In this paper, convergence of series and almost sure convergence are established for weighted random variables under a sub-linear expectation space. Our results are very extensive versions which contain the related convergence of series and almost sure convergence for sequences of random variables and so on, and are extensions and improvements of classical convergence of series and almost sure convergence from the traditional probability space to the sub-linear expectation space.
{"title":"Convergence of series and almost sure convergence for weighted random variables under sub-linear expectations","authors":"Qunying Wu","doi":"10.2298/fil2302615w","DOIUrl":"https://doi.org/10.2298/fil2302615w","url":null,"abstract":"In this paper, convergence of series and almost sure convergence are established for weighted random variables under a sub-linear expectation space. Our results are very extensive versions which contain the related convergence of series and almost sure convergence for sequences of random variables and so on, and are extensions and improvements of classical convergence of series and almost sure convergence from the traditional probability space to the sub-linear expectation space.","PeriodicalId":12305,"journal":{"name":"Filomat","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68267327","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we describe the main principles of our approach for the visualization of surfaces and curves on them in three-dimensional space by the use of line graphics. We also compare our approach with the standard method of polygon mesh. Mainly, we discuss the representation of surfaces, special lines on surfaces and lines of intersections of surfaces. Furthermore, we address the problems of visibility and finding the contour lines of surfaces. Finally we apply our method for visualizing some selected topic in mathematics.
{"title":"Line graphics for visualization of surfaces and curves on them","authors":"Vesna Veličković, E. Dolicanin","doi":"10.2298/fil2304017v","DOIUrl":"https://doi.org/10.2298/fil2304017v","url":null,"abstract":"In this paper, we describe the main principles of our approach for the visualization of surfaces and curves on them in three-dimensional space by the use of line graphics. We also compare our approach with the standard method of polygon mesh. Mainly, we discuss the representation of surfaces, special lines on surfaces and lines of intersections of surfaces. Furthermore, we address the problems of visibility and finding the contour lines of surfaces. Finally we apply our method for visualizing some selected topic in mathematics.","PeriodicalId":12305,"journal":{"name":"Filomat","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68268581","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we introduce a prey-predator system with Allee effect in prey where both the prey and predator species are subject to harvesting and exhibit herd behaviour. The new idea of this paper is to consider the Allee effect, herd behaviour and harversing together. Herd behaviour may be proved as a buffer against environmental obstacles. On the contrary, Allee effect and harvesting together may wash out the population from the system. So, the optimal harvesting policy is significant for the ecosystem concerned with our proposed model. Moreover, taking some hypothetical data, a rigorous numerical illustration and sensitivity analysis of the main parameters are offered here to validate the mathematical findings. To summarise, we can say that our model is an endeavor aiming at the ecological balance in nature.
{"title":"Harvesting effect on prey-predator system with strong Allee effect in prey and herd behaviour in both","authors":"S. Biswas, D. Pal, G. Mahapatra","doi":"10.2298/fil2305561b","DOIUrl":"https://doi.org/10.2298/fil2305561b","url":null,"abstract":"In this paper, we introduce a prey-predator system with Allee effect in prey where both the prey and predator species are subject to harvesting and exhibit herd behaviour. The new idea of this paper is to consider the Allee effect, herd behaviour and harversing together. Herd behaviour may be proved as a buffer against environmental obstacles. On the contrary, Allee effect and harvesting together may wash out the population from the system. So, the optimal harvesting policy is significant for the ecosystem concerned with our proposed model. Moreover, taking some hypothetical data, a rigorous numerical illustration and sensitivity analysis of the main parameters are offered here to validate the mathematical findings. To summarise, we can say that our model is an endeavor aiming at the ecological balance in nature.","PeriodicalId":12305,"journal":{"name":"Filomat","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68269884","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The Steklov averages (Steklov or integral means) are used in approximation theory of functions in different aspects. This article concerns the Steklov averages by using the operator cosine function framework. The operator cosine function offers a counterpart of the translation operator, which forms the basic concept for the modulus of continuity and for some approximation processes as well. We will show that the operator cosine function concept allows to define very general Steklov averages in an abstract Banach space. The approximation properties of these generalized Steklov averages appear to be quite similar to the properties of the Steklov averages in trigonometric approximation.
{"title":"On the Steklov averages in operator cosine function framework","authors":"A. Kivinukk, A. Šeletski","doi":"10.2298/fil2305635k","DOIUrl":"https://doi.org/10.2298/fil2305635k","url":null,"abstract":"The Steklov averages (Steklov or integral means) are used in approximation theory of functions in different aspects. This article concerns the Steklov averages by using the operator cosine function framework. The operator cosine function offers a counterpart of the translation operator, which forms the basic concept for the modulus of continuity and for some approximation processes as well. We will show that the operator cosine function concept allows to define very general Steklov averages in an abstract Banach space. The approximation properties of these generalized Steklov averages appear to be quite similar to the properties of the Steklov averages in trigonometric approximation.","PeriodicalId":12305,"journal":{"name":"Filomat","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68270425","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we first introduce the notion of Reynolds operators on Hom-Leibniz algebras and give some constructions. Furthermore, we define the cohomology of Reynolds operators, and use this cohomology to study deformations of Reynolds operators. As applications, we introduce and study NS-Hom-Leibniz algebras as the underlying structure of Reynolds operators.
{"title":"Reynolds operators on Hom-Leibniz algebras","authors":"Dingguo Wanga, Yuanyuan Keb","doi":"10.2298/fil2307117w","DOIUrl":"https://doi.org/10.2298/fil2307117w","url":null,"abstract":"In this paper, we first introduce the notion of Reynolds operators on Hom-Leibniz algebras and give some constructions. Furthermore, we define the cohomology of Reynolds operators, and use this cohomology to study deformations of Reynolds operators. As applications, we introduce and study NS-Hom-Leibniz algebras as the underlying structure of Reynolds operators.","PeriodicalId":12305,"journal":{"name":"Filomat","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68271827","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we aim to obtain Massera type theorems for both linear and nonlinear dynamic equations by using a generalized periodicity notion, namely (T, ?)-periodicity, on time scales. To achieve this task, first we define a new boundedness concept so-called ?-boundedness, and then we establish a linkage between the existence of ?-bounded solutions and (T, ?)-periodic solutions of dynamic equations in both linear and nonlinear cases. In our analysis, we assume that the time scale T is periodic in shifts ?? which does not need to be translation invariant. Thus, outcomes of this work are valid for a large class of time-domains not restricted to T = R or T = Z.
{"title":"Unified Massera type theorems for dynamic equations on time scales","authors":"H. Koyuncuoğlu","doi":"10.2298/fil2308405k","DOIUrl":"https://doi.org/10.2298/fil2308405k","url":null,"abstract":"In this paper, we aim to obtain Massera type theorems for both linear and nonlinear dynamic equations by using a generalized periodicity notion, namely (T, ?)-periodicity, on time scales. To achieve this task, first we define a new boundedness concept so-called ?-boundedness, and then we establish a linkage between the existence of ?-bounded solutions and (T, ?)-periodic solutions of dynamic equations in both linear and nonlinear cases. In our analysis, we assume that the time scale T is periodic in shifts ?? which does not need to be translation invariant. Thus, outcomes of this work are valid for a large class of time-domains not restricted to T = R or T = Z.","PeriodicalId":12305,"journal":{"name":"Filomat","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68272864","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we consider the Robin-Dirichlet problem for a nonlinear wave equation of Kirchhoff-Carrier type with Balakrishnan-Taylor damping. First, under suitable conditions on the initial data, the local existence and uniqueness of a weak solution are proved. Next, an asymptotic expansion of solutions in a small parameter with high order is established. The used main tools are the linearization method for nonlinear terms together with the Faedo-Galerkin method, and the key lemmas of the expansion of high-order polynomials and the Taylor expansion for multi-variable functions.
{"title":"Asymptotic expansion of solutions for the Robin-Dirichlet problem of Kirchhoff-Carrier type with Balakrishnan-Taylor damping","authors":"Huu-Bao Nhan, B. Nam, L. Ngoc, N. Long","doi":"10.2298/fil2308321n","DOIUrl":"https://doi.org/10.2298/fil2308321n","url":null,"abstract":"In this paper, we consider the Robin-Dirichlet problem for a nonlinear wave equation of Kirchhoff-Carrier type with Balakrishnan-Taylor damping. First, under suitable conditions on the initial data, the local existence and uniqueness of a weak solution are proved. Next, an asymptotic expansion of solutions in a small parameter with high order is established. The used main tools are the linearization method for nonlinear terms together with the Faedo-Galerkin method, and the key lemmas of the expansion of high-order polynomials and the Taylor expansion for multi-variable functions.","PeriodicalId":12305,"journal":{"name":"Filomat","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68273002","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we study the finite Gabor system for oversampling schemes. A characterization of dual finite Gabor tight frame using discrete time Zak transform is given. Also, a method to calculate the coefficients of the finite Gabor system expansion in the case of oversampling and a necessary and sufficient condition for the existence of biorthogonal pair of Riesz basis in l2(ZL) is given. Further, we introduce the notion of block sliding discrete Fourier transform (BSDFT) which reduces the computational complexity and give uncertainty principle for BSDFT. An uncertainty principle for two finite Parseval Gabor frames in terms of sparse representations is given. Finally, using the notion of numerical sparsity, an uncertainty principle for finite Gabor frames is given.
{"title":"Finite Gabor systems and uncertainty principle for block sliding discrete fourier transform","authors":"K. Poumai, N. Khanna, S. K. Kaushik","doi":"10.2298/fil2308361p","DOIUrl":"https://doi.org/10.2298/fil2308361p","url":null,"abstract":"In this paper, we study the finite Gabor system for oversampling schemes. A characterization of dual finite Gabor tight frame using discrete time Zak transform is given. Also, a method to calculate the coefficients of the finite Gabor system expansion in the case of oversampling and a necessary and sufficient condition for the existence of biorthogonal pair of Riesz basis in l2(ZL) is given. Further, we introduce the notion of block sliding discrete Fourier transform (BSDFT) which reduces the computational complexity and give uncertainty principle for BSDFT. An uncertainty principle for two finite Parseval Gabor frames in terms of sparse representations is given. Finally, using the notion of numerical sparsity, an uncertainty principle for finite Gabor frames is given.","PeriodicalId":12305,"journal":{"name":"Filomat","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68273075","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we are concerned with the rate of convergence of parabolic systems with large diffusion. We exhibit the exact moment that spatial homogenization occurs and estimate the continuity of attractors by a rate of convergence. We present an example where our estimate is optimal.
{"title":"Large diffusivity and rate of convergence of attractors in parabolic systems","authors":"Leonardo Pires","doi":"10.2298/fil2309675p","DOIUrl":"https://doi.org/10.2298/fil2309675p","url":null,"abstract":"In this paper, we are concerned with the rate of convergence of parabolic systems with large diffusion. We exhibit the exact moment that spatial homogenization occurs and estimate the continuity of attractors by a rate of convergence. We present an example where our estimate is optimal.","PeriodicalId":12305,"journal":{"name":"Filomat","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135784812","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we present an analytical method to solve a time-conformable fractional telegraph equation with three boundary conditions namely, Dirichlet, Neumann and Robin. This method based on Fourier method and conformable fractional calculus properties. We give three examples to validate this method.
{"title":"Analytical method for solving a time-conformable fractional telegraph equation","authors":"Saad Abdelkebir, Brahim Nouiri","doi":"10.2298/fil2309773a","DOIUrl":"https://doi.org/10.2298/fil2309773a","url":null,"abstract":"In this paper, we present an analytical method to solve a time-conformable fractional telegraph equation with three boundary conditions namely, Dirichlet, Neumann and Robin. This method based on Fourier method and conformable fractional calculus properties. We give three examples to validate this method.","PeriodicalId":12305,"journal":{"name":"Filomat","volume":"101 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135594178","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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