The qualitative solutions of dynamical system expressed with nonlinear differential equation can be divided into two categories. One is that the motion of phase point may approach infinite or stable equilibrium point ...The qualitative solutions of dynamical system expressed with nonlinear differential equation can be divided into two categories. One is that the motion of phase point may approach infinite or stable equilibrium point eventually. Neither periodic excited source nor self-excited oscillation exists in such nonlinear dynamic circuits, so its solution cannot be treated as the synthesis of multiharmonic. And the other is that the endless vibration of phase point is limited within certain range, moreover possesses character of sustained oscillation, namely the bounded nonlinear oscillation. It can persistently and repeatedly vibration after dynamic variable entering into steady state;moreover the motion of phase point will not approach infinite at last;system has not stable equilibrium point. The motional trajectory can be described by a bounded space curve. So far, the curve cannot be represented by concretely explicit parametric form in math. It cannot be expressed analytically by human. The chaos is a most universally common form of bounded nonlinear oscillation. A number of chaotic systems, such as Lorenz equation, Chua’s circuit and lossless system in modern times are some examples among thousands of chaotic equations. In this work, basic properties related to the bounded space curve will be comprehensively summarized by analyzing these examples.展开更多
The Besov spaces B_p^(α,4)(Γ)and Triebel-Lizorkin spaces F_p^(α,4)(Γ)with high order x∈R on a Lipschitz curve Γ are defind,when 1≤p≤∞,1≤q≤∞.To compare to the classical case.a difference characterization of...The Besov spaces B_p^(α,4)(Γ)and Triebel-Lizorkin spaces F_p^(α,4)(Γ)with high order x∈R on a Lipschitz curve Γ are defind,when 1≤p≤∞,1≤q≤∞.To compare to the classical case.a difference characterization of such spaces in the case|x|<1 is given also.展开更多
In this paper, we study the extremals of the curvature energy actions on non-null curves in the four-dimensional Lorentz-Minkowski space. We derive the motion equations and find three Killing fields along the generali...In this paper, we study the extremals of the curvature energy actions on non-null curves in the four-dimensional Lorentz-Minkowski space. We derive the motion equations and find three Killing fields along the generalized elastic curves. We also construct a cylindrical coordinate system using these Killing fields and express the generalized elastic curves by means of quadratures.展开更多
Many database applications currently deal with objects in a metric space.Examples of such objects include unstructured multimedia objects and points of interest(POIs)in a road network.The M-tree is a dynamic index str...Many database applications currently deal with objects in a metric space.Examples of such objects include unstructured multimedia objects and points of interest(POIs)in a road network.The M-tree is a dynamic index structure that facilitates an efficient search for objects in a metric space.Studies have been conducted on the bulk loading of large datasets in an M-tree.However,because previous algorithms involve excessive distance computations and disk accesses,they perform poorly in terms of their index construction and search capability.This study proposes two efficient M-tree bulk loading algorithms.Our algorithms minimize the number of distance computations and disk accesses using FastMap and a space-filling curve,thereby significantly improving the index construction and search performance.Our second algorithm is an extension of the first,and it incorporates a partitioning clustering technique and flexible node architecture to further improve the search performance.Through the use of various synthetic and real-world datasets,the experimental results demonstrated that our algorithms improved the index construction performance by up to three orders of magnitude and the search performance by up to 20.3 times over the previous algorithm.展开更多
In this paper, evolutions of ruled surfaces generated by the quasi normal and quasi binormal vector fields of space curve are presented. These evolutions of the ruled surfaces depend on the evolutions of their directr...In this paper, evolutions of ruled surfaces generated by the quasi normal and quasi binormal vector fields of space curve are presented. These evolutions of the ruled surfaces depend on the evolutions of their directrix using quasi frame along a space curve.展开更多
<span style="font-family:Verdana;">Plank quantum and classical string energy relations seem to be uncorrelated. This work correlated them. The relativistic energy-momentum relation has been used togeth...<span style="font-family:Verdana;">Plank quantum and classical string energy relations seem to be uncorrelated. This work correlated them. The relativistic energy-momentum relation has been used together with plank and de Brogglie hypothesis to prove that the wave group velocity is equal to the particle velocity in both ordinary and curved space. The plank energy relation is shown also to be related to the classical energy relation of an oscillating string. Starting from plank energy relation for n photons and performing integration, the expression of classical string energy was obtained. This means that one can treat electromagnetic waves as a collection of continuous photons having frequencies ranging from zero to w. Conversely, starting from classical string energy relation by differentiating it with respect to angular frequency, the plank quantum energy for n photons has been found. This means that the quanta results from separation of electromagnetic waves to single isolated waves. Each wave consists of n photons or quanta.</span>展开更多
We start from quantum field theory in curved spacetime to derive a new Einstein-like energy mass relation of the type E=γmc2 where γ=1/22 is a Yang-Mills Lorentzian factor, m is the mass and c is the velocity of lig...We start from quantum field theory in curved spacetime to derive a new Einstein-like energy mass relation of the type E=γmc2 where γ=1/22 is a Yang-Mills Lorentzian factor, m is the mass and c is the velocity of light. Although quantum field in curved spacetime is not a complete quantum gravity theory, our prediction here of 95.4545% dark energy missing in the cosmos is almost in complete agreement with the WMAP and supernova measurements. Finally, it is concluded that the WMAP and type 1a supernova 4.5% measured energy is the ordinary energy density of the quantum particle while the 95.5% missing dark energy is the energy density of the quantum wave. Recalling that measurement leads to quantum wave collapse, it follows that dark energy as given by E(D) = mc2 (21/22) cannot be detected using conventional direct measurement although its antigravity effect is manifested through the increasing rather than decreasing speed of cosmic expansion.展开更多
In arbitrary Riemannian 4-spaces, continuity equations are constructed which could be interpreted as conservation laws for the energy and momentum of the gravitational field. Special attention is given to general rela...In arbitrary Riemannian 4-spaces, continuity equations are constructed which could be interpreted as conservation laws for the energy and momentum of the gravitational field. Special attention is given to general relativity to obtain, of natural manner, the pseudotensors of Einstein, Landau-Lifshitz, Mller, Goldberg and Stachel, and also the conservation equations of Komar, Trautman, DuPlessis and Moss.展开更多
Tool path generated by space-filling curve always turns frequently causing trembling to machine,reducing toollife and affecting workpiece quality. Length and generation time of tool paths are both relatively long. In ...Tool path generated by space-filling curve always turns frequently causing trembling to machine,reducing toollife and affecting workpiece quality. Length and generation time of tool paths are both relatively long. In order to solve these problems,a toolpath generation method of NC milling based on space-filling curve is proposed. First,T-spline surface is regarded as the modeling surface,the grid,which is based on the limited scallop-height,can be got in the parameter space,and the influence value of grid node is determined. Second,a box is defined and planned,and the tool paths are got preliminarily,which is based on minimal spanning tree; Finally,based on an improved chamfering algorithm,the whole tool paths are got. A simulation system is developed for computer simulation,and an experiment is carried out to verify the method. The results of simulation and experiment show that the method is effective and feasible,and length and time of the tool paths are reduced.展开更多
Fine-grained clayey soils are prone to substantial volume changes during desiccation in response to the dynamics of their moisture regime,and are of critical importance in several geotechnical and geoenvironmental eng...Fine-grained clayey soils are prone to substantial volume changes during desiccation in response to the dynamics of their moisture regime,and are of critical importance in several geotechnical and geoenvironmental engineering applications. As such, the complex interactions between the fraction of soil solids and the ionic pore fluid play a critical role in governing such volume changes, and have been the focus in studies dealing with marine geotechnology, mine-tailing ponds, engineered barrier systems, etc.With this in mind, the present investigation evaluates the volume changes and accompanying densification from a saturated slurry state to a constant volume state of a reference fine-grained geomaterial,kaolin, subjected to evaporative dewatering. For this purpose, several parametric studies involving determination of soil shrinkage characteristic curves(SSCCs) of kaolin under the influence of varied salt constituents and concentrations of pore fluid are performed. Furthermore, a critical assessment of SSCCs depicting progressive shrinkage and volume change behaviour of geomaterials is provided, followed by the analysis of experimentally obtained SSCCs of the kaolin to explore the impacts of pore fluid salinity.Moreover, the SSCCs are parameterised with a predictive model and the fitting parameters are used to quantitatively demonstrate the salinity-dependent volume change response of a representative finegrained porous system.展开更多
In this paper,we extend the concept of holomorphic curves sharing hyperplanes and introduce definitions of restricted hyperplanes and partial shared hypersurfaces.Then,we prove several normal criteria of the family of...In this paper,we extend the concept of holomorphic curves sharing hyperplanes and introduce definitions of restricted hyperplanes and partial shared hypersurfaces.Then,we prove several normal criteria of the family of holomorphic curves and holomorphic mappings that concern restricted hyperplanes and partial shared hypersurfaces.These results generalize the Montel-type normal criterion of holomorphic curves.展开更多
The design of an optimum spacing between oil wells entails both reservoir characterization and economics considerations. High hydrocarbon recovery requires short distances between wells. However, higher well density l...The design of an optimum spacing between oil wells entails both reservoir characterization and economics considerations. High hydrocarbon recovery requires short distances between wells. However, higher well density leads to a greater development cost. Accordingly, determination of an optimum well spacing is primordial in the development of oil fields. As a matter of fact, the identification of optimum well spacing for heterogeneous sandstone reservoirs undergoing waterflooding requires extensive analytical and numerical studies. The intent of this work is therefore to develop type curves as a quick tool in estimating ultimate recovery and reduce excessive reservoir simulation cost in analog reservoirs. These type curves utilize reservoir heterogeneity and well spacing in the estimating of oil recovery. In this work, we investigated numerically the effects of heterogeneity and well spacing on ultimate recovery using Eclipse black oil simulation and PEEP economic software 2015 and 2009 versions, respectively. The study involved a 50-ft thick Middle Eastern reservoir with porosity variability ranging from 0.2 to 0.9. Corresponding average matrix permeabilities of 1, 10 and 100 md were considered. Type curves relating well spacing and heterogeneity to ultimate oil recovery were developed. Type curves and net present value calculations indicated that there is exists an ultimate well spacing for each of the considered matrix permeabilities.展开更多
The main result of this paper is a theorem about the convexity of curves of degree n on a plane. As its application ,we obtained a sufficient condition that a space curve of degree n in R^3 has no singularity points a...The main result of this paper is a theorem about the convexity of curves of degree n on a plane. As its application ,we obtained a sufficient condition that a space curve of degree n in R^3 has no singularity points and staying points.展开更多
Microcavity photon dynamics in curved space is an emerging interesting area at the crossing point of nanophotonics,chaotic science,and non-Euclidean geometry.We report the sharp difference between the regular and chao...Microcavity photon dynamics in curved space is an emerging interesting area at the crossing point of nanophotonics,chaotic science,and non-Euclidean geometry.We report the sharp difference between the regular and chaotic motions of cavity photons subjected to the varying space curvature.While the island modes of regular motion rise in the phase diagram in the curved space,the chaotic modes show special mechanisms to adapt to the space curvature,including the fast diffusion of ray dynamics,and the localization and hybridization of the Husimi wavepackets among different periodic orbits.These observations are unique effects enabled by the combination of the chaotic trajectory,the wave nature of light,and the non-Euclidean orbital motion,and therefore make the system a versatile optical simulator for chaotic science under quantum mechanics in curved space-time.展开更多
文摘The qualitative solutions of dynamical system expressed with nonlinear differential equation can be divided into two categories. One is that the motion of phase point may approach infinite or stable equilibrium point eventually. Neither periodic excited source nor self-excited oscillation exists in such nonlinear dynamic circuits, so its solution cannot be treated as the synthesis of multiharmonic. And the other is that the endless vibration of phase point is limited within certain range, moreover possesses character of sustained oscillation, namely the bounded nonlinear oscillation. It can persistently and repeatedly vibration after dynamic variable entering into steady state;moreover the motion of phase point will not approach infinite at last;system has not stable equilibrium point. The motional trajectory can be described by a bounded space curve. So far, the curve cannot be represented by concretely explicit parametric form in math. It cannot be expressed analytically by human. The chaos is a most universally common form of bounded nonlinear oscillation. A number of chaotic systems, such as Lorenz equation, Chua’s circuit and lossless system in modern times are some examples among thousands of chaotic equations. In this work, basic properties related to the bounded space curve will be comprehensively summarized by analyzing these examples.
基金The author is supported in part by the Foundation of Zhongshan University Advanced Research Centre and NSF of China.
文摘The Besov spaces B_p^(α,4)(Γ)and Triebel-Lizorkin spaces F_p^(α,4)(Γ)with high order x∈R on a Lipschitz curve Γ are defind,when 1≤p≤∞,1≤q≤∞.To compare to the classical case.a difference characterization of such spaces in the case|x|<1 is given also.
基金supported by the National Natural Science Foundation of China (No. 10671066)the Shanghai Leading Academic Discipline Project (No. B407)
文摘In this paper, we study the extremals of the curvature energy actions on non-null curves in the four-dimensional Lorentz-Minkowski space. We derive the motion equations and find three Killing fields along the generalized elastic curves. We also construct a cylindrical coordinate system using these Killing fields and express the generalized elastic curves by means of quadratures.
基金the National Research Foundation of Korea(NRF,www.nrf.re.kr)grant funded by the Korean government(MSIT,www.msit.go.kr)(No.2018R1A2B6009188)(received by W.-K.Loh).
文摘Many database applications currently deal with objects in a metric space.Examples of such objects include unstructured multimedia objects and points of interest(POIs)in a road network.The M-tree is a dynamic index structure that facilitates an efficient search for objects in a metric space.Studies have been conducted on the bulk loading of large datasets in an M-tree.However,because previous algorithms involve excessive distance computations and disk accesses,they perform poorly in terms of their index construction and search capability.This study proposes two efficient M-tree bulk loading algorithms.Our algorithms minimize the number of distance computations and disk accesses using FastMap and a space-filling curve,thereby significantly improving the index construction and search performance.Our second algorithm is an extension of the first,and it incorporates a partitioning clustering technique and flexible node architecture to further improve the search performance.Through the use of various synthetic and real-world datasets,the experimental results demonstrated that our algorithms improved the index construction performance by up to three orders of magnitude and the search performance by up to 20.3 times over the previous algorithm.
文摘In this paper, evolutions of ruled surfaces generated by the quasi normal and quasi binormal vector fields of space curve are presented. These evolutions of the ruled surfaces depend on the evolutions of their directrix using quasi frame along a space curve.
文摘<span style="font-family:Verdana;">Plank quantum and classical string energy relations seem to be uncorrelated. This work correlated them. The relativistic energy-momentum relation has been used together with plank and de Brogglie hypothesis to prove that the wave group velocity is equal to the particle velocity in both ordinary and curved space. The plank energy relation is shown also to be related to the classical energy relation of an oscillating string. Starting from plank energy relation for n photons and performing integration, the expression of classical string energy was obtained. This means that one can treat electromagnetic waves as a collection of continuous photons having frequencies ranging from zero to w. Conversely, starting from classical string energy relation by differentiating it with respect to angular frequency, the plank quantum energy for n photons has been found. This means that the quanta results from separation of electromagnetic waves to single isolated waves. Each wave consists of n photons or quanta.</span>
文摘We start from quantum field theory in curved spacetime to derive a new Einstein-like energy mass relation of the type E=γmc2 where γ=1/22 is a Yang-Mills Lorentzian factor, m is the mass and c is the velocity of light. Although quantum field in curved spacetime is not a complete quantum gravity theory, our prediction here of 95.4545% dark energy missing in the cosmos is almost in complete agreement with the WMAP and supernova measurements. Finally, it is concluded that the WMAP and type 1a supernova 4.5% measured energy is the ordinary energy density of the quantum particle while the 95.5% missing dark energy is the energy density of the quantum wave. Recalling that measurement leads to quantum wave collapse, it follows that dark energy as given by E(D) = mc2 (21/22) cannot be detected using conventional direct measurement although its antigravity effect is manifested through the increasing rather than decreasing speed of cosmic expansion.
文摘In arbitrary Riemannian 4-spaces, continuity equations are constructed which could be interpreted as conservation laws for the energy and momentum of the gravitational field. Special attention is given to general relativity to obtain, of natural manner, the pseudotensors of Einstein, Landau-Lifshitz, Mller, Goldberg and Stachel, and also the conservation equations of Komar, Trautman, DuPlessis and Moss.
基金Supported by the National Natural Science Foundation of China(No.51575143)
文摘Tool path generated by space-filling curve always turns frequently causing trembling to machine,reducing toollife and affecting workpiece quality. Length and generation time of tool paths are both relatively long. In order to solve these problems,a toolpath generation method of NC milling based on space-filling curve is proposed. First,T-spline surface is regarded as the modeling surface,the grid,which is based on the limited scallop-height,can be got in the parameter space,and the influence value of grid node is determined. Second,a box is defined and planned,and the tool paths are got preliminarily,which is based on minimal spanning tree; Finally,based on an improved chamfering algorithm,the whole tool paths are got. A simulation system is developed for computer simulation,and an experiment is carried out to verify the method. The results of simulation and experiment show that the method is effective and feasible,and length and time of the tool paths are reduced.
基金funded by scholarship supports through 'Australian Government Research Training Program Scholarship' (formerly 'International Postgraduate Research Scholarship'),UQ Centennial Scholarship (University of Queensland)and Top-up Scholarship(School of Civil Engineering, University of Queensland) awarded to Mr. Partha Narayan Mishra
文摘Fine-grained clayey soils are prone to substantial volume changes during desiccation in response to the dynamics of their moisture regime,and are of critical importance in several geotechnical and geoenvironmental engineering applications. As such, the complex interactions between the fraction of soil solids and the ionic pore fluid play a critical role in governing such volume changes, and have been the focus in studies dealing with marine geotechnology, mine-tailing ponds, engineered barrier systems, etc.With this in mind, the present investigation evaluates the volume changes and accompanying densification from a saturated slurry state to a constant volume state of a reference fine-grained geomaterial,kaolin, subjected to evaporative dewatering. For this purpose, several parametric studies involving determination of soil shrinkage characteristic curves(SSCCs) of kaolin under the influence of varied salt constituents and concentrations of pore fluid are performed. Furthermore, a critical assessment of SSCCs depicting progressive shrinkage and volume change behaviour of geomaterials is provided, followed by the analysis of experimentally obtained SSCCs of the kaolin to explore the impacts of pore fluid salinity.Moreover, the SSCCs are parameterised with a predictive model and the fitting parameters are used to quantitatively demonstrate the salinity-dependent volume change response of a representative finegrained porous system.
基金The second author was supported by the National Natural Science Foundation of China(11501127)Foundation for Distinguished Young Talents in Higher Education of Guangdong Province(2014KQNCX068)The third author was supported by the Foundation of Guangzhou Civil Aviation College(18X0428).
文摘In this paper,we extend the concept of holomorphic curves sharing hyperplanes and introduce definitions of restricted hyperplanes and partial shared hypersurfaces.Then,we prove several normal criteria of the family of holomorphic curves and holomorphic mappings that concern restricted hyperplanes and partial shared hypersurfaces.These results generalize the Montel-type normal criterion of holomorphic curves.
文摘The design of an optimum spacing between oil wells entails both reservoir characterization and economics considerations. High hydrocarbon recovery requires short distances between wells. However, higher well density leads to a greater development cost. Accordingly, determination of an optimum well spacing is primordial in the development of oil fields. As a matter of fact, the identification of optimum well spacing for heterogeneous sandstone reservoirs undergoing waterflooding requires extensive analytical and numerical studies. The intent of this work is therefore to develop type curves as a quick tool in estimating ultimate recovery and reduce excessive reservoir simulation cost in analog reservoirs. These type curves utilize reservoir heterogeneity and well spacing in the estimating of oil recovery. In this work, we investigated numerically the effects of heterogeneity and well spacing on ultimate recovery using Eclipse black oil simulation and PEEP economic software 2015 and 2009 versions, respectively. The study involved a 50-ft thick Middle Eastern reservoir with porosity variability ranging from 0.2 to 0.9. Corresponding average matrix permeabilities of 1, 10 and 100 md were considered. Type curves relating well spacing and heterogeneity to ultimate oil recovery were developed. Type curves and net present value calculations indicated that there is exists an ultimate well spacing for each of the considered matrix permeabilities.
文摘The main result of this paper is a theorem about the convexity of curves of degree n on a plane. As its application ,we obtained a sufficient condition that a space curve of degree n in R^3 has no singularity points and staying points.
基金supported by the National Key R&D Program of China(Grant No.2023YFA1407100)the National Natural Science Foundation of China(Grant Nos.12074303,and 11804267)+2 种基金the Shaanxi Key Science and Technology Innovation Team Project(Grant No.2021TD-56)the Sichuan Science and Technology Program(Grant No.2022NSFSC1811)the Xiaomi Young Scholar Program。
文摘Microcavity photon dynamics in curved space is an emerging interesting area at the crossing point of nanophotonics,chaotic science,and non-Euclidean geometry.We report the sharp difference between the regular and chaotic motions of cavity photons subjected to the varying space curvature.While the island modes of regular motion rise in the phase diagram in the curved space,the chaotic modes show special mechanisms to adapt to the space curvature,including the fast diffusion of ray dynamics,and the localization and hybridization of the Husimi wavepackets among different periodic orbits.These observations are unique effects enabled by the combination of the chaotic trajectory,the wave nature of light,and the non-Euclidean orbital motion,and therefore make the system a versatile optical simulator for chaotic science under quantum mechanics in curved space-time.
