This paper has two aims. The first is to give a description of irreducible tempered representations of classical p-adic groups which follows naturMly the classification of irreducible square integrable representations...This paper has two aims. The first is to give a description of irreducible tempered representations of classical p-adic groups which follows naturMly the classification of irreducible square integrable representations modulo cuspidal data obtained by Mceglin and the author of this article （2002）. The second aim of the paper is to give a description of an invariant （partially defined function） of irreducible square integrable representation of a classical p-adic group （defined by Mceglin using embeddings） in terms of subquotients of Jacquet modules. As an application, we describe behavior of partially defined function in one construction of square integrable representations of a bigger group from such representations of a smaller group （which is related to deformation of Jordan blocks of representations）.展开更多
A notion of an irreducible representation, as well as of a square integrable representation on an arbitrary locally compact groupoid, is introduced. A generalization of a version of Schur＇s lemma on a locally compact...A notion of an irreducible representation, as well as of a square integrable representation on an arbitrary locally compact groupoid, is introduced. A generalization of a version of Schur＇s lemma on a locally compact groupoid is given. This is used in order to extend some well-known results from locally compact groups to the case of locally compact groupoids. Indeed, we have proved that if L is a continuous irreducible representation of a compact groupoid G defined by a continuous Hilbert bundle H = （Hu）u∈G^0, then each Hu is finite dimensional. It is also shown that if L is an irreducible representation of a principal locally compact groupoid defined by a Hilbert bundle （G^0, （Hu）,μ）, then dimHu = 1 （u ∈ G^0）. Furthermore it is proved that every square integrable representation of a locally compact groupoid is unitary equivalent to a subrepresentation of the left regular representation. Furthermore, for r-discrete groupoids, it is shown that every irreducible subrepresentation of the left regular representation is square integrable.展开更多
Under the constrained condition induced by the eigenfunction expresson of the potential (u, v)T = (-[A2q, q], [A2p, p])T = f (q, p), the spatial part of the Lax pair of the Kaup-Newell equation is non linearized to be...Under the constrained condition induced by the eigenfunction expresson of the potential (u, v)T = (-[A2q, q], [A2p, p])T = f (q, p), the spatial part of the Lax pair of the Kaup-Newell equation is non linearized to be a completely integrable system (R2N, Adp AND dq, H = H-1) with the Hamiltonian H-1 = -[A3q, p]-1/2[A2p, p][A2q, q]. while the nonlinearization of the time part leads to its N-involutive system {H(m)}. The involutive solution of the compatible fsystem (H-1), (H(m)) is mapped by into the solution of the higher order Kaup-Newell equation.展开更多
Failuremode and effects analysis(FMEA)is a widely used safety assessmentmethod inmany fields.Z-number was previously applied in FMEA since it can take both possibility and reliability of information into consideration...Failuremode and effects analysis(FMEA)is a widely used safety assessmentmethod inmany fields.Z-number was previously applied in FMEA since it can take both possibility and reliability of information into consideration.However,the use of fuzzy weighted mean to integrate Z-valuations may have some drawbacks and is not suitable for some situations.In this paper,an improved method is proposed based on Z-numbers and the graded mean integration representation(GMIR)to deal with the uncertain information in FMEA.First,Z-numbers are constructed based on the evaluations of risk factors O,S,D for each failure mode by different experts.Second,weights of the three risk factors and experts are determined.Third,the integration representations of Z-numbers are obtained by a newmethod based on the GMIRmethod.Finally,risk priorities of the failure modes are derived considering the weights of experts and risk factors.Two examples and a case study are given to show the use of the proposed method and comparison with other methods.The results show that the proposed method is more reasonable,universal and simple in calculation.展开更多
The aim of this paper is to construct the integral representation of the solution of Sturm-Liouville equation with eigenparameter-dependent discontinuity conditions at an interior point of the finite interval. Moreove...The aim of this paper is to construct the integral representation of the solution of Sturm-Liouville equation with eigenparameter-dependent discontinuity conditions at an interior point of the finite interval. Moreover, we examine the properties of the kernel function of this integral representation and obtain the partial differential equation provided by this kernel function.展开更多
We generalized the Bochner-Martinelli integral representation to that on Riemannian manifolds. Things become quite different in such case. First we define a kind of Newtonian potential and take the interior product of...We generalized the Bochner-Martinelli integral representation to that on Riemannian manifolds. Things become quite different in such case. First we define a kind of Newtonian potential and take the interior product of its gradient to be the integral kernel. Then we prove that this kernel is harmonic in some sense. At last an integral representative theorem is proved.展开更多
In this paper we consider polynomial splines S(x) with equidistant nodes which may grow a5 O (|x|~5). We present an integral representation of such splines with a distribution kernel. This repre- sentation is related ...In this paper we consider polynomial splines S(x) with equidistant nodes which may grow a5 O (|x|~5). We present an integral representation of such splines with a distribution kernel. This repre- sentation is related to the Fourier integral of slowly growing functions. The part of the Fourier ex- ponentials herewith play the so called exponential splines by Schoenberg. The integral representation provides a flexible tool for dealing with the growing equidistant splines. First. it allows us to con- struct a rich library of splines possessing the property that translations of any such spline form a ba- sis of corresponding spline space. It is shown that any such spline is associated with a dual spline whose translations form a biorthogonal basis. As examples we present solutions of the problems of projection of a growing function onto spline spaces and of spline interpolation of growing func- tion. We derive formulas for approximate evaluation of splines projecting a function onto the spline space and establish therewith exact estimations of the approximation errors.展开更多
In this paper,we first obtain a unified integral representation on the analytic varieties of the general bounded domain in Stein manifolds(the two types bounded domains in[3]are regarded as its special cases).Secondly...In this paper,we first obtain a unified integral representation on the analytic varieties of the general bounded domain in Stein manifolds(the two types bounded domains in[3]are regarded as its special cases).Secondly we get the integral formulas of the solution of∂-equation.And we use a new and unique method to give a uniform estimate of the solution of∂-equation,which is different from Henkin's method.展开更多
The objective is to develop a model considering demand dependent on selling price and deterioration occurs after a certain period of time, which follows two-parameter Weibull distribution. Shortages are allowed and fu...The objective is to develop a model considering demand dependent on selling price and deterioration occurs after a certain period of time, which follows two-parameter Weibull distribution. Shortages are allowed and fully backlogged. Fuzzy optimal solution is obtained by considering hexagonal fuzzy numbers and for defuzzification Graded Mean Integration Representation Method. A numerical example is provided for the illustration of crisp and fuzzy, both models. To observe the effect of changes in parameters, sensitivity analysis is carried out.展开更多
Let the elastic body only be acted by gravity. By investigating the relations of bianalytic functions and biharmonic functions, the uniqueness and existence of the stress functions (Airy functions) are established in ...Let the elastic body only be acted by gravity. By investigating the relations of bianalytic functions and biharmonic functions, the uniqueness and existence of the stress functions (Airy functions) are established in planar simple connected region. Moreover, the integral representation formula of the stress functions in the unit disk of the plane is obtained.展开更多
In this paper, a new risk model is studied in which the rate of premium income is regarded as a random variable, the arrival of insurance policies is a Poisson process and the process of claim occurring is p-thinning ...In this paper, a new risk model is studied in which the rate of premium income is regarded as a random variable, the arrival of insurance policies is a Poisson process and the process of claim occurring is p-thinning process. The integral representations of the survival probability are gotten. The explicit formula of the survival probability on the infinite interval is obtained in the special casc cxponential distribution.The Lundberg inequality and the common formula of the ruin probability are gotten in terms of some techniques from martingale theory.展开更多
The present article is an account of results on univalent functions in multiply connected domains obtained by the author. It contains two rery simple proofs of Villat's formula; Schwarz's formula, Poisson'...The present article is an account of results on univalent functions in multiply connected domains obtained by the author. It contains two rery simple proofs of Villat's formula; Schwarz's formula, Poisson's formula and Poisson-Jensen formula in multiply connected domains; the differentiability theorem with respect to the parameter of analytic function family containing one parametric variable on multiply connected domains; variation theorem and parametric representation theorem of univalent functions in multiply connected domains; the solution of an extremal problem of differentiable functionals.展开更多
The original online version of this article (Durmagambetov, A.A. (2016) The Riemann Hypothesis-Millennium Prize Problem. Advances in Pure Mathematics, 6, 915-920. 10.4236/apm.2016.612069) unfortunately contains a mist...The original online version of this article (Durmagambetov, A.A. (2016) The Riemann Hypothesis-Millennium Prize Problem. Advances in Pure Mathematics, 6, 915-920. 10.4236/apm.2016.612069) unfortunately contains a mistake. The author wishes to correct the errors in Theorem 2 of the result part.展开更多
The present work is much motivated by finding an explicit way in the construction of the Jack symmetric function,which is the spectrum generating function for the Calogero-Sutherland (CS) model.To accomplish this work...The present work is much motivated by finding an explicit way in the construction of the Jack symmetric function,which is the spectrum generating function for the Calogero-Sutherland (CS) model.To accomplish this work,the hidden Virasoro structure in the CS model is much explored.In particular,we found that the Virasoro singular vectors form a skew hierarchy in the CS model.Literally,skew is analogous to coset,but here specifically refer to the operation on the Young tableaux.In fact,based on the construction of the Virasoro singular vectors,this hierarchical structure can be used to give a complete construction of the CS states,i.e.the Jack symmetric functions,recursively.The construction is given both in operator formalism as well as in integral representation.This new integral representation for the Jack symmetric functions may shed some insights on the spectrum constructions for the other integrable systems.展开更多
The integral representation of differentiable functions in Octonion space is obtained and the explicit solution of the inhomogeneous Cauchy-Riemann equation is given by integral representation. As an application, the ...The integral representation of differentiable functions in Octonion space is obtained and the explicit solution of the inhomogeneous Cauchy-Riemann equation is given by integral representation. As an application, the Cousin problem analogue of Mittag-Laffier problem is discussed.展开更多
In this article,the authors obtain an integral representation for the relaxation of the functionalF（x,u,Ω）：={∫^f（x,u（x）,εu（x））dx Ω if u∈W^1,1（Ω,R^N）, ＋∞ otherwise, in the space of functions of bound...In this article,the authors obtain an integral representation for the relaxation of the functionalF（x,u,Ω）：={∫^f（x,u（x）,εu（x））dx Ω if u∈W^1,1（Ω,R^N）, ＋∞ otherwise, in the space of functions of bounded deformation,with respect to L^1-convergence.Here Eu represents the absolutely continuous part of the symmetrized distributional derivative Eu.f（x,p,ξ）satisfying weak convexity assumption.展开更多
This work is dedicated to the promotion of the results C. Muntz obtained modifying zeta functions. The properties of zeta functions are studied;these properties lead to new regularities of zeta functions. The choice o...This work is dedicated to the promotion of the results C. Muntz obtained modifying zeta functions. The properties of zeta functions are studied;these properties lead to new regularities of zeta functions. The choice of a special type of modified zeta functions allows estimating the Riemann’s zeta function and solving Riemann Problem-Millennium Prize Problem.展开更多
In the face of complicated, diversified three-dimensional world, the existing 3D GIS data models suffer from certain issues such as data incompatibility, insufficiency in data representation and representation types, ...In the face of complicated, diversified three-dimensional world, the existing 3D GIS data models suffer from certain issues such as data incompatibility, insufficiency in data representation and representation types, among others. It is often hard to meet the requirements of multiple application purposes(users) related to GIS spatial data management and data query and analysis, especially in the case of massive spatial objects. In this study, according to the habits of human thinking and recognition, discrete expressions(such as discrete curved surface(DCS), and discrete body(DB)) were integrated and two novel representation types(including function structure and mapping structure) were put forward. A flexible and extensible ubiquitous knowledgeable data representation model(UKRM) was then constructed, in which structurally heterogeneous multiple expressions(including boundary representation(B-rep), constructive solid geometry(CSG), functional/parameter representation, etc.) were normalized. GIS's ability in representing the massive, complicated and diversified 3D world was thus greatly enhanced. In addition, data reuse was realized, and the bridge linking static GIS to dynamic GIS was built up. Primary experimental results illustrated that UKRM was overwhelmingly superior to the current data models(e.g. IFC, City GML) in describing both regular and irregular spatial objects.展开更多
A new technique of integral representations in Cn, which is different from the well-known Henkin technique, is given. By means of this new technique, a new integral formula for smooth functions and a new integral repr...A new technique of integral representations in Cn, which is different from the well-known Henkin technique, is given. By means of this new technique, a new integral formula for smooth functions and a new integral representation of solutions of the -equations on strictly pseudoconvex domains in Cn are obtained. These new formulas are simpler than the classical ones, especially the solutions of the -equations admit simple uniform estimates. Moreover, this new technique can be further applied to arbitrary bounded domains in Cn so that all corresponding formulas are simplified.展开更多
In this paper we give some sufficient conditions for analytic functions which are not identically zero and belong to Nevanlinna class in the sector and angular domain. Moreover, their integral expressions or factoriza...In this paper we give some sufficient conditions for analytic functions which are not identically zero and belong to Nevanlinna class in the sector and angular domain. Moreover, their integral expressions or factorization theorems are obtained.展开更多
基金supported by Croatian Ministry of Science,Education and Sports(Grant No.#037-0372794-2804)
文摘This paper has two aims. The first is to give a description of irreducible tempered representations of classical p-adic groups which follows naturMly the classification of irreducible square integrable representations modulo cuspidal data obtained by Mceglin and the author of this article （2002）. The second aim of the paper is to give a description of an invariant （partially defined function） of irreducible square integrable representation of a classical p-adic group （defined by Mceglin using embeddings） in terms of subquotients of Jacquet modules. As an application, we describe behavior of partially defined function in one construction of square integrable representations of a bigger group from such representations of a smaller group （which is related to deformation of Jordan blocks of representations）.
基金Supported by the office of Graduate Studies and the Center of Excellence for Mathematics of the University of Isfahan
文摘A notion of an irreducible representation, as well as of a square integrable representation on an arbitrary locally compact groupoid, is introduced. A generalization of a version of Schur＇s lemma on a locally compact groupoid is given. This is used in order to extend some well-known results from locally compact groups to the case of locally compact groupoids. Indeed, we have proved that if L is a continuous irreducible representation of a compact groupoid G defined by a continuous Hilbert bundle H = （Hu）u∈G^0, then each Hu is finite dimensional. It is also shown that if L is an irreducible representation of a principal locally compact groupoid defined by a Hilbert bundle （G^0, （Hu）,μ）, then dimHu = 1 （u ∈ G^0）. Furthermore it is proved that every square integrable representation of a locally compact groupoid is unitary equivalent to a subrepresentation of the left regular representation. Furthermore, for r-discrete groupoids, it is shown that every irreducible subrepresentation of the left regular representation is square integrable.
文摘Under the constrained condition induced by the eigenfunction expresson of the potential (u, v)T = (-[A2q, q], [A2p, p])T = f (q, p), the spatial part of the Lax pair of the Kaup-Newell equation is non linearized to be a completely integrable system (R2N, Adp AND dq, H = H-1) with the Hamiltonian H-1 = -[A3q, p]-1/2[A2p, p][A2q, q]. while the nonlinearization of the time part leads to its N-involutive system {H(m)}. The involutive solution of the compatible fsystem (H-1), (H(m)) is mapped by into the solution of the higher order Kaup-Newell equation.
基金supported by Shanghai Rising-Star Program(Grant No.21QA1403400)Shanghai Natural Science Foundation(Grant No.19ZR1420700)Shanghai Key Laboratory of Power Station Automation Technology(Grant No.13DZ2273800).
文摘Failuremode and effects analysis(FMEA)is a widely used safety assessmentmethod inmany fields.Z-number was previously applied in FMEA since it can take both possibility and reliability of information into consideration.However,the use of fuzzy weighted mean to integrate Z-valuations may have some drawbacks and is not suitable for some situations.In this paper,an improved method is proposed based on Z-numbers and the graded mean integration representation(GMIR)to deal with the uncertain information in FMEA.First,Z-numbers are constructed based on the evaluations of risk factors O,S,D for each failure mode by different experts.Second,weights of the three risk factors and experts are determined.Third,the integration representations of Z-numbers are obtained by a newmethod based on the GMIRmethod.Finally,risk priorities of the failure modes are derived considering the weights of experts and risk factors.Two examples and a case study are given to show the use of the proposed method and comparison with other methods.The results show that the proposed method is more reasonable,universal and simple in calculation.
基金supported by the Scientific and Technological Research Council of Turkey(TüBìTAK)
文摘The aim of this paper is to construct the integral representation of the solution of Sturm-Liouville equation with eigenparameter-dependent discontinuity conditions at an interior point of the finite interval. Moreover, we examine the properties of the kernel function of this integral representation and obtain the partial differential equation provided by this kernel function.
文摘We generalized the Bochner-Martinelli integral representation to that on Riemannian manifolds. Things become quite different in such case. First we define a kind of Newtonian potential and take the interior product of its gradient to be the integral kernel. Then we prove that this kernel is harmonic in some sense. At last an integral representative theorem is proved.
文摘In this paper we consider polynomial splines S(x) with equidistant nodes which may grow a5 O (|x|~5). We present an integral representation of such splines with a distribution kernel. This repre- sentation is related to the Fourier integral of slowly growing functions. The part of the Fourier ex- ponentials herewith play the so called exponential splines by Schoenberg. The integral representation provides a flexible tool for dealing with the growing equidistant splines. First. it allows us to con- struct a rich library of splines possessing the property that translations of any such spline form a ba- sis of corresponding spline space. It is shown that any such spline is associated with a dual spline whose translations form a biorthogonal basis. As examples we present solutions of the problems of projection of a growing function onto spline spaces and of spline interpolation of growing func- tion. We derive formulas for approximate evaluation of splines projecting a function onto the spline space and establish therewith exact estimations of the approximation errors.
文摘In this paper,we first obtain a unified integral representation on the analytic varieties of the general bounded domain in Stein manifolds(the two types bounded domains in[3]are regarded as its special cases).Secondly we get the integral formulas of the solution of∂-equation.And we use a new and unique method to give a uniform estimate of the solution of∂-equation,which is different from Henkin's method.
文摘The objective is to develop a model considering demand dependent on selling price and deterioration occurs after a certain period of time, which follows two-parameter Weibull distribution. Shortages are allowed and fully backlogged. Fuzzy optimal solution is obtained by considering hexagonal fuzzy numbers and for defuzzification Graded Mean Integration Representation Method. A numerical example is provided for the illustration of crisp and fuzzy, both models. To observe the effect of changes in parameters, sensitivity analysis is carried out.
文摘Let the elastic body only be acted by gravity. By investigating the relations of bianalytic functions and biharmonic functions, the uniqueness and existence of the stress functions (Airy functions) are established in planar simple connected region. Moreover, the integral representation formula of the stress functions in the unit disk of the plane is obtained.
文摘In this paper, a new risk model is studied in which the rate of premium income is regarded as a random variable, the arrival of insurance policies is a Poisson process and the process of claim occurring is p-thinning process. The integral representations of the survival probability are gotten. The explicit formula of the survival probability on the infinite interval is obtained in the special casc cxponential distribution.The Lundberg inequality and the common formula of the ruin probability are gotten in terms of some techniques from martingale theory.
文摘The present article is an account of results on univalent functions in multiply connected domains obtained by the author. It contains two rery simple proofs of Villat's formula; Schwarz's formula, Poisson's formula and Poisson-Jensen formula in multiply connected domains; the differentiability theorem with respect to the parameter of analytic function family containing one parametric variable on multiply connected domains; variation theorem and parametric representation theorem of univalent functions in multiply connected domains; the solution of an extremal problem of differentiable functionals.
文摘The original online version of this article (Durmagambetov, A.A. (2016) The Riemann Hypothesis-Millennium Prize Problem. Advances in Pure Mathematics, 6, 915-920. 10.4236/apm.2016.612069) unfortunately contains a mistake. The author wishes to correct the errors in Theorem 2 of the result part.
基金Supported by the Chinese Academy of Sciences Program "Frontier Topics in Mathematical Physics" (KJCX3-SYW-S03)Supported Partially by the National Natural Science Foundation of China under Grant No.11035008
文摘The present work is much motivated by finding an explicit way in the construction of the Jack symmetric function,which is the spectrum generating function for the Calogero-Sutherland (CS) model.To accomplish this work,the hidden Virasoro structure in the CS model is much explored.In particular,we found that the Virasoro singular vectors form a skew hierarchy in the CS model.Literally,skew is analogous to coset,but here specifically refer to the operation on the Young tableaux.In fact,based on the construction of the Virasoro singular vectors,this hierarchical structure can be used to give a complete construction of the CS states,i.e.the Jack symmetric functions,recursively.The construction is given both in operator formalism as well as in integral representation.This new integral representation for the Jack symmetric functions may shed some insights on the spectrum constructions for the other integrable systems.
基金Supported by the National Natural Science Foundation of China(11171298)the Zhejiang Natural Science Foundation of China(Y6110425)
文摘The integral representation of differentiable functions in Octonion space is obtained and the explicit solution of the inhomogeneous Cauchy-Riemann equation is given by integral representation. As an application, the Cousin problem analogue of Mittag-Laffier problem is discussed.
基金the Doctorial Programme Foundation of EducationMinistry of of China(20030288002)the Science Foundation of Jiangsu Province(BK2006209)+1 种基金NaturalScience Foundation of Jiangsu Higher Education Bureau(07KJD110206)NNSF of China(10771181)
文摘In this article,the authors obtain an integral representation for the relaxation of the functionalF（x,u,Ω）：={∫^f（x,u（x）,εu（x））dx Ω if u∈W^1,1（Ω,R^N）, ＋∞ otherwise, in the space of functions of bounded deformation,with respect to L^1-convergence.Here Eu represents the absolutely continuous part of the symmetrized distributional derivative Eu.f（x,p,ξ）satisfying weak convexity assumption.
文摘This work is dedicated to the promotion of the results C. Muntz obtained modifying zeta functions. The properties of zeta functions are studied;these properties lead to new regularities of zeta functions. The choice of a special type of modified zeta functions allows estimating the Riemann’s zeta function and solving Riemann Problem-Millennium Prize Problem.
基金supported by the National Natural Science Foundation of China(Grant No.41271196)the Key Project of the 12th Five-year Plan,Chinese Academy of Sciences(Grant No.KZZD-EW-07-02-003)
文摘In the face of complicated, diversified three-dimensional world, the existing 3D GIS data models suffer from certain issues such as data incompatibility, insufficiency in data representation and representation types, among others. It is often hard to meet the requirements of multiple application purposes(users) related to GIS spatial data management and data query and analysis, especially in the case of massive spatial objects. In this study, according to the habits of human thinking and recognition, discrete expressions(such as discrete curved surface(DCS), and discrete body(DB)) were integrated and two novel representation types(including function structure and mapping structure) were put forward. A flexible and extensible ubiquitous knowledgeable data representation model(UKRM) was then constructed, in which structurally heterogeneous multiple expressions(including boundary representation(B-rep), constructive solid geometry(CSG), functional/parameter representation, etc.) were normalized. GIS's ability in representing the massive, complicated and diversified 3D world was thus greatly enhanced. In addition, data reuse was realized, and the bridge linking static GIS to dynamic GIS was built up. Primary experimental results illustrated that UKRM was overwhelmingly superior to the current data models(e.g. IFC, City GML) in describing both regular and irregular spatial objects.
基金the National Natural Science Foundation of China(Grant No.19771068).
文摘A new technique of integral representations in Cn, which is different from the well-known Henkin technique, is given. By means of this new technique, a new integral formula for smooth functions and a new integral representation of solutions of the -equations on strictly pseudoconvex domains in Cn are obtained. These new formulas are simpler than the classical ones, especially the solutions of the -equations admit simple uniform estimates. Moreover, this new technique can be further applied to arbitrary bounded domains in Cn so that all corresponding formulas are simplified.
基金Supported by the National Natural Science Foundation of China (Grant No30800244)
文摘In this paper we give some sufficient conditions for analytic functions which are not identically zero and belong to Nevanlinna class in the sector and angular domain. Moreover, their integral expressions or factorization theorems are obtained.
