The calculation of the diffraction field radiated from the ultrasonic transducer can be simplified by using the Gaussian beam expansion technique. The key problem of this technique is how to determine the coefficients...The calculation of the diffraction field radiated from the ultrasonic transducer can be simplified by using the Gaussian beam expansion technique. The key problem of this technique is how to determine the coefficients of Gaussian functions. We present a simple and accurate optimization method to calculate the Gaussian beam expansion coefficients, Half of the coefficients are obtained by solving linear equations. The other half are derived from the Fourier series expansion. Wave field simulation results demonstrate the validity of the new method.展开更多
The magnetohydrodynamic （MHD） flow under slip conditions over a shrinking sheet is solved analytically. The solution is given in a closed form equation and is an exact solution of the full governing Navier-Stokes eq...The magnetohydrodynamic （MHD） flow under slip conditions over a shrinking sheet is solved analytically. The solution is given in a closed form equation and is an exact solution of the full governing Navier-Stokes equations. Interesting solution behavior ＆ observed with multiple solution branches for certain parameter domain. The effects of the mass transfer, slip, and magnetic parameters are discussed.展开更多
We find that π represents dual attributes. One is within the purely mathematical domain and can be derived for example, from infinite series, among several other methods. The other is within a 2D geometric-physical d...We find that π represents dual attributes. One is within the purely mathematical domain and can be derived for example, from infinite series, among several other methods. The other is within a 2D geometric-physical domain. This paper analyzes several physical constants from an analogous perspective where they are defined solely by mathematical and 2D geometric properties independent of any actual physical scaling data. The constants are evaluated as natural unit frequency equivalents of the neutron, electron, Bohr radius, Rydberg constant, Planck’s constant, Planck time, a Black hole with a Schwarzschild radius, the distance light travels in one time unit;and the fine structure constant. These constants are defined within two inter-related harmonic domains. In the linear domain, the ratios of the frequency equivalents of the Rydberg constant, Bohr radius, electron;and the fine structure constant are related to products of 2 and π. In the power law domain, their partial harmonic fraction powers, and the integer fraction powers of the fundamental frequency for Planck time are known. All of the constants are then derived at the point where a single fundamental frequency simultaneously fulfills both domains independent of any direct physical scale data. The derived values relative errors from the known values range from 10-3 to 10-1 supporting the concept and method.展开更多
In the case of bipartite two-qubit systems, we derive an analytical expression of bound Bell operator for any given pure state. Our result not only manifests some properties of Bell inequality, for example, which may ...In the case of bipartite two-qubit systems, we derive an analytical expression of bound Bell operator for any given pure state. Our result not only manifests some properties of Bell inequality, for example, which may be violated by any pure entangled state and only be maximally violated for a maximally entangled state, but also gives the explicit values of maximal violation for any pure state. Finally we point out that any mixed states which can produce maximal violation of Bell inequality must have a maximal concurrence value.展开更多
The aim of this article is to present the contribution of Wu Wen-Tsün to Algebraic Topology and more precisely to the theory of characteristic classes. Several papers provide complete and welldocumented biography...The aim of this article is to present the contribution of Wu Wen-Tsün to Algebraic Topology and more precisely to the theory of characteristic classes. Several papers provide complete and welldocumented biography and academic career of Wu Wen-Tsün, in particular, Hudecek, 2014; O'Connor and Robertson, 2006; Wen-Tsün Wu's Academic Career, 2006; Selected works of Wen-Tsun Wu, 2008.The author does not repeat the details provided in these papers concerning the Wu Wen-Tsün's bibliography, we will just mention people involved in the Wu Wen-Tsün's period in France.In addition to Wu Wen-Tsün's papers, the Dieudonné's book(Dieudonné, 1960) provides an excellent presentation of main results of Wu Wen-Tsün in Algebraic and Differential Topology. The author will use and abuse of this book(and refer to) when suitable.In the introduction, the author recalls mainly historical facts concerning the contribution of Wu Wen-Tsün to Algebraic Topology. The second section shows speci?cally the contribution of Wu WenTsün to the Stiefel-Whitney classes and introduces the third section, dealing with the(real) Wu classes.The author provides de?nition, properties as well as further developments and generalizations of the Wu classes. The fourth and ?fth sections are devoted to recent applications: In Cobordism theory and in Mathematical Physics. The author notices that Wu classes have been used as well in other domains,in particular surgery theory(Madsen and Milgram, 1979). The last section concerns the complex Wu classes and shows that the more recent Mather classes coincide with the previously de?ned complex Wu classes, that is a result from Zhou(1994)(see also Liu, 1996).This article is devoted to the contribution of Wu Wen-Tsün to the theory of Characteristic Classes,which coincides with his "French period"(1947–1951). However, speaking of Algebraic Topology, it is worthwhile to mention the important contribution of Wu Wen-Tsün to the Theory of realization of complexes or manifolds in Euclidean spaces and of embedding cla展开更多
Special Lie-Mei symmetry and conserved quantities for Appell equations expressed by Appell functions in a holonomic mechanical system are investigated. On the basis of the Appell equation in a holonomic system, the de...Special Lie-Mei symmetry and conserved quantities for Appell equations expressed by Appell functions in a holonomic mechanical system are investigated. On the basis of the Appell equation in a holonomic system, the definition and the criterion of special Lie-Mei symmetry of Appell equations expressed by Appell functions are given. The expressions of the determining equation of special Lie-Mei symmetry of Appell equations expressed by Appell functions, Hojman conserved quantity and Mei conserved quantity deduced from special Lie-Mei symmetry in a holonomic mechanical system are gained. An example is given to illustrate the application of the results.展开更多
Structural equations and Mei conserved quantity of Mei symmetry for Appell equations in a holonomic system with redundant coordinates are studied. Some aspects, including the differential equations of motion, the defi...Structural equations and Mei conserved quantity of Mei symmetry for Appell equations in a holonomic system with redundant coordinates are studied. Some aspects, including the differential equations of motion, the definition and the criterion of Mei symmetry, the form of structural equations and Mei conserved quantity of Mei symmetry of Appell equations for a holonomic system with redundant coordinates, are also investigated. Finally, an example is given to illustrate the application of the results.展开更多
The perturbation to Noether symmetry and Noether adiabatic invariants of general discrete holonomic systems are studied. First, the discrete Noether exact invariant induced directly from the Noether symmetry of the sy...The perturbation to Noether symmetry and Noether adiabatic invariants of general discrete holonomic systems are studied. First, the discrete Noether exact invariant induced directly from the Noether symmetry of the system without perturbation is given. Secondly, the concept of discrete high-order adiabatic invariant is presented, the criterion of the perturbation to Noether symmetry is established, and the discrete Noether adiabatic invariant induced directly from the perturbation to Noether symmetry is obtained. Lastly, an example is discussed to illustrate the application of the results.展开更多
By introducing the coordination function f, the generalized Mei conserved quantities for the nonholonomic systems in terms of quasi-coordinates are given. Then based on the concept of adiabatic invariant, the perturba...By introducing the coordination function f, the generalized Mei conserved quantities for the nonholonomic systems in terms of quasi-coordinates are given. Then based on the concept of adiabatic invariant, the perturbation to Mei symmetry and the generalized Mei adiabatic invariants for nonholonomic systems in terms of quasi-coordinates are studied.展开更多
The physical objective of solving for eigen-modes of a 1D quasiperiodic structure in photonics has been achieved. This was achieved thru considering this structure as a 1D projection or cut of a 2D periodic structure....The physical objective of solving for eigen-modes of a 1D quasiperiodic structure in photonics has been achieved. This was achieved thru considering this structure as a 1D projection or cut of a 2D periodic structure. And the problem is solved in a manner similar to 2D periodic photonic structures. A mechanical analogy (quasiperiodic orbits) helps to bring conceptual clarity.展开更多
文摘The calculation of the diffraction field radiated from the ultrasonic transducer can be simplified by using the Gaussian beam expansion technique. The key problem of this technique is how to determine the coefficients of Gaussian functions. We present a simple and accurate optimization method to calculate the Gaussian beam expansion coefficients, Half of the coefficients are obtained by solving linear equations. The other half are derived from the Fourier series expansion. Wave field simulation results demonstrate the validity of the new method.
文摘The magnetohydrodynamic （MHD） flow under slip conditions over a shrinking sheet is solved analytically. The solution is given in a closed form equation and is an exact solution of the full governing Navier-Stokes equations. Interesting solution behavior ＆ observed with multiple solution branches for certain parameter domain. The effects of the mass transfer, slip, and magnetic parameters are discussed.
文摘We find that π represents dual attributes. One is within the purely mathematical domain and can be derived for example, from infinite series, among several other methods. The other is within a 2D geometric-physical domain. This paper analyzes several physical constants from an analogous perspective where they are defined solely by mathematical and 2D geometric properties independent of any actual physical scaling data. The constants are evaluated as natural unit frequency equivalents of the neutron, electron, Bohr radius, Rydberg constant, Planck’s constant, Planck time, a Black hole with a Schwarzschild radius, the distance light travels in one time unit;and the fine structure constant. These constants are defined within two inter-related harmonic domains. In the linear domain, the ratios of the frequency equivalents of the Rydberg constant, Bohr radius, electron;and the fine structure constant are related to products of 2 and π. In the power law domain, their partial harmonic fraction powers, and the integer fraction powers of the fundamental frequency for Planck time are known. All of the constants are then derived at the point where a single fundamental frequency simultaneously fulfills both domains independent of any direct physical scale data. The derived values relative errors from the known values range from 10-3 to 10-1 supporting the concept and method.
基金Supported by the National Natural Science Foundation of China Grant Nos 10947142 and 11005031.
文摘In the case of bipartite two-qubit systems, we derive an analytical expression of bound Bell operator for any given pure state. Our result not only manifests some properties of Bell inequality, for example, which may be violated by any pure entangled state and only be maximally violated for a maximally entangled state, but also gives the explicit values of maximal violation for any pure state. Finally we point out that any mixed states which can produce maximal violation of Bell inequality must have a maximal concurrence value.
文摘The aim of this article is to present the contribution of Wu Wen-Tsün to Algebraic Topology and more precisely to the theory of characteristic classes. Several papers provide complete and welldocumented biography and academic career of Wu Wen-Tsün, in particular, Hudecek, 2014; O'Connor and Robertson, 2006; Wen-Tsün Wu's Academic Career, 2006; Selected works of Wen-Tsun Wu, 2008.The author does not repeat the details provided in these papers concerning the Wu Wen-Tsün's bibliography, we will just mention people involved in the Wu Wen-Tsün's period in France.In addition to Wu Wen-Tsün's papers, the Dieudonné's book(Dieudonné, 1960) provides an excellent presentation of main results of Wu Wen-Tsün in Algebraic and Differential Topology. The author will use and abuse of this book(and refer to) when suitable.In the introduction, the author recalls mainly historical facts concerning the contribution of Wu Wen-Tsün to Algebraic Topology. The second section shows speci?cally the contribution of Wu WenTsün to the Stiefel-Whitney classes and introduces the third section, dealing with the(real) Wu classes.The author provides de?nition, properties as well as further developments and generalizations of the Wu classes. The fourth and ?fth sections are devoted to recent applications: In Cobordism theory and in Mathematical Physics. The author notices that Wu classes have been used as well in other domains,in particular surgery theory(Madsen and Milgram, 1979). The last section concerns the complex Wu classes and shows that the more recent Mather classes coincide with the previously de?ned complex Wu classes, that is a result from Zhou(1994)(see also Liu, 1996).This article is devoted to the contribution of Wu Wen-Tsün to the theory of Characteristic Classes,which coincides with his "French period"(1947–1951). However, speaking of Algebraic Topology, it is worthwhile to mention the important contribution of Wu Wen-Tsün to the Theory of realization of complexes or manifolds in Euclidean spaces and of embedding cla
文摘Special Lie-Mei symmetry and conserved quantities for Appell equations expressed by Appell functions in a holonomic mechanical system are investigated. On the basis of the Appell equation in a holonomic system, the definition and the criterion of special Lie-Mei symmetry of Appell equations expressed by Appell functions are given. The expressions of the determining equation of special Lie-Mei symmetry of Appell equations expressed by Appell functions, Hojman conserved quantity and Mei conserved quantity deduced from special Lie-Mei symmetry in a holonomic mechanical system are gained. An example is given to illustrate the application of the results.
基金Supported by the National Natural Science Foundation of China under Grant No 10572021, and the Preparatory Research Foundation of Jiangnan University （2008LYY011）.
文摘Structural equations and Mei conserved quantity of Mei symmetry for Appell equations in a holonomic system with redundant coordinates are studied. Some aspects, including the differential equations of motion, the definition and the criterion of Mei symmetry, the form of structural equations and Mei conserved quantity of Mei symmetry of Appell equations for a holonomic system with redundant coordinates, are also investigated. Finally, an example is given to illustrate the application of the results.
文摘The perturbation to Noether symmetry and Noether adiabatic invariants of general discrete holonomic systems are studied. First, the discrete Noether exact invariant induced directly from the Noether symmetry of the system without perturbation is given. Secondly, the concept of discrete high-order adiabatic invariant is presented, the criterion of the perturbation to Noether symmetry is established, and the discrete Noether adiabatic invariant induced directly from the perturbation to Noether symmetry is obtained. Lastly, an example is discussed to illustrate the application of the results.
文摘By introducing the coordination function f, the generalized Mei conserved quantities for the nonholonomic systems in terms of quasi-coordinates are given. Then based on the concept of adiabatic invariant, the perturbation to Mei symmetry and the generalized Mei adiabatic invariants for nonholonomic systems in terms of quasi-coordinates are studied.
文摘The physical objective of solving for eigen-modes of a 1D quasiperiodic structure in photonics has been achieved. This was achieved thru considering this structure as a 1D projection or cut of a 2D periodic structure. And the problem is solved in a manner similar to 2D periodic photonic structures. A mechanical analogy (quasiperiodic orbits) helps to bring conceptual clarity.
