In this paper, I give out an algorithm of the witten' s invariants of the 3-manifolds obtained by surgery on the links whose corresponding graphs may be no longer trees.
Lie symmetry analysis is applied to a(3+1)-dimensional Virasoro integrable model and the corresponding similarity reduction equations are obtained with the different infinitesimal generators.Invariant solutions with a...Lie symmetry analysis is applied to a(3+1)-dimensional Virasoro integrable model and the corresponding similarity reduction equations are obtained with the different infinitesimal generators.Invariant solutions with arbitrary functions for the(3+1)-dimensional Virasoro integrable model,including the interaction solution between a kink and a soliton,the lump-type solution and periodic solutions,have been studied analytically and graphically.展开更多
In this paper the entanglement of pure 3-qubit states is discussed. The local unitary （LU） polynomial invariants that are closely related to the canonical forms are constructed and the relations of the coefficients ...In this paper the entanglement of pure 3-qubit states is discussed. The local unitary （LU） polynomial invariants that are closely related to the canonical forms are constructed and the relations of the coefficients of the canonical forms are given. Then the stochastic local operations and classlcal communication （SLOCC） classification of the states are discussed on the basis of the canonical forms, and the symmetric canonical form of the states without 3-tangle is discussed. Finally, we give the relation between the LU polynomial invariants and SLOCC classification.展开更多
The （3＋1）-dimensional Jimbo-Miwa （JM） equation is solved approximately by using the conformal invariant asymptotic expansion approach presented by Ruan. By solving the new （3＋1）-dimensional integrable models, ...The （3＋1）-dimensional Jimbo-Miwa （JM） equation is solved approximately by using the conformal invariant asymptotic expansion approach presented by Ruan. By solving the new （3＋1）-dimensional integrable models, which are conformal invariant and possess Painlevé property, the approximate solutions are obtained for the JM equation, containing not only one-soliton solutions but also periodic solutions and multi-soliton solutions. Some approximate solutions happen to be exact and some approximate solutions can become exact by choosing relations between the parameters properly.展开更多
For any scheme M with a perfect obstruction theory,Jiang and Thomas associated a scheme N with a symmetric perfect obstruction theory.The scheme N is a cone over M given by the dual of the obstruction sheaf of M,and c...For any scheme M with a perfect obstruction theory,Jiang and Thomas associated a scheme N with a symmetric perfect obstruction theory.The scheme N is a cone over M given by the dual of the obstruction sheaf of M,and contains M as its zero section.Locally,N is the critical locus of a regular function.In this note we prove that N is a d-critical scheme in the sense of Joyce.There exists a global motive for N locally given by the motive of the vanishing cycle of the local regular function.We prove a motivic localization formula under the good and circle compact C*-action for N.When taking the Euler characteristic,the weighted Euler characteristic of N weighted by the Behrend function is the signed Euler characteristic of M by motivic method.As applications,using the main theorem we study the motivic generating series of the motivic Vafa-Witten invariants for K3 surfaces.展开更多
The wave/particle duality of particles in Physics is well known. Particles have properties that uniquely characterize them from one another, such as mass, charge and spin. Charged particles have associated Electric an...The wave/particle duality of particles in Physics is well known. Particles have properties that uniquely characterize them from one another, such as mass, charge and spin. Charged particles have associated Electric and Magnetic fields. Also, every moving particle has a De Broglie wavelength determined by its mass and velocity. This paper shows that all of these properties of a particle can be derived from a single wave function equation for that particle. Wave functions for the Electron and the Positron are presented and principles are provided that can be used to calculate the wave functions of all the fundamental particles in Physics. Fundamental particles such as electrons and positrons are considered to be point particles in the Standard Model of Physics and are not considered to have a structure. This paper demonstrates that they do indeed have structure and that this structure extends into the space around the particle’s center (in fact, they have infinite extent), but with rapidly diminishing energy density with the distance from that center. The particles are formed from Electromagnetic standing waves, which are stable solutions to the Schrödinger and Classical wave equations. This stable structure therefore accounts for both the wave and particle nature of these particles. In fact, all of their properties such as mass, spin and electric charge, can be accounted for from this structure. These particle properties appear to originate from a single point at the center of the wave function structure, in the same sort of way that the Shell theorem of gravity causes the gravity of a body to appear to all originate from a central point. This paper represents the first two fully characterized fundamental particles, with a complete description of their structure and properties, built up from the underlying Electromagnetic waves that comprise these and all fundamental particles.展开更多
Lie group analysis method is applied to the extended(3+1)-dimensional Kadomtsev–Petviashvili–Boussinesq equation and the corresponding similarity reduction equations are obtained with various infinitesimal generator...Lie group analysis method is applied to the extended(3+1)-dimensional Kadomtsev–Petviashvili–Boussinesq equation and the corresponding similarity reduction equations are obtained with various infinitesimal generators.By selecting suitable arbitrary functions in the similarity reduction solutions,we obtain abundant invariant solutions,including the trigonometric solution,the kink-lump interaction solution,the interaction solution between lump wave and triangular periodic wave,the two-kink solution,the lump solution,the interaction between a lump and two-kink and the periodic lump solution in different planes.These exact solutions are also given graphically to show the detailed structures of this high dimensional integrable system.展开更多
A 3D motion and geometric information system of single-antenna radar is proposed,which can be supported by spotlight synthetic aperture radar（SAR） system and inverse SAR（ISAR） system involving relative 3D motion o...A 3D motion and geometric information system of single-antenna radar is proposed,which can be supported by spotlight synthetic aperture radar（SAR） system and inverse SAR（ISAR） system involving relative 3D motion of the rigid target.In this system,applying the geometry invariance of the rigid target,the unknown 3D shape and motion of the radar target can be reconstructed from the 1D range data of some scatterers extracted from the high-resolution range image.Compared with the current 1D-to-3D algorithm,in the proposed algorithm,the requirement of the 1D range data is expanded to incomplete formation involving large angular motion of the target and hence,the quantity of the scatterers and the abundance of 3D motion are enriched.Furthermore,with the three selected affine coordinates fixed,the multi-solution problem of the reconstruction is solved and the technique of nonlinear optimization can be successfully utilized in the system.Two simulations are implemented which verify the higher robustness of the system and the better performance of the 3D reconstruction for the radar target with unknown relative motion.展开更多
This paper proposes a new set of 3D rotation scaling and translation invariants of 3D radially shifted Legendre moments. We aim to develop two kinds of transformed shifted Legendre moments： a 3D substituted radial sh...This paper proposes a new set of 3D rotation scaling and translation invariants of 3D radially shifted Legendre moments. We aim to develop two kinds of transformed shifted Legendre moments： a 3D substituted radial shifted Legendre moments （3DSRSLMs） and a 3D weighted radial one （3DWRSLMs）. Both are centered on two types of polynomials. In the first case, a new 3D ra- dial complex moment is proposed. In the second case, new 3D substituted/weighted radial shifted Legendremoments （3DSRSLMs/3DWRSLMs） are introduced using a spherical representation of volumetric image. 3D invariants as derived from the sug- gested 3D radial shifted Legendre moments will appear in the third case. To confirm the proposed approach, we have resolved three is- sues. To confirm the proposed approach, we have resolved three issues： rotation, scaling and translation invariants. The result of experi- ments shows that the 3DSRSLMs and 3DWRSLMs have done better than the 3D radial complex moments with and without noise. Sim- ultaneously, the reconstruction converges rapidly to the original image using 3D radial 3DSRSLMs and 3DWRSLMs, and the test of 3D images are clearly recognized from a set of images that are available in Princeton shape benchmark （PSB） database for 3D image.展开更多
Recently, orthogonal moments have become efficient tools for two-dimensional and three-dimensional（2D and 3D） image not only in pattern recognition, image vision, but also in image processing and applications engine...Recently, orthogonal moments have become efficient tools for two-dimensional and three-dimensional（2D and 3D） image not only in pattern recognition, image vision, but also in image processing and applications engineering. Yet, there is still a major difficulty in 3D rotation invariants. In this paper, we propose new sets of invariants for 2D and 3D rotation, scaling and translation based on orthogonal radial Hahn moments. We also present theoretical mathematics to derive them. Thus, this paper introduces in the first case new 2D radial Hahn moments based on polar representation of an object by one-dimensional orthogonal discrete Hahn polynomials, and a circular function. In the second case, we present new 3D radial Hahn moments using a spherical representation of volumetric image by one-dimensional orthogonal discrete Hahn polynomials and a spherical function. Further 2D and 3D invariants are derived from the proposed 2D and 3D radial Hahn moments respectively, which appear as the third case. In order to test the proposed approach, we have resolved three issues： the image reconstruction, the invariance of rotation, scaling and translation, and the pattern recognition. The result of experiments show that the Hahn moments have done better than the Krawtchouk moments, with and without noise. Simultaneously, the mentioned reconstruction converges quickly to the original image using 2D and 3D radial Hahn moments, and the test images are clearly recognized from a set of images that are available in COIL-20 database for 2D image, and Princeton shape benchmark（PSB） database for 3D image.展开更多
This paper investigates an important high-dimensional model in the atmospheric and oceanic dynamics-（3＋1）- dimensional nonlinear baroclinic potential vorticity equation by the classical Lie group method. Its symmet...This paper investigates an important high-dimensional model in the atmospheric and oceanic dynamics-（3＋1）- dimensional nonlinear baroclinic potential vorticity equation by the classical Lie group method. Its symmetry algebra, symmetry group and group-invariant solutions are analysed. Otherwise, some exact explicit solutions are obtained from the corresponding （2＋1）-dimensional equation, the inviscid barotropic nondivergent vorticy equation. To show the properties and characters of these solutions, some plots as well as their possible physical meanings of the atmospheric circulation are given out.展开更多
文摘In this paper, I give out an algorithm of the witten' s invariants of the 3-manifolds obtained by surgery on the links whose corresponding graphs may be no longer trees.
文摘Lie symmetry analysis is applied to a(3+1)-dimensional Virasoro integrable model and the corresponding similarity reduction equations are obtained with the different infinitesimal generators.Invariant solutions with arbitrary functions for the(3+1)-dimensional Virasoro integrable model,including the interaction solution between a kink and a soliton,the lump-type solution and periodic solutions,have been studied analytically and graphically.
基金The project supported by National Natural Science Foundation of China under Grant No. 6J3433050 and the Natural Science Foundation of Xuzhou Normal University （Key Project） under Grant No. 03XLA04
文摘In this paper the entanglement of pure 3-qubit states is discussed. The local unitary （LU） polynomial invariants that are closely related to the canonical forms are constructed and the relations of the coefficients of the canonical forms are given. Then the stochastic local operations and classlcal communication （SLOCC） classification of the states are discussed on the basis of the canonical forms, and the symmetric canonical form of the states without 3-tangle is discussed. Finally, we give the relation between the LU polynomial invariants and SLOCC classification.
基金The project supported by the Natural Science Foundation of Zhejiang Province of China under Grant No. Y604036 and State Key Laboratory of 0il/Gas Reservoir Geology and Exploitation ＂PLN0402＂ The authors would like to thank Prof. Sen-Yue Lou for his help and discussion.
文摘The （3＋1）-dimensional Jimbo-Miwa （JM） equation is solved approximately by using the conformal invariant asymptotic expansion approach presented by Ruan. By solving the new （3＋1）-dimensional integrable models, which are conformal invariant and possess Painlevé property, the approximate solutions are obtained for the JM equation, containing not only one-soliton solutions but also periodic solutions and multi-soliton solutions. Some approximate solutions happen to be exact and some approximate solutions can become exact by choosing relations between the parameters properly.
文摘For any scheme M with a perfect obstruction theory,Jiang and Thomas associated a scheme N with a symmetric perfect obstruction theory.The scheme N is a cone over M given by the dual of the obstruction sheaf of M,and contains M as its zero section.Locally,N is the critical locus of a regular function.In this note we prove that N is a d-critical scheme in the sense of Joyce.There exists a global motive for N locally given by the motive of the vanishing cycle of the local regular function.We prove a motivic localization formula under the good and circle compact C*-action for N.When taking the Euler characteristic,the weighted Euler characteristic of N weighted by the Behrend function is the signed Euler characteristic of M by motivic method.As applications,using the main theorem we study the motivic generating series of the motivic Vafa-Witten invariants for K3 surfaces.
文摘The wave/particle duality of particles in Physics is well known. Particles have properties that uniquely characterize them from one another, such as mass, charge and spin. Charged particles have associated Electric and Magnetic fields. Also, every moving particle has a De Broglie wavelength determined by its mass and velocity. This paper shows that all of these properties of a particle can be derived from a single wave function equation for that particle. Wave functions for the Electron and the Positron are presented and principles are provided that can be used to calculate the wave functions of all the fundamental particles in Physics. Fundamental particles such as electrons and positrons are considered to be point particles in the Standard Model of Physics and are not considered to have a structure. This paper demonstrates that they do indeed have structure and that this structure extends into the space around the particle’s center (in fact, they have infinite extent), but with rapidly diminishing energy density with the distance from that center. The particles are formed from Electromagnetic standing waves, which are stable solutions to the Schrödinger and Classical wave equations. This stable structure therefore accounts for both the wave and particle nature of these particles. In fact, all of their properties such as mass, spin and electric charge, can be accounted for from this structure. These particle properties appear to originate from a single point at the center of the wave function structure, in the same sort of way that the Shell theorem of gravity causes the gravity of a body to appear to all originate from a central point. This paper represents the first two fully characterized fundamental particles, with a complete description of their structure and properties, built up from the underlying Electromagnetic waves that comprise these and all fundamental particles.
文摘Lie group analysis method is applied to the extended(3+1)-dimensional Kadomtsev–Petviashvili–Boussinesq equation and the corresponding similarity reduction equations are obtained with various infinitesimal generators.By selecting suitable arbitrary functions in the similarity reduction solutions,we obtain abundant invariant solutions,including the trigonometric solution,the kink-lump interaction solution,the interaction solution between lump wave and triangular periodic wave,the two-kink solution,the lump solution,the interaction between a lump and two-kink and the periodic lump solution in different planes.These exact solutions are also given graphically to show the detailed structures of this high dimensional integrable system.
基金supported by the National Natural Science Foundation of China (60572093)the Doctoral Program of Higher Education(20050004016)the Outstanding Doctoral Science Innovation Foundation of Beijing Jiaotong University (141095522)
文摘A 3D motion and geometric information system of single-antenna radar is proposed,which can be supported by spotlight synthetic aperture radar（SAR） system and inverse SAR（ISAR） system involving relative 3D motion of the rigid target.In this system,applying the geometry invariance of the rigid target,the unknown 3D shape and motion of the radar target can be reconstructed from the 1D range data of some scatterers extracted from the high-resolution range image.Compared with the current 1D-to-3D algorithm,in the proposed algorithm,the requirement of the 1D range data is expanded to incomplete formation involving large angular motion of the target and hence,the quantity of the scatterers and the abundance of 3D motion are enriched.Furthermore,with the three selected affine coordinates fixed,the multi-solution problem of the reconstruction is solved and the technique of nonlinear optimization can be successfully utilized in the system.Two simulations are implemented which verify the higher robustness of the system and the better performance of the 3D reconstruction for the radar target with unknown relative motion.
文摘This paper proposes a new set of 3D rotation scaling and translation invariants of 3D radially shifted Legendre moments. We aim to develop two kinds of transformed shifted Legendre moments： a 3D substituted radial shifted Legendre moments （3DSRSLMs） and a 3D weighted radial one （3DWRSLMs）. Both are centered on two types of polynomials. In the first case, a new 3D ra- dial complex moment is proposed. In the second case, new 3D substituted/weighted radial shifted Legendremoments （3DSRSLMs/3DWRSLMs） are introduced using a spherical representation of volumetric image. 3D invariants as derived from the sug- gested 3D radial shifted Legendre moments will appear in the third case. To confirm the proposed approach, we have resolved three is- sues. To confirm the proposed approach, we have resolved three issues： rotation, scaling and translation invariants. The result of experi- ments shows that the 3DSRSLMs and 3DWRSLMs have done better than the 3D radial complex moments with and without noise. Sim- ultaneously, the reconstruction converges rapidly to the original image using 3D radial 3DSRSLMs and 3DWRSLMs, and the test of 3D images are clearly recognized from a set of images that are available in Princeton shape benchmark （PSB） database for 3D image.
文摘Recently, orthogonal moments have become efficient tools for two-dimensional and three-dimensional（2D and 3D） image not only in pattern recognition, image vision, but also in image processing and applications engineering. Yet, there is still a major difficulty in 3D rotation invariants. In this paper, we propose new sets of invariants for 2D and 3D rotation, scaling and translation based on orthogonal radial Hahn moments. We also present theoretical mathematics to derive them. Thus, this paper introduces in the first case new 2D radial Hahn moments based on polar representation of an object by one-dimensional orthogonal discrete Hahn polynomials, and a circular function. In the second case, we present new 3D radial Hahn moments using a spherical representation of volumetric image by one-dimensional orthogonal discrete Hahn polynomials and a spherical function. Further 2D and 3D invariants are derived from the proposed 2D and 3D radial Hahn moments respectively, which appear as the third case. In order to test the proposed approach, we have resolved three issues： the image reconstruction, the invariance of rotation, scaling and translation, and the pattern recognition. The result of experiments show that the Hahn moments have done better than the Krawtchouk moments, with and without noise. Simultaneously, the mentioned reconstruction converges quickly to the original image using 2D and 3D radial Hahn moments, and the test images are clearly recognized from a set of images that are available in COIL-20 database for 2D image, and Princeton shape benchmark（PSB） database for 3D image.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.10735030,90718041 and 40975038)Shanghai Leading Academic Discipline Project(Grant No.B412)Program for Changjiang Scholars and Innovative Research Team in University(Grant No.IRT0734)
文摘This paper investigates an important high-dimensional model in the atmospheric and oceanic dynamics-（3＋1）- dimensional nonlinear baroclinic potential vorticity equation by the classical Lie group method. Its symmetry algebra, symmetry group and group-invariant solutions are analysed. Otherwise, some exact explicit solutions are obtained from the corresponding （2＋1）-dimensional equation, the inviscid barotropic nondivergent vorticy equation. To show the properties and characters of these solutions, some plots as well as their possible physical meanings of the atmospheric circulation are given out.
