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INVARIANT SUBSPACES AND GENERALIZED FUNCTIONAL SEPARABLE SOLUTIONS TO THE TWO-COMPONENT b-FAMILY SYSTEM 认领 引用 被引量：1
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作者 闫璐 时振华 +1 位作者 王昊 康静 《Acta Mathematica Scientia》 SCIE CSCD 2016年第3期753-764,共12页
Invariant subspace method is exploited to obtain exact solutions of the two- component b-family system. It is shown that the two-component b-family system admits the generalized functional separable solutions. Further... Invariant subspace method is exploited to obtain exact solutions of the two- component b-family system. It is shown that the two-component b-family system admits the generalized functional separable solutions. Furthermore, blow up and behavior of those exact solutions are also investigated. 展开更多
关键词 invariant subspace generalized conditional symmetry generalized functional separable solution Camassa-Holm equation two-component b-family system
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The Fourier Transform of a Sort of Generalized Function 认领 引用
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作者 祝同江 《Journal of Beijing Institute of Technology》 EI CAS 1996年第2期106+101-106,共107页
The Fourier transforms of functions X ln e are given. where λ is a complex constant (λ≠-1,-2. …), a is a complex number. m=0. 1. 2,…,and
关键词 Fourier transform generalized function analytic exextension
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On Applications of Generalized Functions in the Discontinuous Beam Bending Differential Equations 认领 引用 被引量：1
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作者 Dimplekumar Chalishajar Austin States Brad Lipscomb 《Applied Mathematics》 2016年第16期1943-1970,共28页
This paper discusses the mathematical modeling for the mechanics of solid using the distribution theory of Schwartz to the beam bending differential Equations. This problem is solved by the use of generalized function... This paper discusses the mathematical modeling for the mechanics of solid using the distribution theory of Schwartz to the beam bending differential Equations. This problem is solved by the use of generalized functions, among which is the well known Dirac delta function. The governing differential Equation is Euler-Bernoulli beams with jump discontinuities on displacements and rotations. Also, the governing differential Equations of a Timoshenko beam with jump discontinuities in slope, deflection, flexural stiffness, and shear stiffness are obtained in the space of generalized functions. The operator of one of the governing differential Equations changes so that for both Equations the Dirac Delta function and its first distributional derivative appear in the new force terms as we present the same in a Euler-Bernoulli beam. Examples are provided to illustrate the abstract theory. This research is useful to Mechanical Engineering, Ocean Engineering, Civil Engineering, and Aerospace Engineering. 展开更多
关键词 Mechanics of Solids Discontinuities in a Beam Bending Differential Equations Generalized Functions Jump Discontinuities
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Functional generalized estimating equation model to detect glaucomatous visual field progression 认领 引用
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作者 Sanghun Jeong Hwayeong Kim +4 位作者 Sangwoo Moon EunAh Kim Hojin Yang Jiwoong Lee Kouros Nouri-Mahdavi 《International Journal of Ophthalmology(English edition)》 SCIE CAS 2026年第2期302-311,共10页
AIM:To build a functional generalized estimating equation(GEE)model to detect glaucomatous visual field progression and compare the performance of the proposed method with that of commonly employed algorithms.METHODS:... AIM:To build a functional generalized estimating equation(GEE)model to detect glaucomatous visual field progression and compare the performance of the proposed method with that of commonly employed algorithms.METHODS:Totally 716 eyes of 716 patients with primary open angle glaucoma(POAG)with at least 5 reliable 24-2 test results and 2y of follow-up were selected.The functional GEE model was used to detect perimetric progression in the training dataset(501 eyes).In the testing dataset(215 eyes),progression was evaluated the functional GEE model,mean deviation(MD)and visual field index(VFI)rates of change,Advanced Glaucoma Intervention Study(AGIS)and Collaborative Initial Glaucoma Treatment Study(CIGTS)scores,and pointwise linear regression(PLR).RESULTS:The proposed method showed the highest proportion of eyes detected as progression(54.4%),followed by the VFI rate(34.4%),PLR(23.3%),and MD rate(21.4%).The CIGTS and AGIS scores had a lower proportion of eyes detected as progression(7.9%and 5.1%,respectively).The time to detection of progression was significantly shorter for the proposed method than that of other algorithms(adjusted P≤0.019).The VFI rate displayed moderate pairwise agreement with the proposed method(k=0.47).CONCLUSION:The functional GEE model shows the highest proportion of eyes detected as perimetric progression and the shortest time to detect perimetric progression in patients with POAG. 展开更多
关键词 functional generalized estimating equation model primary open angle glaucoma perimetric progression
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Predetermined-Time Output Projective Synchronization of Coupled Fuzzy Neural Networks via Generalized Exponential Function 认领 引用
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作者 Ting Liu Shiwen Xie +2 位作者 Yongfang Xie Peng Liu Tingwen Huang 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2025年第12期2602-2611,共10页
The main motivation of this paper arises from the fact that some complex systems have high demands for time precision, which need to reach the desired state in a pre-specified time interval. This paper addresses the p... The main motivation of this paper arises from the fact that some complex systems have high demands for time precision, which need to reach the desired state in a pre-specified time interval. This paper addresses the predetermined-time output projective synchronization of coupled fuzzy neural networks.To mimic the uncertainty and relatedness among complex systems, coupled fuzzy neural networks are introduced to characterize complex systems in this paper. First, a novel controller is developed by means of a generalized exponential function and output states information, which can effectively avoid the chattering situations arising from the sign function. Under the controller,the output states of coupled fuzzy neural networks eventually converge to the projective state in the predefined time, which can reduce the requirements for sensor devices and improve the flexibility and efficiency of the control scheme. Second, in light of Lyapunov function and inequality techniques, sufficient criteria for ensuring to achieve the predetermined-time output projective synchronization of coupled fuzzy neural networks are deduced based on the assumption of the digraph containing a spanning tree. Furthermore, the results obtained in this paper not only represent an extension of master-slave systems but also demonstrate that the output synchronization of coupled fuzzy neural networks is a specific case of projective synchronization exemplified by a corollary. Finally, numerical examples are offered to reveal the correctness of theoretical results. 展开更多
关键词 Fuzzy neural networks generalized exponential function output projective synchronization predetermined-time
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GENERALIZED COUNTING FUNCTIONS AND COMPOSITION OPERATORS ON WEIGHTED BERGMAN SPACES OF DIRICHLET SERIES 认领 引用
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作者 Min HE Maofa WANG Jiale CHEN 《Acta Mathematica Scientia》 SCIE CSCD 2025年第2期291-309,共19页
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
关键词 generalized counting function Dirichlet series composition operator weighted Bergman space
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A Moment Characterization of B-Valued Generalized Functionals of White Noise 认领 引用 被引量：4
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作者 Cai Shi WANG Zhi Yuan HUANG 《Acta Mathematica Sinica,English Series》 SCIE 2006年第1期157-168,共12页
Kernel theorems are established for Bananch space-valued multilinear mappings, A moment characterization theorem for Banach space-valued generalized functionals of white noise is proved by using the above kernel theor... Kernel theorems are established for Bananch space-valued multilinear mappings, A moment characterization theorem for Banach space-valued generalized functionals of white noise is proved by using the above kernel theorems. A necessary and sufficient condition in terms of moments is given for sequences of Banach space-valued generalized functionals of white noise to converge strongly. The integration is also discussed of functions valued in the space of Banach space-valued generalized functionals. 展开更多
关键词 White noise analysis B-valued generalized functionals Moment characterization
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Problems and solutions regarding generalized functional safety in cyberspace 认领 引用 被引量：7
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作者 JiangXing Wu 《Security and Safety》 2022年第1期90-102,共13页
The common endogenous security problems in cyberspace and related attack threats have posed subversive challenges to conventional theories and methods of functional safety.In the current design of the cyber physical s... The common endogenous security problems in cyberspace and related attack threats have posed subversive challenges to conventional theories and methods of functional safety.In the current design of the cyber physical system(CPS),functional safety and cyber security are increasingly intertwined and inseparable,which evolve into the generalized functional safety(S&S)problem.The conventional reliability and cybersecurity technologies are unable to provide security assurance with quanti able design and veri cation metrics in response to the cyberattacks in hardware and software with common endogenous security problems,and the functional safety of CPS facilities or device has become a frightening ghost.The dynamic heterogeneity redundancy(DHR)architecture and coding channel theory(CCT)proposed by the cyberspace endogenous security paradigm could handle random failures and uncertain network attacks in an integrated manner,and its generalized robust control mechanism can solve the universal problem of quantitative design for functional safety under probability or improbability perturbation.As a generalized functional safety enabling structure,DHR opens up a new direction to solve the common endogenous security problems in the cross-disciplinary elds of cyberspace. 展开更多
关键词 Common endogenous security problem Generalized functional safety(S&S) Dynamic heterogeneity redundancy(DHR)architecture General robust control mechanism Coding channel theory Common cross-disciplinary eld problems
The generalized Chapman-Richards function and applications to tree and stand growth 认领 引用 被引量：14
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作者 刘兆刚 李凤日 《Journal of Forestry Research》 CAS 2003年第1期19-26,共8页
The generalized Chapman-Richards model was derived from the Chapman-Richards function in which parameters h, k and m were unconstrained. Based on the structure of solutions and biological interpretations, the model co... The generalized Chapman-Richards model was derived from the Chapman-Richards function in which parameters h, k and m were unconstrained. Based on the structure of solutions and biological interpretations, the model could be classified into eight cases (three categories) at all and among them only 4 kinds of cases are suitable in forestry that represent four typical growth patterns of trees and stands. For each of 4 equations, the model properties and biological interpretations for parameters were discussed in detail. The generalized Chapman-Richards model was capable of describing a wide range of growth curves that was asymptotic or nonasymptotic, with or without inflection point. In order to illustrate the versatility of the model, it was fitted to a group of data sets concerning the DBH growth of cryptomeria plantations with 4 initial densities and the DBH and height growth of natural Korean pine tree. Comparing the generalized Chapman-Richards function and the Schnute model, it was found that the parameters and expressions of the two models were interchangeable in theory, and the fitting results were explicitly identical in empirical applications. 展开更多
关键词 Generalized Chapman-Richards function Schnute model Growth model Growth pattern Cryptomeria japonica Pinus koraiensis
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MONOTONICITY AND INEQUALITIES FOR THE GENERALIZED DISTORTION FUNCTION 认领 引用 被引量：3
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作者 马晓艳 褚玉明 王飞 《Acta Mathematica Scientia》 SCIE CSCD 2013年第6期1759-1766,共8页
The authors prove some monotonicity properties of functions involving the generalized Agard distortion function ηg（a,t）, and obtain some inequalities for ηk（a, t） and relative distortion functions.
关键词 generalized modular equation generalized η-distortion function monotonic-ity inequality
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APPROXIMATE CONVEXITY AND CONCAVITY OFGENERALIZED GROTZSCH RING FUNCTION 认领 引用 被引量：3
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作者 王根娣 裘松良 +1 位作者 张孝惠 褚玉明 《Applied Mathematics(A Journal of Chinese Universities)》 2006年第2期203-206,共4页
In this paper, the so-called approximate convexity and concavity properties of generalized Groetzsch ring function μa （r） by studying the monotonieity,convexity or concavity of certain composites of μa（r） are ob... In this paper, the so-called approximate convexity and concavity properties of generalized Groetzsch ring function μa （r） by studying the monotonieity,convexity or concavity of certain composites of μa（r） are obtained. 展开更多
关键词 generalized Grotzsch ring function Ramanujan＇s modular equation convexity concawty.
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Some inequalities for the generalized linear distortion function 认领 引用 被引量：2
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作者 MA Xiao-yan QIU Song-liang +1 位作者 ZHONG Gen-hong CHU Yu-ming 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2012年第1期87-93,共7页
In this paper, we establish several inequalities for the the generalized linear distortion function λ（a, K） by using the monotonicity and convexity of certain combinations λ（a, K）.
关键词 modular equation generalized linear distortion function inequality.
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THE HILBERT BOUNDARY VALUE PROBLEM FOR GENERALIZED ANALYTIC FUNCTIONS IN CLIFFORD ANALYSIS 认领 引用 被引量：2
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作者 司中伟 杜金元 《Acta Mathematica Scientia》 SCIE CSCD 2013年第2期393-403,共11页
Let R0,n be the real Clifford algebra generated by e1, e2,... , en satisfying eiej＋ejei=-2δij,i,j=1,2…,ne0 is the unit element.Let Ω be an open set. A function f is called left generalized analytic in ft if f sati... Let R0,n be the real Clifford algebra generated by e1, e2,... , en satisfying eiej＋ejei=-2δij,i,j=1,2…,ne0 is the unit element.Let Ω be an open set. A function f is called left generalized analytic in ft if f satisfies the equation Lf=0,where ……qi 〉0, i =-, 1, - ……, n. In this article, we first give the kernel function for the generalized analytic function. Further, the Hilbert boundary value problem for generalized analytic functions in Rn＋1 will be investigated. 展开更多
关键词 Generalized analytic function Hilbert boundary value problem H^u function
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THIRD-ORDER DIFFERENTIAL SUBORDINATION RESULTS FOR ANALYTIC FUNCTIONS INVOLVING THE GENERALIZED BESSEL FUNCTIONS 认领 引用 被引量：4
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作者 汤获 Erhan DENIZ 《Acta Mathematica Scientia》 SCIE CSCD 2014年第6期1707-1719,共13页
In the present paper, we derive some third-order differential subordination results for analytic functions in the open unit disk, using the operator Bcκf by means of normalized form of the generalized Bessel function... In the present paper, we derive some third-order differential subordination results for analytic functions in the open unit disk, using the operator Bcκf by means of normalized form of the generalized Bessel functions of the first kind, which is defined as z（Bκ＋1^c f（z））′= κBκ^c f（z）-（κ- 1）Bκ＋1^c f（z）,where b, c, p ∈ C and κ = p ＋（b ＋ 1）/2 ∈ C ／ Z0^-（Z0^-= {0,-1,-2, … }）. The results are obtained by considering suitable classes of admissible functions. Various known or new special cases of our main results are also pointed out. 展开更多
关键词 differential subordination univalent functions Hadamard product admissible functions generalized Bessel functions
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Generalized Gr?tzsch ring function and generalized elliptic integrals 认领 引用 被引量：1
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作者 MA Xiao-yan QIU Song-liang TU Guo-yan 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2016年第4期458-468,共11页
Abstract. In this paper, we study the quotient of hypergeometric functions μα （r） in the theory of Ramanujan＇s generalized modular equation for α ∈（0, 1/2]. Several new inequalities are given for this and rela... Abstract. In this paper, we study the quotient of hypergeometric functions μα （r） in the theory of Ramanujan＇s generalized modular equation for α ∈（0, 1/2]. Several new inequalities are given for this and related functions. Our main results complement and generalize some known results in the literature. 展开更多
关键词 Gaussian hypergeometric function generalized GrStzsch ring function generalized elliptic func-tion.
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A Characterization Theorem of the Differential of Functions Valued in B-Valued Generalized Functionals 认领 引用 被引量：2
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作者 Jin Shu CHEN 《Journal of Mathematical Research and Exposition》 CSCD 2011年第5期840-844,共5页
Banach space-valued generalized functionals of white noise form an important part of vector-valued generalized functionals of white noise. In this paper, we discuss the differential of abstract function valued in B-va... Banach space-valued generalized functionals of white noise form an important part of vector-valued generalized functionals of white noise. In this paper, we discuss the differential of abstract function valued in B-valued generalized functional space. A characterized theorem is obtained by using their S-transform. 展开更多
关键词 white noise analysis B-valued generalized functionals differential S-transform.
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Linear and Nonlinear Formulation of Phase Field Model with Generalized Polynomial Degradation Functions for Brittle Fractures 认领 引用
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作者 Ala Tabiei Li Meng 《Acta Mechanica Solida Sinica》 SCIE EI CSCD 2024年第5期643-661,共19页
The classical phase field model has wide applications for brittle materials,but nonlinearity and inelasticity are found in its stress-strain curve.The degradation function in the classical phase field model makes it a... The classical phase field model has wide applications for brittle materials,but nonlinearity and inelasticity are found in its stress-strain curve.The degradation function in the classical phase field model makes it a linear formulation of phase field and computationally attractive,but stiffness reduction happens even at low strain.In this paper,generalized polynomial degradation functions are investigated to solve this problem.The first derivative of degradation function at zero phase is added as an extra constraint,which renders higher-order polynomial degradation function and nonlinear formulation of phase field.Compared with other degradation functions(like algebraic fraction function,exponential function,and trigonometric function),this polynomial degradation function enables phase in[0,1](should still avoid the first derivative of degradation function at zero phase to be 0),so there is noconvergence problem.The good and meaningful finding is that,under the same fracture strength,the proposed phase field model has a larger length scale,which means larger element size and better computational efficiency.This proposed phase field model is implemented in LS-DYNA user-defined element and user-defined material and solved by the Newton-Raphson method.A tensile test shows that the first derivative of degradation function at zero phase does impact stress-strain curve.Mode I,mode II,and mixed-mode examples show the feasibility of the proposed phase field model in simulating brittle fracture. 展开更多
关键词 Nonlinear formulation Generalized polynomial degradation function Brittle materials Stress-strain curve convergence
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New Computation of Unified Bounds via a More General Fractional Operator Using Generalized Mittag-Leffler Function in the Kernel 认领 引用
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作者 Saima Rashid Zakia Hammouch +1 位作者 Rehana Ashraf Yu-Ming Chu 《Computer Modeling in Engineering & Sciences》 SCIE EI 2021年第1期359-378,共20页
In the present case,we propose the novel generalized fractional integral operator describing Mittag-Leffler function in their kernel with respect to another function Φ.The proposed technique is to use graceful amalga... In the present case,we propose the novel generalized fractional integral operator describing Mittag-Leffler function in their kernel with respect to another function Φ.The proposed technique is to use graceful amalgamations of the Riemann-Liouville(RL)fractional integral operator and several other fractional operators.Meanwhile,several generalizations are considered in order to demonstrate the novel variants involving a family of positive functions n(n∈N)for the proposed fractional operator.In order to confirm and demonstrate the proficiency of the characterized strategy,we analyze existing fractional integral operators in terms of classical fractional order.Meanwhile,some special cases are apprehended and the new outcomes are also illustrated.The obtained consequences illuminate that future research is easy to implement,profoundly efficient,viable,and exceptionally precise in its investigation of the behavior of non-linear differential equations of fractional order that emerge in the associated areas of science and engineering. 展开更多
关键词 Integral inequality generalized fractional integral with respect to another function increasing and decreasing functions Mittag-Leffler function
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On the generalized Cauchy function and new Conjecture on its exterior singularities 认领 引用 被引量：1
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作者 Theodore Yaotsu Wu 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2011年第2期135-151,共17页
This article studies on Cauchy’s function f （z） and its integral, （2πi）J[ f （z）] ≡ ■C f （t）dt/（t z） taken along a closed simple contour C, in regard to their comprehensive properties over the entire z =... This article studies on Cauchy’s function f （z） and its integral, （2πi）J[ f （z）] ≡ ■C f （t）dt/（t z） taken along a closed simple contour C, in regard to their comprehensive properties over the entire z = x ＋ iy plane consisted of the simply connected open domain D ＋ bounded by C and the open domain D outside C. （1） With f （z） assumed to be C n （n ∞-times continuously differentiable） z ∈ D ＋ and in a neighborhood of C, f （z） and its derivatives f （n） （z） are proved uniformly continuous in the closed domain D ＋ = [D ＋ ＋ C]. （2） Cauchy’s integral formulas and their derivatives z ∈ D ＋ （or z ∈ D ） are proved to converge uniformly in D ＋ （or in D = [D ＋C]）, respectively, thereby rendering the integral formulas valid over the entire z-plane. （3） The same claims （as for f （z） and J[ f （z）]） are shown extended to hold for the complement function F（z）, defined to be C n z ∈ D and about C. （4） The uniform convergence theorems for f （z） and F（z） shown for arbitrary contour C are adapted to find special domains in the upper or lower half z-planes and those inside and outside the unit circle ｜z｜ = 1 such that the four general- ized Hilbert-type integral transforms are proved. （5） Further, the singularity distribution of f （z） in D is elucidated by considering the direct problem exemplified with several typ- ical singularities prescribed in D . （6） A comparative study is made between generalized integral formulas and Plemelj’s formulas on their differing basic properties. （7） Physical sig- nificances of these formulas are illustrated with applicationsto nonlinear airfoil theory. （8） Finally, an unsolved inverse problem to determine all the singularities of Cauchy function f （z） in domain D , based on the continuous numerical value of f （z） z ∈ D ＋ = [D ＋ ＋ C], is presented for resolution as a conjecture. 展开更多
关键词 Uniform continuity of Cauchy’s function · Uni- form convergence of Cauchy’s integral formula · Generalized Hilbert-type integral transforms · Functional properties and singularity distributions
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Optimization of the Dressing Parameters in Cylindrical Grinding Based on a Generalized Utility Function 认领 引用 被引量：2
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作者 ALEKSANDROVA Irina 《Chinese Journal of Mechanical Engineering》 SCIE EI CAS CSCD 2016年第1期63-73,共11页
The existing studies, concerning the dressing process, focus on the major influence of the dressing conditions on the grinding response variables. However, the choice of the dressing conditions is often made, based on... The existing studies, concerning the dressing process, focus on the major influence of the dressing conditions on the grinding response variables. However, the choice of the dressing conditions is often made, based on the experience of the qualified staff or using data from reference books. The optimal dressing parameters, which are only valid for the particular methods and dressing and grinding conditions, are also used. The paper presents a methodology for optimization of the dressing parameters in cylindrical grinding. The generalized utility function has been chosen as an optimization parameter. It is a complex indicator determining the economic, dynamic and manufacturing characteristics of the grinding process. The developed methodology is implemented for the dressing of aluminium oxide grinding wheels by using experimental diamond roller dressers with different grit sizes made of medium- and high-strength synthetic diamonds type AC32 and AC80. To solve the optimization problem, a model of the generalized utility function is created which reflects the complex impact of dressing parameters. The model is built based on the results from the conducted complex study and modeling of the grinding wheel lifetime, cutting ability, production rate and cutting forces during grinding. They are closely related to the dressing conditions （dressing speed ratio, radial in-feed of the diamond roller dresser and dress-out time）, the diamond roller dresser grit size/grinding wheel grit size ratio, the type of synthetic diamonds and the direction of dressing. Some dressing parameters are determined for which the generalized utility fimction has a maximum and which guarantee an optimum combination of the following： the lifetime and cutting ability of the abrasive wheels, the tangential cutting force magnitude and the production rate of the grinding process. The results obtained prove the possibility of control and optimization of grinding by selecting particular dressing parameters. 展开更多
关键词 dressing conditions cylindrical grinding diamond roller dresser generalized utility function based optimization
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