By using the spectrum expanding theory of random processes and Hudson's crack model,we developed a random medium model for rocks with spatial random distributed number density of cracks. This model could connect t...By using the spectrum expanding theory of random processes and Hudson's crack model,we developed a random medium model for rocks with spatial random distributed number density of cracks. This model could connect the micro-parameters of the cracks with the macro- mechanical properties, and can be effectively applied to model the real inhomogeneous medium. Numerical example indicates that the random distribution characters could be different for different elastic constants under the same random distribution of number density of cracks. By changing the value of the autocorrelation length pair, it is possible to model the difference of the distribution in the two coordinate directions. Numerical modeling results for seismic wave propagating in rocks with random distributed fractures using a staggered high-order finite-difference (SHOFD) are also presented.展开更多
Let B be a p type Banach space (1<p<2),φ(x) be some slow increasing functions on [0,+∞), if {X, X n,n≥1} is a sequence of i.i.d B valued random variables, then we obtain a necessary and sufficient condition f...Let B be a p type Banach space (1<p<2),φ(x) be some slow increasing functions on [0,+∞), if {X, X n,n≥1} is a sequence of i.i.d B valued random variables, then we obtain a necessary and sufficient condition for the moments of Sup n ‖S n(nφ(n)) 1/p ‖ being bounded.展开更多
This paper studies electrical resistivity dataset acquired for a groundwater study in the Domail Plain in the northwestern Himalayan section of Pakistan. Through a combination of geostatistical analysis,geophysical in...This paper studies electrical resistivity dataset acquired for a groundwater study in the Domail Plain in the northwestern Himalayan section of Pakistan. Through a combination of geostatistical analysis,geophysical inversion and visualization techniques,it is possible to re-model and visualize the single dimension resistivity data into 2D and 3D space.The variogram models are utilized to extend the interpretation of the data and to distinguish individual lithologic units and the occurrence of saline water within the subsurface. The resistivity data has been calibrated with the lithological logs taken from the available boreholes. As such the alluvial system of the Domail Plain has formed during episodes of local tectonic activity with fluvial erosion and depositionyielding coarse sediments with high electrical resistivities near to the mountain ranges and finer sediments with medium to low electrical resistivities which tend to settle in the basin center. Thus a change is depositional setting happened from basin lacustrine environment to flash flooding during the Himalayan orogeny. The occurrence of rock salt in the northern mountains has imparted a great influence on the groundwater quality of the study area. The salt is dissolved by water which infiltrates into the subsurface through the water channels. Variogram aided gridding of resistivity data helps to identify the occurrence and distribution of saline water in the subsurface.展开更多
We introduce a modification of Kantorovich-type operators in polynomial weighted spaces of functions. Then we study some approximation properties of these operators. We give some inequalities for these operators by me...We introduce a modification of Kantorovich-type operators in polynomial weighted spaces of functions. Then we study some approximation properties of these operators. We give some inequalities for these operators by means of the weighted modulus continuity and also obtain a Voronovskaya-type theorem. Furthermore, in our paper show that the operators give better degree of approximation of functions belonging to weighted spaces than classical Szaisz- Kantorovich operators.展开更多
In this paper, the authers introduce certain entire exponential type interpolation operatots and study the convergence problem of these operatots in c(R) or Lp(R) (1≤p<∞)
The identification of Wiener systems has been an active research topic for years. A Wiener system is a series connection of a linear dynamic system followed by a static nonlinearity. The difficulty in obtaining a repr...The identification of Wiener systems has been an active research topic for years. A Wiener system is a series connection of a linear dynamic system followed by a static nonlinearity. The difficulty in obtaining a representation of the Wiener model is the need to estimate the nonlinear function from the input and output data, without the intermediate signal availability. This paper presents a methodology for the nonlinear system identification of a Wiener type model, using methods for subspaces and polynomials of Chebyshev. The subspace methods used are MOESP （multivariable output-error state space） and N4SID （numerical algorithms for subspace state space system identification）. A simulated example is presented to compare the performance of these algorithms.展开更多
The authors mainly study the Hausdorff operators on Euclidean space Rn. They establish boundedness of the Hausdorff operators in various function spaces, such as Lebesgue spaces, Hardy spaces, local Hardy spaces and H...The authors mainly study the Hausdorff operators on Euclidean space Rn. They establish boundedness of the Hausdorff operators in various function spaces, such as Lebesgue spaces, Hardy spaces, local Hardy spaces and Herz type spaces. The results reveal that the Hausdorff operators have better performance on the Herz type Hardy spaces HKP（Rn） than their performance on the Hardy spaces Hv（Rn） when 0 〈 p 〈 1. Also, the authors obtain some new results and reprove or generalize some known results for the high dimensional Hardy operator and adjoint Hardy operator.展开更多
In this paper, we first introduce the concept of the inclusive regular separation in L-fuzzy topological spaces. Then we compare the inclusive regular separation with pointed regular separation and regular separation,...In this paper, we first introduce the concept of the inclusive regular separation in L-fuzzy topological spaces. Then we compare the inclusive regular separation with pointed regular separation and regular separation, and discuss the implicative and non-implicative relations among the above three separations. Finally, we illustrate that the inclusive regular separation is harmonic with the inclusive normal separation and inclusive completely regular separation.展开更多
It is known that the space of homogeneous type introduced by Coifman and Weiss(1971) provides a very natural setting for establishing a theory of Hardy spaces. This paper concentrates on how the geometrical conditions...It is known that the space of homogeneous type introduced by Coifman and Weiss(1971) provides a very natural setting for establishing a theory of Hardy spaces. This paper concentrates on how the geometrical conditions of the space of homogeneous type play a crucial role in building a theory of Hardy spaces via the Littlewood-Paley functions.展开更多
In this article we consider a sequence of hierarchical space model of inverse problems.The underlying function is estimated from indirect observations over a variety of error distributions including those that are hea...In this article we consider a sequence of hierarchical space model of inverse problems.The underlying function is estimated from indirect observations over a variety of error distributions including those that are heavy-tailed and may not even possess variances or means.The main contribution of this paper is that we establish some oracle inequalities for the inverse problems by using quantile coupling technique that gives a tight bound for the quantile coupling between an arbitrary sample p-quantile and a normal variable,and an automatic selection principle for the nonrandom filters.This leads to the data-driven choice of weights.We also give an algorithm for its implementation.The quantile coupling inequality developed in this paper is of independent interest,because it includes the median coupling inequality in literature as a special case.展开更多
文摘By using the spectrum expanding theory of random processes and Hudson's crack model,we developed a random medium model for rocks with spatial random distributed number density of cracks. This model could connect the micro-parameters of the cracks with the macro- mechanical properties, and can be effectively applied to model the real inhomogeneous medium. Numerical example indicates that the random distribution characters could be different for different elastic constants under the same random distribution of number density of cracks. By changing the value of the autocorrelation length pair, it is possible to model the difference of the distribution in the two coordinate directions. Numerical modeling results for seismic wave propagating in rocks with random distributed fractures using a staggered high-order finite-difference (SHOFD) are also presented.
文摘Let B be a p type Banach space (1<p<2),φ(x) be some slow increasing functions on [0,+∞), if {X, X n,n≥1} is a sequence of i.i.d B valued random variables, then we obtain a necessary and sufficient condition for the moments of Sup n ‖S n(nφ(n)) 1/p ‖ being bounded.
基金Water and Power Development Authority(WAPDA)is hereby acknowledged for their support in th e present study.
文摘This paper studies electrical resistivity dataset acquired for a groundwater study in the Domail Plain in the northwestern Himalayan section of Pakistan. Through a combination of geostatistical analysis,geophysical inversion and visualization techniques,it is possible to re-model and visualize the single dimension resistivity data into 2D and 3D space.The variogram models are utilized to extend the interpretation of the data and to distinguish individual lithologic units and the occurrence of saline water within the subsurface. The resistivity data has been calibrated with the lithological logs taken from the available boreholes. As such the alluvial system of the Domail Plain has formed during episodes of local tectonic activity with fluvial erosion and depositionyielding coarse sediments with high electrical resistivities near to the mountain ranges and finer sediments with medium to low electrical resistivities which tend to settle in the basin center. Thus a change is depositional setting happened from basin lacustrine environment to flash flooding during the Himalayan orogeny. The occurrence of rock salt in the northern mountains has imparted a great influence on the groundwater quality of the study area. The salt is dissolved by water which infiltrates into the subsurface through the water channels. Variogram aided gridding of resistivity data helps to identify the occurrence and distribution of saline water in the subsurface.
文摘We introduce a modification of Kantorovich-type operators in polynomial weighted spaces of functions. Then we study some approximation properties of these operators. We give some inequalities for these operators by means of the weighted modulus continuity and also obtain a Voronovskaya-type theorem. Furthermore, in our paper show that the operators give better degree of approximation of functions belonging to weighted spaces than classical Szaisz- Kantorovich operators.
文摘In this paper, the authers introduce certain entire exponential type interpolation operatots and study the convergence problem of these operatots in c(R) or Lp(R) (1≤p<∞)
文摘The identification of Wiener systems has been an active research topic for years. A Wiener system is a series connection of a linear dynamic system followed by a static nonlinearity. The difficulty in obtaining a representation of the Wiener model is the need to estimate the nonlinear function from the input and output data, without the intermediate signal availability. This paper presents a methodology for the nonlinear system identification of a Wiener type model, using methods for subspaces and polynomials of Chebyshev. The subspace methods used are MOESP （multivariable output-error state space） and N4SID （numerical algorithms for subspace state space system identification）. A simulated example is presented to compare the performance of these algorithms.
基金supported by the National Natural Science Foundation of China (Nos. 10931001, 10871173)
文摘The authors mainly study the Hausdorff operators on Euclidean space Rn. They establish boundedness of the Hausdorff operators in various function spaces, such as Lebesgue spaces, Hardy spaces, local Hardy spaces and Herz type spaces. The results reveal that the Hausdorff operators have better performance on the Herz type Hardy spaces HKP（Rn） than their performance on the Hardy spaces Hv（Rn） when 0 〈 p 〈 1. Also, the authors obtain some new results and reprove or generalize some known results for the high dimensional Hardy operator and adjoint Hardy operator.
基金the National Natural Science Foundation of China (10471083)Teaching and Research Award Program for Outstanding Young Teachers in Higher Education Institutions of MOE
文摘In this paper, we first introduce the concept of the inclusive regular separation in L-fuzzy topological spaces. Then we compare the inclusive regular separation with pointed regular separation and regular separation, and discuss the implicative and non-implicative relations among the above three separations. Finally, we illustrate that the inclusive regular separation is harmonic with the inclusive normal separation and inclusive completely regular separation.
基金supported by Guangdong Province Natural Science Foundation (Grant Nos. 2014A030313417 and 2017A030313028)the Australian Research Council by Macquarie University New Staff Grant (Grant No. ARC-DP160100153)
文摘It is known that the space of homogeneous type introduced by Coifman and Weiss(1971) provides a very natural setting for establishing a theory of Hardy spaces. This paper concentrates on how the geometrical conditions of the space of homogeneous type play a crucial role in building a theory of Hardy spaces via the Littlewood-Paley functions.
基金supported by the Major Project of Humanities Social Science Foundation of Ministry of Education(Grant No. 08JJD910247)Key Project of Chinese Ministry of Education (Grant No. 108120)+4 种基金National Natural Science Foundation of China (Grant No. 10871201)Beijing Natural Science Foundation (Grant No. 1102021)the Fundamental Research Funds for the Central Universitiesthe Research Funds of Renmin University of China(Grant No. 10XNL018)the China Statistical Research Project (Grant No. 2011LZ031)
文摘In this article we consider a sequence of hierarchical space model of inverse problems.The underlying function is estimated from indirect observations over a variety of error distributions including those that are heavy-tailed and may not even possess variances or means.The main contribution of this paper is that we establish some oracle inequalities for the inverse problems by using quantile coupling technique that gives a tight bound for the quantile coupling between an arbitrary sample p-quantile and a normal variable,and an automatic selection principle for the nonrandom filters.This leads to the data-driven choice of weights.We also give an algorithm for its implementation.The quantile coupling inequality developed in this paper is of independent interest,because it includes the median coupling inequality in literature as a special case.
