2022/2

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    On μ-proximity spaces
    (Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky, 2022) Singh, Beenu; Singh, Davinder
    The purpose of this paper is to introduce the notion of a μ-proximity base and to explore some properties and results of μ-proximity spaces. We show that the collection of all μ-proximities constitutes a complete lattice.
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    Closed form expressions for curved surface area of revolution of hyperbolas: A hypergeometric function approach
    (Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky, 2022) Qureshi, M. I.; Akhtar, Naved; Husain, Iftikhar; Ara , Jahan
    In this paper, we provide the exact expressions (not found in the liter- ature) for the curved surface area of revolution (about the x-axis and y-axis) of horizontal and oblique hyperbolas. Closed-form expressions for the curved surface area are obtained in terms of Gauss function, Clausen function, and Appell’s hy- pergeometric function of the first kind.
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    Bayesian variable selection for linear regression with the κ-G priors
    (Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky, 2022) Ma, Zichen; Fokoué, Ernest P.
    In this paper, we propose a method that balances between variable se- lection and variable shrinkage in linear regression. A diagonal matrix G is injected to the covariance matrix of prior distribution of the coefficient vector β, with each gj , bounded between 0 and 1, on the diagonal serving as a stabilizer of the corre- sponding βj . Mathematically, a gj value close to 0 indicates that the βj is nonzero, and hence the corresponding variable should be selected, whereas the value of gj close to 1 indicates otherwise. We prove this property under orthogonality. Com- putationally, the proposed method is easy to fit using automated programs such as JAGS. We provide three examples to verify the capability of this methodology in variable selection and shrinkage.
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    On Bourbaki-bounded sets on quasi-pseudometric spaces
    (Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky, 2022) Otafudu, Olivier Olela; Mukonda, Danny
    In metric spaces, a set is Bourbaki-bounded if and only if every real- valued uniformily continuous function on it is bounded. In this article, we study Bourbaki-boundedness on quasi-pseudometric spaces. It turns out that if a set is Bourbaki-bounded on a symmetrized quasi-pseudometric space, then it is Bourbaki- bounded in the quasi-metric space but the converse need not to be true. We show that an asymmetric normed space is Bourbaki-bounded if and only if it is bounded. Consequently, we prove that every real-valued semi-Lipschitz in the small function on a quasi-metric space is bounded if and only if the quasi-metric is Bourbaki-bounded. This article extends some results from Beer and Garrido’s paper [2] from the metric point of view to the context of quasi-metric spaces.
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    Existence and uniqueness results for nonlinear fractional Langevin integro-differential equations with boundary conditions
    (Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky, 2022) Lachouri, Adel; Ardjouni, Abdelouaheb; Djoudi, Ahcene
    This paper is devoted to the study of nonlinear fractional Langevin inte- gro differential equations with boundary conditions. Some effective results concern- ing the existence and uniqueness are obtained by applying the Banach contraction mapping principle and the Schauder fixed point theorem. An example is presented illustrating the effectiveness of the theoretical results.