Delta function is an important function in mathematics and physics. In this paper, the Laplace transforms of δ(t)and δ(t-τ)have been discussed in detail. After the Laplace transform of δ(t)is analyzed, the author ...Delta function is an important function in mathematics and physics. In this paper, the Laplace transforms of δ(t)and δ(t-τ)have been discussed in detail. After the Laplace transform of δ(t)is analyzed, the author has found that three aspects should be taken into account, i.e. τ→0+, τ→0- andτ=0; and it is the same with the Laplace transform of δ(t-τ). Then the results of the Laplace transform of Delta function have been obtained in a rigorous and comprehensive sense.展开更多
We study optimal insider control problems,i.e.,optimal control problems of stochastic systemswhere the controller at any time t,in addition to knowledge about the history of the system up to this time,also has additio...We study optimal insider control problems,i.e.,optimal control problems of stochastic systemswhere the controller at any time t,in addition to knowledge about the history of the system up to this time,also has additional information related to a future value of the system.Since this puts the associated controlled systems outside the context of semimartingales,we apply anticipative white noise analysis,including forward integration and Hida-Malliavin calculus to study the problem.Combining this with Donsker delta functionals,we transform the insider control problem into a classical(but parametrised)adapted control system,albeit with a non-classical performance functional.We establish a sufficient and a necessary maximum principle for such systems.Then we apply the results to obtain explicit solutions for some optimal insider portfolio problems in financial markets described by Itô-Lévy processes.Finally,in the Appendix,we give a brief survey of the concepts and results we need from the theory of white noise,forward integrals and Hida-Malliavin calculus.展开更多
In expansions of arbitrary functions in Bessel functions or Spherical Bessel functions, a dual partner set of polynomials play a role. For the Bessel functions, these are the Chebyshev polynomials of first kind and fo...In expansions of arbitrary functions in Bessel functions or Spherical Bessel functions, a dual partner set of polynomials play a role. For the Bessel functions, these are the Chebyshev polynomials of first kind and for the Spherical Bessel functions the Legendre polynomials. These two sets of functions appear in many formulas of the expansion and in the completeness and (bi)-orthogonality relations. The analogy to expansions of functions in Taylor series and in moment series and to expansions in Hermite functions is elaborated. Besides other special expansion, we find the expansion of Bessel functions in Spherical Bessel functions and their inversion and of Chebyshev polynomials of first kind in Legendre polynomials and their inversion. For the operators which generate the Spherical Bessel functions from a basic Spherical Bessel function, the normally ordered (or disentangled) form is found.展开更多
Many numerical methods,such as tensor network approaches including density matrix renormalization group calculations,have been developed to calculate the extreme/ground states of quantum many-body systems.However,litt...Many numerical methods,such as tensor network approaches including density matrix renormalization group calculations,have been developed to calculate the extreme/ground states of quantum many-body systems.However,little attention has been paid to the central states,which are exponentially close to each other in terms of system size.We propose a delta-Davidson(DELDAV)method to efficiently find such interior(including the central)states in many-spin systems.The DELDAV method utilizes a delta filter in Chebyshev polynomial expansion combined with subspace diagonalization to overcome the nearly degenerate problem.Numerical experiments on Ising spin chain and spin glass shards show the correctness,efficiency,and robustness of the proposed method in finding the interior states as well as the ground states.The sought interior states may be employed to identify many-body localization phase,quantum chaos,and extremely long-time dynamical structure.展开更多
Plasticity is a natural property of living organisms that is crucial for adaptation and evolution.Over the last decades,the availability of sophisticated neuroimaging techniques（in particular,functional magnetic reso...Plasticity is a natural property of living organisms that is crucial for adaptation and evolution.Over the last decades,the availability of sophisticated neuroimaging techniques（in particular,functional magnetic resonance imaging（f MRI）,and transcranial magnetic stimulation（TMS））,has made it possible to explore in vivo the on-line functioning of brain and its plasticity.However,展开更多
In this paper, we present a new representation of gamma function as a series of complex delta functions. We establish the convergence of this representation in the sense of distributions. It turns out that the gamma f...In this paper, we present a new representation of gamma function as a series of complex delta functions. We establish the convergence of this representation in the sense of distributions. It turns out that the gamma function can be defined over a space of complex test functions of slow growth denoted by Z. Some properties of gamma function are discussed by using the properties of delta function.展开更多
The delta-sigma converter is one of the high speed and resolution analog-to-digital modulators. Its implementation needs the low oversampling technique and the multi-bit D/A converter. The noise induced by the multi-b...The delta-sigma converter is one of the high speed and resolution analog-to-digital modulators. Its implementation needs the low oversampling technique and the multi-bit D/A converter. The noise induced by the multi-bit D/A converter becomes one of the key factors deteriorating the signal-to-noise rate of the delta-sigma A/D converter. A novel structure with signal unity transfunction, dynamic element matching(DEM) and noise-shaping is discussed. The method is investigated to design converter based on the proposed structure. The behavior simulation indicates that the structure and the design method are feasible.展开更多
In recent years,wetland ecological water requirements (EWRs) have been estimated by using hydrological and functional approaches,but those approaches have not yet been integrated for a whole ecosystem.This paper prese...In recent years,wetland ecological water requirements (EWRs) have been estimated by using hydrological and functional approaches,but those approaches have not yet been integrated for a whole ecosystem.This paper presents a new method for calculating wetland EWRs,which is based on the response of habitats to water level,and determines water level threshold through the functional integrity of habitats.Results show that in the Huanghe (Yellow) River Delta water levels between 5.0 m and 5.5 m are required to maintain the functional integrity of the wetland at a value higher than 0.7.One of the dominant plants in the delta,Phragmites australis,tolerates water level fluctuation of about ± 0.25 m without the change in wetland functional integrity.The minimum,optimum and maximum EWRs for the Huanghe River Delta are 9.42×106 m3,15.56×106 m3 and 24.12×106 m3 with water levels of 5.0 m,5.2 m and 5.5 m,corresponding to functional integrity indices of 0.70,0.84 and 0.72,respectively.A wetland restoration program has been performed,which aims to meet these EWRs in attempt to recover from losses of up to 98% in the delta's former wetland area.展开更多
In traditional urban geography, city contact research is a classic study element in city research. In general, researchers use the traditional gravity model to characterize the contacts that exist between two cities. ...In traditional urban geography, city contact research is a classic study element in city research. In general, researchers use the traditional gravity model to characterize the contacts that exist between two cities. The traditional gravity model assumes ideal conditions, but these preconditions and their results often do not exist in realistic conditions. Thus, we used a modified gravity model to characterize the city contacts within a specific region. This model considers factors such as intercity complementarities, government intervention, and the diversity of the transportation infrastructure which is characterized as the transportation distance instead of the traditional Euclidean distance. We applied this model to an empirical study of city contact in the Zhujiang(Pearl) River Delta(PRD) of China. The regression results indicated that the modified gravity model could measure city contact more accurately and comprehensively than the traditional gravity model, i.e., it yielded a higher adjusted R2 value(0.379) than the traditional gravity model result(0.259). Our study also suggests that, in addition to urban-regional and metropolitan development, the complementarities of the basic functions of cities at the administrative and market levels, as well as the corporeal and immaterial levels, play very significant roles in the characterization of city contact. Given the complexity of city contact, it will be necessary to consider more relevant influential factors in the modified gravity model to characterize the features of city contact in the future.展开更多
基金Funded by by Natural Science Foundation Project of CQ CSTC (Grant No: cstc2012jjA50018)the Basic Research of Chongqing Municipal Education Commission (Grant No:KJ120613)
文摘Delta function is an important function in mathematics and physics. In this paper, the Laplace transforms of δ(t)and δ(t-τ)have been discussed in detail. After the Laplace transform of δ(t)is analyzed, the author has found that three aspects should be taken into account, i.e. τ→0+, τ→0- andτ=0; and it is the same with the Laplace transform of δ(t-τ). Then the results of the Laplace transform of Delta function have been obtained in a rigorous and comprehensive sense.
文摘We study optimal insider control problems,i.e.,optimal control problems of stochastic systemswhere the controller at any time t,in addition to knowledge about the history of the system up to this time,also has additional information related to a future value of the system.Since this puts the associated controlled systems outside the context of semimartingales,we apply anticipative white noise analysis,including forward integration and Hida-Malliavin calculus to study the problem.Combining this with Donsker delta functionals,we transform the insider control problem into a classical(but parametrised)adapted control system,albeit with a non-classical performance functional.We establish a sufficient and a necessary maximum principle for such systems.Then we apply the results to obtain explicit solutions for some optimal insider portfolio problems in financial markets described by Itô-Lévy processes.Finally,in the Appendix,we give a brief survey of the concepts and results we need from the theory of white noise,forward integrals and Hida-Malliavin calculus.
文摘In expansions of arbitrary functions in Bessel functions or Spherical Bessel functions, a dual partner set of polynomials play a role. For the Bessel functions, these are the Chebyshev polynomials of first kind and for the Spherical Bessel functions the Legendre polynomials. These two sets of functions appear in many formulas of the expansion and in the completeness and (bi)-orthogonality relations. The analogy to expansions of functions in Taylor series and in moment series and to expansions in Hermite functions is elaborated. Besides other special expansion, we find the expansion of Bessel functions in Spherical Bessel functions and their inversion and of Chebyshev polynomials of first kind in Legendre polynomials and their inversion. For the operators which generate the Spherical Bessel functions from a basic Spherical Bessel function, the normally ordered (or disentangled) form is found.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.91836101,U1930201,and 11574239).
文摘Many numerical methods,such as tensor network approaches including density matrix renormalization group calculations,have been developed to calculate the extreme/ground states of quantum many-body systems.However,little attention has been paid to the central states,which are exponentially close to each other in terms of system size.We propose a delta-Davidson(DELDAV)method to efficiently find such interior(including the central)states in many-spin systems.The DELDAV method utilizes a delta filter in Chebyshev polynomial expansion combined with subspace diagonalization to overcome the nearly degenerate problem.Numerical experiments on Ising spin chain and spin glass shards show the correctness,efficiency,and robustness of the proposed method in finding the interior states as well as the ground states.The sought interior states may be employed to identify many-body localization phase,quantum chaos,and extremely long-time dynamical structure.
文摘Plasticity is a natural property of living organisms that is crucial for adaptation and evolution.Over the last decades,the availability of sophisticated neuroimaging techniques（in particular,functional magnetic resonance imaging（f MRI）,and transcranial magnetic stimulation（TMS））,has made it possible to explore in vivo the on-line functioning of brain and its plasticity.However,
文摘In this paper, we present a new representation of gamma function as a series of complex delta functions. We establish the convergence of this representation in the sense of distributions. It turns out that the gamma function can be defined over a space of complex test functions of slow growth denoted by Z. Some properties of gamma function are discussed by using the properties of delta function.
基金National Natural Science Foundation of China(50677014)Doctoral Special Found of Ministry of Education(20060532016)+2 种基金Natural Science Foundation of Hunan Province(06JJ2024)Program for New CenturyExcellent Talents in University(NCET-04-0767)Found of Hunan Education depart ment(05C141)
文摘The delta-sigma converter is one of the high speed and resolution analog-to-digital modulators. Its implementation needs the low oversampling technique and the multi-bit D/A converter. The noise induced by the multi-bit D/A converter becomes one of the key factors deteriorating the signal-to-noise rate of the delta-sigma A/D converter. A novel structure with signal unity transfunction, dynamic element matching(DEM) and noise-shaping is discussed. The method is investigated to design converter based on the proposed structure. The behavior simulation indicates that the structure and the design method are feasible.
基金Under the auspices of Major State Basic Research Development Program of China (No. 2006CB403303)National Natural Science Foundation of China (No. U0833002,40571149)Scientific Research Foundation of Beijing Normal University (No. 2009SD-24)
文摘In recent years,wetland ecological water requirements (EWRs) have been estimated by using hydrological and functional approaches,but those approaches have not yet been integrated for a whole ecosystem.This paper presents a new method for calculating wetland EWRs,which is based on the response of habitats to water level,and determines water level threshold through the functional integrity of habitats.Results show that in the Huanghe (Yellow) River Delta water levels between 5.0 m and 5.5 m are required to maintain the functional integrity of the wetland at a value higher than 0.7.One of the dominant plants in the delta,Phragmites australis,tolerates water level fluctuation of about ± 0.25 m without the change in wetland functional integrity.The minimum,optimum and maximum EWRs for the Huanghe River Delta are 9.42×106 m3,15.56×106 m3 and 24.12×106 m3 with water levels of 5.0 m,5.2 m and 5.5 m,corresponding to functional integrity indices of 0.70,0.84 and 0.72,respectively.A wetland restoration program has been performed,which aims to meet these EWRs in attempt to recover from losses of up to 98% in the delta's former wetland area.
基金Under the auspices of National Natural Science Foundation of China(No.41271177)Guangdong Natural Science Foundation(No.S2012010008902)
文摘In traditional urban geography, city contact research is a classic study element in city research. In general, researchers use the traditional gravity model to characterize the contacts that exist between two cities. The traditional gravity model assumes ideal conditions, but these preconditions and their results often do not exist in realistic conditions. Thus, we used a modified gravity model to characterize the city contacts within a specific region. This model considers factors such as intercity complementarities, government intervention, and the diversity of the transportation infrastructure which is characterized as the transportation distance instead of the traditional Euclidean distance. We applied this model to an empirical study of city contact in the Zhujiang(Pearl) River Delta(PRD) of China. The regression results indicated that the modified gravity model could measure city contact more accurately and comprehensively than the traditional gravity model, i.e., it yielded a higher adjusted R2 value(0.379) than the traditional gravity model result(0.259). Our study also suggests that, in addition to urban-regional and metropolitan development, the complementarities of the basic functions of cities at the administrative and market levels, as well as the corporeal and immaterial levels, play very significant roles in the characterization of city contact. Given the complexity of city contact, it will be necessary to consider more relevant influential factors in the modified gravity model to characterize the features of city contact in the future.
