The shot-range interaction and the atomic anharmonic vibration are both considered, and then the analytic functions of the Debye temperature, the specific capacity and the thermal conductivity of graphene with the tem...The shot-range interaction and the atomic anharmonic vibration are both considered, and then the analytic functions of the Debye temperature, the specific capacity and the thermal conductivity of graphene with the temperature are obtained. The influence of anharmonic vibration on these thermal physical properties is also investigated. Some theoretical results are given. If only the harmonic approximation is considered, the Debye temperature of the graphene is unrelated to the temperature. If the anharmonic terms are considered, it increases slowly with the increasing temperature. The molar heat capacity of the graphene increases nonlinearly with the increasing temperature. The mean free path of phonons and the thermal conductivity of the graphene decrease nonlinearly with the increasing temperature. The relative changes of the Debye temperature, the specific heat capacity and the thermal conductivity caused by the anharmonic terms increase with the increasing temperature. The anharmonic effect of atomic vibration becomes more significant under higher temperature.展开更多
This article deals with the conditions that ensure the blow-up phenomenon or its absence for solutions of the system ut= △u^l ＋ u^p1v^q1 and vt = △v ^m ＋ u^p2 v^q2 with homogeneous Dirichlet boundary conditions....This article deals with the conditions that ensure the blow-up phenomenon or its absence for solutions of the system ut= △u^l ＋ u^p1v^q1 and vt = △v ^m ＋ u^p2 v^q2 with homogeneous Dirichlet boundary conditions. The results depend crucially on the sign of the difference p2q1 - （l -p1）（m- q2）, the initial data, and the domain Ω.展开更多
By constructing two suitable generalized Lyapunov functions,we derived a generalized ellipsoidal estimate of the globally attractive set and positively invariant set of the unified chaotic system with the parameters ...By constructing two suitable generalized Lyapunov functions,we derived a generalized ellipsoidal estimate of the globally attractive set and positively invariant set of the unified chaotic system with the parameters α=1/29 and 1/29<α<2/29,respectively,which extends some related results of Li,et al. [Li DM,Lu JA,Wu XQ,Chen GR,Estimating the global basin of attraction and positively invariant set for the Lorenz system and a unified chaotic system,Journal of Mathematical Analysis and Applications,2006,323(2): 844-853]. The theoretical results obtained in this paper will find wide application in chaos control and synchronization.展开更多
To describe properties of the high frequency gravitational wave （HFGW） propagating through the vacuum gravitational field in Robertson-Walker background space-time, we calculated its energy momentum pseudo-tensor （...To describe properties of the high frequency gravitational wave （HFGW） propagating through the vacuum gravitational field in Robertson-Walker background space-time, we calculated its energy momentum pseudo-tensor （EMPT） in the limit of short wavelengths by taking the Brill-Hartle average on the second order perturbation of the Einstein tensor over several wavelengths. By rewriting the EMPT as a form of perfect fluid, the dynamical back-reaction of HIFGW on the background spacetime was discussed. The result shows that the energy density of HFGW, which is in the gauge we chose, is positive definite. The HFGW serves as a source for curving the background space-time and affects the dynamical evolution and time evolution of the scale factor of the Robertson-Walker metric.展开更多
The existences of the global attractor Ae for a degenerate parabolic equation and of the homogenized attractor A0 for the corresponding homogenized equation are studied, and explicit estimates for the distance between...The existences of the global attractor Ae for a degenerate parabolic equation and of the homogenized attractor A0 for the corresponding homogenized equation are studied, and explicit estimates for the distance between Ae and A0 are given.展开更多
In this article, the existence and uniqueness of positive solution for a class of nonlinear fractional differential equations is proved by constructing the upper and lower control functions of the nonlinear term witho...In this article, the existence and uniqueness of positive solution for a class of nonlinear fractional differential equations is proved by constructing the upper and lower control functions of the nonlinear term without any monotone requirement. Our main method to the problem is the method of upper and lower solutions and Schauder fixed point theorem. Finally, we give an example to illuminate our results.展开更多
This article studies the asymptotic behaviors of the solution for a stochastic hydrodynamical equation in Heisenberg paramagnet in a two-dimensional periodic domain. We obtain the existence of random attractors in H1.
Let F be a family of mermorphic functions in a domain D, and let a, b, c be complex numbers, a ≠ b. If for each f ∈ F, the zeros of f-c are of multiplicity ≥ k ＋ 1, and -↑Ef（k）（a） belong to -↑Ef （a）, -↑Ef...Let F be a family of mermorphic functions in a domain D, and let a, b, c be complex numbers, a ≠ b. If for each f ∈ F, the zeros of f-c are of multiplicity ≥ k ＋ 1, and -↑Ef（k）（a） belong to -↑Ef （a）, -↑Ef（k）（b）belong to -↑Ef （b）, then F is normal in D.展开更多
A generalized Lyapunov function was employed to investigate the ultimate bound and positively invariant set of a generalized Lorenz system.We derived an ellipsoidal estimate of the ultimate bound and positively invari...A generalized Lyapunov function was employed to investigate the ultimate bound and positively invariant set of a generalized Lorenz system.We derived an ellipsoidal estimate of the ultimate bound and positively invariant set for the generalized Lorenz system,for all the positive values of system parameters a,b,and c.Our results extend the related result of Li,et al.[Li DM,Lu JA,Wu XQ,et al.,Estimating the ultimate bound and positively invariant set for the Lorenz system and a unified chaotic system,Journal of Mathematical Analysis and Application,2006,323(2):844-653].展开更多
Several rocksalt Sr4X3N （X = O, S, Se, and Te） are predicted to be potential half-metallic ferromagnets free of transition-metal and rare-earth elements by performing the first-principles calculations. Then their ma...Several rocksalt Sr4X3N （X = O, S, Se, and Te） are predicted to be potential half-metallic ferromagnets free of transition-metal and rare-earth elements by performing the first-principles calculations. Then their magnetic properties, such as the half metallicity and the crystal-cell magnetic moments are investigated. The Sr4X3N possibly have higher Curie temperatures and have more stable half metallicity than the Sr4X3C. Their crystal-cell magnetic moments are all 1.00 μB. The crystal-cell magnetic moments and the half metallicity arise mainly from the N ions. The main mechanism is the strong covalent interaction leading to the sp2 hybridized orbitals in the Sr4X3N. Then two Sr-5s and three N-2p electrons enter into three sp2 hybridized orbitals. Among these five electrons, four electrons are paired and one is unpaired, so there are three spin-up electrons and two spin-down electrons in these sp2 hybridized orbitals.展开更多
Indium-doped ZnO thin films are deposited on quartz glass slides by RF magnetron sputtering at ambient temperature. The as-deposited films are annealed at different temperatures from 400℃ to 800 ℃ in air for 1 h. Tr...Indium-doped ZnO thin films are deposited on quartz glass slides by RF magnetron sputtering at ambient temperature. The as-deposited films are annealed at different temperatures from 400℃ to 800 ℃ in air for 1 h. Transmittance spectra are used to determine the optical parameters and the thicknesses of the films before and after annealing using a nonlinear programming method, and the effects of the annealing temperatures on the optical parameters and the thickness are investigated. The optical band gap is determined from the absorption coefficient. The calculated results show that the film thickness and optical parameters both increase first and then decrease with increasing annealing temperature from 400℃ to 800℃. The band gap of the as-deposited ZnO：In thin film is 3.28 eV, and it decreases to 3.17 eV after annealing at 400℃. Then the band gap increases from 3.17 eV to 3.23 eV with increasing annealing temperature from 400℃ to 800℃.展开更多
Based on piezoresistive effect, the acceleration sensitivity of multi-walled canbon nanotube (MWNT) films was investigated. A three-point bending technique was presented to measure the piezoresistivity, which used a b...Based on piezoresistive effect, the acceleration sensitivity of multi-walled canbon nanotube (MWNT) films was investigated. A three-point bending technique was presented to measure the piezoresistivity, which used a bending stress applied to the samples while making MWNT films wheeling with a rotational machine. The experimental results showed that the fractional increase in resistance increases linearly versus the increase of centripetal acceleration, and there is a linear relationship between the acceleration and the strain. These shed light on using carbon nanotube films as acceleration sensors for many potential applications.展开更多
The homogenization of one kind of nonlinear parabolic equation is studied. The weak convergence and corrector results are obtained by combining carefully the compactness method and two-scale convergence method in the ...The homogenization of one kind of nonlinear parabolic equation is studied. The weak convergence and corrector results are obtained by combining carefully the compactness method and two-scale convergence method in the homogenization theory.展开更多
This paper is concerned with the following nonlinear difference equation:x_(n+1)=sum from i=1 to l A_(s_i)x_(n-s_i)/B+C multiply from j=1 to k x_(n-t_j) +D_x_n,n=0,1,…(1.1).The more simple suffcient conditions of asy...This paper is concerned with the following nonlinear difference equation:x_(n+1)=sum from i=1 to l A_(s_i)x_(n-s_i)/B+C multiply from j=1 to k x_(n-t_j) +D_x_n,n=0,1,…(1.1).The more simple suffcient conditions of asymptotic stability are obtained by using a smart technique,which extends and includes partially corresponding results obtained in the references [6-9].The global behavior of the solutions is investigated.In addition,in order to support analytic results,some numerical simulations to the special equations are presented.展开更多
Rodin and Sullivan （1987） proved Thurston＇s conjecture that a scheme based on the Circle Packing Theorem converges to the Riemann mapping, thereby proved a refreshing geometric view of the Riemann Mapping Theorem. ...Rodin and Sullivan （1987） proved Thurston＇s conjecture that a scheme based on the Circle Packing Theorem converges to the Riemann mapping, thereby proved a refreshing geometric view of the Riemann Mapping Theorem. Naturally, we consider to use the ellipses to pack the bounded simply connected domain and obtain similarly a sequence simplicial homeomorphism between the ellipse packing and the circle packing. In this paper, we prove that these simplicial homeomorphism approximate a quasiconformal mapping from the bounded simply connected domain onto the unit disk with the modulus of their complex dilatations tending to 1 almost everywhere in the domain when the ratio of the longer axis and shorter axis of the ellipse tending to ∞.展开更多
The dependences of electrochemical potential at the interface between carbon nanotubes and electrolyte upon temperature and electrolyte concentration are studied. Carbon nanotubes were synthesized by hot filament chem...The dependences of electrochemical potential at the interface between carbon nanotubes and electrolyte upon temperature and electrolyte concentration are studied. Carbon nanotubes were synthesized by hot filament chemical vapor deposition with Si as the substrate. Four substances were tested: NaCl solution, KCl solution, water and alcohol. It is found that for NaCl and KCl solutions, at the interface, there is a large electrochemical potential which increases with temperature and is larger for an electrolyte of higher concentration. There is a significant field effect of carbon nanotubes with electrolyte as the gate, and the effect depends on the ionizability of the electrolyte. Such physicochemical property invests carbon nanotube a potential application in nanoelectronics.展开更多
We consider a binary dipolar Bose–Einstein condensate confined in a rotating harmonic plus quartic potential trap.The ground-state vortex structures are numerically obtained as a function of the contact interactions ...We consider a binary dipolar Bose–Einstein condensate confined in a rotating harmonic plus quartic potential trap.The ground-state vortex structures are numerically obtained as a function of the contact interactions and the dipole–dipole interaction in both slow and rapid rotation cases. The results show that the vortex configurations depend strongly on the strength of the contact interactions, the relative strength between dipolar and contact interactions, as well as on the orientation of the dipoles. A variety of exotic ground-state vortex structures, such as pentagonal and hexagon vortex lattice,square vortex lattice with a central vortex, annular vortex lines, and straight vortex lines, are observed by turning such controllable parameters. Our results deepen the understanding of effects of dipole–dipole interaction on the topological defects.展开更多
The uniqueness problem of entire functions concerning weighted sharing was discussed, and the following theorem was proved. Let f and 8 be two non-constant entire functions, m, n and k three positive integers, and n...The uniqueness problem of entire functions concerning weighted sharing was discussed, and the following theorem was proved. Let f and 8 be two non-constant entire functions, m, n and k three positive integers, and n〉2k＋4. If Em（1,（f^n）^（k））= Em（1,（g^n）^（k））, then either f（z）=c1c^cz and 8（z）= c2c^cz or f=ts, where c, c1 and c2 are three constants satisfying （-1）^k（c1c2）^n（nc）^2k=], and t is a constant satisfying t^n=1. The theorem generalizes the result of Fang [Fang ML, Uniqueness and value sharing of entire functions, Computer ＆ Mathematics with Applications, 2002, 44： 823-831].展开更多
Skyrmion bags are spin structures with arbitrary topological charges, each of which is composed of a big skyrmion and several small skyrmions. In this work, by using an in-plane alternating current(AC) magnetic field,...Skyrmion bags are spin structures with arbitrary topological charges, each of which is composed of a big skyrmion and several small skyrmions. In this work, by using an in-plane alternating current(AC) magnetic field, we investigate the spinwave modes of skyrmion bags, which behave differently from the clockwise(CW) rotation mode and the counterclockwise(CCW) rotation mode of skyrmions because of their complex spin topological structures. The in-plane excitation power spectral density shows that each skyrmion bag possesses four resonance frequencies. By further studying the spin dynamics of a skyrmion bag at each resonance frequency, the four spin-wave modes, i.e., a CCW-CW mode, two CW-breathing modes with different resonance strengths, and an inner CCW mode, appear as a composition mode of outer skyrmion–inner skyrmions. Our results are helpful in understanding the in-plane spin excitation of skyrmion bags, which may contribute to the characterization and detection of skyrmion bags, as well as the applications in logic devices.展开更多
The relation between the global attractors Aε for a calss of quasilinear parabolic equations and the global attractor A0 for the homogenized equation is discussed, and an explicit error estimate between Aε and A0 is...The relation between the global attractors Aε for a calss of quasilinear parabolic equations and the global attractor A0 for the homogenized equation is discussed, and an explicit error estimate between Aε and A0 is given.展开更多
基金Supported by the National Natural Science Foundation of China under Grant No 11574253the Scientific and Technological Research Program of Chongqing Municipal Education Commission under Grant Nos KJ1601111 and KJ1601118the Basic and Frontier Research Projects of Chongqing under Grant No cstc2015jcyjA40054
文摘The shot-range interaction and the atomic anharmonic vibration are both considered, and then the analytic functions of the Debye temperature, the specific capacity and the thermal conductivity of graphene with the temperature are obtained. The influence of anharmonic vibration on these thermal physical properties is also investigated. Some theoretical results are given. If only the harmonic approximation is considered, the Debye temperature of the graphene is unrelated to the temperature. If the anharmonic terms are considered, it increases slowly with the increasing temperature. The molar heat capacity of the graphene increases nonlinearly with the increasing temperature. The mean free path of phonons and the thermal conductivity of the graphene decrease nonlinearly with the increasing temperature. The relative changes of the Debye temperature, the specific heat capacity and the thermal conductivity caused by the anharmonic terms increase with the increasing temperature. The anharmonic effect of atomic vibration becomes more significant under higher temperature.
基金This work is supported in part by NNSF of China (10571126)in part by Program for New Century Excellent Talents in University.
文摘This article deals with the conditions that ensure the blow-up phenomenon or its absence for solutions of the system ut= △u^l ＋ u^p1v^q1 and vt = △v ^m ＋ u^p2 v^q2 with homogeneous Dirichlet boundary conditions. The results depend crucially on the sign of the difference p2q1 - （l -p1）（m- q2）, the initial data, and the domain Ω.
文摘By constructing two suitable generalized Lyapunov functions,we derived a generalized ellipsoidal estimate of the globally attractive set and positively invariant set of the unified chaotic system with the parameters α=1/29 and 1/29<α<2/29,respectively,which extends some related results of Li,et al. [Li DM,Lu JA,Wu XQ,Chen GR,Estimating the global basin of attraction and positively invariant set for the Lorenz system and a unified chaotic system,Journal of Mathematical Analysis and Applications,2006,323(2): 844-853]. The theoretical results obtained in this paper will find wide application in chaos control and synchronization.
基金the National Basic Research Program of China (No.2003 CB 716300)the National Natural Science Foundation of China (No.10575140)+1 种基金the Nature Science Foundation of Chongqing (No. 8562)the Foundation of China Academy of Engineering Physics.
文摘To describe properties of the high frequency gravitational wave （HFGW） propagating through the vacuum gravitational field in Robertson-Walker background space-time, we calculated its energy momentum pseudo-tensor （EMPT） in the limit of short wavelengths by taking the Brill-Hartle average on the second order perturbation of the Einstein tensor over several wavelengths. By rewriting the EMPT as a form of perfect fluid, the dynamical back-reaction of HIFGW on the background spacetime was discussed. The result shows that the energy density of HFGW, which is in the gauge we chose, is positive definite. The HFGW serves as a source for curving the background space-time and affects the dynamical evolution and time evolution of the scale factor of the Robertson-Walker metric.
基金the Scientific Research Foundation for Returned Overseas Chinese Scholars under the State Education Ministrythe Key Teachers’Foundation of Chongqing University
文摘The existences of the global attractor Ae for a degenerate parabolic equation and of the homogenized attractor A0 for the corresponding homogenized equation are studied, and explicit estimates for the distance between Ae and A0 are given.
基金supported by Science and Technology Project of Chongqing Municipal Education Committee (kJ110501) of ChinaNatural Science Foundation Project of CQ CSTC (cstc2012jjA20016) of ChinaNational Natural Science Foundation of China (11101298)
文摘In this article, the existence and uniqueness of positive solution for a class of nonlinear fractional differential equations is proved by constructing the upper and lower control functions of the nonlinear term without any monotone requirement. Our main method to the problem is the method of upper and lower solutions and Schauder fixed point theorem. Finally, we give an example to illuminate our results.
文摘This article studies the asymptotic behaviors of the solution for a stochastic hydrodynamical equation in Heisenberg paramagnet in a two-dimensional periodic domain. We obtain the existence of random attractors in H1.
文摘Let F be a family of mermorphic functions in a domain D, and let a, b, c be complex numbers, a ≠ b. If for each f ∈ F, the zeros of f-c are of multiplicity ≥ k ＋ 1, and -↑Ef（k）（a） belong to -↑Ef （a）, -↑Ef（k）（b）belong to -↑Ef （b）, then F is normal in D.
文摘A generalized Lyapunov function was employed to investigate the ultimate bound and positively invariant set of a generalized Lorenz system.We derived an ellipsoidal estimate of the ultimate bound and positively invariant set for the generalized Lorenz system,for all the positive values of system parameters a,b,and c.Our results extend the related result of Li,et al.[Li DM,Lu JA,Wu XQ,et al.,Estimating the ultimate bound and positively invariant set for the Lorenz system and a unified chaotic system,Journal of Mathematical Analysis and Application,2006,323(2):844-653].
基金Project supported by Chongqing Natural Science Foundation,China (Grant Nos.CSCT2010BB4405 and CSTC2008BB4083)the Doctoral Foundation of Chongqing University of Posts and Telecommunications,China(Grant No.A2008-63)
文摘Several rocksalt Sr4X3N （X = O, S, Se, and Te） are predicted to be potential half-metallic ferromagnets free of transition-metal and rare-earth elements by performing the first-principles calculations. Then their magnetic properties, such as the half metallicity and the crystal-cell magnetic moments are investigated. The Sr4X3N possibly have higher Curie temperatures and have more stable half metallicity than the Sr4X3C. Their crystal-cell magnetic moments are all 1.00 μB. The crystal-cell magnetic moments and the half metallicity arise mainly from the N ions. The main mechanism is the strong covalent interaction leading to the sp2 hybridized orbitals in the Sr4X3N. Then two Sr-5s and three N-2p electrons enter into three sp2 hybridized orbitals. Among these five electrons, four electrons are paired and one is unpaired, so there are three spin-up electrons and two spin-down electrons in these sp2 hybridized orbitals.
基金supported by the National Natural Science Foundation of China (Grant Nos. 50942021 and 11075314)the Fundamental Research Fund for the Central Universities (Grant No. CDJXS10102207)
文摘Indium-doped ZnO thin films are deposited on quartz glass slides by RF magnetron sputtering at ambient temperature. The as-deposited films are annealed at different temperatures from 400℃ to 800 ℃ in air for 1 h. Transmittance spectra are used to determine the optical parameters and the thicknesses of the films before and after annealing using a nonlinear programming method, and the effects of the annealing temperatures on the optical parameters and the thickness are investigated. The optical band gap is determined from the absorption coefficient. The calculated results show that the film thickness and optical parameters both increase first and then decrease with increasing annealing temperature from 400℃ to 800℃. The band gap of the as-deposited ZnO：In thin film is 3.28 eV, and it decreases to 3.17 eV after annealing at 400℃. Then the band gap increases from 3.17 eV to 3.23 eV with increasing annealing temperature from 400℃ to 800℃.
基金Funded by the National Natural Science Foundation of China (No. 60376032 and No. 90406024) and the Key Teacher Foundation of Chongqing University.
文摘Based on piezoresistive effect, the acceleration sensitivity of multi-walled canbon nanotube (MWNT) films was investigated. A three-point bending technique was presented to measure the piezoresistivity, which used a bending stress applied to the samples while making MWNT films wheeling with a rotational machine. The experimental results showed that the fractional increase in resistance increases linearly versus the increase of centripetal acceleration, and there is a linear relationship between the acceleration and the strain. These shed light on using carbon nanotube films as acceleration sensors for many potential applications.
基金Funded by the Scientific Research Foundation for Returned Overseas Chinese Scholars under the State Education Ministry, and the Key Teachers’ Foundation of Chongqing University.
文摘The homogenization of one kind of nonlinear parabolic equation is studied. The weak convergence and corrector results are obtained by combining carefully the compactness method and two-scale convergence method in the homogenization theory.
基金Supported by the Science and Technology Project of Chongqing Municiple Education Commission(KJ110501)Supported by the Research Initiation Project for High-level Talents of North China University of Water Resources and Electric Power(201035)Supported by the NSF of the Hebei Higher Education Institutions(Z2011111)
文摘This paper is concerned with the following nonlinear difference equation:x_(n+1)=sum from i=1 to l A_(s_i)x_(n-s_i)/B+C multiply from j=1 to k x_(n-t_j) +D_x_n,n=0,1,…(1.1).The more simple suffcient conditions of asymptotic stability are obtained by using a smart technique,which extends and includes partially corresponding results obtained in the references [6-9].The global behavior of the solutions is investigated.In addition,in order to support analytic results,some numerical simulations to the special equations are presented.
基金supported by the National Natural Science Foundation of China(10701084)Chongqing Natural Science Foundation (2008BB0151)
文摘Rodin and Sullivan （1987） proved Thurston＇s conjecture that a scheme based on the Circle Packing Theorem converges to the Riemann mapping, thereby proved a refreshing geometric view of the Riemann Mapping Theorem. Naturally, we consider to use the ellipses to pack the bounded simply connected domain and obtain similarly a sequence simplicial homeomorphism between the ellipse packing and the circle packing. In this paper, we prove that these simplicial homeomorphism approximate a quasiconformal mapping from the bounded simply connected domain onto the unit disk with the modulus of their complex dilatations tending to 1 almost everywhere in the domain when the ratio of the longer axis and shorter axis of the ellipse tending to ∞.
文摘The dependences of electrochemical potential at the interface between carbon nanotubes and electrolyte upon temperature and electrolyte concentration are studied. Carbon nanotubes were synthesized by hot filament chemical vapor deposition with Si as the substrate. Four substances were tested: NaCl solution, KCl solution, water and alcohol. It is found that for NaCl and KCl solutions, at the interface, there is a large electrochemical potential which increases with temperature and is larger for an electrolyte of higher concentration. There is a significant field effect of carbon nanotubes with electrolyte as the gate, and the effect depends on the ionizability of the electrolyte. Such physicochemical property invests carbon nanotube a potential application in nanoelectronics.
基金Project supported by the Sichuan Province Education Department Key Natural Science Fund,China(Grant No.17ZA339)the Chongqing Research Program of Basic Research and Frontier Technology,China(Grant No.cstc2014jcyjA50016)the National Natural Science Foundation of China(Grant No.61504016)
文摘We consider a binary dipolar Bose–Einstein condensate confined in a rotating harmonic plus quartic potential trap.The ground-state vortex structures are numerically obtained as a function of the contact interactions and the dipole–dipole interaction in both slow and rapid rotation cases. The results show that the vortex configurations depend strongly on the strength of the contact interactions, the relative strength between dipolar and contact interactions, as well as on the orientation of the dipoles. A variety of exotic ground-state vortex structures, such as pentagonal and hexagon vortex lattice,square vortex lattice with a central vortex, annular vortex lines, and straight vortex lines, are observed by turning such controllable parameters. Our results deepen the understanding of effects of dipole–dipole interaction on the topological defects.
文摘The uniqueness problem of entire functions concerning weighted sharing was discussed, and the following theorem was proved. Let f and 8 be two non-constant entire functions, m, n and k three positive integers, and n〉2k＋4. If Em（1,（f^n）^（k））= Em（1,（g^n）^（k））, then either f（z）=c1c^cz and 8（z）= c2c^cz or f=ts, where c, c1 and c2 are three constants satisfying （-1）^k（c1c2）^n（nc）^2k=], and t is a constant satisfying t^n=1. The theorem generalizes the result of Fang [Fang ML, Uniqueness and value sharing of entire functions, Computer ＆ Mathematics with Applications, 2002, 44： 823-831].
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 12104124 and 12274111)the Natural Science Foundation of Hebei Province, China (Grant Nos. A2021201001 and A2021201008)+4 种基金the Central Guidance Fund on the Local Science and Technology Development of Hebei Province, China (Grant No. 236Z0601G)the Post-graduate’s Innovation Fund Project of Hebei Province, China (Grant No. CXZZSS2023007)the Advanced Talents Incubation Program of the Hebei University, China (Grant Nos. 521000981395, 521000981423, 521000981394, and 521000981390)the Research Foundation of Chongqing University of Science and technology, China (Grant No. ckrc2019017)the High-Performance Computing Center of Hebei University, China。
文摘Skyrmion bags are spin structures with arbitrary topological charges, each of which is composed of a big skyrmion and several small skyrmions. In this work, by using an in-plane alternating current(AC) magnetic field, we investigate the spinwave modes of skyrmion bags, which behave differently from the clockwise(CW) rotation mode and the counterclockwise(CCW) rotation mode of skyrmions because of their complex spin topological structures. The in-plane excitation power spectral density shows that each skyrmion bag possesses four resonance frequencies. By further studying the spin dynamics of a skyrmion bag at each resonance frequency, the four spin-wave modes, i.e., a CCW-CW mode, two CW-breathing modes with different resonance strengths, and an inner CCW mode, appear as a composition mode of outer skyrmion–inner skyrmions. Our results are helpful in understanding the in-plane spin excitation of skyrmion bags, which may contribute to the characterization and detection of skyrmion bags, as well as the applications in logic devices.
文摘The relation between the global attractors Aε for a calss of quasilinear parabolic equations and the global attractor A0 for the homogenized equation is discussed, and an explicit error estimate between Aε and A0 is given.
