With respect to oceanic fluid dynamics,certain models have appeared,e.g.,an extended time-dependent(3+1)-dimensional shallow water wave equation in an ocean or a river,which we investigate in this paper.Using symbolic...With respect to oceanic fluid dynamics,certain models have appeared,e.g.,an extended time-dependent(3+1)-dimensional shallow water wave equation in an ocean or a river,which we investigate in this paper.Using symbolic computation,we find out,on one hand,a set of bilinear auto-Backlund transformations,which could connect certain solutions of that equation with other solutions of that equation itself,and on the other hand,a set of similarity reductions,which could go from that equation to a known ordinary differential equation.The results in this paper depend on all the oceanic variable coefficients in that equation.展开更多
This paper proposes a novel cargo loading algorithm applicable to automated conveyor-type loading systems.The algorithm offers improvements in computational efficiency and robustness by utilizing the concept of discre...This paper proposes a novel cargo loading algorithm applicable to automated conveyor-type loading systems.The algorithm offers improvements in computational efficiency and robustness by utilizing the concept of discrete derivatives and introducing logistics-related constraints.Optional consideration of the rotation of the cargoes was made to further enhance the optimality of the solutions,if possible to be physically implemented.Evaluation metrics were developed for accurate evaluation and enhancement of the algorithm’s ability to efficiently utilize the loading space and provide a high level of dynamic stability.Experimental results demonstrate the extensive robustness of the proposed algorithm to the diversity of cargoes present in Business-to-Consumer environments.This study contributes practical advancements in both cargo loading optimization and automation of the logistics industry,with potential applications in last-mile delivery services,warehousing,and supply chain management.展开更多
Recently, during the investigations on planetary oceans, Hirota-Satsuma-Ito-type models have been developed. In this paper, for a(2+1)-dimensional generalized variable-coefficient Hirota-Satsuma-Ito system describing ...Recently, during the investigations on planetary oceans, Hirota-Satsuma-Ito-type models have been developed. In this paper, for a(2+1)-dimensional generalized variable-coefficient Hirota-Satsuma-Ito system describing the fluid dynamics of shallow-water waves in an open ocean, non-characteristic movable singular manifold and symbolic computation enable an oceanic auto-B?cklund transformation with three sets of the oceanic solitonic solutions. The results rely on the oceanic variable coefficients in that system. Future oceanic observations might detect some nonlinear features predicted in this paper, and relevant oceanographic insights might be expected.展开更多
The fracture and migration patterns of direct roofs play a critical role in excavation stability and mining pressure.However,current methods fail to capture the irregular three-dimensional(3D)behavior of these roofs.I...The fracture and migration patterns of direct roofs play a critical role in excavation stability and mining pressure.However,current methods fail to capture the irregular three-dimensional(3D)behavior of these roofs.In this study,the problem was solved by introducing an innovative 2.5-dimensional(2.5D)Voronoi numerical simulation method,dividing rock layers into 2.5D Voronoi blocks and developing cohesive element-based failure models,supported by a strain-softening HoekeBrown model.The method was applied to the 8311 working face in the Taishan Mine in China,and its accuracy was confirmed through physical experiments.The following conclusions were drawn.The first roof break typically followed an"O-X"pattern.The direct roof did not break randomly over time;instead,it followed three distinct scenarios:(1)A complete break of the direct roof occurred,followed by a sequential collapse(ScenarioⅠ).(2)Regional irregular stacking in one area was followed by sequential collapse in other zones(ScenarioⅡ).(3)The staged breakdown of the direct roof led to separate and sequential collapses on the left and right flanks(ScenarioⅢ).Scenario I was quite common during the 400 m advance of the working face and occurred five times.The fracture characteristics in Scenario I led to widespread pressure on the hydraulic supports in the middle of the working face.Finally,the direct roof from the working face towards the goaf area underwent phases of overhanging,hinging,and collapsing plates.After the first and periodic breaks,the basic roof formed stable hinged plate structures reinforced by overhanging plates and irregular accumulations of the direct roof.展开更多
In this work,we study wave state transitions of the(2+1)-dimensional Kortewegde Vries-Sawada-Kotera-Ramani(2KdVSKR)equation by analyzing the characteristic line and phase shift.By converting the wave parameters of the...In this work,we study wave state transitions of the(2+1)-dimensional Kortewegde Vries-Sawada-Kotera-Ramani(2KdVSKR)equation by analyzing the characteristic line and phase shift.By converting the wave parameters of the N-soliton solution into complex numbers,the breath wave solution is constructed.The lump wave solution is derived through the long wave limit method.Then,by choosing appropriate parameter values,we acquire a number of transformed nonlinear waves whose gradient relation is discussed according to the ratio of the wave parameters.Furthermore,we reveal transition mechanisms of the waves by exploring the nonlinear superposition of the solitary and periodic wave components.Subsequently,locality,oscillation properties and evolutionary phenomenon of the transformed waves are presented.And we also prove the change in the geometrical properties of the characteristic lines leads to the phenomena of wave evolution.Finally,for higher-order waves,a range of interaction models are depicted along with their evolutionary phenomena.And we demonstrate that their diversity is due to the fact that the solitary and periodic wave components produce different phase shifts caused by time evolution and collisions.展开更多
In this paper,we investigate the(2+1)-dimensional three-component long-wave-short-wave resonance interaction system,which describes complex systems and nonlinear wave phenomena in physics.By employing the Hirota bilin...In this paper,we investigate the(2+1)-dimensional three-component long-wave-short-wave resonance interaction system,which describes complex systems and nonlinear wave phenomena in physics.By employing the Hirota bilinear method,we derive the general nondegenerate N-soliton solution of the system,where each short-wave component contains N arbitrary functions of the independent variable y.The presence of these arbitrary functions in the analytical solution enables the construction of a wide range of nondegenerate soliton types.Finally,we illustrate the structural features of several novel nondegenerate solitons,including M-shaped,multiple double-hump,and sawtooth double-striped solitons,as well as interactions between nondegenerate solitons,such as dromion-like solitons and solitoffs,with the aid of figures.展开更多
Lie symmetry analysis is applied to a(3+1)-dimensional combined potential Kadomtsev-Petviashvili equation with B-type Kadomtsev-Petviashvili equation(pKP-BKP equation)and the corresponding similarity reduction equatio...Lie symmetry analysis is applied to a(3+1)-dimensional combined potential Kadomtsev-Petviashvili equation with B-type Kadomtsev-Petviashvili equation(pKP-BKP equation)and the corresponding similarity reduction equations are obtained with the different infinitesimal generators.Invariant solutions with arbitrary functions and constants for the(3+1)-dimensional pKP-BKP equation,including the lump solution,the periodic-lump solution,the two-kink solution,the breather solution and the lump-two-kink solution,have been studied analytically and graphically.展开更多
Two Darboux transformations of the(2+1)-dimensional Caudrey–Dodd–Gibbon–Kotera–Sawaka(CDGKS)equation and(2+1)-dimensional modified Korteweg-de Vries(mKdV) equation are constructed through the Darboux matrix method...Two Darboux transformations of the(2+1)-dimensional Caudrey–Dodd–Gibbon–Kotera–Sawaka(CDGKS)equation and(2+1)-dimensional modified Korteweg-de Vries(mKdV) equation are constructed through the Darboux matrix method, respectively. N-soliton solutions of these two equations are presented by applying the Darboux transformations N times. The right-going bright single-soliton solution and interactions of two and three-soliton overtaking collisions of the(2+1)-dimensional CDGKS equation are studied. By choosing different seed solutions, the right-going bright and left-going dark single-soliton solutions, the interactions of two and three-soliton overtaking collisions, and kink soliton solutions of the(2+1)-dimensional mKdV equation are investigated. The results can be used to illustrate the interactions of water waves in shallow water.展开更多
Based on the extended mapping deformation method and symbolic computation, many exact travelling wave solutions are found for the (3+1)-dimensional JM equation and the (3+1)-dimensional KP equation. The obtained solut...Based on the extended mapping deformation method and symbolic computation, many exact travelling wave solutions are found for the (3+1)-dimensional JM equation and the (3+1)-dimensional KP equation. The obtained solutions include solitary solution, periodic wave solution, rational travelling wave solution, and Jacobian and Weierstrass function solution, etc.展开更多
The purpose of this review is to provide a definitive account of small intestinal mucosal structure and interpretation. The coeliac lesion has been well known, but not well described to date and this review aims to id...The purpose of this review is to provide a definitive account of small intestinal mucosal structure and interpretation. The coeliac lesion has been well known, but not well described to date and this review aims to identify the interpretative difficulties which have arisen over time with the histological assessment of coeliac disease. In early coeliac interpretation, there were significant inaccuracies, particularly surrounding intraepithelial lymphocyte counts and the degree of villous flattening which occurred in the tissue. Many of these interpretive pitfalls are still encountered today, increasing the potential for diagnostic errors. These difficulties are mostly due to the fact that stained 2-dimensional sections can never truly represent the 3-dimensional framework of the intestinal tissue under investigation. Therefore, this review offers a critical account occasioned by these 2-dimensional interpretative errors and which, in our opinion, should in general be jettisoned. As a result, we leave a framework regarding the true 3-dimensional knowledge of mucosal structure accrued over the 70-year period of study, and one which is available for future reference.展开更多
For describing various complex nonlinear phenomena in the realistic world,the higher-dimensional nonlinearevolution equations appear more attractive in many fields of physical and engineering sciences.In this paper,by...For describing various complex nonlinear phenomena in the realistic world,the higher-dimensional nonlinearevolution equations appear more attractive in many fields of physical and engineering sciences.In this paper,by virtueof the Hirota bilinear method and Riemann theta functions,the periodic wave solutions for the(2+1)-dimensionalBoussinesq equation and(3+1)-dimensional Kadomtsev-Petviashvili(KP)equation are obtained.Furthermore,it isshown that the known soliton solutions for the two equations can be reduced from the periodic wave solutions.展开更多
In this paper, we introduce the notion of a （2＋1）-dimenslonal differential equation describing three-dimensional hyperbolic spaces （3-h.s.）. The （2＋1）-dimensional coupled nonlinear Schrodinger equation and its...In this paper, we introduce the notion of a （2＋1）-dimenslonal differential equation describing three-dimensional hyperbolic spaces （3-h.s.）. The （2＋1）-dimensional coupled nonlinear Schrodinger equation and its sister equation, the （2＋1）-dimensional coupled derivative nonlinear Schrodinger equation, are shown to describe 3-h.s, The （2 ＋ 1 ）-dimensional generalized HF model：St=（1/2i[S,Sy]＋2iσS）x,σx=-1/4i tr（SSxSy）, in which S ∈ GLc（2）/GLc（1）×GLc（1）,provides another example of （2＋1）-dimensional differential equations describing 3-h.s. As a direct con-sequence, the geometric construction of an infinire number of conservation lairs of such equations is illustrated. Furthermore we display a new infinite number of conservation lairs of the （2＋1）-dimensional nonlinear Schrodinger equation and the （2＋1）-dimensional derivative nonlinear Schrodinger equation by a geometric way.展开更多
In this paper, the entangled mapping approach （EMA） is applied to obtain variable separation solutions of （1＋1）-dimensional and （3＋1）-dimensional systems. By analysis, we firstly find that there also exists a ...In this paper, the entangled mapping approach （EMA） is applied to obtain variable separation solutions of （1＋1）-dimensional and （3＋1）-dimensional systems. By analysis, we firstly find that there also exists a common formula to describe suitable physical fields or potentials for these （1＋1）-dimensional models such as coupled integrable dispersionless （CID） and shallow water wave equations. Moreover, we find that the variable separation solution of the （3＋1）-dimensional Burgers system satisfies the completely same form as the universal quantity U1 in （2＋1）-dimensional systems. The only difference is that the function q is a solution of a constraint equation and p is an arbitrary function of three independent variables.展开更多
A theory of（N＋1）-dimensional gravity is developed on the basis of the teleparallel equivalent of general relativity（TEGR）.The fundamental gravitational field variables are the（N＋1）-dimensional vector fields,de...A theory of（N＋1）-dimensional gravity is developed on the basis of the teleparallel equivalent of general relativity（TEGR）.The fundamental gravitational field variables are the（N＋1）-dimensional vector fields,defined globally on a manifold M,and the gravitational field is attributed to the torsion.The form of Lagrangian density is quadratic in torsion tensor.We then give an exact five-dimensional spherically symmetric solution（Schwarzschild（4＋1）-dimensions）.Finally,we calculate energy and spatial momentum using gravitational energy-momentum tensor and superpotential 2-form.展开更多
A theory of （1＋1）-dimensional gravity is constructed on the basis of the teleparallel equivalent of general relativity. The fundamental field variables are the tetrad fields ei^μ and the gravity is attributed to t...A theory of （1＋1）-dimensional gravity is constructed on the basis of the teleparallel equivalent of general relativity. The fundamental field variables are the tetrad fields ei^μ and the gravity is attributed to the torsion. A dilatonic spherically symmetric exact solution of the gravitational field equations characterized by two parameters M and Q is derived. The energy associated with this solution is calculated using the two-dimensional gravitational energy- momentum formula.展开更多
The variable separation approach is used to obtain localized coherent structures of the new (2+1)-dimensional nonlinear partialdifferential equation. Applying the Backlund transformation and introducing the arbitraryf...The variable separation approach is used to obtain localized coherent structures of the new (2+1)-dimensional nonlinear partialdifferential equation. Applying the Backlund transformation and introducing the arbitraryfunctions of the seed solutions, the abundance of the localized structures of this model are derived. Some special types ofsolutions solitoff, dromions, dromion lattice, breathers and instantons are discussed by selecting the arbitrary functionsappropriately. The breathers may breath in their amplititudes, shapes, distances among the peaks and even the numberof the peaks.展开更多
We study the localized coherent structures ofa generally nonintegrable (2+ 1 )-dimensional KdV equation via a variable separation approach. In a special integrable case, the entrance of some arbitrary functions leads ...We study the localized coherent structures ofa generally nonintegrable (2+ 1 )-dimensional KdV equation via a variable separation approach. In a special integrable case, the entrance of some arbitrary functions leads to abundant coherent structures. However, in the general nonintegrable case, an additional condition has to be introduced for these arbitrary functions. Although the additional condition has been introduced into the solutions of the nonintegrable KdV equation, there still exist many interesting solitary wave structures. Especially, the nonintegrable KdV equation possesses the breather-like localized excitations, and the similar static ring soliton solutions as in the integrable case. Furthermor,in the integrable case, the interaction between two travelling ring solitons is elastic, while in the nonintegrable case we cannot find even the single travelling ring soliton solution.展开更多
A complete discrimination system for the fourth order polynomial is given. As an application, we have reduced a （1＋1）-dimensional dispersive long wave equation with general coefficients to an elementary integral fo...A complete discrimination system for the fourth order polynomial is given. As an application, we have reduced a （1＋1）-dimensional dispersive long wave equation with general coefficients to an elementary integral form and obtained its all possible exact travelling wave solutions including rational function type solutions, solitary wave solutions, triangle function type periodic solutions and Jacobian elliptic functions double periodic solutions. This method can be also applied to many other similar problems.展开更多
The research work has been seldom done about cloverleaf junction expression in a 3-dimensional city model (3DCM). The main reason is that the cloverleaf junction is often in a complex and enormous construction. Its ma...The research work has been seldom done about cloverleaf junction expression in a 3-dimensional city model (3DCM). The main reason is that the cloverleaf junction is often in a complex and enormous construction. Its main body is bestraddle in air,and has aerial intersections between its parts. This complex feature made cloverleaf junction quite different from buildings and terrain, therefore, it is difficult to express this kind of spatial objects in the same way as for buildings and terrain. In this paper,authors analyze spatial characteristics of cloverleaf junction, propose an all-constraint points TIN algorithm to partition cloverleaf junction road surface, and develop a method to visualize cloverleaf junction road surface using TIN. In order to manage cloverleaf junction data efficiently, the authors also analyzed the mechanism of 3DCM data management, extended BLOB type in relational database, and combined R-tree index to manage 3D spatial data. Based on this extension, an appropriate data展开更多
In this paper, a class of lump solutions to the (2+1)-dimensional Sawada–Kotera equation is studied by searching for positive quadratic function solutions to the associated bilinear equation. To guarantee rational lo...In this paper, a class of lump solutions to the (2+1)-dimensional Sawada–Kotera equation is studied by searching for positive quadratic function solutions to the associated bilinear equation. To guarantee rational localization and analyticity of the lumps, some sufficient and necessary conditions are presented on the parameters involved in the solutions. Then, a completely non-elastic interaction between a lump and a stripe of the(2+1)-dimensional Sawada–Kotera equation is obtained, which shows a lump solution is drowned or swallowed by a stripe soliton. Finally, 2-dimensional curves, 3-dimensional plots and density plots with particular choices of the involved parameters are presented to show the dynamic characteristics of the obtained lump and interaction solutions.展开更多
基金financially supported by the Scientific Research Foundation of North China University of Technology(Grant Nos.11005136024XN147-87 and 110051360024XN151-86).
文摘With respect to oceanic fluid dynamics,certain models have appeared,e.g.,an extended time-dependent(3+1)-dimensional shallow water wave equation in an ocean or a river,which we investigate in this paper.Using symbolic computation,we find out,on one hand,a set of bilinear auto-Backlund transformations,which could connect certain solutions of that equation with other solutions of that equation itself,and on the other hand,a set of similarity reductions,which could go from that equation to a known ordinary differential equation.The results in this paper depend on all the oceanic variable coefficients in that equation.
基金supported by the BK21 FOUR funded by the Ministry of Education of Korea and National Research Foundation of Korea,a Korea Agency for Infrastructure Technology Advancement(KAIA)grant funded by the Ministry of Land,Infrastructure,and Transport(Grant 1615013176)IITP(Institute of Information&Coummunications Technology Planning&Evaluation)-ICAN(ICT Challenge and Advanced Network of HRD)grant funded by the Korea government(Ministry of Science and ICT)(RS-2024-00438411).
文摘This paper proposes a novel cargo loading algorithm applicable to automated conveyor-type loading systems.The algorithm offers improvements in computational efficiency and robustness by utilizing the concept of discrete derivatives and introducing logistics-related constraints.Optional consideration of the rotation of the cargoes was made to further enhance the optimality of the solutions,if possible to be physically implemented.Evaluation metrics were developed for accurate evaluation and enhancement of the algorithm’s ability to efficiently utilize the loading space and provide a high level of dynamic stability.Experimental results demonstrate the extensive robustness of the proposed algorithm to the diversity of cargoes present in Business-to-Consumer environments.This study contributes practical advancements in both cargo loading optimization and automation of the logistics industry,with potential applications in last-mile delivery services,warehousing,and supply chain management.
基金financially supported by the Scientific Research Foundation of North China University of Technology (Grant Nos.11005136024XN147-87 and 110051360024XN151-86)。
文摘Recently, during the investigations on planetary oceans, Hirota-Satsuma-Ito-type models have been developed. In this paper, for a(2+1)-dimensional generalized variable-coefficient Hirota-Satsuma-Ito system describing the fluid dynamics of shallow-water waves in an open ocean, non-characteristic movable singular manifold and symbolic computation enable an oceanic auto-B?cklund transformation with three sets of the oceanic solitonic solutions. The results rely on the oceanic variable coefficients in that system. Future oceanic observations might detect some nonlinear features predicted in this paper, and relevant oceanographic insights might be expected.
基金supported by the Autonomous General Projects of the State Key Laboratory of Coal Mine Disaster Dynamics and Control,Chongqing University,China(Grant No.2011DA105287-MS202209)the National Natural Science Foundation of China,China(Grant Nos.52304149 and 52204127).
文摘The fracture and migration patterns of direct roofs play a critical role in excavation stability and mining pressure.However,current methods fail to capture the irregular three-dimensional(3D)behavior of these roofs.In this study,the problem was solved by introducing an innovative 2.5-dimensional(2.5D)Voronoi numerical simulation method,dividing rock layers into 2.5D Voronoi blocks and developing cohesive element-based failure models,supported by a strain-softening HoekeBrown model.The method was applied to the 8311 working face in the Taishan Mine in China,and its accuracy was confirmed through physical experiments.The following conclusions were drawn.The first roof break typically followed an"O-X"pattern.The direct roof did not break randomly over time;instead,it followed three distinct scenarios:(1)A complete break of the direct roof occurred,followed by a sequential collapse(ScenarioⅠ).(2)Regional irregular stacking in one area was followed by sequential collapse in other zones(ScenarioⅡ).(3)The staged breakdown of the direct roof led to separate and sequential collapses on the left and right flanks(ScenarioⅢ).Scenario I was quite common during the 400 m advance of the working face and occurred five times.The fracture characteristics in Scenario I led to widespread pressure on the hydraulic supports in the middle of the working face.Finally,the direct roof from the working face towards the goaf area underwent phases of overhanging,hinging,and collapsing plates.After the first and periodic breaks,the basic roof formed stable hinged plate structures reinforced by overhanging plates and irregular accumulations of the direct roof.
基金supported by the National Natural Science Foundation of China(12371255,11975306)the Xuzhou Basic Research Program Project(KC23048)+1 种基金the Six Talent Peaks Project in Jiangsu Province(JY-059)the 333 Project in Jiangsu Province and the Fundamental Research Funds for the Central Universities of CUMT(2024ZDPYJQ1003).
文摘In this work,we study wave state transitions of the(2+1)-dimensional Kortewegde Vries-Sawada-Kotera-Ramani(2KdVSKR)equation by analyzing the characteristic line and phase shift.By converting the wave parameters of the N-soliton solution into complex numbers,the breath wave solution is constructed.The lump wave solution is derived through the long wave limit method.Then,by choosing appropriate parameter values,we acquire a number of transformed nonlinear waves whose gradient relation is discussed according to the ratio of the wave parameters.Furthermore,we reveal transition mechanisms of the waves by exploring the nonlinear superposition of the solitary and periodic wave components.Subsequently,locality,oscillation properties and evolutionary phenomenon of the transformed waves are presented.And we also prove the change in the geometrical properties of the characteristic lines leads to the phenomena of wave evolution.Finally,for higher-order waves,a range of interaction models are depicted along with their evolutionary phenomena.And we demonstrate that their diversity is due to the fact that the solitary and periodic wave components produce different phase shifts caused by time evolution and collisions.
基金supported by the National Natural Science Foundation of China,Grant No.12375006。
文摘In this paper,we investigate the(2+1)-dimensional three-component long-wave-short-wave resonance interaction system,which describes complex systems and nonlinear wave phenomena in physics.By employing the Hirota bilinear method,we derive the general nondegenerate N-soliton solution of the system,where each short-wave component contains N arbitrary functions of the independent variable y.The presence of these arbitrary functions in the analytical solution enables the construction of a wide range of nondegenerate soliton types.Finally,we illustrate the structural features of several novel nondegenerate solitons,including M-shaped,multiple double-hump,and sawtooth double-striped solitons,as well as interactions between nondegenerate solitons,such as dromion-like solitons and solitoffs,with the aid of figures.
文摘Lie symmetry analysis is applied to a(3+1)-dimensional combined potential Kadomtsev-Petviashvili equation with B-type Kadomtsev-Petviashvili equation(pKP-BKP equation)and the corresponding similarity reduction equations are obtained with the different infinitesimal generators.Invariant solutions with arbitrary functions and constants for the(3+1)-dimensional pKP-BKP equation,including the lump solution,the periodic-lump solution,the two-kink solution,the breather solution and the lump-two-kink solution,have been studied analytically and graphically.
基金Supported by the National Natural Science Foundation of China under Grant Nos.11075055,11275072Innovative Research Team Program of the National Science Foundation of China under Grant No.61021104+3 种基金National High Technology Research and Development Program under Grant No.2011AA010101Shanghai Knowledge Service Platform for Trustworthy Internet of Things under Grant No.ZF1213Talent FundK.C.Wong Magna Fund in Ningbo University
文摘Two Darboux transformations of the(2+1)-dimensional Caudrey–Dodd–Gibbon–Kotera–Sawaka(CDGKS)equation and(2+1)-dimensional modified Korteweg-de Vries(mKdV) equation are constructed through the Darboux matrix method, respectively. N-soliton solutions of these two equations are presented by applying the Darboux transformations N times. The right-going bright single-soliton solution and interactions of two and three-soliton overtaking collisions of the(2+1)-dimensional CDGKS equation are studied. By choosing different seed solutions, the right-going bright and left-going dark single-soliton solutions, the interactions of two and three-soliton overtaking collisions, and kink soliton solutions of the(2+1)-dimensional mKdV equation are investigated. The results can be used to illustrate the interactions of water waves in shallow water.
文摘Based on the extended mapping deformation method and symbolic computation, many exact travelling wave solutions are found for the (3+1)-dimensional JM equation and the (3+1)-dimensional KP equation. The obtained solutions include solitary solution, periodic wave solution, rational travelling wave solution, and Jacobian and Weierstrass function solution, etc.
文摘The purpose of this review is to provide a definitive account of small intestinal mucosal structure and interpretation. The coeliac lesion has been well known, but not well described to date and this review aims to identify the interpretative difficulties which have arisen over time with the histological assessment of coeliac disease. In early coeliac interpretation, there were significant inaccuracies, particularly surrounding intraepithelial lymphocyte counts and the degree of villous flattening which occurred in the tissue. Many of these interpretive pitfalls are still encountered today, increasing the potential for diagnostic errors. These difficulties are mostly due to the fact that stained 2-dimensional sections can never truly represent the 3-dimensional framework of the intestinal tissue under investigation. Therefore, this review offers a critical account occasioned by these 2-dimensional interpretative errors and which, in our opinion, should in general be jettisoned. As a result, we leave a framework regarding the true 3-dimensional knowledge of mucosal structure accrued over the 70-year period of study, and one which is available for future reference.
基金supported by the National Natural Science Foundation of China under Grant Nos.60772023 and 60372095the Key Project of the Ministry of Education under Grant No.106033+3 种基金the Open Fund of the State Key Laboratory of Software Development Environment under Grant No.SKLSDE-07-001Beijing University of Aeronautics and Astronauticsthe National Basic Research Program of China(973 Program)under Grant No.2005CB321901the Specialized Research Fund for the Doctoral Program of Higher Education of the Ministry of Education under Grant No.20060006024
文摘For describing various complex nonlinear phenomena in the realistic world,the higher-dimensional nonlinearevolution equations appear more attractive in many fields of physical and engineering sciences.In this paper,by virtueof the Hirota bilinear method and Riemann theta functions,the periodic wave solutions for the(2+1)-dimensionalBoussinesq equation and(3+1)-dimensional Kadomtsev-Petviashvili(KP)equation are obtained.Furthermore,it isshown that the known soliton solutions for the two equations can be reduced from the periodic wave solutions.
基金The project partially supported by National Natural Science Foundation of China
文摘In this paper, we introduce the notion of a （2＋1）-dimenslonal differential equation describing three-dimensional hyperbolic spaces （3-h.s.）. The （2＋1）-dimensional coupled nonlinear Schrodinger equation and its sister equation, the （2＋1）-dimensional coupled derivative nonlinear Schrodinger equation, are shown to describe 3-h.s, The （2 ＋ 1 ）-dimensional generalized HF model：St=（1/2i[S,Sy]＋2iσS）x,σx=-1/4i tr（SSxSy）, in which S ∈ GLc（2）/GLc（1）×GLc（1）,provides another example of （2＋1）-dimensional differential equations describing 3-h.s. As a direct con-sequence, the geometric construction of an infinire number of conservation lairs of such equations is illustrated. Furthermore we display a new infinite number of conservation lairs of the （2＋1）-dimensional nonlinear Schrodinger equation and the （2＋1）-dimensional derivative nonlinear Schrodinger equation by a geometric way.
基金The authors express their sincere thanks to the anonymous referees for their constructive suggestions and kind help.
文摘In this paper, the entangled mapping approach （EMA） is applied to obtain variable separation solutions of （1＋1）-dimensional and （3＋1）-dimensional systems. By analysis, we firstly find that there also exists a common formula to describe suitable physical fields or potentials for these （1＋1）-dimensional models such as coupled integrable dispersionless （CID） and shallow water wave equations. Moreover, we find that the variable separation solution of the （3＋1）-dimensional Burgers system satisfies the completely same form as the universal quantity U1 in （2＋1）-dimensional systems. The only difference is that the function q is a solution of a constraint equation and p is an arbitrary function of three independent variables.
文摘A theory of（N＋1）-dimensional gravity is developed on the basis of the teleparallel equivalent of general relativity（TEGR）.The fundamental gravitational field variables are the（N＋1）-dimensional vector fields,defined globally on a manifold M,and the gravitational field is attributed to the torsion.The form of Lagrangian density is quadratic in torsion tensor.We then give an exact five-dimensional spherically symmetric solution（Schwarzschild（4＋1）-dimensions）.Finally,we calculate energy and spatial momentum using gravitational energy-momentum tensor and superpotential 2-form.
文摘A theory of （1＋1）-dimensional gravity is constructed on the basis of the teleparallel equivalent of general relativity. The fundamental field variables are the tetrad fields ei^μ and the gravity is attributed to the torsion. A dilatonic spherically symmetric exact solution of the gravitational field equations characterized by two parameters M and Q is derived. The energy associated with this solution is calculated using the two-dimensional gravitational energy- momentum formula.
基金The project supported by National Natural Science Foundation of China
文摘The variable separation approach is used to obtain localized coherent structures of the new (2+1)-dimensional nonlinear partialdifferential equation. Applying the Backlund transformation and introducing the arbitraryfunctions of the seed solutions, the abundance of the localized structures of this model are derived. Some special types ofsolutions solitoff, dromions, dromion lattice, breathers and instantons are discussed by selecting the arbitrary functionsappropriately. The breathers may breath in their amplititudes, shapes, distances among the peaks and even the numberof the peaks.
文摘We study the localized coherent structures ofa generally nonintegrable (2+ 1 )-dimensional KdV equation via a variable separation approach. In a special integrable case, the entrance of some arbitrary functions leads to abundant coherent structures. However, in the general nonintegrable case, an additional condition has to be introduced for these arbitrary functions. Although the additional condition has been introduced into the solutions of the nonintegrable KdV equation, there still exist many interesting solitary wave structures. Especially, the nonintegrable KdV equation possesses the breather-like localized excitations, and the similar static ring soliton solutions as in the integrable case. Furthermor,in the integrable case, the interaction between two travelling ring solitons is elastic, while in the nonintegrable case we cannot find even the single travelling ring soliton solution.
文摘A complete discrimination system for the fourth order polynomial is given. As an application, we have reduced a （1＋1）-dimensional dispersive long wave equation with general coefficients to an elementary integral form and obtained its all possible exact travelling wave solutions including rational function type solutions, solitary wave solutions, triangle function type periodic solutions and Jacobian elliptic functions double periodic solutions. This method can be also applied to many other similar problems.
文摘The research work has been seldom done about cloverleaf junction expression in a 3-dimensional city model (3DCM). The main reason is that the cloverleaf junction is often in a complex and enormous construction. Its main body is bestraddle in air,and has aerial intersections between its parts. This complex feature made cloverleaf junction quite different from buildings and terrain, therefore, it is difficult to express this kind of spatial objects in the same way as for buildings and terrain. In this paper,authors analyze spatial characteristics of cloverleaf junction, propose an all-constraint points TIN algorithm to partition cloverleaf junction road surface, and develop a method to visualize cloverleaf junction road surface using TIN. In order to manage cloverleaf junction data efficiently, the authors also analyzed the mechanism of 3DCM data management, extended BLOB type in relational database, and combined R-tree index to manage 3D spatial data. Based on this extension, an appropriate data
基金Supported by the Global Change Research Program of China under Grant No.2015CB953904National Natural Science Foundation of China under Grant Nos.11675054 and 11435005+1 种基金Outstanding Doctoral Dissertation Cultivation Plan of Action under Grant No.YB2016039Shanghai Collaborative Innovation Center of Trustworthy Software for Internet of Things under Grant No.ZF1213
文摘In this paper, a class of lump solutions to the (2+1)-dimensional Sawada–Kotera equation is studied by searching for positive quadratic function solutions to the associated bilinear equation. To guarantee rational localization and analyticity of the lumps, some sufficient and necessary conditions are presented on the parameters involved in the solutions. Then, a completely non-elastic interaction between a lump and a stripe of the(2+1)-dimensional Sawada–Kotera equation is obtained, which shows a lump solution is drowned or swallowed by a stripe soliton. Finally, 2-dimensional curves, 3-dimensional plots and density plots with particular choices of the involved parameters are presented to show the dynamic characteristics of the obtained lump and interaction solutions.
