A precise diagnosis of the complex post-fracturing characteristics and parameter variations in tight gas reservoirs is essential for optimizing fracturing technology,enhancing treatment effectiveness,and assessing pos...A precise diagnosis of the complex post-fracturing characteristics and parameter variations in tight gas reservoirs is essential for optimizing fracturing technology,enhancing treatment effectiveness,and assessing post-fracturing production capacity.Tight gas reservoirs face challenges due to the interaction between natural fractures and induced fractures.To address these issues,a theoretical model for diagnosing fractures under varying leak-off mechanisms has been developed,incorporating the closure behavior of natural fractures.This model,grounded in material balance theory,also accounts for shut-in pressure.The study derived and plotted typical G-function charts,which capture fracture behavior during closure.By superimposing the G-function in the closure phase of natural fractures with pressure derivative curves,the study explored how fracture parameters—including leak-off coefficient,fracture area,closure pressure,and closure time—impact these diagnostic charts.Findings show that variations in natural fracture flexibility,fracture area,and controlling factors influence the superimposed G-function pressure derivative curve,resulting in distinctive“concave”or“convex”patterns.Field data from Well Y in a specific tight gas reservoir were used to validate the model,confirming both its reliability and practicality.展开更多
In this paper, the Schr?dinger equation is solved by Modified separation of variables (MSV) method suggested by Pishkoo and Darus. Using this method, Meijer’s G-function solutions are derived in cylindrical coordinat...In this paper, the Schr?dinger equation is solved by Modified separation of variables (MSV) method suggested by Pishkoo and Darus. Using this method, Meijer’s G-function solutions are derived in cylindrical coordinate system for quantum particle in cylindrical can. All elementary functions and most of the special functions which are the solution of extensive problems in physics and engineering are special cases of Meijer’s G-functions.展开更多
The distribution of Votaw’s λ1（vc） criterion for testing compound symmetryof the covariance matrix of a t-variate Gaussian model has been obtained in terms ofMeijer’s G-function as well as in computable series fo...The distribution of Votaw’s λ1（vc） criterion for testing compound symmetryof the covariance matrix of a t-variate Gaussian model has been obtained in terms ofMeijer’s G-function as well as in computable series form. Special cases of the densityhave also been derived using reduction formulae for G-function.展开更多
The ratio R of two random quantities is frequently encountered in probability and statistics. But while for unidimensional statistical variables the distribution of R can be computed relatively easily, for symmetric p...The ratio R of two random quantities is frequently encountered in probability and statistics. But while for unidimensional statistical variables the distribution of R can be computed relatively easily, for symmetric positive definite random matrices, this ratio can take various forms and its distribution, and even its definition, can offer many challenges. However, for the distribution of its determinant, Meijer G-function often provides an effective analytic and computational tool, applicable at any division level, because of its reproductive property.展开更多
In this paper, we establish the following limiting weak-type behaviors of Littlewood-Paley g-function g_φ: for nonnegative function f∈ L^1(R^n),■and ■where f_t(x) =t^(-n)f(t^(-1) x) for t > 0. Meanwhile, the co...In this paper, we establish the following limiting weak-type behaviors of Littlewood-Paley g-function g_φ: for nonnegative function f∈ L^1(R^n),■and ■where f_t(x) =t^(-n)f(t^(-1) x) for t > 0. Meanwhile, the corresponding results for Marcinkiewicz integral and its fractional version with kernels satisfying L_α~q-Dini condition are also given.展开更多
In this paper,the L2-boundedness of a class of parametric Marcinkiewicz integral μρ Ω,h with kernel function Ω in B 0,0 q(S n-1) for some q>1,and the radial function h(x)∈l∞(Ls)(R +) for 1<s≤∞ are...In this paper,the L2-boundedness of a class of parametric Marcinkiewicz integral μρ Ω,h with kernel function Ω in B 0,0 q(S n-1) for some q>1,and the radial function h(x)∈l∞(Ls)(R +) for 1<s≤∞ are given.The Lp(Rn)(2≤p<∞) boundedness of μ *,ρ Ω,h,λ and μ ρ Ω,h,S with Ω in B 0,0 q(S n-1) and h(|x|)∈l∞(Ls)(R +) in application are obtained.Here μ *,ρ Ω,h,λ and μ ρ Ω,h,S are parametric Marcinkiewicz integrals corresponding to the Littlewood-Paley g* λ function and the Lusin area function S,respectively.展开更多
We first give alternative expressions of some generalized countably compact spaces such as quasi-γspaces, quasi-Nagata spaces, M^#-spaces and wM-spaces with g-functions. Then by means of these expressions, we present...We first give alternative expressions of some generalized countably compact spaces such as quasi-γspaces, quasi-Nagata spaces, M^#-spaces and wM-spaces with g-functions. Then by means of these expressions, we present some characterizations of the corresponding spaces with real-valued functions.展开更多
For the case where the multivariate normal population does not have null correlations, we give the exact expression of the distribution of the sample matrix of correlations R, with the sample variances acting as param...For the case where the multivariate normal population does not have null correlations, we give the exact expression of the distribution of the sample matrix of correlations R, with the sample variances acting as parameters. Also, the distribution of its determinant is established in terms of Meijer G-functions in the null-correlation case. Several numerical examples are given, and applications to the concept of system de- pendence in Reliability Theory are presented.展开更多
In this paper, we make further discussions and improvements on the results presented in the previously published work ＂Block H-matrices and spectrum of block matrices＂. Furthermore, a new bound for eigenvalues of bl...In this paper, we make further discussions and improvements on the results presented in the previously published work ＂Block H-matrices and spectrum of block matrices＂. Furthermore, a new bound for eigenvalues of block matrices is given with examples to show advantages of the new result.展开更多
The block H-matrices are studied by the concept of G-functions, several concepts of block matrices are introduced. Equivalent characters of block H-matrices are obtained. Spectrum localizations characterized by G-func...The block H-matrices are studied by the concept of G-functions, several concepts of block matrices are introduced. Equivalent characters of block H-matrices are obtained. Spectrum localizations characterized by G-functions for block matrices are got.展开更多
With the development of the market, it becomes a demanding task for producers to make flexible production schedules to shorten production cycle. Schedule-free rolling is needed. If the CVC work roll of the F6 and F7 s...With the development of the market, it becomes a demanding task for producers to make flexible production schedules to shorten production cycle. Schedule-free rolling is needed. If the CVC work roll of the F6 and F7 stands in certain 2050 mm hot rolled strip mill are substituted by flat roll (aim to SFR) and the strip profile is controlled by the existing bending force, the control ability is not adequate. This fact has been tested through on-line experiment and has been given in this article. The NBCM (new backup roll crowning method) is recommended to improve the profile control ability. Finally the plastic deformation of the strip and the elastic deformation of the roll are analyzed by employing coupled calculation of rigid-plastic finite element method and G-function method, and the optimal range of the crown of backup roll is given theoretically.展开更多
In this paper,we consider the boundedness of multilinear Littlewood-Paley operators which include multilinear g-function,multilinear Lusin's area integral and multilinear Littlewood-Paley g^*λ-function.Furthermor...In this paper,we consider the boundedness of multilinear Littlewood-Paley operators which include multilinear g-function,multilinear Lusin's area integral and multilinear Littlewood-Paley g^*λ-function.Furthermore,norm inequalities of the above operators hold on the corresponding Amalgam-Campanato spaces.展开更多
文摘A precise diagnosis of the complex post-fracturing characteristics and parameter variations in tight gas reservoirs is essential for optimizing fracturing technology,enhancing treatment effectiveness,and assessing post-fracturing production capacity.Tight gas reservoirs face challenges due to the interaction between natural fractures and induced fractures.To address these issues,a theoretical model for diagnosing fractures under varying leak-off mechanisms has been developed,incorporating the closure behavior of natural fractures.This model,grounded in material balance theory,also accounts for shut-in pressure.The study derived and plotted typical G-function charts,which capture fracture behavior during closure.By superimposing the G-function in the closure phase of natural fractures with pressure derivative curves,the study explored how fracture parameters—including leak-off coefficient,fracture area,closure pressure,and closure time—impact these diagnostic charts.Findings show that variations in natural fracture flexibility,fracture area,and controlling factors influence the superimposed G-function pressure derivative curve,resulting in distinctive“concave”or“convex”patterns.Field data from Well Y in a specific tight gas reservoir were used to validate the model,confirming both its reliability and practicality.
文摘In this paper, the Schr?dinger equation is solved by Modified separation of variables (MSV) method suggested by Pishkoo and Darus. Using this method, Meijer’s G-function solutions are derived in cylindrical coordinate system for quantum particle in cylindrical can. All elementary functions and most of the special functions which are the solution of extensive problems in physics and engineering are special cases of Meijer’s G-functions.
文摘The distribution of Votaw’s λ1（vc） criterion for testing compound symmetryof the covariance matrix of a t-variate Gaussian model has been obtained in terms ofMeijer’s G-function as well as in computable series form. Special cases of the densityhave also been derived using reduction formulae for G-function.
文摘The ratio R of two random quantities is frequently encountered in probability and statistics. But while for unidimensional statistical variables the distribution of R can be computed relatively easily, for symmetric positive definite random matrices, this ratio can take various forms and its distribution, and even its definition, can offer many challenges. However, for the distribution of its determinant, Meijer G-function often provides an effective analytic and computational tool, applicable at any division level, because of its reproductive property.
文摘In this paper, we establish the following limiting weak-type behaviors of Littlewood-Paley g-function g_φ: for nonnegative function f∈ L^1(R^n),■and ■where f_t(x) =t^(-n)f(t^(-1) x) for t > 0. Meanwhile, the corresponding results for Marcinkiewicz integral and its fractional version with kernels satisfying L_α~q-Dini condition are also given.
文摘In this paper,the L2-boundedness of a class of parametric Marcinkiewicz integral μρ Ω,h with kernel function Ω in B 0,0 q(S n-1) for some q>1,and the radial function h(x)∈l∞(Ls)(R +) for 1<s≤∞ are given.The Lp(Rn)(2≤p<∞) boundedness of μ *,ρ Ω,h,λ and μ ρ Ω,h,S with Ω in B 0,0 q(S n-1) and h(|x|)∈l∞(Ls)(R +) in application are obtained.Here μ *,ρ Ω,h,λ and μ ρ Ω,h,S are parametric Marcinkiewicz integrals corresponding to the Littlewood-Paley g* λ function and the Lusin area function S,respectively.
基金Supported by the National Natural Science Foundation of China(Grant No.11401262)
文摘We first give alternative expressions of some generalized countably compact spaces such as quasi-γspaces, quasi-Nagata spaces, M^#-spaces and wM-spaces with g-functions. Then by means of these expressions, we present some characterizations of the corresponding spaces with real-valued functions.
文摘For the case where the multivariate normal population does not have null correlations, we give the exact expression of the distribution of the sample matrix of correlations R, with the sample variances acting as parameters. Also, the distribution of its determinant is established in terms of Meijer G-functions in the null-correlation case. Several numerical examples are given, and applications to the concept of system de- pendence in Reliability Theory are presented.
基金Project supported by the National Natural Science Foundation of China (No.10671164)Important Project Foundation of Hunan Education Department (No.06A070)
文摘In this paper, we make further discussions and improvements on the results presented in the previously published work ＂Block H-matrices and spectrum of block matrices＂. Furthermore, a new bound for eigenvalues of block matrices is given with examples to show advantages of the new result.
文摘The block H-matrices are studied by the concept of G-functions, several concepts of block matrices are introduced. Equivalent characters of block H-matrices are obtained. Spectrum localizations characterized by G-functions for block matrices are got.
文摘With the development of the market, it becomes a demanding task for producers to make flexible production schedules to shorten production cycle. Schedule-free rolling is needed. If the CVC work roll of the F6 and F7 stands in certain 2050 mm hot rolled strip mill are substituted by flat roll (aim to SFR) and the strip profile is controlled by the existing bending force, the control ability is not adequate. This fact has been tested through on-line experiment and has been given in this article. The NBCM (new backup roll crowning method) is recommended to improve the profile control ability. Finally the plastic deformation of the strip and the elastic deformation of the roll are analyzed by employing coupled calculation of rigid-plastic finite element method and G-function method, and the optimal range of the crown of backup roll is given theoretically.
基金Supported in part by the Natural Science Foundation of China(11471309 and 11561062)。
文摘In this paper,we consider the boundedness of multilinear Littlewood-Paley operators which include multilinear g-function,multilinear Lusin's area integral and multilinear Littlewood-Paley g^*λ-function.Furthermore,norm inequalities of the above operators hold on the corresponding Amalgam-Campanato spaces.
