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[CT042]

CT042 (1/1) : Hyperbolic equations and hyperbolic systems (35L) / Functional equations and inequalities (39B) / Designs and configurations (05B)

Session Time & Room : 3E (Aug.23, 17:40-19:20) @G601
Type : Contributed Talk
Abstract : We study the exact internal and boundary controllability for a second order linear evolution problem defined in a two-component domain. We prescribe a homogeneous Dirichlet condition on the exterior boundary and a jump of the displacement proportional to the conormal derivatives on the interface. This last condition is the mathematical interpretation of an imperfect interface. The results are achieved via a constructive method known as Hilbert Uniqueness Method, HUM for short, introduced by J. -L. Lions. Unlike classical cases, we find lower bounds for the control times depending not only on the geometry of the domain and on the coefficient matrix of our problems but also on the coefficient of proportionality of the jump with respect to the conormal derivatives. References [1] S. Monsurro`, A. K. Nandakumaran, C. Perugia, Exact Internal Con- trollability for a Problem with Imperfect Interface, Appl. Math. Op- tim. (2022), 1-33. [2] S. Monsurro`, A. K. Nandakumaran, C. Perugia, A Note on the Exact Boundary Controllability for an Imperfect Transmission Problem, Ric. Mat. 40 (2021), 1-18.
Classification : 35LXX, 35QXX
Format : Talk at Waseda University
Author(s) :
- Sara Monsurrò (University of Salerno)

Session Time & Room : 3E (Aug.23, 17:40-19:20) @G601
Type : Contributed Talk
Abstract : Motivated by the interplay of multiple species in several real world transport processes, we propose a bidirectional totally asymmetric simple exclusion process with two finite reservoirs regulating the inflow of oppositely directed particles corresponding to two different species. The system’s stationary characteristics such as densities, currents, etc., are investigated using a theoretical framework based on mean-field approximation and are supported by extensive Monte Carlo simulations. The impact of species, quantified by filling factor, has been comprehensively analyzed.
Classification : 35Lxx, 70Exx, 70Lxx, 37Axx
Format : Talk at Waseda University
Author(s) :
- Ankita Gupta (Indian Institute of Technology Ropar)
- Bipasha Pal (Stockholm University)
- Arvind Kumar Gupta (Indian Institute of Technology Ropar)

Session Time & Room : 3E (Aug.23, 17:40-19:20) @G601
Type : Contributed Talk
Abstract : Algebraic Riccati equations (AREs) have been extensively applied in linear optimal control problems and many efficient numerical methods were developed. The stabilizing (or almost stabilizing) solution has attracted the most attention among all Hermitian solutions of the ARE in the past works. Nevertheless, it is an interesting and challenging issue in finding the extremal solutions of AREs which play an important role in the applications. The contribution of this paper is twofold. Firstly, the existence of these extremal solutions is established under the framework of fixed-point iteration. Secondly, an accelerated fixed-point iteration (AFPI) based on the semigroup property is developed for computing four extremal solutions of the discrete-time algebraic Riccati equation. In addition, we prove that the convergence of the AFPI is at least R-suplinear with order $r>1$ under some mild assumptions. Numerical examples are shown to illustrate the feasibility and accuracy of the proposed algorithm.
Classification : 39B12, 39B42, 65H05, 15A24
Author(s) :
- Chun-Yueh Chiang (Center for General Education, National Formosa University)
- Hung-Yuan Fan (National Taiwan Normal University )

Session Time & Room : 3E (Aug.23, 17:40-19:20) @G601
Type : Contributed Talk
Abstract : Monte Carlo methods are effective to avoid the "Curse of Dimensionality," while not perfect since their convergences are late. To overcome the weakness, quasi-Monte Carlo methods have been developed. Some of the methods use low discrepancy point sets called $(T, M, S)$-nets. In this talk, I present a new construction procedure of $(T, M, S)$-nets from orthogonal arrays as an application of the extension of Sudoku to higher dimensions named Sudoku hypercubes.
Classification : 05B15, 65C05
Format : Talk at Waseda University
Author(s) :
- Shigetaka Taga (University of Tsukuba)

Session Time & Room : 3E (Aug.23, 17:40-19:20) @G601
Type : Contributed Talk
Abstract : A set of $\ell$ orthogonal $n$-ary operations or hypercubes of order $m$ is equivalent to an $(\ell,m^n,\ell-n+1)$ maximum distance separable or MDS code. Consequently, the problem of constructing MDS codes can be reduced to constructing orthogonal operations. We research constructing a ternary medial quasigroup possessing parastrophic orthogonality property. A necessary and sufficient condition that the quasigroup is self-orthogonal, strongly self-orthogonal or totally parastrophically orthogonal is that each polynomial of a certain set is invertible-valued.
Classification : 05B15, 20N05
Format : Online Talk on Zoom
Author(s) :
- Fedir Sokhatsky (Vasyl` Stus Donetsk National University)
- Iryna Fryz (Vasyl` Stus Donetsk National University)