• Journal of applied mathematics & informatics
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• v.42 no.1
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• pp.169-178
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• 2024

The purpose of this paper is to introduce the concept of pairwise fuzzy semi door spaces and study its properties and applications. The conditions for a pairwise fuzzy semi door space to become a pairwise fuzzy semi Volterra space and for a pairwise fuzzy semi Volterra space together with a pairwise fuzzy semi door space to become a pairwise fuzzy semi Baire space are established. Also, the inter-relations between pairwise fuzzy semi Volterra spaces and other fuzzy bitopological spaces such as pairwise fuzzy semi Baire space, pairwise fuzzy semi σ-Baire space, pairwise fuzzy semi D-Baire space, pairwise fuzzy semi GID-space, pairwise fuzzy semi door space are also discussed in this paper.

• Journal of applied mathematics & informatics
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• v.33 no.5_6
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• pp.503-515
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• 2015

In this paper the concepts of pairwise fuzzy regular Volterra spaces and pairwise fuzzy weakly regular Volterra spaces are introduced. Several characterizations of pairwise fuzzy regular Volterra spaces and pair-wise fuzzy weakly regular Volterra spaces are investigated.

• Kyungpook Mathematical Journal
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• v.53 no.1
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• pp.125-133
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• 2013

In this paper, we introduce the notion of near pairwise compactness which generalizes the notion of pairwise compactness.

• Journal of applied mathematics & informatics
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• v.26 no.3_4
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• pp.757-766
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• 2008

We define and characterize a fuzzy pairwise $\gamma$-irresolute open mapping (fuzzy pairwise $\gamma$-irresolute closed mapping) on a fuzzy bitopological space. We also characterize a fuzzy pairwise $\gamma$-irresolute homeomorphism on a fuzzy bitopological space.

• Journal of the Korean Mathematical Society
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• v.36 no.1
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• pp.37-49
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• 1999

We derive the almost sure convergence for weighted sums of random variables which are either pairwise positive quadrant dependent or pairwise positive quadrant dependent or pairwise negative quadrant dependent and then apply this result to obtain the almost sure convergence of weighted averages. e also extend some results on the strong law of large numbers for pairwise independent identically distributed random variables established in Petrov to the weighted sums of pairwise negative quadrant dependent random variables.

• Journal of applied mathematics & informatics
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• v.42 no.1
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• pp.15-29
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• 2024

Many academics employ various structures to expand topological space, including the idea of topology, as a result of the importance of topological space in analysis and some applications. One of the most notable of the generalizations was the definition of perfect functions in bitopological spaces, which was presented by Ali.A.Atoom and H.Z.Hdeib. We propose the notion of α- pairwise perfect functions in bitopological spaces and define different types of this concept in this study. Pairwise -T - α- perfect functions, pairwise -α-irr-perfect functions, and pairwise -T - α- irr-perfect functions, are all characterized in addition to pairwise -α-perfect functions. We go through their primary characteristics and show how they interact. Finally, under these functions, we introduce the images and inverse images of certain bitopological features. About these concepts, some product theorems have been discovered.

• Journal of the Korean Mathematical Society
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• v.59 no.6
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• pp.1047-1065
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• 2022

For two dimensional lattices, a Gaussian basis achieves all two successive minima. For dimension larger than two, constructing a pairwise Gaussian basis is useful to compute short vectors of the lattice. For three dimensional lattices, Semaev showed that one can convert a pairwise Gaussian basis to a basis achieving all three successive minima by one simple reduction. A pairwise Gaussian basis can be obtained from a given basis by executing Gauss algorithm for each pair of basis vectors repeatedly until it returns a pairwise Gaussian basis. In this article, we prove a necessary and sufficient condition for a pairwise Gaussian basis to achieve the first k successive minima for three dimensional lattices for each k ∈ {1, 2, 3} by modifying Semaev's condition. Our condition directly checks whether a pairwise Gaussian basis contains the first k shortest independent vectors for three dimensional lattices. LLL is the most basic lattice basis reduction algorithm and we study how to use LLL to compute a pairwise Gaussian basis. For δ ≥ 0.9, we prove that LLL(δ) with an additional simple reduction turns any basis for a three dimensional lattice into a pairwise SV-reduced basis. By using this, we convert an LLL reduced basis to a pairwise Gaussian basis in a few simple reductions. Our result suggests that the LLL algorithm is quite effective to compute a basis with all three successive minima for three dimensional lattices.

• Journal of applied mathematics & informatics
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• v.34 no.5_6
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• pp.519-526
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• 2016

The concept of somewhat pairwise fuzzy pre-irresolute continuous mapping and somewhat pairwise fuzzy irresolute preopen mappings have been introduced and studied. Besides, some interesting properties of those mappings are given.

• Journal of the Chungcheong Mathematical Society
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• v.32 no.4
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• pp.465-473
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• 2019

We introduce the intuitionistic fuzzy pairwise preopen and preclosed mappings in the intuitionistic smooth bitopological spaces, and obtain the characterizations for the mappings.

• Journal of the Chungcheong Mathematical Society
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• v.32 no.3
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• pp.309-318
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• 2019

We introduce the concepts of double pairwise strongly (r, s)(u, v)-semiopen mappings and double pairwise strongly (r, s)(u, v)-semiclosed mappings, and investigate some of their characteristic properties.