The Schrodinger equation for a particle in the V-shaped potential decorated by a repulsive or attractive Dirac delta function interaction at the center is solved, demonstrating the crucial influence of point interacti...The Schrodinger equation for a particle in the V-shaped potential decorated by a repulsive or attractive Dirac delta function interaction at the center is solved, demonstrating the crucial influence of point interaction on the even-parity states of the original system without decoration. As strength of the attraction increases, the ground state energy falls down without limit; and in limit of infinitely large attraction, the ground state approaches a singular state. Our analysis and conclusion can be readily generalized to any one-dimensional system a particle interacts with symmetrical potential plus the Dirac delta function interaction at the center.展开更多
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
随着数字音源的普及,数模转换器(Digital to Analog Converter, DAC)成为音频设备中不可或缺的元件,其精度往往决定着整个系统的信号保真度。基于此,利用噪声整形技术对用于高精度音频DAC的Sigma-Delta调制器进行设计和现场可编程门阵列...随着数字音源的普及,数模转换器(Digital to Analog Converter, DAC)成为音频设备中不可或缺的元件,其精度往往决定着整个系统的信号保真度。基于此,利用噪声整形技术对用于高精度音频DAC的Sigma-Delta调制器进行设计和现场可编程门阵列(Field Programmable Gate Array, FPGA)实现。通过搭建测试系统,测试结果表明,所设计的Sigma-Delta调制器在输入信号为1 411.2 kHz采样频率、1 kHz频率、0 dBFS(Full Scale)幅度的正弦信号条件下,其输出信噪比(Signal to Noise Ratio, SNR)可达107.4 dB;当输入信号频率在音频频带内时(输入信号幅度为0dBFS),其输出SNR稳定保持在104 dB以上;并可用于WAV音乐播放器中。展开更多
Extensive spatiotemporal analyses of long-trend surface ozone in the Yangtze River Delta(YRD)region and itsmeteorology-related and emission-related have not been systematically analyzed.In this study,by using 8-year-l...Extensive spatiotemporal analyses of long-trend surface ozone in the Yangtze River Delta(YRD)region and itsmeteorology-related and emission-related have not been systematically analyzed.In this study,by using 8-year-long(2015–2022)surface ozone observation data,we attempted to reveal the variation ofmultiple timescale components using the Kolmogorov–Zurbenko filter,and the effects of meteorology and emissions were quantitatively isolated using multiple linear regression with meteorological variables.The results showed that the short-term,seasonal,and long-term components accounted for daily maximum 8-hr average O_(3)(O_(3–8)hr)concentration,46.4%,45.9%,and 1.0%,respectively.The meteorological impacts account for an average of 71.8%of O_(3–8)hr,and the YRD’s eastern and northern sections aremeteorology-sensitive areas.Based on statistical analysis technology with empirical orthogonal function,the contribution of meteorology,local emission,and transport in the long-term component of O_(3–8)hr were 0.21%,0.12%,and 0.6%,respectively.The spatiotemporal analysis indicated that a distinct decreasing spatial pattern could be observed from coastal cities towards the northwest,influenced by the monsoon and synoptic conditions.The central urban agglomeration north and south of the YRD was particularly susceptible to local pollution.Among the cities studied,Shanghai,Anqing,and Xuancheng,located at similar latitudes,were significantly impacted by atmospheric transmission—the contribution of Shanghai,the maximum accounting for 3.6%.展开更多
目的:探讨Delta大通道内镜辅助下后路椎管减压椎间植骨融合术治疗退变性腰椎疾病的效果。方法:回顾性分析2021年9月~2022年9月我院收治的80例退变性腰椎疾病患者的病历资料,根据患者治疗方式分为观察组(38例,男17例,女21例,年龄61.0...目的:探讨Delta大通道内镜辅助下后路椎管减压椎间植骨融合术治疗退变性腰椎疾病的效果。方法:回顾性分析2021年9月~2022年9月我院收治的80例退变性腰椎疾病患者的病历资料,根据患者治疗方式分为观察组(38例,男17例,女21例,年龄61.0±4.9岁)和对照组(42例,男20例,女22例,年龄60.5±5.4岁),观察组患者采取Delta大通道内镜下Endo-PLIF治疗,对照组采取开放后路腰椎椎间融合术治疗,记录两组患者术中出血量、术后引流量、手术时间、手术切口长度、住院时间,比较患者并发症发生情况。于术前、术后1周、1个月、3个月、6个月使用视觉模拟量表(visual analogue scale,VAS)评分评估患者腰痛情况,并采用Oswestry功能障碍指数(Oswestry disability index,ODI)评估患者腰椎功能;使用改良Macnab标准对患者进行疗效评估。根据患者术后1年随访时的腰椎影像学复查结果,使用Bridwell椎间融合标准对患者手术节段融合情况进行评估。结果:观察组患者的术中出血量及术后引流量分别低于对照组(88.46±10.98mL vs 112.99±12.01mL、159.73±18.42mL vs 201.36±23.06mL,P<0.05),手术切口及住院时间分别短于对照组(1.54±0.36cm vs 5.43±1.01cm、6.79±1.22d vs 8.03±1.43d,P<0.05),手术时间长于对照组(162.33±19.57min vs 126.87±23.15min,P<0.05)。80例患者术后均获随访,随访时间15~40个月(19.0±6.3个月)。观察组患者术后1周、术后1个月的VAS评分分别为2.46±0.51分、1.21±0.38分,ODI分别为(17.84±4.15)%、(10.69±1.88)%,均低于对照组[VAS评分分别为3.68±0.62分、2.01±0.41分,ODI分别为(21.33±3.48)%、(12.33±2.17)%,均P<0.05],两组患者术后3个月、术后6个月的VAS评分比较无统计学差异(P>0.05)。观察组治疗优良率为92.11%,与对照组的85.71%比较无统计学意义(P=0.487)。两组患者融合分级比较,差异无统计学意义(Z=0.487,P=0.624)。观察组术后并发症发生率为5.26%,与对照组的9.52%比较无统计学差异(P=0.678)。结论:Delta大通道内镜辅助下后路椎管减压椎间植骨融合术治疗退变性腰椎疾病效果良好,可以减少术中出血量,缩短手术切口和住院时间,更快改善患者术后短期内疼痛、腰椎功能,安全性较好。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
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
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
基金Supported by the Natural Science Foundation of China under Grant Nos. 50831003, 50571037, and 10774041
文摘The Schrodinger equation for a particle in the V-shaped potential decorated by a repulsive or attractive Dirac delta function interaction at the center is solved, demonstrating the crucial influence of point interaction on the even-parity states of the original system without decoration. As strength of the attraction increases, the ground state energy falls down without limit; and in limit of infinitely large attraction, the ground state approaches a singular state. Our analysis and conclusion can be readily generalized to any one-dimensional system a particle interacts with symmetrical potential plus the Dirac delta function interaction at the center.
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.
基金supported by the National Natural Science Foundation of China(No.42075177)the National Key Research and Development Program of China(No.2017YFC0210003).
文摘Extensive spatiotemporal analyses of long-trend surface ozone in the Yangtze River Delta(YRD)region and itsmeteorology-related and emission-related have not been systematically analyzed.In this study,by using 8-year-long(2015–2022)surface ozone observation data,we attempted to reveal the variation ofmultiple timescale components using the Kolmogorov–Zurbenko filter,and the effects of meteorology and emissions were quantitatively isolated using multiple linear regression with meteorological variables.The results showed that the short-term,seasonal,and long-term components accounted for daily maximum 8-hr average O_(3)(O_(3–8)hr)concentration,46.4%,45.9%,and 1.0%,respectively.The meteorological impacts account for an average of 71.8%of O_(3–8)hr,and the YRD’s eastern and northern sections aremeteorology-sensitive areas.Based on statistical analysis technology with empirical orthogonal function,the contribution of meteorology,local emission,and transport in the long-term component of O_(3–8)hr were 0.21%,0.12%,and 0.6%,respectively.The spatiotemporal analysis indicated that a distinct decreasing spatial pattern could be observed from coastal cities towards the northwest,influenced by the monsoon and synoptic conditions.The central urban agglomeration north and south of the YRD was particularly susceptible to local pollution.Among the cities studied,Shanghai,Anqing,and Xuancheng,located at similar latitudes,were significantly impacted by atmospheric transmission—the contribution of Shanghai,the maximum accounting for 3.6%.
文摘目的:探讨Delta大通道内镜辅助下后路椎管减压椎间植骨融合术治疗退变性腰椎疾病的效果。方法:回顾性分析2021年9月~2022年9月我院收治的80例退变性腰椎疾病患者的病历资料,根据患者治疗方式分为观察组(38例,男17例,女21例,年龄61.0±4.9岁)和对照组(42例,男20例,女22例,年龄60.5±5.4岁),观察组患者采取Delta大通道内镜下Endo-PLIF治疗,对照组采取开放后路腰椎椎间融合术治疗,记录两组患者术中出血量、术后引流量、手术时间、手术切口长度、住院时间,比较患者并发症发生情况。于术前、术后1周、1个月、3个月、6个月使用视觉模拟量表(visual analogue scale,VAS)评分评估患者腰痛情况,并采用Oswestry功能障碍指数(Oswestry disability index,ODI)评估患者腰椎功能;使用改良Macnab标准对患者进行疗效评估。根据患者术后1年随访时的腰椎影像学复查结果,使用Bridwell椎间融合标准对患者手术节段融合情况进行评估。结果:观察组患者的术中出血量及术后引流量分别低于对照组(88.46±10.98mL vs 112.99±12.01mL、159.73±18.42mL vs 201.36±23.06mL,P<0.05),手术切口及住院时间分别短于对照组(1.54±0.36cm vs 5.43±1.01cm、6.79±1.22d vs 8.03±1.43d,P<0.05),手术时间长于对照组(162.33±19.57min vs 126.87±23.15min,P<0.05)。80例患者术后均获随访,随访时间15~40个月(19.0±6.3个月)。观察组患者术后1周、术后1个月的VAS评分分别为2.46±0.51分、1.21±0.38分,ODI分别为(17.84±4.15)%、(10.69±1.88)%,均低于对照组[VAS评分分别为3.68±0.62分、2.01±0.41分,ODI分别为(21.33±3.48)%、(12.33±2.17)%,均P<0.05],两组患者术后3个月、术后6个月的VAS评分比较无统计学差异(P>0.05)。观察组治疗优良率为92.11%,与对照组的85.71%比较无统计学意义(P=0.487)。两组患者融合分级比较,差异无统计学意义(Z=0.487,P=0.624)。观察组术后并发症发生率为5.26%,与对照组的9.52%比较无统计学差异(P=0.678)。结论:Delta大通道内镜辅助下后路椎管减压椎间植骨融合术治疗退变性腰椎疾病效果良好,可以减少术中出血量,缩短手术切口和住院时间,更快改善患者术后短期内疼痛、腰椎功能,安全性较好。
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.
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,
