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Existence of solutions to a one-dimensional Hamilton–Jacobi equation with a degenerate Hamiltonian 具有退化哈密顿量的一维哈密顿-雅可比方程解的存在性
Applicationes Mathematicae Pub Date : 2020-01-01 DOI: 10.4064/am2407-7-2020
Tomasz Cieślak, H. Wakui
{"title":"Existence of solutions to a one-dimensional Hamilton–Jacobi equation with a degenerate Hamiltonian","authors":"Tomasz Cieślak, H. Wakui","doi":"10.4064/am2407-7-2020","DOIUrl":"https://doi.org/10.4064/am2407-7-2020","url":null,"abstract":"We study a one-dimensional Hamilton–Jacobi initial value problem for a degenerate Hamiltonian occurring in multipeakon dynamics. Such a degenerate problem does not obey the usual viscosity solutions theory; viability type extensions do not seem to cover it either. Thanks to a particular change of variables, we reduce the problem to the case where Hopf theory is sufficient. Moreover, we show that our solutions are solutions in the viscosity sense.","PeriodicalId":52313,"journal":{"name":"Applicationes Mathematicae","volume":"42 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80612246","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: 3
On least squares discrete Fourier analysis of unequally spaced data 非等间距数据的最小二乘离散傅立叶分析
Applicationes Mathematicae Pub Date : 2020-01-01 DOI: 10.4064/am2399-6-2020
W. Popiński
{"title":"On least squares discrete Fourier analysis of unequally spaced data","authors":"W. Popiński","doi":"10.4064/am2399-6-2020","DOIUrl":"https://doi.org/10.4064/am2399-6-2020","url":null,"abstract":". The problem of discrete Fourier analysis of observations at non-equidistant times using the standard set of complex harmonics exp( i 2 πkt ) , t ∈ R , k = 0 , ± 1 , ± 2 , . . . , and the least squares method is studied. The observation model y j = f ( t j )+ η j , j = 1 , . . . , n , is considered for f ∈ L 2 [0 , 1] , where t j ∈ [( j − 1) /n, j/n ) , and η j are correlated complex valued random variables with E η η j = 0 and E η | η j | 2 = σ 2 η < ∞ . Uniqueness and finite sample properties of the observed function Fourier coefficient estimators ˆ c k , k = 0 , ± 1 , . . . , ± m , where m < n/ (8 π ) , obtained by the least squares method, as well as of the corresponding orthogonal projection estimator ˆ f N ( t ) = (cid:80) mk = − m ˆ c k exp( i 2 πkt ) , where N = 2 m + 1 , are examined and compared with those of the standard Discrete Fourier Transform.","PeriodicalId":52313,"journal":{"name":"Applicationes Mathematicae","volume":"15 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73456046","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
Exact weak laws of large numbers with applications to ratios of random variables 大数的精确弱定律，应用于随机变量的比率
Applicationes Mathematicae Pub Date : 2020-01-01 DOI: 10.4064/am2396-2-2020
Pawel Kurasinski, P. Matuła
{"title":"Exact weak laws of large numbers with applications to ratios of random variables","authors":"Pawel Kurasinski, P. Matuła","doi":"10.4064/am2396-2-2020","DOIUrl":"https://doi.org/10.4064/am2396-2-2020","url":null,"abstract":"We study convergence in probability of weighted sums of independent random variables which are not necessarily identically distributed. The results obtained are applied to ratios of independent random variables and ratios of smallest order statistics.","PeriodicalId":52313,"journal":{"name":"Applicationes Mathematicae","volume":"47 1","pages":"59-66"},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76835082","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
Expanding the applicability ofNewton’s method and of a robustmodified Newton’s method 扩展了牛顿法的适用性，并提出了一种鲁棒修正牛顿法
Applicationes Mathematicae Pub Date : 2019-01-01 DOI: 10.4064/am2289-4-2016
I. Argyros, S. George
{"title":"Expanding the applicability ofNewton’s method and of a robustmodified Newton’s method","authors":"I. Argyros, S. George","doi":"10.4064/am2289-4-2016","DOIUrl":"https://doi.org/10.4064/am2289-4-2016","url":null,"abstract":"","PeriodicalId":52313,"journal":{"name":"Applicationes Mathematicae","volume":"74 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80147361","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 dynamic contact problem with friction, damage and adhesion 分析了具有摩擦、损伤和粘附的动态接触问题
Applicationes Mathematicae Pub Date : 2019-01-01 DOI: 10.4064/AM2312-6-2018
A. Kasri, A. Touzaline
{"title":"Analysis of a dynamic contact problem with friction, damage and adhesion","authors":"A. Kasri, A. Touzaline","doi":"10.4064/AM2312-6-2018","DOIUrl":"https://doi.org/10.4064/AM2312-6-2018","url":null,"abstract":"We study a dynamic contact problem for viscoelastic materials with damage. The contact is modelled with Tresca’s friction law and a first order differential equation which describes adhesion effect of contact surfaces; the damage of the material is described by a function whose evolution is governed by a parabolic inclusion. Under appropriate assumptions, we provide a variational formulation of the mechanical problem and establish the existence and uniqueness of a weak solution.","PeriodicalId":52313,"journal":{"name":"Applicationes Mathematicae","volume":"9 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77954715","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: 4
The prior distribution of a random measure 随机测度的先验分布
Applicationes Mathematicae Pub Date : 2019-01-01 DOI: 10.4064/am2362-7-2018
Nguyen Bac-Van
{"title":"The prior distribution of a random measure","authors":"Nguyen Bac-Van","doi":"10.4064/am2362-7-2018","DOIUrl":"https://doi.org/10.4064/am2362-7-2018","url":null,"abstract":". It is known that an infinite, exchangeable sequence of observations from a Borel space, in particular a Polish one, is underlain by an almost surely (a.s.) unique random probability measure on this space such that, conditioned on it, the observations are independent and identically distributed with that measure. The distribution of that random measure is the prior distribution involved in Bayes inference. The present paper proves that the prior distribution of the a.s. unique random measure underlying an infinite, exchangeable sequence of observations from a Polish space is a Radon probability measure on the σ -field generated by the narrow topology in the space of Borel probability measures on the starting Polish space.","PeriodicalId":52313,"journal":{"name":"Applicationes Mathematicae","volume":"41 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86910319","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
Selfadjoint operator Chebyshev–Grüss type inequalities 自伴随算子chebyhev - gr<e:1>型不等式
Applicationes Mathematicae Pub Date : 2019-01-01 DOI: 10.4064/AM2300-7-2018
G. Anastassiou
{"title":"Selfadjoint operator Chebyshev–Grüss type inequalities","authors":"G. Anastassiou","doi":"10.4064/AM2300-7-2018","DOIUrl":"https://doi.org/10.4064/AM2300-7-2018","url":null,"abstract":"","PeriodicalId":52313,"journal":{"name":"Applicationes Mathematicae","volume":"11 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74675624","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
Quantile estimation via distribution fitting 通过分布拟合进行分位数估计
Applicationes Mathematicae Pub Date : 2019-01-01 DOI: 10.4064/AM2384-3-2019
Alicja Jokiel-Rokita, Agnieszka Siedlaczek
{"title":"Quantile estimation via distribution fitting","authors":"Alicja Jokiel-Rokita, Agnieszka Siedlaczek","doi":"10.4064/AM2384-3-2019","DOIUrl":"https://doi.org/10.4064/AM2384-3-2019","url":null,"abstract":"","PeriodicalId":52313,"journal":{"name":"Applicationes Mathematicae","volume":"105 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79536737","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
Bernoulli property of smooth extensions of Bernoulli shifts 伯努利位移光滑扩展的伯努利性质
Applicationes Mathematicae Pub Date : 2019-01-01 DOI: 10.4064/am2376-2-2019
Z. Kowalski
{"title":"Bernoulli property of smooth extensions of Bernoulli shifts","authors":"Z. Kowalski","doi":"10.4064/am2376-2-2019","DOIUrl":"https://doi.org/10.4064/am2376-2-2019","url":null,"abstract":"The paper gives a characterization of smooth extensions of Bernoulli shifts which have the Bernoulli property, i.e. their natural extensions to automorphisms are Bernoulli.","PeriodicalId":52313,"journal":{"name":"Applicationes Mathematicae","volume":"31 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85690946","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
Convergence for variants of Chebyshev–Halley methods using restricted convergence domains Chebyshev-Halley方法在有限收敛域上的收敛性
Applicationes Mathematicae Pub Date : 2019-01-01 DOI: 10.4064/AM2321-4-2017
I. Argyros, S. George
{"title":"Convergence for variants of Chebyshev–Halley methods using restricted convergence domains","authors":"I. Argyros, S. George","doi":"10.4064/AM2321-4-2017","DOIUrl":"https://doi.org/10.4064/AM2321-4-2017","url":null,"abstract":"We present a local convergence analysis for some variants of Chebyshev–Halley methods of approximating a locally unique solution of a nonlinear equation in a Banach space setting. We only use hypotheses reaching up to the second Fréchet derivative of the operator involved in contrast to earlier studies using Lipschitz hypotheses on the second Fréchet derivative and other more restrictive conditions. This way the applicability of these methods is expanded. We also show how to improve the semilocal convergence in the earlier studies under the same conditions using our new idea of restricted convergence domains leading to: weaker sufficient convergence criteria, tighter error bounds on the distances involved and an at least as precise information on the location of the solution. Numerical examples where earlier results cannot be applied but our results can, are also provided.","PeriodicalId":52313,"journal":{"name":"Applicationes Mathematicae","volume":"22 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81978387","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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