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1
Content available Cn - pseudo almost automorphic solutions of class r for neutral partial functional differential equations under the light of measure theory
Napo Miailou, Zabsonre Issa, Bayili Gilbert
Silesian Journal of Pure and Applied Mathematics
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2022
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Vol. 12, iss. 1
1--32
EN
The aim of this work is to present new approach to study Cn-(µ,v)-pseudo almost automorphic solutions of class r for some neutral partial functional differential equations in a Banach space when the delay is distributed. We use the variation of constants formula and the spectral decomposition of the phase space.
2
Content available Pseudo almost periodic solutions of infinite class under the light of measure theory
Votsia Djokata, Zabsonre Issa
Silesian Journal of Pure and Applied Mathematics
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2020
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vol. 10, iss. 1
15--43
EN
The aim of this work is to present new approach to study weighted pseudo almost periodic functions with infinite delay using the measure theory. We present a new concept of weighted ergodic functions which is more general than the classical one. Then we establish many interesting results on the functional space of such functions. We study the existence and uniqueness of (μ, ν)-pseudo almost periodic solutions of infinite class for some neutral partial functional differential equations in a Banach space when the delay is distributed on ]−∞, 0] using the spectra decomposition of the phase space developed in Adimy and co-authors.
3
Content available Why the area of a rectangle is calculated by the formula P = a ∙ b?
Jędrzejewski J., Tyrala I.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
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2014
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Vol. 19
67--70
EN
It is evident for many people that the area of a rectangle can be calculated according to the very well known formula: P = a ∙ b. We, mathematicians do believe in no statement without the proof. Then we can ask whether it is possible to prove that this formula is correct. This article answers to that question.
4
Content available remote On the Accuracy of Rough Approximations of Regular Languages
Torres G. M.
Fundamenta Informaticae
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2014
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Vol. 132, nr 4
533--545
EN
In this paper we attempt to measure the accuracy of approximations of regular languages by languages in +−varieties (as defined by Eilenberg). These approximations are upper approximations in the sense of Pawlak’s rough set theory with respect to congruences belonging to the variety of congruences corresponding to the given +−variety. In our approach, the accuracy of an approximation is measured by the relative density of the object language in the approximation language and the asymptotic behavior of this quotient. In particular, we apply our measures of accuracy to k-definite, reverse k-definite, i, j-definite and k-testable approximations.
5
Content available remote OLAPing Field Data : a Theoretical and Implementation Framework
Bimonte S., Kang M.-A., Paolino L., Sebillo M., Zaamoune M., Vitiello G.
Fundamenta Informaticae
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2014
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Vol. 132, nr 2
267--290
EN
Integration of spatial data into multidimensional models leads to the concept of Spatial OLAP (SOLAP). Usually, SOLAP models exploit discrete spatial data. Few works integrate continuous field data into dimensions and measures. In this paper, we provide a formal multidimensional model that supports measures and dimension as continuous field data, independently of their implementation. We provide also a proposal for a logical model allowing aggregation of field measures in a feasible ROLAP architecture.
6
Content available Poincaré-Wirtinger inequalities in bounded variation function spaces
Bergounioux M.
Control and Cybernetics
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2011
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Vol. 40, no 4
921-929
EN
The goal of this paper is to extend Poincaré-Wirtinger inequalities from Sobolev spaces to spaces of functions of bounded variation of second order.
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