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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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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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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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Generalized multiple-mode prolate spheroidal wave functions multi-carrier waveform with index modulation 认领 引用
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作者 XU Zhichao LU Faping +5 位作者 ZHANG Lifan YANG Dongkai LIU Chuanhui KANG Jiafang AN Qi ZHANG Zhilin 《Journal of Systems Engineering and Electronics》 SCIE CSCD 2025年第2期311-322,共12页
A generalized multiple-mode prolate spherical wave functions (PSWFs) multi-carrier with index modulation approach is proposed with the purpose of improving the spectral efficiency of PSWFs multi-carrier systems. The p... A generalized multiple-mode prolate spherical wave functions (PSWFs) multi-carrier with index modulation approach is proposed with the purpose of improving the spectral efficiency of PSWFs multi-carrier systems. The proposed method,based on the optimized multi-index modulation, does not limit the number of signals in the first and second constellations and abandons the concept of limiting the number of signals in different constellations. It successfully increases the spectrum efficiency of the system while expanding the number of modulation symbol combinations and the index dimension of PSWFs signals. The proposed method outperforms the PSWFs multi-carrier index modulation method based on optimized multiple indexes in terms of spectrum efficiency, but at the expense of system computational complexity and bit error performance. For example, with n=10 subcarriers and a bit error rate of 1×10-5,spectral efficiency can be raised by roughly 12.4%. 展开更多
关键词 prolate spherical wave function(PSWF) generalized multiple-mode index modulation spectral efficiency.
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Generalized Energy-Based Fragmentation TDDFT-ris Method and its Application to Electronic Spectra and Asymmetry Factors of Large Systems 认领 引用
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作者 Ziyi Lv Fengmin Wang +5 位作者 Junhui Sun Xuerong Wang Shuhua Li Zehao Zhou Jingxiang Zou Wei Li 《Chinese Journal of Chemical Physics》 SCIE EI CAS CSCD 2026年第3期303-312,共10页
Accurately and efficiently calculating electronic excited states remains a major challenge in quantum chemistry,especially for complex photophysical and photochemical systems.Conventional approaches such as time-depen... Accurately and efficiently calculating electronic excited states remains a major challenge in quantum chemistry,especially for complex photophysical and photochemical systems.Conventional approaches such as time-dependent density functional theory(TDDFT)are limited by unfavorable computational scaling,limiting their applicability to large systems.To address this,we present a computational framework combining the generalized energy-based fragmentation(GEBF)approach with TDDFT-ris,which requires only one s-type auxiliary basis function per atom via the resolution-of-the-identity technique.This approach enables efficient and reliable excited-state computations for macromolecules,including fluorescent materials and proteins with thousands of atoms,and provides accurate predictions of asymmetry factors(g-factors)in chiral optoelectronic materials and fluorescent protein. 展开更多
关键词 Generalized energy-based fragmentation Time-dependent density functional theory Electronic spectra Asymmetry factor Fluorescent protein
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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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DUAL FUNCTIONALS OF SAID-BZIER TYPE GENERALIZED BALL BASES OVER TRIANGLE DOMAIN AND THEIR APPLICATION 认领 引用
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作者 Wu Hongyi 《Applied Mathematics(A Journal of Chinese Universities)》 2006年第1期96-106,共11页
A family of Said-Bézier type generalized Ball （SBGB） bases and surfaces with a parameter H over triangular domain is introduced,which unifies Bézier surface and Said-Ball surface and includes several inter... A family of Said-Bézier type generalized Ball （SBGB） bases and surfaces with a parameter H over triangular domain is introduced,which unifies Bézier surface and Said-Ball surface and includes several intermediate surfaces. To convert different bases and surfaces,the dual functionals of bases are presented. As an application of dual functionals,the subdivision formulas for surfaces are established. 展开更多
关键词 Bézier basis Said-Bézier type generalized Ball （SBGB） basis triangular domain dual functional ,subdivision formula.
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Integrated spatial generalized additive modeling for forest fire prediction:a case study in Fujian Province,China 认领 引用 被引量：1
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作者 Chunhui Li Zhangwen Su +4 位作者 Rongyu Ni Guangyu Wang Yiyun Ouyang Aicong Zeng Futao Guo 《Journal of Forestry Research》 SCIE EI CAS CSCD 2025年第3期208-223,共16页
The increasing frequency of extreme weather events raises the likelihood of forest wildfires.Therefore,establishing an effective fire prediction model is vital for protecting human life and property,and the environmen... The increasing frequency of extreme weather events raises the likelihood of forest wildfires.Therefore,establishing an effective fire prediction model is vital for protecting human life and property,and the environment.This study aims to build a prediction model to understand the spatial characteristics and piecewise effects of forest fire drivers.Using monthly grid data from 2006 to 2020,a modeling study analyzed fire occurrences during the September to April fire season in Fujian Province,China.We compared the fitting performance of the logistic regression model(LRM),the generalized additive logistic model(GALM),and the spatial generalized additive logistic model(SGALM).The results indicate that SGALMs had the best fitting results and the highest prediction accuracy.Meteorological factors significantly impacted forest fires in Fujian Province.Areas with high fire incidence were mainly concentrated in the northwest and southeast.SGALMs improved the fitting effect of fire prediction models by considering spatial effects and the flexible fitting ability of nonlinear interpretation.This model provides piecewise interpretations of forest wildfire occurrences,which can be valuable for relevant departments and will assist forest managers in refining prevention measures based on temporal and spatial differences. 展开更多
关键词 Forest fire prediction Logistic regression Spatial generalized additive model Spline functions Piecewise effects
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Wigner function for the generalized excited pair coherent state 认领 引用 被引量：11
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作者 孟祥国 王继锁 +1 位作者 梁宝龙 李洪奇 《Chinese Physics B》 SCIE EI CAS 2008年第5期1791-1797,共7页
This paper introduces the generalized excited pair coherent state （GEPCS）. Using the entangled state 〈η〉 representation of Wigner operator, it obtains the Wigner function for the GEPCS. In the ρ-γ phase space, ... This paper introduces the generalized excited pair coherent state （GEPCS）. Using the entangled state 〈η〉 representation of Wigner operator, it obtains the Wigner function for the GEPCS. In the ρ-γ phase space, the variations of the Wigner function distributions with the parameters q, α, k and l are discussed. The tomogram of the GEPCS is calculated with the help of the Radon transform between the Wigner operator and the projection operator of the entangled state ｜η1, η2, τ1, τ2｜. The entangled states ｜η〉 and ｜η1, η2, τ1, τ2〉 provide two good representative space for studying the Wigner functions and tomograms of various two-mode correlated quantum states. 展开更多
关键词 generalized excited pair coherent state Wigner function tomogram entangled state representation
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Some new exact solutions of Jacobian elliptic function about the generalized Boussinesq equation and Boussinesq-Burgers equation 认领 引用 被引量：20
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作者 张亮 张立凤 李崇银 《Chinese Physics B》 SCIE EI CAS 2008年第2期403-410,共8页
By using the modified mapping method, we find some new exact solutions of the generalized Boussinesq equation and the Boussinesq-Burgers equation. The solutions obtained in this paper include Jacobian elliptic functio... By using the modified mapping method, we find some new exact solutions of the generalized Boussinesq equation and the Boussinesq-Burgers equation. The solutions obtained in this paper include Jacobian elliptic function solutions, combined Jacobian elliptic function solutions, soliton solutions, triangular function solutions. 展开更多
关键词 generalized Boussinesq equation Boussinesq-Burgers equation Jacobian elliptic function modified mapping method
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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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Hash function based on the generalized Henon map 认领 引用 被引量：4
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作者 郑凡 田小建 +1 位作者 李雪妍 吴斌 《Chinese Physics B》 SCIE EI CAS 2008年第5期1685-1690,共6页
A new Hash function based on the generalized Henon map is proposed. We have obtained a binary sequence with excellent pseudo-random characteristics through improving the sequence generated by the generalized Henon map... A new Hash function based on the generalized Henon map is proposed. We have obtained a binary sequence with excellent pseudo-random characteristics through improving the sequence generated by the generalized Henon map, and use it to construct Hash function. First we divide the message into groups, and then carry out the Xor operation between the ASCII value of each group and the binary sequence, the result can be used as the initial values of the next loop. Repeat the procedure until all the groups have been processed, and the final binary sequence is the Hash value. In the scheme, the initial values of the generalized Henon map are used as the secret key and the messages are mapped to Hash values with a designated length. Simulation results show that the proposed scheme has strong diffusion and confusion capability, good collision resistance, large key space, extreme sensitivity to message and secret key, and it is easy to be realized and extended. 展开更多
关键词 the generalized Henon map Hash function chaos
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Adaptive generalized functional synchronization of chaotic systems with unknown parameters 认领 引用 被引量：8
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作者 王东风 韩璞 《Chinese Physics B》 SCIE EI CAS 2008年第10期3603-3608,共6页
A universal adaptive generalized functional synchronization approach to any two different or identical chaotic systems with unknown parameters is proposed, based on a unified mathematical expression of a large class o... A universal adaptive generalized functional synchronization approach to any two different or identical chaotic systems with unknown parameters is proposed, based on a unified mathematical expression of a large class of chaotic system. Self-adaptive parameter law and control law are given in the form of a theorem. The synchronization between the three-dimensional R6ssler chaotic system and the four-dimensional Chen＇s hyper-chaotic system is studied as an example for illustration. The computer simulation results demonstrate the feasibility of the method proposed. 展开更多
关键词 chaotic system adaptive synchronization generalized synchronization functional synchronization
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Optimizing basis wave functions in the generator coordinate method for microscopic cluster models (Ⅰ) 认领 引用
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作者 Yi‑Fan Liu Bo Zhou Yu‑Gang Ma 《Nuclear Science and Techniques》 SCIE EI CAS CSCD 2025年第10期183-191,共9页
We employed random distributions and gradient descent methods for the Generator Coordinate Method(GCM)to identify effective basis wave functions,taking halo nuclei 6He and 6Li as examples.By comparing the ground... We employed random distributions and gradient descent methods for the Generator Coordinate Method(GCM)to identify effective basis wave functions,taking halo nuclei 6He and 6Li as examples.By comparing the ground state(0+)energy of 6He and the excited state(0+)energy of 6 Li calculated with various random distributions and manually selected generation coordinates,we found that the heavy tail characteristic of the logistic distribution better describes the features of the halo nuclei.Subsequently,the Adam algorithm from machine learning was applied to optimize the basis wave functions,indicating that a limited number of basis wave functions can approximate the converged values.These results offer some empirical insights for selecting basis wave functions and contribute to the broader application of machine learning methods in predicting effective basis wave functions. 展开更多
关键词 Generator Coordinate Method Effective basis wave functions Nuclear cluster model Machine learning Halo nuclei
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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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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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Influence of Generalized (r, q) Distribution Function on Electrostatic Waves 认领 引用 被引量：3
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作者 M.N.S. Qureshi SHI Jian-Kui MA Shi-Zhuang 《Communications in Theoretical Physics》 SCIE CAS 2006年第3期550-554,共5页
Non-Maxwellian particle distribution functions possessing high energy tail and shoulder in the profile of distribution function considerably change the damping characteristics of the waves. In the present paper Landau... Non-Maxwellian particle distribution functions possessing high energy tail and shoulder in the profile of distribution function considerably change the damping characteristics of the waves. In the present paper Landau damping of electron plasma （Langmuir） waves and ion-acoustic waves in a hot, isotropic, unmagnetized plasma is studied with the generalized （r, q） distribution function. The results show that for the Langmuir oscillations Landau damping becomes severe as the spectral index r or q reduces. However, for the ion-acoustic waves Landau damping is more sensitive to the ion temperature than the spectral indices. 展开更多
关键词 generalized （r q） distribution function electrostatic waves damping
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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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Approximate Derivative-Dependent Functional Variable Separation for the Generalized Diffusion Equations with Perturbation 认领 引用 被引量：2
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作者 张顺利 吉飞宇 屈长征 《Communications in Theoretical Physics》 SCIE CAS CSCD 2012年第8期175-181,共7页
As an extension to the derivative-dependent functional variable separation approach, the approximate derivative-dependent functional variable separation approach is proposed, and it is applied to study the generalized... As an extension to the derivative-dependent functional variable separation approach, the approximate derivative-dependent functional variable separation approach is proposed, and it is applied to study the generalized diffusion equations with perturbation. Complete classification of these perturbed equations which admit approximate derivative-dependent functional separable solutions is obtained. As a result, the corresponding approximate derivative-dependent functional separable solutions to some resulting perturbed equations are derived by way of examples. 展开更多
关键词 generalized diffusion equation approximate derivative-dependent functional separable solution approximate generalized conditional symmetry
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