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
This paper proposes a concurrent neural network model to mitigate non-linear distortion in power amplifiers using a basis function generation approach.The model is designed using polynomial expansion and comprises a f...This paper proposes a concurrent neural network model to mitigate non-linear distortion in power amplifiers using a basis function generation approach.The model is designed using polynomial expansion and comprises a feedforward neural network(FNN)and a convolutional neural network(CNN).The proposed model takes the basic elements that form the bases as input,defined by the generalized memory polynomial(GMP)and dynamic deviation reduction(DDR)models.The FNN generates the basis function and its output represents the basis values,while the CNN generates weights for the corresponding bases.Through the concurrent training of FNN and CNN,the hidden layer coefficients are updated,and the complex multiplication of their outputs yields the trained in-phase/quadrature(I/Q)signals.The proposed model was trained and tested using 300 MHz and 400 MHz broadband data in an orthogonal frequency division multiplexing(OFDM)communication system.The results show that the model achieves an adjacent channel power ratio(ACPR)of less than-48 d B within a 100 MHz integral bandwidth for both the training and test datasets.展开更多
By virtue of the operator-Hermite-polynomial method, we derive some new generating function formulas of the product of two bivariate Hermite polynomials. Their applications in studying quantum optical states are prese...By virtue of the operator-Hermite-polynomial method, we derive some new generating function formulas of the product of two bivariate Hermite polynomials. Their applications in studying quantum optical states are presented.展开更多
The magnetic flux in a permanent magnet transverse flux generator(PMTFG) is three-dimensional(3D), therefore, its efficacy is evaluated using 3D magnetic field analysis. Although the 3D finite-element method(FEM) is h...The magnetic flux in a permanent magnet transverse flux generator(PMTFG) is three-dimensional(3D), therefore, its efficacy is evaluated using 3D magnetic field analysis. Although the 3D finite-element method(FEM) is highly accurate and reliable for machine simulation, it requires a long computation time, which is crucial when it is to be used in an iterative optimization process. Therefore, an alternative to 3DFEM is required as a rapid and accurate analytical technique. This paper presents an analytical model for PMTFG analysis using winding function method. To obtain the air gap MMF distribution, the excitation magneto-motive force(MMF) and the turn function are determined based on certain assumptions. The magnetizing inductance, flux density, and back-electro-magnetomotive force of the winding are then determined. To assess the accuracy of the proposed method, the analytically calculated parameters of the generator are compared to those obtained by a 3D-FEM. The presented method requires significantly shorter computation time than the 3D-FEM with comparable accuracy.展开更多
We derive some new generating function formulae of the two-variable Hermite polynomials, such as ∞∑n=0tm/m!Hn,2m（x）,∞∑n=0sntm/n!m!H2n,2m（x,y）,and ∞∑n=0sntm/n!m!H2n＋l,2m＋k（x,y）.We employ the operator Herm...We derive some new generating function formulae of the two-variable Hermite polynomials, such as ∞∑n=0tm/m!Hn,2m（x）,∞∑n=0sntm/n!m!H2n,2m（x,y）,and ∞∑n=0sntm/n!m!H2n＋l,2m＋k（x,y）.We employ the operator Hermite polynomial method and the technique of integration within an ordered product of operators to solve these problems, which will be useful in constructing new optical field states.展开更多
By combining the operator Hermite polynomial method and the technique of integration within an ordered product of operators, for the first time we derive the generating function of even- and odd-Hermite polynomials wh...By combining the operator Hermite polynomial method and the technique of integration within an ordered product of operators, for the first time we derive the generating function of even- and odd-Hermite polynomials which will be useful in constructing new optical field states. We then show that the squeezed state and photon-added squeezed state can be expressed by even- and odd-Hermite polynomials.展开更多
A generalized form of the error function, Gp(x)=pΓ(1/p)∫0xe−tpdt, which is directly associated with the gamma function, is evaluated for arbitrary real values of p>1and 0x≤+∞by employing a fast-converging power...A generalized form of the error function, Gp(x)=pΓ(1/p)∫0xe−tpdt, which is directly associated with the gamma function, is evaluated for arbitrary real values of p>1and 0x≤+∞by employing a fast-converging power series expansion developed in resolving the so-called Grandi’s paradox. Comparisons with accurate tabulated values for well-known cases such as the error function are presented using the expansions truncated at various orders.展开更多
A new concept generalized(h,m)−preinvex function on Yang’s fractal sets is proposed.Some Ostrowski’s type inequalities with two parameters for generalized(h,m)−preinvex function are established,where three local fra...A new concept generalized(h,m)−preinvex function on Yang’s fractal sets is proposed.Some Ostrowski’s type inequalities with two parameters for generalized(h,m)−preinvex function are established,where three local fractional inequalities involving generalized midpoint type,trapezoid type and Simpson type are derived as consequences.Furthermore,as some applications,special means inequalities and numerical quadratures for local fractional integrals are discussed.展开更多
For the sequences satisfying the recurrence relation of the second order,the generating functions for the products of the powers of these sequences are established.This study was from Carlita and Riordan who began a s...For the sequences satisfying the recurrence relation of the second order,the generating functions for the products of the powers of these sequences are established.This study was from Carlita and Riordan who began a study on closed form of generating functions for powers of second-order recurrence sequences.This investigation was completed by Stnica.Inspired by the recent work of Istva＇n about the non-closed generating functions of the products of the powers of the second-order sequences,the authors give several extensions of Istva＇n＇s results in this paper.展开更多
Several kinds of stream ciphers—complementary sequences of period sequences,partial sum of period sequences,inverse order sequences and finitely generated sequences,arestudied by using techniques of generating functi...Several kinds of stream ciphers—complementary sequences of period sequences,partial sum of period sequences,inverse order sequences and finitely generated sequences,arestudied by using techniques of generating functions.Their minimal polynomials,periods,as wellas generating functions are given.As to finitely generated sequences,the change of their linearcomplexity profiles as well as the relationship between the two generated sequences usder thecase in which the degree of connected polynomials are fixed,are discussed.展开更多
We discuss three-dimensional uniform distribution and its property in a sphere;give a method of assessing the tactical and technical indices of cartridge ejection uniformity in some type of weapon systems. Meanwhile w...We discuss three-dimensional uniform distribution and its property in a sphere;give a method of assessing the tactical and technical indices of cartridge ejection uniformity in some type of weapon systems. Meanwhile we obtain the test of generating function and the estimation of equivalent radius. The uniformity of distribution is tested and verified with ω2 test method on the basis of stochastic simulation example.展开更多
This paper is concerned with construction of quantum fields presentation and generating functions of symplectic Schur functions and symplectic universal characters.The boson-fermion correspondence for these symmetric ...This paper is concerned with construction of quantum fields presentation and generating functions of symplectic Schur functions and symplectic universal characters.The boson-fermion correspondence for these symmetric functions have been presented.In virtue of quantum fields,we derive a series of infinite order nonlinear integrable equations,namely,universal character hierarchy,symplectic KP hierarchy and symplectic universal character hierarchy,respectively.In addition,the solutions of these integrable systems have been discussed.展开更多
In practical engineering,sometimes the probability density functions( PDFs) of stress and strength can not be exactly determined,or only limited experiment data are available. In these cases,the traditional stress-str...In practical engineering,sometimes the probability density functions( PDFs) of stress and strength can not be exactly determined,or only limited experiment data are available. In these cases,the traditional stress-strength interference( SSI) model based on classical probabilistic approach can not be used to evaluate reliabilities of components. To solve this issue, the traditional universal generating function( UGF) is introduced and then it is extended to represent the discrete interval-valued random variable.Based on the extended UGF,an improved discrete interval-valued SSI model is proposed, which has higher calculation precision compared with the existing methods. Finally,an illustrative case is given to demonstrate the validity of the proposed model.展开更多
In this paper explicit expressions and some recurrence relations are derived for marginal and joint moment generating functions of generalized order statistics from Erlang-truncated exponential distribution. The resul...In this paper explicit expressions and some recurrence relations are derived for marginal and joint moment generating functions of generalized order statistics from Erlang-truncated exponential distribution. The results for k-th record values and order statistics are deduced from the relations derived. Further, a characterizing result of this distribution on using the conditional expectation of function of generalized order statistics is discussed.展开更多
Present paper deals a M/M/1:(∞;GD) queueing model with interdependent controllable arrival and service rates where- in customers arrive in the system according to poisson distribution with two different arrivals rate...Present paper deals a M/M/1:(∞;GD) queueing model with interdependent controllable arrival and service rates where- in customers arrive in the system according to poisson distribution with two different arrivals rates-slower and faster as per controllable arrival policy. Keeping in view the general trend of interdependent arrival and service processes, it is presumed that random variables of arrival and service processes follow a bivariate poisson distribution and the server provides his services under general discipline of service rule in an infinitely large waiting space. In this paper, our central attention is to explore the probability generating functions using Rouche’s theorem in both cases of slower and faster arrival rates of the queueing model taken into consideration;which may be helpful for mathematicians and researchers for establishing significant performance measures of the model. Moreover, for the purpose of high-lighting the application aspect of our investigated result, very recently Maurya [1] has derived successfully the expected busy periods of the server in both cases of slower and faster arrival rates, which have also been presented by the end of this paper.展开更多
We construct the quantum fields presentation of the generalized universal character and the generalized B-type universal character,and by acting the quantum fields presentations to the constant 1,the generating functi...We construct the quantum fields presentation of the generalized universal character and the generalized B-type universal character,and by acting the quantum fields presentations to the constant 1,the generating functions are derived.Furthermore,we introduce two integrable systems known as the generalized UC(GUC)hierarchy and the generalized Btype UC(GBUC)hierarchy satisfied by the generalized universal character and the generalized B-type universal character,respectively.Based on infinite sequences of complex numbers,we further establish the multiparameter generalized universal character and the multiparameter generalized B-type universal character,which have been proved to be solutions of the GUC hierarchy and the GBUC hierarchy,respectively.展开更多
With the rapid development of large-scale regional interconnected power grids,the risk of cascading failures under extreme condi-tions,such as natural disasters and military strikes,has increased significantly.To enha...With the rapid development of large-scale regional interconnected power grids,the risk of cascading failures under extreme condi-tions,such as natural disasters and military strikes,has increased significantly.To enhance the response capability of power systems to extreme events,this study focuses on a method for generator coherency detection.To overcome the shortcomings of the traditional slow coherency method,this paper introduces a novel coherent group identification algorithm based on the theory of nonlinear dynam-ical systems.By analyzing the changing trend of the Euclidean norm of the state variable derivatives in the reduced system,the algorithm can accurately identify the magnitude of the disturbances.Based on the slow coherency methods,the algorithm can correctly recognize coherent generator groups by analyzing system characteristics under varying disturbance magnitudes.This improvement enhances the applicability and accuracy of the coherency detection algorithm under extreme conditions,providing support for emergency control and protection in the power system.Simulations and comparison analyses on IEEE 39-bus system are conducted to validate the accuracy and superiority of the proposed coherent generator group identification method under extreme conditions.展开更多
A method for estimating the component reliability is proposed when the probability density functions of stress and strength can not be exactly determined. For two groups of finite experimental data about the stress an...A method for estimating the component reliability is proposed when the probability density functions of stress and strength can not be exactly determined. For two groups of finite experimental data about the stress and strength, an interval statistics method is introduced. The processed results are formulated as two interval-valued random variables and are graphically represented component reliability are proposed based on the by using two histograms. The lower and upper bounds of universal generating function method and are calculated by solving two discrete stress-strength interference models. The graphical calculations of the proposed reliability bounds are presented through a numerical example and the confidence of the proposed reliability bounds is discussed to demonstrate the validity of the proposed method. It is showed that the proposed reliability bounds can undoubtedly bracket the real reliability value. The proposed method extends the exciting universal generating function method and can give an interval estimation of component reliability in the case of lake of sufficient experimental data. An application example is given to illustrate the proposed method展开更多
This work shows that each kind of Chebyshev polynomials may be calculated from a symbolic formula similar to the Lucas formula for Bernoulli polynomials. It exposes also a new approach for obtaining generating functio...This work shows that each kind of Chebyshev polynomials may be calculated from a symbolic formula similar to the Lucas formula for Bernoulli polynomials. It exposes also a new approach for obtaining generating functions of them by operator calculus built from the derivative and the positional operators.展开更多
基金supported by the National Natural Science Foundation of China(12171373)Chen's work also supported by the Fundamental Research Funds for the Central Universities of China(GK202207018).
文摘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.
基金supported by ZTE Industry-University-Institute Cooperation Funds under Grant No.HC-CN-20220722010。
文摘This paper proposes a concurrent neural network model to mitigate non-linear distortion in power amplifiers using a basis function generation approach.The model is designed using polynomial expansion and comprises a feedforward neural network(FNN)and a convolutional neural network(CNN).The proposed model takes the basic elements that form the bases as input,defined by the generalized memory polynomial(GMP)and dynamic deviation reduction(DDR)models.The FNN generates the basis function and its output represents the basis values,while the CNN generates weights for the corresponding bases.Through the concurrent training of FNN and CNN,the hidden layer coefficients are updated,and the complex multiplication of their outputs yields the trained in-phase/quadrature(I/Q)signals.The proposed model was trained and tested using 300 MHz and 400 MHz broadband data in an orthogonal frequency division multiplexing(OFDM)communication system.The results show that the model achieves an adjacent channel power ratio(ACPR)of less than-48 d B within a 100 MHz integral bandwidth for both the training and test datasets.
基金supported by the National Natural Science Foundation of China(Grant No.11175113)the Fundamental Research Funds for the Central Universities of China(Grant No.WK2060140013)the Natural Science Foundation of Jiangsu Higher Education Institution of China(Grant No.14KJD140001)
文摘By virtue of the operator-Hermite-polynomial method, we derive some new generating function formulas of the product of two bivariate Hermite polynomials. Their applications in studying quantum optical states are presented.
文摘The magnetic flux in a permanent magnet transverse flux generator(PMTFG) is three-dimensional(3D), therefore, its efficacy is evaluated using 3D magnetic field analysis. Although the 3D finite-element method(FEM) is highly accurate and reliable for machine simulation, it requires a long computation time, which is crucial when it is to be used in an iterative optimization process. Therefore, an alternative to 3DFEM is required as a rapid and accurate analytical technique. This paper presents an analytical model for PMTFG analysis using winding function method. To obtain the air gap MMF distribution, the excitation magneto-motive force(MMF) and the turn function are determined based on certain assumptions. The magnetizing inductance, flux density, and back-electro-magnetomotive force of the winding are then determined. To assess the accuracy of the proposed method, the analytically calculated parameters of the generator are compared to those obtained by a 3D-FEM. The presented method requires significantly shorter computation time than the 3D-FEM with comparable accuracy.
基金Project supported by the National Natural Science Foundation of China(Grnat No.11175113)the Fundamental Research Funds for the Central Universities of China(Grant No.WK2060140013)
文摘We derive some new generating function formulae of the two-variable Hermite polynomials, such as ∞∑n=0tm/m!Hn,2m（x）,∞∑n=0sntm/n!m!H2n,2m（x,y）,and ∞∑n=0sntm/n!m!H2n＋l,2m＋k（x,y）.We employ the operator Hermite polynomial method and the technique of integration within an ordered product of operators to solve these problems, which will be useful in constructing new optical field states.
基金supported by the National Natural Science Foundation of China(Grant No.11175113)the Fundamental Research Funds for the Central Universities of China(Grant No.WK2060140013)
文摘By combining the operator Hermite polynomial method and the technique of integration within an ordered product of operators, for the first time we derive the generating function of even- and odd-Hermite polynomials which will be useful in constructing new optical field states. We then show that the squeezed state and photon-added squeezed state can be expressed by even- and odd-Hermite polynomials.
文摘A generalized form of the error function, Gp(x)=pΓ(1/p)∫0xe−tpdt, which is directly associated with the gamma function, is evaluated for arbitrary real values of p>1and 0x≤+∞by employing a fast-converging power series expansion developed in resolving the so-called Grandi’s paradox. Comparisons with accurate tabulated values for well-known cases such as the error function are presented using the expansions truncated at various orders.
基金Supported by the National Natural Science Foundation of China(Grant No.11801342)the Natural Science Foundation of Shaanxi Province(Grant No.2023-JC-YB-043).
文摘A new concept generalized(h,m)−preinvex function on Yang’s fractal sets is proposed.Some Ostrowski’s type inequalities with two parameters for generalized(h,m)−preinvex function are established,where three local fractional inequalities involving generalized midpoint type,trapezoid type and Simpson type are derived as consequences.Furthermore,as some applications,special means inequalities and numerical quadratures for local fractional integrals are discussed.
基金Project supported by the Shanghai Leading Academic Discipline Project (Grant No.S30104)
文摘For the sequences satisfying the recurrence relation of the second order,the generating functions for the products of the powers of these sequences are established.This study was from Carlita and Riordan who began a study on closed form of generating functions for powers of second-order recurrence sequences.This investigation was completed by Stnica.Inspired by the recent work of Istva＇n about the non-closed generating functions of the products of the powers of the second-order sequences,the authors give several extensions of Istva＇n＇s results in this paper.
文摘Several kinds of stream ciphers—complementary sequences of period sequences,partial sum of period sequences,inverse order sequences and finitely generated sequences,arestudied by using techniques of generating functions.Their minimal polynomials,periods,as wellas generating functions are given.As to finitely generated sequences,the change of their linearcomplexity profiles as well as the relationship between the two generated sequences usder thecase in which the degree of connected polynomials are fixed,are discussed.
文摘We discuss three-dimensional uniform distribution and its property in a sphere;give a method of assessing the tactical and technical indices of cartridge ejection uniformity in some type of weapon systems. Meanwhile we obtain the test of generating function and the estimation of equivalent radius. The uniformity of distribution is tested and verified with ω2 test method on the basis of stochastic simulation example.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11965014 and 12061051)the National Science Foundation of Qinghai Province,China(Grant No.2021-ZJ-708)。
文摘This paper is concerned with construction of quantum fields presentation and generating functions of symplectic Schur functions and symplectic universal characters.The boson-fermion correspondence for these symmetric functions have been presented.In virtue of quantum fields,we derive a series of infinite order nonlinear integrable equations,namely,universal character hierarchy,symplectic KP hierarchy and symplectic universal character hierarchy,respectively.In addition,the solutions of these integrable systems have been discussed.
基金National Natural Science Foundation of China(No.51265025)
文摘In practical engineering,sometimes the probability density functions( PDFs) of stress and strength can not be exactly determined,or only limited experiment data are available. In these cases,the traditional stress-strength interference( SSI) model based on classical probabilistic approach can not be used to evaluate reliabilities of components. To solve this issue, the traditional universal generating function( UGF) is introduced and then it is extended to represent the discrete interval-valued random variable.Based on the extended UGF,an improved discrete interval-valued SSI model is proposed, which has higher calculation precision compared with the existing methods. Finally,an illustrative case is given to demonstrate the validity of the proposed model.
文摘In this paper explicit expressions and some recurrence relations are derived for marginal and joint moment generating functions of generalized order statistics from Erlang-truncated exponential distribution. The results for k-th record values and order statistics are deduced from the relations derived. Further, a characterizing result of this distribution on using the conditional expectation of function of generalized order statistics is discussed.
文摘Present paper deals a M/M/1:(∞;GD) queueing model with interdependent controllable arrival and service rates where- in customers arrive in the system according to poisson distribution with two different arrivals rates-slower and faster as per controllable arrival policy. Keeping in view the general trend of interdependent arrival and service processes, it is presumed that random variables of arrival and service processes follow a bivariate poisson distribution and the server provides his services under general discipline of service rule in an infinitely large waiting space. In this paper, our central attention is to explore the probability generating functions using Rouche’s theorem in both cases of slower and faster arrival rates of the queueing model taken into consideration;which may be helpful for mathematicians and researchers for establishing significant performance measures of the model. Moreover, for the purpose of high-lighting the application aspect of our investigated result, very recently Maurya [1] has derived successfully the expected busy periods of the server in both cases of slower and faster arrival rates, which have also been presented by the end of this paper.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.12461048 and 12061051)the Natural Science Foundation of Inner Mongolia Autonomous Region(Grant No.2023MS01003)+2 种基金the Program for Young Talents of Science and Technology in Universities of Inner Mongolia Autonomous Region(Grant No.NJYT23096)the financial support from the Program of China Scholarships Council(Grant No.202306810054)for one year study at the University of Leedsthe support of Professor Ke Wu and Professor Weizhong Zhao at Capital Normal University,China。
文摘We construct the quantum fields presentation of the generalized universal character and the generalized B-type universal character,and by acting the quantum fields presentations to the constant 1,the generating functions are derived.Furthermore,we introduce two integrable systems known as the generalized UC(GUC)hierarchy and the generalized Btype UC(GBUC)hierarchy satisfied by the generalized universal character and the generalized B-type universal character,respectively.Based on infinite sequences of complex numbers,we further establish the multiparameter generalized universal character and the multiparameter generalized B-type universal character,which have been proved to be solutions of the GUC hierarchy and the GBUC hierarchy,respectively.
基金supported by National Natural Science Foundation of China(Grant No:52477133)Science and Technology Project of China Southern Power Grid(Grant No.GDKJXM20231178(036100KC23110012)+1 种基金GDKJXM20240389(030000KC24040053))Sanya Yazhou Bay Science and Technology City(Grant No:SKJC-JYRC-2024-66).
文摘With the rapid development of large-scale regional interconnected power grids,the risk of cascading failures under extreme condi-tions,such as natural disasters and military strikes,has increased significantly.To enhance the response capability of power systems to extreme events,this study focuses on a method for generator coherency detection.To overcome the shortcomings of the traditional slow coherency method,this paper introduces a novel coherent group identification algorithm based on the theory of nonlinear dynam-ical systems.By analyzing the changing trend of the Euclidean norm of the state variable derivatives in the reduced system,the algorithm can accurately identify the magnitude of the disturbances.Based on the slow coherency methods,the algorithm can correctly recognize coherent generator groups by analyzing system characteristics under varying disturbance magnitudes.This improvement enhances the applicability and accuracy of the coherency detection algorithm under extreme conditions,providing support for emergency control and protection in the power system.Simulations and comparison analyses on IEEE 39-bus system are conducted to validate the accuracy and superiority of the proposed coherent generator group identification method under extreme conditions.
基金supported by the Foundation of Hunan Provincial Natural Science of China(13JJ6095,2015JJ2015)the Key Project of Science and Technology Program of Changsha,China(ZD1601010)
文摘A method for estimating the component reliability is proposed when the probability density functions of stress and strength can not be exactly determined. For two groups of finite experimental data about the stress and strength, an interval statistics method is introduced. The processed results are formulated as two interval-valued random variables and are graphically represented component reliability are proposed based on the by using two histograms. The lower and upper bounds of universal generating function method and are calculated by solving two discrete stress-strength interference models. The graphical calculations of the proposed reliability bounds are presented through a numerical example and the confidence of the proposed reliability bounds is discussed to demonstrate the validity of the proposed method. It is showed that the proposed reliability bounds can undoubtedly bracket the real reliability value. The proposed method extends the exciting universal generating function method and can give an interval estimation of component reliability in the case of lake of sufficient experimental data. An application example is given to illustrate the proposed method
文摘This work shows that each kind of Chebyshev polynomials may be calculated from a symbolic formula similar to the Lucas formula for Bernoulli polynomials. It exposes also a new approach for obtaining generating functions of them by operator calculus built from the derivative and the positional operators.
