Scalar fields should have no spin angular momentum according to conventional textbook understandings inclassical field theory.Yet,recent studies demonstrate the undoubted existence of wave spin endowed by acousticand ...Scalar fields should have no spin angular momentum according to conventional textbook understandings inclassical field theory.Yet,recent studies demonstrate the undoubted existence of wave spin endowed by acousticand elastic longitudinal waves,which are of irrotational curl-free nature without vorticity and can be describedby scalar fields.Moreover,the conventional theory cannot even answer the question of whether wave spin existsin dissipative fields,given the ubiquitous dissipation in reality.Here,to resolve the seeming paradox and answerthe challenging question,we uncover the origin of wave spin in scalar fields beyond traditional formalism byclarifying that the presence of higher-order derivatives in scalar field Lagrangians can give rise to non-vanishingwave spin.For“spinless”scalar fields of only first-order derivatives,we can make the hidden wave spin emergeby revealing a latent field that leads to the original field through a time derivative,thus giving higher-order termsin Lagrangian.Based on the standard Noether theorem approach,we exemplify the wave spin for unconventionaldrifted acoustic fields,and even for dissipative media,in scalar fields with higher-order derivative Lagrangian.The results would prompt people to build more comprehensive and fundamental understandings of structuralwave spin in classical fields.展开更多
The novel free-form deformation (FFD) technique presented in the paper uses scalar fields definedby skeletons with arbitrary topology. The technique embeds objects into the scalar field by assigning a field value to e...The novel free-form deformation (FFD) technique presented in the paper uses scalar fields definedby skeletons with arbitrary topology. The technique embeds objects into the scalar field by assigning a field value to each point of the objects. When the space of the skeleton is changed, the distribution of the scalar field changes accordingly, which implicitly defines a deformation of the space. The generality of skeletons assures that the technique can freely define deformable regions to produce a broader range of shape deformations.展开更多
We study the dynamic of scalar bosons in the presence of Aharonov-Bohm magnetic field. First, we give the differential equation that governs this dynamic. Secondly, we use variational techniques to show that the follo...We study the dynamic of scalar bosons in the presence of Aharonov-Bohm magnetic field. First, we give the differential equation that governs this dynamic. Secondly, we use variational techniques to show that the following Schrödinger-Newton equation: , where A is an Aharonov-Bohm magnetic potential, has a unique ground-state solution.展开更多
Some extended solution mapping relations of the nonlinear coupled scalar field and the well-known φ^4 model are presented. Simultaneously, inspired by the new solutions of the famous φ^4 model recently proposed by J...Some extended solution mapping relations of the nonlinear coupled scalar field and the well-known φ^4 model are presented. Simultaneously, inspired by the new solutions of the famous φ^4 model recently proposed by Jia, Huang and Lou, five kinds of new localized excitations of the nonlinear coupled scaiar field （NCSF） system are obtained.展开更多
QED(quantum electrodynamics)is the QFT(quantum field theory)describing the interaction between light and matter.While conventional QED is based on TEM(transverse electromagnetic)waves,there has been increasing interes...QED(quantum electrodynamics)is the QFT(quantum field theory)describing the interaction between light and matter.While conventional QED is based on TEM(transverse electromagnetic)waves,there has been increasing interest in the theoretical and experimental exploration of LSW(longitudinal scalar waves)solutions that are often omitted in CED(classical electrodynamics)but may have physical significance in nontrivial vacuum conditions.This paper delves into the theoretical foundation of LSW,their role in QED,and the associated mathematical equations governing their dynamics.展开更多
Reasonable approximations are introduced to investigate the real scalar field scattering in the nearly extremal Schwarzschild-de Sitter （SdS） space. The approximations naturally lead to the invertible x（r） and the...Reasonable approximations are introduced to investigate the real scalar field scattering in the nearly extremal Schwarzschild-de Sitter （SdS） space. The approximations naturally lead to the invertible x（r） and the global replacement of the true potential by a PSshl-Teller one. Meanwhile, the Schr6dinger-like wave equation is transformed into a solvable form. Our numerical solutions to the wave equation show that the wave is characteristically similar to the harmonic under the tortoise coordinate x, while the wave piles up near the two horizons and the wavelength tends to its maximum as the potential approaches to the peak under the radial coordinate τ.展开更多
As one of the fitting methods, the polynomial approximation is effective to process sophisticated problem. In this paper, we employ this approach to handle the scattering of scalar field around the Schwarzschild-de Si...As one of the fitting methods, the polynomial approximation is effective to process sophisticated problem. In this paper, we employ this approach to handle the scattering of scalar field around the Schwarzschild-de Sitter blackhole. The complicated relationship between tortoise coordinate and radial coordinate is replaced by the approximate polynomial. The Schroedinger-like equation, the real boundary conditions and the polynomial approximation construct a full Sturm Liouville type problem. Then this boundary value problem can be solved numerically for two limiting cases： the first one is the Nariai black-hole whose horizons are close to each other, the second one is the black-hole with the horizons widely separated. Compared with previous results （Brevik and Tian）, the field near the event horizon and cosmological horizon can have a better description.展开更多
Named entity recognition is a fundamental task in biomedical data mining. In this letter, a named entity recognition system based on CRFs （Conditional Random Fields） for biomedical texts is presented. The system mak...Named entity recognition is a fundamental task in biomedical data mining. In this letter, a named entity recognition system based on CRFs （Conditional Random Fields） for biomedical texts is presented. The system makes extensive use of a diverse set of features, including local features, full text features and external resource features. All features incorporated in this system are described in detail, and the impacts of different feature sets on the performance of the system are evaluated. In order to improve the performance of system, post-processing modules are exploited to deal with the abbreviation phenomena, cascaded named entity and boundary errors identification. Evaluation on this system proved that the feature selection has important impact on the system performance, and the post-processing explored has an important contribution on system performance to achieve better resuits.展开更多
In the present paper, we study the finite time domain dynamics of a scalar field interacting with external sources. We expand both the scalar field and the corresponding Hamiltonian in annihilation and creation operat...In the present paper, we study the finite time domain dynamics of a scalar field interacting with external sources. We expand both the scalar field and the corresponding Hamiltonian in annihilation and creation operators and evaluate the relevant path integral. So, we get the Green function within a finite time interval. We apply the solution to the relevant Cauchy problem and further, we study the dynamics of scalar fields coupled with electromagnetic fields via perturbative methods.展开更多
In this paper we investigate the scalar field evolution in the dyadosphere spacetime by using the third-order WKB approximation. We find that the coupling term between the gravitation and the nonlinear electrodynamics...In this paper we investigate the scalar field evolution in the dyadosphere spacetime by using the third-order WKB approximation. We find that the coupling term between the gravitation and the nonlinear electrodynamics makes the scalar field decay more quickly and it also makes the scalar field oscillate more slowly. On the o＇ther words, this coupling term takes effect on the scalar field evolution as a damping factor. At the same time these effects become more obvious for the scalar field with higher angle quantum number.展开更多
This paper is devoted to study the modified holographic dark energy model by taking its different aspects in the t/at Kaiuza-Klein universe. We construct the equation of state parameter which evolutes the universe fro...This paper is devoted to study the modified holographic dark energy model by taking its different aspects in the t/at Kaiuza-Klein universe. We construct the equation of state parameter which evolutes the universe from quintessence region towards the vacuum. It is found that the modified holographic model exhibits instability against small perturbations in the early epoch of the universe but becomes stable in the later times. We also develop its correspondence with some scalar field dark energy models. It is interesting to mention here that ail the results are consistent with the present observations.展开更多
We assume generalized ghost Pilgrim dark energy(GGPDE) model in the presence of cold dark matter in flat FRW universe.With suitable choice of interaction term between GGPDE and cold dark matter,we investigate the natu...We assume generalized ghost Pilgrim dark energy(GGPDE) model in the presence of cold dark matter in flat FRW universe.With suitable choice of interaction term between GGPDE and cold dark matter,we investigate the nature of equation of state parameter for GGPDE.Also,we investigate the natures of dynamical scalar field models(such as quintessence,tachyon,k-essence,and dilaton dark energy) and concerned potentials through the correspondence phenomenon between GGPDE and these models.展开更多
In this paper,we study the thermodynamics and the weak cosmic censorship conjecture of the nonlinear electrodynamics black hole under the scattering of a charged complex scalar field.According to the energy and charge...In this paper,we study the thermodynamics and the weak cosmic censorship conjecture of the nonlinear electrodynamics black hole under the scattering of a charged complex scalar field.According to the energy and charge fluxes of the scalar field,the variations of this black hole’s energy and charge can be calculated during an infinitesimal time interval.With scalar field scattering,the variation of the black hole is calculated in the extended and normal phase spaces.In the normal phase space,the cosmological constant and the normalization parameter are fixed,and the first and second laws of thermodynamics can also be satisfied.In the extended phase space,the cosmological constant and the normalization parameter are considered as thermodynamic variables,and the first law of thermodynamics is valid,but the second law of thermodynamics is not valid.Furthermore,the weak cosmic censorship conjecture is both valid in the extended and normal phase spaces.展开更多
This research work is related to soliton solutions considered as models that can describe the complex configuration of elementary particles from the study of the interactions of their fields. It is interested in the i...This research work is related to soliton solutions considered as models that can describe the complex configuration of elementary particles from the study of the interactions of their fields. It is interested in the interaction of fields between two different elementary particles by expressing their physical properties. For that, we have obtained, exact static plane symmetric soliton-like solutions to the nonlinear equations of interacting electromagnetic and scalar fields taking into account the own gravitational field of elementary particles using the calibrated invariance function <i>P</i>(<i>I</i>). It has been proved that all solutions of the Einstein, nonlinear electromagnetic and scalar field equations are regular with the localized energy density. Moreover, the total charge of particles is finite and the total energy of the interaction fields is bounded. It have been emphasized the importance to the own gravitational field of elementary particles and the role of the nonlinearity of fields in the determination of these solutions. In flat space-time, soliton-like solutions exist but the total energy of the interaction fields is equal to zero. We have also shown that in the linear case, soliton-like solutions are absent.展开更多
This paper investigates the resonant frequencies of the massless scalar field in the near extremal Kerr-like black-brane spacetime. It is shown that the different angular quantum number will present different resonant...This paper investigates the resonant frequencies of the massless scalar field in the near extremal Kerr-like black-brane spacetime. It is shown that the different angular quantum number will present different resonant frequencies. It is also shown that the real part of the resonant frequencies increases as the compact dimensions parameter μi increases, but the magnitude of the imaginary part decreases as μi increases.展开更多
By using two different transformations, several types of exact analytic solutions for a class of nonlinear coupled scalar field equation are obtained, which contain soliton solutions, singular solitary wave solutions ...By using two different transformations, several types of exact analytic solutions for a class of nonlinear coupled scalar field equation are obtained, which contain soliton solutions, singular solitary wave solutions and triangle function solutions. These results can be applied to other nonlinear equations. In addition, parts of conclusions in some references are corrected.展开更多
We discuss the coupling between dark energy and matter by considering a homogeneous tachyonic scalar field as a candidate for dark energy.We obtained the functional form of scale factor by assuming that the coupling s...We discuss the coupling between dark energy and matter by considering a homogeneous tachyonic scalar field as a candidate for dark energy.We obtained the functional form of scale factor by assuming that the coupling strength depends linearly on the Hubble parameter and energy density.We also estimated the cosmic age of the Universe for different values of coupling constant.展开更多
This paper studies phantom linear scalar field （LSF） and phantom non-linear Born-Infeld （NLBI） scalar field with square potential of the form V（Ф） =1/2m^2Ф^2. The equation of state parameter w（z）, and evolut...This paper studies phantom linear scalar field （LSF） and phantom non-linear Born-Infeld （NLBI） scalar field with square potential of the form V（Ф） =1/2m^2Ф^2. The equation of state parameter w（z）, and evolution of scale factor a（t） in both phantom LSF and phantom NLBI scalar model are explored. The age of universe Hot and the transition redshift Z are obtained. The Gold data set of 157-SN-Ia is used to constrain parameters of the two models by numerical calculation. The phantom LSF is slightly better than the phantom NLBI type scalar field model for a large m. Although a smaller m corresponding to a slower rolling of field Ф better fits the observation data, the difference between phantom NLBI scalar field and phantom LSF is not distinct in this case.展开更多
Recently, considerable progress has been made in understanding the early universe by loop quantum cosmology. Modesto et al. investigated the loop quantum black hole （LQBH）using improved semiclassical analysis and th...Recently, considerable progress has been made in understanding the early universe by loop quantum cosmology. Modesto et al. investigated the loop quantum black hole （LQBH）using improved semiclassical analysis and they found that the LQBH has two horizons, an event horizon and a Cauchy horizon, just like the Reissner-NordstrSm black hole. This paper focuses on the dynamical evolution of a massless scalar wave in the LQBH background. By investigating the relation between the complex frequencies of the massless scalar field and the LQBH parameters using the numerical method, we find that the polymeric parameter P makes the massless scalar field decay more quickly and makes the ground scalar wave oscillate slowly. However, the polymeric parameter P causes the frequency of the high harmonic massless scalar wave to shift according to its value. We also find that the loop quantum gravity area gap parameter a0 causes the massless scalar field to decay more slowly and makes the period of the massless scalar field wave become longer. In the complex ω plane, the frequency curves move counterclockwise when the polymeric parameter P increases and this spiral effect is more obvious for a higher harmonic scalar wave.展开更多
Some new estimations of scalar products of vector fields in unbounded domains are investigated. Lp-estimations for the vector fields were proved in special weighted functional spaces. The paper generalizes our earlier...Some new estimations of scalar products of vector fields in unbounded domains are investigated. Lp-estimations for the vector fields were proved in special weighted functional spaces. The paper generalizes our earlier results for bounded domains. Estimations for scalar products make it possible to investigate wide classes of mathematical physics problems in physically inhomogeneous domains. Such estimations allow studying issues of correctness for problems with non-smooth coefficients. The paper analyses solvability of stationary set of Maxwell equations in inhomogeneous unbounded domains based on the proved Lp-estimations.展开更多
基金supported by the National Key R&D Program of China(Grant Nos.2022YFA1404400 and 2023YFA1406900)the Natural Science Foundation of Shanghai(Grant No.23ZR1481200)the Program of Shanghai Academic Research Leader(Grant No.23XD1423800)。
文摘Scalar fields should have no spin angular momentum according to conventional textbook understandings inclassical field theory.Yet,recent studies demonstrate the undoubted existence of wave spin endowed by acousticand elastic longitudinal waves,which are of irrotational curl-free nature without vorticity and can be describedby scalar fields.Moreover,the conventional theory cannot even answer the question of whether wave spin existsin dissipative fields,given the ubiquitous dissipation in reality.Here,to resolve the seeming paradox and answerthe challenging question,we uncover the origin of wave spin in scalar fields beyond traditional formalism byclarifying that the presence of higher-order derivatives in scalar field Lagrangians can give rise to non-vanishingwave spin.For“spinless”scalar fields of only first-order derivatives,we can make the hidden wave spin emergeby revealing a latent field that leads to the original field through a time derivative,thus giving higher-order termsin Lagrangian.Based on the standard Noether theorem approach,we exemplify the wave spin for unconventionaldrifted acoustic fields,and even for dissipative media,in scalar fields with higher-order derivative Lagrangian.The results would prompt people to build more comprehensive and fundamental understandings of structuralwave spin in classical fields.
文摘The novel free-form deformation (FFD) technique presented in the paper uses scalar fields definedby skeletons with arbitrary topology. The technique embeds objects into the scalar field by assigning a field value to each point of the objects. When the space of the skeleton is changed, the distribution of the scalar field changes accordingly, which implicitly defines a deformation of the space. The generality of skeletons assures that the technique can freely define deformable regions to produce a broader range of shape deformations.
文摘We study the dynamic of scalar bosons in the presence of Aharonov-Bohm magnetic field. First, we give the differential equation that governs this dynamic. Secondly, we use variational techniques to show that the following Schrödinger-Newton equation: , where A is an Aharonov-Bohm magnetic potential, has a unique ground-state solution.
基金National Natural Science Foundation of China under Grant Nos.10475055 and 90503006the Scientific Research Fund of the Education Department of Zhejiang Province under Grant No.20040969
文摘Some extended solution mapping relations of the nonlinear coupled scalar field and the well-known φ^4 model are presented. Simultaneously, inspired by the new solutions of the famous φ^4 model recently proposed by Jia, Huang and Lou, five kinds of new localized excitations of the nonlinear coupled scaiar field （NCSF） system are obtained.
文摘QED(quantum electrodynamics)is the QFT(quantum field theory)describing the interaction between light and matter.While conventional QED is based on TEM(transverse electromagnetic)waves,there has been increasing interest in the theoretical and experimental exploration of LSW(longitudinal scalar waves)solutions that are often omitted in CED(classical electrodynamics)but may have physical significance in nontrivial vacuum conditions.This paper delves into the theoretical foundation of LSW,their role in QED,and the associated mathematical equations governing their dynamics.
基金Project supported by Doctoral Fund of QUST (Grant No. 0022171)
文摘Reasonable approximations are introduced to investigate the real scalar field scattering in the nearly extremal Schwarzschild-de Sitter （SdS） space. The approximations naturally lead to the invertible x（r） and the global replacement of the true potential by a PSshl-Teller one. Meanwhile, the Schr6dinger-like wave equation is transformed into a solvable form. Our numerical solutions to the wave equation show that the wave is characteristically similar to the harmonic under the tortoise coordinate x, while the wave piles up near the two horizons and the wavelength tends to its maximum as the potential approaches to the peak under the radial coordinate τ.
基金supported by the National Basic Research Program of China (Grant No 2003CB716300)National Natural Science Foundation of China (Grant No 10573003)
文摘As one of the fitting methods, the polynomial approximation is effective to process sophisticated problem. In this paper, we employ this approach to handle the scattering of scalar field around the Schwarzschild-de Sitter blackhole. The complicated relationship between tortoise coordinate and radial coordinate is replaced by the approximate polynomial. The Schroedinger-like equation, the real boundary conditions and the polynomial approximation construct a full Sturm Liouville type problem. Then this boundary value problem can be solved numerically for two limiting cases： the first one is the Nariai black-hole whose horizons are close to each other, the second one is the black-hole with the horizons widely separated. Compared with previous results （Brevik and Tian）, the field near the event horizon and cosmological horizon can have a better description.
基金Supported by The National Natural Science Foundation of China(No.60302021).
文摘Named entity recognition is a fundamental task in biomedical data mining. In this letter, a named entity recognition system based on CRFs （Conditional Random Fields） for biomedical texts is presented. The system makes extensive use of a diverse set of features, including local features, full text features and external resource features. All features incorporated in this system are described in detail, and the impacts of different feature sets on the performance of the system are evaluated. In order to improve the performance of system, post-processing modules are exploited to deal with the abbreviation phenomena, cascaded named entity and boundary errors identification. Evaluation on this system proved that the feature selection has important impact on the system performance, and the post-processing explored has an important contribution on system performance to achieve better resuits.
文摘In the present paper, we study the finite time domain dynamics of a scalar field interacting with external sources. We expand both the scalar field and the corresponding Hamiltonian in annihilation and creation operators and evaluate the relevant path integral. So, we get the Green function within a finite time interval. We apply the solution to the relevant Cauchy problem and further, we study the dynamics of scalar fields coupled with electromagnetic fields via perturbative methods.
基金Supported by the National Natural Science Foundation of China under Grant No.10873004the Program for Excellent Talents in Hunan Normal University,the State Key Development Program for Basic Research Program of China under Grant No.2010CB832803+1 种基金the Key project of the National Natural Science Foundation of China under Grant No.10935013Construct Program of the National Key Discipline and the Program for Changjiang Scholars and Innovative Research Team in University under Grant No.IRT0964
文摘In this paper we investigate the scalar field evolution in the dyadosphere spacetime by using the third-order WKB approximation. We find that the coupling term between the gravitation and the nonlinear electrodynamics makes the scalar field decay more quickly and it also makes the scalar field oscillate more slowly. On the o＇ther words, this coupling term takes effect on the scalar field evolution as a damping factor. At the same time these effects become more obvious for the scalar field with higher angle quantum number.
文摘This paper is devoted to study the modified holographic dark energy model by taking its different aspects in the t/at Kaiuza-Klein universe. We construct the equation of state parameter which evolutes the universe from quintessence region towards the vacuum. It is found that the modified holographic model exhibits instability against small perturbations in the early epoch of the universe but becomes stable in the later times. We also develop its correspondence with some scalar field dark energy models. It is interesting to mention here that ail the results are consistent with the present observations.
文摘We assume generalized ghost Pilgrim dark energy(GGPDE) model in the presence of cold dark matter in flat FRW universe.With suitable choice of interaction term between GGPDE and cold dark matter,we investigate the nature of equation of state parameter for GGPDE.Also,we investigate the natures of dynamical scalar field models(such as quintessence,tachyon,k-essence,and dilaton dark energy) and concerned potentials through the correspondence phenomenon between GGPDE and these models.
基金supported in part by NSFC(Grant No.11375121,11747171,11747302 and 11847305)Natural Science Foundation of Chengdu University of TCM(Grants No.ZRYY1729 and ZRQN1656)+2 种基金Discipline Talent Promotion Program of Xinglin Scholars(Grant No.QNXZ2018050)The Key Fund Project for Education Department of Sichuan(Grant No.18ZA0173)Sichuan University Students Platform for Innovation and Entrepreneurship Training Program(Grant No.C2019104639).
文摘In this paper,we study the thermodynamics and the weak cosmic censorship conjecture of the nonlinear electrodynamics black hole under the scattering of a charged complex scalar field.According to the energy and charge fluxes of the scalar field,the variations of this black hole’s energy and charge can be calculated during an infinitesimal time interval.With scalar field scattering,the variation of the black hole is calculated in the extended and normal phase spaces.In the normal phase space,the cosmological constant and the normalization parameter are fixed,and the first and second laws of thermodynamics can also be satisfied.In the extended phase space,the cosmological constant and the normalization parameter are considered as thermodynamic variables,and the first law of thermodynamics is valid,but the second law of thermodynamics is not valid.Furthermore,the weak cosmic censorship conjecture is both valid in the extended and normal phase spaces.
文摘This research work is related to soliton solutions considered as models that can describe the complex configuration of elementary particles from the study of the interactions of their fields. It is interested in the interaction of fields between two different elementary particles by expressing their physical properties. For that, we have obtained, exact static plane symmetric soliton-like solutions to the nonlinear equations of interacting electromagnetic and scalar fields taking into account the own gravitational field of elementary particles using the calibrated invariance function <i>P</i>(<i>I</i>). It has been proved that all solutions of the Einstein, nonlinear electromagnetic and scalar field equations are regular with the localized energy density. Moreover, the total charge of particles is finite and the total energy of the interaction fields is bounded. It have been emphasized the importance to the own gravitational field of elementary particles and the role of the nonlinearity of fields in the determination of these solutions. In flat space-time, soliton-like solutions exist but the total energy of the interaction fields is equal to zero. We have also shown that in the linear case, soliton-like solutions are absent.
基金Project supported by the National Natural Science Foundation of China (Grant No 10675045)the Foundation for the Author of National Excellent Doctoral Dissertation of China (Grant No 200317)
文摘This paper investigates the resonant frequencies of the massless scalar field in the near extremal Kerr-like black-brane spacetime. It is shown that the different angular quantum number will present different resonant frequencies. It is also shown that the real part of the resonant frequencies increases as the compact dimensions parameter μi increases, but the magnitude of the imaginary part decreases as μi increases.
文摘By using two different transformations, several types of exact analytic solutions for a class of nonlinear coupled scalar field equation are obtained, which contain soliton solutions, singular solitary wave solutions and triangle function solutions. These results can be applied to other nonlinear equations. In addition, parts of conclusions in some references are corrected.
文摘We discuss the coupling between dark energy and matter by considering a homogeneous tachyonic scalar field as a candidate for dark energy.We obtained the functional form of scale factor by assuming that the coupling strength depends linearly on the Hubble parameter and energy density.We also estimated the cosmic age of the Universe for different values of coupling constant.
基金Project supported by the National Natural Science Foundation of China （Grant Nos.10573012, 10575068）, and the Shanghai Municipal Science and Technology Commission （Grant No.04dz05905）
文摘This paper studies phantom linear scalar field （LSF） and phantom non-linear Born-Infeld （NLBI） scalar field with square potential of the form V（Ф） =1/2m^2Ф^2. The equation of state parameter w（z）, and evolution of scale factor a（t） in both phantom LSF and phantom NLBI scalar model are explored. The age of universe Hot and the transition redshift Z are obtained. The Gold data set of 157-SN-Ia is used to constrain parameters of the two models by numerical calculation. The phantom LSF is slightly better than the phantom NLBI type scalar field model for a large m. Although a smaller m corresponding to a slower rolling of field Ф better fits the observation data, the difference between phantom NLBI scalar field and phantom LSF is not distinct in this case.
基金supported Project supported by the National Natural Science Foundation of China (Grant No. 10873004)the Program for Excellent Talents at Hunan Normal University,China+4 种基金the National Basic Research Program of China (Grant No. 2010CB832803)the Key Program of the National Natural Science Foundation of China (Grant No. 10935013)the Construct Program of the National Key Disciplinethe Program for Changjiang Scholarsthe Innovative Research Team in University,China(Grant No. IRT0964)
文摘Recently, considerable progress has been made in understanding the early universe by loop quantum cosmology. Modesto et al. investigated the loop quantum black hole （LQBH）using improved semiclassical analysis and they found that the LQBH has two horizons, an event horizon and a Cauchy horizon, just like the Reissner-NordstrSm black hole. This paper focuses on the dynamical evolution of a massless scalar wave in the LQBH background. By investigating the relation between the complex frequencies of the massless scalar field and the LQBH parameters using the numerical method, we find that the polymeric parameter P makes the massless scalar field decay more quickly and makes the ground scalar wave oscillate slowly. However, the polymeric parameter P causes the frequency of the high harmonic massless scalar wave to shift according to its value. We also find that the loop quantum gravity area gap parameter a0 causes the massless scalar field to decay more slowly and makes the period of the massless scalar field wave become longer. In the complex ω plane, the frequency curves move counterclockwise when the polymeric parameter P increases and this spiral effect is more obvious for a higher harmonic scalar wave.
文摘Some new estimations of scalar products of vector fields in unbounded domains are investigated. Lp-estimations for the vector fields were proved in special weighted functional spaces. The paper generalizes our earlier results for bounded domains. Estimations for scalar products make it possible to investigate wide classes of mathematical physics problems in physically inhomogeneous domains. Such estimations allow studying issues of correctness for problems with non-smooth coefficients. The paper analyses solvability of stationary set of Maxwell equations in inhomogeneous unbounded domains based on the proved Lp-estimations.
