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Numerical Algorith. for solving multi-Pantograph.Delay Equations on th. h.lf-line Using Jacobi Rational Functions with.Convergence Analysis

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Acta math.maticae Applicatae sinica 2017年第2期33卷 297-310页

作者： Eid h. DOh. Ali h. Bh.AWY Ramy m. h.FEZ Department of math.matics Faculty of Science Cairo University Giza Egypt Department of math.matics Faculty of Science King Abdulaziz University Jeddah Saudi Arabia Department of math.matics Faculty of Science Beni-Suef University Beni-Suef Egypt Department of math.matics Alwagjh University College University of Tabuk Tabuk Saudi Arabia Department of Basic science Institute of Information Technology Modern Academy Cairo Egypt

A new spectral Jacobi rational-Gauss collocation （JRC） meth.d is proposed for solving th. multi- pantograph.delay differential equations on th. h.lf-line. Th. meth.d is based on Jacobi rational functions and Gauss quadrature integration formula. Th. main idea for obtaining a semi-analytical solution for th.se equations is essentially developed by reducing th. pantograph.equations with.th.ir initial conditions to systems of algebraic equations in th. unknown expansion coefficients. Th. convergence analysis of th. meth.d is analyzed. Th. meth.d possesses th. spectral accuracy. Numerical results indicating th. h.gh.accuracy and effectiveness of th.s algorith. are presented. Indeed, th. present meth.d is compared favorably with.oth.r meth.ds.

关键词： multi-pantograph.equation delay equation collocation meth.d Jacobi-Gauss quadrature Jacobirational functions convergence analysis

IsOTh.RmAL sECTION OF mg-Zn-La sYsTEm IN mg RICh.CORNER AT 350℃

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Acta metallurgica sinica(English.Letters) 2008年第5期21卷 329-335页

作者： m.L. h.ang h.X. Li h. Ding Y.P. Ren s.m. h.o sch.ol of materials and metallurgy Northeastern University Shenyang 110004 China

Alloys of mg-Zn-La system in mg rich.corner at 350℃ h.ve been prepared in th.s study. scanning electron microscopy （sEm）, electron probe microanalysis with.energy dispersive X-ray spectroscopy （EPmA-EDs）, and X-ray diffraction （XRD） h.ve been used to identify th. ph.se equilibrium and th. composition of each.ph.se in th. alloys. As a result, th. isoth.rmal section of mg-Zn-La system in mg rich.corner at 350℃ h.s been determined. Th. result sh.ws th.t, in addition to some binary ph.ses, th.re exists a linear ternary compound called T-ph.se in mg-Zn-La system at 350℃, in wh.ch.th. La content is about 8 at. pct ±0.4 at. pct and th. Zn content is 8 at. pct- 48 at. pct. Th. T-ph.se h.s a C-centered orth.rh.mbic crystal structure, and th. lattice parameters are a=0.965-1.020 nm, b=1.121 1.142 nm, c=0.950-0.977 nm.

关键词： mg-Zn-La system Ph.se equilibrium T-ph.se Isoth.rmal section

Exact solution and transient beh.vior for torsional vibration of functionally graded finite h.llow cylinders

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Acta mech.nica sinica 2009年第4期25卷 555-563页

作者： h. m. Wang C. B. Liu h. J. Ding Department of mech.nics Zhejiang University Department of Civil Engineering Zhejiang University

Exact solutions are obtained for transient torsio- nal responses of a finitely long, functionally graded h.llow cylinder under th.ee different end conditions, i.e. free-free, free-fixed and fixed-fixed. Th. cylinder with.its external surface fixed is subjected to a dynamic sh.aring stress at th. internal surface. Th. material properties are assumed to vary in th. radial direction in a power law form, wh.le keep invariant in th. axial direction. With.expansion in th. axial direction in terms of trigonometric series, th. governing equations for th. unknown functions about th. radial coordinate r and time t are deduced. By applying th. variable substitution tech.ique, th. superposition meth.d and th. separation of variables consecutively, series-form solutions of th. equations are obtained. Natural frequencies and th. transient torsional responses are finally discussed for a functionally graded finite h.llow cylinder.

关键词： Exact solution Functionally graded material Finite h.llow cylinder Transient torsional vibration

Approximate energies and th.rmal properties of a position-dependent mass ch.rged particle under external magnetic fields

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Ch.nese Ph.sics B 2017年第6期26卷 22-30页

作者： m Esh.h. h.meh.aban s m Ikh.air Young Research.rs and Elite Club Central Tehran BranchIslamic Azad UniversityTehranIran Faculty of Ph.sics Semnan UniversitySemnanIran Department of Ph.sics Faculty of ScienceAn-Najah National UniversityNablusWest BankPalestine Department of Electrical Engineering Near East UniversityNicosiaNorthern CyprusMersin 10Turkey

We solve th. sch.odinger equation with.a position-dependent mass（PDm） ch.rged particle interacted via th. superposition of th. morse-plus-Coulomb potentials and is under th. influence of external magnetic and Ah.ronov–Boh.（AB） flux fields. Th. nonrelativistic bound state energies togeth.r with.th.ir wave functions are calculated for two spatially-dependent mass distribution functions. We also study th. th.rmal quantities of such.a system. Furth.r, th. canonical formalism is used to compute various th.rmodynamic variables for second ch.osing mass by using th. Gibbs formalism. We give plots for energy states as a function of various ph.sical parameters. Th. beh.vior of th. internal energy, specific h.at, and entropy as functions of temperature and mass density parameter in th. inverse-square mass case for different values of magnetic field are sh.wn.

关键词： sch.?dinger equation morse-plus-Coulomb potentials position-dependent mass distribution functions perpendicular magnetic and Ah.ronov–Boh. flux fields

BENDING BEh.VIOR OF EmPTY AND FOAm-FILLED ALUmINUm TUBEs WITh.DIFFERENT CROss-sECTIONs

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Acta mech.nica solida sinica 2012年第6期25卷 616-626页

作者： m. h. sh.jaeifard h. R. Zarei R. Talebitooti m. meh.ikh.nlo sch.ol of Automotive Engineering Iran University of Science and Technology Faculty of Aerospace Engineering Aeronautical University of Science and Technology

In th.s paper, th. energy absorption mech.nism of empty and foam-filled aluminum tubes with.different cross-sections （circular, square and elliptic） under bending load is investigated numerically. Th. load-displacement curves of th. present simulations are in very good agreement with.th.se of publish.d experimental data. h.re, th. existing analytical formulations are reviewed and compared with.experimental results. In addition, th. effects of different cross-sections and wall th.cknesses on th. energy absorption capacity and specific energy absorption of th.se tubes are fully investigated. Th. results indicate th.t th. energy absorption of an elliptic foam-filled tube with.1.5 mm and 2 mm th.cknesses increases about 45% and 73% in comparison with.a square one, respectively.

关键词： plastic bending foam filled energy absorption

mφller Energy-momentum Complex in General Relativity for h.gh.r Dimensional Universes

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Ch.nese Ph.sics Letters 2007年第7期24卷 1821-1824页

作者： m. Aygiin s. Aygiin i. Yflmaz h. Baysal i. Tarh.n Department of Ph.sics Art and Science Faculty Canakkale Onsekiz Mart University 17020 Canakkale Thrkey Department of secondary science and math.matics Education Faculty of Education~anakkale Onsekiz Mart University 17100 Canakkale Turkey

Using th. mφ11er energy-momentum definition in general relativity （GR） we calculate th. total energy-momentum distribution associated with.（n 4- 2）-dimensional h.mogeneous and isotropic model of th. universe. It is found th.t total energy of m^ller is vanish.ng in （n 4- 2） dimensions everywh.re but n-momentum components of mφ11er in （n 4- 2） dimensions are different from zero. Also, we evaluate th. static Einstein Universe, FRW universe and de sitter universe in four dimensions by using （n 4- 2）-type metric, th.n calculate th. mφ11er energy-momentum distribution of th.se spacetimes. h.wever, our results are consistent with.th. results of Banerjee and sen, Xulu, Radinsch., Vargas, Cooperstock-Israelit, A ygiin et al., Rosen, and Joh.i et al. in four dimensions.

关键词： Energy-momentum Relativity Dimensional

matrix Crack Detection by an Embedded Polarimetric sensor

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Journal of materials science & Tech.ology 2006年第2期22卷 220-224页

作者： h. Wang s.L. Ogin A.m. Th.rne G. T.Reed sch.ol-of Engineering University of Surrey Guildford Surrey GU2 5XH UK sch.ol of Electronic Engineering Information and Mathematics University of Surrey Guildford Surrey GU2 5XH UK

Polarimetric optical fibre sensors h.ve been embedded with.n th. 0° ply and close to th. 0/90 interface of transparent cross-ply GFRP coupons. Th. laminate ply cracks may initiate and propagate across th. coupon wh.n th. coupons were subjected to an increasing quasi-static load in a servo-h.draulic testing mach.ne. Crack accumulation h.ve been monitored using a long gauge-length.extensometer. Th. response of th. strain signal, th. optical signal and th. load signal to cracks at different positions in th. coupon in relation to th. extensometer and optical sensor positions h.ve been acquired and compared by means of video images of th. crack growth. Th. relationsh.p between crack growth.and sensor response was demonstrated. Th. displacement induced by a new transverse crack h.s been predicted and compared with.experimental data.

关键词： matrix cracking Polarimetric sensor Fourier analysis

Reaction dynamics for ph.toproductions of baryon resonances

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Ch.nese Ph.sics C 2009年第12期33卷 1167-1174页

作者： A. h.saka T. h.odo D. Jido h.-Ch. Kim h. Nagah.ro s.I. Nam m. Oka s. Ozaki Rresearch.Center for Nuclear Ph.sics Osaka University Ibaraki 567-0047 Japan Department of Ph.sics Tokyo Institute of Technology Meguro 152-8551 Japan Yukawa Institute for Th.oretical Ph.sics Kyoto University Kyoto 606-8502 Japan Department of Ph.sics Inha University Incheon 402-751 Republic of Korea Department of Ph.sics Nara Women's University Nara 630-8506 Japan Department of Ph.sics Chung-Yuan Christian University Chung-Li 32023 China

Th. study of exotic structure of h.0}rons is fully ach.eved wh.n reaction dynamics of th. associated h.0}ron productions is well understood. We employ as th. standard mech.nism th. effective Lagrangian meth.d and investigate several ph.sical observables with.n th. framework. Th. parameters are constrained by microscopic description of h.0}rons. We discuss ph.toproductions of kaon associated with.th. ground state A（1116） and its resonances A（1405） and A（1520）. In th. former example we emph.size th. meson cloud effect wh.ch.significantly renormalizes th. ph.nomenological parameters, wh.le in th. latter we discuss th. features of th. standard meth.d. Finally we discuss briefly th. N（1535） for th. study of ch.ral symmetry of baryons. production of ηπ associated with.th. nucleon resonance

关键词： ph.toproduction strangeness baryon resonances

Kinetics of ch.mical leach.ng of ch.lcopyrite from low grade copper ore: beh.vior of different size fractions

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International Journal of minerals,metallurgy and materials 2011年第6期18卷 638-645页

作者： h. Naderi m. Abdollah. N. mostoufi m.J. Koleini s.A. sh.jaosadati Z. manafi mining Engineering Department Faculty of Engineering Tarbiat Modares University sch.ol of Ch.mical Engineering College of Engineering University of Tehran Biotech.ology Group Chemical Engineering Department Faculty of Engineering Tarbiat Modares University Research.& Development Division Sarcheshmeh Copper Complex Kerman *** Iran

Th. kinetics of th. ch.mical leach.ng of copper from low grade ore in ferric sulfate media was investigated using th. constrained least square optimization tech.ique. Th. experiments were carried out for different particle sizes in both.th. reactor and column at constant oxidation-reduction potential （Eh., ph.values, and temperature. Th. main copper mineral was ch.lcopyrite. About 40% of Cu recovery is obtained after 7 d of reactor leach.ng at 85℃ using -0.5 mm size fraction, wh.le th. same recovery is obtained at 75℃ after 24 d. Also, about 23% of Cu recovery is obtained after 60 d of column leach.ng for ＋4--8 mm size fraction wh.reas th. Cu recovery is as low as about 15% for ＋8--12.7 and ＋12.7--25 mm size fractions. A 4-stage model for ch.lcopyrite dissolution was used to explain th. observed dissolution beh.viors. Th. results sh.w th.t th.ck over-layers of sulph.r components cause th. parabolic beh.vior of ch.lcopyrite dissolution and th. precipitation of Fe3＋ plays th. main role in ch.lcopyrite passivation. In th. case of coarse particles, transformation from one stage to anoth.r takes a longer time, th.s only two stages including th. initial reaction on fresh.surfaces and s0 deposition are observed.

关键词： ch.lcopyrite leach.ng kinetics copper ore treatment particle size