Freezing of gait is a significant and debilitating motor symptom often observed in individuals with Parkinson's disease.Resting-state functional magnetic resonance imaging,along with its multi-level feature indice...Freezing of gait is a significant and debilitating motor symptom often observed in individuals with Parkinson's disease.Resting-state functional magnetic resonance imaging,along with its multi-level feature indices,has provided a fresh perspective and valuable insight into the study of freezing of gait in Parkinson's disease.It has been revealed that Parkinson's disease is accompanied by widespread irregularities in inherent brain network activity.However,the effective integration of the multi-level indices of resting-state functional magnetic resonance imaging into clinical settings for the diagnosis of freezing of gait in Parkinson's disease remains a challenge.Although previous studies have demonstrated that radiomics can extract optimal features as biomarkers to identify or predict diseases,a knowledge gap still exists in the field of freezing of gait in Parkinson's disease.This cross-sectional study aimed to evaluate the ability of radiomics features based on multi-level indices of resting-state functional magnetic resonance imaging,along with clinical features,to distinguish between Parkinson's disease patients with and without freezing of gait.We recruited 28 patients with Parkinson's disease who had freezing of gait(15 men and 13 women,average age 63 years)and 30 patients with Parkinson's disease who had no freezing of gait(16 men and 14 women,average age 64 years).Magnetic resonance imaging scans were obtained using a 3.0T scanner to extract the mean amplitude of low-frequency fluctuations,mean regional homogeneity,and degree centrality.Neurological and clinical characteristics were also evaluated.We used the least absolute shrinkage and selection operator algorithm to extract features and established feedforward neural network models based solely on resting-state functional magnetic resonance imaging indicators.We then performed predictive analysis of three distinct groups based on resting-state functional magnetic resonance imaging indicators indicators combined with clinical features.Subsequently,we conducted 100 additional five-fold cross-validations to determine the most effective model for each classification task and evaluated the performance of the model using the area under the receiver operating characteristic curve.The results showed that when differentiating patients with Parkinson's disease who had freezing of gait from those who did not have freezing of gait,or from healthy controls,the models using only the mean regional homogeneity values achieved the highest area under the receiver operating characteristic curve values of 0.750(with an accuracy of 70.9%)and 0.759(with an accuracy of 65.3%),respectively.When classifying patients with Parkinson's disease who had freezing of gait from those who had no freezing of gait,the model using the mean amplitude of low-frequency fluctuation values combined with two clinical features achieved the highest area under the receiver operating characteristic curve of 0.847(with an accuracy of 74.3%).The most significant features for patients with Parkinson's disease who had freezing of gait were amplitude of low-frequency fluctuation alterations in the left parahippocampal gyrus and two clinical characteristics:Montreal Cognitive Assessment and Hamilton Depression Scale scores.Our findings suggest that radiomics features derived from resting-state functional magnetic resonance imaging indices and clinical information can serve as valuable indices for the identification of freezing of gait in Parkinson's disease.展开更多
To extract and display the significant information of combat systems,this paper introduces the methodology of functional cartography into combat networks and proposes an integrated framework named“functional cartogra...To extract and display the significant information of combat systems,this paper introduces the methodology of functional cartography into combat networks and proposes an integrated framework named“functional cartography of heterogeneous combat networks based on the operational chain”(FCBOC).In this framework,a functional module detection algorithm named operational chain-based label propagation algorithm(OCLPA),which considers the cooperation and interactions among combat entities and can thus naturally tackle network heterogeneity,is proposed to identify the functional modules of the network.Then,the nodes and their modules are classified into different roles according to their properties.A case study shows that FCBOC can provide a simplified description of disorderly information of combat networks and enable us to identify their functional and structural network characteristics.The results provide useful information to help commanders make precise and accurate decisions regarding the protection,disintegration or optimization of combat networks.Three algorithms are also compared with OCLPA to show that FCBOC can most effectively find functional modules with practical meaning.展开更多
In this paper,we study composition operators on weighted Bergman spaces of Dirichlet series.We first establish some Littlewood-type inequalities for generalized mean counting functions.Then we give sufficient conditio...In this paper,we study composition operators on weighted Bergman spaces of Dirichlet series.We first establish some Littlewood-type inequalities for generalized mean counting functions.Then we give sufficient conditions for a composition operator with zero characteristic to be bounded or compact on weighted Bergman spaces of Dirichlet series.The corresponding sufficient condition for compactness in the case of positive characteristics is also obtained.展开更多
This paper proposed a new systematic approach-functional evidential reasoning model(FERM) for exploring hazardous chemical operational accidents under uncertainty. First, FERM was introduced to identify various causal...This paper proposed a new systematic approach-functional evidential reasoning model(FERM) for exploring hazardous chemical operational accidents under uncertainty. First, FERM was introduced to identify various causal factors and their performance changes in hazardous chemical operational accidents, along with determining the functional failure link relationships. Subsequently, FERM was employed to elucidate both qualitative and quantitative operational accident information within a unified framework, which could be regarded as the input of information fusion to obtain the fuzzy belief distribution of each cause factor. Finally, the derived risk values of the causal factors were ranked while constructing multi-level accident causation chains to unveil the weak links in system functionality and the primary roots of operational accidents. Using the specific case of the “1·15” major explosion and fire accident at Liaoning Panjin Haoye Chemical Co., Ltd., seven causal factors and their corresponding performance changes were identified. Additionally, five accident causation chains were uncovered based on the fuzzy joint distribution of the functional assessment level(FAL) and reliability distribution(RD),revealing an overall increase in risk along the accident evolution path. The research findings demonstrated that FERM enabled the effective characterization, rational quantification and accurate analysis of the inherent uncertainties in hazardous chemical operational accident risks from a systemic perspective.展开更多
By using a certain hybrid-type convolution operator,we first introduce a new subclass of normalized analytic functions in the open unit disk.For members of this analytic function class,we then derive several propertie...By using a certain hybrid-type convolution operator,we first introduce a new subclass of normalized analytic functions in the open unit disk.For members of this analytic function class,we then derive several properties and characteristics including(for example)the modified Hadamard products,Holder's inequalities and convolution properties as well as some closure properties under a general family of integral transforms.展开更多
The objective of the present study is to define two important aspects of the computer operating system concerning the number of its vulnerabilities behavior. We identify the Vulnerability Intensity Function (VIF), and...The objective of the present study is to define two important aspects of the computer operating system concerning the number of its vulnerabilities behavior. We identify the Vulnerability Intensity Function (VIF), and the Vulnerability Index Indicator (VII) of a computer operating network. Both of these functions, VIF and VII are entities of the stochastic process that we have identified, which characterizes the probabilistic behavior of the number of vulnerabilities of a computer operating network. The VIF identifies the rate at which the number of vulnerabilities changes with respect to time. The VII is an important index indicator that conveys the following information about the number of vulnerabilities of Desktop Operating Systems: the numbers are increasing, decreasing, or remaining the same at a particular time of interest. This decision type of index indicator is crucial in every strategic planning and decision-making. The proposed VIF and VII illustrate their importance by using real data for Microsoft Windows Operating Systems 10, 8, 7, and Apple MacOS. The results of the actual data attest to the importance of VIF and VII in the cybersecurity problem we are currently facing.展开更多
Let M(u) be an N function, A=D r+∑r-1k=0a k(x)D k a linear differential operator and W M(A) the Sobolev Orlicz class defined by M(u) and A. In this paper we give the asymptotic estimates...Let M(u) be an N function, A=D r+∑r-1k=0a k(x)D k a linear differential operator and W M(A) the Sobolev Orlicz class defined by M(u) and A. In this paper we give the asymptotic estimates of the n K width d n(W M(A),L 2[0,1]) .展开更多
Let M(u) be an N function, A=D r+∑r-1k=0a k(x)D k a linear differential operator and W M(A) the Sobolev Orlicz class defined by M(u) and A. In this paper we give the asymptotic estimates...Let M(u) be an N function, A=D r+∑r-1k=0a k(x)D k a linear differential operator and W M(A) the Sobolev Orlicz class defined by M(u) and A. In this paper we give the asymptotic estimates of the n K width d n(W M(A),L 2[0,1]) .展开更多
In this paper, we introduce new subclasses Sp,q,^mj,l λ[A,B;γ]and Hp,q,λ^m,j,l（α,β）of certain p-valent analytic functions defined by a generalized differential operator. Majorizationproperties for functions bel...In this paper, we introduce new subclasses Sp,q,^mj,l λ[A,B;γ]and Hp,q,λ^m,j,l（α,β）of certain p-valent analytic functions defined by a generalized differential operator. Majorizationproperties for functions belonging to the classes Sp,q,^mj,l λ[A,B;γ]and Hp,q,λ^m,j,l（α,β）are investigated. Also, we point out some new or known consequences of our main results.展开更多
A complex-valued harmonic functions that are univalent and sense preserving in the unit disk U can be written in the form f = h ＋ g^-, where h and g are analytic in U. We define and investigate a new class SHPλ（α...A complex-valued harmonic functions that are univalent and sense preserving in the unit disk U can be written in the form f = h ＋ g^-, where h and g are analytic in U. We define and investigate a new class SHPλ（α,β）by generalized Salagean operator of harmonic univalent functions. We give sufficient coefficient conditions for normalized harmonic functions in the class SHPλ（α,β） These conditions are also shown to be necessary when the coefficients are negative. This leads to distortion bounds and extreme points.展开更多
We obtain several estimates of the essential norms of the products of differen- tiation operators and weighted composition operators between weighted Banach spaces of analytic functions with general weights. As applic...We obtain several estimates of the essential norms of the products of differen- tiation operators and weighted composition operators between weighted Banach spaces of analytic functions with general weights. As applications, we also give estimates of the es- sential norms of weighted composition operators between weighted Banach space of analytic functions and Bloch-type spaces.展开更多
Making use of the Carlson-Shaffer convolution operator, we introduce and study a new class of analytic functions related to conic domains. The main object of this paper is to investigate inclusion relations, coefficie...Making use of the Carlson-Shaffer convolution operator, we introduce and study a new class of analytic functions related to conic domains. The main object of this paper is to investigate inclusion relations, coefficient bound for this class. We also show that this class is closed under convolution with a convex function. Some applications are also discussed.展开更多
In this article, we mainly devote to proving uniqueness results for entire functionssharing one small function CM with their shift and difference operator simultaneously. Letf（z） be a nonconstant entire function of ...In this article, we mainly devote to proving uniqueness results for entire functionssharing one small function CM with their shift and difference operator simultaneously. Letf（z） be a nonconstant entire function of finite order, c be a nonzero finite complex constant, and n be a positive integer. If f（z）, f（z＋c）, and △n cf（z） share 0 CM, then f（z＋c）≡Af（z）, where A（≠0） is a complex constant. Moreover, let a（z）, b（z）（ O） ∈ S（f） be periodic entire functions with period c and if f（z） - a（z）, f（z ＋ c） - a（z）, △cn f（z） - b（z） share 0 CM, then f（z ＋ c） ≡ f（z）.展开更多
As an important type of polynomial approximation, approximation of functions by Bernstein operators is an important topic in approximation theory and computational theory. This paper gives global and pointwise estimat...As an important type of polynomial approximation, approximation of functions by Bernstein operators is an important topic in approximation theory and computational theory. This paper gives global and pointwise estimates for weighted approximation of functions with singularities by Bernstein operators. The main results are the Jackson＇s estimates of functions f∈ （Wwλ）2 andre Cw, which extends the result of （Della Vecchia et al., 2004）.展开更多
The staggered-grid finite-difference （SGFD） method has been widely used in seismic forward modeling. The precision of the forward modeling results directly affects the results of the subsequent seismic inversion and...The staggered-grid finite-difference （SGFD） method has been widely used in seismic forward modeling. The precision of the forward modeling results directly affects the results of the subsequent seismic inversion and migration. Numerical dispersion is one of the problems in this method. The window function method can reduce dispersion by replacing the finite-difference operators with window operators, obtained by truncating the spatial convolution series of the pseudospectral method. Although the window operators have high precision in the low-wavenumber domain, their precision decreases rapidly in the high-wavenumber domain. We develop a least squares optimization method to enhance the precision of operators obtained by the window function method. We transform the SGFD problem into a least squares problem and find the best solution iteratively. The window operator is chosen as the initial value and the optimized domain is set by the error threshold. The conjugate gradient method is also adopted to increase the stability of the solution. Approximation error analysis and numerical simulation results suggest that the proposed method increases the precision of the window function operators and decreases the numerical dispersion.展开更多
In this paper, the author gives a characterization of atomic Hardy spaces associated to Schrodinger operators by using area functions, and hence gets the dual spaces of atomic Hardy spaces.
Let Hn(p)be the class of functions of the form f(z)=z p+ +∞Σ k=n akzk+p,which are analytic in the open unit disk U={z:|z|<1}.In the paper,we introduce a new subclass Bn(μ,a,c,α,p;φ)of Hn(p)and investigate its ...Let Hn(p)be the class of functions of the form f(z)=z p+ +∞Σ k=n akzk+p,which are analytic in the open unit disk U={z:|z|<1}.In the paper,we introduce a new subclass Bn(μ,a,c,α,p;φ)of Hn(p)and investigate its subordination relations,inclusion relations and distortion theorems.The results obtained include the related results of some authors as their special case.展开更多
In this paper,We mainly discuss some subclasses of analytic functions for operators onac, and determine a representation formula and sufficient condition for the class 4;(a.p,r,E,7) and prove a sufficient and necessar...In this paper,We mainly discuss some subclasses of analytic functions for operators onac, and determine a representation formula and sufficient condition for the class 4;(a.p,r,E,7) and prove a sufficient and necessary condition.coefficient estimates and distortiontheorem for the subclass O;o (a,p,Y,e,9) of the class ac;(a,p,y,c,V).Furthermore,the analogues also are true for operators on Hilbert space.展开更多
Area integral functions are introduced for sectorial operators on L^p-spaces. We establish the equivalence between the square and area integral functions for sectorial operators on L^p spaces. This follows that the re...Area integral functions are introduced for sectorial operators on L^p-spaces. We establish the equivalence between the square and area integral functions for sectorial operators on L^p spaces. This follows that the results of Cowling, Doust, McIntosh, Yagi, and Le Merdy on H^∞ functional calculus of seetorial operators on LP-spaces hold true when the square functions are replaced by the area integral functions.展开更多
Let Mφ be the operator of multiplication by φ on a Hilbert space of functions analytic on the open unit disk. For an invariant subspace F for the multiplication operator Mz, we derive some spectral properties of the...Let Mφ be the operator of multiplication by φ on a Hilbert space of functions analytic on the open unit disk. For an invariant subspace F for the multiplication operator Mz, we derive some spectral properties of the multiplication operator Mφ ： F→F. We characterize norm, spectrum, essential norm and essential spectrum of such operators when F has the codimension n property with n∈{1,2,...,＋∞}.展开更多
基金supported by the National Natural Science Foundation of China,No.82071909(to GF)the Natural Science Foundation of Liaoning Province,No.2023-MS-07(to HL)。
文摘Freezing of gait is a significant and debilitating motor symptom often observed in individuals with Parkinson's disease.Resting-state functional magnetic resonance imaging,along with its multi-level feature indices,has provided a fresh perspective and valuable insight into the study of freezing of gait in Parkinson's disease.It has been revealed that Parkinson's disease is accompanied by widespread irregularities in inherent brain network activity.However,the effective integration of the multi-level indices of resting-state functional magnetic resonance imaging into clinical settings for the diagnosis of freezing of gait in Parkinson's disease remains a challenge.Although previous studies have demonstrated that radiomics can extract optimal features as biomarkers to identify or predict diseases,a knowledge gap still exists in the field of freezing of gait in Parkinson's disease.This cross-sectional study aimed to evaluate the ability of radiomics features based on multi-level indices of resting-state functional magnetic resonance imaging,along with clinical features,to distinguish between Parkinson's disease patients with and without freezing of gait.We recruited 28 patients with Parkinson's disease who had freezing of gait(15 men and 13 women,average age 63 years)and 30 patients with Parkinson's disease who had no freezing of gait(16 men and 14 women,average age 64 years).Magnetic resonance imaging scans were obtained using a 3.0T scanner to extract the mean amplitude of low-frequency fluctuations,mean regional homogeneity,and degree centrality.Neurological and clinical characteristics were also evaluated.We used the least absolute shrinkage and selection operator algorithm to extract features and established feedforward neural network models based solely on resting-state functional magnetic resonance imaging indicators.We then performed predictive analysis of three distinct groups based on resting-state functional magnetic resonance imaging indicators indicators combined with clinical features.Subsequently,we conducted 100 additional five-fold cross-validations to determine the most effective model for each classification task and evaluated the performance of the model using the area under the receiver operating characteristic curve.The results showed that when differentiating patients with Parkinson's disease who had freezing of gait from those who did not have freezing of gait,or from healthy controls,the models using only the mean regional homogeneity values achieved the highest area under the receiver operating characteristic curve values of 0.750(with an accuracy of 70.9%)and 0.759(with an accuracy of 65.3%),respectively.When classifying patients with Parkinson's disease who had freezing of gait from those who had no freezing of gait,the model using the mean amplitude of low-frequency fluctuation values combined with two clinical features achieved the highest area under the receiver operating characteristic curve of 0.847(with an accuracy of 74.3%).The most significant features for patients with Parkinson's disease who had freezing of gait were amplitude of low-frequency fluctuation alterations in the left parahippocampal gyrus and two clinical characteristics:Montreal Cognitive Assessment and Hamilton Depression Scale scores.Our findings suggest that radiomics features derived from resting-state functional magnetic resonance imaging indices and clinical information can serve as valuable indices for the identification of freezing of gait in Parkinson's disease.
文摘To extract and display the significant information of combat systems,this paper introduces the methodology of functional cartography into combat networks and proposes an integrated framework named“functional cartography of heterogeneous combat networks based on the operational chain”(FCBOC).In this framework,a functional module detection algorithm named operational chain-based label propagation algorithm(OCLPA),which considers the cooperation and interactions among combat entities and can thus naturally tackle network heterogeneity,is proposed to identify the functional modules of the network.Then,the nodes and their modules are classified into different roles according to their properties.A case study shows that FCBOC can provide a simplified description of disorderly information of combat networks and enable us to identify their functional and structural network characteristics.The results provide useful information to help commanders make precise and accurate decisions regarding the protection,disintegration or optimization of combat networks.Three algorithms are also compared with OCLPA to show that FCBOC can most effectively find functional modules with practical meaning.
基金supported by the National Natural Science Foundation of China(12171373)Chen's work also supported by the Fundamental Research Funds for the Central Universities of China(GK202207018).
文摘In this paper,we study composition operators on weighted Bergman spaces of Dirichlet series.We first establish some Littlewood-type inequalities for generalized mean counting functions.Then we give sufficient conditions for a composition operator with zero characteristic to be bounded or compact on weighted Bergman spaces of Dirichlet series.The corresponding sufficient condition for compactness in the case of positive characteristics is also obtained.
基金supported by the National Key Research&Development Program of China(2021YFB3301100)the National Natural Science Foundation of China(52004014)the Fundamental Research Funds for the Central Universities(ZY2406).
文摘This paper proposed a new systematic approach-functional evidential reasoning model(FERM) for exploring hazardous chemical operational accidents under uncertainty. First, FERM was introduced to identify various causal factors and their performance changes in hazardous chemical operational accidents, along with determining the functional failure link relationships. Subsequently, FERM was employed to elucidate both qualitative and quantitative operational accident information within a unified framework, which could be regarded as the input of information fusion to obtain the fuzzy belief distribution of each cause factor. Finally, the derived risk values of the causal factors were ranked while constructing multi-level accident causation chains to unveil the weak links in system functionality and the primary roots of operational accidents. Using the specific case of the “1·15” major explosion and fire accident at Liaoning Panjin Haoye Chemical Co., Ltd., seven causal factors and their corresponding performance changes were identified. Additionally, five accident causation chains were uncovered based on the fuzzy joint distribution of the functional assessment level(FAL) and reliability distribution(RD),revealing an overall increase in risk along the accident evolution path. The research findings demonstrated that FERM enabled the effective characterization, rational quantification and accurate analysis of the inherent uncertainties in hazardous chemical operational accident risks from a systemic perspective.
文摘By using a certain hybrid-type convolution operator,we first introduce a new subclass of normalized analytic functions in the open unit disk.For members of this analytic function class,we then derive several properties and characteristics including(for example)the modified Hadamard products,Holder's inequalities and convolution properties as well as some closure properties under a general family of integral transforms.
文摘The objective of the present study is to define two important aspects of the computer operating system concerning the number of its vulnerabilities behavior. We identify the Vulnerability Intensity Function (VIF), and the Vulnerability Index Indicator (VII) of a computer operating network. Both of these functions, VIF and VII are entities of the stochastic process that we have identified, which characterizes the probabilistic behavior of the number of vulnerabilities of a computer operating network. The VIF identifies the rate at which the number of vulnerabilities changes with respect to time. The VII is an important index indicator that conveys the following information about the number of vulnerabilities of Desktop Operating Systems: the numbers are increasing, decreasing, or remaining the same at a particular time of interest. This decision type of index indicator is crucial in every strategic planning and decision-making. The proposed VIF and VII illustrate their importance by using real data for Microsoft Windows Operating Systems 10, 8, 7, and Apple MacOS. The results of the actual data attest to the importance of VIF and VII in the cybersecurity problem we are currently facing.
文摘Let M(u) be an N function, A=D r+∑r-1k=0a k(x)D k a linear differential operator and W M(A) the Sobolev Orlicz class defined by M(u) and A. In this paper we give the asymptotic estimates of the n K width d n(W M(A),L 2[0,1]) .
文摘Let M(u) be an N function, A=D r+∑r-1k=0a k(x)D k a linear differential operator and W M(A) the Sobolev Orlicz class defined by M(u) and A. In this paper we give the asymptotic estimates of the n K width d n(W M(A),L 2[0,1]) .
基金Supported by the National Natural Science Foundation of China(Grant No.11271045)the Funds of Doctoral Programme of China(Grant No.20100003110004)the Natural Science Foundation of Inner Mongolia Province(Grant No.2010MS0117)
文摘In this paper, we introduce new subclasses Sp,q,^mj,l λ[A,B;γ]and Hp,q,λ^m,j,l（α,β）of certain p-valent analytic functions defined by a generalized differential operator. Majorizationproperties for functions belonging to the classes Sp,q,^mj,l λ[A,B;γ]and Hp,q,λ^m,j,l（α,β）are investigated. Also, we point out some new or known consequences of our main results.
基金Supported by the Key Scientific Research Fund of Inner Mongolian Educational Bureau (NJ04115)
文摘A complex-valued harmonic functions that are univalent and sense preserving in the unit disk U can be written in the form f = h ＋ g^-, where h and g are analytic in U. We define and investigate a new class SHPλ（α,β）by generalized Salagean operator of harmonic univalent functions. We give sufficient coefficient conditions for normalized harmonic functions in the class SHPλ（α,β） These conditions are also shown to be necessary when the coefficients are negative. This leads to distortion bounds and extreme points.
文摘We obtain several estimates of the essential norms of the products of differen- tiation operators and weighted composition operators between weighted Banach spaces of analytic functions with general weights. As applications, we also give estimates of the es- sential norms of weighted composition operators between weighted Banach space of analytic functions and Bloch-type spaces.
文摘Making use of the Carlson-Shaffer convolution operator, we introduce and study a new class of analytic functions related to conic domains. The main object of this paper is to investigate inclusion relations, coefficient bound for this class. We also show that this class is closed under convolution with a convex function. Some applications are also discussed.
基金supported by the Natural Science Foundation of Guangdong Province in China(2014A030313422,2016A030310106,2016A030313745)
文摘In this article, we mainly devote to proving uniqueness results for entire functionssharing one small function CM with their shift and difference operator simultaneously. Letf（z） be a nonconstant entire function of finite order, c be a nonzero finite complex constant, and n be a positive integer. If f（z）, f（z＋c）, and △n cf（z） share 0 CM, then f（z＋c）≡Af（z）, where A（≠0） is a complex constant. Moreover, let a（z）, b（z）（ O） ∈ S（f） be periodic entire functions with period c and if f（z） - a（z）, f（z ＋ c） - a（z）, △cn f（z） - b（z） share 0 CM, then f（z ＋ c） ≡ f（z）.
文摘As an important type of polynomial approximation, approximation of functions by Bernstein operators is an important topic in approximation theory and computational theory. This paper gives global and pointwise estimates for weighted approximation of functions with singularities by Bernstein operators. The main results are the Jackson＇s estimates of functions f∈ （Wwλ）2 andre Cw, which extends the result of （Della Vecchia et al., 2004）.
基金jointly supported by the NSF(No.41720104006)the Strategic Priority Research Program of the Chinese Academy of Sciences(A)(No.XDA14010303)+2 种基金the National Oil and Gas Project(Nos.2016ZX05002-005-007HZ and 2016ZX05014-001-008HZ)the Shandong Innovation Project(No.2017CXGC1602)the Qingdao Innovation Project(Nos.16-5-1-40-jch and 17CX05011)
文摘The staggered-grid finite-difference （SGFD） method has been widely used in seismic forward modeling. The precision of the forward modeling results directly affects the results of the subsequent seismic inversion and migration. Numerical dispersion is one of the problems in this method. The window function method can reduce dispersion by replacing the finite-difference operators with window operators, obtained by truncating the spatial convolution series of the pseudospectral method. Although the window operators have high precision in the low-wavenumber domain, their precision decreases rapidly in the high-wavenumber domain. We develop a least squares optimization method to enhance the precision of operators obtained by the window function method. We transform the SGFD problem into a least squares problem and find the best solution iteratively. The window operator is chosen as the initial value and the optimized domain is set by the error threshold. The conjugate gradient method is also adopted to increase the stability of the solution. Approximation error analysis and numerical simulation results suggest that the proposed method increases the precision of the window function operators and decreases the numerical dispersion.
文摘In this paper, the author gives a characterization of atomic Hardy spaces associated to Schrodinger operators by using area functions, and hence gets the dual spaces of atomic Hardy spaces.
基金Supported by the Doctoral Foundation of the Education Committee of China(20050574002)
文摘Let Hn(p)be the class of functions of the form f(z)=z p+ +∞Σ k=n akzk+p,which are analytic in the open unit disk U={z:|z|<1}.In the paper,we introduce a new subclass Bn(μ,a,c,α,p;φ)of Hn(p)and investigate its subordination relations,inclusion relations and distortion theorems.The results obtained include the related results of some authors as their special case.
文摘In this paper,We mainly discuss some subclasses of analytic functions for operators onac, and determine a representation formula and sufficient condition for the class 4;(a.p,r,E,7) and prove a sufficient and necessary condition.coefficient estimates and distortiontheorem for the subclass O;o (a,p,Y,e,9) of the class ac;(a,p,y,c,V).Furthermore,the analogues also are true for operators on Hilbert space.
文摘Area integral functions are introduced for sectorial operators on L^p-spaces. We establish the equivalence between the square and area integral functions for sectorial operators on L^p spaces. This follows that the results of Cowling, Doust, McIntosh, Yagi, and Le Merdy on H^∞ functional calculus of seetorial operators on LP-spaces hold true when the square functions are replaced by the area integral functions.
文摘Let Mφ be the operator of multiplication by φ on a Hilbert space of functions analytic on the open unit disk. For an invariant subspace F for the multiplication operator Mz, we derive some spectral properties of the multiplication operator Mφ ： F→F. We characterize norm, spectrum, essential norm and essential spectrum of such operators when F has the codimension n property with n∈{1,2,...,＋∞}.
