Pub Date : 2021-01-01DOI: 10.56082/annalsarscimath.2022.1-2.93
Ghodrat Moazzaf
In this paper we study the evolution of closed convex hypersurfacesunder the mixed volume preserving curvature flow in Euclidean spacewith the speed given by reversed function that is symmetric and ho-mogeneous of degree one. We prove that the hypersurfaces preserveconvexity under the flow, the maximum existence time is infinite andthe hypersurfaces asymptotically approach to sphere
{"title":"EVOLUTION OF CONVEX HYPERSURFACES BY A FULLY NONLINEAR MIXED VOLUME PRESERVING CURVATURE FLOW","authors":"Ghodrat Moazzaf","doi":"10.56082/annalsarscimath.2022.1-2.93","DOIUrl":"https://doi.org/10.56082/annalsarscimath.2022.1-2.93","url":null,"abstract":"In this paper we study the evolution of closed convex hypersurfacesunder the mixed volume preserving curvature flow in Euclidean spacewith the speed given by reversed function that is symmetric and ho-mogeneous of degree one. We prove that the hypersurfaces preserveconvexity under the flow, the maximum existence time is infinite andthe hypersurfaces asymptotically approach to sphere","PeriodicalId":38807,"journal":{"name":"Annals of the Academy of Romanian Scientists: Series on Mathematics and its Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76491336","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}
Pub Date : 2021-01-01DOI: 10.56082/annalsarscimath.2022.1-2.142
A. Kasri
This paper is devoted to study a quasistatic contact problem be-tween a viscoelastic material with long memory and a foundation. Thecontact is modelled with a version of Coulomb’s law of dry friction anda general normal compliance condition. We derive a variational formu-lation of the model and, under a smallness assumption, we establishthe existence of a weak solution to the problem. The proof is based onthe time-discretization method, the Banach fixed point theorem andarguments of compactness, lower semicontinuity and monotonicity
{"title":"A FRICTIONAL CONTACT PROBLEM WITH NORMAL COMPLIANCE FOR VISCOELASTIC MATERIALS WITH LONG MEMORY","authors":"A. Kasri","doi":"10.56082/annalsarscimath.2022.1-2.142","DOIUrl":"https://doi.org/10.56082/annalsarscimath.2022.1-2.142","url":null,"abstract":"This paper is devoted to study a quasistatic contact problem be-tween a viscoelastic material with long memory and a foundation. Thecontact is modelled with a version of Coulomb’s law of dry friction anda general normal compliance condition. We derive a variational formu-lation of the model and, under a smallness assumption, we establishthe existence of a weak solution to the problem. The proof is based onthe time-discretization method, the Banach fixed point theorem andarguments of compactness, lower semicontinuity and monotonicity","PeriodicalId":38807,"journal":{"name":"Annals of the Academy of Romanian Scientists: Series on Mathematics and its Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84047069","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}
Pub Date : 2021-01-01DOI: 10.56082/annalsarscimath.2022.1-2.122
N. Zhao, Huiyan Zhang, Peng Shi
This paper investigates the stabilization problem for stochastic net-worked control systems under periodic denial-of-service (DoS) jammingattacks. First, the resilient hybrid-triggered communication scheme isdeveloped to reduce the network transmission data and improve theutilization efficiency, where a Bernoulli distribution is used to charac-terize the switching protocol between time-triggered scheme and event-triggered scheme. Then, a resilient hybrid-driven control protocol isdesigned, and a new switched stochastic system is constructed. Suffi-cient conditions of the mean-square exponential stability are derivedfor the underlying system under DoS attacks. Furthermore, a co-designscheme of the feedback gain and the hybrid-triggering parameter is ob-tained by solving linear matrix inequalities. Finally, a satellite controlsystem is employed to illustrate the virtue and applicability of the pro-posed approach.
{"title":"RESILIENT HYBRID-TRIGGERED CONTROL FOR NETWORKED STOCHASTIC SYSTEMS UNDER DENIAL-OF-SERVICE ATTACKS","authors":"N. Zhao, Huiyan Zhang, Peng Shi","doi":"10.56082/annalsarscimath.2022.1-2.122","DOIUrl":"https://doi.org/10.56082/annalsarscimath.2022.1-2.122","url":null,"abstract":"This paper investigates the stabilization problem for stochastic net-worked control systems under periodic denial-of-service (DoS) jammingattacks. First, the resilient hybrid-triggered communication scheme isdeveloped to reduce the network transmission data and improve theutilization efficiency, where a Bernoulli distribution is used to charac-terize the switching protocol between time-triggered scheme and event-triggered scheme. Then, a resilient hybrid-driven control protocol isdesigned, and a new switched stochastic system is constructed. Suffi-cient conditions of the mean-square exponential stability are derivedfor the underlying system under DoS attacks. Furthermore, a co-designscheme of the feedback gain and the hybrid-triggering parameter is ob-tained by solving linear matrix inequalities. Finally, a satellite controlsystem is employed to illustrate the virtue and applicability of the pro-posed approach.","PeriodicalId":38807,"journal":{"name":"Annals of the Academy of Romanian Scientists: Series on Mathematics and its Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76798857","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}
Pub Date : 2021-01-01DOI: 10.56082/annalsarscimath.2022.1-2.70
N. Das, Madhusmita Sahoo
In this paper we introduce a class A ⊂ L∞(D) such that if φ ∈ Aand satisfies certain positive-definite condition, then there exists aψ ∈ A such that φ(z) ≤ αeψ(z), for some constant α > 0. Further,if φ(z) = hAkz, kzi, for some bounded positive, invertible operator Afrom the Bergman space L2a(D) into itself then ψ(z) = h(log A)kz, kzi.Here kz, z ∈ D are the normalized reproducing kernel of L2a(D). Ap-plications of these results are also discusseonly a non-standard growth condition. We show that our problem admits at least one weak solution. In order to do this, the main tool is the Berkovits degree theory for abstract Hammerstein type mappings.
{"title":"BEREZIN TRANSFORM OF INVERTIBLE POSITIVE OPERATORS","authors":"N. Das, Madhusmita Sahoo","doi":"10.56082/annalsarscimath.2022.1-2.70","DOIUrl":"https://doi.org/10.56082/annalsarscimath.2022.1-2.70","url":null,"abstract":"In this paper we introduce a class A ⊂ L∞(D) such that if φ ∈ Aand satisfies certain positive-definite condition, then there exists aψ ∈ A such that φ(z) ≤ αeψ(z), for some constant α > 0. Further,if φ(z) = hAkz, kzi, for some bounded positive, invertible operator Afrom the Bergman space L2a(D) into itself then ψ(z) = h(log A)kz, kzi.Here kz, z ∈ D are the normalized reproducing kernel of L2a(D). Ap-plications of these results are also discusseonly a non-standard growth condition. We show that our problem admits at least one weak solution. In order to do this, the main tool is the Berkovits degree theory for abstract Hammerstein type mappings.","PeriodicalId":38807,"journal":{"name":"Annals of the Academy of Romanian Scientists: Series on Mathematics and its Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85812115","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}
Pub Date : 2021-01-01DOI: 10.56082/annalsarscimath.2021.1-2.166
A. Cernea
A Cauchy problem associated to a fractional integro-differential de-fined by a Caputo type fractional derivative is studied. It is proved thearcwise connectedness of the solution set and that the set of selectionscorresponding to the solutions of the problem considered is a retractof the space of integrable functions on a given interval.
{"title":"ON A CAPUTO TYPE FRACTIONAL INTEGRO-DIFFERENTIAL INCLUSION","authors":"A. Cernea","doi":"10.56082/annalsarscimath.2021.1-2.166","DOIUrl":"https://doi.org/10.56082/annalsarscimath.2021.1-2.166","url":null,"abstract":"A Cauchy problem associated to a fractional integro-differential de-fined by a Caputo type fractional derivative is studied. It is proved thearcwise connectedness of the solution set and that the set of selectionscorresponding to the solutions of the problem considered is a retractof the space of integrable functions on a given interval.","PeriodicalId":38807,"journal":{"name":"Annals of the Academy of Romanian Scientists: Series on Mathematics and its Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84664856","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}
Pub Date : 2021-01-01DOI: 10.56082/annalsarscimath.2021.1-2.5
V. Hasanov
In this paper we study a special case of linearly perturbed discrete-time algebraic Riccati equation. We give some sufficient conditions forthe existence of a positive definite solution of the considered equation.We propose a basic fixed point iteration and its inversion free variantfor finding a positive definite solution. Moreover, by specially choosingthe initial value in the basic fixed point iteration we prove that it con-verges to the largest solution. The theoretical results are illustratedby numerical examples.
{"title":"POSITIVE DEFINITE SOLUTIONS OF A LINEARLY PERTURBED MATRIX EQUATION","authors":"V. Hasanov","doi":"10.56082/annalsarscimath.2021.1-2.5","DOIUrl":"https://doi.org/10.56082/annalsarscimath.2021.1-2.5","url":null,"abstract":"In this paper we study a special case of linearly perturbed discrete-time algebraic Riccati equation. We give some sufficient conditions forthe existence of a positive definite solution of the considered equation.We propose a basic fixed point iteration and its inversion free variantfor finding a positive definite solution. Moreover, by specially choosingthe initial value in the basic fixed point iteration we prove that it con-verges to the largest solution. The theoretical results are illustratedby numerical examples.","PeriodicalId":38807,"journal":{"name":"Annals of the Academy of Romanian Scientists: Series on Mathematics and its Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73925327","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}
Pub Date : 2021-01-01DOI: 10.56082/annalsarscimath.2022.1-2.59
G. Nedzhibov
IIn the present research, we take another look at the relatively newmethod for computing eigenvalues and eigenvectors of the Frobeniuscompanion matrix. The purpose of the paper is to interpret the methodconsidered in terms of oblique projection methods, i.e. as a Galerkintype method. Based on this dependence, we derive some new theoreti-cal results. We establish certain error estimates, which will contributeto further studies of the convergence analysis of the method under con-sideration
{"title":"ON AN OBLIQUE PROJECTION METHOD FOR SOLVING THE EIGENVALUE PROBLEM OF THE COMPANION MATRIX","authors":"G. Nedzhibov","doi":"10.56082/annalsarscimath.2022.1-2.59","DOIUrl":"https://doi.org/10.56082/annalsarscimath.2022.1-2.59","url":null,"abstract":"IIn the present research, we take another look at the relatively newmethod for computing eigenvalues and eigenvectors of the Frobeniuscompanion matrix. The purpose of the paper is to interpret the methodconsidered in terms of oblique projection methods, i.e. as a Galerkintype method. Based on this dependence, we derive some new theoreti-cal results. We establish certain error estimates, which will contributeto further studies of the convergence analysis of the method under con-sideration","PeriodicalId":38807,"journal":{"name":"Annals of the Academy of Romanian Scientists: Series on Mathematics and its Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74584007","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}
Pub Date : 2021-01-01DOI: 10.56082/annalsarscimath.2022.1-2.111
S. Karpagam
We introduce a new contraction map called p-cyclic Boyd-Wongcontraction, defined on the union of p (p ≥ 2) non empty subsets of ametric space. We give sufficient conditions for the existence of a uniquefixed point, best proximity point or periodic point for the map and aniterative method is used to approximate the fixed point and the bestproximate point.variable exponents where the right-hand side f is in L q(·) , q(·) : Ω → (1, +∞). The functional setting involves anisotropic Sobolev spaces with variable exponents as well as weak Lebesgue (Marcinkiewicz) spaces with variable exponents.
{"title":"EXISTENCE OF FIXED POINTS AND BEST PROXIMITY POINTS OF p-CYCLIC BOYD-WONG CONTRACTIONS","authors":"S. Karpagam","doi":"10.56082/annalsarscimath.2022.1-2.111","DOIUrl":"https://doi.org/10.56082/annalsarscimath.2022.1-2.111","url":null,"abstract":"We introduce a new contraction map called p-cyclic Boyd-Wongcontraction, defined on the union of p (p ≥ 2) non empty subsets of ametric space. We give sufficient conditions for the existence of a uniquefixed point, best proximity point or periodic point for the map and aniterative method is used to approximate the fixed point and the bestproximate point.variable exponents where the right-hand side f is in L q(·) , q(·) : Ω → (1, +∞). The functional setting involves anisotropic Sobolev spaces with variable exponents as well as weak Lebesgue (Marcinkiewicz) spaces with variable exponents.","PeriodicalId":38807,"journal":{"name":"Annals of the Academy of Romanian Scientists: Series on Mathematics and its Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79599486","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}
Pub Date : 2021-01-01DOI: 10.56082/annalsarscimath.2022.1-2.195
V. Drăgan, I. Ivanov
In this paper we consider the problem of minimization of the mean square value of the deviation of a random signal z(tf ) from a given target ζ. The random signal z(tf ) represents the value at instant time tf of an output of a controlled dynamical system described by an Itˆo differential equation. Both the case when the set of admissible controls consist of general nonanticipative stochastic processes and the case when only piecewise constant controls are available are analyzed. We show that in both cases the optimal controls are in affine state feedback forms. Explicit formulae of the gain matrices of the optimal controls are provided.
{"title":"THE MINIMIZATION OF THE MEAN SQUARE OF THE DEVIATION OF A RANDOM SIGNAL FROM A GIVEN TARGET","authors":"V. Drăgan, I. Ivanov","doi":"10.56082/annalsarscimath.2022.1-2.195","DOIUrl":"https://doi.org/10.56082/annalsarscimath.2022.1-2.195","url":null,"abstract":"In this paper we consider the problem of minimization of the mean square value of the deviation of a random signal z(tf ) from a given target ζ. The random signal z(tf ) represents the value at instant time tf of an output of a controlled dynamical system described by an Itˆo differential equation. Both the case when the set of admissible controls consist of general nonanticipative stochastic processes and the case when only piecewise constant controls are available are analyzed. We show that in both cases the optimal controls are in affine state feedback forms. Explicit formulae of the gain matrices of the optimal controls are provided.","PeriodicalId":38807,"journal":{"name":"Annals of the Academy of Romanian Scientists: Series on Mathematics and its Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82943668","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}
Pub Date : 2021-01-01DOI: 10.56082/annalsarscimath.2022.1-2.178
N. Das, Swarupa Roy
In this paper we have shown that if φ ∈ (L2h(dAα))⊥∩ L∞(D) andRangeT(α)φis closed, then the Toeplitz operator T(α)φ∈ LL2a(dAα)is a Fredholm operator of index zero and T(α)φis not of finite rank.Several applications of the result were also obtained. We further showthat if φ ∈ L∞Mn(D) is such that Tφis Fredholm and of index zero inLL2,Cna(dAα)then there exists ψ ∈ En×n= E ⊗Mnsuch that Tφ+δψis invertible for all sufficiently small nonzero δ. Here E is a total sub-space of L∞(D) and Mnis the set of all n × n matrices with complexentries.
{"title":"FREDHOLM TOEPLITZ OPERATORS ON THE WEIGHTED BERGMAN SPACES","authors":"N. Das, Swarupa Roy","doi":"10.56082/annalsarscimath.2022.1-2.178","DOIUrl":"https://doi.org/10.56082/annalsarscimath.2022.1-2.178","url":null,"abstract":"In this paper we have shown that if φ ∈ (L2h(dAα))⊥∩ L∞(D) andRangeT(α)φis closed, then the Toeplitz operator T(α)φ∈ LL2a(dAα)is a Fredholm operator of index zero and T(α)φis not of finite rank.Several applications of the result were also obtained. We further showthat if φ ∈ L∞Mn(D) is such that Tφis Fredholm and of index zero inLL2,Cna(dAα)then there exists ψ ∈ En×n= E ⊗Mnsuch that Tφ+δψis invertible for all sufficiently small nonzero δ. Here E is a total sub-space of L∞(D) and Mnis the set of all n × n matrices with complexentries.","PeriodicalId":38807,"journal":{"name":"Annals of the Academy of Romanian Scientists: Series on Mathematics and its Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85346272","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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