The novel ZnⅡ complex, ｛[Zn(TSC)(MAL)]·H2O｝n (1), where TSC is thiosemicarbazide and MAL is malonate radicle), was synthesized by self-assembling from the reaction of stoichiometric zinc chloride, thiosemicarb...The novel ZnⅡ complex, ｛[Zn(TSC)(MAL)]·H2O｝n (1), where TSC is thiosemicarbazide and MAL is malonate radicle), was synthesized by self-assembling from the reaction of stoichiometric zinc chloride, thiosemicarbazide and malonic acid in solution at pH 4.5￣5.0. The structural and physicochemical properties were characterized by X-ray diffraction, infrared spectroscopy, electronic spectra and thermal analysis. The crystal data for the title coordination polymer: Monoclinic, P21/c, β=107.808(1)°, a=0.93759(1) nm, b=1.11083(1) nm, c= 0.92100 (2) nm, Z=2, μ=2.919 mm-1, R1=0.0390, wR2=0.0994. The structure feature is that the bridging dicarboxylates effectively link the zinc centers to form polymeric chain in a zig-zag way, which is stabilized by N- H…O, N- H…S and O- H…O hydrogen bonds. CCDC: 231861.展开更多
From the nonlinear sine-Gordon equation, new transformations are obtained in this paper, which are applied to propose a new approach to construct exact periodic solutions to nonlinear wave equations. It is shown that ...From the nonlinear sine-Gordon equation, new transformations are obtained in this paper, which are applied to propose a new approach to construct exact periodic solutions to nonlinear wave equations. It is shown that more new periodic solutions can be obtained by this new approach, and more shock wave solutions or solitary wave solutions can be got under their limit conditions.展开更多
The elliptic equation is taken as a transformation and applied to solve nonlinear wave equations. It is shown that this method is more powerful to give more kinds of solutions, such as rational solutions, solitary wav...The elliptic equation is taken as a transformation and applied to solve nonlinear wave equations. It is shown that this method is more powerful to give more kinds of solutions, such as rational solutions, solitary wave solutions,periodic wave solutions and so on, so it can be taken as a generalized method.展开更多
Trial function method is applied to solve generalized mKdV (GmKdV for short) equations. It is shownthat GmKdV equations with a real number parameter can be solved directly by this method without a transformation,and m...Trial function method is applied to solve generalized mKdV (GmKdV for short) equations. It is shownthat GmKdV equations with a real number parameter can be solved directly by this method without a transformation,and more new kinds of solitary wave solutions are obtained.展开更多
A transformation is introduced for generalized mKdV (GmKdV for short) equation and Jacobi elliptic function expansion method is applied to solve it. It is shown that GmKdV equation with a real number parameter can be ...A transformation is introduced for generalized mKdV (GmKdV for short) equation and Jacobi elliptic function expansion method is applied to solve it. It is shown that GmKdV equation with a real number parameter can be solved directly by using Jacobi elliptic function expansion method when this transformation is introduced, and periodic solution and solitary wave solution are obtained. Then the generalized solution to GmKdV equation deduces to some special solutions to some well-known nonlinear equations, such as KdV equation, mKdV equation, when the real parameter is set specific values.展开更多
In this paper, new basic functions, which are composed of three basic Jacobi elliptic functions, are chosen as components of finite expansion. This finite expansion can be taken as an ansatz and applied to solve nonli...In this paper, new basic functions, which are composed of three basic Jacobi elliptic functions, are chosen as components of finite expansion. This finite expansion can be taken as an ansatz and applied to solve nonlinear wave equations. As an example, mKdV equation is solved, and more new rational form solutions are derived, such as periodic solutions of rational form, solitary wave solutions of rational form, and so on.展开更多
The magnetic properties of Heisenberg ferromagnetic films in an external magnetic field are investigated by means of the variational cumulant expansion (VCE). The magnetization can be in principle calculated analytica...The magnetic properties of Heisenberg ferromagnetic films in an external magnetic field are investigated by means of the variational cumulant expansion (VCE). The magnetization can be in principle calculated analytically as the function of the temperature and the number of atomic layers in the film to an arbitrary order of accuracy in the VCE. We calculate the spontaneous magnetization and coercivity to the third order for spin-1/2 Heisenberg films with simple cubic lattices by using a graphic technique.展开更多
A simple shallow-water model with influence of external forcing on a β-planeis applied to investigate the nonlinear equatorial Rossby waves in a shear flow. By theperturbation method, the extended variable-coefficien...A simple shallow-water model with influence of external forcing on a β-planeis applied to investigate the nonlinear equatorial Rossby waves in a shear flow. By theperturbation method, the extended variable-coefficient KdV equation under an external forcing isderived for large amplitude equatorial Rossby wave in a shear How. And then various periodic-likestructures for these equatorial Rossby waves are obtained with the help of Jacobi ellipticfunctions. It is shown that the external forcing plays an important role in various periodic-likestructures.展开更多
A transformation is introduced and applied to solve Burgers-type equations,such as Burgers equation,Burgers-KdV equation and Burgers-KdV-Kuramoto equation.Many kinds of travelling wave solutions including solitary wav...A transformation is introduced and applied to solve Burgers-type equations,such as Burgers equation,Burgers-KdV equation and Burgers-KdV-Kuramoto equation.Many kinds of travelling wave solutions including solitary wave solution are obtained,and it is shown that this is a powerful method to solve nonlinear equations with odd-order and even-order derivatives simultaneously.展开更多
From the controlling equations of atmosphere motion, Prandtl's mixing length theory is used to derive the atmospheric turbulence models, such as Burgers equation model and Burgers-KdV equation model. And then the ...From the controlling equations of atmosphere motion, Prandtl's mixing length theory is used to derive the atmospheric turbulence models, such as Burgers equation model and Burgers-KdV equation model. And then the projective Riccati equations are applied to solve these atmospheric turbulence models, where much more patterns are obtained, including solitary wave pattern, singular pattern, and so on.展开更多
A simple shallow-water model with influence of diabatic heating on aβ-plane is applied to investigate the nonlinear equatorial Rossby waves in a shear flow. By the asymptotic method of multiple scales, the cubic nonl...A simple shallow-water model with influence of diabatic heating on aβ-plane is applied to investigate the nonlinear equatorial Rossby waves in a shear flow. By the asymptotic method of multiple scales, the cubic nonlinear Schrodinger (NLS for short) equation with an external heating source is derived for large amplitude equatorial envelope Rossby wave in a shear flow. And then various periodic structures for these equatorial envelope Rossby waves are obtained with the help of Jacobi elliptic functions and elliptic equation. It is shown that phase-locked diabatic heating plays an important role in periodic structures of rational form.展开更多
The (2+ 1)-dimensional Boussinesq equation and (3+ 1)-dimensional KP equation are studied by using the extended Jacobi elliptic-function method. The exact periodic-wave solutions for the two equations are obtained.
The conjecture that ultra-high-energy cosmic rays (UHECRS) are actually strangelets is discussed. Besides the reason that strangelets can do as cosmic rays beyond the Greisen-Zatsepin-Kuzmin-cutoff, another argument t...The conjecture that ultra-high-energy cosmic rays (UHECRS) are actually strangelets is discussed. Besides the reason that strangelets can do as cosmic rays beyond the Greisen-Zatsepin-Kuzmin-cutoff, another argument to bombarding bare strange stars. It is proposed that the exotic quark surface of a bare strange star could be an effective astro-laboratory in the investigations of the extra dimensions and of the detection of ultra-high-energy neutrino fluxes. The flux of neutrinos (and other point-like particles) with energy larger than 2.3×10^20 eV could be expected to be smaller than 10^-26 cm^-2 s^-1 if there are two extra spatial dimensions.展开更多
Based on the Lame function and Jacobi elliptic function, the perturbation method is applied to some nonlinear coupled systems, and there many multi-order solutions are derived to these nonlinear coupled systems.
In the present paper, we study the existence of metallic ferromagnetism in a cluster of nanometer scale,which is described by the Hubbard model defined on a complete graph. Therefore, the system is highly frustrated w...In the present paper, we study the existence of metallic ferromagnetism in a cluster of nanometer scale,which is described by the Hubbard model defined on a complete graph. Therefore, the system is highly frustrated with respect to electron hopping. By solving the model exactly, we show that its ground state is fully spin-polarized at half-filling, even if the Coulomb interaction is finite. This conclusion is in sharp contrast to the well-known result for the Hubbard model on a bipartite lattice. As a result, our exact solution strongly suggests that frustration may play an important role in causing metallic ferromagnetism.展开更多
In this paper, the linear ordinary differential equations with variable coefficients are obtained from thecontrolling equations satisfied by wavelet transform or atmospheric internal gravity waves, and these linear eq...In this paper, the linear ordinary differential equations with variable coefficients are obtained from thecontrolling equations satisfied by wavelet transform or atmospheric internal gravity waves, and these linear equationscan be further transformed into Weber equations. From Weber equations, the homoclinic orbit solutions can be derived,so the solitary wave solutions to linear equations with variable coefficients are obtained.展开更多
In the present paper, we study the zero-temperature phase diagram of the doped perovskite manganitesat filling x = 0.5 by the real-space Hartree-Fock approximation method. Our purpose is to resolve a controversialissu...In the present paper, we study the zero-temperature phase diagram of the doped perovskite manganitesat filling x = 0.5 by the real-space Hartree-Fock approximation method. Our purpose is to resolve a controversialissue arising recently on the origin of the charge ordered phases in these systems. We find that the antiferromagneticsuperexchange interaction between the localized spins plays the central role in producing the concerned phases. Ourresults confirm some speculations on this issue.展开更多
The new solutions to elliptic equation are shown, and then the elliptic equation is taken as a transformationand is applied to solve nonlinear wave equations. It is shown that more kinds of solutions are derived, such...The new solutions to elliptic equation are shown, and then the elliptic equation is taken as a transformationand is applied to solve nonlinear wave equations. It is shown that more kinds of solutions are derived, such as periodicsolutions of rational form, solitary wave solutions of rational form, and so on.展开更多
文摘The novel ZnⅡ complex, ｛[Zn(TSC)(MAL)]·H2O｝n (1), where TSC is thiosemicarbazide and MAL is malonate radicle), was synthesized by self-assembling from the reaction of stoichiometric zinc chloride, thiosemicarbazide and malonic acid in solution at pH 4.5￣5.0. The structural and physicochemical properties were characterized by X-ray diffraction, infrared spectroscopy, electronic spectra and thermal analysis. The crystal data for the title coordination polymer: Monoclinic, P21/c, β=107.808(1)°, a=0.93759(1) nm, b=1.11083(1) nm, c= 0.92100 (2) nm, Z=2, μ=2.919 mm-1, R1=0.0390, wR2=0.0994. The structure feature is that the bridging dicarboxylates effectively link the zinc centers to form polymeric chain in a zig-zag way, which is stabilized by N- H…O, N- H…S and O- H…O hydrogen bonds. CCDC: 231861.
文摘From the nonlinear sine-Gordon equation, new transformations are obtained in this paper, which are applied to propose a new approach to construct exact periodic solutions to nonlinear wave equations. It is shown that more new periodic solutions can be obtained by this new approach, and more shock wave solutions or solitary wave solutions can be got under their limit conditions.
文摘The elliptic equation is taken as a transformation and applied to solve nonlinear wave equations. It is shown that this method is more powerful to give more kinds of solutions, such as rational solutions, solitary wave solutions,periodic wave solutions and so on, so it can be taken as a generalized method.
基金The project supported by National Natural Science Foundation of China under Grant Nos.40045016 and 40175016
文摘Trial function method is applied to solve generalized mKdV (GmKdV for short) equations. It is shownthat GmKdV equations with a real number parameter can be solved directly by this method without a transformation,and more new kinds of solitary wave solutions are obtained.
文摘A transformation is introduced for generalized mKdV (GmKdV for short) equation and Jacobi elliptic function expansion method is applied to solve it. It is shown that GmKdV equation with a real number parameter can be solved directly by using Jacobi elliptic function expansion method when this transformation is introduced, and periodic solution and solitary wave solution are obtained. Then the generalized solution to GmKdV equation deduces to some special solutions to some well-known nonlinear equations, such as KdV equation, mKdV equation, when the real parameter is set specific values.
基金The project supported by National Natural Science Foundation of China under Grant No.40305006the Ministry of Science and Technology of China through Special Public Welfare Project under Grant No.2002DIB20070
文摘In this paper, new basic functions, which are composed of three basic Jacobi elliptic functions, are chosen as components of finite expansion. This finite expansion can be taken as an ansatz and applied to solve nonlinear wave equations. As an example, mKdV equation is solved, and more new rational form solutions are derived, such as periodic solutions of rational form, solitary wave solutions of rational form, and so on.
文摘The magnetic properties of Heisenberg ferromagnetic films in an external magnetic field are investigated by means of the variational cumulant expansion (VCE). The magnetization can be in principle calculated analytically as the function of the temperature and the number of atomic layers in the film to an arbitrary order of accuracy in the VCE. We calculate the spontaneous magnetization and coercivity to the third order for spin-1/2 Heisenberg films with simple cubic lattices by using a graphic technique.
文摘A simple shallow-water model with influence of external forcing on a β-planeis applied to investigate the nonlinear equatorial Rossby waves in a shear flow. By theperturbation method, the extended variable-coefficient KdV equation under an external forcing isderived for large amplitude equatorial Rossby wave in a shear How. And then various periodic-likestructures for these equatorial Rossby waves are obtained with the help of Jacobi ellipticfunctions. It is shown that the external forcing plays an important role in various periodic-likestructures.
文摘A transformation is introduced and applied to solve Burgers-type equations,such as Burgers equation,Burgers-KdV equation and Burgers-KdV-Kuramoto equation.Many kinds of travelling wave solutions including solitary wave solution are obtained,and it is shown that this is a powerful method to solve nonlinear equations with odd-order and even-order derivatives simultaneously.
文摘From the controlling equations of atmosphere motion, Prandtl's mixing length theory is used to derive the atmospheric turbulence models, such as Burgers equation model and Burgers-KdV equation model. And then the projective Riccati equations are applied to solve these atmospheric turbulence models, where much more patterns are obtained, including solitary wave pattern, singular pattern, and so on.
文摘A simple shallow-water model with influence of diabatic heating on aβ-plane is applied to investigate the nonlinear equatorial Rossby waves in a shear flow. By the asymptotic method of multiple scales, the cubic nonlinear Schrodinger (NLS for short) equation with an external heating source is derived for large amplitude equatorial envelope Rossby wave in a shear flow. And then various periodic structures for these equatorial envelope Rossby waves are obtained with the help of Jacobi elliptic functions and elliptic equation. It is shown that phase-locked diabatic heating plays an important role in periodic structures of rational form.
文摘The (2+ 1)-dimensional Boussinesq equation and (3+ 1)-dimensional KP equation are studied by using the extended Jacobi elliptic-function method. The exact periodic-wave solutions for the two equations are obtained.
文摘The conjecture that ultra-high-energy cosmic rays (UHECRS) are actually strangelets is discussed. Besides the reason that strangelets can do as cosmic rays beyond the Greisen-Zatsepin-Kuzmin-cutoff, another argument to bombarding bare strange stars. It is proposed that the exotic quark surface of a bare strange star could be an effective astro-laboratory in the investigations of the extra dimensions and of the detection of ultra-high-energy neutrino fluxes. The flux of neutrinos (and other point-like particles) with energy larger than 2.3×10^20 eV could be expected to be smaller than 10^-26 cm^-2 s^-1 if there are two extra spatial dimensions.
文摘Based on the Lame function and Jacobi elliptic function, the perturbation method is applied to some nonlinear coupled systems, and there many multi-order solutions are derived to these nonlinear coupled systems.
文摘In the present paper, we study the existence of metallic ferromagnetism in a cluster of nanometer scale,which is described by the Hubbard model defined on a complete graph. Therefore, the system is highly frustrated with respect to electron hopping. By solving the model exactly, we show that its ground state is fully spin-polarized at half-filling, even if the Coulomb interaction is finite. This conclusion is in sharp contrast to the well-known result for the Hubbard model on a bipartite lattice. As a result, our exact solution strongly suggests that frustration may play an important role in causing metallic ferromagnetism.
文摘In this paper, the linear ordinary differential equations with variable coefficients are obtained from thecontrolling equations satisfied by wavelet transform or atmospheric internal gravity waves, and these linear equationscan be further transformed into Weber equations. From Weber equations, the homoclinic orbit solutions can be derived,so the solitary wave solutions to linear equations with variable coefficients are obtained.
文摘In the present paper, we study the zero-temperature phase diagram of the doped perovskite manganitesat filling x = 0.5 by the real-space Hartree-Fock approximation method. Our purpose is to resolve a controversialissue arising recently on the origin of the charge ordered phases in these systems. We find that the antiferromagneticsuperexchange interaction between the localized spins plays the central role in producing the concerned phases. Ourresults confirm some speculations on this issue.
文摘The new solutions to elliptic equation are shown, and then the elliptic equation is taken as a transformationand is applied to solve nonlinear wave equations. It is shown that more kinds of solutions are derived, such as periodicsolutions of rational form, solitary wave solutions of rational form, and so on.
