Issue 3, Volume 48, September 2023

2023

1. On Local (like) Derivations on Path Algebras Abderrahim Adrabi , Driss Bennis , Brahim Fahid PDF

   ▸ Abstract

   In this paper, we investigate local derivations and local generalized derivations on path algebras associated with finite acyclic quivers. We show that every local derivation on a path algebra is a derivation, and every local generalized derivation on a path algebra is a generalized derivation. Also, we apply main results on several related maps to local derivations. The established results generalize several ones on some known algebras such as incidence algebras.

   387-399
2. The Carleman Contraction Mapping Method for Quasilinear Elliptic Equations with Over-determined Boundary Data Loc H. Nguyen PDF

   ▸ Abstract

   We propose a globally convergent numerical method to compute solutions to a general class of quasi-linear PDEs with both Neumann and Dirichlet boundary conditions. Combining the quasi-reversibility method and a suitable Carleman weight function, we define a map of which fixed point is the solution to the PDE under consideration. To find this fixed point, we define a recursive sequence with an arbitrary initial term using the same manner as in the proof of the contraction principle. Applying a Carleman estimate, we show that the sequence above converges to the desired solution. On the other hand, we also show that our method delivers reliable solutions even when the given data are noisy. Numerical examples are presented.

   401-422
3. Real Interpolation Between Strong Martingale Hardy Spaces Kaituo Liu , Jianzhong Lu , Lihua Peng PDF

   ▸ Abstract

   In this paper, we establish a decomposition theorem for strong martingale Hardy space $sH^{\sigma}_p$, which is based on its atomic decomposition theorem. By using of this decomposition theorem, we investigate the real interpolation spaces between $sH^{\sigma}_p $ $(0 < p \leq 1)$ and $sL_2$. Furthermore, with the help of the decomposition theorem and the real interpolation method, a sufficient condition to ensure the boundedness of a sublinear operator defined on strong martingale Hardy-Lorentz spaces is given.

   423-443
4. The Constraint Equations of the Einstein-Vlasov-Maxwell System in the Maximal-isotropic Coordinates Timothée Raoul Moutngui See , Pierre Noundjeu PDF

   445-458
5. Modified Subgradient Extragradient Methods for Solving Bilevel Split Variational Inequality Problems in Hilbert Spaces Le Huynh My Van , Dang Le Thuy , Tran Viet Anh PDF

   ▸ Abstract

   In this work, we propose a new method for solving a bilevel split variational inequality problem (BSVIP) in Hilbert spaces. The proposed method is inspired by the subgradient extragradient method for solving a monotone variational inequality problem. A strong convergence theorem for an algorithm for solving such a BSVIP is proved without knowing any information of the Lipschitz and strongly monotone constants of the mappings. Moreover, we do not require any prior information regarding the norm of the given bounded linear operator. Special cases are considered. Two numerical examples are given to illustrate the performance of our algorithm.

   459-478
6. Respondent-Driven Sampling on Sparse Erdös-Rényi Graphs Anthony Cousien , Jean-Stéphane Dhersin , Viet Chi Tran , Thi Phuong Thuy Vo PDF

   ▸ Abstract

   We study the exploration of an Erdös-Rényi random graph by a respondent-driven sampling method, where discovered vertices reveal their neighbors. Some of them receive coupons to reveal in their turn their own neighborhood. This leads to the study of a Markov chain on the random graph that we study. For sparse Erdös-Rényi graphs of large sizes, this process correctly renormalized converges to the solution of a deterministic curve, solution of a system of ODEs absorbed on the abscissa axis. The associated fluctuation process is also studied, providing a functional central limit theorem, with a Gaussian limiting process. Simulations and numerical computation illustrate the study.

   479-513