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Subfield Codes of Linear Codes from Perfect Nonlinear Functions and Their Duals 认领 引用
1
作者 Dabin Zheng Xiaoqiang Wang +1 位作者 Yayao Li Mu Yuan 《Communications in Mathematical Research》 CSCD 2022年第2期157-183,共27页
Let Fpm be a finite field with pm elements,where p is an odd prime and m is a positive integer.Recently,[17]and[35]determined the weight distributions of subfield codes with the form C f={((T r(a f(x)+b x)+c)... Let Fpm be a finite field with pm elements,where p is an odd prime and m is a positive integer.Recently,[17]and[35]determined the weight distributions of subfield codes with the form C f={((T r(a f(x)+b x)+c)_(x∈Fpm),T r(a)):a,b∈Fpm,c∈Fp}for f(x)=x2 and f(x)=x p k+1,respectively,where Tr(⋅)is the trace function from Fpm to Fp,and k is a nonnegative integer.In this paper,we further investigate the subfield code C f for f(x)being a known perfect nonlinear function over Fpm and generalize some results in[17,35].The weight distributions of the constructed codes are determined by applying the theory of quadratic forms and the properties of perfect nonlinear functions over finite fields.In addition,the parameters of the duals of these codes are also determined.Several examples show that some of our codes and their duals have the best known parameters according to the code tables in[16].The duals of some proposed codes are optimal according to the Sphere Packing bound if p≥5. 展开更多
关键词 Subfield code perfect nonlinear function quadratic form weight distribution Sphere Packing bound
A large-range convergence iterative method for solving a nonlinear functional equation 认领 引用
2
作者 母丽华 沈继红 杜红 《Journal of Harbin Institute of Technology(New Series)》 EI CAS 2008年第5期631-634,共4页
The existence and representation of the exact solution are given for a nonlinear functional equation in the reproducing kernel space. For a numerical computation, we present a large-range convergence iterative method ... The existence and representation of the exact solution are given for a nonlinear functional equation in the reproducing kernel space. For a numerical computation, we present a large-range convergence iterative method for solving the nonlinear functional equation. In the iterative method, the convergent condition is simple and the convergence is irrespective to the choice of the initial function. It is worthy to note that the presented method can be generalized to solve other nonlinear operator equations. 展开更多
关键词 nonlinear functional equation nonlinear Voherra integral equation reproducing kernel
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SOME OSCILLATION CRITERIA FOR SECOND ORDER NONLINEAR FUNCTIONAL ORDINARY DIFFERENTIAL EQUATIONS 认领 引用
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作者 E.M.E.Zayed M.A.El-Moneam 《Acta Mathematica Scientia》 SCIE 2007年第3期602-610,共9页
The main objective of this article is to study the oscillatory behavior of the solutions of the following nonlinear functional differential equations（a（t）x＇（t））＇＋δ1p（t）x＇（t） ＋δ2q（t）f（x（g（t））） ... The main objective of this article is to study the oscillatory behavior of the solutions of the following nonlinear functional differential equations（a（t）x＇（t））＇＋δ1p（t）x＇（t） ＋δ2q（t）f（x（g（t））） = 0,for 0 ≤ to≤ t, where 51 = ：El and δ±1. The functions p,q,g ： [t0, ∞） → R, f ： R → are continuous, a（t） 〉 0,p（t） ≥0,q（t） 〉 0 for t ≥ to,lirn g（t） = ∞, and q is not identically zero on any subinterval of [to, ∞）. Moreover, the functions q（t）, g（t）, and a（t） are continuously differentiable. 展开更多
关键词 Oscillatory and nonoscillatory solutions nonlinear functional differential equations
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Massively parallel and universal approximation of nonlinear functions using diffractive processors 认领 引用 被引量：1
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作者 Md Sadman Sakib Rahman Yuhang Li +2 位作者 Xilin Yang Shiqi Chen Aydogan Ozcan 《eLight》 SCIE EI 2025年第1期343-366,共24页
Nonlinear computation is essential for a wide range of information processing tasks,yet implementing nonlinear functions using optical systems remains a challenge due to the weak and power-intensive nature of optical ... Nonlinear computation is essential for a wide range of information processing tasks,yet implementing nonlinear functions using optical systems remains a challenge due to the weak and power-intensive nature of optical nonlinearities.Overcoming this limitation without relying on nonlinear optical materials could unlock unprecedented opportunities for ultrafast and parallel optical computing systems.Here,we demonstrate that large-scale nonlinear computation can be performed using linear optics through optimized diffractive processors composed of passive phase-only surfaces.In this framework,the input variables of nonlinear functions are encoded into the phase of an optical wavefront—e.g.,via a spatial light modulator(SLM)—and transformed by an optimized diffractive structure with spatially varying point-spread functions to yield output intensities that approximate a large set of unique nonlinear functions–all in parallel.We provide proof establishing that this architecture serves as a universal function approximator for an arbitrary set of bandlimited nonlinear functions,also covering wavelength-multiplexed nonlinear functions as well as multi-variate and complex-valued functions that are all-optically cascadable.Our analysis also indicates the successful approximation of typical nonlinear activation functions commonly used in neural networks,including the sigmoid,tanh,ReLU(rectified linear unit),and softplus.We numerically demonstrate the parallel computation of one million distinct nonlinear functions,accurately executed at wavelength-scale spatial density at the output of a diffractive optical processor.Furthermore,we experimentally validated this framework using in situ optical learning and approximated 35 unique nonlinear functions in a single shot using a compact setup consisting of an SLM and an image sensor.These results establish diffractive optical processors as a scalable platform for massively parallel universal nonlinear function approximation,paving the way for new capabilities in analog optical computing based on linear materials. 展开更多
关键词 massively parallel computation information processing tasksyet linear optics nonlinear functions nonlinear computation universal approximation diffractive processors nonlinear optical materials
Approximate solutions and nonlinear scalarizations for set optimization with a co-radiant set 认领 引用
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作者 ZHANG Qi XU Yi-hong 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2026年第2期367-385,共19页
In normed linear spaces,by applying the Minkowski difference,the concepts of efficient solutions,weakly efficient solutions,proper efficient solutions and Henig efficient solutions are introduced for set optimization ... In normed linear spaces,by applying the Minkowski difference,the concepts of efficient solutions,weakly efficient solutions,proper efficient solutions and Henig efficient solutions are introduced for set optimization with respect to co-radiant sets,and the relationships among them is discussed.Optimality conditions for minimal solutions and strictly minimal solutions of scalar set optimization are established by using the generalized oriented distance functions,respectively.The relationship between the solutions of set optimization problem and the solutions of scalar problem is studied.Several examples are given to explain our result.Properties of Gerstewitz’s functions with respect to co-radiant sets are discussed,which are used to establish sufficient conditions for weakly efficient solutions of set optimization. 展开更多
关键词 set optimization nonlinear function approximate solution co-radiant set
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On the constructions of constant-composition codes from perfect nonlinear functions 认领 引用 被引量：1
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作者 LI Chao LI Qiang LING San 《Science in China(Series F)》 2009年第6期964-973,共10页
A new construction of constant-composition codes based on all known perfect nonlinear functions from Fqm to itself is presented,which provides a kind of unified constructions of constant-composition codes based on all... A new construction of constant-composition codes based on all known perfect nonlinear functions from Fqm to itself is presented,which provides a kind of unified constructions of constant-composition codes based on all known perfect nonlinear functions from F qm to itself.It is proved that the new constant-composition codes are optimal with respect to the Luo-Fu-Vinck-Chen bound,when m is an odd positive integer greater than 1.Finally,we point out that two constructions of constant-composition codes,proposed by Ding Cunsheng et al.in 2005,are equivalent to two special types of the new constant-composition codes. 展开更多
关键词 constant-composition codes perfect nonlinear functions quadratic forms
Fuzzy Prescribed-Time Control for Uncertain Nonlinear Pure Feedback Systems 认领 引用
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作者 Qidong Li Changchun Hua Kuo Li 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2025年第10期2162-2164,共3页
Dear Editor,This letter investigates the fuzzy prescribed-time control(PTC)problem for a class of uncertain pure feedback nonlinear systems.Firstly,a novel prescribed-time stability lemma is introduced,which plays a c... Dear Editor,This letter investigates the fuzzy prescribed-time control(PTC)problem for a class of uncertain pure feedback nonlinear systems.Firstly,a novel prescribed-time stability lemma is introduced,which plays a critical role in stability analysis.Unlike existing PTC algorithms,where the nonlinear functions are typically known or satisfy a linear growth condition,our approach does not require such assumptions.To address these unknown factors,fuzzy logic systems(FLSs)are employed.Based on the new prescribed-time stability lemma,it is proven that the controller and all system states converge to the origin within the prescribed time and remain there.Finally,the effectiveness of the proposed algorithm is validated through a simulation example. 展开更多
关键词 pure feedback nonlinear systemsfirstlya nonlinear functions pure feedback systems stability analysis logic systems flss prescribed time control nonlinear systems stability analysisunlike
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Dynamics Analysis of Active Variable Stiffness Vibration Isolator for Whole-Spacecraft Systems Based on Nonlinear Output Frequency Response Functions 认领 引用 被引量：6
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作者 Kefan Xu Yewei Zhang +2 位作者 Yunpeng Zhu Jian Zang Liqun Chen 《Acta Mechanica Solida Sinica》 SCIE EI CSCD 2020年第6期731-743,共13页
In order to improve the harsh dynamic environment experienced by heavy rockets during different external excitations,this study presents a novel active variable stiffness vibration isolator(AVS-VI)used as the vibratio... In order to improve the harsh dynamic environment experienced by heavy rockets during different external excitations,this study presents a novel active variable stiffness vibration isolator(AVS-VI)used as the vibration isolation device to reduce excessive vibration of the whole-spacecraft isolation system.The AVS-VI is composed of horizontal stiffness spring,positive stiffness spring,parallelogram linkage mechanism,piezoelectric actuator,acceleration sensor,viscoelastic damping,and PID active controller.Based on the AVS-VI,the generalized vibration transmissibility determined by the nonlinear output frequency response functions and the energy absorption rate is applied to analyze the isolation performance of the whole-spacecraft system with AVS-VI.The AVS-VI can conduct adaptive vibration suppression with variable stiffness to the whole-spacecraft system,and the analysis results indicate that the AVS-VI is efTective in reducing the extravagant vibration of the whole-spacecraft system,where the vibration isolation is decreased up to above 65%under different acceleration excitations.Finally,different parameters of AVS-VI are considered to optimize the whole-spacecraft system based on the generalized vibration transmissibility and the energy absorption rate. 展开更多
关键词 Vibration isolation Active variable stiffness vibration isolator Nonlinear output frequency response functions(NOFRFs) Transmissibility
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The nonlinear Wannier function in square Krnig-Penney model 认领 引用 被引量：1
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作者 薛锐 梁兆新 李卫东 《Chinese Physics B》 SCIE EI CAS 2009年第10期4130-4135,共6页
The nonlinear Wannier functions in square Kronig-Penney potential are investigated with the help of a set of exact nonlinear Bloch solutions. The nonlinear interaction makes the Wannier functions fall off as non-expon... The nonlinear Wannier functions in square Kronig-Penney potential are investigated with the help of a set of exact nonlinear Bloch solutions. The nonlinear interaction makes the Wannier functions fall off as non-exponential law with distance and enhances the tunneling coupling between the neighbor sites. 展开更多
关键词 exact nonlinear Bloch solution nonlinear Wannier function
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A DUAL-RELAX PENALTY FUNCTION APPROACH FOR SOLVING NONLINEAR BILEVEL PROGRAMMING WITH LINEAR LOWER LEVEL PROBLEM 认领 引用 被引量：7
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作者 万仲平 王广民 吕一兵 《Acta Mathematica Scientia》 SCIE CSCD 2011年第2期652-660,共9页
The penalty function method, presented many years ago, is an important nu- merical method for the mathematical programming problems. In this article, we propose a dual-relax penalty function approach, which is signifi... The penalty function method, presented many years ago, is an important nu- merical method for the mathematical programming problems. In this article, we propose a dual-relax penalty function approach, which is significantly different from penalty func- tion approach existing for solving the bilevel programming, to solve the nonlinear bilevel programming with linear lower level problem. Our algorithm will redound to the error analysis for computing an approximate solution to the bilevel programming. The error estimate is obtained among the optimal objective function value of the dual-relax penalty problem and of the original bilevel programming problem. An example is illustrated to show the feasibility of the proposed approach. 展开更多
关键词 Nonlinear bilevel programming penalty function approach dual-relax strategy
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Properties of Certain Nonlinear Integral Operator Associated with Janowski Starlike and Convex Functions 认领 引用 被引量：1
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作者 Liangpeng XIONG 《Journal of Mathematical Research with Applications》 CSCD 2016年第4期432-440,共9页
In this paper, we consider a general nonlinear integral operator Hαi, βi （ f1,..., fn ; g1,..., gn）（z）. Some results including coefficient problems, univalency condition and radius of convexity for this integral... In this paper, we consider a general nonlinear integral operator Hαi, βi （ f1,..., fn ; g1,..., gn）（z）. Some results including coefficient problems, univalency condition and radius of convexity for this integral operator are given. Furthermore, we discuss the mapping properties between Hαi,βi （f1 , fn, ; g1,..., gn）（z） and subclasses of analytic functions with bounded boundary rotation. The same subjects for some corresponding classes are shown upon specializing the parameters in our main results. 展开更多
关键词 analytic functions Janowski functions nonlinear integral operators functions with bounded boundary rotation subordination
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Nonlinear Oscillation Analysis by an Orthogonal Function Method 认领 引用
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作者 孙丕忠 唐乾刚 孙世贤 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1995年第7期695-704,共10页
In this paper an orthogonal function method is presented based on the idea to suppose perioche sohuion with the method of harmonie balance The displaeement is expressed in the form of trigonometric fumctions a group o... In this paper an orthogonal function method is presented based on the idea to suppose perioche sohuion with the method of harmonie balance The displaeement is expressed in the form of trigonometric fumctions a group of simplified digenequationsare obtained by the use of orthogonarity of trigonometric fumetions and linear mondes The method overcomes the diffieulty of a drifi term existing in systems with quadratic nonlinearities .The ealeulation examples show that the method has thd advantages of high caleulation preeision high convergenee speed and littld ealeulation work 展开更多
关键词 orthogonal function method nonlinearity oseillation characteristies eigenequations.
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Joint probability density function of the stochastic responses of nonlinear structures 认领 引用 被引量：3
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作者 陈建兵 李杰 《Earthquake Engineering and Engineering Vibration》 SCIE EI 2007年第1期35-47,共13页
The joint probability density fimction （PDF） of different structural responses is a very important topic in the stochastic response analysis of nonlinear structures. In this paper, the probability density evolution ... The joint probability density fimction （PDF） of different structural responses is a very important topic in the stochastic response analysis of nonlinear structures. In this paper, the probability density evolution method, which is successfully developed to capture the instantaneous PDF of an arbitrary single response of interest, is extended to evaluate the joint PDF of any two responses. A two-dimensional partial differential equation in terms of the joint PDF is established. The strategy of selecting representative points via the number theoretical method and sieved by a hyper-ellipsoid is outlined. A two-dimensional difference scheme is developed. The free vibration of an SDOF system is examined to verify the proposed method, and a flame structure exhibiting hysteresis subjected to stochastic ground motion is investigated. It is pointed out that the correlation of different responses results from the fact that randomness of different responses comes from the same set of basic random parameters involved. In other words, the essence of the probabilistic correlation is a physical correlation. 展开更多
关键词 stochastic response nonlinearity joint probability density function probability density evolution method number theoretical method finite difference method
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Wave functions of a new kind of nonlinear single-mode squeezed state 认领 引用
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作者 范洪义 笪诚 陈俊华 《Chinese Physics B》 SCIE EI CAS CSCD 2014年第12期34-37,共4页
We explore the theoretical possibility of extending the usual squeezed state to those produced by nonlinear singlemode squeezing operators. We derive the wave functions of exp[-（ig/2）（（1-X2）1/2P ＋ P（1-X2）1/2）... We explore the theoretical possibility of extending the usual squeezed state to those produced by nonlinear singlemode squeezing operators. We derive the wave functions of exp[-（ig/2）（（1-X2）1/2P ＋ P（1-X2）1/2）]｜0 in the coordinate representation. A new operator＇s disentangling formula is derived as a by-product. 展开更多
关键词 wave functions nonlinear single-mode squeezed states coordinate representation disentangling formula
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Filter-sequence of quadratic programming method with nonlinear complementarity problem function 认领 引用
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作者 金中 濮定国 +1 位作者 张宇 蔡力 《Journal of Shanghai University(English Edition)》 2008年第2期97-101,共5页
A mechanism for proving global convergence in filter-SQP （sequence of quadratic programming） method with the nonlinear complementarity problem （NCP） function is described for constrained nonlinear optimization pro... A mechanism for proving global convergence in filter-SQP （sequence of quadratic programming） method with the nonlinear complementarity problem （NCP） function is described for constrained nonlinear optimization problem.We introduce an NCP function into the filter and construct a new SQP-filter algorithm.Such methods are characterized by their use of the dominance concept of multi-objective optimization,instead of a penalty parameter whose adjustment can be problematic.We prove that the algorithm has global convergence and superlinear convergence rates under some mild conditions. 展开更多
关键词 nonlinear complementarity problem （NCP） function filter sequence of quadratic programming （SQP） globalconvergence.
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EXACT AUGMENTED LAGRANGIAN FUNCTION FOR NONLINEAR PROGRAMMING PROBLEMS WITH INEQUALITY CONSTRAINTS 认领 引用
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作者 杜学武 张连生 +1 位作者 尚有林 李铭明 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2005年第12期1649-1656,共8页
An exact augmented Lagrangian function for the nonlinear nonconvex programming problems with inequality constraints was discussed. Under suitable hypotheses, the relationship was established between the local unconstr... An exact augmented Lagrangian function for the nonlinear nonconvex programming problems with inequality constraints was discussed. Under suitable hypotheses, the relationship was established between the local unconstrained minimizers of the augmented Lagrangian function on the space of problem variables and the local minimizers of the original constrained problem. Furthermore, under some assumptions, the relationship was also established between the global solutions of the augmented Lagrangian function on some compact subset of the space of problem variables and the global solutions of the constrained problem. Therefore, f^om the theoretical point of view, a solution of the inequality constrained problem and the corresponding values of the Lagrange multipliers can be found by the well-known method of multipliers which resort to the unconstrained minimization of the augmented Lagrangian function presented. 展开更多
关键词 local minimizer global minimizer nonlinear programming exact penalty function augmented Lagrangian function
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Tool Condition Monitoring Based on Nonlinear Output Frequency Response Functions and Multivariate Control Chart 认领 引用
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作者 Yufei Gui Ziqiang Lang +1 位作者 Zepeng Liu Hatim Laalej 《Journal of Dynamics, Monitoring and Diagnostics》 2023年第4期243-251,共9页
Tool condition monitoring(TCM)is a key technology for intelligent manufacturing.The objective is to monitor the tool operation status and detect tool breakage so that the tool can be changed in time to avoid significa... Tool condition monitoring(TCM)is a key technology for intelligent manufacturing.The objective is to monitor the tool operation status and detect tool breakage so that the tool can be changed in time to avoid significant damage to workpieces and reduce manufacturing costs.Recently,an innovative TCM approach based on sensor data modelling and model frequency analysis has been proposed.Different from traditional signal feature-based monitoring,the data from sensors are utilized to build a dynamic process model.Then,the nonlinear output frequency response functions,a concept which extends the linear system frequency response function to the nonlinear case,over the frequency range of the tooth passing frequency of the machining process are extracted to reveal tool health conditions.In order to extend the novel sensor data modelling and model frequency analysis to unsupervised condition monitoring of cutting tools,in the present study,a multivariate control chart is proposed for TCM based on the frequency domain properties of machining processes derived from the innovative sensor data modelling and model frequency analysis.The feature dimension is reduced by principal component analysis first.Then the moving average strategy is exploited to generate monitoring variables and overcome the effects of noises.The milling experiments of titanium alloys are conducted to verify the effectiveness of the proposed approach in detecting excessive flank wear of solid carbide end mills.The results demonstrate the advantages of the new approach over conventional TCM techniques and its potential in industrial applications. 展开更多
关键词 intelligent manufacturing multivariate control chart Nonlinear Autoregressive with eXogenous Input modelling Nonlinear Output Frequency Response Functions tool condition monitoring
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EXISTENCE AND UNIQUENESS OF THE SOLUTION OF A CLASS OF NONLINEAR FUNCTIONAL DIFFERENTIAL EQUATIONS 认领 引用
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作者 Y.A.Fiagbedzi M.A.El-Gebeily 《Annals of Differential Equations》 2000年第4期381-390,共10页
The unicity of the solution, if any, of a class of nonlinear functional differential equations (fde) is established with the help of a transformation. The transformation reduces the fde to an ordinary differential equ... The unicity of the solution, if any, of a class of nonlinear functional differential equations (fde) is established with the help of a transformation. The transformation reduces the fde to an ordinary differential equation. Existence of the solution is established by means of a fixed point theorem. 展开更多
关键词 Golomb's sequence nonlinear functional differential equation transformation ordinary differential equation
CONSERVATIVE ESTIMATING FUNCTION IN THE NONLINEAR REGRESSION MODEL WITH AGGREGATED DATA 认领 引用 被引量：1
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作者 林路 《Acta Mathematica Scientia》 SCIE 2000年第3期335-340,共6页
The purpose of this paper is to study the theory of conservative estimating functions in nonlinear regression model with aggregated data. In this model, a quasi-score function with aggregated data is defined. When thi... The purpose of this paper is to study the theory of conservative estimating functions in nonlinear regression model with aggregated data. In this model, a quasi-score function with aggregated data is defined. When this function happens to be conservative, it is projection of the true score function onto a class of estimation functions. By constructing, the potential function for the projected score with aggregated data is obtained, which have some properties of log-likelihood function. 展开更多
关键词 nonlinear regression model with aggregated data quasi-score function conservative vector field potential function
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A STUDY OF THE CONSTRUCTION OF LYAPUNOV FUNCTION FOR A CLASS OF FOURTH ORDER NONLINEAR SYSTEMS 认领 引用 被引量：1
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作者 梁在中 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1995年第2期195-202,共8页
In the paper Lyapunov function for a fourth order linear system is given and stability of the trivial solutions to a class of.fourth order nonlinear systems is studied
关键词 nonlinear. stability. Lyapunov function
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