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CARATHEODORY INEQUALITY FOR ANALYTIC OPERATOR FUNCTION 认领 引用
1
作者 Yang Changsenof Math., Henan Normal Univ., Xinxiang 453002. 《Applied Mathematics(A Journal of Chinese Universities)》 2001年第3期285-289,共5页
Suppose H is a complex Hilbert space, A H(Δ) denotes the set of all analytic operator functions on Δ, and the set N H(Δ)=｛f(z)｜f(z) is an analytic operator function on the open uint disk Δ, f(z)f(w)=f(w)f(z),f *... Suppose H is a complex Hilbert space, A H(Δ) denotes the set of all analytic operator functions on Δ, and the set N H(Δ)=｛f(z)｜f(z) is an analytic operator function on the open uint disk Δ, f(z)f(w)=f(w)f(z),f *(z)f(z)=f(z)f *(z),z,w∈Δ｝. The note proves that if f(z)∈N H(Δ),(or A H(Δ))‖f(z)‖≤1,z∈Δ then‖f′(T)‖≤(1-‖T‖ 2) -1 ‖I-f *(T)f(T)‖ 12 ‖I-f(T)f *(T)‖ 12 , where T∈L(H)(orT *T=TT *,respectively),‖T‖<1,Tf=fT. 展开更多
关键词 Analytic operator function proper contraction resolution of identity.
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THE PROBABILISTIC REPRESENTATION FORMULAE FOR COSINE OPERATOR FUNCTIONS 认领 引用
2
作者 周密 陈文忠 《Analysis in Theory and Applications》 1993年第1期42-52,共11页
In this paper we obtained general representation formulae for strongly continuous cosine operator functions via probabilistic approach,which include Webb's[1]and Shaw's[2]formulae and some new one as special c... In this paper we obtained general representation formulae for strongly continuous cosine operator functions via probabilistic approach,which include Webb's[1]and Shaw's[2]formulae and some new one as special cases.We also give the quantitative estimations for the general formulae. 展开更多
关键词 Th THE PROBABILISTIC REPRESENTATION FORMULAE FOR COSINE OPERATOR FUNCTIONS
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STRONGLY CONTINUOUS INTEGRATED COSINE OPERATOR FUNCTIONS WITH GROWTHω 认领 引用
3
作者 Meiying Wang Guoxiang Chen 《Analysis in Theory and Applications》 2007年第1期1-8,共8页
For a continuous increasing function ω ： [0, ∞） → （0, ∞） of finite exponetial type, we establish a Hille-Yosida type theorem for strongly continuous integrated cosine operator functions with O（ω）. It includ... For a continuous increasing function ω ： [0, ∞） → （0, ∞） of finite exponetial type, we establish a Hille-Yosida type theorem for strongly continuous integrated cosine operator functions with O（ω）. It includes the well-known polynomially bounded and exponentially bounded cases. 展开更多
关键词 cosine operator functions with growth ω generator generation theorem
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α-times Integrated Cosine Operator Functions with Growth ω 认领 引用 被引量：1
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作者 WANG Mei-ying XU Fei 《Chinese Quarterly Journal of Mathematics》 CSCD 2011年第2期229-233,共5页
For a continuous,increasing functionω:[0,∞)→C of finite exponential type,we establish a Hille-Yosida type theorem for strongly continuous α-times(α>0)integrated cosine operator functions with O(ω).It includes... For a continuous,increasing functionω:[0,∞)→C of finite exponential type,we establish a Hille-Yosida type theorem for strongly continuous α-times(α>0)integrated cosine operator functions with O(ω).It includes the corresponding results for n-times integrated cosine operator functions that are polynomially bounded and exponentially bounded. 展开更多
关键词 integrated cosine operator functions with growthω generator generation theorem
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C-cosine Operator Functions and the Second Order Abstract Cauchy Problem 认领 引用 被引量：1
5
作者 Wang Haiyan 《Northeastern Mathematical Journal》 1995年第1期85-94,共10页
In this paper we first define a notion of the C-cosine operator function that may not beexponentially bounded fro a given bounded injective operator C whose range may not be dense on a Banach space X.We then study the... In this paper we first define a notion of the C-cosine operator function that may not beexponentially bounded fro a given bounded injective operator C whose range may not be dense on a Banach space X.We then study the basic properties and characterize the generator of a C-cosineoperator function Finally we apply the obtained results to a class of second abstract Cauchy problems. 展开更多
关键词 C-cosine Operator Function Generator Second Order Abstract Cauchy Problems
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On Dual Cosine Operator Function 认领 引用
6
作者 Ding Tianbiao Tian Liqin 《Chinese Quarterly Journal of Mathematics》 1996年第3期87-90,共4页
Some basic properties of daul cosine operator function are given.The concept and characterization ofθ-reflexivity with respect to cosine operator function are first studied.
关键词 cosine operator function duality θ-reflexivity
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Hille-Yosida Type Theorem of Polynomial Bounded Cosine Operator Function 认领 引用
7
作者 Zhang Xiaoxia 《Northeastern Mathematical Journal》 1998年第3期73-78,共6页
In this paper,with the help of Laplace transforms,we give a necessary and suff-i cient condition for an operator A to be an infinitesimal generator of a strongly continuous cosine operator function with‖C(t)‖≤M〔1+... In this paper,with the help of Laplace transforms,we give a necessary and suff-i cient condition for an operator A to be an infinitesimal generator of a strongly continuous cosine operator function with‖C(t)‖≤M〔1+|t|〕m,t∈R. 展开更多
关键词 Cosine Operator Function Infinitesimal Generator Resolvent Equation
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Properties of Subgenerators of Integrated C-cosine Operator Functions 认领 引用
8
作者 Zhao Rongxia Huang Zhenyou 《Northeastern Mathematical Journal》 1998年第3期29-38,共10页
For the set G of subgenerators of a given n-times integrated C-cosine operater function,we define two operations > and ,< and the operator inclusion ⊆,study the other properties of G,and give some examples.
关键词 n-times Integrated C-cosine Operators Function Subgenerator Lattice
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BFROU: A Reconfigurable Operation Unit Design Approach Using NPN Equivalence and Reed-Muller Logic Unit for Boolean Functions in Stream Ciphers 认领 引用
9
作者 Zhaoxu Zhou Yanjiang Liu +1 位作者 Zibin Dai Junwei Li 《Computers, Materials & Continua》 SCIE EI 2026年第8期806-832,共27页
Stream ciphers are simple to implement and fast at encrypting and decrypting data,making them very important in information security.Boolean functions are a core part of stream ciphers.However,their mainstream hardwar... Stream ciphers are simple to implement and fast at encrypting and decrypting data,making them very important in information security.Boolean functions are a core part of stream ciphers.However,their mainstream hardware implementations face two main problems,including wasted area resources and excessive critical path delay.These issues limit the energy efficiency and integration level of stream cipher chips.To address these problems,this paper proposes an energy-efficient design method for a 64-bit Boolean function reconfigurable operation unit(BFROU),aiming to improve the computational efficiency of Boolean functions in stream ciphers.To optimize the design of BFROU,this paper takes the NPN equivalence theory as a guide.First,customized designs at the transistor level were performed for both 2-and 3-variable RM logic units(denoted as TRM).On this basis,this paper uses the port sharing strategy to further optimize the design of 4-to-6-variable TRM logic units and construct a multi-variable TRM process library.Then,by combining multi-variable TRM logic units with the mathematical definition of Boolean functions,this paper proposes a theoretical model of BFROU.Based on this model and combined with the statistical analysis results of Boolean functions,the optimal TRM unit configuration is determined,and the overall optimization of the 64-bit BFROU is finally completed.Experimental results show that when TRM-3 and TRM-4 units are mixed as the first-level operation module of BFROU,its area-delay product(ADP)reaches the minimum.The 64-bit BFROU unit implemented according to this scheme has an actual measured area of 137.28μm2 and a critical path delay of 0.278 ns under the SMIC 40 nm typical process corner.This unit supports Boolean function operations with up to 64 variables,and 94.4%of the functions can complete mapping within 2 iterations.Compared with existing schemes such as look-up table(LUT)architecture and And-Inverter Cone(AIC)array,the BFROU proposed in this paper has obvious advantages in area,delay,ADP and number of iterations,providing effective hardware support for the design of high-energy-efficiency stream cipher chips. 展开更多
关键词 Boolean function reconfigurable operation unit stream cipher TRM units NPN equivalence theory
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Band Structure Calculations of Dispersive Photonic Crystals in 3D using Holomorphic Operator Functions 认领 引用
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作者 Wenqiang Xiao Bo Gong +1 位作者 Junshan Lin Jiguang Sun 《Communications in Computational Physics》 SCIE 2023年第2期628-646,共19页
We propose a finite element method to compute the band structures of dispersive photonic crystals in 3D.The nonlinear Maxwell’s eigenvalue problem is formulated as the eigenvalue problem of a holomorphic operator fun... We propose a finite element method to compute the band structures of dispersive photonic crystals in 3D.The nonlinear Maxwell’s eigenvalue problem is formulated as the eigenvalue problem of a holomorphic operator function.The N´ed´elec edge elements are employed to discretize the operators,where the divergence free condition for the electric field is realized by a mixed form using a Lagrange multiplier.The convergence of the eigenvalues is proved using the abstract approximation theory for holomorphic operator functions with the regular approximation of the edge elements.The spectral indicator method is then applied to compute the discrete eigenvalues.Numerical examples are presented demonstrating the effectiveness of the proposed method. 展开更多
关键词 Band structure dispersive photonic crystal Maxwell’s equations nonlinear eigenvalue problem edge element holomorphic operator function
Some Results on Dual Cosine Operator Function 认领 引用
11
作者 丁天彪 《Journal of Mathematical Research and Exposition》 1998年第2期197-200,共4页
Some basic properties of dual cosine operator function are given. The concept and characterization of θ reflexivity with respect to cosine operator function are first studied.
关键词 cosine operator function duality θ reflexivity.
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Two Sequences of Operator Monotone Functions and Strictly Chaotic Order 认领 引用
12
作者 ZHA NG Lei JIANG Jian-fei 《Chinese Quarterly Journal of Mathematics》 北大核心 2006年第4期597-607,共11页
In this paper we introduce two sequences of operator functions and their dualfunctions： fk（t） = （flogt）k-（t-1）k/log^k＋2t （k = 1,2,...）, gk（t） = （t-1）k-logkt /log^k＋1t （k = 1,2,...） and fk（t）tklog^k... In this paper we introduce two sequences of operator functions and their dualfunctions： fk（t） = （flogt）k-（t-1）k/log^k＋2t （k = 1,2,...）, gk（t） = （t-1）k-logkt /log^k＋1t （k = 1,2,...） and fk（t）tklog^k＋1t/（tlogt）k-（t-1）^k（k=1,2…）,gk（t）=t^klog^k＋1t/（t-1）^k-log^kt（k=1,2…）defined onWe find that they are all operator monotone functions with respect to the strictly chaoticorder and some ordinary orders among positive invertible operators. Indeed, we extend theresults of the operator monotone function tlogt-t＋1/log^2t which is widely used in the theory of heat transfer of the heat engineering and fluid mechanics[1]. 展开更多
关键词 sequence of operator functions LSwner-Heinz inequality strictly Chaotic order
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Critical station identification of metro networks based on the integrated topological-functional algorithm:A case study of Chengdu 认领 引用
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作者 Zi-Qiang Zeng Sheng-Jie He Wang Tian 《Chinese Physics B》 SCIE EI CAS CSCD 2025年第2期509-520,共12页
As a key mode of transportation, urban metro networks have significantly enhanced urban traffic environments and travel efficiency, making the identification of critical stations within these networks increasingly ess... As a key mode of transportation, urban metro networks have significantly enhanced urban traffic environments and travel efficiency, making the identification of critical stations within these networks increasingly essential. This study presents a novel integrated topological-functional(ITF) algorithm for identifying critical nodes, combining topological metrics such as K-shell decomposition, node information entropy, and neighbor overlapping interaction with the functional attributes of passenger flow operations, while also considering the coupling effects between metro and bus networks. Using the Chengdu metro network as a case study, the effectiveness of the algorithm under different conditions is validated.The results indicate significant differences in passenger flow patterns between working and non-working days, leading to varying sets of critical nodes across these scenarios. Moreover, the ITF algorithm demonstrates a marked improvement in the accuracy of critical node identification compared to existing methods. This conclusion is supported by the analysis of changes in the overall network structure and relative global operational efficiency following targeted attacks on the identified critical nodes. The findings provide valuable insight into urban transportation planning, offering theoretical and practical guidance for improving metro network safety and resilience. 展开更多
关键词 critical node metro network topological structure functional operation
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A SHARP ESTIMATE ON THE DEGREE OF APPROXIMATION TO FUNCTIONS OF BOUNDED VARIATION BY CERTAIN OPERATORS 认领 引用 被引量：1
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作者 Vijay Gupta 《Analysis in Theory and Applications》 1995年第3期106-107,共2页
Recently Guo introduced integrated Meyer -Konig and Zeller operators and studied the rate of convergence for function of bounded variation. In this note we give a sharp estimate for these operators.
关键词 A SHARP ESTIMATE ON THE DEGREE OF APPROXIMATION TO FUNCTIONS OF BOUNDED VARIATION BY CERTAIN OPERATORS
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Inclusion Relationships for p-Valent Analytic Functions Involving the Dziok-Srivastava Operator 认领 引用
15
作者 Huo TANG Guantie DENG 《Journal of Mathematical Research with Applications》 CSCD 2014年第6期696-702,共7页
In this paper, we use the methods of differential subordination and the properties of convolution to investigate the class Wp（H（ai, bj）; φ） of multivalent analytic functions, which is defined by the Dziok-Srivast... In this paper, we use the methods of differential subordination and the properties of convolution to investigate the class Wp（H（ai, bj）; φ） of multivalent analytic functions, which is defined by the Dziok-Srivastava operator H（a1,..., aq; b1,..., bs）. Some inclusion properties for this class are obtained. 展开更多
关键词 analytic functions subordination Hadmard product（or convolution） DziokSrivastava operator
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REFERENCE FUNCTIONAL AND CHARACTERISTIC SPACE FOR LAGRANGE AND BERNSTEIN OPERATORS 认领 引用
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作者 S.De Marchi M.Morandi Cecchi 《Analysis in Theory and Applications》 1995年第4期6-14,共9页
This paper deals with the description and the representation of polynomials defined over n-simplices, The polynomials are computed by using two recurrent schemes: the Neville-Aitken one for the Lagrange interpolating ... This paper deals with the description and the representation of polynomials defined over n-simplices, The polynomials are computed by using two recurrent schemes: the Neville-Aitken one for the Lagrange interpolating operator and the De Casteljau one for the Bernstein-Bezier approximating operator. Both schemes fall intothe framework of transformations of the form where the F iare given numbers (forexample, at the initial step they coincide with the values of the function on a given lattice), and the coefficients (x) are linear polynomials valued in x and x is fixed. A general theory for such sequence of transformations can be found in [2] where it is also proved that these tranformations are completely characterized in term of a linear functional, reference functional. This functional is associated with a linear space., characteristic space.The concepts of reference functionals and characteristic spaces will be used and we shall prove the existence of a characteristic space for the reference functional: associated with these operators. 展开更多
关键词 REFERENCE FUNCTIONAL AND CHARACTERISTIC SPACE FOR LAGRANGE AND BERNSTEIN OPERATORS
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Coefficient Bounds for a New Subclass of Bi-Univalent Functions Defined by Salagean Operator 认领 引用 被引量：1
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作者 Fan CHEN Xiaofei LI 《Journal of Mathematical Research with Applications》 CSCD 2017年第3期290-298,共9页
In this paper, a new subclass N_Σ^（h,p）（m, λ, μ） of analytic and bi-univalent functions in the open unit disk U is defined by salagean operator. We obtain coefficients bounds ｜a_2｜ and ｜a_3｜ for functions o... In this paper, a new subclass N_Σ^（h,p）（m, λ, μ） of analytic and bi-univalent functions in the open unit disk U is defined by salagean operator. We obtain coefficients bounds ｜a_2｜ and ｜a_3｜ for functions of the class. Moreover, we verify Brannan and Clunie＇s conjecture ｜a_2｜ ≤2^（1/2）for some of our classes. The results in this paper extend many results recently researched by many authors. 展开更多
关键词 analytic functions univalent functions bi-univalent functions coefficient bounds Salagean operator
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A NOTE ON MEYER-KONIG AND ZELLER OPERATORS FOR FUNCTIONS OF BOUNDED VARIATION 认领 引用 被引量：1
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作者 Vijay Gupta 《Approximation Theory and Its Applications》 2002年第3期99-102,共4页
In the present note we give the correct and improved estimate on the rate of convergence of integrated Meyer-Konig and Zetter operators for function of bounded variation.
关键词 rate In Math A NOTE ON MEYER-KONIG AND ZELLER OPERATORS FOR FUNCTIONS OF BOUNDED VARIATION
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On Invertibility of Functional Operators with Shift in Weighted Holder Spaces 认领 引用
19
作者 Anna Tarasenko Oleksandr Karelin 《Advances in Pure Mathematics》 2014年第11期595-600,共6页
In this paper, we consider functional operators with shift in weighted H?lder spaces. We present the main idea and the scheme of proof of the conditions of invertibility for these operators. As an application, we prop... In this paper, we consider functional operators with shift in weighted H?lder spaces. We present the main idea and the scheme of proof of the conditions of invertibility for these operators. As an application, we propose to use these results for solution of equations with shift which arise in the study of cyclic models for natural systems with renewable resources. 展开更多
关键词 Functional Operator with Shift Holder Space Conditions of Invertibility Renewable Resources
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A theorem for quantum operator correspondence to the solution of the Helmholtz equation 认领 引用
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作者 范洪义 陈俊华 +1 位作者 张鹏飞 何锐 《Chinese Physics B》 SCIE EI CAS CSCD 2014年第11期157-160,共4页
We propose a theorem for the quantum operator that corresponds to the solution of the Helmholtz equation, i.e., ∫∫∫V （x1 ,x2,x3）〈X1 ,x2,x3〉〈x1 ,x2,x3〉d3x = V （X1 ,X2,X3） = e-λ2/4 ：V （X1 ,X2,X3）：,where... We propose a theorem for the quantum operator that corresponds to the solution of the Helmholtz equation, i.e., ∫∫∫V （x1 ,x2,x3）〈X1 ,x2,x3〉〈x1 ,x2,x3〉d3x = V （X1 ,X2,X3） = e-λ2/4 ：V （X1 ,X2,X3）：,where V （X1 ,X2,X3） is the solution to the Helmholtz equation △2V ＋λ2V = 0, the symbol ： ： denotes normal ordering, and X1, X2, X3 are three-dimensional coordinate operators. This helps to derive the normally ordered expansion of Dirac＇s radius operator functions. We also discuss the normally ordered expansion of Bessel operator functions. 展开更多
关键词 normally ordered expansion radius operators Helmholtz equation Bessel operator function
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