The sweetpotato whitefly Bemisia tabaci(Homoptera:Aleyrodidae)is a destructive pest of agriculture and horticulture worldwide.Recent phylogenetic analysis using mitochondrial cytochrome oxidase 1 sequences indicate...The sweetpotato whitefly Bemisia tabaci(Homoptera:Aleyrodidae)is a destructive pest of agriculture and horticulture worldwide.Recent phylogenetic analysis using mitochondrial cytochrome oxidase 1 sequences indicates that this whitefly is a species complex including at least 24 morphologically indistinguishable but genetically distinct cryptic species.In this study,the inter-species crosses of Middle East-Asia Minor 1(MEAM1),Mediterranean(MED)and Asia II 7 cryptic species,which were referred to as B,Q and Cv biotypes before,were conducted in two different devices,leaf cages(7 cm3)and cylinder cages(280 cm3),and at three temperatures of 22,30 and 38°C.Results indicated that no female progeny were produced in the reciprocal cross between MEAM1×Asia II 7,between MED×Asia II 7 cryptic species neither in leaf cage nor in cylinder cages,while 0.81 and 1.37% of females in the offspring were recorded in the reciprocal cross between MEAM1×MED in leaf cage experiments.Approximately 0.95-0.98% female progeny were recorded in the reciprocal cross between MEAM1×MED at 30°C,0.77% female progeny were recorded in the single cross direction between MEAM1 × MED at 22°C,and no female progeny were found in their reciprocal cross at 38°C in leaf cage.Our findings indicated that neither space dimension nor temperature have a significant effect on the hybridization of different B.tabaci cryptic species.展开更多
It is important to study the propagation and interaction of progressing waves of nonlinear equations in the class of piecewise smooth function. However, there has not been many works on that in multidimensional case. ...It is important to study the propagation and interaction of progressing waves of nonlinear equations in the class of piecewise smooth function. However, there has not been many works on that in multidimensional case. In 1985, J, Rauch & M. Reed have provad the existence and uniqueness of piecewise smooth solution for展开更多
This paper explains how a model of the universe can be constructed by incorporating time and space into geometry in a unique way to produce a 4-space dimension/1-time dimension model. The model can then show how dark ...This paper explains how a model of the universe can be constructed by incorporating time and space into geometry in a unique way to produce a 4-space dimension/1-time dimension model. The model can then show how dark matter can be the gravity that is produced by real matter that exists throughout our entire universe. The model can also show how dark energy is not an increase in energy that is causing the accelerated expansion of the universe, but is an accelerating decrease in matter throughout the universe as the stars and galaxies in the universe continue to convert matter into energy during their life cycles. And then the model can show how a fourth space dimension must exist in our universe to locate a point in space.展开更多
Kunio Hidano[4] has shown that the global and local C2-solutions for semilinear wave equations with spherical symmetry in three space dimensions. This paper studies the global and local C2-solutions for the semilinea...Kunio Hidano[4] has shown that the global and local C2-solutions for semilinear wave equations with spherical symmetry in three space dimensions. This paper studies the global and local C2-solutions for the semilinear wave equations without spherical symmetry in three space dimensions. A problem put forward by Hiroyuki Takamura[2] is partially answered.展开更多
In this paper, we consider a system of two cubic quasi-linear Klein-Gordon equations with different masses for small, smooth, compactly supported Cauchy data in one space dimension. We show that such a system has glob...In this paper, we consider a system of two cubic quasi-linear Klein-Gordon equations with different masses for small, smooth, compactly supported Cauchy data in one space dimension. We show that such a system has global existence when the nonlinearities satisfy a convenient null condition. Our results extend the global existence proved by Sunagawa recently under the non-resonance assumption to that under the resonance assumption.展开更多
Let {(Xi, Si, μi) : i ℃ N} be a sequence of probability measure spaces and (*Xi, L(*Si), L(*μi)) be the Loeb measure space with respect to (Xi, Si, μi) for i ℃ N. Let X =× Xi, S = ×Si,μ = ×μi. We...Let {(Xi, Si, μi) : i ℃ N} be a sequence of probability measure spaces and (*Xi, L(*Si), L(*μi)) be the Loeb measure space with respect to (Xi, Si, μi) for i ℃ N. Let X =× Xi, S = ×Si,μ = ×μi. We prove that × L(*Si) CL(*S) and in embedding meaning.展开更多
A variable dimensional state space(VDSS) has been proposed to improve the re-planning time when the robotic systems operate in large unknown environments.VDSS is constructed by uniforming lattice state space and gri...A variable dimensional state space(VDSS) has been proposed to improve the re-planning time when the robotic systems operate in large unknown environments.VDSS is constructed by uniforming lattice state space and grid state space.In VDSS,the lattice state space is only used to construct search space in the local area which is a small circle area near the robot,and grid state space elsewhere.We have tested VDSS with up to 80 indoor and outdoor maps in simulation and on segbot robot platform.Through the simulation and segbot robot experiments,it shows that exploring on VDSS is significantly faster than exploring on lattice state space by Anytime Dynamic A*(AD*) planner and VDSS is feasible to be used on robotic systems.展开更多
Outlier detection has very important applied value in data mining literature. Different outlier detection algorithms based on distinct theories have different definitions and mining processes. The three-dimensional sp...Outlier detection has very important applied value in data mining literature. Different outlier detection algorithms based on distinct theories have different definitions and mining processes. The three-dimensional space graph for constructing applied algorithms and an improved GridOf algorithm were proposed in terms of analyzing the existing outlier detection algorithms from criterion and theory. Key words outlier - detection - three-dimensional space graph - data mining CLC number TP 311. 13 - TP 391 Foundation item: Supported by the National Natural Science Foundation of China (70371015)Biography: ZHANG Jing (1975-), female, Ph. D, lecturer, research direction: data mining and knowledge discovery.展开更多
Assume that X and Y are real Banach spaces with the same finite dimension.In this paper we show that if a standard coarse isometry f:X→Y satisfies an integral convergence condition or weak stability on a basis,then t...Assume that X and Y are real Banach spaces with the same finite dimension.In this paper we show that if a standard coarse isometry f:X→Y satisfies an integral convergence condition or weak stability on a basis,then there exists a surjective linear isometry U:X→Y such that∥f(x)−Ux∥=o(∥x∥)as∥x∥→∞.This is a generalization about the result of Lindenstrauss and Szankowski on the same finite dimensional Banach spaces without the assumption of surjectivity.As a consequence,we also obtain a stability result forε-isometries which was established by Dilworth.展开更多
We report an integral imaging method with continuous imaging space. This method simultaneously reconstructs real and virtual images in the virtual mode, with a minimum gap that separates the entire imaging space into ...We report an integral imaging method with continuous imaging space. This method simultaneously reconstructs real and virtual images in the virtual mode, with a minimum gap that separates the entire imaging space into real and virtual space. Experimental results show that the gap is reduced to 45% of that in a conventional integral imaging system with the same parameters.展开更多
We present a new algorithm for manifold learning and nonlinear dimensionality reduction. Based on a set of unorganized data points sampled with noise from a parameterized manifold, the local geometry of the manifold i...We present a new algorithm for manifold learning and nonlinear dimensionality reduction. Based on a set of unorganized data points sampled with noise from a parameterized manifold, the local geometry of the manifold is learned by constructing an approximation for the tangent space at each point, and those tangent spaces are then aligned to give the global coordinates of the data points with respect to the underlying manifold. We also present an error analysis of our algorithm showing that reconstruction errors can be quite small in some cases. We illustrate our algorithm using curves and surfaces both in 2D/3D Euclidean spaces and higher dimensional Euclidean spaces. We also address several theoretical and algorithmic issues for further research and improvements.展开更多
为了解立体绿化领域研究进展、热点及趋势,基于中国知网(CNKI)和科学引文索引数据库(Web of Science),运用文献计量法和可视化文献分析软件(Cite Space)可视化分析法,分析2002—2021年立体绿化领域中英文文献资料。发现英文文献发文量...为了解立体绿化领域研究进展、热点及趋势,基于中国知网(CNKI)和科学引文索引数据库(Web of Science),运用文献计量法和可视化文献分析软件(Cite Space)可视化分析法,分析2002—2021年立体绿化领域中英文文献资料。发现英文文献发文量及其增长幅度均高于中文文献;目前立体绿化领域主要研究机构均集中于各大高校;英文文献相关研究涵盖的学科领域主要为环境科学与生态学、工程学、城市研究、科学技术等,中文文献相关研究主要集中在建筑科学与工程、林业、园艺等方面;立体绿化的热点研究领域集中在立体绿化生态效益、施工技术和植物研究等方面;英文文献相关研究早期关注生物多样性、气候调节等,近年来关注微气候、城市农业等,中文文献相关研究的发展趋势从早期对立体绿化的理论研究、技术探索逐渐拓展到对城市雨洪、建筑节能等层面的精细化研究。基于此,提出未来立体绿化研究应在学术交流合作、学科交叉研究、创新研究方法等层面逐步深入,以此丰富立体绿化研究对象和主题,并进一步把握其研究态势。展开更多
The solutions of the Laplace equation in n-dimensional space are studied.The angular eigenfunctions have the form of associated Jacobi polynomials.The radial solution of the Helmholtz equation is derived.
Let χ= be a metric space and let ε be a positive real number. Then a function f: X→Y is defined to be an ε-map if and only if for all y∈Y, the diameter of f-1(y)?is at most ε. In Theorem 10 we will give a new pr...Let χ= be a metric space and let ε be a positive real number. Then a function f: X→Y is defined to be an ε-map if and only if for all y∈Y, the diameter of f-1(y)?is at most ε. In Theorem 10 we will give a new proof for the following well known fact: if χ is totally bounded, then for all ε there exists a finite number n and a continuous ε-map fε: X→Rn (here Rn is the usual n-dimensional Euclidean space endowed with the Euclidean metric). If ε is “small”, then fε is “almost injective”;and still exists even if χ has infinite covering dimension (in this case, n depends on ε, of course). Contrary to the known proofs, our proof technique is effective in the sense, that it allows establishing estimations for n in terms of ε and structural properties of χ.展开更多
This paper advances a three-dimensional space interpolation method of grey / depth image sequence, which breaks free from the limit of original practical photographing route. Pictures can cruise at will in space. By u...This paper advances a three-dimensional space interpolation method of grey / depth image sequence, which breaks free from the limit of original practical photographing route. Pictures can cruise at will in space. By using space sparse sampling, great memorial capacity can be saved and reproduced scenes can be controlled. To solve time consuming and complex computations in three-dimensional interpolation algorithm, we have studied a fast and practical algorithm of scattered space lattice and that of 'Warp' algorithm with proper depth. By several simple aspects of three dimensional space interpolation, we succeed in developing some simple and practical algorithms. Some results of simulated experiments with computers have shown that the new method is absolutely feasible.展开更多
Various index structures have recently been proposed to facilitate high-dimensional KNN queries, among which the techniques of approximate vector presentation and one-dimensional (1D) transformation can break the curs...Various index structures have recently been proposed to facilitate high-dimensional KNN queries, among which the techniques of approximate vector presentation and one-dimensional (1D) transformation can break the curse of dimensionality. Based on the two techniques above, a novel high-dimensional index is proposed, called Bit-code and Distance based index (BD). BD is based on a special partitioning strategy which is optimized for high-dimensional data. By the definitions of bit code and transformation function, a high-dimensional vector can be first approximately represented and then transformed into a 1D vector, the key managed by a B+-tree. A new KNN search algorithm is also proposed that exploits the bit code and distance to prune the search space more effectively. Results of extensive experiments using both synthetic and real data demonstrated that BD out- performs the existing index structures for KNN search in high-dimensional spaces.展开更多
Mine safety have top-five disasters,which including the water,gas,fire,dust and geological dynamic disaster.The coal mine water disaster is one of the important factors which restricted the development of China’s coa...Mine safety have top-five disasters,which including the water,gas,fire,dust and geological dynamic disaster.The coal mine water disaster is one of the important factors which restricted the development of China’s coal production.It is showed by statistics that 60%of mine accidents are affected by groundwater,which not only result in the production losses,casualties and a variety of展开更多
The eigenvalue space of the canonical four-dimensional Chua's circuit which can realize every eigenvalue for fourdimensional system is studied in this paper. First, the analytical relations between the circuit parame...The eigenvalue space of the canonical four-dimensional Chua's circuit which can realize every eigenvalue for fourdimensional system is studied in this paper. First, the analytical relations between the circuit parameters and the eigenvalues of the system are established, and therefore all the circuit parameters can be determined explicitly by any given set of eigenvalues. Then, the eigenvalue space of the circuit is investigated in two cases by the nonlinear elements used. According to the types of the eigenvalues, some novel hyperchaotic attractors are presented. Further, the dynamic behaviours of the circuit are studied by the bifurcation diagrams and the Lyapunov spectra of the eigenvalues.展开更多
In two previous papers <a href="#ref1">[1]</a> and <a href="#ref2">[2]</a>, a structure for vector products in <em>n</em> dimensions was presented, and at the sa...In two previous papers <a href="#ref1">[1]</a> and <a href="#ref2">[2]</a>, a structure for vector products in <em>n</em> dimensions was presented, and at the same time it was possible to propose the existence of a vector analogous to the curl of a vector field, for a space of four dimensions. In continuation of these works, the objective is to develop, through dimensional analogy, the idea of a hypothetical vector field, associated with the classical electromagnetic wave. This hypothetical field has a possible mathematical existence only when considering a space of four dimensions. The properties of the electromagnetic wave are preserved and equations with mathematical forms analogous to those of Maxwell’s equations are presented.展开更多
In Newton’s classical physics, space and time are treated as absolute quantities. Space and time are treated as independent quantities and can be discussed sepa-rately. With his theory of relativity, Einstein proved ...In Newton’s classical physics, space and time are treated as absolute quantities. Space and time are treated as independent quantities and can be discussed sepa-rately. With his theory of relativity, Einstein proved that space and time are de-pendent and must be treated inseparably. Minkowski adopted a four-dimensional space-time frame and indirectly revealed the dependency of space and time by adding a constraint for an event interval. Since space and time are inseparable, a three-dimensional space-time frame can be constructed by embedding time into space to directly show the interdependency of space and time. The formula for time dilation, length contraction, and the Lorenz transformation can be derived from graphs utilizing this new frame. The proposed three-dimensional space-time frame is an alternate frame that can be used to describe motions of objects, and it may improve teaching and learning Special Relativity and provide additional insights into space and time.展开更多
基金funded by the National Basic Research Program of China(2009CB119203)the National NaturalScience Foundation of China(31071732)the Foundation of Lingnan Fruit Innovation Team of GuangdongProvince,China(2009-14)
文摘The sweetpotato whitefly Bemisia tabaci(Homoptera:Aleyrodidae)is a destructive pest of agriculture and horticulture worldwide.Recent phylogenetic analysis using mitochondrial cytochrome oxidase 1 sequences indicates that this whitefly is a species complex including at least 24 morphologically indistinguishable but genetically distinct cryptic species.In this study,the inter-species crosses of Middle East-Asia Minor 1(MEAM1),Mediterranean(MED)and Asia II 7 cryptic species,which were referred to as B,Q and Cv biotypes before,were conducted in two different devices,leaf cages(7 cm3)and cylinder cages(280 cm3),and at three temperatures of 22,30 and 38°C.Results indicated that no female progeny were produced in the reciprocal cross between MEAM1×Asia II 7,between MED×Asia II 7 cryptic species neither in leaf cage nor in cylinder cages,while 0.81 and 1.37% of females in the offspring were recorded in the reciprocal cross between MEAM1×MED in leaf cage experiments.Approximately 0.95-0.98% female progeny were recorded in the reciprocal cross between MEAM1×MED at 30°C,0.77% female progeny were recorded in the single cross direction between MEAM1 × MED at 22°C,and no female progeny were found in their reciprocal cross at 38°C in leaf cage.Our findings indicated that neither space dimension nor temperature have a significant effect on the hybridization of different B.tabaci cryptic species.
基金This paper is supported by the National Foundations.
文摘It is important to study the propagation and interaction of progressing waves of nonlinear equations in the class of piecewise smooth function. However, there has not been many works on that in multidimensional case. In 1985, J, Rauch & M. Reed have provad the existence and uniqueness of piecewise smooth solution for
文摘This paper explains how a model of the universe can be constructed by incorporating time and space into geometry in a unique way to produce a 4-space dimension/1-time dimension model. The model can then show how dark matter can be the gravity that is produced by real matter that exists throughout our entire universe. The model can also show how dark energy is not an increase in energy that is causing the accelerated expansion of the universe, but is an accelerating decrease in matter throughout the universe as the stars and galaxies in the universe continue to convert matter into energy during their life cycles. And then the model can show how a fourth space dimension must exist in our universe to locate a point in space.
基金Supported by youth foundation of Sichuan province (1999-09)
文摘Kunio Hidano[4] has shown that the global and local C2-solutions for semilinear wave equations with spherical symmetry in three space dimensions. This paper studies the global and local C2-solutions for the semilinear wave equations without spherical symmetry in three space dimensions. A problem put forward by Hiroyuki Takamura[2] is partially answered.
文摘In this paper, we consider a system of two cubic quasi-linear Klein-Gordon equations with different masses for small, smooth, compactly supported Cauchy data in one space dimension. We show that such a system has global existence when the nonlinearities satisfy a convenient null condition. Our results extend the global existence proved by Sunagawa recently under the non-resonance assumption to that under the resonance assumption.
基金The Special Science Foundation (00jk207) of the Educational Committee of Shaanxi Province.
文摘Let {(Xi, Si, μi) : i ℃ N} be a sequence of probability measure spaces and (*Xi, L(*Si), L(*μi)) be the Loeb measure space with respect to (Xi, Si, μi) for i ℃ N. Let X =× Xi, S = ×Si,μ = ×μi. We prove that × L(*Si) CL(*S) and in embedding meaning.
基金Supported by the National Natural Science Foundation of China(90920304)
文摘A variable dimensional state space(VDSS) has been proposed to improve the re-planning time when the robotic systems operate in large unknown environments.VDSS is constructed by uniforming lattice state space and grid state space.In VDSS,the lattice state space is only used to construct search space in the local area which is a small circle area near the robot,and grid state space elsewhere.We have tested VDSS with up to 80 indoor and outdoor maps in simulation and on segbot robot platform.Through the simulation and segbot robot experiments,it shows that exploring on VDSS is significantly faster than exploring on lattice state space by Anytime Dynamic A*(AD*) planner and VDSS is feasible to be used on robotic systems.
文摘Outlier detection has very important applied value in data mining literature. Different outlier detection algorithms based on distinct theories have different definitions and mining processes. The three-dimensional space graph for constructing applied algorithms and an improved GridOf algorithm were proposed in terms of analyzing the existing outlier detection algorithms from criterion and theory. Key words outlier - detection - three-dimensional space graph - data mining CLC number TP 311. 13 - TP 391 Foundation item: Supported by the National Natural Science Foundation of China (70371015)Biography: ZHANG Jing (1975-), female, Ph. D, lecturer, research direction: data mining and knowledge discovery.
基金Supported by National Natural Science Foundation of China(11731010 and 12071388)。
文摘Assume that X and Y are real Banach spaces with the same finite dimension.In this paper we show that if a standard coarse isometry f:X→Y satisfies an integral convergence condition or weak stability on a basis,then there exists a surjective linear isometry U:X→Y such that∥f(x)−Ux∥=o(∥x∥)as∥x∥→∞.This is a generalization about the result of Lindenstrauss and Szankowski on the same finite dimensional Banach spaces without the assumption of surjectivity.As a consequence,we also obtain a stability result forε-isometries which was established by Dilworth.
基金Project supported by the National Basic Research Program of China (Grant No. 2010CB327702)
文摘We report an integral imaging method with continuous imaging space. This method simultaneously reconstructs real and virtual images in the virtual mode, with a minimum gap that separates the entire imaging space into real and virtual space. Experimental results show that the gap is reduced to 45% of that in a conventional integral imaging system with the same parameters.
文摘We present a new algorithm for manifold learning and nonlinear dimensionality reduction. Based on a set of unorganized data points sampled with noise from a parameterized manifold, the local geometry of the manifold is learned by constructing an approximation for the tangent space at each point, and those tangent spaces are then aligned to give the global coordinates of the data points with respect to the underlying manifold. We also present an error analysis of our algorithm showing that reconstruction errors can be quite small in some cases. We illustrate our algorithm using curves and surfaces both in 2D/3D Euclidean spaces and higher dimensional Euclidean spaces. We also address several theoretical and algorithmic issues for further research and improvements.
文摘为了解立体绿化领域研究进展、热点及趋势,基于中国知网(CNKI)和科学引文索引数据库(Web of Science),运用文献计量法和可视化文献分析软件(Cite Space)可视化分析法,分析2002—2021年立体绿化领域中英文文献资料。发现英文文献发文量及其增长幅度均高于中文文献;目前立体绿化领域主要研究机构均集中于各大高校;英文文献相关研究涵盖的学科领域主要为环境科学与生态学、工程学、城市研究、科学技术等,中文文献相关研究主要集中在建筑科学与工程、林业、园艺等方面;立体绿化的热点研究领域集中在立体绿化生态效益、施工技术和植物研究等方面;英文文献相关研究早期关注生物多样性、气候调节等,近年来关注微气候、城市农业等,中文文献相关研究的发展趋势从早期对立体绿化的理论研究、技术探索逐渐拓展到对城市雨洪、建筑节能等层面的精细化研究。基于此,提出未来立体绿化研究应在学术交流合作、学科交叉研究、创新研究方法等层面逐步深入,以此丰富立体绿化研究对象和主题,并进一步把握其研究态势。
基金Supported by the Nationa1 Natural Science Foundation of China under Grant No.10874018"the Fundamental Research Funds for the Central Universities"
文摘The solutions of the Laplace equation in n-dimensional space are studied.The angular eigenfunctions have the form of associated Jacobi polynomials.The radial solution of the Helmholtz equation is derived.
文摘Let χ= be a metric space and let ε be a positive real number. Then a function f: X→Y is defined to be an ε-map if and only if for all y∈Y, the diameter of f-1(y)?is at most ε. In Theorem 10 we will give a new proof for the following well known fact: if χ is totally bounded, then for all ε there exists a finite number n and a continuous ε-map fε: X→Rn (here Rn is the usual n-dimensional Euclidean space endowed with the Euclidean metric). If ε is “small”, then fε is “almost injective”;and still exists even if χ has infinite covering dimension (in this case, n depends on ε, of course). Contrary to the known proofs, our proof technique is effective in the sense, that it allows establishing estimations for n in terms of ε and structural properties of χ.
文摘This paper advances a three-dimensional space interpolation method of grey / depth image sequence, which breaks free from the limit of original practical photographing route. Pictures can cruise at will in space. By using space sparse sampling, great memorial capacity can be saved and reproduced scenes can be controlled. To solve time consuming and complex computations in three-dimensional interpolation algorithm, we have studied a fast and practical algorithm of scattered space lattice and that of 'Warp' algorithm with proper depth. By several simple aspects of three dimensional space interpolation, we succeed in developing some simple and practical algorithms. Some results of simulated experiments with computers have shown that the new method is absolutely feasible.
基金Project (No. [2005]555) supported by the Hi-Tech Research and De-velopment Program (863) of China
文摘Various index structures have recently been proposed to facilitate high-dimensional KNN queries, among which the techniques of approximate vector presentation and one-dimensional (1D) transformation can break the curse of dimensionality. Based on the two techniques above, a novel high-dimensional index is proposed, called Bit-code and Distance based index (BD). BD is based on a special partitioning strategy which is optimized for high-dimensional data. By the definitions of bit code and transformation function, a high-dimensional vector can be first approximately represented and then transformed into a 1D vector, the key managed by a B+-tree. A new KNN search algorithm is also proposed that exploits the bit code and distance to prune the search space more effectively. Results of extensive experiments using both synthetic and real data demonstrated that BD out- performs the existing index structures for KNN search in high-dimensional spaces.
文摘Mine safety have top-five disasters,which including the water,gas,fire,dust and geological dynamic disaster.The coal mine water disaster is one of the important factors which restricted the development of China’s coal production.It is showed by statistics that 60%of mine accidents are affected by groundwater,which not only result in the production losses,casualties and a variety of
基金Project supported by the National Natural Science Foundation of China (Grant No. 50877007)
文摘The eigenvalue space of the canonical four-dimensional Chua's circuit which can realize every eigenvalue for fourdimensional system is studied in this paper. First, the analytical relations between the circuit parameters and the eigenvalues of the system are established, and therefore all the circuit parameters can be determined explicitly by any given set of eigenvalues. Then, the eigenvalue space of the circuit is investigated in two cases by the nonlinear elements used. According to the types of the eigenvalues, some novel hyperchaotic attractors are presented. Further, the dynamic behaviours of the circuit are studied by the bifurcation diagrams and the Lyapunov spectra of the eigenvalues.
文摘In two previous papers <a href="#ref1">[1]</a> and <a href="#ref2">[2]</a>, a structure for vector products in <em>n</em> dimensions was presented, and at the same time it was possible to propose the existence of a vector analogous to the curl of a vector field, for a space of four dimensions. In continuation of these works, the objective is to develop, through dimensional analogy, the idea of a hypothetical vector field, associated with the classical electromagnetic wave. This hypothetical field has a possible mathematical existence only when considering a space of four dimensions. The properties of the electromagnetic wave are preserved and equations with mathematical forms analogous to those of Maxwell’s equations are presented.
文摘In Newton’s classical physics, space and time are treated as absolute quantities. Space and time are treated as independent quantities and can be discussed sepa-rately. With his theory of relativity, Einstein proved that space and time are de-pendent and must be treated inseparably. Minkowski adopted a four-dimensional space-time frame and indirectly revealed the dependency of space and time by adding a constraint for an event interval. Since space and time are inseparable, a three-dimensional space-time frame can be constructed by embedding time into space to directly show the interdependency of space and time. The formula for time dilation, length contraction, and the Lorenz transformation can be derived from graphs utilizing this new frame. The proposed three-dimensional space-time frame is an alternate frame that can be used to describe motions of objects, and it may improve teaching and learning Special Relativity and provide additional insights into space and time.