Let T_(ϕ,a)be a Fourier integral operator with amplitude a and phase functions ϕ.In this paper,we study the boundedness of Fourier integral operator of rough amplitude a∈L^(∞)S_(ρ)^(m)and rough phase functionsϕ∈L^...Let T_(ϕ,a)be a Fourier integral operator with amplitude a and phase functions ϕ.In this paper,we study the boundedness of Fourier integral operator of rough amplitude a∈L^(∞)S_(ρ)^(m)and rough phase functionsϕ∈L^(m)ϕ^(2)with some measure condition.We prove the global L^(1)boundedness for T_(ϕ,a),when 1/<ρ≤1 and m<ρ-n+1/2.Our theorem improves some known results.展开更多
Amplitude-integrated EEG (aEEG) is a popular method for monitoring cerebral function. Although various commercial aEEG recorders have been produced, a detailed aEEG algorithm currently is not available. The upper and ...Amplitude-integrated EEG (aEEG) is a popular method for monitoring cerebral function. Although various commercial aEEG recorders have been produced, a detailed aEEG algorithm currently is not available. The upper and lower margins in the aEEG tracing are the discriminating features for data inspection and tracing classification. However, most aEEG devices require that these margins be measured semi-subjectively. This paper proposes a step-by-step signal-processing method to calculate a compact aEEG tracing and the upper/lower margin using raw EEG data. The high accuracy of the algorithm was verified by comparison with a recognized commercial aEEG device based on a representative testing dataset composed of 72 aEEG data. The introduced digital algorithm achieved compact aEEG tracing with a small data size. Moreover, the algorithm precisely represented the upper and lower margins in the tracing for objective data interpretation. The described method should facilitate aEEG signal processing and further establish the clinical and experimental application of aEEG methods.展开更多
The Z component and X component profiles of seismic waves extracted with the prestack Kirchhoff integral migration could approximate to the primary wave （P wave） and converted shear wave （PS wave） profiles under c...The Z component and X component profiles of seismic waves extracted with the prestack Kirchhoff integral migration could approximate to the primary wave （P wave） and converted shear wave （PS wave） profiles under certain conditions. The relative change of their reflection amplitude reflects the formation stress anomaly and subsurface media anisotropy. The principle and method for extracting amplitude ratios were studied and the application of amplitude ratio profiles was also examined when processing and interpreting actual seismic data. The amplitude ratio profile is an effective supplementary means of identifying the stratigraphic boundary and lithology.展开更多
The purpose of this article is to develop an integral derived from the double transfer and excitation theory. The reduced form of this integral, so obtained, can serve in the computation of the transition amplitude wh...The purpose of this article is to develop an integral derived from the double transfer and excitation theory. The reduced form of this integral, so obtained, can serve in the computation of the transition amplitude which is from numerical point of view difficult to implement. This amplitude is of great interest in the resonant and non resonant transfer and excitation （RTE and NTE） processes.展开更多
We show how the famous soliton solution of the classical sine-Gordon field theory in (1 + 1)-dimensions may be obtained as a particular case of a solution expressed in terms of the Jacobi amplitude, which is the inver...We show how the famous soliton solution of the classical sine-Gordon field theory in (1 + 1)-dimensions may be obtained as a particular case of a solution expressed in terms of the Jacobi amplitude, which is the inverse function of the incomplete elliptic integral of the first kind.展开更多
Prognostication of coma patients after brain injury is important, yet challenging. In this study, we evaluated the predictive value of amplitude-integrated electroencephalography （aEEG） for neurological outcomes in ...Prognostication of coma patients after brain injury is important, yet challenging. In this study, we evaluated the predictive value of amplitude-integrated electroencephalography （aEEG） for neurological outcomes in coma patients. From January 2013 to January 2016, 128 coma patients after acute brain injury were prospectively enrolled and monitored with aEEG. The 6-month neurological outcome was evaluated using the Cerebral Performance Category Scale. aEEG monitoring commenced at a median of 7.5 days after coma onset. Continuous normal voltage predicted a good 6-month neurological outcome with a sensitivity of 93.6% and specificity of 85.2%. In contrast, continuous extremely low voltage, burst-suppression, or a flat tracing was correlated with poor 6-month neurological outcome with a sensitivity of 76.5% and specificity of 100%. In conclusion, aEEG is a promising predictor of 6-month neurological outcome for coma patients after acute brain injury.展开更多
A systematization for the manipulations and calculations involving divergent (or not) Feynman integrals, typical of the one loop perturbative solutions of Quantum Field Theory, is proposed. A previous work on the same...A systematization for the manipulations and calculations involving divergent (or not) Feynman integrals, typical of the one loop perturbative solutions of Quantum Field Theory, is proposed. A previous work on the same issue is generalized to treat theories and models having different species of massive fields. An improvement on the strategy is adopted so that no regularization needs to be used. The final results produced, however, can be converted into the ones of reasonable regularizations, especially those belonging to the dimensional regularization (in situations where the method applies). Through an adequate interpretation of the Feynman rules and a convenient representation for involved propagators, the finite and divergent parts are separated before the introduction of the integration in the loop momentum. Only the finite integrals obtained are in fact integrated. The divergent content of the amplitudes are written as a combination of standard mathematical object which are never really integrated. Only very general scale properties of such objects are used. The finite parts, on the other hand, are written in terms of basic functions conveniently introduced. The scale properties of such functions relate them to a well defined way to the basic divergent objects providing simple and transparent connection between both parts in the assintotic regime. All the arbitrariness involved in this type of calculations are preserved in the intermediary steps allowing the identification of universal properties for the divergent integrals, which are required for the maintenance of fundamental symmetries like translational invariance and scale independence in the perturbative amplitudes. Once these consistency relations are imposed no other symmetry is violated in perturbative calculations neither ambiguous terms survive at any theory or model formulated at any space-time dimension including nonrenormalizable cases. Representative examples of perturbative amplitudes involving different species of massive fermions are considered as examples. The referred amplitudes are calculated in detail within the context of the presented strategy (and systematization) and their relations among other Green functions are explicitly verified. At the end a generalization for the finite functions is presented.展开更多
The quantum probability theory of fuzzy event is suggested by using the idea and method of fuzzy mathematics, giving the form of fuzzy event path integral, membership degree amplitude, fuzzy field function, Green func...The quantum probability theory of fuzzy event is suggested by using the idea and method of fuzzy mathematics, giving the form of fuzzy event path integral, membership degree amplitude, fuzzy field function, Green function, physical quantity and fuzzy diagram. This theory reforms quantum mechanics, making the later become its special case. This theory breaks unitarity, gauge invariance, probability conservation and information conservation, making these principles become approximate ones under certain conditions. This new theory, which needs no renormalization and can naturally give meaningful results which are in accordance with the experiments, is the proper theory to describe microscopic high-speed phenomenon, whereas quantum mechanics is only a proper theory to describe microscopic low-speed phenomenon. This theory is not divergent under the condition of there being no renormalization and infinitely many offsetting terms, thereby it can become the theoretical framework required for the quantization of gravity.展开更多
Background： The patients with early-onset epileptic encephalopathy （EOEE） suffer from neurodevelopmental delay. The aim of this study was to analyze the clinical manifestations and amplitude-integrated encephalogr...Background： The patients with early-onset epileptic encephalopathy （EOEE） suffer from neurodevelopmental delay. The aim of this study was to analyze the clinical manifestations and amplitude-integrated encephalogram （aEEG） characteristics of infants with EOEE with onset within the neonatal period, to make early diagnosis to improve the prognosis. Methods： One-hundred and twenty-eight patients with neonatal seizure were enrolled and followed up till 1 year old. Sixty-six neonates evolved into EOEE were as the EOEE group, the other 62 were as the non-EOEE （nEOEE） group. Then we compared the clinical and aEEG characteristics between the two groups to analyze the manifestations in neonates with EOEE. Results： Compared to the nEOEE group, the incidence of daily seizure attacks, more than two types of convulsions, more than two antiepileptic drugs （AEDs） application, severely abnormal aEEG background, absence of cyclicity, and more than two seizures detection were significantly higher in the EOEE group （P 〈 0.05） （97% vs. 54.8%; 30.3% vs. 14.5%; 97.0% vs. 25.4%; 39.4% vs. 3.2%; 57.6% vs. 9.7%; and 56% vs. 3.2%, respectively）. Severely abnormal background pattern （odds ratio [OR] = 0.081, 95% confidence interval [CI]：0.009-0.729, P = 0.025） and more than two seizures detection by aEEG （OR = 0.158, 95% CI： 0.043-0.576, P = 0.005） were the independent risk factors for the evolvement into EOEE. The upper and lower margins of active sleep （AS） and quiet sleep （QS） were significantly higher in EOEE group than those of the control group （P 〈 0.05） （34.3 ± 13.6 vs. 21.3 ± 6.4; 9.9 ± 3.7 vs. 6.7 ± 2.2; 41.2 ± 15.1 vs. 30.4 ± 11.4;and 11.9 ± 4.4 vs. 9.4 ± 4.0; unit： μV, respectively）. AS upper margin was demonstrated a higher diagnostic specificity and sensitivity for EOEE than another three parameters according to the receiver operating characteristic curves; the area under the curve was 0.827. Conclusions： The clinical characteristics of the neonatal seizure which will evolve into EOEE were more than two AEDs application, high seizure frequency （daily attack）, and more than two types of the seizure. Significant high voltage, severely abnormal background, absence of cyclicity, and more than two seizures detected on aEEG were the meaningful indicators to the prediction of EOEE.展开更多
基金Supported by the National Natural Science Foundation of China(11801518)the Natural Science Foundation of Zhejiang Province(LQ18A010005)the Science Foundation of Zhejiang Education Department(Y201738640)。
文摘Let T_(ϕ,a)be a Fourier integral operator with amplitude a and phase functions ϕ.In this paper,we study the boundedness of Fourier integral operator of rough amplitude a∈L^(∞)S_(ρ)^(m)and rough phase functionsϕ∈L^(m)ϕ^(2)with some measure condition.We prove the global L^(1)boundedness for T_(ϕ,a),when 1/<ρ≤1 and m<ρ-n+1/2.Our theorem improves some known results.
文摘Amplitude-integrated EEG (aEEG) is a popular method for monitoring cerebral function. Although various commercial aEEG recorders have been produced, a detailed aEEG algorithm currently is not available. The upper and lower margins in the aEEG tracing are the discriminating features for data inspection and tracing classification. However, most aEEG devices require that these margins be measured semi-subjectively. This paper proposes a step-by-step signal-processing method to calculate a compact aEEG tracing and the upper/lower margin using raw EEG data. The high accuracy of the algorithm was verified by comparison with a recognized commercial aEEG device based on a representative testing dataset composed of 72 aEEG data. The introduced digital algorithm achieved compact aEEG tracing with a small data size. Moreover, the algorithm precisely represented the upper and lower margins in the tracing for objective data interpretation. The described method should facilitate aEEG signal processing and further establish the clinical and experimental application of aEEG methods.
文摘The Z component and X component profiles of seismic waves extracted with the prestack Kirchhoff integral migration could approximate to the primary wave （P wave） and converted shear wave （PS wave） profiles under certain conditions. The relative change of their reflection amplitude reflects the formation stress anomaly and subsurface media anisotropy. The principle and method for extracting amplitude ratios were studied and the application of amplitude ratio profiles was also examined when processing and interpreting actual seismic data. The amplitude ratio profile is an effective supplementary means of identifying the stratigraphic boundary and lithology.
基金Supported in part by the M.E.R.S (Ministere de l'Enseignement et de la Recherche Scientifique) under Grant No. D01420060012
文摘The purpose of this article is to develop an integral derived from the double transfer and excitation theory. The reduced form of this integral, so obtained, can serve in the computation of the transition amplitude which is from numerical point of view difficult to implement. This amplitude is of great interest in the resonant and non resonant transfer and excitation （RTE and NTE） processes.
文摘We show how the famous soliton solution of the classical sine-Gordon field theory in (1 + 1)-dimensions may be obtained as a particular case of a solution expressed in terms of the Jacobi amplitude, which is the inverse function of the incomplete elliptic integral of the first kind.
基金supported by the National Natural Science Foundation of China(81671198)Shanghai Municipal Education Commission-Gaofeng Clinical Medicine Grant(20152212)the Shanghai Shenkang Clinical Research Plan of the Shenkang Hospital Development Center(16CR3011A)
文摘Prognostication of coma patients after brain injury is important, yet challenging. In this study, we evaluated the predictive value of amplitude-integrated electroencephalography （aEEG） for neurological outcomes in coma patients. From January 2013 to January 2016, 128 coma patients after acute brain injury were prospectively enrolled and monitored with aEEG. The 6-month neurological outcome was evaluated using the Cerebral Performance Category Scale. aEEG monitoring commenced at a median of 7.5 days after coma onset. Continuous normal voltage predicted a good 6-month neurological outcome with a sensitivity of 93.6% and specificity of 85.2%. In contrast, continuous extremely low voltage, burst-suppression, or a flat tracing was correlated with poor 6-month neurological outcome with a sensitivity of 76.5% and specificity of 100%. In conclusion, aEEG is a promising predictor of 6-month neurological outcome for coma patients after acute brain injury.
文摘A systematization for the manipulations and calculations involving divergent (or not) Feynman integrals, typical of the one loop perturbative solutions of Quantum Field Theory, is proposed. A previous work on the same issue is generalized to treat theories and models having different species of massive fields. An improvement on the strategy is adopted so that no regularization needs to be used. The final results produced, however, can be converted into the ones of reasonable regularizations, especially those belonging to the dimensional regularization (in situations where the method applies). Through an adequate interpretation of the Feynman rules and a convenient representation for involved propagators, the finite and divergent parts are separated before the introduction of the integration in the loop momentum. Only the finite integrals obtained are in fact integrated. The divergent content of the amplitudes are written as a combination of standard mathematical object which are never really integrated. Only very general scale properties of such objects are used. The finite parts, on the other hand, are written in terms of basic functions conveniently introduced. The scale properties of such functions relate them to a well defined way to the basic divergent objects providing simple and transparent connection between both parts in the assintotic regime. All the arbitrariness involved in this type of calculations are preserved in the intermediary steps allowing the identification of universal properties for the divergent integrals, which are required for the maintenance of fundamental symmetries like translational invariance and scale independence in the perturbative amplitudes. Once these consistency relations are imposed no other symmetry is violated in perturbative calculations neither ambiguous terms survive at any theory or model formulated at any space-time dimension including nonrenormalizable cases. Representative examples of perturbative amplitudes involving different species of massive fermions are considered as examples. The referred amplitudes are calculated in detail within the context of the presented strategy (and systematization) and their relations among other Green functions are explicitly verified. At the end a generalization for the finite functions is presented.
文摘The quantum probability theory of fuzzy event is suggested by using the idea and method of fuzzy mathematics, giving the form of fuzzy event path integral, membership degree amplitude, fuzzy field function, Green function, physical quantity and fuzzy diagram. This theory reforms quantum mechanics, making the later become its special case. This theory breaks unitarity, gauge invariance, probability conservation and information conservation, making these principles become approximate ones under certain conditions. This new theory, which needs no renormalization and can naturally give meaningful results which are in accordance with the experiments, is the proper theory to describe microscopic high-speed phenomenon, whereas quantum mechanics is only a proper theory to describe microscopic low-speed phenomenon. This theory is not divergent under the condition of there being no renormalization and infinitely many offsetting terms, thereby it can become the theoretical framework required for the quantization of gravity.
文摘Background： The patients with early-onset epileptic encephalopathy （EOEE） suffer from neurodevelopmental delay. The aim of this study was to analyze the clinical manifestations and amplitude-integrated encephalogram （aEEG） characteristics of infants with EOEE with onset within the neonatal period, to make early diagnosis to improve the prognosis. Methods： One-hundred and twenty-eight patients with neonatal seizure were enrolled and followed up till 1 year old. Sixty-six neonates evolved into EOEE were as the EOEE group, the other 62 were as the non-EOEE （nEOEE） group. Then we compared the clinical and aEEG characteristics between the two groups to analyze the manifestations in neonates with EOEE. Results： Compared to the nEOEE group, the incidence of daily seizure attacks, more than two types of convulsions, more than two antiepileptic drugs （AEDs） application, severely abnormal aEEG background, absence of cyclicity, and more than two seizures detection were significantly higher in the EOEE group （P 〈 0.05） （97% vs. 54.8%; 30.3% vs. 14.5%; 97.0% vs. 25.4%; 39.4% vs. 3.2%; 57.6% vs. 9.7%; and 56% vs. 3.2%, respectively）. Severely abnormal background pattern （odds ratio [OR] = 0.081, 95% confidence interval [CI]：0.009-0.729, P = 0.025） and more than two seizures detection by aEEG （OR = 0.158, 95% CI： 0.043-0.576, P = 0.005） were the independent risk factors for the evolvement into EOEE. The upper and lower margins of active sleep （AS） and quiet sleep （QS） were significantly higher in EOEE group than those of the control group （P 〈 0.05） （34.3 ± 13.6 vs. 21.3 ± 6.4; 9.9 ± 3.7 vs. 6.7 ± 2.2; 41.2 ± 15.1 vs. 30.4 ± 11.4;and 11.9 ± 4.4 vs. 9.4 ± 4.0; unit： μV, respectively）. AS upper margin was demonstrated a higher diagnostic specificity and sensitivity for EOEE than another three parameters according to the receiver operating characteristic curves; the area under the curve was 0.827. Conclusions： The clinical characteristics of the neonatal seizure which will evolve into EOEE were more than two AEDs application, high seizure frequency （daily attack）, and more than two types of the seizure. Significant high voltage, severely abnormal background, absence of cyclicity, and more than two seizures detected on aEEG were the meaningful indicators to the prediction of EOEE.
