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Relaxation and linear programs in a hybrid control model 混合控制模型中的松弛和线性规划
Applicationes Mathematicae Pub Date : 2019-01-01 DOI: 10.4064/am2387-6-2019
Héctor Jasso-Fuentes, J. Menaldi
{"title":"Relaxation and linear programs in a hybrid control model","authors":"Héctor Jasso-Fuentes, J. Menaldi","doi":"10.4064/am2387-6-2019","DOIUrl":"https://doi.org/10.4064/am2387-6-2019","url":null,"abstract":". Some optimality results for hybrid control problems are pre-sented. The hybrid model under study consists of two subdynamics, one of a standard type governed by an ordinary differential equation, and the other of a special type having a discrete evolution. We focus on the case when the interaction between the subdynamics takes place only when the state of the system reaches a given fixed region of the state space. The controller is able to apply two controls, each applied to one of the two subdynamics, whereas the state follows a composite evolution, of continuous type and discrete type. By the relaxation technique, we prove the existence of a pair of controls that minimizes an incurred (discounted) cost. We conclude the analysis by introducing an auxiliary infinite-dimensional linear program to show the equivalence between the initial control problem and its associated relaxed counterpart.","PeriodicalId":52313,"journal":{"name":"Applicationes Mathematicae","volume":"216 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76731211","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Ball convergence for a two-step fourth order derivative-free method for nonlinear equations 非线性方程的两步四阶无导数法的球收敛性
Applicationes Mathematicae Pub Date : 2019-01-01 DOI: 10.4064/AM2331-7-2017
I. Argyros, R. Behl, S. Motsa
{"title":"Ball convergence for a two-step fourth order derivative-free method for nonlinear equations","authors":"I. Argyros, R. Behl, S. Motsa","doi":"10.4064/AM2331-7-2017","DOIUrl":"https://doi.org/10.4064/AM2331-7-2017","url":null,"abstract":"","PeriodicalId":52313,"journal":{"name":"Applicationes Mathematicae","volume":"8 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84754111","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Some new properties of generalized Bessel polynomials 广义贝塞尔多项式的一些新性质
Applicationes Mathematicae Pub Date : 2019-01-01 DOI: 10.4064/AM2378-4-2019
Nejla Özmen
{"title":"Some new properties of generalized Bessel polynomials","authors":"Nejla Özmen","doi":"10.4064/AM2378-4-2019","DOIUrl":"https://doi.org/10.4064/AM2378-4-2019","url":null,"abstract":". We obtain some new properties of generalized Bessel polynomials. We mainly investigate bilinear and bilateral generating function relations for these polynomials. We also derive a result giving certain families of bilateral generating functions for generalized Bessel polynomials and generalized Lauricella functions. We also discuss some special cases. relations, hypergeometric function.","PeriodicalId":52313,"journal":{"name":"Applicationes Mathematicae","volume":"95 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86709070","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Global exponential stability in Lagrange sense for periodic neural networks with various activation functions and time-varying delays 具有各种激活函数和时变时滞的周期神经网络在拉格朗日意义上的全局指数稳定性
Applicationes Mathematicae Pub Date : 2019-01-01 DOI: 10.4064/AM2320-10-2017
Swati Tyagi, Syed Abbas, M. Pinto
{"title":"Global exponential stability in Lagrange sense for periodic neural networks with various activation functions and time-varying delays","authors":"Swati Tyagi, Syed Abbas, M. Pinto","doi":"10.4064/AM2320-10-2017","DOIUrl":"https://doi.org/10.4064/AM2320-10-2017","url":null,"abstract":". In recent years, the concept of Lyapunov stability has received a remarkable attention in the field of neural networks. However the stability in Lagrange sense for neural networks has not been studied much. It is to be noticed that while Lyapunov stability refers to stability of the equilibrium point, Lagrange stability refers to the stability of the total system. In this paper, we study the global exponential stability in Lagrange sense for periodic neural networks with multiple time delays and more general activation functions including general bounded and sigmoidal type activation functions. By constructing suitable Lyapunov-like functions, we provide easily verifiable criteria for the boundedness and global exponential attractivity of periodic neural networks. We present a detailed estimation of global exponential attractive sets from the system parameters without any supposition on existence. We investigate whether the equilibrium point of the network system is globally exponentially stable by means of globally exponentially attractive sets. At the end, we give some numerical examples to validate our analytical findings. The results obtained are helpful in designing globally asymptotically stable cellular neural networks and reduce the search domain of optimization.","PeriodicalId":52313,"journal":{"name":"Applicationes Mathematicae","volume":"16 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77714942","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On counting distributions related to the Delaporte distribution 关于与Delaporte分布有关的计数分布
Applicationes Mathematicae Pub Date : 2019-01-01 DOI: 10.4064/AM2337-8-2018
K. Steliga, D. Szynal
{"title":"On counting distributions related to the Delaporte distribution","authors":"K. Steliga, D. Szynal","doi":"10.4064/AM2337-8-2018","DOIUrl":"https://doi.org/10.4064/AM2337-8-2018","url":null,"abstract":"","PeriodicalId":52313,"journal":{"name":"Applicationes Mathematicae","volume":"53 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85619693","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Two-point methods for solving equations and systems of equations 求解方程和方程组的两点方法
Applicationes Mathematicae Pub Date : 2019-01-01 DOI: 10.4064/am2365-5-2018
I. Argyros, S. George
{"title":"Two-point methods for solving equations and systems of equations","authors":"I. Argyros, S. George","doi":"10.4064/am2365-5-2018","DOIUrl":"https://doi.org/10.4064/am2365-5-2018","url":null,"abstract":"","PeriodicalId":52313,"journal":{"name":"Applicationes Mathematicae","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87596737","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Existence and uniqueness of solution for a unilateral problem in Sobolev spaces with variable exponent 变指数Sobolev空间中单侧问题解的存在唯一性
Applicationes Mathematicae Pub Date : 2019-01-01 DOI: 10.4064/AM2372-2-2019
B. Aharrouch, J. Bennouna
{"title":"Existence and uniqueness of solution for a unilateral problem in Sobolev spaces with variable exponent","authors":"B. Aharrouch, J. Bennouna","doi":"10.4064/AM2372-2-2019","DOIUrl":"https://doi.org/10.4064/AM2372-2-2019","url":null,"abstract":"","PeriodicalId":52313,"journal":{"name":"Applicationes Mathematicae","volume":"46 3 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89384677","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Note on universal algorithms for learning theory 关于学习理论通用算法的说明
Applicationes Mathematicae Pub Date : 2018-11-23 DOI: 10.4064/am34-1-5
K. Dziedziul, B. Wolnik
{"title":"Note on universal algorithms for learning theory","authors":"K. Dziedziul, B. Wolnik","doi":"10.4064/am34-1-5","DOIUrl":"https://doi.org/10.4064/am34-1-5","url":null,"abstract":"We propose the general way of study the universal estimator for the regression problem in learning theory considered in \"Universal algorithms for learning theory Part I: piecewise constant functions\" and \"Universal algorithms for learning theory Part II: piecewise constant functions\" written by Binev, P., Cohen, A., Dahmen, W., DeVore, R., Temlyakov, V. This new approch allows us to improve results.","PeriodicalId":52313,"journal":{"name":"Applicationes Mathematicae","volume":"54 1","pages":"47-52"},"PeriodicalIF":0.0,"publicationDate":"2018-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72486387","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Uncertainty product of the spherical Abel–Poisson wavelet 球面Abel-Poisson小波的不确定积
Applicationes Mathematicae Pub Date : 2018-06-20 DOI: 10.4064/AM2366-2-2019
I. Iglewska-Nowak
{"title":"Uncertainty product of the spherical Abel–Poisson wavelet","authors":"I. Iglewska-Nowak","doi":"10.4064/AM2366-2-2019","DOIUrl":"https://doi.org/10.4064/AM2366-2-2019","url":null,"abstract":"In the present paper, the variances in the space and momentum domains of the spherical Abel-Poisson wavelet, as well as the limit of the uncertainty product for $rhoto0$, where $rho$ is the scale parameter, are computed. The values of these quantities coincide with a certain accuracy with those of the spherical Poisson wavelet with $tfrac{1}{2}$ substituted for the order parameter.","PeriodicalId":52313,"journal":{"name":"Applicationes Mathematicae","volume":"515 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77081298","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Analysis of a frictional contact problem with wear and damage between two thermo-viscoelastic bodies 热粘弹性体间含磨损和损伤的摩擦接触问题分析
Applicationes Mathematicae Pub Date : 2018-01-01 DOI: 10.4064/AM2330-11-2017
Ilyas Boukaroura, S. Djabi
{"title":"Analysis of a frictional contact problem with wear and damage between two thermo-viscoelastic bodies","authors":"Ilyas Boukaroura, S. Djabi","doi":"10.4064/AM2330-11-2017","DOIUrl":"https://doi.org/10.4064/AM2330-11-2017","url":null,"abstract":"","PeriodicalId":52313,"journal":{"name":"Applicationes Mathematicae","volume":"13 1","pages":"129-150"},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82767431","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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