A model of an energy selective electron (ESE) engine with linear heat leakage and Lorentzian transmission probability is established in this paper.The expressions for the main performance parameters of the ESE engine ...A model of an energy selective electron (ESE) engine with linear heat leakage and Lorentzian transmission probability is established in this paper.The expressions for the main performance parameters of the ESE engine operating as a heat engine or a refrigerator are derived by using the theory of finite time thermodynamics.The optimum performances of the ESE engine are explored and the influences of the heat leakage,the central energy level of the resonance,and the width of the resonance on the performance of the ESE engine are analyzed by using detailed numerical examples.The optimal operation regions of power output and efficiency (or cooling load and coefficient of performance (COP)) are also discussed.Moreover,the performances of the ESE engine with Lorentzian transmission probability are compared with those with rectangular transmission probability.It is shown that the power output versus efficiency (or cooling load versus COP) characteristic curves with and without heat leakage are all closed loop-shaped ones.The efficiency (or COP) of the ESE engine decreases as the heat leakage increases.It is found that as the resonance width increases,the power output and efficiency (or cooling load and COP) increase to a maximum and then decrease due to the finite range of energies which contribute positively to the power generation or refrigeration in the electron system.Especially,when heat leakage is taken into account,the characteristic curves of maximum efficiency (or maximum COP) versus half resonance width are parabolic-like ones,which are quite different from the monotonic decreasing characteristic curves obtained in previous analyses without considering heat leakage.The results obtained in this paper can provide some theoretical guidelines for the design and operation of practical electron energy conversion devices such as solid-state thermionic refrigerators.展开更多
Anti de Sitter space is a maximally symmetric, vacuum solution of Einstein's field equation with an attractive cosmological constant, and is the hyperquadric of semi-Euclidean space with index 2. So it is meaningf...Anti de Sitter space is a maximally symmetric, vacuum solution of Einstein's field equation with an attractive cosmological constant, and is the hyperquadric of semi-Euclidean space with index 2. So it is meaningful to study the submanifold in semi-Euclidean 4-space with index 2. However, the research on the submanifold in semi-Euclidean 4-space with index 2 has not been found from theory of singularity until now. In this paper, as a generalization of the study on lightlike hypersurface in Minkowski space and a preparation for the further study on anti de Sitter space, the singularities of lightlike hypersurface and Lorentzian surface in semi- Euclidean 4-space with index 2 will be studied. To do this, we reveal the relationships between the singularity of distance-squared function and that of lightlike hypersurface. In addition some geometric properties of lightlike hypersurface and Lorentzian surface are studied from geometrical point of view.展开更多
This study aimed to investigate the capabilities of hyperspectral scattering imaging in tandem with Gaussian function,Exponential function and Lorentzian function for rapid and nondestructive determination of total vi...This study aimed to investigate the capabilities of hyperspectral scattering imaging in tandem with Gaussian function,Exponential function and Lorentzian function for rapid and nondestructive determination of total viable count(TVC)in pork meat.Two batches of fresh pork meat was purchased from a local market and stored at 10°C for 1-9 d.Totally 60 samples were used,and several samples were taken out randomly for hyperspectral scattering imaging and conventional microbiological tests on each day of the experiments.The functions of Gaussian,Exponential and Lorentzian were employed to model the hyperspectral scattering profiles of pork meat,and good fitting results were obtained by all three functions between 455 nm and 1000 nm.The Lorentzian function performed best for fitting the hyperspectral scattering profiles of pork meat compared with other functions.Both principal component regression(PCR)and partial least squares regression(PLSR)methods were performed to establish the prediction models.Among all the developed models,the models developed using parameters CE(scattering width parameter of Exponential function)and CL(scattering width parameter of Lorentzian function)by PLSR method gave superior results for predicting pork meat TVC,with RV and RMSEV of 0.92,0.59 log CFU/g,and 0.91,0.61 log CFU/g,respectively.In addition,based on the improved hyperspectral scattering system,parameter c which represented the scattering widths in all three functions gave more accurate prediction results,regardless of the modeling methods(PCR or PLSR).The obtained results demonstrated that hyperspectral scattering imaging combined with the presented data analysis algorithm can be a powerful tool for evaluating the microbial safety of meat in the future.展开更多
Let x ：M - Qn＋l be a regular hypersurface in the conformal space Qn＋I. We classify all the space-like Blaschke isoparametric hypersurfaces with two distinct Blaschke eigenvalues in the conformal space up to the con...Let x ：M - Qn＋l be a regular hypersurface in the conformal space Qn＋I. We classify all the space-like Blaschke isoparametric hypersurfaces with two distinct Blaschke eigenvalues in the conformal space up to the conformal equivalence.展开更多
In this study, fresh pork tenderness, drip-loss, pH value and color parameters （ CIE, a ＊ , b ＊ and L ＊ values） were simultaneously predicted using hyperspectral scattering imaging （HSI） technique. The hyperspe...In this study, fresh pork tenderness, drip-loss, pH value and color parameters （ CIE, a ＊ , b ＊ and L ＊ values） were simultaneously predicted using hyperspectral scattering imaging （HSI） technique. The hyperspectral scattering images of dO fresh pork samples were collected at the wavelength of 400 -I 100 nm, and the scattering profiles were fitted via Lorontzian distribution （ LD ） function to give three parameters a （ asymptotic value ）, b （peak value ） and c （ full width at b/2）. Stepwise discrimination was performed to determine the optimal wavelengths combinations. The LD parameters combinations （a, b and c） of optimal wavelengths were used to establish multi-linear regression （MLR） models to predict the pork attributes. The models were able to predict pork with high correlation coefficients of 0.92 for drip-loss, 0.94, 0.92 and 0.98 respectively for color parameters （ a ＊ , b＊ and L ＊ ）, and for tenderness and pH value the models gave the correlation coefficients of 0.69 and 0.76, respectively. These results showed that the hyperspectral scattering technique was capable of predicting quality parameters of perk. The study provides an efficient means for rapid and nondestructive determination of pork quality simultaneously.展开更多
A three dimensional Lorentzian hypersurface x : M_1~3→ R_1~4 is called conformally flat if its induced metric is conformal to the flat Lorentzian metric, and this property is preserved under the conformal transformat...A three dimensional Lorentzian hypersurface x : M_1~3→ R_1~4 is called conformally flat if its induced metric is conformal to the flat Lorentzian metric, and this property is preserved under the conformal transformation of R_1~4. Using the projective light-cone model, for those whose shape operators have three distinct real eigenvalues, we calculate the integrability conditions by constructing a scalar conformal invariant and a canonical moving frame in this paper. Similar to the Riemannian case, these hypersurfaces can be determined by the solutions to some system of partial differential equations.展开更多
Let R13 be the Lorentzian 3-space with inner product (, ). Let Q3 be the conformal compactification of R13, obtained by attaching a light-cone C∞ to R13 in infinity. Then Q3 has a standard conformal Lorentzian struct...Let R13 be the Lorentzian 3-space with inner product (, ). Let Q3 be the conformal compactification of R13, obtained by attaching a light-cone C∞ to R13 in infinity. Then Q3 has a standard conformal Lorentzian structure with the conformal transformation group O(3,2)/{±1}. In this paper, we study local conformal invariants of time-like surfaces in Q3 and dual theorem for Willmore surfaces in Q3. Let M (?) R13 be a time-like surface. Let n be the unit normal and H the mean curvature of the surface M. For any p ∈ M we define S12(p) = {X ∈ R13 (X - c(P),X - c(p)) = 1/H(p)2} with c(p) = P+ 1/H(p)n(P) ∈ R13. Then S12 (p) is a one-sheet-hyperboloid in R3, which has the same tangent plane and mean curvature as M at the point p. We show that the family {S12(p),p ∈ M} of hyperboloid in R13 defines in general two different enveloping surfaces, one is M itself, another is denoted by M (may be degenerate), and called the associated surface of M. We show that (i) if M is a time-like Willmore surface in Q3 with non-degenerate associated surface M, then M is also a time-like Willmore surface in Q3 satisfying M = M; (ii) if M is a single point, then M is conformally equivalent to a minimal surface in R13.展开更多
Let Q^3 be the common conformal compactification space of the Lorentzian space forms Q^3 1 ,S^3 1,We study the conformal geometry of space-like surfaces in Q^3 ,It is shown that any conformal CMC-surface in Q^3 must b...Let Q^3 be the common conformal compactification space of the Lorentzian space forms Q^3 1 ,S^3 1,We study the conformal geometry of space-like surfaces in Q^3 ,It is shown that any conformal CMC-surface in Q^3 must be conformally equivalent to a constant mean curvature surface in R^3 1,or,H^3 1,We also show that if x ：M→Q^3 is a space-like Willmore surface whose conformal metric g has constant curvature K,the either K = -1 and x is conformally equivalent to a minimal surface in R^3 1,or K=0 and x is conformally equivalent to the surface H^1（1/√2）×H^1（1/√2） in H^3 1.展开更多
Contractions of the Lie algebras d = u(2), f = u(1 ,1) to the oscillator Lie algebra l are realized via the adjoint action of SU(2,2) when d, l, f are viewed as subalgebras of su(2,2). Here D, L, F are the correspondi...Contractions of the Lie algebras d = u(2), f = u(1 ,1) to the oscillator Lie algebra l are realized via the adjoint action of SU(2,2) when d, l, f are viewed as subalgebras of su(2,2). Here D, L, F are the corresponding (four-dimensional) real Lie groups endowed with bi-invariant metrics of Lorentzian signature. Similar contractions of (seven-dimensional) isometry Lie algebras iso(D), iso(F) to iso(L) are determined. The group SU(2,2) acts on each of the D, L, F by conformal transformation which is a core feature of the DLF-theory. Also, d and f are contracted to T, S-abelian subalgebras, generating parallel translations, T, and proper conformal transformations, S (from the decomposition of su(2,2) as a graded algebra T + Ω + S, where Ω is the extended Lorentz Lie algebra of dimension 7).展开更多
In this article, we give the area formula of the closed projection curve of a closed space curve in Lorentzian 3-space L3. For the 1-parameter closed Lorentzian space motion in L3, we obtain a Holditch Theorem taking ...In this article, we give the area formula of the closed projection curve of a closed space curve in Lorentzian 3-space L3. For the 1-parameter closed Lorentzian space motion in L3, we obtain a Holditch Theorem taking into account the Lorentzian matrix multiplication for the closed space curves by using their othogonal projections onto the Euclidean plane in the fixed Lorentzian space. Moreover, we generalize this Holditch Theorem for noncollinear three fixed points of the moving Lorentzian space and any other fixed point on the plane which is determined by these three fixed points.展开更多
We consider <i>multiverses</i> as time-amalgamated multiply warped products of Lorentzian (Einstein) manifolds. We define the Local Multiverse as a time-connected component associated with our physical (3 ...We consider <i>multiverses</i> as time-amalgamated multiply warped products of Lorentzian (Einstein) manifolds. We define the Local Multiverse as a time-connected component associated with our physical (3 + 1)-spacetime. It is a collection of “parallel universes” with (mutually) synchronized timelines. Metaphysical considerations suggest that the Local Multiverse could be an extremely complex agglomeration with, at least, several hundred parallel universes in the Solar neighbourhood (and many thousands in galaxy bulks). In this paper we study a simplified time-almagamated globally hyperbolic model. Our picture implies the multiversality of elementary particles which are, actually, transcosmic (super)strings with multiple endpoints on parallel universes considered as D-branes.展开更多
Time evolution dynamics of three non-coupled two-level atoms independently interacting with their reservoirs is solved exactly by considering a damping Lorentzian spectral density.For three atoms initially prepared in...Time evolution dynamics of three non-coupled two-level atoms independently interacting with their reservoirs is solved exactly by considering a damping Lorentzian spectral density.For three atoms initially prepared in Greenberger-Horne-Zeilinger-type state,quantum correlation dynamics in a Markovian reservoir is compared with that in a nonMarkovian reservoir.By increasing detuning quantity in the non-Markovian reservoir,three-atom correlation dynamics measured by negative eigenvalue presents a trapping phenomenon which provides long-time quantum entanglement.Then we compare the correlation dynamics of three atoms with that of two atoms,measured by quantum entanglement and quantum discord for an initial robuster-entangled type state.The result further confirms that quantum discord is indeed different from quantum entanglement in identifying quantum correlation of many bodies.展开更多
A hypersurface x(M)in Lorentzian space R41 is called conformal homogeneous,if for any two points p,q on M,there exists,a conformal transformation of R41,such that(x(M))=x(M),(x(p))=x(q).In this paper,the authors gi...A hypersurface x(M)in Lorentzian space R41 is called conformal homogeneous,if for any two points p,q on M,there exists,a conformal transformation of R41,such that(x(M))=x(M),(x(p))=x(q).In this paper,the authors give a complete classifica-tion for regular time-like conformal homogeneous hypersurfaces in R41 with three distinct principal curvatures.展开更多
We investigate a parabolic-elliptic system which is related to a harmonic map from a compact Riemann surface with a smooth boundary into a Lorentzian manifold with a warped product metric.We prove that there exists a ...We investigate a parabolic-elliptic system which is related to a harmonic map from a compact Riemann surface with a smooth boundary into a Lorentzian manifold with a warped product metric.We prove that there exists a unique global weak solution for this system which is regular except for at most finitely many singular points.展开更多
Starting with the original sub-quantum dark energy model, the current accelerating phase of the evolution of the universe is considered by constructing most economical cosmic models that use just general relativity an...Starting with the original sub-quantum dark energy model, the current accelerating phase of the evolution of the universe is considered by constructing most economical cosmic models that use just general relativity and some dominating quantum effects associated with the probabilistic description of quantum physics. Two of such models are explicitly considered. They support an interpretation of dark energy in terms of the entangled energy of the universe. The model only violates the dominant energy condition quantum mechanically, that is by an amount given by the entanglement energy density, and gives rise to an asymptotically anti-de Sitter wormhole that becomes an asymptotically flat wormhole in the classical limit. It is shown that for most cosmic solutions such a wormhole does not predict any big trip phenomenon when it accretes phantom like energy.展开更多
It is well known that a totally geodesic Lagrangian surface in a Lorentzian complex space form M12（4ε） of constant holomorphic sectional curvature 4s is of constant curvature 6. A natural question is ＂Besides tota...It is well known that a totally geodesic Lagrangian surface in a Lorentzian complex space form M12（4ε） of constant holomorphic sectional curvature 4s is of constant curvature 6. A natural question is ＂Besides totally geodesic ones how many Lagrangian surfaces of constant curvature εin M12（46） are there？＂ In an earlier paper an answer to this question was obtained for the case e = 0 by Chen and Fastenakels. In this paper we provide the answer to this question for the case ε≠0. Our main result states that there exist thirty-five families of Lagrangian surfaces of curvature ε in M12（4ε） with ε ≠ 0. Conversely, every Lagrangian surface of curvature ε≠0 in M12（4ε） is locally congruent to one of the Lagrangian surfaces given by the thirty-five families.展开更多
In this article, the properties of the homothetic motions in three-dimensional Lorentz space are investigated. Also, some geometric results between velocity and acceleration vectors of a point in a spatial motion are ...In this article, the properties of the homothetic motions in three-dimensional Lorentz space are investigated. Also, some geometric results between velocity and acceleration vectors of a point in a spatial motion are obtained.展开更多
One of the most fundamental problems in the study of Lagrangian submanifolds from Riemannian geometric point of view is to classify Lagrangian immersions of real space forms into complex space forms. The main purpose ...One of the most fundamental problems in the study of Lagrangian submanifolds from Riemannian geometric point of view is to classify Lagrangian immersions of real space forms into complex space forms. The main purpose of this paper is thus to classify flat Lagrangian surfaces in the Lorentzian complex plane C1^2. Our main result states that there are thirty-eight families of flat Lagrangian surfaces in C1^2. Conversely, every flat Lagrangian surface in C1^2 is locally congruent to one of the thirty-eight families.展开更多
The dynamics of two non-coupled qubits independently interacting with their reservoirs is solved by the time convolutionless projection operator method. We study two-qubit quantum correlation dynamics for two differen...The dynamics of two non-coupled qubits independently interacting with their reservoirs is solved by the time convolutionless projection operator method. We study two-qubit quantum correlation dynamics for two different types of spectral densities, which are a Lorentzian distribution and an Ohmic spectral density with a Lorentzian–Drude cutoff function. For two qubits initially prepared in the initial Bell state, quantum discord can keep longer time and reach larger values in nonMarkovian reservoirs for the first spectral distribution or by reducing the cutoff frequency for the second case. For the initial Bell-like state, the dynamic behaviors of quantum discord and entanglement are compared. The results show that a long time of quantum correlation can be obtained by adjusting some parameters in experiment and further confirm that the discord can capture quantum correlation in addition to entanglement.展开更多
Phase noise analysis of an oscillator is implemented with its periodic time-varying small signal state equations by perturbing the autonomous large signal state equations of the oscillator. In this paper, the time dom...Phase noise analysis of an oscillator is implemented with its periodic time-varying small signal state equations by perturbing the autonomous large signal state equations of the oscillator. In this paper, the time domain steady solutions of oscillators are perturbed with traditional regular method; the periodic time-varying Jocobian modulus matrices are decomposed with Sylvester theorem, and on the resulting space spanned by periodic vectors, the conditions under which the oscillator holds periodic steady states with any perturbations are analyzed. In this paper, stochastic calculus is applied to disclose the generation process of phase noise and calculate the phase jitter of the oscillator by injecting a pseudo sinusoidal signal in frequency domain, representing the white noise, and a δcorrelation signal in time domain into the oscillator. Applying the principle of frequency modulation, we learned how the power-law and the Lorentzian spectrums are formed. Their relations and the Lorentzian spectrums of harmonics are also worked out. Based on the periodic Jacobian modulus matrix, the simple algorithms for Floquet exponents and phase noise are constructed, as well as a simple case is demonstrated. The analysis difficulties and the future directions for the phase noise of oscillators are also pointed out at the end.展开更多
基金supported by the National Natural Science Foundation of China (Grant No. 10905093)the Program for New Century Excellent Talents in Universities of China (Grant No. NCET-04-1006)the Foundation for the Author of National Excellent Doctoral Dissertation ofChina (Grant No. 200136)
文摘A model of an energy selective electron (ESE) engine with linear heat leakage and Lorentzian transmission probability is established in this paper.The expressions for the main performance parameters of the ESE engine operating as a heat engine or a refrigerator are derived by using the theory of finite time thermodynamics.The optimum performances of the ESE engine are explored and the influences of the heat leakage,the central energy level of the resonance,and the width of the resonance on the performance of the ESE engine are analyzed by using detailed numerical examples.The optimal operation regions of power output and efficiency (or cooling load and coefficient of performance (COP)) are also discussed.Moreover,the performances of the ESE engine with Lorentzian transmission probability are compared with those with rectangular transmission probability.It is shown that the power output versus efficiency (or cooling load versus COP) characteristic curves with and without heat leakage are all closed loop-shaped ones.The efficiency (or COP) of the ESE engine decreases as the heat leakage increases.It is found that as the resonance width increases,the power output and efficiency (or cooling load and COP) increase to a maximum and then decrease due to the finite range of energies which contribute positively to the power generation or refrigeration in the electron system.Especially,when heat leakage is taken into account,the characteristic curves of maximum efficiency (or maximum COP) versus half resonance width are parabolic-like ones,which are quite different from the monotonic decreasing characteristic curves obtained in previous analyses without considering heat leakage.The results obtained in this paper can provide some theoretical guidelines for the design and operation of practical electron energy conversion devices such as solid-state thermionic refrigerators.
基金supported by National Natural Science Foundation of China (Grant No.10871035)the New Century Excellent Talents in University of China (Grant No. 05-0319)
文摘Anti de Sitter space is a maximally symmetric, vacuum solution of Einstein's field equation with an attractive cosmological constant, and is the hyperquadric of semi-Euclidean space with index 2. So it is meaningful to study the submanifold in semi-Euclidean 4-space with index 2. However, the research on the submanifold in semi-Euclidean 4-space with index 2 has not been found from theory of singularity until now. In this paper, as a generalization of the study on lightlike hypersurface in Minkowski space and a preparation for the further study on anti de Sitter space, the singularities of lightlike hypersurface and Lorentzian surface in semi- Euclidean 4-space with index 2 will be studied. To do this, we reveal the relationships between the singularity of distance-squared function and that of lightlike hypersurface. In addition some geometric properties of lightlike hypersurface and Lorentzian surface are studied from geometrical point of view.
基金The authors gratefully acknowledge the China Postdoctoral Science Foundation(Project No.2014M561096)the Special Fund for Agro-scientific Research in the Public Interest Program(Project No.201003008)the National Science and Technology Support Program(Project No.2012BAH04B00)for supporting this research.
文摘This study aimed to investigate the capabilities of hyperspectral scattering imaging in tandem with Gaussian function,Exponential function and Lorentzian function for rapid and nondestructive determination of total viable count(TVC)in pork meat.Two batches of fresh pork meat was purchased from a local market and stored at 10°C for 1-9 d.Totally 60 samples were used,and several samples were taken out randomly for hyperspectral scattering imaging and conventional microbiological tests on each day of the experiments.The functions of Gaussian,Exponential and Lorentzian were employed to model the hyperspectral scattering profiles of pork meat,and good fitting results were obtained by all three functions between 455 nm and 1000 nm.The Lorentzian function performed best for fitting the hyperspectral scattering profiles of pork meat compared with other functions.Both principal component regression(PCR)and partial least squares regression(PLSR)methods were performed to establish the prediction models.Among all the developed models,the models developed using parameters CE(scattering width parameter of Exponential function)and CL(scattering width parameter of Lorentzian function)by PLSR method gave superior results for predicting pork meat TVC,with RV and RMSEV of 0.92,0.59 log CFU/g,and 0.91,0.61 log CFU/g,respectively.In addition,based on the improved hyperspectral scattering system,parameter c which represented the scattering widths in all three functions gave more accurate prediction results,regardless of the modeling methods(PCR or PLSR).The obtained results demonstrated that hyperspectral scattering imaging combined with the presented data analysis algorithm can be a powerful tool for evaluating the microbial safety of meat in the future.
基金Supported by China Scholarship Council(Grant No.[2011]5025)
文摘Let x ：M - Qn＋l be a regular hypersurface in the conformal space Qn＋I. We classify all the space-like Blaschke isoparametric hypersurfaces with two distinct Blaschke eigenvalues in the conformal space up to the conformal equivalence.
基金Supported by Scientific and Technological Innovation Programs of Higher Education Institutions in Shanxi Province(2013123)
文摘In this study, fresh pork tenderness, drip-loss, pH value and color parameters （ CIE, a ＊ , b ＊ and L ＊ values） were simultaneously predicted using hyperspectral scattering imaging （HSI） technique. The hyperspectral scattering images of dO fresh pork samples were collected at the wavelength of 400 -I 100 nm, and the scattering profiles were fitted via Lorontzian distribution （ LD ） function to give three parameters a （ asymptotic value ）, b （peak value ） and c （ full width at b/2）. Stepwise discrimination was performed to determine the optimal wavelengths combinations. The LD parameters combinations （a, b and c） of optimal wavelengths were used to establish multi-linear regression （MLR） models to predict the pork attributes. The models were able to predict pork with high correlation coefficients of 0.92 for drip-loss, 0.94, 0.92 and 0.98 respectively for color parameters （ a ＊ , b＊ and L ＊ ）, and for tenderness and pH value the models gave the correlation coefficients of 0.69 and 0.76, respectively. These results showed that the hyperspectral scattering technique was capable of predicting quality parameters of perk. The study provides an efficient means for rapid and nondestructive determination of pork quality simultaneously.
基金supported by National Natural Science Foundation of China (Grant Nos. 11331002, 11471021 and 11601513)the Fundamental Research Funds for Central Universitiesthe Project of Fujian Provincial Department of Education (Grant No. JA15123)
文摘A three dimensional Lorentzian hypersurface x : M_1~3→ R_1~4 is called conformally flat if its induced metric is conformal to the flat Lorentzian metric, and this property is preserved under the conformal transformation of R_1~4. Using the projective light-cone model, for those whose shape operators have three distinct real eigenvalues, we calculate the integrability conditions by constructing a scalar conformal invariant and a canonical moving frame in this paper. Similar to the Riemannian case, these hypersurfaces can be determined by the solutions to some system of partial differential equations.
基金supported by Research Foundation for Doctor Programme(Grant No.20040001034)National Natural Science Foundation of China(Grant No.10125105).
文摘Let R13 be the Lorentzian 3-space with inner product (, ). Let Q3 be the conformal compactification of R13, obtained by attaching a light-cone C∞ to R13 in infinity. Then Q3 has a standard conformal Lorentzian structure with the conformal transformation group O(3,2)/{±1}. In this paper, we study local conformal invariants of time-like surfaces in Q3 and dual theorem for Willmore surfaces in Q3. Let M (?) R13 be a time-like surface. Let n be the unit normal and H the mean curvature of the surface M. For any p ∈ M we define S12(p) = {X ∈ R13 (X - c(P),X - c(p)) = 1/H(p)2} with c(p) = P+ 1/H(p)n(P) ∈ R13. Then S12 (p) is a one-sheet-hyperboloid in R3, which has the same tangent plane and mean curvature as M at the point p. We show that the family {S12(p),p ∈ M} of hyperboloid in R13 defines in general two different enveloping surfaces, one is M itself, another is denoted by M (may be degenerate), and called the associated surface of M. We show that (i) if M is a time-like Willmore surface in Q3 with non-degenerate associated surface M, then M is also a time-like Willmore surface in Q3 satisfying M = M; (ii) if M is a single point, then M is conformally equivalent to a minimal surface in R13.
基金the National Natural Science Foundation of China (No. 10125105) the Research Fund for the Doctoral Program of Higher Education.
文摘Let Q^3 be the common conformal compactification space of the Lorentzian space forms Q^3 1 ,S^3 1,We study the conformal geometry of space-like surfaces in Q^3 ,It is shown that any conformal CMC-surface in Q^3 must be conformally equivalent to a constant mean curvature surface in R^3 1,or,H^3 1,We also show that if x ：M→Q^3 is a space-like Willmore surface whose conformal metric g has constant curvature K,the either K = -1 and x is conformally equivalent to a minimal surface in R^3 1,or K=0 and x is conformally equivalent to the surface H^1（1/√2）×H^1（1/√2） in H^3 1.
文摘Contractions of the Lie algebras d = u(2), f = u(1 ,1) to the oscillator Lie algebra l are realized via the adjoint action of SU(2,2) when d, l, f are viewed as subalgebras of su(2,2). Here D, L, F are the corresponding (four-dimensional) real Lie groups endowed with bi-invariant metrics of Lorentzian signature. Similar contractions of (seven-dimensional) isometry Lie algebras iso(D), iso(F) to iso(L) are determined. The group SU(2,2) acts on each of the D, L, F by conformal transformation which is a core feature of the DLF-theory. Also, d and f are contracted to T, S-abelian subalgebras, generating parallel translations, T, and proper conformal transformations, S (from the decomposition of su(2,2) as a graded algebra T + Ω + S, where Ω is the extended Lorentz Lie algebra of dimension 7).
文摘In this article, we give the area formula of the closed projection curve of a closed space curve in Lorentzian 3-space L3. For the 1-parameter closed Lorentzian space motion in L3, we obtain a Holditch Theorem taking into account the Lorentzian matrix multiplication for the closed space curves by using their othogonal projections onto the Euclidean plane in the fixed Lorentzian space. Moreover, we generalize this Holditch Theorem for noncollinear three fixed points of the moving Lorentzian space and any other fixed point on the plane which is determined by these three fixed points.
文摘We consider <i>multiverses</i> as time-amalgamated multiply warped products of Lorentzian (Einstein) manifolds. We define the Local Multiverse as a time-connected component associated with our physical (3 + 1)-spacetime. It is a collection of “parallel universes” with (mutually) synchronized timelines. Metaphysical considerations suggest that the Local Multiverse could be an extremely complex agglomeration with, at least, several hundred parallel universes in the Solar neighbourhood (and many thousands in galaxy bulks). In this paper we study a simplified time-almagamated globally hyperbolic model. Our picture implies the multiversality of elementary particles which are, actually, transcosmic (super)strings with multiple endpoints on parallel universes considered as D-branes.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 11104113 and 11264011)the Natural Science Foundation of Hunan Province,China (Grant Nos. 09JJ6011 and 11JJ6007)
文摘Time evolution dynamics of three non-coupled two-level atoms independently interacting with their reservoirs is solved exactly by considering a damping Lorentzian spectral density.For three atoms initially prepared in Greenberger-Horne-Zeilinger-type state,quantum correlation dynamics in a Markovian reservoir is compared with that in a nonMarkovian reservoir.By increasing detuning quantity in the non-Markovian reservoir,three-atom correlation dynamics measured by negative eigenvalue presents a trapping phenomenon which provides long-time quantum entanglement.Then we compare the correlation dynamics of three atoms with that of two atoms,measured by quantum entanglement and quantum discord for an initial robuster-entangled type state.The result further confirms that quantum discord is indeed different from quantum entanglement in identifying quantum correlation of many bodies.
基金supported by the Principal’s Fund(No.KJ2020002)the second is supported by the National Natural Science Foundation of China(Nos.11671330 and 11871405)the third is supported by the National Natural Science Foundation of China(Nos.11831005,1196131001).
文摘A hypersurface x(M)in Lorentzian space R41 is called conformal homogeneous,if for any two points p,q on M,there exists,a conformal transformation of R41,such that(x(M))=x(M),(x(p))=x(q).In this paper,the authors give a complete classifica-tion for regular time-like conformal homogeneous hypersurfaces in R41 with three distinct principal curvatures.
基金supported by National Natural Science Foundation of China(Grant Nos.11471014 and 11471299)the Fundamental Research Funds for the Central Universities
文摘We investigate a parabolic-elliptic system which is related to a harmonic map from a compact Riemann surface with a smooth boundary into a Lorentzian manifold with a warped product metric.We prove that there exists a unique global weak solution for this system which is regular except for at most finitely many singular points.
文摘Starting with the original sub-quantum dark energy model, the current accelerating phase of the evolution of the universe is considered by constructing most economical cosmic models that use just general relativity and some dominating quantum effects associated with the probabilistic description of quantum physics. Two of such models are explicitly considered. They support an interpretation of dark energy in terms of the entangled energy of the universe. The model only violates the dominant energy condition quantum mechanically, that is by an amount given by the entanglement energy density, and gives rise to an asymptotically anti-de Sitter wormhole that becomes an asymptotically flat wormhole in the classical limit. It is shown that for most cosmic solutions such a wormhole does not predict any big trip phenomenon when it accretes phantom like energy.
文摘It is well known that a totally geodesic Lagrangian surface in a Lorentzian complex space form M12（4ε） of constant holomorphic sectional curvature 4s is of constant curvature 6. A natural question is ＂Besides totally geodesic ones how many Lagrangian surfaces of constant curvature εin M12（46） are there？＂ In an earlier paper an answer to this question was obtained for the case e = 0 by Chen and Fastenakels. In this paper we provide the answer to this question for the case ε≠0. Our main result states that there exist thirty-five families of Lagrangian surfaces of curvature ε in M12（4ε） with ε ≠ 0. Conversely, every Lagrangian surface of curvature ε≠0 in M12（4ε） is locally congruent to one of the Lagrangian surfaces given by the thirty-five families.
文摘In this article, the properties of the homothetic motions in three-dimensional Lorentz space are investigated. Also, some geometric results between velocity and acceleration vectors of a point in a spatial motion are obtained.
基金a research grant for Research Assistant of the Fund for Scientific Research Flanders(Belgium)(FWO)
文摘One of the most fundamental problems in the study of Lagrangian submanifolds from Riemannian geometric point of view is to classify Lagrangian immersions of real space forms into complex space forms. The main purpose of this paper is thus to classify flat Lagrangian surfaces in the Lorentzian complex plane C1^2. Our main result states that there are thirty-eight families of flat Lagrangian surfaces in C1^2. Conversely, every flat Lagrangian surface in C1^2 is locally congruent to one of the thirty-eight families.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 11264011 and 11104113)the Natural Science Foundation of Hunan Province, China (Grant Nos. 13JJ6059 and 11JJ6007)the Natural Science Foundation of Education Department of Hunan Province, China (GrantNo. 11C1057)
文摘The dynamics of two non-coupled qubits independently interacting with their reservoirs is solved by the time convolutionless projection operator method. We study two-qubit quantum correlation dynamics for two different types of spectral densities, which are a Lorentzian distribution and an Ohmic spectral density with a Lorentzian–Drude cutoff function. For two qubits initially prepared in the initial Bell state, quantum discord can keep longer time and reach larger values in nonMarkovian reservoirs for the first spectral distribution or by reducing the cutoff frequency for the second case. For the initial Bell-like state, the dynamic behaviors of quantum discord and entanglement are compared. The results show that a long time of quantum correlation can be obtained by adjusting some parameters in experiment and further confirm that the discord can capture quantum correlation in addition to entanglement.
基金the National Fundamental Research Project (Grant Nos. G1999032903 and 90307016)the National Natural Science Founda-tion of China (Grant No. 60025101)and the "863" Program (Grant No. 2003AA1Z1390)
文摘Phase noise analysis of an oscillator is implemented with its periodic time-varying small signal state equations by perturbing the autonomous large signal state equations of the oscillator. In this paper, the time domain steady solutions of oscillators are perturbed with traditional regular method; the periodic time-varying Jocobian modulus matrices are decomposed with Sylvester theorem, and on the resulting space spanned by periodic vectors, the conditions under which the oscillator holds periodic steady states with any perturbations are analyzed. In this paper, stochastic calculus is applied to disclose the generation process of phase noise and calculate the phase jitter of the oscillator by injecting a pseudo sinusoidal signal in frequency domain, representing the white noise, and a δcorrelation signal in time domain into the oscillator. Applying the principle of frequency modulation, we learned how the power-law and the Lorentzian spectrums are formed. Their relations and the Lorentzian spectrums of harmonics are also worked out. Based on the periodic Jacobian modulus matrix, the simple algorithms for Floquet exponents and phase noise are constructed, as well as a simple case is demonstrated. The analysis difficulties and the future directions for the phase noise of oscillators are also pointed out at the end.
