2022/2
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- ItemOn μ-proximity spaces(Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky, 2022) Singh, Beenu; Singh, DavinderThe 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.
- ItemClosed 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 , JahanIn 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.
- ItemBayesian 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.
- ItemOn Bourbaki-bounded sets on quasi-pseudometric spaces(Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky, 2022) Otafudu, Olivier Olela; Mukonda, DannyIn 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.
- ItemCompositions and decompositions of binary relations(Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky, 2022) Chajda, Iva; Länger, HelmutIt is well known that to every binary relation on a non-void set I there can be assigned its incidence matrix, also in the case when I is infinite. We show that a certain kind of “multiplication” of such incidence matrices corresponds to the composition of the corresponding relations. Using this fact we investigate the solvability of the equation R ◦ X = S for given binary relations R and S on I and derive an algorithm for solving this equation by using the connections between the corresponding incidence matrices. Moreover, we describe how one can obtain the incidence matrix of a product of binary relations from the incidence matrices of its factors.