Pub Date : 2020-01-01DOI: 10.56082/annalsarscimath.2020.1-2.344
H. Bonnel
The paper deals with semivectorial bilevel optimization problems. The upper level is a scalar optimization problem to be solved by the leader, and the lower level is a multiobjective optimization problem to be solved by several followers acting in a cooperative way inside the greatest coalition, so choosing among Pareto solutions. In the so-called “optimistic problem”, the followers choose among their best responses (i.e. Pareto solutions) one which is the most favorable for the leader. The opposite is the “pessimistic problem”, when there is no cooperation between the leader and the followers, and the followers choice among their best responses may be the worst for the leader. The paper presents a general method which allows, under certain mild hypotheses, to transform a semivectorial bilevel problem into an ordinary bilevel optimization. Some applications are given.
{"title":"WHEN SEMIVECTORIAL BILEVEL OPTIMIZATION REDUCES TO ORDINARY BILEVEL OPTIMIZATION","authors":"H. Bonnel","doi":"10.56082/annalsarscimath.2020.1-2.344","DOIUrl":"https://doi.org/10.56082/annalsarscimath.2020.1-2.344","url":null,"abstract":"The paper deals with semivectorial bilevel optimization problems. The upper level is a scalar optimization problem to be solved by the leader, and the lower level is a multiobjective optimization problem to be solved by several followers acting in a cooperative way inside the greatest coalition, so choosing among Pareto solutions. In the so-called “optimistic problem”, the followers choose among their best responses (i.e. Pareto solutions) one which is the most favorable for the leader. The opposite is the “pessimistic problem”, when there is no cooperation between the leader and the followers, and the followers choice among their best responses may be the worst for the leader. The paper presents a general method which allows, under certain mild hypotheses, to transform a semivectorial bilevel problem into an ordinary bilevel optimization. Some applications are given.","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":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90262710","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 : 2020-01-01DOI: 10.56082/annalsarscimath.2020.1-2.312
D. Tiba, Masahiro Yamamoto
In this article, we discuss some approximation methods for optimal design problems governed by evolution equations of parabolic type. The two investigated approaches are of fixed domain type. We also formulate supplementary questions and problems, related to this subject
{"title":"A PARABOLIC SHAPE OPTIMIZATION PROBLEM","authors":"D. Tiba, Masahiro Yamamoto","doi":"10.56082/annalsarscimath.2020.1-2.312","DOIUrl":"https://doi.org/10.56082/annalsarscimath.2020.1-2.312","url":null,"abstract":"In this article, we discuss some approximation methods for optimal design problems governed by evolution equations of parabolic type. The two investigated approaches are of fixed domain type. We also formulate supplementary questions and problems, related to this subject","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":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80327713","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 : 2020-01-01DOI: 10.56082/annalsarscimath.2020.1-2.476
H. Mukaidani, R. Saravanakumar, Hua Xu, W. Zhuang
In this study, a robust static output feedback (SOF) Stackelberg strategy for a class of uncertain Markov Jump linear stochastic delay systems (UMJLSDSs) is investigated. After introducing certain preliminaries, a SOF Stackelberg strategy is derived. It is shown that the strategy set is established by solving two constraint optimization problems and cross-coupled stochastic matrix equations that consist of bilinear matrix inequalities (BMIs). In order to obtain the corresponding solutions of the constraint optimization problems and cross coupled stochastic matrix equations (CCSMEs), an algorithm based on the Krasnoselskii iterative algorithm is proposed instead of solving BMI. It is also shown that weak convergence can be achieved using this approach. A practical example is provided to demonstrate the effectiveness and convergence of the proposed algorithm.
{"title":"ROBUST STATIC OUTPUT FEEDBACK STACKELBERG STRATEGY FOR MARKOV JUMP DELAY STOCHASTIC SYSTEMS","authors":"H. Mukaidani, R. Saravanakumar, Hua Xu, W. Zhuang","doi":"10.56082/annalsarscimath.2020.1-2.476","DOIUrl":"https://doi.org/10.56082/annalsarscimath.2020.1-2.476","url":null,"abstract":"In this study, a robust static output feedback (SOF) Stackelberg strategy for a class of uncertain Markov Jump linear stochastic delay systems (UMJLSDSs) is investigated. After introducing certain preliminaries, a SOF Stackelberg strategy is derived. It is shown that the strategy set is established by solving two constraint optimization problems and cross-coupled stochastic matrix equations that consist of bilinear matrix inequalities (BMIs). In order to obtain the corresponding solutions of the constraint optimization problems and cross coupled stochastic matrix equations (CCSMEs), an algorithm based on the Krasnoselskii iterative algorithm is proposed instead of solving BMI. It is also shown that weak convergence can be achieved using this approach. A practical example is provided to demonstrate the effectiveness and convergence of the proposed algorithm.","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":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80779075","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 : 2020-01-01DOI: 10.56082/annalsarscimath.2020.1-2.274
G. Moroşanu, A. Petruşel
In a real Hilbert space H, let us consider the boundary-value problem −εu00(t) + µu0 (t) + Au(t) + Bu(t) 3 f(t), t ∈ [0, T]; u(0) = u0, u0 (T) = 0, where T > 0 is a given time instant, ε, µ are positive parameters, A : D(A) ⊂ H → H is a (possibly set-valued) maximal monotone operator, and B : H → H is a Lipschitz operator. In this paper, we investigate the behavior of the solutions to this problem in two cases: (i) µ > 0 fixed, 0 < ε → 0, and (ii) ε > 0 fixed and 0 < µ → 0. Notice that if µ = 1 and ε is a positive small parameter, the above problem is a Lions-type regularization of the Cauchy problem u 0 (t) + Au(t) + Bu(t) 3 f(t), t ∈ [0, T]; u(0) = u0, which was recently studied by L. Barbu and G. Moro¸sanu [Commun. Contemp. Math. 19 (2017)]. Our abstract results are illustrated with examples related to the heat equation and the telegraph differential system.
{"title":"TWO-PARAMETER SECOND-ORDER DIFFERENTIAL INCLUSIONS IN HILBERT SPACES","authors":"G. Moroşanu, A. Petruşel","doi":"10.56082/annalsarscimath.2020.1-2.274","DOIUrl":"https://doi.org/10.56082/annalsarscimath.2020.1-2.274","url":null,"abstract":"In a real Hilbert space H, let us consider the boundary-value problem −εu00(t) + µu0 (t) + Au(t) + Bu(t) 3 f(t), t ∈ [0, T]; u(0) = u0, u0 (T) = 0, where T > 0 is a given time instant, ε, µ are positive parameters, A : D(A) ⊂ H → H is a (possibly set-valued) maximal monotone operator, and B : H → H is a Lipschitz operator. In this paper, we investigate the behavior of the solutions to this problem in two cases: (i) µ > 0 fixed, 0 < ε → 0, and (ii) ε > 0 fixed and 0 < µ → 0. Notice that if µ = 1 and ε is a positive small parameter, the above problem is a Lions-type regularization of the Cauchy problem u 0 (t) + Au(t) + Bu(t) 3 f(t), t ∈ [0, T]; u(0) = u0, which was recently studied by L. Barbu and G. Moro¸sanu [Commun. Contemp. Math. 19 (2017)]. Our abstract results are illustrated with examples related to the heat equation and the telegraph differential system.","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":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90089976","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 : 2020-01-01DOI: 10.56082/annalsarscimath.2020.1-2.87
R. Budaca
The D-dimensional Schr¨odinger equation for an isotropic sextic potential is brought to a form compatible with the canonical bi-confluent Heun differential equation. The quasi-exactly solvable properties of the model are recovered by considering polynomial solutions for the bi-confluent Heun equation which constrains the potential parameters in terms of rotation quantum number, space dimension and order of the exact solvability. It is shown that the state independence of the potential can be maintained by using a see-saw adjustment between the rotation quantum number and the exact solvability order. An analysis on the exactly solvable instances of the sextic potential is presented in correlation with the extended set of exactly solvable states.
{"title":"QUASI-EXACT SOLVABILITY OF THE D-DIMENSIONAL SEXTIC POTENTIAL IN TERMS OF TRUNCATED BI-CONFLUENT HEUN FUNCTIONS","authors":"R. Budaca","doi":"10.56082/annalsarscimath.2020.1-2.87","DOIUrl":"https://doi.org/10.56082/annalsarscimath.2020.1-2.87","url":null,"abstract":"The D-dimensional Schr¨odinger equation for an isotropic sextic potential is brought to a form compatible with the canonical bi-confluent Heun differential equation. The quasi-exactly solvable properties of the model are recovered by considering polynomial solutions for the bi-confluent Heun equation which constrains the potential parameters in terms of rotation quantum number, space dimension and order of the exact solvability. It is shown that the state independence of the potential can be maintained by using a see-saw adjustment between the rotation quantum number and the exact solvability order. An analysis on the exactly solvable instances of the sextic potential is presented in correlation with the extended set of exactly solvable states.","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":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76476094","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 : 2020-01-01DOI: 10.56082/annalsarscimath.2020.1-2.117
Subhasis Das
Let p(z) be a polynomial of degree n with real or complex coefficients. Using the Lacunary type polynomial, Gugenheimer generalized the Cauchy bound concerning the moduli of zeros of a polynomial p (z). Jain further improved the Gugenheimer bound. In the present paper an attempt to investigate and extend the previous results were made. In many cases we found that the new bounds are much better than some of the other well-known bounds
{"title":"ON CAUCHY’S TYPE BOUND FOR ZEROS OF A POLYNOMIAL","authors":"Subhasis Das","doi":"10.56082/annalsarscimath.2020.1-2.117","DOIUrl":"https://doi.org/10.56082/annalsarscimath.2020.1-2.117","url":null,"abstract":"Let p(z) be a polynomial of degree n with real or complex coefficients. Using the Lacunary type polynomial, Gugenheimer generalized the Cauchy bound concerning the moduli of zeros of a polynomial p (z). Jain further improved the Gugenheimer bound. In the present paper an attempt to investigate and extend the previous results were made. In many cases we found that the new bounds are much better than some of the other well-known bounds","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":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73039125","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 : 2020-01-01DOI: 10.56082/annalsarscimath.2020.1-2.238
Hristo Paraskevov, A. Stefanov, B. Stoyanov
We present a novel pseudorandom insertion least significant bit (LSB) based hiding scheme using Circle map byte output. The proposed algorithm is analysed by means of computer simulation. We evaluated the designed LSB method with NIST and ENT statistical packages, peak signal-to-noise ratio, and histogram analysis. The results data show good performance of the novel stego hiding
{"title":"YASH: YET ANOTHER STEGO HIDING","authors":"Hristo Paraskevov, A. Stefanov, B. Stoyanov","doi":"10.56082/annalsarscimath.2020.1-2.238","DOIUrl":"https://doi.org/10.56082/annalsarscimath.2020.1-2.238","url":null,"abstract":"We present a novel pseudorandom insertion least significant bit (LSB) based hiding scheme using Circle map byte output. The proposed algorithm is analysed by means of computer simulation. We evaluated the designed LSB method with NIST and ENT statistical packages, peak signal-to-noise ratio, and histogram analysis. The results data show good performance of the novel stego hiding","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":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90692875","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 : 2020-01-01DOI: 10.56082/annalsarscimath.2020.1-2.11
V. Berinde
In this paper we introduce a new class of mappings, obtained by merging the concepts of almost contraction and convex contraction and called almost convex contractions. This general class includes both the almost contractions and convex contractions. Existence fixed point theorems for almost convex contractions of order 2 and of order p are established.
{"title":"APPROXIMATING FIXED POINTS OF ALMOST CONVEX CONTRACTIONS IN METRIC SPACES","authors":"V. Berinde","doi":"10.56082/annalsarscimath.2020.1-2.11","DOIUrl":"https://doi.org/10.56082/annalsarscimath.2020.1-2.11","url":null,"abstract":"In this paper we introduce a new class of mappings, obtained by merging the concepts of almost contraction and convex contraction and called almost convex contractions. This general class includes both the almost contractions and convex contractions. Existence fixed point theorems for almost convex contractions of order 2 and of order p are established.","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":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77879925","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 : 2020-01-01DOI: 10.56082/annalsarscimath.2020.1-2.295
C. Fetecau, M. Agop
Analytical expressions for the steady-state components of the dimensionless starting solutions corresponding to some oscillatory motions through a horizontal rectangular channel of two classes of incompressible Newtonian fluids with power-law dependence of viscosity on the pressure are established in the simplest forms. The fluid motion is generated by the lower plate that oscillates in its plane. For validation, three limiting cases are considered and interesting graphical representations are provided. It is worth pointing out the fact that such solutions are important in practice for those who want to eliminate the transients from their experiments. In addition, the dimensionless steady shear stresses corresponding to the simple Couette flow of such fluids are constants on the whole flow domain although the adequate velocity fields are functions of y
{"title":"EXACT SOLUTIONS FOR OSCILLATING MOTIONS OF SOME FLUIDS WITH POWER-LAW DEPENDENCE OF VISCOSITY ON THE PRESSURE","authors":"C. Fetecau, M. Agop","doi":"10.56082/annalsarscimath.2020.1-2.295","DOIUrl":"https://doi.org/10.56082/annalsarscimath.2020.1-2.295","url":null,"abstract":"Analytical expressions for the steady-state components of the dimensionless starting solutions corresponding to some oscillatory motions through a horizontal rectangular channel of two classes of incompressible Newtonian fluids with power-law dependence of viscosity on the pressure are established in the simplest forms. The fluid motion is generated by the lower plate that oscillates in its plane. For validation, three limiting cases are considered and interesting graphical representations are provided. It is worth pointing out the fact that such solutions are important in practice for those who want to eliminate the transients from their experiments. In addition, the dimensionless steady shear stresses corresponding to the simple Couette flow of such fluids are constants on the whole flow domain although the adequate velocity fields are functions of y","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":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78051526","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 : 2020-01-01DOI: 10.56082/annalsarscimath.2020.1-2.132
S. Gal
In this paper we obtain quantitative estimates in approximation by the so-called polynomial possibilistic operators of Durrmeyer type and of Kantorovich type, whose expressions are obtained from their classical correspondents by replacing the usual integral with the possibilistic integral.
{"title":"APPROXIMATION BY POLYNOMIAL POSSIBILISTIC INTEGRAL OPERATORS","authors":"S. Gal","doi":"10.56082/annalsarscimath.2020.1-2.132","DOIUrl":"https://doi.org/10.56082/annalsarscimath.2020.1-2.132","url":null,"abstract":"In this paper we obtain quantitative estimates in approximation by the so-called polynomial possibilistic operators of Durrmeyer type and of Kantorovich type, whose expressions are obtained from their classical correspondents by replacing the usual integral with the possibilistic integral.","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":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76332683","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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