A new conserved quantity is deduced from Mei symmetry of Tzenoff equations for holonomic systems. The expression of this new conserved quantity is given, and the determining equation to induce this new conserved quant...A new conserved quantity is deduced from Mei symmetry of Tzenoff equations for holonomic systems. The expression of this new conserved quantity is given, and the determining equation to induce this new conserved quantity is presented. The results exhibit that this new method is easier to find more conserved quantities than the previously reported ones. Finally, application of this new result is presented by a practical example.展开更多
Search speed, quality of resulting paths and the cost of pre-processing are the principle evaluation metrics of a pathfinding algorithm. In this paper, a new algorithm for grid-based maps, rectangle expansion A＊ （RE...Search speed, quality of resulting paths and the cost of pre-processing are the principle evaluation metrics of a pathfinding algorithm. In this paper, a new algorithm for grid-based maps, rectangle expansion A＊ （REA＊）, is presented that improves the performance of A＊ significantly. REA＊ explores maps in units of unblocked rectangles. All unnecessary points inside the rectangles are pruned and boundaries of the rectangles （instead of individual points within those boundaries） are used as search nodes. This makes the algorithm plot fewer points and have a much shorter open list than A＊. REA＊ returns jump and grid-optimal path points, but since the line of sight between jump points is protected by the unblocked rectangles, the resulting path of REA＂ is usually better than grid-optimal. The algorithm is entirely online and requires no offline pre-processing. Experimental results for typical benchmark problem sets show that REA＊ can speed up a highly optimized A＊ by an order of magnitude and more while preserving completeness and optimality. This new algorithm is competitive with other highly successful variants of A＊.展开更多
Painleve property and infinite symmetries of the （2＋1）-dimensional higher-order Broer-Kaup （HBK） system are studied in this paper. Using the modified direct method, we derive the theorem of general symmetry gro.u...Painleve property and infinite symmetries of the （2＋1）-dimensional higher-order Broer-Kaup （HBK） system are studied in this paper. Using the modified direct method, we derive the theorem of general symmetry gro.ups to （2＋1）-dimensional HBK system. Based on our theorem, some new forms of solutions are obtained. We also find infinite number of conservation laws of the （2＋1）-dimensional HBK system.展开更多
The concept of approximate generalized conditional symmetry （A GCS） as a generalization to both approximate Lie point symmetry and generalized conditional symmetry is introduced, and it is applied to study the pertu...The concept of approximate generalized conditional symmetry （A GCS） as a generalization to both approximate Lie point symmetry and generalized conditional symmetry is introduced, and it is applied to study the perturbed nonlinear diffusion-convection equations. Complete classification of those perturbed equations which admit cerrain types of AGCSs is derived. Some approximate solutions to the resulting equations can be obtained via the AGCS and the corresponding unperturbed equations.展开更多
We demonstrate a single-exposure holographic fabrication of two-dimensional photonic crystal with round- cornered triangular ＇atoms＇ arranged in a triangular lattice. Simulation results show that double absolute pho...We demonstrate a single-exposure holographic fabrication of two-dimensional photonic crystal with round- cornered triangular ＇atoms＇ arranged in a triangular lattice. Simulation results show that double absolute photonic band gaps exist in this structure. Our experimental results show that holographic lithography can be used to fabricate photonic crystals not only with various lattice structures but also with various kinds of structures of the atoms, to obtain absolute band gaps or a particular band gap structure. Furthermore, the single-exposure holographic method not only makes the fabrication process simple and convenient but also makes the structures of the atoms more perfect.展开更多
A consistent tanh expansion （CTE） method is developed for the dispersion water wave （DWW） system. For the CTE solvable DlVVC system, there are two branches related to tanh expansion, the main branch is consistent ...A consistent tanh expansion （CTE） method is developed for the dispersion water wave （DWW） system. For the CTE solvable DlVVC system, there are two branches related to tanh expansion, the main branch is consistent while the auxiliary branch is not consistent. From the consistent branch, we can obtain infinitely many exact significant solutions including the soliton-resonant solutions and soliton-periodic wave interactions. From the inconsistent branch, only one special solution can be found. The CTE related nonlocal symmetries are also proposed. The nonlocai symmetries can be localized to find finite Backlund transformations by prolonging the model to an enlarged one.展开更多
Nanophotonic engineering provides an effective platform to manipulate thermal emission on-demand,enabling unprecedented heat management superior to conventional bulk materials.Amongst a plethora of nanophotonic struct...Nanophotonic engineering provides an effective platform to manipulate thermal emission on-demand,enabling unprecedented heat management superior to conventional bulk materials.Amongst a plethora of nanophotonic structures,symmetries play an important role in controlling radiative heat transfer in both near-field and far-field.In physics,broken symmetries generally increase the degree of freedom in a system,enriching the understanding of physical mechanisms and bringing many exciting opportunities for novel applications.In this review,we discussed the underlying physics and functionalities of nanophotonic structures with broken geometrical symmetries,engineered mode symmetries,and broken reciprocity for the control of thermal emission.We overview a variety of physical phenomena and interesting applications,and provide the outlook for future development.展开更多
The modified Kadomtsev-Petviashvili hierarchy of B type(mBKP hierarchy)and its constrained cases are investigated from the aspect of the Lax formulation.Starting from the Lax equation of the mBKP hierarchy,we firstly ...The modified Kadomtsev-Petviashvili hierarchy of B type(mBKP hierarchy)and its constrained cases are investigated from the aspect of the Lax formulation.Starting from the Lax equation of the mBKP hierarchy,we firstly derive the bilinear equations and show the existence of the tau functions.Then the additional symmetries are constructed,and the corresponding generator is showed to be the squared eigenfunction symmetry.After that,the actions of the additional symmetries on the tau functions are given.At last,the Lax formulation of the constrained mBKP hierarchy is investigated and the corresponding bilinear equations are also discussed.展开更多
A universe consisting of protons, neutrons, and electrons with electrical neutrality is consistent with an equal number of c and preons, assuming the rishon preon theory of Shupe and Harari. Similarly, a universe cons...A universe consisting of protons, neutrons, and electrons with electrical neutrality is consistent with an equal number of c and preons, assuming the rishon preon theory of Shupe and Harari. Similarly, a universe consisting of antiprotons, antineutrons, and positrons with electrical neutrality is consistent with an equal number of c and preons. Hence, any combination of such matter-antimatter compositions is also consistent with an equal number of c and preons and overall electrical neutrality. It is proposed that the difference observed in baryon-antibaryon number density relative to photon number density, ~5 × 10<sup>-10</sup>, is due to allocation of preons between matter and antimatter during preon condensation into normal matter. Three approaches of increasing rigor and complexity are considered: 1) an allocation at times corresponding to the Planck temperature due to fluctuations, 2) an allocation at times corresponding to quark formation due to preon bonding, and 3) an allocation at times corresponding to the electroweak scale. All approaches can give the correct order of magnitude of the asymmetry assuming out-of-equili-brium freeze-out and a slight and allowed charge (C) asymmetry in preon condensation in a self-consistent quantum field theory. Sakharov’s baryon non-conservation condition is evidently circumvented with these approaches, because they assume another level of matter (preons) which is present before quark formation. Thus, preons can provide an elementary explanation of primordial matter-antimatter asymmetry. A relationship between Higgs boson states and preons is proposed.展开更多
We constructed a gauge B-L model with D_(4)×Z_(4)×Z_(2)symmetry to explain the quark and lepton mass hierarchies and their mixings with realistic CP phases via the type-I seesaw mechanism.Six quark mases,thr...We constructed a gauge B-L model with D_(4)×Z_(4)×Z_(2)symmetry to explain the quark and lepton mass hierarchies and their mixings with realistic CP phases via the type-I seesaw mechanism.Six quark mases,three quark mixing angles,and the CP phase in the quark sector take the central values whereas Yukawa couplings in the quark sector are diluted in a range of difference of three orders of magnitude by the perturbation theory at the first order.Concerning the neutrino sector,a small neutrino mass is achieved by the type-I seesaw mechanism.Both inverted and normal neutrino mass hierarchies are consistent with the experimental data.The predicted sum of neutrino masses for normal and inverted hierarchies,the effective neutrino masses,and the Dirac CP phase are also consistent with recently reported limits.展开更多
The nonlinear evolution equations have a wide range of applications,more precisely in physics,biology,chemistry and engineering fields.This domain serves as a point of interest to a large extent in the world’s mathem...The nonlinear evolution equations have a wide range of applications,more precisely in physics,biology,chemistry and engineering fields.This domain serves as a point of interest to a large extent in the world’s mathematical community.Thus,this paper purveys an analytical study of a generalized extended(2+1)-dimensional quantum Zakharov-Kuznetsov equation with power-law nonlinearity in oceanography and ocean engineering.The Lie group theory of differential equations is utilized to compute an optimal system of one dimension for the Lie algebra of the model.We further reduce the equation using the subalgebras obtained.Besides,more general solutions of the underlying equation are secured for some special cases of n with the use of extended Jacobi function expansion technique.Consequently,we secure new bounded and unbounded solutions of interest for the equation in various solitonic structures including bright,dark,periodic(cnoidal and snoidal),compact-type as well as singular solitons.The applications of cnoidal and snoidal waves of the model in oceanography and ocean engineering for the first time,are outlined with suitable diagrams.This can be of interest to oceanographers and ocean engineers for future analysis.Furthermore,to visualize the dynamics of the results found,we present the graphic display of each of the solutions.Conclusively,we construct conservation laws of the understudy equation via the application of Noether’s theorem.展开更多
A new type of symmetry,ren-symmetry,describing anyon physics and corresponding topological physics,is proposed.Ren-symmetry is a generalization of super-symmetry which is widely applied in super-symmetric physics such...A new type of symmetry,ren-symmetry,describing anyon physics and corresponding topological physics,is proposed.Ren-symmetry is a generalization of super-symmetry which is widely applied in super-symmetric physics such as super-symmetric quantum mechanics,super-symmetric gravity,super-symmetric string theory,super-symmetric integrable systems and so on.Supersymmetry and Grassmann numbers are,in some sense,dual conceptions,and it turns out that these conceptions coincide for the ren situation,that is,a similar conception of ren-number(R-number)is devised for ren-symmetry.In particular,some basic results of the R-number and ren-symmetry are exposed which allow one to derive,in principle,some new types of integrable systems including ren-integrable models and ren-symmetric integrable systems.Training examples of ren-integrable KdV-type systems and ren-symmetric KdV equations are explicitly given.展开更多
基金Supported by the National Natural Science Foundation of China under Grant Nos 10672143 and 10572021.
文摘A new conserved quantity is deduced from Mei symmetry of Tzenoff equations for holonomic systems. The expression of this new conserved quantity is given, and the determining equation to induce this new conserved quantity is presented. The results exhibit that this new method is easier to find more conserved quantities than the previously reported ones. Finally, application of this new result is presented by a practical example.
基金supported by the National Natural Science Foundation of China (No.61573283)
文摘Search speed, quality of resulting paths and the cost of pre-processing are the principle evaluation metrics of a pathfinding algorithm. In this paper, a new algorithm for grid-based maps, rectangle expansion A＊ （REA＊）, is presented that improves the performance of A＊ significantly. REA＊ explores maps in units of unblocked rectangles. All unnecessary points inside the rectangles are pruned and boundaries of the rectangles （instead of individual points within those boundaries） are used as search nodes. This makes the algorithm plot fewer points and have a much shorter open list than A＊. REA＊ returns jump and grid-optimal path points, but since the line of sight between jump points is protected by the unblocked rectangles, the resulting path of REA＂ is usually better than grid-optimal. The algorithm is entirely online and requires no offline pre-processing. Experimental results for typical benchmark problem sets show that REA＊ can speed up a highly optimized A＊ by an order of magnitude and more while preserving completeness and optimality. This new algorithm is competitive with other highly successful variants of A＊.
基金The project supported by the Natural Science Foundation of Shandong Province of China under Grant No. 2004 zx 16
文摘Painleve property and infinite symmetries of the （2＋1）-dimensional higher-order Broer-Kaup （HBK） system are studied in this paper. Using the modified direct method, we derive the theorem of general symmetry gro.ups to （2＋1）-dimensional HBK system. Based on our theorem, some new forms of solutions are obtained. We also find infinite number of conservation laws of the （2＋1）-dimensional HBK system.
基金Supported by the National Natural Science Foundation of China under Grant Nos 10371098 and 10447007, the Natural Science Foundation of Shaanxi Province （No 2005A13）, and the Special Research Project of Educational Department of Shaanxi Province （No 03JK060）.
文摘The concept of approximate generalized conditional symmetry （A GCS） as a generalization to both approximate Lie point symmetry and generalized conditional symmetry is introduced, and it is applied to study the perturbed nonlinear diffusion-convection equations. Complete classification of those perturbed equations which admit cerrain types of AGCSs is derived. Some approximate solutions to the resulting equations can be obtained via the AGCS and the corresponding unperturbed equations.
基金Supported by the National Natural Science Foundation of China under Grant No 10674183, the National Basic Research Program of China under Grant No 2004CB719804, and PhD Foundation of the Ministry of Education of China （20060558068）.
文摘We demonstrate a single-exposure holographic fabrication of two-dimensional photonic crystal with round- cornered triangular ＇atoms＇ arranged in a triangular lattice. Simulation results show that double absolute photonic band gaps exist in this structure. Our experimental results show that holographic lithography can be used to fabricate photonic crystals not only with various lattice structures but also with various kinds of structures of the atoms, to obtain absolute band gaps or a particular band gap structure. Furthermore, the single-exposure holographic method not only makes the fabrication process simple and convenient but also makes the structures of the atoms more perfect.
基金Supported by the National Natural Science Foundations of China under Grant Nos.11175092,11275123,11205092,and 10905038Talent FundK.C.Wong Magna Fund in Ningbo University
文摘A consistent tanh expansion （CTE） method is developed for the dispersion water wave （DWW） system. For the CTE solvable DlVVC system, there are two branches related to tanh expansion, the main branch is consistent while the auxiliary branch is not consistent. From the consistent branch, we can obtain infinitely many exact significant solutions including the soliton-resonant solutions and soliton-periodic wave interactions. From the inconsistent branch, only one special solution can be found. The CTE related nonlocal symmetries are also proposed. The nonlocai symmetries can be localized to find finite Backlund transformations by prolonging the model to an enlarged one.
基金S.F.acknowledges the support of the US Department of Energy(grant no.DE-FG02-07ER46426)W.L.acknowledges the support of the National Natural Science Foundation of China(grant nos.62134009,62121005)Development Program of the Science and Technology of Jilin Province(20200802001GH).
文摘Nanophotonic engineering provides an effective platform to manipulate thermal emission on-demand,enabling unprecedented heat management superior to conventional bulk materials.Amongst a plethora of nanophotonic structures,symmetries play an important role in controlling radiative heat transfer in both near-field and far-field.In physics,broken symmetries generally increase the degree of freedom in a system,enriching the understanding of physical mechanisms and bringing many exciting opportunities for novel applications.In this review,we discussed the underlying physics and functionalities of nanophotonic structures with broken geometrical symmetries,engineered mode symmetries,and broken reciprocity for the control of thermal emission.We overview a variety of physical phenomena and interesting applications,and provide the outlook for future development.
基金supported by National Natural Science Foundation of China(Grant No.12171472)。
文摘The modified Kadomtsev-Petviashvili hierarchy of B type(mBKP hierarchy)and its constrained cases are investigated from the aspect of the Lax formulation.Starting from the Lax equation of the mBKP hierarchy,we firstly derive the bilinear equations and show the existence of the tau functions.Then the additional symmetries are constructed,and the corresponding generator is showed to be the squared eigenfunction symmetry.After that,the actions of the additional symmetries on the tau functions are given.At last,the Lax formulation of the constrained mBKP hierarchy is investigated and the corresponding bilinear equations are also discussed.
文摘A universe consisting of protons, neutrons, and electrons with electrical neutrality is consistent with an equal number of c and preons, assuming the rishon preon theory of Shupe and Harari. Similarly, a universe consisting of antiprotons, antineutrons, and positrons with electrical neutrality is consistent with an equal number of c and preons. Hence, any combination of such matter-antimatter compositions is also consistent with an equal number of c and preons and overall electrical neutrality. It is proposed that the difference observed in baryon-antibaryon number density relative to photon number density, ~5 × 10<sup>-10</sup>, is due to allocation of preons between matter and antimatter during preon condensation into normal matter. Three approaches of increasing rigor and complexity are considered: 1) an allocation at times corresponding to the Planck temperature due to fluctuations, 2) an allocation at times corresponding to quark formation due to preon bonding, and 3) an allocation at times corresponding to the electroweak scale. All approaches can give the correct order of magnitude of the asymmetry assuming out-of-equili-brium freeze-out and a slight and allowed charge (C) asymmetry in preon condensation in a self-consistent quantum field theory. Sakharov’s baryon non-conservation condition is evidently circumvented with these approaches, because they assume another level of matter (preons) which is present before quark formation. Thus, preons can provide an elementary explanation of primordial matter-antimatter asymmetry. A relationship between Higgs boson states and preons is proposed.
基金funded by Tay Nguyen University under grant number T2023-45CBTD。
文摘We constructed a gauge B-L model with D_(4)×Z_(4)×Z_(2)symmetry to explain the quark and lepton mass hierarchies and their mixings with realistic CP phases via the type-I seesaw mechanism.Six quark mases,three quark mixing angles,and the CP phase in the quark sector take the central values whereas Yukawa couplings in the quark sector are diluted in a range of difference of three orders of magnitude by the perturbation theory at the first order.Concerning the neutrino sector,a small neutrino mass is achieved by the type-I seesaw mechanism.Both inverted and normal neutrino mass hierarchies are consistent with the experimental data.The predicted sum of neutrino masses for normal and inverted hierarchies,the effective neutrino masses,and the Dirac CP phase are also consistent with recently reported limits.
文摘The nonlinear evolution equations have a wide range of applications,more precisely in physics,biology,chemistry and engineering fields.This domain serves as a point of interest to a large extent in the world’s mathematical community.Thus,this paper purveys an analytical study of a generalized extended(2+1)-dimensional quantum Zakharov-Kuznetsov equation with power-law nonlinearity in oceanography and ocean engineering.The Lie group theory of differential equations is utilized to compute an optimal system of one dimension for the Lie algebra of the model.We further reduce the equation using the subalgebras obtained.Besides,more general solutions of the underlying equation are secured for some special cases of n with the use of extended Jacobi function expansion technique.Consequently,we secure new bounded and unbounded solutions of interest for the equation in various solitonic structures including bright,dark,periodic(cnoidal and snoidal),compact-type as well as singular solitons.The applications of cnoidal and snoidal waves of the model in oceanography and ocean engineering for the first time,are outlined with suitable diagrams.This can be of interest to oceanographers and ocean engineers for future analysis.Furthermore,to visualize the dynamics of the results found,we present the graphic display of each of the solutions.Conclusively,we construct conservation laws of the understudy equation via the application of Noether’s theorem.
基金sponsored by the National Natural Science Foundation of China(Nos.12235007,11975131)。
文摘A new type of symmetry,ren-symmetry,describing anyon physics and corresponding topological physics,is proposed.Ren-symmetry is a generalization of super-symmetry which is widely applied in super-symmetric physics such as super-symmetric quantum mechanics,super-symmetric gravity,super-symmetric string theory,super-symmetric integrable systems and so on.Supersymmetry and Grassmann numbers are,in some sense,dual conceptions,and it turns out that these conceptions coincide for the ren situation,that is,a similar conception of ren-number(R-number)is devised for ren-symmetry.In particular,some basic results of the R-number and ren-symmetry are exposed which allow one to derive,in principle,some new types of integrable systems including ren-integrable models and ren-symmetric integrable systems.Training examples of ren-integrable KdV-type systems and ren-symmetric KdV equations are explicitly given.
