The Experts below are selected from a list of 282 Experts worldwide ranked by ideXlab platform
Vo Thi Le Hang - One of the best experts on this subject based on the ideXlab platform.
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On regular semimetric spaces having strong Triangle Functions
Journal of Fixed Point Theory and Applications, 2016Co-Authors: Nguyen Van Dung, Vo Thi Le HangAbstract:In this paper, we show that every regular semimetric space having a strong Triangle Function \(\Phi \) is metrizable if \(\Phi \) is continuous in each of its variables at (0, 0). We also construct a counterexample to give a negative answer to an open question on such spaces posed in Kirk and Shahzad (J Fixed Point Theory Appl 17(3):541–555, 2015).
Jiacheng Chen - One of the best experts on this subject based on the ideXlab platform.
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The Study of the Solution to a Generalized KdV-mKdV Equation
Abstract and Applied Analysis, 2013Co-Authors: Tengwei Shao, Jiacheng ChenAbstract:A mathematical technique based on an auxiliary equation and the symbolic computation system Matlab is employed to investigate a generalized KdV-mKdV equation which possesses high-order nonlinear terms. Some new solutions including the Jacobi elliptic Function solutions, the degenerated soliton-like solutions, and the Triangle Function solutions to the equation are obtained.
Jun-hee Moon - One of the best experts on this subject based on the ideXlab platform.
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Design of a Double Triangular Parallel Mechanism for Precision Positioning and Large Force Generation
IEEE ASME Transactions on Mechatronics, 2014Co-Authors: Hyun-pyo Shin, Jun-hee MoonAbstract:This paper presents the design of a double triangular parallel mechanism for precision positioning and large force generation. In recent years, with the acceleration of miniaturization in mobile appliances, the demand for precision aligning and bonding has been increasing.Such processes require both high precision and large force generation, which are difficult to obtain simultaneously. This study aimed at constructing a precision stage that can perform submicrometer resolution alignment, several-hundred micrometer stroke, and several-hundred Newton force generation.Piezoelectric actuators were tactically placed to constitute a parallel mechanism with a double triangular configuration. In addition, flexure hinges were carefully designed and optimized. The three actuators in the inner Triangle Function as an in-plane positioner, whereas the three actuators in the outer Triangle as an out-of-plane positioner. To facilitate rapid control of the developed stage, two mapping matrices were derived from the inverse and forward kinematics and the corresponding iterative numerical calculations. Finite-element analyses and experimental results proved that the developed stage with the double triangular configuration sufficiently met the requirements of precision positioning and large force generation.
Nguyen Van Dung - One of the best experts on this subject based on the ideXlab platform.
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On regular semimetric spaces having strong Triangle Functions
Journal of Fixed Point Theory and Applications, 2016Co-Authors: Nguyen Van Dung, Vo Thi Le HangAbstract:In this paper, we show that every regular semimetric space having a strong Triangle Function \(\Phi \) is metrizable if \(\Phi \) is continuous in each of its variables at (0, 0). We also construct a counterexample to give a negative answer to an open question on such spaces posed in Kirk and Shahzad (J Fixed Point Theory Appl 17(3):541–555, 2015).
Bruno Nazaret - One of the best experts on this subject based on the ideXlab platform.
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Metrization of probabilistic metric spaces. Applications to fixed point theory and Arzela-Ascoli type theorem
'Elsevier BV', 2021Co-Authors: Bachir Mohammed, Bruno NazaretAbstract:International audienceThis work is devoted to the metrization of probabilistic spaces. More precisely, given such a space $(G,D,\star)$ and provided that the Triangle Function $\star$ is continuous, we exhibit an explicit and canonical metric $\sigma_D$ on $G$ such that the associated topology is homeomorphic to the so-called strong topology. As applications, we make advantage of this explicit metric to present some fixed point theorems on such probabilistic metric structures and we prove a probabilistic version of the Arzela-Ascoli theorem
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Metrization of probabilistic metric spaces. Applications to fixed point theory and Arzela-Ascoli type theorem
2019Co-Authors: Mohammed Bachir, Bruno NazaretAbstract:Schweizer, Sklar and Thorp proved in 1960 that a Menger space $(G,D,T)$ under a continuous $t$-norm $T$, induce a natural topology $\tau$ wich is metrizable. We extend this result to any probabilistic metric space $(G,D,\star)$ provided that the Triangle Function $\star$ is continuous. We prove in this case, that the topological space $(G,\tau)$ is uniformly homeomorphic to a (deterministic) metric space $(G,\sigma_D)$ for some canonical metric $\sigma_D$ on $G$. As applications, we extend the fixed point theorem of Hicks to probabilistic metric spaces which are not necessarily Menger spaces and we prove a probabilistic Arzela-Ascoli type theorem.
