In recent years, the problem of incomplete data has been behind the appearance of several completion methods and algorithms. The truncated nuclear norm has been known as a powerful low-rank approach both for the matrix and the tensor cases. However, the low-rank approaches are unable to characterize some additional information exhibited in data such as the smoothness or feature-preserving properties. In this work, a tensor completion model based on the convex truncated nuclear norm and the nonconvex-sparse total variation is introduced. Notably, we develop an alternating minimization algorithm that combines the accelerating proximal gradient for the convex step and a projection operator for the nonconvex step to solve the optimization problem. Experiments and comparative results show that our algorithm has a significant impact on the completion process.
{"title":"Color image completion using tensor truncated nuclear norm with l0 total variationColor image completion using tensor truncated nuclear norm with l0 total variation","authors":"K. EL Qate, S. Mohaoui, A. Hakim, S. Raghay","doi":"10.52846/ami.v49i2.1532","DOIUrl":"https://doi.org/10.52846/ami.v49i2.1532","url":null,"abstract":"In recent years, the problem of incomplete data has been behind the appearance of several completion methods and algorithms. The truncated nuclear norm has been known as a powerful low-rank approach both for the matrix and the tensor cases. However, the low-rank approaches are unable to characterize some additional information exhibited in data such as the smoothness or feature-preserving properties. In this work, a tensor completion model based on the convex truncated nuclear norm and the nonconvex-sparse total variation is introduced. Notably, we develop an alternating minimization algorithm that combines the accelerating proximal gradient for the convex step and a projection operator for the nonconvex step to solve the optimization problem. Experiments and comparative results show that our algorithm has a significant impact on the completion process.","PeriodicalId":43654,"journal":{"name":"Annals of the University of Craiova-Mathematics and Computer Science Series","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2022-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76327703","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}
A method of finite approximation of zero-sum games defined on a product of staircase-function continuous spaces is presented. The method consists in uniformly sampling the player’s pure strategy value set, solving “smaller” matrix games, each defined on a subinterval where the pure strategy value is constant, and stacking their solutions if they are consistent. The stack of the “smaller” matrix game solutions is an approximate solution to the initial staircase game. The (weak) consistency, equivalent to the approxi-mate solution acceptability, is studied by how much the payoff and optimal situation change as the sampling density minimally increases. The consistency is decomposed into the payoff, optimal strategy support cardinality, optimal strategy sampling density, and support probability consistency. The most important parts are the payoff consistency and optimal strategy support cardinality (weak) consistency. However, it is practically reasonable to consider a relaxed payoff consistency, by which the game optimal value change in an appropriate approximation may grow at most by epsilon as the sampling density minimally increases. The weak consistency itself is a relaxation to the consistency, where the minimal decrement of the sampling density is ignored.
{"title":"Finite uniform approximation of zero-sum games defined on a product of staircase-function continuous spaces","authors":"V. Romanuke","doi":"10.52846/ami.v49i2.1554","DOIUrl":"https://doi.org/10.52846/ami.v49i2.1554","url":null,"abstract":"A method of finite approximation of zero-sum games defined on a product of staircase-function continuous spaces is presented. The method consists in uniformly sampling the player’s pure strategy value set, solving “smaller” matrix games, each defined on a subinterval where the pure strategy value is constant, and stacking their solutions if they are consistent. The stack of the “smaller” matrix game solutions is an approximate solution to the initial staircase game. The (weak) consistency, equivalent to the approxi-mate solution acceptability, is studied by how much the payoff and optimal situation change as the sampling density minimally increases. The consistency is decomposed into the payoff, optimal strategy support cardinality, optimal strategy sampling density, and support probability consistency. The most important parts are the payoff consistency and optimal strategy support cardinality (weak) consistency. However, it is practically reasonable to consider a relaxed payoff consistency, by which the game optimal value change in an appropriate approximation may grow at most by epsilon as the sampling density minimally increases. The weak consistency itself is a relaxation to the consistency, where the minimal decrement of the sampling density is ignored.","PeriodicalId":43654,"journal":{"name":"Annals of the University of Craiova-Mathematics and Computer Science Series","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2022-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83820180","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}
In this paper, we define a new sequence which is called the complex-type Fibonacci p-sequence and we obtain the generating matrix of this complex-type Fibonacci p-sequence. We also derive the determinantal and the permanental representations. Then, using the roots of the characteristic polynomial of the complex-type Fibonacci p-sequence, we produce the Binet formula for this defined sequence. In addition, we give the combinatorial representations, the generating function, the exponential representation and the sums of the complex-type Fibonacci p-numbers.
{"title":"The complex-type Fibonacci p-Sequences","authors":"Ö. Deveci, A. Shannon, E. Karaduman","doi":"10.52846/ami.v49i2.1534","DOIUrl":"https://doi.org/10.52846/ami.v49i2.1534","url":null,"abstract":"In this paper, we define a new sequence which is called the complex-type Fibonacci p-sequence and we obtain the generating matrix of this complex-type Fibonacci p-sequence. We also derive the determinantal and the permanental representations. Then, using the roots of the characteristic polynomial of the complex-type Fibonacci p-sequence, we produce the Binet formula for this defined sequence. In addition, we give the combinatorial representations, the generating function, the exponential representation and the sums of the complex-type Fibonacci p-numbers.","PeriodicalId":43654,"journal":{"name":"Annals of the University of Craiova-Mathematics and Computer Science Series","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2022-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86290345","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}
In this paper, we analyze various classes of multi-dimensional asymptotically ρ-almost periodic type functions in general metric. We clarify the main structural properties for the introduced classes of asymptotically ρ-almost periodic type functions, and provide some applications of our results to the abstract Volterra integro-differential equations.
{"title":"Asymptotically ρ-almost periodic type functions in general metric","authors":"M. Kostic","doi":"10.52846/ami.v49i2.1595","DOIUrl":"https://doi.org/10.52846/ami.v49i2.1595","url":null,"abstract":"In this paper, we analyze various classes of multi-dimensional asymptotically ρ-almost periodic type functions in general metric. We clarify the main structural properties for the introduced classes of asymptotically ρ-almost periodic type functions, and provide some applications of our results to the abstract Volterra integro-differential equations.","PeriodicalId":43654,"journal":{"name":"Annals of the University of Craiova-Mathematics and Computer Science Series","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2022-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79266978","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}
"The aim of this paper is to provide a characterization diagram for a family of B'{e}zier flexible interpolation curves as well as to present an application of our results in cryptography. In our interpolation scheme, two parameters, $t_1, t_2in (0,1)$ determine the position of the interpolation points on the B'{e}zier curve. Consequently we obtain a family of B'{e}zier interpolation curves depending on two parameters. Altering the values of the parameters we modify the intermediary control points and implicitly the shape of the interpolation curve. In order to control the shape of the interpolation curves from this family, we provide a partition of the domain $T=(0,1)times (0,1)$ where the parameters lie according to the geometric characterization of these curves: with zero, one or two inflexion points; with loop; with cusp and degenerated in quadratic curves. The characterization diagram can be used as a tool for the choice of parameters, with possible applications in different fields. We present one of its application in cryptography, for finding certain subspaces over which particular elliptic sub-curves are defined. Computation, implementation and graphics are made using MATLAB."
{"title":"Characterization of a cubic interpolation scheme dependent on two parameters and applications","authors":"D. Simian, O. Ticleanu, N. Constantinescu","doi":"10.52846/ami.v49i2.1703","DOIUrl":"https://doi.org/10.52846/ami.v49i2.1703","url":null,"abstract":"\"The aim of this paper is to provide a characterization diagram for a family of B'{e}zier flexible interpolation curves as well as to present an application of our results in cryptography. In our interpolation scheme, two parameters, $t_1, t_2in (0,1)$ determine the position of the interpolation points on the B'{e}zier curve. Consequently we obtain a family of B'{e}zier interpolation curves depending on two parameters. Altering the values of the parameters we modify the intermediary control points and implicitly the shape of the interpolation curve. In order to control the shape of the interpolation curves from this family, we provide a partition of the domain $T=(0,1)times (0,1)$ where the parameters lie according to the geometric characterization of these curves: with zero, one or two inflexion points; with loop; with cusp and degenerated in quadratic curves. The characterization diagram can be used as a tool for the choice of parameters, with possible applications in different fields. We present one of its application in cryptography, for finding certain subspaces over which particular elliptic sub-curves are defined. Computation, implementation and graphics are made using MATLAB.\"","PeriodicalId":43654,"journal":{"name":"Annals of the University of Craiova-Mathematics and Computer Science Series","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2022-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86333164","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}
Y. Sarala, Popuri Seetha Mani, K. Hila, Gokarakonda Jaya Lalitha
The main objective of this study is to introduce a new class of hyperideals called pseudosymmetric and semipseudosymmetric hyperideals in ternary semihypergroups. We try to investigate the properties of these hyperideals by giving some suitable examples for the same. In particular we prove that every pseudosymmetric hyperideal of a ternary semihypergroups is a semipseudosymmetric hyperideal. We study the fundamental relations among these hyperideals and provide few results.
{"title":"Semipseudosymmetric hyperideals in ternary semihypergroups","authors":"Y. Sarala, Popuri Seetha Mani, K. Hila, Gokarakonda Jaya Lalitha","doi":"10.52846/ami.v49i2.1573","DOIUrl":"https://doi.org/10.52846/ami.v49i2.1573","url":null,"abstract":"The main objective of this study is to introduce a new class of hyperideals called pseudosymmetric and semipseudosymmetric hyperideals in ternary semihypergroups. We try to investigate the properties of these hyperideals by giving some suitable examples for the same. In particular we prove that every pseudosymmetric hyperideal of a ternary semihypergroups is a semipseudosymmetric hyperideal. We study the fundamental relations among these hyperideals and provide few results.","PeriodicalId":43654,"journal":{"name":"Annals of the University of Craiova-Mathematics and Computer Science Series","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2022-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88179311","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}
In this article, our main concern is the study of the effect of a distributed time-delay in boundary stabilization of a strongly coupled multi-dimensional wave equations. We will establish that the system with time-delay inherits the same exponential decay rate from the corresponding one without delay.
{"title":"Indirect boundary stabilization with distributed delay of coupled multi-dimensional wave equations","authors":"Roland Silga, B. A. Kyelem, G. Bayili","doi":"10.52846/ami.v49i1.1430","DOIUrl":"https://doi.org/10.52846/ami.v49i1.1430","url":null,"abstract":"In this article, our main concern is the study of the effect of a distributed time-delay in boundary stabilization of a strongly coupled multi-dimensional wave equations. We will establish that the system with time-delay inherits the same exponential decay rate from the corresponding one without delay.","PeriodicalId":43654,"journal":{"name":"Annals of the University of Craiova-Mathematics and Computer Science Series","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2022-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73687824","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}
In this paper, we define the notions of MV-pseudo norm and MV-pseudo metric on MV-algebras and study some of their algebraic properties. The notion of uniform MV-algebra is also introduced and its relationship to MV-pseudo metrics is studied.
{"title":"MV-pseudo metrics on MV-algebras","authors":"F. Rajabisotudeh, N. Kouhestani","doi":"10.52846/ami.v49i1.1443","DOIUrl":"https://doi.org/10.52846/ami.v49i1.1443","url":null,"abstract":"In this paper, we define the notions of MV-pseudo norm and MV-pseudo metric on MV-algebras and study some of their algebraic properties. The notion of uniform MV-algebra is also introduced and its relationship to MV-pseudo metrics is studied.","PeriodicalId":43654,"journal":{"name":"Annals of the University of Craiova-Mathematics and Computer Science Series","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2022-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90332245","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}
In this paper, we study the existence of mild solutions of Hilfer fractional stochastic differential inclusions driven by sub fractional Brownian motion in the cases when the multivalued map is convex and non convex. The results are obtained by using fixed point theorem. Finally an example is given to illustrate the obtained results.
{"title":"Stochastic differential inclusions with Hilfer fractional derivative","authors":"Meryem Chaouche, Toufik Guendouzi","doi":"10.52846/ami.v49i1.1524","DOIUrl":"https://doi.org/10.52846/ami.v49i1.1524","url":null,"abstract":"In this paper, we study the existence of mild solutions of Hilfer fractional stochastic differential inclusions driven by sub fractional Brownian motion in the cases when the multivalued map is convex and non convex. The results are obtained by using fixed point theorem. Finally an example is given to illustrate the obtained results.","PeriodicalId":43654,"journal":{"name":"Annals of the University of Craiova-Mathematics and Computer Science Series","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2022-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73411351","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}
"We propose a new computational proof for the division algorithm that, using vector algebra, generalizes the remainder theorem to divisions for polynomials of any degree over a generic integral domain. Then, we extend this result to calculate the pseudo-divisions. Later, starting from the previous theorems, we obtain some algorithms that calculate the pseudo-remainder and the pseudo-quotient while avoiding long division. Finally, we provide examples and comparisons indicating that these algorithms are efficient in divisions by sparse polynomials and their divisors, as cyclotomic polynomials."
{"title":"A vectorial approach to generalize the remainder theorem","authors":"Marcos A. Hidalgo Rosas, F. Laudano","doi":"10.52846/ami.v49i1.1478","DOIUrl":"https://doi.org/10.52846/ami.v49i1.1478","url":null,"abstract":"\"We propose a new computational proof for the division algorithm that, using vector algebra, generalizes the remainder theorem to divisions for polynomials of any degree over a generic integral domain. Then, we extend this result to calculate the pseudo-divisions. Later, starting from the previous theorems, we obtain some algorithms that calculate the pseudo-remainder and the pseudo-quotient while avoiding long division. Finally, we provide examples and comparisons indicating that these algorithms are efficient in divisions by sparse polynomials and their divisors, as cyclotomic polynomials.\"","PeriodicalId":43654,"journal":{"name":"Annals of the University of Craiova-Mathematics and Computer Science Series","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2022-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83500358","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}
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