param.te.s are.plotte. for e.ch 2-wave.and 3-wave.solutions.

关键词： m.difie. sim.le.e.uation m.thod m.ltiple.e.p-function m.thod nonline.r fractional partialdiffe.e.tial e.uations e.act solution solitary wave.solutions 1-wave.solution 2-wave.solution 3-wave.solution

Ne. sub-e.uation m.thod to construct solitons and othe. solutions for pe.turbe. nonline.r Schrödinge. e.uation with Ke.r law nonline.rity in optical fibe. m.te.ials

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Journal of Oce.n e.gine.ring and Scie.ce 2019年第1期4卷 14-23页

作者： elsayed m.e.zayed Abdul-Ghani Al-Nowe.y Re.am.m.A.Shohib De.artm.nt of m.the.0}tics Faculty of ScienceZagazig UniversityZagazigEgypt De.artm.nt of m.the.0}tics Faculty of Education and ScienceTaiz UniversityTaizYemen

In a pre.ious work,zayed and Al-Nowe.y have.applie. the.Riccati e.uation m.pping m.thod com.ine. with the.ge.e.alize. e.te.de.(G/G)-e.pansion m.thod and found ne. e.act solutions of the.nonline.r KPP *** the.pre.e.t article.we.propose.a diffe.e.t m.thod,nam.ly,a ne. sub-e.uation m.thod consists of the.Riccati e.uation m.pping m.thod and the.G/G,1/G)-e.pansion m.thod to find ne. e.act solutions of the.pe.turbe. nonline.r Schrödinge. e.uation with Ke.r law nonline.rity in optical fibe. *** propose. m.thod is not found ***,trigonom.tric and rational function solutions are.*** solutions of the.ge.e.alize. Riccati e.uation are.pre.e.te. for the.first tim. which are.not re.orte. *** solutions of the.give. nonline.r e.uation can be.applie. in oce.n e.gine.ring for calculating the.he.ght of tide. in the.oce.n.

关键词： Ne. sub-e.uation m.thod (G/G,1/G)-e.pansion m.thod Ge.e.alize. Riccati e.uation m.pping m.thod Pe.turbe. nonline.r Schrödinge. e.uation e.act solutions.

An e.pansion The.re.0}for an e.ge.value.Proble.0}of an Arbitrary m.ltiply Conne.te. Dom.in with an e.ge.param.te. in a Ge.e.al Type.of Boundary Conditions

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Acta m.the.0}tica Sinica,e.glish Se.ie. 1995年第4期11卷 399-407页

作者： e. m. e. zayed S. F. m. Ibrahim m.the.0}tics De.artm.nt Faculty of Scie.ce Zagazig University Zagazig Egypt m.the.0}tics De.artm.nt Faculty of Scie.ce Ain Shams University Heliopolis Cairo Egypt

The.obje.t of this pape. is to e.tablish an e.pansion the.re.0}for a re.ular right- de.inite.e.ge.value.proble.0}with an e.ge.value.param.te. λ which is containe. in the.Schrodinge. partial diffe.e.tial,e.uation and in a ge.e.al type.of boundary conditions on the.boundary of an arbitrary m.ltiply conne.te. bounde. dom.in in R^n(n≥2).We.associate.with this proble.0}an e.se.tially se.f-adjoint ope.ator in a suitably de.ine. Hilbe.t space.and the. we.de.e.op an associate. e.ge.function e.pansion the.re.0}

关键词： e.ge.value.proble. m.ltiply conne.te. dom.in e.ge.function e.pansion

The.3D Inve.se.Proble.0}of the.Wave.e.uation for a Ge.e.al m.lti-conne.te. Vibrating m.m.rane.with a Finite.Num.e. of Pie.e.ise.Sm.oth Boundary Conditions

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Acta m.the.0}tica Sinica,e.glish Se.ie. 2005年第4期21卷 733-752页

作者： e.m.e.zayed m.the.0}tics De.artm.nt Faculty of ScienceZagazig UniversityZagazig.Egypt

The.trace.of the.wave.ke.ne. μ（t） =∑ω=1^∞ e.p（-ite.^1/2）, whe.e.{e.}ω^∞=1 are.the.e.ge.value. of the.ne.ative.Laplacian -△↓2 = -∑k^3=1 （δ/δxk）^2 in the.（x^1, x^2, x^3）-space. is studie. for a varie.y of bounde. dom.ins, whe.e.-∞ 〈 t 〈 ∞ and i= √-1. The.de.e.de.ce.of μ （t） on the.conne.tivity of bounde. dom.ins and the.Dirichle., Ne.m.nn and Robin boundary conditions are.analyze.. Particular atte.tion is give. for a m.lti-conne.te. vibrating m.m.rane.Ω in Ra surrounde. by sim.ly conne.te. bounde. dom.ins Ω j with sm.oth bounding surface. S j （j = 1,……, n）, whe.e.a finite.num.e. of pie.e.ise.sm.oth Dirichle., Ne.m.nn and Robin boundary conditions on the.pie.e.ise.sm.oth com.one.ts Si^＊（i = 1 ＋ kj-1,……, kj） of the.bounding surface. S j are.conside.e., such that S j = Ui-1＋kj-1^kj Si^＊, whe.e.k0=0. The.basic proble.0}is to e.tract inform.tion on the.ge.m.try Ω by using the.wave.e.uation approach from.a com.le.e.knowle.ge.of its e.ge.value.. Som. ge.m.trical quantitie. of Ω （e.g. the.volum., the.surface.are., the.m.an curvuture.and the.Gaussian curvature. are.de.e.m.ne. from.the.asym.totic e.pansion ofe.pansion of μ（t） for sm.ll │t│.

关键词： Inve.se.proble. Wave.ke.nal e.ge.value. Gre.ns function m.lti-conne.te. vibrating m.m.rane Ne.ative.Laplacian He.t ke.ne.

Ine.ualitie. and Se.aration for a Biharm.nic Laplace.Be.tram. Diffe.e.tial Ope.ator in a Hilbe.t Space.Associate. with the.e.iste.ce.and Unique.e.s The.re.

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Journal of Partial Diffe.e.tial e.uations 2016年第1期29卷 59-70页

作者： zayed e. m. e. De.artm.nt of m.the.0}tics Faculty of Science Zagazig University P.O. Box 44519 Zagazig Egypt.

In this pape., we.have.studie. the.se.aration for the.biharm.nic Laplace.Be.tram. diffe.e.tial ope.atorAu（x） = -△△u（x）＋ V（x）u（x）,for all x ∈ R^n, in the.Hilbe.t space.H = L2（R^n,H1） with the.ope.ator pote.tial V（x） ∈ C^1 （R^n, L （H1））, whe.e.L （H1 ） is the.space.of all bounde. line.r ope.ators on the.Hilbe.t space.H1, while.AAu is the.biharm.nic diffe.e.tial ope.ator and△u=-∑i,j=1^n 1/√de.g δ/δxi[√de.gg-1（x）δu/δxj]is the.Laplace.Be.tram. diffe.e.tial ope.ator in R^n. He.e.g（x） = （gij（x）） is the.Rie.0}nnian m.trix, while.g^-1 （x） is the.inve.se.of the.m.trix g（x）. m.re.ve., we.have.studie. the.e.iste.ce.and unique.e.s The.re.0}for the.solution of the.non-hom.ge.e.us biharm.nic Laplace.Be.tram. diffe.e.tial e.uation Au = - △△u ＋ V（x） u （x） = f（x） in the.Hilbe.t space.H whe.e.f（x） ∈ H as an application of the.se.aration approach.

关键词： Se.aration biharm.nic Laplace.Be.tram. ope.ator ope.ator pote.tial Hilbe.t space.L2 (R^n, H1) coe.cive.e.tim.te e.iste.ce.and unique.e.s The.re.0}

Asym.totic e.pansions of the.He.t Ke.ne. of the.Laplacian for Ge.e.al Annular Bounde. Dom.ins with Robin Boundary Conditions：Furthe. Re.ults

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Acta m.the.0}tica Sinica,e.glish Se.ie. 2003年第4期19卷 679-694页

作者： e.m.e.zayed De.artm.ntofm.the.0}tics FacultyofScienceZagazigUniversityZagazigEgypt

The.asym.totic e.pansions of the.trace.of the.he.t ke.ne. Θ(t) = Σ_(v =1)~∞e.p(-tλ_v) for sm.ll positive.t, whe.e.{λ_v} are.the.e.ge.value. of the.ne.ative.Laplacian-△_n = -Σ_(i = 1)~n(partial de.iv/(partial de.iv)x^i)~2 in R^n (n = 2 or 3), are.studie. for age.e.al annular bounde. dom.in Ω with a sm.oth inne. boundary (partial de.iv)Ω_1 and a sm.othoute. boundary (partial de.iv)Ω_2, whe.e.a finite.num.e. of pie.e.ise.sm.oth Robin boundaryconditions (partial de.iv/(partial de.iv)n_j + γ_j)φ = 0 on the.com.one.ts Γ_j(j = 1, …, k) of(partial de.iv)Ω_1 and on the.com.one.ts Γ_j(j = k + 1, …, m. of (partial de.iv)Ω_2 are.onside.e. such that (partial de.iv)Ω_1 = ∪_(j = 1)~kΓ_j and (partial de.iv)Ω_2 = ∪_(j = k +1)~m._j and whe.e.the.coe.ficie.ts γ_j(j = 1, …, m. are.pie.e.ise.sm.oth positive.functions. Som.applications of Θ(t) for an ide.l gas e.close. in the.ge.e.al annular bounde. dom.in Ω are.*** re.ults are.also obtaine..

关键词： inve.se.proble. he.t ke.ne. e.ge.value. Robin boundary conditions classical ide.l gas