For the N-parameter d-dimensional Generalized Brownian Sheet (in short G. B. S.) satisfying some conditions, this paper proves that when 2N≤αd, with probability one, E∈B(R_+~N), there holds 2/βdim E+2N-2Nβ/α≤d...For the N-parameter d-dimensional Generalized Brownian Sheet (in short G. B. S.) satisfying some conditions, this paper proves that when 2N≤αd, with probability one, E∈B(R_+~N), there holds 2/βdim E+2N-2Nβ/α≤dim (E)≤2/αdim E. Especially when α=β=1, we have dim (E)=2 dim E. Noting that even if α=β=1, the G. B. S. is wider than the Brownian Sheet, thus we have extended the uniform dimension result of Mountford, T,S.展开更多
To reduce computational costs, an improved form of the frequency domain boundary element method（BEM） is proposed for two-dimensional radiation and propagation acoustic problems in a subsonic uniform flow with arbitr...To reduce computational costs, an improved form of the frequency domain boundary element method（BEM） is proposed for two-dimensional radiation and propagation acoustic problems in a subsonic uniform flow with arbitrary orientation. The boundary integral equation（BIE） representation solves the two-dimensional convected Helmholtz equation（CHE） and its fundamental solution, which must satisfy a new Sommerfeld radiation condition（SRC） in the physical space. In order to facilitate conventional formulations, the variables of the advanced form are expressed only in terms of the acoustic pressure as well as its normal and tangential derivatives, and their multiplication operators are based on the convected Green＇s kernel and its modified derivative. The proposed approach significantly reduces the CPU times of classical computational codes for modeling acoustic domains with arbitrary mean flow. It is validated by a comparison with the analytical solutions for the sound radiation problems of monopole,dipole and quadrupole sources in the presence of a subsonic uniform flow with arbitrary orientation.展开更多
In this paper we find that a set of energy eigenstates of a two-dimensional anisotropic harmonic potential in a uniform magnetic field is classified as the atomic coherent states ｜τ） in terms of the spin values of ...In this paper we find that a set of energy eigenstates of a two-dimensional anisotropic harmonic potential in a uniform magnetic field is classified as the atomic coherent states ｜τ） in terms of the spin values of j in the Schwinger bosonic realization. The correctness of the above conclusions can be verified by virtue of the entangled state 〈η｜ representation of the state ｜τ）.展开更多
The position decoding accuracy and the spatial resolution of positron emission tomography detectors are greatly influenced by the performance of the two-dimensional position map,including the gain uniformity of photom...The position decoding accuracy and the spatial resolution of positron emission tomography detectors are greatly influenced by the performance of the two-dimensional position map,including the gain uniformity of photomultiplier tube (PMT),the baseline offset of the PMT signals and the accuracy of analogue to digital converter (ADC).In this work,a PMT-quadrant sharing detector was designed.Two data acquisition platforms are employed to conduct the influence factors on the two-dimensional position map performances,one was that the waveforms of the PMT signals were scanned by the sequence acquisition mode based on the oscilloscope of LeCroy waveRunner 204MXi-A,and another was a self-developed high speed ADC data acquisition module.Results show that the event decoding positions were concentrated on the PMT with higher gain,the position map was distorted at the baseline offset of signal,and the cross-line artifacts were caused by the insufficient ADC sampling bit for a larger size position map.All the parameters need be adjusted properly to stabilize a real system,and the flexible oscilloscope platform can be used to design the detector block and the other platform with high ADC accuracy.Likely,the electrical circuit with a proper ADC accuracy adjusts the PMT gains and baseline offsets.展开更多
Let X={X(t),t∈R^(N)}be a centered space-time anisotropic Gaussian random field with values in R^(d).Under some general conditions,the existence,joint continuity and Hölder conditions of higher-order derivative o...Let X={X(t),t∈R^(N)}be a centered space-time anisotropic Gaussian random field with values in R^(d).Under some general conditions,the existence,joint continuity and Hölder conditions of higher-order derivative of local times of X are studied.Moreover,we obtain the uniform Hausdorff dimension of the inverse images of X.The existing results of Gaussian random fields are extended to space-time anisotropic Gaussian random fields with approximate independent components.展开更多
基金Supported by the National Natural Science Foundation of China
文摘For the N-parameter d-dimensional Generalized Brownian Sheet (in short G. B. S.) satisfying some conditions, this paper proves that when 2N≤αd, with probability one, E∈B(R_+~N), there holds 2/βdim E+2N-2Nβ/α≤dim (E)≤2/αdim E. Especially when α=β=1, we have dim (E)=2 dim E. Noting that even if α=β=1, the G. B. S. is wider than the Brownian Sheet, thus we have extended the uniform dimension result of Mountford, T,S.
基金supported by National Engineering School of Tunis (No.13039.1)
文摘To reduce computational costs, an improved form of the frequency domain boundary element method（BEM） is proposed for two-dimensional radiation and propagation acoustic problems in a subsonic uniform flow with arbitrary orientation. The boundary integral equation（BIE） representation solves the two-dimensional convected Helmholtz equation（CHE） and its fundamental solution, which must satisfy a new Sommerfeld radiation condition（SRC） in the physical space. In order to facilitate conventional formulations, the variables of the advanced form are expressed only in terms of the acoustic pressure as well as its normal and tangential derivatives, and their multiplication operators are based on the convected Green＇s kernel and its modified derivative. The proposed approach significantly reduces the CPU times of classical computational codes for modeling acoustic domains with arbitrary mean flow. It is validated by a comparison with the analytical solutions for the sound radiation problems of monopole,dipole and quadrupole sources in the presence of a subsonic uniform flow with arbitrary orientation.
基金Project supported by the National Natural Science Foundation of China (Grant No. 10574060)the Natural Science Foundation of Shandong Province of China (Grant No. Y2008A23)the Shandong Provincal Higher Educational Science and Technology Program of China (Grant Nos. J09LA07 and J10LA15)
文摘In this paper we find that a set of energy eigenstates of a two-dimensional anisotropic harmonic potential in a uniform magnetic field is classified as the atomic coherent states ｜τ） in terms of the spin values of j in the Schwinger bosonic realization. The correctness of the above conclusions can be verified by virtue of the entangled state 〈η｜ representation of the state ｜τ）.
基金Supported by in part by Specialized Research Fund for the Doctoral Program of Higher Education (SRFDP200800031071)National Natural Science Foundation of China (No. 10975086)the National High Technology Research and Development Program (863 Program) of China (No. 2006AA020802)
文摘The position decoding accuracy and the spatial resolution of positron emission tomography detectors are greatly influenced by the performance of the two-dimensional position map,including the gain uniformity of photomultiplier tube (PMT),the baseline offset of the PMT signals and the accuracy of analogue to digital converter (ADC).In this work,a PMT-quadrant sharing detector was designed.Two data acquisition platforms are employed to conduct the influence factors on the two-dimensional position map performances,one was that the waveforms of the PMT signals were scanned by the sequence acquisition mode based on the oscilloscope of LeCroy waveRunner 204MXi-A,and another was a self-developed high speed ADC data acquisition module.Results show that the event decoding positions were concentrated on the PMT with higher gain,the position map was distorted at the baseline offset of signal,and the cross-line artifacts were caused by the insufficient ADC sampling bit for a larger size position map.All the parameters need be adjusted properly to stabilize a real system,and the flexible oscilloscope platform can be used to design the detector block and the other platform with high ADC accuracy.Likely,the electrical circuit with a proper ADC accuracy adjusts the PMT gains and baseline offsets.
基金Supported by the National Natural Science Foundation of China(Grant No.12371150)National Key R&D Program of China(Grant No.2024YFA1013500)+1 种基金Zhejiang Province Philosophy and Social Science Planning Routine Subject(Grant No.24NDJC131YB)the Summit Advancement Disciplines of Zhejiang Province(Zhejiang Gongshang University-Statistics)。
文摘Let X={X(t),t∈R^(N)}be a centered space-time anisotropic Gaussian random field with values in R^(d).Under some general conditions,the existence,joint continuity and Hölder conditions of higher-order derivative of local times of X are studied.Moreover,we obtain the uniform Hausdorff dimension of the inverse images of X.The existing results of Gaussian random fields are extended to space-time anisotropic Gaussian random fields with approximate independent components.
