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THE ASYMPTOTIC BEHAVIOR AND OSCILLATION FOR A CLASS OF THIRD-ORDER NONLINEAR DELAY DYNAMIC EQUATIONS
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作者 黄先勇 邓勋环 王其如 《Acta Mathematica Scientia》 SCIE CSCD 2024年第3期925-946,共22页
In this paper,we consider a class of third-order nonlinear delay dynamic equations.First,we establish a Kiguradze-type lemma and some useful estimates.Second,we give a sufficient and necessary condition for the existe... In this paper,we consider a class of third-order nonlinear delay dynamic equations.First,we establish a Kiguradze-type lemma and some useful estimates.Second,we give a sufficient and necessary condition for the existence of eventually positive solutions having upper bounds and tending to zero.Third,we obtain new oscillation criteria by employing the Potzsche chain rule.Then,using the generalized Riccati transformation technique and averaging method,we establish the Philos-type oscillation criteria.Surprisingly,the integral value of the Philos-type oscillation criteria,which guarantees that all unbounded solutions oscillate,is greater than θ_(4)(t_(1),T).The results of Theorem 3.5 and Remark 3.6 are novel.Finally,we offer four examples to illustrate our results. 展开更多
关键词 nonlinear delay dynamic equations NONOSCILLATION asymptotic behavior Philostype oscillation criteria generalized Riccati transformation
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Reinforcement learning based adaptive control for uncertain mechanical systems with asymptotic tracking
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作者 Xiang-long Liang Zhi-kai Yao +1 位作者 Yao-wen Ge Jian-yong Yao 《Defence Technology(防务技术)》 SCIE EI CAS CSCD 2024年第4期19-28,共10页
This paper mainly focuses on the development of a learning-based controller for a class of uncertain mechanical systems modeled by the Euler-Lagrange formulation.The considered system can depict the behavior of a larg... This paper mainly focuses on the development of a learning-based controller for a class of uncertain mechanical systems modeled by the Euler-Lagrange formulation.The considered system can depict the behavior of a large class of engineering systems,such as vehicular systems,robot manipulators and satellites.All these systems are often characterized by highly nonlinear characteristics,heavy modeling uncertainties and unknown perturbations,therefore,accurate-model-based nonlinear control approaches become unavailable.Motivated by the challenge,a reinforcement learning(RL)adaptive control methodology based on the actor-critic framework is investigated to compensate the uncertain mechanical dynamics.The approximation inaccuracies caused by RL and the exogenous unknown disturbances are circumvented via a continuous robust integral of the sign of the error(RISE)control approach.Different from a classical RISE control law,a tanh(·)function is utilized instead of a sign(·)function to acquire a more smooth control signal.The developed controller requires very little prior knowledge of the dynamic model,is robust to unknown dynamics and exogenous disturbances,and can achieve asymptotic output tracking.Eventually,co-simulations through ADAMS and MATLAB/Simulink on a three degrees-of-freedom(3-DOF)manipulator and experiments on a real-time electromechanical servo system are performed to verify the performance of the proposed approach. 展开更多
关键词 Adaptive control Reinforcement learning Uncertain mechanical systems asymptotic tracking
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Modeling Method of C/C-ZrC Composites and Prediction of Equivalent Thermal Conductivity Tensor Based on Asymptotic Homogenization
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作者 Junpeng Lyu Hai Mei +2 位作者 Liping Zu Lisheng Liu Liangliang Chu 《Computer Modeling in Engineering & Sciences》 SCIE EI 2024年第1期391-410,共20页
This article proposes a modeling method for C/C-ZrC composite materials.According to the superposition of Gaussian random field,the original gray model is obtained,and the threshold segmentation method is used to gene... This article proposes a modeling method for C/C-ZrC composite materials.According to the superposition of Gaussian random field,the original gray model is obtained,and the threshold segmentation method is used to generate the C-ZrC inclusion model.Finally,the fiber structure is added to construct the microstructure of the three-phase plain weave composite.The reconstructed inclusions can meet the randomness of the shape and have a uniform distribution.Using an algorithm based on asymptotic homogenization and finite element method,the equivalent thermal conductivity prediction of the microstructure finite element model was carried out,and the influence of component volume fraction on material thermal properties was explored.The sensitivity of model parameters was studied,including the size,mesh sensitivity,Gaussian complexity,and correlation length of the RVE model,and the optimal calculation model was selected.The results indicate that the volume fraction of the inclusion phase has a significant impact on the equivalent thermal conductivity of the material.As the volume fraction of carbon fiber and ZrC increases,the equivalent thermal conductivity tensor gradually decreases.This model can be used to explore the impact of materialmicrostructure on the results,and numerical simulations have studied the relationship between structure and performance,providing the possibility of designing microstructure based on performance. 展开更多
关键词 3D reconstruction randomheterogeneous media microstructure asymptotic homogenization effective properties
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Asymptotic normality of error density estimator in stationary and explosive autoregressive models
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作者 WU Shi-peng YANG Wen-zhi +1 位作者 GAO Min HU Shu-he 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2024年第1期140-158,共19页
In this paper,we consider the limit distribution of the error density function estima-tor in the rst-order autoregressive models with negatively associated and positively associated random errors.Under mild regularity... In this paper,we consider the limit distribution of the error density function estima-tor in the rst-order autoregressive models with negatively associated and positively associated random errors.Under mild regularity assumptions,some asymptotic normality results of the residual density estimator are obtained when the autoregressive models are stationary process and explosive process.In order to illustrate these results,some simulations such as con dence intervals and mean integrated square errors are provided in this paper.It shows that the residual density estimator can replace the density\estimator"which contains errors. 展开更多
关键词 explosive autoregressive models residual density estimator asymptotic distribution association sequence
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Multiple Soliton Asymptotics in a Spin-1 Bose–Einstein Condensate
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作者 Zhong-Zhou Lan 《Chinese Physics Letters》 SCIE EI CAS CSCD 2024年第9期15-22,共8页
Spinor Bose–Einstein condensates(BECs)are formed when atoms in the multi-component BECs possess single hyperfine spin states but retain internal spin degrees of freedom.This study concentrates on a(1+1)-dimensional t... Spinor Bose–Einstein condensates(BECs)are formed when atoms in the multi-component BECs possess single hyperfine spin states but retain internal spin degrees of freedom.This study concentrates on a(1+1)-dimensional three-couple Gross–Pitaevskii system to depict the macroscopic spinor BEC waves within the meanfield approximation.Regarding the distribution of the atoms corresponding to the three vertical spin projections,a known binary Darboux transformation is utilized to derive the𝑁matter-wave soliton solutions and triple-pole matter-wave soliton solutions on the zero background,where𝑁is a positive integer.For those multiple matterwave solitons,the asymptotic analysis is performed to obtain the algebraic expressions of the soliton components in the𝑁matter-wave solitons and triple-pole matter-wave solitons.The asymptotic results indicate that the matter-wave solitons in the spinor BECs possess the property of maintaining their energy content and coherence during the propagation and interactions.Particularly,in the𝑁matter-wave solitons,each soliton component contributes to the phase shifts of the other soliton components;and in the triple-pole matter-wave solitons,stable attractive forces exist between the different matter-wave soliton components.Those multiple matter-wave solitons are graphically illustrated through three-dimensional plots,density plot and contour plot,which are consistent with the asymptotic analysis results.The present analysis may provide the explanations for the complex natural mechanisms of the matter waves in the spinor BECs,and may have potential applications in designs of atom lasers,atom interferometry and coherent atom transport. 展开更多
关键词 SOLITON SOLITONS asymptotic
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An Arbitrarily High Order and Asymptotic Preserving Kinetic Scheme in Compressible Fluid Dynamic
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作者 Remi Abgrall Fatemeh Nassajian Mojarrad 《Communications on Applied Mathematics and Computation》 EI 2024年第2期963-991,共29页
We present a class of arbitrarily high order fully explicit kinetic numerical methods in compressible fluid dynamics,both in time and space,which include the relaxation schemes by Jin and Xin.These methods can use the... We present a class of arbitrarily high order fully explicit kinetic numerical methods in compressible fluid dynamics,both in time and space,which include the relaxation schemes by Jin and Xin.These methods can use the CFL number larger or equal to unity on regular Cartesian meshes for the multi-dimensional case.These kinetic models depend on a small parameter that can be seen as a"Knudsen"number.The method is asymptotic preserving in this Knudsen number.Also,the computational costs of the method are of the same order of a fully explicit scheme.This work is the extension of Abgrall et al.(2022)[3]to multidimensional systems.We have assessed our method on several problems for two-dimensional scalar problems and Euler equations and the scheme has proven to be robust and to achieve the theoretically predicted high order of accuracy on smooth solutions. 展开更多
关键词 Kinetic scheme Compressible fluid dynamics High order methods Explicit schemes asymptotic preserving Defect correction method
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Enhanced Differentiable Architecture Search Based on Asymptotic Regularization
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作者 Cong Jin Jinjie Huang +1 位作者 Yuanjian Chen Yuqing Gong 《Computers, Materials & Continua》 SCIE EI 2024年第2期1547-1568,共22页
In differentiable search architecture search methods,a more efficient search space design can significantly improve the performance of the searched architecture,thus requiring people to carefully define the search spa... In differentiable search architecture search methods,a more efficient search space design can significantly improve the performance of the searched architecture,thus requiring people to carefully define the search space with different complexity according to various operations.Meanwhile rationalizing the search strategies to explore the well-defined search space will further improve the speed and efficiency of architecture search.With this in mind,we propose a faster and more efficient differentiable architecture search method,AllegroNAS.Firstly,we introduce a more efficient search space enriched by the introduction of two redefined convolution modules.Secondly,we utilize a more efficient architectural parameter regularization method,mitigating the overfitting problem during the search process and reducing the error brought about by gradient approximation.Meanwhile,we introduce a natural exponential cosine annealing method to make the learning rate of the neural network training process more suitable for the search procedure.Moreover,group convolution and data augmentation are employed to reduce the computational cost.Finally,through extensive experiments on several public datasets,we demonstrate that our method can more swiftly search for better-performing neural network architectures in a more efficient search space,thus validating the effectiveness of our approach. 展开更多
关键词 Differentiable architecture search allegro search space asymptotic regularization natural exponential cosine annealing
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THE LOGARITHMIC SOBOLEV INEQUALITY FOR A SUBMANIFOLD IN MANIFOLDS WITH ASYMPTOTICALLY NONNEGATIVE SECTIONAL CURVATURE
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作者 东瑜昕 林和子 陆琳根 《Acta Mathematica Scientia》 SCIE CSCD 2024年第1期189-194,共6页
In this note,we prove a logarithmic Sobolev inequality which holds for compact submanifolds without a boundary in manifolds with asymptotically nonnegative sectional curvature.Like the Michale-Simon Sobolev inequality... In this note,we prove a logarithmic Sobolev inequality which holds for compact submanifolds without a boundary in manifolds with asymptotically nonnegative sectional curvature.Like the Michale-Simon Sobolev inequality,this inequality contains a term involving the mean curvature. 展开更多
关键词 asymptotically nonnegative sectional curvature logarithmic Sobolev inequality ABP method
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Exact Tail Asymptotics for a Queueing System with a Retrial Orbit and Batch Service
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作者 Huijun Lu 《Applied Mathematics》 2024年第6期406-420,共15页
This paper discusses a queueing system with a retrial orbit and batch service, in which the quantity of customers’ rooms in the queue is finite and the space of retrial orbit is infinite. When the server starts servi... This paper discusses a queueing system with a retrial orbit and batch service, in which the quantity of customers’ rooms in the queue is finite and the space of retrial orbit is infinite. When the server starts serving, it serves all customers in the queue in a single batch, which is the so-called batch service. If a new customer or a retrial customer finds all the customers’ rooms are occupied, he will decide whether or not to join the retrial orbit. By using the censoring technique and the matrix analysis method, we first obtain the decay function of the stationary distribution for the quantity of customers in the retrial orbit and the quantity of customers in the queue. Then based on the form of decay rate function and the Karamata Tauberian theorem, we finally get the exact tail asymptotics of the stationary distribution. 展开更多
关键词 Exact Tail asymptotics Batch Service Censoring Technique Matrix Analysis Method Karamata Tauberian Theorem
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Asymptotic Dynamics of a Single-species Model with Resource-dependent Dispersal in One Dimension
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作者 Huang Yun Zhang Dawei 《数学理论与应用》 2024年第3期11-24,共14页
In this paper,we study the asymptotic dynamics of a single-species model with resource-dependent dispersal in one dimension.To overcome the analytical difficulties brought by the resource-dependent dispersal,we use th... In this paper,we study the asymptotic dynamics of a single-species model with resource-dependent dispersal in one dimension.To overcome the analytical difficulties brought by the resource-dependent dispersal,we use the idea of changing variables to transform the model into a uniform dispersal one.Then the existence and uniqueness of positive stationary solution to the model can be verified by the squeezing argument,where the solution plays a crucial role in later analyses.Moreover,the asymptotic behavior of solutions to the model is obtained by the upper-lower solutions method.The result indicates that the solutions of the model converge to the corresponding positive stationary solution locally uniformly in one dimension as time goes to infinity. 展开更多
关键词 asymptotic dynamics Resource-dependent dispersal Stationary solution Upper-lower solutions method
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Rectal Cancer Stages T2 and T3 Identification Based on Asymptotic Hybrid Feature Maps
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作者 Shujing Sun Jiale Wu +4 位作者 Jian Yao Yang Cheng Xin Zhang Zhihua Lu Pengjiang Qian 《Computer Modeling in Engineering & Sciences》 SCIE EI 2023年第10期923-938,共16页
Many existing intelligent recognition technologies require huge datasets for model learning.However,it is not easy to collect rectal cancer images,so the performance is usually low with limited training samples.In add... Many existing intelligent recognition technologies require huge datasets for model learning.However,it is not easy to collect rectal cancer images,so the performance is usually low with limited training samples.In addition,traditional rectal cancer staging is time-consuming,error-prone,and susceptible to physicians’subjective awareness as well as professional expertise.To settle these deficiencies,we propose a novel deep-learning model to classify the rectal cancer stages of T2 and T3.First,a novel deep learning model(RectalNet)is constructed based on residual learning,which combines the squeeze-excitation with the asymptotic output layer and new cross-convolution layer links in the residual block group.Furthermore,a two-stage data augmentation is designed to increase the number of images and reduce deep learning’s dependence on the volume of data.The experiment results demonstrate that the proposed method is superior to many existing ones,with an overall accuracy of 0.8583.Oppositely,other traditional techniques,such as VGG16,DenseNet121,EL,and DERNet,have an average accuracy of 0.6981,0.7032,0.7500,and 0.7685,respectively. 展开更多
关键词 Rectal cancer staging T2WI images data expansion asymptotic output layer
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Distributed Adaptive Asymptotic Tracking of 2-D Vehicular Platoon Systems With Actuator Faults and Spacing Constraints
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作者 Jiayi Lei Yuan-Xin Li Shaocheng Tong 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2023年第5期1352-1354,共3页
Dear Editor,This letter investigates the adaptive asymptotic tracking slidingmode control for nonlinear 2-D vehicular platoon systems subject to actuator faults.Firstly,by using the Nussbaum function,the disadvantageo... Dear Editor,This letter investigates the adaptive asymptotic tracking slidingmode control for nonlinear 2-D vehicular platoon systems subject to actuator faults.Firstly,by using the Nussbaum function,the disadvantageous factors brought by the unknown direction actuator faults can be attenuated. 展开更多
关键词 asymptotic asymptotic LETTER
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ASYMPTOTICAL STABILITY OF NEUTRAL REACTION-DIFFUSION EQUATIONS WITH PCAS AND THEIR FINITE ELEMENT METHODS
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作者 韩豪 张诚坚 《Acta Mathematica Scientia》 SCIE CSCD 2023年第4期1865-1880,共16页
This paper focuses on the analytical and numerical asymptotical stability of neutral reaction-diffusion equations with piecewise continuous arguments.First,for the analytical solutions of the equations,we derive their... This paper focuses on the analytical and numerical asymptotical stability of neutral reaction-diffusion equations with piecewise continuous arguments.First,for the analytical solutions of the equations,we derive their expressions and asymptotical stability criteria.Second,for the semi-discrete and one-parameter fully-discrete finite element methods solving the above equations,we work out the sufficient conditions for assuring that the finite element solutions are asymptotically stable.Finally,with a typical example with numerical experiments,we illustrate the applicability of the obtained theoretical results. 展开更多
关键词 neutral reaction-diffusion equations piecewise continuous arguments asymptotical stability finite element methods numerical experiment
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The Stochastic Asymptotic Stability Analysis in Two Species Lotka-Volterra Model
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作者 Yuqin Li Yuehua He 《Applied Mathematics》 2023年第7期450-459,共10页
The asymptotic stability of two species stochastic Lotka-Volterra model is explored in this paper. Firstly, the Lotka-Volterra model with random parameter is built and reduced into the equivalent deterministic system ... The asymptotic stability of two species stochastic Lotka-Volterra model is explored in this paper. Firstly, the Lotka-Volterra model with random parameter is built and reduced into the equivalent deterministic system by orthogonal polynomial approximation. Then, the linear stability theory and Routh-Hurwitz criterion for nonlinear deterministic systems are applied to the equivalent one. At last, at the aid of Lyapunov second method, we obtain that as the random intensity or statistical parameter of random variable is changed, the stability about stochastic Lotka-Volterra model is different from the deterministic system. 展开更多
关键词 asymptotic Stability Stochastic Lotka-Volterra Model Lyapunov Method
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Asymptotic Consistency of the James-Stein Shrinkage Estimator
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作者 Alex Samuel Mungo Victor Mooto Nawa 《Open Journal of Statistics》 2023年第6期872-892,共21页
The study explores the asymptotic consistency of the James-Stein shrinkage estimator obtained by shrinking a maximum likelihood estimator. We use Hansen’s approach to show that the James-Stein shrinkage estimator con... The study explores the asymptotic consistency of the James-Stein shrinkage estimator obtained by shrinking a maximum likelihood estimator. We use Hansen’s approach to show that the James-Stein shrinkage estimator converges asymptotically to some multivariate normal distribution with shrinkage effect values. We establish that the rate of convergence is of order  and rate , hence the James-Stein shrinkage estimator is -consistent. Then visualise its consistency by studying the asymptotic behaviour using simulating plots in R for the mean squared error of the maximum likelihood estimator and the shrinkage estimator. The latter graphically shows lower mean squared error as compared to that of the maximum likelihood estimator. 展开更多
关键词 asymptotic CONSISTENCY CONVERGENCE EFFICIENCY Mean Squared Error SHRINKAGE
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Zeno’s Paradoxes and Lie Tzu’s Dichotomic Wisdom Explained with Alpha Beta (αβ) Asymptotic Nonlinear Math (Including One Example on Second Order Nonlinear Phenomena)
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作者 Ralph W. Lai Melisa W. Lai-Becker Evgenios Agathokleous 《Journal of Applied Mathematics and Physics》 2023年第5期1209-1249,共41页
Zeno’s paradoxes are a set of philosophical problems that were first introduced by the ancient Greek philosopher Zeno of Elea. Here is the first attempt to use asymptotic approach and nonlinear concepts to address th... Zeno’s paradoxes are a set of philosophical problems that were first introduced by the ancient Greek philosopher Zeno of Elea. Here is the first attempt to use asymptotic approach and nonlinear concepts to address the paradoxes. Among the paradoxes, two of the most famous ones are Zeno’s Room Walk and Zeno’s Achilles. Lie Tsu’s pole halving dichotomy is also discussed in relation to these paradoxes. These paradoxes are first-order nonlinear phenomena, and we expressed them with the concepts of linear and nonlinear variables. In the new nonlinear concepts, variables are classified as either linear or nonlinear. Changes in linear variables are simple changes, while changes in nonlinear variables are nonlinear changes relative to their asymptotes. Continuous asymptotic curves are used to describe and derive the equations for expressing the relationship between two variables. For example, in Zeno’s Room Walk, the equations and curves for a person to walk from the initial wall towards the other wall are different from the equations and curves for a person to walk from the other wall towards the initial wall. One walk has a convex asymptotic curve with a nonlinear equation having two asymptotes, while the other walk has a concave asymptotic curve with a nonlinear equation having a finite starting number and a bottom asymptote. Interestingly, they have the same straight-line expression in a proportionality graph. The Appendix of this discussion includes an example of a second-order nonlinear phenomenon. . 展开更多
关键词 DICHOTOMY asymptotic Concave and Convex Curve Upper and Bottom As-ymptote Cumulative and Demulative Numbers (Opposite to Cumulative Numbers) Coefficient of Determination Skewed Bell Sigmoid Curve
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On the Asymptotic Stability of Discrete Crocodilians Model
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作者 Kaori Saito Yoshihiro Hamaya 《Advances in Pure Mathematics》 2023年第5期211-225,共15页
The sex ratio of crocodiles is strongly biased towards females, often as high as 10 females to 1 male. In crocodilians, the temperature of egg incubation is the environmental factor determining sex. If the temperature... The sex ratio of crocodiles is strongly biased towards females, often as high as 10 females to 1 male. In crocodilians, the temperature of egg incubation is the environmental factor determining sex. If the temperature is low, around 30˚C, the hatchlings are all females. Higher temperature, around 34˚C, hatch all males. This study was made to consider the asymptotic stability of a positive equilibrium point in a nonlinear discrete model of the basic nesting population model, which is described in three-region depending on the temperature of egg incubation. This model is based on key life-historical data and Murray’s research. To study above, we have applied the classical linearization method and P. Cull’s method and moreover, we employ non-standard discretization methods for later our Equations (6)-(8) and (15). 展开更多
关键词 asymptotic Stability Crocodilians Population Model Positive Equilibrium Point
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LIMITING BEHAVIOR OF RECURSIVE M-ESTIMATORS IN MULTIVARIATE LINEAR REGRESSION MODELS AND THEIR ASYMPTOTIC EFFICIENCIES
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作者 缪柏其 吴月华 刘东海 《Acta Mathematica Scientia》 SCIE CSCD 2010年第1期319-329,共11页
Recursive algorithms are very useful for computing M-estimators of regression coefficients and scatter parameters. In this article, it is shown that for a nondecreasing ul (t), under some mild conditions the recursi... Recursive algorithms are very useful for computing M-estimators of regression coefficients and scatter parameters. In this article, it is shown that for a nondecreasing ul (t), under some mild conditions the recursive M-estimators of regression coefficients and scatter parameters are strongly consistent and the recursive M-estimator of the regression coefficients is also asymptotically normal distributed. Furthermore, optimal recursive M-estimators, asymptotic efficiencies of recursive M-estimators and asymptotic relative efficiencies between recursive M-estimators of regression coefficients are studied. 展开更多
关键词 asymptotic efficiency asymptotic normality asymptotic relative efficiency least absolute deviation least squares M-ESTIMATION multivariate linear optimal estimator reeursive algorithm regression coefficients robust estimation regression model
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Asymptotic Stability in the Large of Zero Solution of Second Order Nonlinear Differential Equation 被引量:2
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作者 王德利 谭远顺 《Chinese Quarterly Journal of Mathematics》 CSCD 2001年第2期13-16,共4页
There are many works on the asymptotic stability of second dimensional nonlinear differential equation. In particular, these results only concern with the system which includes one or two terms, whereas few works conc... There are many works on the asymptotic stability of second dimensional nonlinear differential equation. In particular, these results only concern with the system which includes one or two terms, whereas few works concern with system which includes more than two terms. In this paper, system which includes four nonlinear terms are studies. We obtain the global asymptotic stability of zero solution, and discard the condition which require the Liapunov function trends to infinity, and only require that the positive orbit is bounded. 展开更多
关键词 nonlinear differential equation zero solution globally asymptotic stability
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ASYMPTOTIC BEHAVIOR FOR COMMUTATIVE SEMIGROUPS OF ALMOST ASYMPTOTICALLY NONEXPANSIVE TYPE MAPPINGS 被引量:1
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作者 曾六川 《Acta Mathematica Scientia》 SCIE CSCD 2006年第2期246-254,共9页
This article introduces the concept of commutative semigroups of almost asymptotically nonexpansive-type mappings in a Banach space X which has the Opial property and whose norm is UKK, and establishes the weak conver... This article introduces the concept of commutative semigroups of almost asymptotically nonexpansive-type mappings in a Banach space X which has the Opial property and whose norm is UKK, and establishes the weak convergence theorems for almostorbits of this class of commutative semigroups. The author improves, extends and develops some recent and earlier results. 展开更多
关键词 Semitopological semigroup almost asymptotically nonexpansive type mapping almost orbit asymptotic behavior
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