This paper investigates the stability and bifurcation phenomena of a cholera transmission model in which individuals who have recovered from the disease may become susceptible again.The threshold for determining disea...This paper investigates the stability and bifurcation phenomena of a cholera transmission model in which individuals who have recovered from the disease may become susceptible again.The threshold for determining disease prevalence is established,and the parameter conditions for the existence of equilibria are discussed.The Routh-Hurwitz criterion is applied to demonstrate the local asymptotic stability of equilibria.By utilizing composite matrices and geometric techniques,the global dynamic behavior of the endemic equilibrium is investigated,and the sufficient conditions for its global asymptotic stability are derived.Furthermore,the disease-free equilibrium is a saddle-node when the basic reproductive number is 1,and tthe transcritical bifurcation in this case is discussed.展开更多
Bagging is not quite suitable for stable classifiers such as nearest neighbor classifiers due to the lack of diversity and it is difficult to be directly applied to face recognition as well due to the small sample si...Bagging is not quite suitable for stable classifiers such as nearest neighbor classifiers due to the lack of diversity and it is difficult to be directly applied to face recognition as well due to the small sample size (SSS) property of face recognition. To solve the two problems,local Bagging (L-Bagging) is proposed to simultaneously make Bagging apply to both nearest neighbor classifiers and face recognition. The major difference between L-Bagging and Bagging is that L-Bagging performs the bootstrap sampling on each local region partitioned from the original face image rather than the whole face image. Since the dimensionality of local region is usually far less than the number of samples and the component classifiers are constructed just in different local regions,L-Bagging deals with SSS problem and generates more diverse component classifiers. Experimental results on four standard face image databases (AR,Yale,ORL and Yale B) indicate that the proposed L-Bagging method is effective and robust to illumination,occlusion and slight pose variation.展开更多
A local improvement procedure based on tabu search(TS) was incorporated into a basic genetic algorithm(GA) and a global optimal algorithm,i.e.,hybrid genetic algorithm(HGA) approach was used to search the circular and...A local improvement procedure based on tabu search(TS) was incorporated into a basic genetic algorithm(GA) and a global optimal algorithm,i.e.,hybrid genetic algorithm(HGA) approach was used to search the circular and noncircular slip surfaces associated with their minimum safety factors.The slope safety factors of circular and noncircular critical slip surfaces were calculated by the simplified Bishop method and an improved Morgenstern-Price method which can be conveniently programmed,respectively.Comparisons with other methods were made which indicate the high efficiency and accuracy of the HGA approach.The HGA approach was used to calculate one case example and the results demonstrated its applicability to practical engineering.展开更多
We report on the localized spatial soliton excitations in the multidimensional nonlinear Schrodinger equation with radially variable nonlinearity coefficient and an external potential. By using Hirota's binary differ...We report on the localized spatial soliton excitations in the multidimensional nonlinear Schrodinger equation with radially variable nonlinearity coefficient and an external potential. By using Hirota's binary differential operators, we determine a variety of external potentials and nonlinearity coefficients that can support nonlinear localized solutions of different but desired forms. For some specific external potentials and nonlinearity coefficients, we discuss features of the corresponding (2+1)-dimensional multisolitonic solutions, including ring solitons, lump solitons, and soliton clusters.展开更多
Ferruginol, a phenolic diterpenoid, was isolated from Prumnupitys andina, a Chilean native plant, as the main compound. Ferruginol has displayed an interesting range of biological activities such as in vitro anti-infl...Ferruginol, a phenolic diterpenoid, was isolated from Prumnupitys andina, a Chilean native plant, as the main compound. Ferruginol has displayed an interesting range of biological activities such as in vitro anti-inflammatory activity. Aim of this research is to evaluate the dermal anti-inflammatory activity of ferruginol, using in vivo models at first time. Ferruginol was subjected to topical assays for the inhibition of inflammation elicited by AA (arachidonic acid) or TPA (phorbol ester) in the murine model. The topical anti-inflammatory activity was evaluated in vivo using groups of 8 animals were treated with a single dose of ferruginol, equimolar doses with regard to the reference drugs, indomethacin and nimesulide. We showed a chemical data were consistent with a type-abietane diterpenoid known as ferruginol. Ferruginol showed topical anti-inflammatory activity at 21.0% and 20.5% in AA and TPA models, respectively. Our results provide data to support further investigations about ferruginol, a type-abietane diterpenoid, as a potential anti-inflammatory agent.展开更多
The objective of this paper is to demonstrate that the processual aspect of literary works of art deserves much more attention than it normally receives by readers, critics, and theorists. The most important reason fo...The objective of this paper is to demonstrate that the processual aspect of literary works of art deserves much more attention than it normally receives by readers, critics, and theorists. The most important reason for this is seen in the fact that texts since the advent of print culture have been disseminated and passed on in written form and that in the medium of writing the processual character of language is only insufficiently taken care of by a cultural convention of arranging and approaching the presented signs in an particular sequence. Whereas in an oral culture the dynamic processuality of a speech or recitation was directly experienced by the listeners, the spatial arrangement of signs in writing enables and even entices readers and critics to read this or that part of a written text in a sequence of their own making. What remains out of focus is that in doing so they miss the particular semantic profile and aesthetic character of the work as created by the author--a procedure particularly hurtful in the case of literary works of art. There is hope, however, that this will somewhat change by our moving towards a performance culture展开更多
The vegetation of alpine tundra in the Changbai Mountains has experienced great changes in recent decades. Narrowleaf small reed(Deyeuxia angustifolia), a perennial herb from the birch forest zone had crossed the tree...The vegetation of alpine tundra in the Changbai Mountains has experienced great changes in recent decades. Narrowleaf small reed(Deyeuxia angustifolia), a perennial herb from the birch forest zone had crossed the tree line and invaded into the alpine tundra zone. To reveal the driven mechanism of D. angustifolia invasion, there is an urgent need to figure out the effective seed distribution pattern, which could tell us where the potential risk regions are and help us to interpret the invasion process. In this study, we focus on the locations of the seeds in the soil layer and mean to characterize the effective seed distribution pattern of D. angustifolia. The relationship between the environmental variables and the effective seed distribution pattern was also assessed by redundancy analysis. Results showed that seeds of D. angustifolia spread in the alpine tundra with a considerable number(mean value of 322 per m2). They were mainly distributed in the low elevation areas with no significant differences in different slope positions. Effective seed number(ESN) occurrences of D. angustifolia were different in various plant communities. Plant communities with lower canopy cover tended to have more seeds of D. angustifolia. Our research indicated reliable quantitative information on the extent to which habitats are susceptible to invasion.展开更多
The novel Ragtime, written by the contemporary American writer Edgar Lawrence Doctorow, imaginatively reconstructs the urban space in the Progressive Era. In the period of social transformation and change, all kinds o...The novel Ragtime, written by the contemporary American writer Edgar Lawrence Doctorow, imaginatively reconstructs the urban space in the Progressive Era. In the period of social transformation and change, all kinds of contradictions in New York City are becoming increasingly acute. The division of space reflects the power discourse of different classes, races, and genders. The connection, extension and expansion of space promote the features of urban modernity and open up new patterns of social behavior and opportunities for survival, but cannot fundamentally alleviate the capitalist crisis. Spatial layout and distribution of the city are not only the reflection of social relations, but also the "time capsule", bearing the history of the city, and the writing of space offers a mirror for the author's emotion and value judgment.展开更多
Distributed key value storage systems are among the most important types of distributed storage systems currently deployed in data centers. Nowadays, enterprise data centers are facing growing pressure in reducing the...Distributed key value storage systems are among the most important types of distributed storage systems currently deployed in data centers. Nowadays, enterprise data centers are facing growing pressure in reducing their power consumption. In this paper, we propose GreenCHT, a reliable power management scheme for consistent hashing based distributed key value storage systems. It consists of a multi-tier replication scheme, a reliable distributed log store, and a predictive power mode scheduler (PMS). Instead of randomly placing replicas of each object on a number of nodes in the consistent hash ring, we arrange the replicas of objects on nonoverlapping tiers of nodes in the ring. This allows the system to fall in various power modes by powering down subsets of servers while not violating data availability. The predictive PMS predicts workloads and adapts to load fluctuation. It cooperates with the multi-tier replication strategy to provide power proportionality for the system. To ensure that the reliability of the system is maintained when replicas are powered down, we distribute the writes to standby replicas to active servers, which ensures failure tolerance of the system. GreenCHT is implemented based on Sheepdog, a distributed key value storage system that uses consistent hashing as an underlying distributed hash table. By replaying 12 typical real workload traces collected from Microsoft, the evaluation results show that GreenCHT can provide significant power savings while maintaining a desired performance. We observe that GreenCHT can reduce power consumption by up to 35%-61%.展开更多
Aims Morphological variation of leaves is a key indicator of plant response to climatic change.Leaf size and shape are associated with carbon,water and energy exchange of plants with their environment.However,whether ...Aims Morphological variation of leaves is a key indicator of plant response to climatic change.Leaf size and shape are associated with carbon,water and energy exchange of plants with their environment.However,whether and how leaf size and shape responded to climate change over the past decades remains poorly studied.Moreover,many studies have only explored inter-but not intraspecific variation in leaf size and shape across space and time.Methods We collected>6000 herbarium specimens spanning 98 years(1910–2008)in China for seven representative dicot species and measured their leaf length and width.We explored geographical patterns and temporal trends in leaf size(i.e.leaf length,leaf width and length×width product)and shape(i.e.length/width ratio),and investigated the effects of changes in precipitation and temperature over time and space on the variation in leaf size and shape.Important Findings After accounting for the effects of sampling time,leaf size decreased with latitude for all species combined,but the relationship varied among species.Leaf size and shape were positively correlated with temperature and precipitation across space.After accounting for the effects of sampling locations,leaf size of all species combined increased with time.Leaf size changes over time were mostly positively correlated with precipitation,whereas leaf shape changes were mostly correlated with temperature.Overall,our results indicate significant spatial and temporal intraspecific variation in leaf size and shape in response to climate.Our study also demonstrates that herbarium specimens collected over a considerable period of time provide a good resource to study the impacts of climate change on plant morphological traits.展开更多
In this work,we propose incorporating the finite cell method(FCM)into the absolute nodal coordinate formulation(ANCF)to improve the efficiency and robustness of ANCF elements in simulating structures with complex loca...In this work,we propose incorporating the finite cell method(FCM)into the absolute nodal coordinate formulation(ANCF)to improve the efficiency and robustness of ANCF elements in simulating structures with complex local features.In addition,an adaptive subdomain integration method based on a triangulation technique is devised to avoid excessive subdivisions,largely reducing the computational cost.Numerical examples demonstrate the effectiveness of the proposed method in large deformation,large rotation and dynamics simulation.展开更多
We explore the spin-boson model in a special case, i.e., with zero local field. In contrast to previous studies, we find no possibility for quantum phase transition (QPT) happening between the localized and delocali...We explore the spin-boson model in a special case, i.e., with zero local field. In contrast to previous studies, we find no possibility for quantum phase transition (QPT) happening between the localized and delocalized phases, and the behavior of the model can be fully characterized by the even or odd parity as well as the parity breaking, instead of the QPT, owned by the ground state of the system. The parity breaking mentioned in our case is completely different from the spontaneously broken symmetry relevant to the conventionally defined QPT in previous studies. Our analytical treatment about the eigensolution of the ground state of the model presents for the first time a rigorous proof of no- degeneracy for the ground state of the model, which is independent of the bath type, the degrees of freedom of the bath and the calculation precision. We argue that the QPT mentioned previously appears due to incorrect employment of the ground state of the model and/or unreasonable treatment of the infrared divergence existing in the spectral functions for Ohmic and sub-Ohmic dissipations.展开更多
Let (X, d, μ) be a metric measure space endowed with a distance d and a nonnegative Borel doubling measure μ. Let L be a second order self-adjoint positive operator on L^2(X). Assume that the semigroup e-^tL gen...Let (X, d, μ) be a metric measure space endowed with a distance d and a nonnegative Borel doubling measure μ. Let L be a second order self-adjoint positive operator on L^2(X). Assume that the semigroup e-^tL generated by -L satisfies the Gaussian upper bounds on L2(X). In this article we study a local version of Hardy space hi (X) associated with L in terms of the area function characterization, and prove their atomic characters. Furthermore, we introduce a Moser type local boundedness condition for L, and then we apply this condition to show that the space hzL(X) can be characterized in terms of the Littlewood-Paley function. Finally, a broad class of applications of these results is described.展开更多
In this paper, we consider the localization of a five-dimensional gravitino field on f(R)-thick branes. We obtain the coupled chiral equations of the Kaluza-Klein(KK) modes of gravitinos with the gauge condition Ψ_z=...In this paper, we consider the localization of a five-dimensional gravitino field on f(R)-thick branes. We obtain the coupled chiral equations of the Kaluza-Klein(KK) modes of gravitinos with the gauge condition Ψ_z= 0. The chiral equations of a gravitino's KK modes are found to be almost identical to those of the Dirac fermion. However, their chiralities are exactly opposite. The chiral KK modes of gravitinos could be localized in some types of f(R)-thick branes on introducing a coupling term. We investigate the localization of a gravitino on three types of f(R)-thick branes through a Yukawa-like coupling term with background scalar fields. It has been shown that all the KK modes of gravitinos cannot be localized in the pure geometric f(R)-thick branes by adding a five-dimensional gravitino mass term. However, for the f(R)-thick branes generated by one or two background scalar fields, only the left-or right-handed zero mode could be localized in the branes, and the massive KK resonant modes are the same for both left-and right-handed gravitinos despite their opposing chiralities. All these results are consistent with those of the five-dimensional Dirac fermion except their chiralities, which may be an important sign to distinguish the gravitino field and the Dirac fermion field.展开更多
基金supported by the National Natural Science Foundation of China(No.12171337)the Central Government Guided Local Science and Technology Development Projects(No.2024ZYD0059)+1 种基金the Natural Science Foundation of Sichuan Province(No.2022NSFSC0529)the Open Research Fund Program of Data Recovery Key Laboratory of Sichuan Province(No.DRN2405)。
文摘This paper investigates the stability and bifurcation phenomena of a cholera transmission model in which individuals who have recovered from the disease may become susceptible again.The threshold for determining disease prevalence is established,and the parameter conditions for the existence of equilibria are discussed.The Routh-Hurwitz criterion is applied to demonstrate the local asymptotic stability of equilibria.By utilizing composite matrices and geometric techniques,the global dynamic behavior of the endemic equilibrium is investigated,and the sufficient conditions for its global asymptotic stability are derived.Furthermore,the disease-free equilibrium is a saddle-node when the basic reproductive number is 1,and tthe transcritical bifurcation in this case is discussed.
文摘Bagging is not quite suitable for stable classifiers such as nearest neighbor classifiers due to the lack of diversity and it is difficult to be directly applied to face recognition as well due to the small sample size (SSS) property of face recognition. To solve the two problems,local Bagging (L-Bagging) is proposed to simultaneously make Bagging apply to both nearest neighbor classifiers and face recognition. The major difference between L-Bagging and Bagging is that L-Bagging performs the bootstrap sampling on each local region partitioned from the original face image rather than the whole face image. Since the dimensionality of local region is usually far less than the number of samples and the component classifiers are constructed just in different local regions,L-Bagging deals with SSS problem and generates more diverse component classifiers. Experimental results on four standard face image databases (AR,Yale,ORL and Yale B) indicate that the proposed L-Bagging method is effective and robust to illumination,occlusion and slight pose variation.
基金Project(50878082)supported by the National Natural Science Foundation of ChinaProject(2012C21058)supported by the Public Welfare Technology Application Research of Zhejiang Province,China
文摘A local improvement procedure based on tabu search(TS) was incorporated into a basic genetic algorithm(GA) and a global optimal algorithm,i.e.,hybrid genetic algorithm(HGA) approach was used to search the circular and noncircular slip surfaces associated with their minimum safety factors.The slope safety factors of circular and noncircular critical slip surfaces were calculated by the simplified Bishop method and an improved Morgenstern-Price method which can be conveniently programmed,respectively.Comparisons with other methods were made which indicate the high efficiency and accuracy of the HGA approach.The HGA approach was used to calculate one case example and the results demonstrated its applicability to practical engineering.
基金Supported by the Natural Science Foundation of Guangdong Province under Grant No. 1015283001000000,Chinasupported by the NPRP 09-462-1-074 project with the Qatar National Research Foundation
文摘We report on the localized spatial soliton excitations in the multidimensional nonlinear Schrodinger equation with radially variable nonlinearity coefficient and an external potential. By using Hirota's binary differential operators, we determine a variety of external potentials and nonlinearity coefficients that can support nonlinear localized solutions of different but desired forms. For some specific external potentials and nonlinearity coefficients, we discuss features of the corresponding (2+1)-dimensional multisolitonic solutions, including ring solitons, lump solitons, and soliton clusters.
文摘Ferruginol, a phenolic diterpenoid, was isolated from Prumnupitys andina, a Chilean native plant, as the main compound. Ferruginol has displayed an interesting range of biological activities such as in vitro anti-inflammatory activity. Aim of this research is to evaluate the dermal anti-inflammatory activity of ferruginol, using in vivo models at first time. Ferruginol was subjected to topical assays for the inhibition of inflammation elicited by AA (arachidonic acid) or TPA (phorbol ester) in the murine model. The topical anti-inflammatory activity was evaluated in vivo using groups of 8 animals were treated with a single dose of ferruginol, equimolar doses with regard to the reference drugs, indomethacin and nimesulide. We showed a chemical data were consistent with a type-abietane diterpenoid known as ferruginol. Ferruginol showed topical anti-inflammatory activity at 21.0% and 20.5% in AA and TPA models, respectively. Our results provide data to support further investigations about ferruginol, a type-abietane diterpenoid, as a potential anti-inflammatory agent.
文摘The objective of this paper is to demonstrate that the processual aspect of literary works of art deserves much more attention than it normally receives by readers, critics, and theorists. The most important reason for this is seen in the fact that texts since the advent of print culture have been disseminated and passed on in written form and that in the medium of writing the processual character of language is only insufficiently taken care of by a cultural convention of arranging and approaching the presented signs in an particular sequence. Whereas in an oral culture the dynamic processuality of a speech or recitation was directly experienced by the listeners, the spatial arrangement of signs in writing enables and even entices readers and critics to read this or that part of a written text in a sequence of their own making. What remains out of focus is that in doing so they miss the particular semantic profile and aesthetic character of the work as created by the author--a procedure particularly hurtful in the case of literary works of art. There is hope, however, that this will somewhat change by our moving towards a performance culture
基金Special Fund of National Seismological Bureau,China(No.201208005)Doctorial Innovation Fund of Northeast Normal University(No.10SSXT133,2412013XS001)+1 种基金National Natural Science Foundation of China(No.41171038,41171072,41101523)Doctoral Fund of Ministry of Education of China(No.20120043110014)
文摘The vegetation of alpine tundra in the Changbai Mountains has experienced great changes in recent decades. Narrowleaf small reed(Deyeuxia angustifolia), a perennial herb from the birch forest zone had crossed the tree line and invaded into the alpine tundra zone. To reveal the driven mechanism of D. angustifolia invasion, there is an urgent need to figure out the effective seed distribution pattern, which could tell us where the potential risk regions are and help us to interpret the invasion process. In this study, we focus on the locations of the seeds in the soil layer and mean to characterize the effective seed distribution pattern of D. angustifolia. The relationship between the environmental variables and the effective seed distribution pattern was also assessed by redundancy analysis. Results showed that seeds of D. angustifolia spread in the alpine tundra with a considerable number(mean value of 322 per m2). They were mainly distributed in the low elevation areas with no significant differences in different slope positions. Effective seed number(ESN) occurrences of D. angustifolia were different in various plant communities. Plant communities with lower canopy cover tended to have more seeds of D. angustifolia. Our research indicated reliable quantitative information on the extent to which habitats are susceptible to invasion.
文摘The novel Ragtime, written by the contemporary American writer Edgar Lawrence Doctorow, imaginatively reconstructs the urban space in the Progressive Era. In the period of social transformation and change, all kinds of contradictions in New York City are becoming increasingly acute. The division of space reflects the power discourse of different classes, races, and genders. The connection, extension and expansion of space promote the features of urban modernity and open up new patterns of social behavior and opportunities for survival, but cannot fundamentally alleviate the capitalist crisis. Spatial layout and distribution of the city are not only the reflection of social relations, but also the "time capsule", bearing the history of the city, and the writing of space offers a mirror for the author's emotion and value judgment.
文摘Distributed key value storage systems are among the most important types of distributed storage systems currently deployed in data centers. Nowadays, enterprise data centers are facing growing pressure in reducing their power consumption. In this paper, we propose GreenCHT, a reliable power management scheme for consistent hashing based distributed key value storage systems. It consists of a multi-tier replication scheme, a reliable distributed log store, and a predictive power mode scheduler (PMS). Instead of randomly placing replicas of each object on a number of nodes in the consistent hash ring, we arrange the replicas of objects on nonoverlapping tiers of nodes in the ring. This allows the system to fall in various power modes by powering down subsets of servers while not violating data availability. The predictive PMS predicts workloads and adapts to load fluctuation. It cooperates with the multi-tier replication strategy to provide power proportionality for the system. To ensure that the reliability of the system is maintained when replicas are powered down, we distribute the writes to standby replicas to active servers, which ensures failure tolerance of the system. GreenCHT is implemented based on Sheepdog, a distributed key value storage system that uses consistent hashing as an underlying distributed hash table. By replaying 12 typical real workload traces collected from Microsoft, the evaluation results show that GreenCHT can provide significant power savings while maintaining a desired performance. We observe that GreenCHT can reduce power consumption by up to 35%-61%.
基金supported by the National Key Research Development Program of China(grant number 2018YFA0606104)National Natural Science Foundation of China(grant numbers 31988102,31911530102,and Chinese Academy of Sciences-Peking University Pioneer Collaboration Team.
文摘Aims Morphological variation of leaves is a key indicator of plant response to climatic change.Leaf size and shape are associated with carbon,water and energy exchange of plants with their environment.However,whether and how leaf size and shape responded to climate change over the past decades remains poorly studied.Moreover,many studies have only explored inter-but not intraspecific variation in leaf size and shape across space and time.Methods We collected>6000 herbarium specimens spanning 98 years(1910–2008)in China for seven representative dicot species and measured their leaf length and width.We explored geographical patterns and temporal trends in leaf size(i.e.leaf length,leaf width and length×width product)and shape(i.e.length/width ratio),and investigated the effects of changes in precipitation and temperature over time and space on the variation in leaf size and shape.Important Findings After accounting for the effects of sampling time,leaf size decreased with latitude for all species combined,but the relationship varied among species.Leaf size and shape were positively correlated with temperature and precipitation across space.After accounting for the effects of sampling locations,leaf size of all species combined increased with time.Leaf size changes over time were mostly positively correlated with precipitation,whereas leaf shape changes were mostly correlated with temperature.Overall,our results indicate significant spatial and temporal intraspecific variation in leaf size and shape in response to climate.Our study also demonstrates that herbarium specimens collected over a considerable period of time provide a good resource to study the impacts of climate change on plant morphological traits.
基金supported by the National Natural Science Foundation of China(Grant Nos.52175223,and 11802072)the Fundamental Research Funds for the Central Universities(Grant No.B210201038).
文摘In this work,we propose incorporating the finite cell method(FCM)into the absolute nodal coordinate formulation(ANCF)to improve the efficiency and robustness of ANCF elements in simulating structures with complex local features.In addition,an adaptive subdomain integration method based on a triangulation technique is devised to avoid excessive subdivisions,largely reducing the computational cost.Numerical examples demonstrate the effectiveness of the proposed method in large deformation,large rotation and dynamics simulation.
基金Supported by National Fundamental Research Program of China under Grant No.2012CB922102National Natural Science Foundation of China under Grant Nos.10974225 and 11004226State Key Laboratory Funding of WIPM
文摘We explore the spin-boson model in a special case, i.e., with zero local field. In contrast to previous studies, we find no possibility for quantum phase transition (QPT) happening between the localized and delocalized phases, and the behavior of the model can be fully characterized by the even or odd parity as well as the parity breaking, instead of the QPT, owned by the ground state of the system. The parity breaking mentioned in our case is completely different from the spontaneously broken symmetry relevant to the conventionally defined QPT in previous studies. Our analytical treatment about the eigensolution of the ground state of the model presents for the first time a rigorous proof of no- degeneracy for the ground state of the model, which is independent of the bath type, the degrees of freedom of the bath and the calculation precision. We argue that the QPT mentioned previously appears due to incorrect employment of the ground state of the model and/or unreasonable treatment of the infrared divergence existing in the spectral functions for Ohmic and sub-Ohmic dissipations.
基金supported by China Postdoctoral Science Foundation funded project(Grant No.201104383)the Fundamental Research Funds for the Central Universities(Grant No.11lGPY56)+1 种基金National Natural Science Foundation of China(Grant No.10925106)Guangdong Province Key Laboratory of Computational Science and Grant for Senior Scholars from the Association of Colleges and Universities of Guangdong
文摘Let (X, d, μ) be a metric measure space endowed with a distance d and a nonnegative Borel doubling measure μ. Let L be a second order self-adjoint positive operator on L^2(X). Assume that the semigroup e-^tL generated by -L satisfies the Gaussian upper bounds on L2(X). In this article we study a local version of Hardy space hi (X) associated with L in terms of the area function characterization, and prove their atomic characters. Furthermore, we introduce a Moser type local boundedness condition for L, and then we apply this condition to show that the space hzL(X) can be characterized in terms of the Littlewood-Paley function. Finally, a broad class of applications of these results is described.
基金supported by the National Natural Science Foundation of China(Grant Nos.11647016,11522541,11705106,and 11305095)the Fundamental Research Funds for the Central Universities(Grant No.lzujbky-2016-k04)
文摘In this paper, we consider the localization of a five-dimensional gravitino field on f(R)-thick branes. We obtain the coupled chiral equations of the Kaluza-Klein(KK) modes of gravitinos with the gauge condition Ψ_z= 0. The chiral equations of a gravitino's KK modes are found to be almost identical to those of the Dirac fermion. However, their chiralities are exactly opposite. The chiral KK modes of gravitinos could be localized in some types of f(R)-thick branes on introducing a coupling term. We investigate the localization of a gravitino on three types of f(R)-thick branes through a Yukawa-like coupling term with background scalar fields. It has been shown that all the KK modes of gravitinos cannot be localized in the pure geometric f(R)-thick branes by adding a five-dimensional gravitino mass term. However, for the f(R)-thick branes generated by one or two background scalar fields, only the left-or right-handed zero mode could be localized in the branes, and the massive KK resonant modes are the same for both left-and right-handed gravitinos despite their opposing chiralities. All these results are consistent with those of the five-dimensional Dirac fermion except their chiralities, which may be an important sign to distinguish the gravitino field and the Dirac fermion field.