In this article, we deal with the uniqueness problems on meromorphic functions sharing two finite sets in an angular domain instead of the whole plane C. In particular, we investigate the uniqueness for meromorphic fu...In this article, we deal with the uniqueness problems on meromorphic functions sharing two finite sets in an angular domain instead of the whole plane C. In particular, we investigate the uniqueness for meromorphic functions of infinite order in an angular domain and obtain some results. Moreover, examples show that the conditions in theorems are necessary.展开更多
A new method based on angular momentum theory was proposed to construct the basis functions of the irreducible representations(IRs) of point groups. The transformation coefficients, i. e., coefficients S, are the com...A new method based on angular momentum theory was proposed to construct the basis functions of the irreducible representations(IRs) of point groups. The transformation coefficients, i. e., coefficients S, are the components of the eigenvectors of some Hermitian matrices, and can be made as real numbers for all pure rotation point groups. The general formula for coefficient S was deduced, and applied to constructing the basis functions of single-valued irreducible representations of icosahedral group from the spherical harmonics with angular momentum j≤7.展开更多
This article gives a general model using specific periodic special functions, that is, degenerate elliptic Weierstrass P functions composed with the LambertW function, whose presence in the governing equations through...This article gives a general model using specific periodic special functions, that is, degenerate elliptic Weierstrass P functions composed with the LambertW function, whose presence in the governing equations through the forcing terms simplify the periodic Navier Stokes equations (PNS) at the centers of arbitrary r balls of the 3-Torus. The continuity equation is satisfied together with spatially periodic boundary conditions. The yicomponent forcing terms consist of a function F as part of its expression that is arbitrarily small in an r ball where it is associated with a singular forcing expression both for inviscid and viscous cases. As a result, a significant simplification occurs with a v3(vifor all velocity components) only governing PDE resulting. The extension of three restricted subspaces in each of the principal directions in the Cartesian plane is shown as the Cartesian product ℋ=Jx,t×Jy,t×Jz,t. On each of these subspaces vi,i=1,2,3is continuous and there exists a linear independent subspace associated with the argument of the W function. Here the 3-Torus is built up from each compact segment of length 2R on each of the axes on the 3 principal directions x, y, and z. The form of the scaled velocities for non zero scaled δis related to the definition of the W function such that e−W(ξ)=W(ξ)ξwhere ξdepends on t and proportional to δ→0for infinite time t. The ratio Wξis equal to 1, making the limit δ→0finite and well defined. Considering r balls where the function F=(x−ai)2+(y−bi)2+(z−ci)2−ηset equal to −1e+rwhere r>0. is such that the forcing is singular at every distance r of centres of cubes each containing an r-ball. At the centre of the balls, the forcing is infinite. The main idea is that a system of singular initial value problems with infinite forcing is to be solved for where the velocities are shown to be locally Hölder continuous. It is proven that the limit of these singular problems shifts the finite time blowup time ti∗for first and higher derivatives to t=∞thereby indicating that there is no finite time blowup. Results in the literature can provide a systematic approach to study both large space and time behaviour for singular solutions to the Navier Stokes equations. Among the references, it has been shown that mathematical tools can be applied to study the asymptotic properties of solutions.展开更多
The general regression neural network(GRNN) model was proposed to model and predict the length of day(LOD) change, which has very complicated time-varying characteristics. Meanwhile, considering that the axial atmosph...The general regression neural network(GRNN) model was proposed to model and predict the length of day(LOD) change, which has very complicated time-varying characteristics. Meanwhile, considering that the axial atmospheric angular momentum(AAM) function is tightly correlated with the LOD changes, it was introduced into the GRNN prediction model to further improve the accuracy of prediction. Experiments with the observational data of LOD changes show that the prediction accuracy of the GRNN model is 6.1% higher than that of BP network, and after introducing AAM function, the improvement of prediction accuracy further increases to 14.7%. The results show that the GRNN with AAM function is an effective prediction method for LOD changes.展开更多
Based on the integral representation of the Bessel functions and the generating function of the Tricomi function, an analytical expression of the Wigner distribution function （WDF） for a coherent or partially cohere...Based on the integral representation of the Bessel functions and the generating function of the Tricomi function, an analytical expression of the Wigner distribution function （WDF） for a coherent or partially coherent Bessel Gaussian beam is presented. The reduced two-dimensional WDFs are also demonstrated graphically, which reveals the dependence of the reduced WDFs on the beam parameters.展开更多
The wave function for the spin the early universe is obtained through the adaption of the quantum formalism to one solution of the Wheeler-DeWitt’s equation [1], associated with the wave function of the universe. In ...The wave function for the spin the early universe is obtained through the adaption of the quantum formalism to one solution of the Wheeler-DeWitt’s equation [1], associated with the wave function of the universe. In addition, some observations performed by Stephen Hawking in relation to the vorticity of the universe [2] are used. This wave function for the spin could be used for indirectly to demonstrate the presence of dark matter in the universe.展开更多
The exact thermoelastic analysis of a functionally graded piezoelectrical （FGP） rotating cylinder is investigated analytically. The cylinder is subjected to a com- bination of electrical, thermal, and mechanical loa...The exact thermoelastic analysis of a functionally graded piezoelectrical （FGP） rotating cylinder is investigated analytically. The cylinder is subjected to a com- bination of electrical, thermal, and mechanical loads simultaneously. The structure is a simplified model of a rotational sensor or actuator. The basic governing differential equation of the system is obtained by using the energy method. A novel term, named as the additional energy, is introduced to exact the evaluation of the energy functional. The solution to the governing differential equation is presented for two types of boundary conditions including free rotating and rotating cylinders exposed to the inner pressure. The effect of the angular velocity is investigated on the radial distribution of various components. The mentioned structure can be considered as a sensor for measuring the angular velocity of the cylinder subjected to the pressure and temperature. The obtained results indicate that the electrical potential is proportional to the angular velocity.展开更多
The Paulie’s principle is used for development of the orbital-free (OF) version of the density functional theory. On the example of the three-atomic clusters, Al<sub>3</sub>, Si<sub>3</sub>, a...The Paulie’s principle is used for development of the orbital-free (OF) version of the density functional theory. On the example of the three-atomic clusters, Al<sub>3</sub>, Si<sub>3</sub>, and C<sub>3</sub>, it is shown that the OF approach may lead to equilibrium configurations of atomic systems with both the metallic and covalent bonding. The equilibrium interatomic distances, interbonding angles and binding energies are found in good accordance with the known data. Results will be useful for developing of theoretical study of huge molecules and nanoparticles.展开更多
The excitation functions were measured in the reaction of 27Al+27Al at incident energies from 114MeV to 127MeV in steps of 200keV. The detection angles were continuously covered from 10o to 57° in the laboratory ...The excitation functions were measured in the reaction of 27Al+27Al at incident energies from 114MeV to 127MeV in steps of 200keV. The detection angles were continuously covered from 10o to 57° in the laboratory system. The energy autocorrelation functions of the dissipative fragments were analyzed by using different approaches. The nonself-averaging oscillations in the excitation functions were considered due to the angular momentum coherence and damping of the coherent nuclear rotation. The damping results from a quantum chaotic motion.展开更多
基金Supported by the NNSFC (10671109)the NSFFC(2008J0190)+1 种基金the Research Fund for Talent Introduction of Ningde Teachers College (2009Y019)the Scitific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry
文摘In this article, we deal with the uniqueness problems on meromorphic functions sharing two finite sets in an angular domain instead of the whole plane C. In particular, we investigate the uniqueness for meromorphic functions of infinite order in an angular domain and obtain some results. Moreover, examples show that the conditions in theorems are necessary.
文摘A new method based on angular momentum theory was proposed to construct the basis functions of the irreducible representations(IRs) of point groups. The transformation coefficients, i. e., coefficients S, are the components of the eigenvectors of some Hermitian matrices, and can be made as real numbers for all pure rotation point groups. The general formula for coefficient S was deduced, and applied to constructing the basis functions of single-valued irreducible representations of icosahedral group from the spherical harmonics with angular momentum j≤7.
文摘This article gives a general model using specific periodic special functions, that is, degenerate elliptic Weierstrass P functions composed with the LambertW function, whose presence in the governing equations through the forcing terms simplify the periodic Navier Stokes equations (PNS) at the centers of arbitrary r balls of the 3-Torus. The continuity equation is satisfied together with spatially periodic boundary conditions. The yicomponent forcing terms consist of a function F as part of its expression that is arbitrarily small in an r ball where it is associated with a singular forcing expression both for inviscid and viscous cases. As a result, a significant simplification occurs with a v3(vifor all velocity components) only governing PDE resulting. The extension of three restricted subspaces in each of the principal directions in the Cartesian plane is shown as the Cartesian product ℋ=Jx,t×Jy,t×Jz,t. On each of these subspaces vi,i=1,2,3is continuous and there exists a linear independent subspace associated with the argument of the W function. Here the 3-Torus is built up from each compact segment of length 2R on each of the axes on the 3 principal directions x, y, and z. The form of the scaled velocities for non zero scaled δis related to the definition of the W function such that e−W(ξ)=W(ξ)ξwhere ξdepends on t and proportional to δ→0for infinite time t. The ratio Wξis equal to 1, making the limit δ→0finite and well defined. Considering r balls where the function F=(x−ai)2+(y−bi)2+(z−ci)2−ηset equal to −1e+rwhere r>0. is such that the forcing is singular at every distance r of centres of cubes each containing an r-ball. At the centre of the balls, the forcing is infinite. The main idea is that a system of singular initial value problems with infinite forcing is to be solved for where the velocities are shown to be locally Hölder continuous. It is proven that the limit of these singular problems shifts the finite time blowup time ti∗for first and higher derivatives to t=∞thereby indicating that there is no finite time blowup. Results in the literature can provide a systematic approach to study both large space and time behaviour for singular solutions to the Navier Stokes equations. Among the references, it has been shown that mathematical tools can be applied to study the asymptotic properties of solutions.
基金Projects(U1231105,10878026)supported by the National Natural Science Foundation of China
文摘The general regression neural network(GRNN) model was proposed to model and predict the length of day(LOD) change, which has very complicated time-varying characteristics. Meanwhile, considering that the axial atmospheric angular momentum(AAM) function is tightly correlated with the LOD changes, it was introduced into the GRNN prediction model to further improve the accuracy of prediction. Experiments with the observational data of LOD changes show that the prediction accuracy of the GRNN model is 6.1% higher than that of BP network, and after introducing AAM function, the improvement of prediction accuracy further increases to 14.7%. The results show that the GRNN with AAM function is an effective prediction method for LOD changes.
文摘Based on the integral representation of the Bessel functions and the generating function of the Tricomi function, an analytical expression of the Wigner distribution function （WDF） for a coherent or partially coherent Bessel Gaussian beam is presented. The reduced two-dimensional WDFs are also demonstrated graphically, which reveals the dependence of the reduced WDFs on the beam parameters.
文摘The wave function for the spin the early universe is obtained through the adaption of the quantum formalism to one solution of the Wheeler-DeWitt’s equation [1], associated with the wave function of the universe. In addition, some observations performed by Stephen Hawking in relation to the vorticity of the universe [2] are used. This wave function for the spin could be used for indirectly to demonstrate the presence of dark matter in the universe.
文摘The exact thermoelastic analysis of a functionally graded piezoelectrical （FGP） rotating cylinder is investigated analytically. The cylinder is subjected to a com- bination of electrical, thermal, and mechanical loads simultaneously. The structure is a simplified model of a rotational sensor or actuator. The basic governing differential equation of the system is obtained by using the energy method. A novel term, named as the additional energy, is introduced to exact the evaluation of the energy functional. The solution to the governing differential equation is presented for two types of boundary conditions including free rotating and rotating cylinders exposed to the inner pressure. The effect of the angular velocity is investigated on the radial distribution of various components. The mentioned structure can be considered as a sensor for measuring the angular velocity of the cylinder subjected to the pressure and temperature. The obtained results indicate that the electrical potential is proportional to the angular velocity.
文摘The Paulie’s principle is used for development of the orbital-free (OF) version of the density functional theory. On the example of the three-atomic clusters, Al<sub>3</sub>, Si<sub>3</sub>, and C<sub>3</sub>, it is shown that the OF approach may lead to equilibrium configurations of atomic systems with both the metallic and covalent bonding. The equilibrium interatomic distances, interbonding angles and binding energies are found in good accordance with the known data. Results will be useful for developing of theoretical study of huge molecules and nanoparticles.
基金the National Natural Science Foundation (No.19775057), and by the Chinese Academyof Sciences and the Laboratori Nazionale del
文摘The excitation functions were measured in the reaction of 27Al+27Al at incident energies from 114MeV to 127MeV in steps of 200keV. The detection angles were continuously covered from 10o to 57° in the laboratory system. The energy autocorrelation functions of the dissipative fragments were analyzed by using different approaches. The nonself-averaging oscillations in the excitation functions were considered due to the angular momentum coherence and damping of the coherent nuclear rotation. The damping results from a quantum chaotic motion.
