Reed-Muller logic is becoming increasingly attractive. However, its synthesis and optimization are difficult especially for mixed polarity Reed-Muller logic. In this paper, a function is expressed into a truth vector....Reed-Muller logic is becoming increasingly attractive. However, its synthesis and optimization are difficult especially for mixed polarity Reed-Muller logic. In this paper, a function is expressed into a truth vector. Product shrinkage, general sum shrinkage （GSS）, elimination and extraction operators are proposed to shrink the truth vector. A novel algorithm is presented to derive a compact Multi-level Mixed Polarity Reed-Muller Form （MMPRMF） starting from a given fixed polarity truth vector. The results show that a significant area improvement can be made compared with published results.展开更多
Perovskite solar cells(PSCs)emerging as a promising photovoltaic technology with high efficiency and low manufacturing cost have attracted the attention from all over the world.Both the efficiency and stability of PSC...Perovskite solar cells(PSCs)emerging as a promising photovoltaic technology with high efficiency and low manufacturing cost have attracted the attention from all over the world.Both the efficiency and stability of PSCs have increased steadily in recent years,and the research on reducing lead leakage and developing eco-friendly lead-free perovskites pushes forward the commercialization of PSCs step by step.This review summarizes the main progress of PSCs in 2020 and 2021 from the aspects of efficiency,stability,perovskite-based tandem devices,and lead-free PSCs.Moreover,a brief discussion on the development of PSC modules and its challenges toward practical application is provided.展开更多
With the advancement of modern science and technology, large scientific facilities are increasingly oriented toward demand and application, and can be used for basic research as well as serving multiple disciplines. D...With the advancement of modern science and technology, large scientific facilities are increasingly oriented toward demand and application, and can be used for basic research as well as serving multiple disciplines. Developing large scientific facilities and related analytical technologies enhances understanding of large scientific facilities and popularizes their application in research across multiple disciplines. The combination of light or neutron sources from large scientific facilities and advanced analytical technologies can be achieved for materials structure information, dynamics study of chemical reactions, high dissociation of biomolecules, 3D visualization of energy materials or biological samples, etc. We first introduce the progress of domestic large scientific facilities of synchrotron radiation(SR) and free electron lasers(FELs) with different wavelengths and neutron sources.We further discuss the comparison between Chinese and typical foreign facilities in X-ray radiation from X-ray tubes, synchrotrons, X-ray FELs, and neutron sources based on physical parameters of light and neutron sources. In addition, we focus on the technological progress and perspectives combined with advanced X-ray radiation and neutron sources of large scientific facilities in China, especially in the nanoscience fields of energy catalysis and biological science. We hope that this roadmap will provide references on technology and methods to experimental users, as well as prospects for future development of technologies based on large research infrastructure facilities. Comprehensive studies and guidelines for basic research to practical application in various disciplines can be made with the assistance of large scientific facilities.展开更多
The staggered mode of solitons in polyacetylene which is first discovered by Sun et al.is one of the typical gap soliton studied in lattice system.Using a one dimensional damped and parametrically driven pendulum latt...The staggered mode of solitons in polyacetylene which is first discovered by Sun et al.is one of the typical gap soliton studied in lattice system.Using a one dimensional damped and parametrically driven pendulum lattice,we have observed a stable staggered mode which can be explained successfully by a nonlinear Schrödinger equation under the multiple scale approximation.展开更多
The space-based laser interferometers,LISA,Taiji and TianQin,are targeting to observe milliHz gravitational waves(GWs)in the 2030s.The joint observations from multiple space-based detectors yield significant advantage...The space-based laser interferometers,LISA,Taiji and TianQin,are targeting to observe milliHz gravitational waves(GWs)in the 2030s.The joint observations from multiple space-based detectors yield significant advantages.In this work,we recap the studies and investigations for the joint space-based GW detector networks to highlight:1)the high precision of sky localization for the massive binary black hole(BBH)coalescences and the GW sirens in the cosmological implication,2)the effectiveness to test the parity violation in the stochastic GW background observations,3)the efficiency of subtracting galactic foreground,4)the improvement in stellar-mass BBH observations.We inspect alternative networks by trading off massive BBH observations and stochastic GW background observation.展开更多
Aluminum-metal batteries show great potential as next-generation energy storage due to their abundant resources and intrinsic safety.However,the crucial limitations of metallic Al anodes,such as dendrite and corrosion...Aluminum-metal batteries show great potential as next-generation energy storage due to their abundant resources and intrinsic safety.However,the crucial limitations of metallic Al anodes,such as dendrite and corrosion problems in conventional aluminum-metal batteries,remain challenging and elusive.Here,we report a novel electrodeposition strategy to prepare an optimized 3D Al anode on carbon cloth with an uniform deposition morphology,low local current density,and mitigatory volume change.The symmetrical cells with the 3D Al anode show superior stable cycling(>450 h)and low-voltage hysteresis(~170 mV)at 0.5 mA cm^(−2).High reversibility(~99.7%)is achieved for the Al plating/stripping.The graphite||Al‐4/CC full batteries show a long lifespan of 800 cycles with 54 mAh g^(−1) capacity at a high current density of 1000 mA g^(−1),benefiting from the high capacitive-controlled distribution.This study proposes a novel strategy to design 3D Al anodes for metallic-Al-based batteries by eliminating the problems of planar Al anodes and realizing the potential applications of aluminum-graphite batteries.展开更多
Understanding the factors determining the formation of each community and metacommunity across a landscape is one of the most important ideas in soil animal ecology.However,the variables and parameters that shape soil...Understanding the factors determining the formation of each community and metacommunity across a landscape is one of the most important ideas in soil animal ecology.However,the variables and parameters that shape soil arthropod communities in agroecosystems have not been resolved.These arthropods can serve as important bioindicators of field management and its sustainability.We sampled five com plantations in each of three locations across a region spanning 600 km to come up with these determinants of the community structure of ground-dwelling spiders(Erigoninae:Araneae),carabids(Coleoptara:Carabidae),and ants(Hymenoptera:Formicidae).The analysis of the five fields within each of the three locations represent our local-scale samples,while the comparisons of the 15 sites across all three locations represent the regional scale samples.We tested the hypothesis that in the models we sampled,environmental/soil variables would drivecommunity assembly locally(within location comparisons),but at the regional scale(between location comparisons),climatic and spatial variables would drive metacommunity assembly.The outcomes of our study showed distinct communities at each of the three locations when compared across regions but locally,fields were similar in species composition,as expected.Locally,spatial variables were important but not soil variables,regulated species richness and abundance.Turnover contributed more than nestedness to explain the biodiversity of spiders,carabids,and ants at both the local and regional scales.Neither purely climate variables,nor purely soil or spatial variables were significant enough explanations for the regional scale arthropod community composition.However,spatially structured environmental factors contributed most to explain the patterns supporting our hypothesis.We conclude that biodiversity in this agroecosystem area can be promoted by a mosaic of land uses being encouraged to increase landscape complexity at the regional scale.展开更多
Starting from the similarity reductions of the Kadomtsev-Petviashvili equation, we getthe generalized Boussinesq equation and the generalized KdV equation which possess somearbitrary functions as their variable coeffi...Starting from the similarity reductions of the Kadomtsev-Petviashvili equation, we getthe generalized Boussinesq equation and the generalized KdV equation which possess somearbitrary functions as their variable coefficients. Using the singularity analysis methoddeveloped by J. Weiss and M. D. Kruskal et al. we have proved the sufficient conditionsof the integrabilities and Painleve properties of these two equations. Their Backlund trans-formations and the singularity manifold equations (generalized Schwartz-Boussinesq equationand Schwartz-KdV equation) are obtained. And then these two equations are linearized, i. e.their Lax pairs are given with the time-independent arbitrary spectral parameters includedexplicitly.展开更多
Using the inner parameter dependent symmetry constraints of the modified Kadomtsev-Petviashvili equation,we get an integrable(2+1)-dimensional multi-component Burgers and a(2+1)-dimensional integrable extensions of th...Using the inner parameter dependent symmetry constraints of the modified Kadomtsev-Petviashvili equation,we get an integrable(2+1)-dimensional multi-component Burgers and a(2+1)-dimensional integrable extensions of the derivative nonlinear Schrödinger equation.展开更多
Explicit computation for the Kaup-Kupershmidt(KK)equation shows that there exists an abundant symmetry structure of the KK hierarchy.The recursion operator,inverse recursion operator and the symmetries all can be expr...Explicit computation for the Kaup-Kupershmidt(KK)equation shows that there exists an abundant symmetry structure of the KK hierarchy.The recursion operator,inverse recursion operator and the symmetries all can be expressed explicitly by the pseudopotential of the KK equation.展开更多
Starting from a special nonlocal Lie Backlund symmetry of the KdV,mKdV,potential mKdV and singularity manifold equation system,three sets of higher order nonlocal Olver syiniuetries are reobtained.The soliton solution...Starting from a special nonlocal Lie Backlund symmetry of the KdV,mKdV,potential mKdV and singularity manifold equation system,three sets of higher order nonlocal Olver syiniuetries are reobtained.The soliton solutions of these models can also be obtained from the finite Lie-Backlund transformations.展开更多
For any complex s, let ζ（s） denote Riemann Zeta function. We have ζ（s）=sum from n=1 to ∞ （1/n<sup>s</sup>） when Re（s）】1. Now we define A（n,k,l）=sum from α<sub>1</sub>+α<sub&g...For any complex s, let ζ（s） denote Riemann Zeta function. We have ζ（s）=sum from n=1 to ∞ （1/n<sup>s</sup>） when Re（s）】1. Now we define A（n,k,l）=sum from α<sub>1</sub>+α<sub>2</sub>+……+α<sub>k</sub>=n to （（α<sub>1</sub>α<sub>2</sub>…α<sub>k</sub>）<sup>1</sup>ζ（2α<sub>1</sub>）ζ（2α<sub>2</sub>）…ζ（2α<sub>k</sub>））, where n≥k is a positive integer, α<sub>+</sub>α<sub>2</sub>+…α<sub>k</sub>=n denotes the summation for k-dimensional group of positive integers （α<sub>1</sub>, α<sub>2</sub>,…, α<sub>k</sub>）which satisfies this formula. In this note, our main purpose is to discuss computing problem of summation on equation （1）.展开更多
A non-local symmetry of the Caudrey-Dodd-Gibbon-Sawada-Kotera(CDGSK)equation has been used for finding exact solution in two different ways.Firstly,using the standard prolongation approach,we obtain the finite Lie B&#...A non-local symmetry of the Caudrey-Dodd-Gibbon-Sawada-Kotera(CDGSK)equation has been used for finding exact solution in two different ways.Firstly,using the standard prolongation approach,we obtain the finite Lie Bäcklund transformation and the single soliton solution.Secondly,combining some local symmetries and the nonlocal symmetry,we get the group invariant solution which is described by the Weierstrass elliptic function and is deduced to the so-called interacting soliton for a special parameter.展开更多
Among the solutions of three kinds of nonlinear equations in one dimensional systems, cubic nonlinear Klein-Gordon (including Φ~4), Sine-Gordon and double Sine-Gordon, some mapping relations exist. When a solution of...Among the solutions of three kinds of nonlinear equations in one dimensional systems, cubic nonlinear Klein-Gordon (including Φ~4), Sine-Gordon and double Sine-Gordon, some mapping relations exist. When a solution of any one equation is known, so are the other two.展开更多
A new explanation of quaternary Q gate expression in Post algebra is given in this paper by using transmission function theory proposed in [1] and the quaternary ECL Q gate circuit is de- signed.The SPICE2 simulation ...A new explanation of quaternary Q gate expression in Post algebra is given in this paper by using transmission function theory proposed in [1] and the quaternary ECL Q gate circuit is de- signed.The SPICE2 simulation to this circuit has confirmed that it has desired logical function and is totally compatible with various quaternary ECL circuits proposed before.展开更多
The chaotic behaviors of the time series of the breather(soliton)amplitude have been observed experimentally in the shallow water in the trough subjected to parametric exciting vertically.The results predict that the ...The chaotic behaviors of the time series of the breather(soliton)amplitude have been observed experimentally in the shallow water in the trough subjected to parametric exciting vertically.The results predict that the water solitary waves should be described by some chaotic equations in the higher order approximations as well as by the nonlinear Schördinger equation in the first order.展开更多
The standard model describing the strong, the weak and the electromagnetic interactions has become the foundation of the modern physics. However, there still remain many important problems to be solved. The most impor...The standard model describing the strong, the weak and the electromagnetic interactions has become the foundation of the modern physics. However, there still remain many important problems to be solved. The most important one is how to determine展开更多
Ocean currents are a key element in ocean processes and in meteorology,affecting material transport and modulating climate change patterns.The Doppler frequency shift information of the synthetic aperture radar(SAR)ec...Ocean currents are a key element in ocean processes and in meteorology,affecting material transport and modulating climate change patterns.The Doppler frequency shift information of the synthetic aperture radar(SAR)echo signal can reflect the dynamic characteristics of the sea surface,and has become an essential sea surface dynamic remote sensing parameter.Studies have verified that the instantaneous Doppler frequency shift can realize the SAR detection of the sea surface current.However,the validation of SAR-derived ocean current data and a thorough analysis of the errors associated with them remain lacking.In this study,we derive high spatial resolution flow measurements for the Kuroshio in the East China Sea from SAR data using a theoretical model of shifts in Doppler frequency driven by ocean surface current.Global ocean multi observation(MOB)products and global surface Lagrangian drifter(GLD)data are used to validate the Kuroshio flow retrieved from the SAR data.Results show that the central flow velocity for the Kuroshio derived from the SAR is 0.4–1.5 m/s.The error distribution between SAR ocean currents and MOB products is an approximate standard normal distribution,with the 90%confidence interval concentrated between–0.1 m/s and 0.1 m/s.Comparative analysis of SAR ocean current and GLD products,the correlation coefficient is 0.803,which shows to be significant at a confidence level of 99%.The cross-validation of different ocean current dataset illustrate that the SAR radial current captures the positions and dynamics of the Kuroshio central flow and the Kuroshio Counter Current,and has the capability to monitor current velocity over a wide range of values.展开更多
The method of multiple-scales is used to investigate the nonlinear modulation of capillary-gravity waves with cylindrical symmetry.We find that the evolution of wave-packets is described by a nonlinear schrödinge...The method of multiple-scales is used to investigate the nonlinear modulation of capillary-gravity waves with cylindrical symmetry.We find that the evolution of wave-packets is described by a nonlinear schrödinger-like equation i(U+U/2r)+αUξξ+β|U|2U=0.Some exact and explicit cylindrical envelope solitary wave solutions are also obtained by means of variable transformations.展开更多
By means of the optimized expansion technique, the D + 1-dimensional quantum sine-Gordon (sG) field theory is studied nonperturbatively for both zero and finite temperatures.In 1 + 1 and 2+ 1 dimensions, the theory is...By means of the optimized expansion technique, the D + 1-dimensional quantum sine-Gordon (sG) field theory is studied nonperturbatively for both zero and finite temperatures.In 1 + 1 and 2+ 1 dimensions, the theory is finite when momentum cutoff Λ tends to infinity.The temperature-dependent Coleman phase transition conditions we obtained reduce to theknown results g_(cr)~2 =8π for 1+ 1 dimensions and g_(cr)~2= 16π/m_(RO) for 2+ 1 dimensions whenT→0. Especially, g_(cr) tends to zero at T→∞ limit both for 1 + 1 and 2 + 1 dimensions. Thereis no critical temperature making the Φ= 0 vacuum unstable. In 3 + 1 dimensions, if g^2 isfinite and Λ→∞, the theory is trivial. There is no nontrivial 'precarious' phase for the3+ 1-dimensional sG model. The effective potential for the 'autonomous' phase has asimilar form as the classical potential and the temperature effects only make contribution tothe infinitesimal part of this phase.展开更多
文摘Reed-Muller logic is becoming increasingly attractive. However, its synthesis and optimization are difficult especially for mixed polarity Reed-Muller logic. In this paper, a function is expressed into a truth vector. Product shrinkage, general sum shrinkage （GSS）, elimination and extraction operators are proposed to shrink the truth vector. A novel algorithm is presented to derive a compact Multi-level Mixed Polarity Reed-Muller Form （MMPRMF） starting from a given fixed polarity truth vector. The results show that a significant area improvement can be made compared with published results.
基金supported by the National Natural Science Foundation of China(Grant Nos.11834011 and 12074245)the support from the Energy Materials and Surface Sciences Unit of the Okinawa Institute of Science and Technology Graduate University。
文摘Perovskite solar cells(PSCs)emerging as a promising photovoltaic technology with high efficiency and low manufacturing cost have attracted the attention from all over the world.Both the efficiency and stability of PSCs have increased steadily in recent years,and the research on reducing lead leakage and developing eco-friendly lead-free perovskites pushes forward the commercialization of PSCs step by step.This review summarizes the main progress of PSCs in 2020 and 2021 from the aspects of efficiency,stability,perovskite-based tandem devices,and lead-free PSCs.Moreover,a brief discussion on the development of PSC modules and its challenges toward practical application is provided.
基金supported by the National Basic Research Program of China (2022YFA1603701, 2021YFA1200900)the institutionalized scientific research platform relies on Beijing Synchrotron Radiation Facility of Chinese Academy of Sciences,the Strategic Priority Research Program of Chinese Academy of Sciences (XDB36000000)+2 种基金the National Natural Science Foundation of China (22027810, 82341044,22388101 and 22307028)the CAMS Innovation Fund for Medical Sciences(CIFMS 2019-I2M-5-018)the New Cornerstone Science Foundation。
文摘With the advancement of modern science and technology, large scientific facilities are increasingly oriented toward demand and application, and can be used for basic research as well as serving multiple disciplines. Developing large scientific facilities and related analytical technologies enhances understanding of large scientific facilities and popularizes their application in research across multiple disciplines. The combination of light or neutron sources from large scientific facilities and advanced analytical technologies can be achieved for materials structure information, dynamics study of chemical reactions, high dissociation of biomolecules, 3D visualization of energy materials or biological samples, etc. We first introduce the progress of domestic large scientific facilities of synchrotron radiation(SR) and free electron lasers(FELs) with different wavelengths and neutron sources.We further discuss the comparison between Chinese and typical foreign facilities in X-ray radiation from X-ray tubes, synchrotrons, X-ray FELs, and neutron sources based on physical parameters of light and neutron sources. In addition, we focus on the technological progress and perspectives combined with advanced X-ray radiation and neutron sources of large scientific facilities in China, especially in the nanoscience fields of energy catalysis and biological science. We hope that this roadmap will provide references on technology and methods to experimental users, as well as prospects for future development of technologies based on large research infrastructure facilities. Comprehensive studies and guidelines for basic research to practical application in various disciplines can be made with the assistance of large scientific facilities.
基金Supported by the National Natural Science Foundation of Chinathe Natural Science Foundation of Zhejiang Province of China
文摘The staggered mode of solitons in polyacetylene which is first discovered by Sun et al.is one of the typical gap soliton studied in lattice system.Using a one dimensional damped and parametrically driven pendulum lattice,we have observed a stable staggered mode which can be explained successfully by a nonlinear Schrödinger equation under the multiple scale approximation.
基金supported in part by the National Natural Science Foundation of China(11821505)supported in part by the National Key Research and Development Program of China(2020YFC2201501)+7 种基金in part by the National Natural Science Foundation of China(12075297 and 12235019)supported in part by the National Key R&D Program of China(2021YFC2203001)supported by the National Natural Science Foundation of China(12147132)supported by the National Key Program for Science and Technology Research and Development(2020YFC2201400,2022YFC2205201)supported in part by the National Key R&D Program of China under(2021YFC2201901)supported in part by JSPS Kakenhi Grant-in-Aid for Scientific Research(17H06358,19K03870 and 23K03385)supported by the National Key R&D Program of China(2021YFC2201903)National Natural Science Foundation of China(12003059).
文摘The space-based laser interferometers,LISA,Taiji and TianQin,are targeting to observe milliHz gravitational waves(GWs)in the 2030s.The joint observations from multiple space-based detectors yield significant advantages.In this work,we recap the studies and investigations for the joint space-based GW detector networks to highlight:1)the high precision of sky localization for the massive binary black hole(BBH)coalescences and the GW sirens in the cosmological implication,2)the effectiveness to test the parity violation in the stochastic GW background observations,3)the efficiency of subtracting galactic foreground,4)the improvement in stellar-mass BBH observations.We inspect alternative networks by trading off massive BBH observations and stochastic GW background observation.
基金This study was funded by the Science and Technology Development Fund,Macao SAR(File no.0191/2017/A3,0041/2019/A1,0046/2019/AFJ,0021/2019/AIR)the University of Macao(File no.MYRG2017-00216-FST and MYRG2018-00192-IAPME)+2 种基金the UEA funding,Science and Technology Program of Guangzhou(2019050001)the National Key Research and Development Program of China(2019YFE0198000)Fuming Chen acknowledges the Pearl River Talent Program(2019QN01L951).
文摘Aluminum-metal batteries show great potential as next-generation energy storage due to their abundant resources and intrinsic safety.However,the crucial limitations of metallic Al anodes,such as dendrite and corrosion problems in conventional aluminum-metal batteries,remain challenging and elusive.Here,we report a novel electrodeposition strategy to prepare an optimized 3D Al anode on carbon cloth with an uniform deposition morphology,low local current density,and mitigatory volume change.The symmetrical cells with the 3D Al anode show superior stable cycling(>450 h)and low-voltage hysteresis(~170 mV)at 0.5 mA cm^(−2).High reversibility(~99.7%)is achieved for the Al plating/stripping.The graphite||Al‐4/CC full batteries show a long lifespan of 800 cycles with 54 mAh g^(−1) capacity at a high current density of 1000 mA g^(−1),benefiting from the high capacitive-controlled distribution.This study proposes a novel strategy to design 3D Al anodes for metallic-Al-based batteries by eliminating the problems of planar Al anodes and realizing the potential applications of aluminum-graphite batteries.
基金the National Natural Sciences Foundations of China(grant numbers 41430857,41871042)Special Foundation for National Science and Tech no logy Basic Research Program of China(grant nu mber 2018FY1003000).
文摘Understanding the factors determining the formation of each community and metacommunity across a landscape is one of the most important ideas in soil animal ecology.However,the variables and parameters that shape soil arthropod communities in agroecosystems have not been resolved.These arthropods can serve as important bioindicators of field management and its sustainability.We sampled five com plantations in each of three locations across a region spanning 600 km to come up with these determinants of the community structure of ground-dwelling spiders(Erigoninae:Araneae),carabids(Coleoptara:Carabidae),and ants(Hymenoptera:Formicidae).The analysis of the five fields within each of the three locations represent our local-scale samples,while the comparisons of the 15 sites across all three locations represent the regional scale samples.We tested the hypothesis that in the models we sampled,environmental/soil variables would drivecommunity assembly locally(within location comparisons),but at the regional scale(between location comparisons),climatic and spatial variables would drive metacommunity assembly.The outcomes of our study showed distinct communities at each of the three locations when compared across regions but locally,fields were similar in species composition,as expected.Locally,spatial variables were important but not soil variables,regulated species richness and abundance.Turnover contributed more than nestedness to explain the biodiversity of spiders,carabids,and ants at both the local and regional scales.Neither purely climate variables,nor purely soil or spatial variables were significant enough explanations for the regional scale arthropod community composition.However,spatially structured environmental factors contributed most to explain the patterns supporting our hypothesis.We conclude that biodiversity in this agroecosystem area can be promoted by a mosaic of land uses being encouraged to increase landscape complexity at the regional scale.
基金Project supported by the National Natural Science Foundation of China.
文摘Starting from the similarity reductions of the Kadomtsev-Petviashvili equation, we getthe generalized Boussinesq equation and the generalized KdV equation which possess somearbitrary functions as their variable coefficients. Using the singularity analysis methoddeveloped by J. Weiss and M. D. Kruskal et al. we have proved the sufficient conditionsof the integrabilities and Painleve properties of these two equations. Their Backlund trans-formations and the singularity manifold equations (generalized Schwartz-Boussinesq equationand Schwartz-KdV equation) are obtained. And then these two equations are linearized, i. e.their Lax pairs are given with the time-independent arbitrary spectral parameters includedexplicitly.
基金Supported by the National Natural Science Foundation of Chinathe Natural Science Foundation of Zhejiang Province of China.
文摘Using the inner parameter dependent symmetry constraints of the modified Kadomtsev-Petviashvili equation,we get an integrable(2+1)-dimensional multi-component Burgers and a(2+1)-dimensional integrable extensions of the derivative nonlinear Schrödinger equation.
基金Supported by the Natural Science Foundation of Zhejiang Provincethe National Natural Science Foundation of China.
文摘Explicit computation for the Kaup-Kupershmidt(KK)equation shows that there exists an abundant symmetry structure of the KK hierarchy.The recursion operator,inverse recursion operator and the symmetries all can be expressed explicitly by the pseudopotential of the KK equation.
基金Supported in part,by the Nattual Science Foundation of Zhejiang Piovincethe National Natwal Science Foundation of China。
文摘Starting from a special nonlocal Lie Backlund symmetry of the KdV,mKdV,potential mKdV and singularity manifold equation system,three sets of higher order nonlocal Olver syiniuetries are reobtained.The soliton solutions of these models can also be obtained from the finite Lie-Backlund transformations.
文摘For any complex s, let ζ（s） denote Riemann Zeta function. We have ζ（s）=sum from n=1 to ∞ （1/n<sup>s</sup>） when Re（s）】1. Now we define A（n,k,l）=sum from α<sub>1</sub>+α<sub>2</sub>+……+α<sub>k</sub>=n to （（α<sub>1</sub>α<sub>2</sub>…α<sub>k</sub>）<sup>1</sup>ζ（2α<sub>1</sub>）ζ（2α<sub>2</sub>）…ζ（2α<sub>k</sub>））, where n≥k is a positive integer, α<sub>+</sub>α<sub>2</sub>+…α<sub>k</sub>=n denotes the summation for k-dimensional group of positive integers （α<sub>1</sub>, α<sub>2</sub>,…, α<sub>k</sub>）which satisfies this formula. In this note, our main purpose is to discuss computing problem of summation on equation （1）.
基金Supported by the Natural Science Foundation of Zhejiang Provincethe National Natural Science Foimdation of China.
文摘A non-local symmetry of the Caudrey-Dodd-Gibbon-Sawada-Kotera(CDGSK)equation has been used for finding exact solution in two different ways.Firstly,using the standard prolongation approach,we obtain the finite Lie Bäcklund transformation and the single soliton solution.Secondly,combining some local symmetries and the nonlocal symmetry,we get the group invariant solution which is described by the Weierstrass elliptic function and is deduced to the so-called interacting soliton for a special parameter.
文摘Among the solutions of three kinds of nonlinear equations in one dimensional systems, cubic nonlinear Klein-Gordon (including Φ~4), Sine-Gordon and double Sine-Gordon, some mapping relations exist. When a solution of any one equation is known, so are the other two.
基金The subject is supported by Zhejiang Provincial Natural Science Foundation.
文摘A new explanation of quaternary Q gate expression in Post algebra is given in this paper by using transmission function theory proposed in [1] and the quaternary ECL Q gate circuit is de- signed.The SPICE2 simulation to this circuit has confirmed that it has desired logical function and is totally compatible with various quaternary ECL circuits proposed before.
基金Supported by the National Foundation of Nonlinear Science of P.R.ChinaNingbo Younger Science Foundation in P.R.China.
文摘The chaotic behaviors of the time series of the breather(soliton)amplitude have been observed experimentally in the shallow water in the trough subjected to parametric exciting vertically.The results predict that the water solitary waves should be described by some chaotic equations in the higher order approximations as well as by the nonlinear Schördinger equation in the first order.
文摘The standard model describing the strong, the weak and the electromagnetic interactions has become the foundation of the modern physics. However, there still remain many important problems to be solved. The most important one is how to determine
基金The National Natural Science Foundation of China under contract Nos 42176174 and 41706196the Open Research Fund of the State Key Laboratory of Estuarine and Coastal Research under contract No.SKLECKF202104+3 种基金the Zhejiang Provincial Natural Science Foundation of China under contract No.LY22D010002the National Science Foundation for Post-doctoral Scientists of China under contract No.2020M683258the Chongqing Technology Innovation and Application Development Special Project under contract No.cstc2020jscx-msxm X0193the Sichuan Science and Technology Program under contract No.2018JY0484
文摘Ocean currents are a key element in ocean processes and in meteorology,affecting material transport and modulating climate change patterns.The Doppler frequency shift information of the synthetic aperture radar(SAR)echo signal can reflect the dynamic characteristics of the sea surface,and has become an essential sea surface dynamic remote sensing parameter.Studies have verified that the instantaneous Doppler frequency shift can realize the SAR detection of the sea surface current.However,the validation of SAR-derived ocean current data and a thorough analysis of the errors associated with them remain lacking.In this study,we derive high spatial resolution flow measurements for the Kuroshio in the East China Sea from SAR data using a theoretical model of shifts in Doppler frequency driven by ocean surface current.Global ocean multi observation(MOB)products and global surface Lagrangian drifter(GLD)data are used to validate the Kuroshio flow retrieved from the SAR data.Results show that the central flow velocity for the Kuroshio derived from the SAR is 0.4–1.5 m/s.The error distribution between SAR ocean currents and MOB products is an approximate standard normal distribution,with the 90%confidence interval concentrated between–0.1 m/s and 0.1 m/s.Comparative analysis of SAR ocean current and GLD products,the correlation coefficient is 0.803,which shows to be significant at a confidence level of 99%.The cross-validation of different ocean current dataset illustrate that the SAR radial current captures the positions and dynamics of the Kuroshio central flow and the Kuroshio Counter Current,and has the capability to monitor current velocity over a wide range of values.
基金Supported by the National Natural Science Foundation of China and the Foundation of Doctoral Education of China。
文摘The method of multiple-scales is used to investigate the nonlinear modulation of capillary-gravity waves with cylindrical symmetry.We find that the evolution of wave-packets is described by a nonlinear schrödinger-like equation i(U+U/2r)+αUξξ+β|U|2U=0.Some exact and explicit cylindrical envelope solitary wave solutions are also obtained by means of variable transformations.
基金Project supported by the National Natural Science Foundation of China.
文摘By means of the optimized expansion technique, the D + 1-dimensional quantum sine-Gordon (sG) field theory is studied nonperturbatively for both zero and finite temperatures.In 1 + 1 and 2+ 1 dimensions, the theory is finite when momentum cutoff Λ tends to infinity.The temperature-dependent Coleman phase transition conditions we obtained reduce to theknown results g_(cr)~2 =8π for 1+ 1 dimensions and g_(cr)~2= 16π/m_(RO) for 2+ 1 dimensions whenT→0. Especially, g_(cr) tends to zero at T→∞ limit both for 1 + 1 and 2 + 1 dimensions. Thereis no critical temperature making the Φ= 0 vacuum unstable. In 3 + 1 dimensions, if g^2 isfinite and Λ→∞, the theory is trivial. There is no nontrivial 'precarious' phase for the3+ 1-dimensional sG model. The effective potential for the 'autonomous' phase has asimilar form as the classical potential and the temperature effects only make contribution tothe infinitesimal part of this phase.
