In this paper, we consider the differential equation f''+ Af'+ Bf = 0, where A(z) and B(z) ≡ 0are entire functions. Assume that A(z) has a finite deficient value, then we will give some conditions on B(z)...In this paper, we consider the differential equation f''+ Af'+ Bf = 0, where A(z) and B(z) ≡ 0are entire functions. Assume that A(z) has a finite deficient value, then we will give some conditions on B(z)which can guarantee that every solution f ≡ 0 of the equation has infinite order.展开更多
A noise-reduction method with sliding called the local f-x Cadzow noise-reduction method, windows in the frequency-space （f-x） domain, is presented in this paper. This method is based on the assumption that the sign...A noise-reduction method with sliding called the local f-x Cadzow noise-reduction method, windows in the frequency-space （f-x） domain, is presented in this paper. This method is based on the assumption that the signal in each window is linearly predictable in the spatial direction while the random noise is not. For each Toeplitz matrix constructed by constant frequency slice, a singular value decomposition （SVD） is applied to separate signal from noise. To avoid edge artifacts caused by zero percent overlap between windows and to remove more noise, an appropriate overlap is adopted. Besides flat and dipping events, this method can enhance curved and conflicting events. However, it is not suitable for seismic data that contains big spikes or null traces. It is also compared with the SVD, f-x deconvolution, and Cadzow method without windows. The comparison results show that the local Cadzow method performs well in removing random noise and preserving signal. In addition, a real data example proves that it is a potential noise-reduction technique for seismic data obtained in areas of complex formations.展开更多
In this article, for a transcendental entire function f（z） of finite order which has a finite Borel exceptional value a, we utilize properties of complex difference equations to prove the difference counterpart of B...In this article, for a transcendental entire function f（z） of finite order which has a finite Borel exceptional value a, we utilize properties of complex difference equations to prove the difference counterpart of Bruck＇s conjecture, that is, if △f（z） = f（z ＋ η） - f（z） and f（z） share one value a （≠α） CM, where η ∈ C is a constant such that f（z ＋η） ≠ f（z）,then△f（z）-a/f（z）-a=a/a-α.展开更多
A theory of a class of higher order singular integral under the operator （L f） （u） =[u1 σf/σu1（u） - u1σf/σu1（u） ＋ f（u）] is given. We transform the higher order singular integral to a usual Cauchy integr...A theory of a class of higher order singular integral under the operator （L f） （u） =[u1 σf/σu1（u） - u1σf/σu1（u） ＋ f（u）] is given. We transform the higher order singular integral to a usual Cauchy integral, extend the permutation formula of the higher order singular integral deduced by Qian and Zhong in [4] to a general case, and discuss the regularization problem of the higher order singular integral equations with Cauchy kernel and variable coefficients on complex hypersphere.展开更多
This paper explores the defects in fuzzy (hyper) graphs (as complex (hyper) networks) and extends the fuzzy(hyper) graphs to fuzzy (quasi) superhypergraphs as a new concept.We have modeled the fuzzy superhypergraphsas...This paper explores the defects in fuzzy (hyper) graphs (as complex (hyper) networks) and extends the fuzzy(hyper) graphs to fuzzy (quasi) superhypergraphs as a new concept.We have modeled the fuzzy superhypergraphsas complex superhypernetworks in order to make a relation between labeled objects in the form of details andgeneralities. Indeed, the structure of fuzzy (quasi) superhypergraphs collects groups of labeled objects and analyzesthem in the form of the part to part of objects, the part of objects to the whole group of objects, and the whole tothe whole group of objects at the same time.We have investigated the properties of fuzzy (quasi) superhypergraphsbased on any positive real number as valued fuzzy (quasi) superhypergraphs, considering the complement of valuedfuzzy (quasi) superhypergraphs, the notation of isomorphism of valued fuzzy (quasi) superhypergraphs based onthe permutations, and we have presented the isomorphic conditions of (self complemented) valued fuzzy (quasi)superhypergraphs. The concept of impact membership value of fuzzy (quasi) superhypergraphs is introducedin this study and it is applied in designing the real problem in the real world. Finally, the problem of businesssuperhypernetworks is presented as an application of fuzzy valued quasi superhypergraphs in the real world.展开更多
The Bozhushan Ore Field,located at the western margin of the South China Block,is an important area for Ag-Pb-Zn-W polymetallic mineralization which may be associated with the Late Cretaceous granitic magmaism.In this...The Bozhushan Ore Field,located at the western margin of the South China Block,is an important area for Ag-Pb-Zn-W polymetallic mineralization which may be associated with the Late Cretaceous granitic magmaism.In this paper,the singular value decomposition(SVD)was effectively applied to decompose gravity data at scale of 1:50000 within the Bozhushan Ore Field to extract deep ore-finding information.Two gravity anomaly images displaying different scales of the ore-controlling factors were obtained.(1)The low-pass filtered image may reflect the deeply buried geological structures,hidden intrusions and concealed ore bodies.The negative gravity anomaly may reflect the overall distribution of granite bodies in the Bozhushan Ore Field.One negative gravity anomaly area may correspond to the exposed part of the Baozhushan granitic intrusion and the other corresponds to the concealed part of the granitic intrusion.The granitic intrusions are the main ore-controlling factors in this ore district.(2)The band-pass filtered image depicts the shallow concealed geological structures and geological bodies within this study area.There are two obvious negative gravity anomalies,which may be created by the hidden granites at different depths at both northwestern and southeastern sides of the exposed granitic intrusion.Thus the two negative gravity anomalies are favorable prospecting areas for various type of polymetallic ore deposits at depth.The gravity anomalies extracted by using the SVD exactly reflect the distribution of the ore deposits,structures and intrusions,which will give new insights for further mineral exploration in the study area.展开更多
In this paper, we are concerned with the maximum number of linearly independent transcendental solutions with finite exponent of convergence of the zeros for a higher order homogeneous linear differential equation whe...In this paper, we are concerned with the maximum number of linearly independent transcendental solutions with finite exponent of convergence of the zeros for a higher order homogeneous linear differential equation where its coefficients are entire functions with order less than 1/2 and one dominant. The result obtained here is an extension and a complement of J. K. Langley's.展开更多
文摘In this paper, we consider the differential equation f''+ Af'+ Bf = 0, where A(z) and B(z) ≡ 0are entire functions. Assume that A(z) has a finite deficient value, then we will give some conditions on B(z)which can guarantee that every solution f ≡ 0 of the equation has infinite order.
基金support from the National Key Basic Research Development Program(Grant No.2007CB209600)National Major Science and Technology Program(Grant No.2008ZX05010-002)
文摘A noise-reduction method with sliding called the local f-x Cadzow noise-reduction method, windows in the frequency-space （f-x） domain, is presented in this paper. This method is based on the assumption that the signal in each window is linearly predictable in the spatial direction while the random noise is not. For each Toeplitz matrix constructed by constant frequency slice, a singular value decomposition （SVD） is applied to separate signal from noise. To avoid edge artifacts caused by zero percent overlap between windows and to remove more noise, an appropriate overlap is adopted. Besides flat and dipping events, this method can enhance curved and conflicting events. However, it is not suitable for seismic data that contains big spikes or null traces. It is also compared with the SVD, f-x deconvolution, and Cadzow method without windows. The comparison results show that the local Cadzow method performs well in removing random noise and preserving signal. In addition, a real data example proves that it is a potential noise-reduction technique for seismic data obtained in areas of complex formations.
基金supported by the National Natural Science Foundation of China(11171119)
文摘In this article, for a transcendental entire function f（z） of finite order which has a finite Borel exceptional value a, we utilize properties of complex difference equations to prove the difference counterpart of Bruck＇s conjecture, that is, if △f（z） = f（z ＋ η） - f（z） and f（z） share one value a （≠α） CM, where η ∈ C is a constant such that f（z ＋η） ≠ f（z）,then△f（z）-a/f（z）-a=a/a-α.
基金supported by the Natural Science Foundation of Fujian Province of China(S0850029,2008J0206)Innovation Foundation of Xiamen University(XDKJCX20063019),the National Science Foundation of China (10771174)
文摘A theory of a class of higher order singular integral under the operator （L f） （u） =[u1 σf/σu1（u） - u1σf/σu1（u） ＋ f（u）] is given. We transform the higher order singular integral to a usual Cauchy integral, extend the permutation formula of the higher order singular integral deduced by Qian and Zhong in [4] to a general case, and discuss the regularization problem of the higher order singular integral equations with Cauchy kernel and variable coefficients on complex hypersphere.
文摘This paper explores the defects in fuzzy (hyper) graphs (as complex (hyper) networks) and extends the fuzzy(hyper) graphs to fuzzy (quasi) superhypergraphs as a new concept.We have modeled the fuzzy superhypergraphsas complex superhypernetworks in order to make a relation between labeled objects in the form of details andgeneralities. Indeed, the structure of fuzzy (quasi) superhypergraphs collects groups of labeled objects and analyzesthem in the form of the part to part of objects, the part of objects to the whole group of objects, and the whole tothe whole group of objects at the same time.We have investigated the properties of fuzzy (quasi) superhypergraphsbased on any positive real number as valued fuzzy (quasi) superhypergraphs, considering the complement of valuedfuzzy (quasi) superhypergraphs, the notation of isomorphism of valued fuzzy (quasi) superhypergraphs based onthe permutations, and we have presented the isomorphic conditions of (self complemented) valued fuzzy (quasi)superhypergraphs. The concept of impact membership value of fuzzy (quasi) superhypergraphs is introducedin this study and it is applied in designing the real problem in the real world. Finally, the problem of businesssuperhypernetworks is presented as an application of fuzzy valued quasi superhypergraphs in the real world.
基金funded by the Chinese Research&Development Program for Probing into Deep Earth(No.2016YFC0600509)the National Natural Science Foundation of China(Nos.41672329,41972312)。
文摘The Bozhushan Ore Field,located at the western margin of the South China Block,is an important area for Ag-Pb-Zn-W polymetallic mineralization which may be associated with the Late Cretaceous granitic magmaism.In this paper,the singular value decomposition(SVD)was effectively applied to decompose gravity data at scale of 1:50000 within the Bozhushan Ore Field to extract deep ore-finding information.Two gravity anomaly images displaying different scales of the ore-controlling factors were obtained.(1)The low-pass filtered image may reflect the deeply buried geological structures,hidden intrusions and concealed ore bodies.The negative gravity anomaly may reflect the overall distribution of granite bodies in the Bozhushan Ore Field.One negative gravity anomaly area may correspond to the exposed part of the Baozhushan granitic intrusion and the other corresponds to the concealed part of the granitic intrusion.The granitic intrusions are the main ore-controlling factors in this ore district.(2)The band-pass filtered image depicts the shallow concealed geological structures and geological bodies within this study area.There are two obvious negative gravity anomalies,which may be created by the hidden granites at different depths at both northwestern and southeastern sides of the exposed granitic intrusion.Thus the two negative gravity anomalies are favorable prospecting areas for various type of polymetallic ore deposits at depth.The gravity anomalies extracted by using the SVD exactly reflect the distribution of the ore deposits,structures and intrusions,which will give new insights for further mineral exploration in the study area.
文摘In this paper, we are concerned with the maximum number of linearly independent transcendental solutions with finite exponent of convergence of the zeros for a higher order homogeneous linear differential equation where its coefficients are entire functions with order less than 1/2 and one dominant. The result obtained here is an extension and a complement of J. K. Langley's.
