We study some basic properties of weak Orlicz spaces and their applications to harmonic analysis.We first discuss the absolute continuity of the quasi-norm and its normality,then prove the boundedness of several maxim...We study some basic properties of weak Orlicz spaces and their applications to harmonic analysis.We first discuss the absolute continuity of the quasi-norm and its normality,then prove the boundedness of several maximal operators.We also establish a kind of Marcinkiewicz-type interpolation theorem between weak Orlicz spaces.As applications,the weak type analogues of several classical inequalities in harmonic analysis is obtained.展开更多
Understanding the topography in active tectonic areas and assessing the rates and models of active deformation in the upper crust are primary objectives in tectonic geomorphology studies. The drainage pattern of river...Understanding the topography in active tectonic areas and assessing the rates and models of active deformation in the upper crust are primary objectives in tectonic geomorphology studies. The drainage pattern of river systems is highly sensitive to tectonically induced changes, and it often preserves the records of the formation and progression of most tectono-geomorphic processes within its boundaries. Therefore, the evolution of landforms is a consequence of the evolution of individual drainage basins in which they are formed. Assessing the rates of tectonic deformation using geomorphic data is a traditionally adopted method to characterize the nature of active faults. Globally, the Digital Elevation Model(DEM) is widely used as a crucial tool to analyze the morphotectonic features of drainage basins. In this study, some geomorphic indices were applied to investigate the impact of tectonism on landscape along the Karahay?t Fault and its associated drainage areas. These geomorphic indices are mountain front sinuosity(Smf values between 1.17-1.52), valley floor width-to-height ratio(Vf values between 0.25-1.46), basin asymmetry factor(AF values between 15-72), drainage basin shape(Bs values between 3.18-6.01), hypsometric integral and curve(HI values between 0.32-047), channel sinuosity(S values between 1-1.6), normalized steepness index(Ksn values between 1-390) and Chi integral(χ values between 200-4400). The development of drainage areas on the hanging wall and footwall block of the Karahayit Fault differs depending on the uplift. The drainage areas developed on the hanging wall present different patterns depending on the regional uplift caused by the fault. This reveals that the fault contributed significantly to the development of drainage areas and regional uplift in the region. In addition, the maximum earthquake magnitude that may occur in the future on the Karahayit Fault, whose activity is supported by geomorphic indices, is calculated as 6.23. Since an earthquake of this magnitude may cause loss of li展开更多
The computational methods of the mode attenuation and group velocity in shallow water are discussed and two novel modified weighted integral formulae are presented. The accuracy of the modified weighted integral formu...The computational methods of the mode attenuation and group velocity in shallow water are discussed and two novel modified weighted integral formulae are presented. The accuracy of the modified weighted integral formulae, cycle distance formulae and weighted integral formulae in the Pekeris channel is compared theoretically and numerically. Transmission losses are calculated by those three kinds of formulae in a shallow water. Theoretical analyses and numerical results show that the modified weighted integral formulae provide higher accuracy than the weighted integral formulae. So the modified weighted integral formulae can be widely used for computing the shallow water acoustic field.展开更多
In this thesis,we establish non-linear wavelet density estimators and studying the asymptotic properties of the estimators with data missing at random when covariates are present.The outstanding advantage of non-linea...In this thesis,we establish non-linear wavelet density estimators and studying the asymptotic properties of the estimators with data missing at random when covariates are present.The outstanding advantage of non-linear wavelet method is estimating the unsoothed functions,however,the classical kernel estimation cannot do this work.At the same time,we study the larger sample properties of the ISE for hazard rate estimator.展开更多
基金supported by National Natural Science Foundation of China (Grant No.11071190)
文摘We study some basic properties of weak Orlicz spaces and their applications to harmonic analysis.We first discuss the absolute continuity of the quasi-norm and its normality,then prove the boundedness of several maximal operators.We also establish a kind of Marcinkiewicz-type interpolation theorem between weak Orlicz spaces.As applications,the weak type analogues of several classical inequalities in harmonic analysis is obtained.
文摘Understanding the topography in active tectonic areas and assessing the rates and models of active deformation in the upper crust are primary objectives in tectonic geomorphology studies. The drainage pattern of river systems is highly sensitive to tectonically induced changes, and it often preserves the records of the formation and progression of most tectono-geomorphic processes within its boundaries. Therefore, the evolution of landforms is a consequence of the evolution of individual drainage basins in which they are formed. Assessing the rates of tectonic deformation using geomorphic data is a traditionally adopted method to characterize the nature of active faults. Globally, the Digital Elevation Model(DEM) is widely used as a crucial tool to analyze the morphotectonic features of drainage basins. In this study, some geomorphic indices were applied to investigate the impact of tectonism on landscape along the Karahay?t Fault and its associated drainage areas. These geomorphic indices are mountain front sinuosity(Smf values between 1.17-1.52), valley floor width-to-height ratio(Vf values between 0.25-1.46), basin asymmetry factor(AF values between 15-72), drainage basin shape(Bs values between 3.18-6.01), hypsometric integral and curve(HI values between 0.32-047), channel sinuosity(S values between 1-1.6), normalized steepness index(Ksn values between 1-390) and Chi integral(χ values between 200-4400). The development of drainage areas on the hanging wall and footwall block of the Karahayit Fault differs depending on the uplift. The drainage areas developed on the hanging wall present different patterns depending on the regional uplift caused by the fault. This reveals that the fault contributed significantly to the development of drainage areas and regional uplift in the region. In addition, the maximum earthquake magnitude that may occur in the future on the Karahayit Fault, whose activity is supported by geomorphic indices, is calculated as 6.23. Since an earthquake of this magnitude may cause loss of li
文摘The computational methods of the mode attenuation and group velocity in shallow water are discussed and two novel modified weighted integral formulae are presented. The accuracy of the modified weighted integral formulae, cycle distance formulae and weighted integral formulae in the Pekeris channel is compared theoretically and numerically. Transmission losses are calculated by those three kinds of formulae in a shallow water. Theoretical analyses and numerical results show that the modified weighted integral formulae provide higher accuracy than the weighted integral formulae. So the modified weighted integral formulae can be widely used for computing the shallow water acoustic field.
文摘In this thesis,we establish non-linear wavelet density estimators and studying the asymptotic properties of the estimators with data missing at random when covariates are present.The outstanding advantage of non-linear wavelet method is estimating the unsoothed functions,however,the classical kernel estimation cannot do this work.At the same time,we study the larger sample properties of the ISE for hazard rate estimator.
