• Communications of the Korean Mathematical Society
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• v.38 no.3
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• pp.901-911
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• 2023

In this paper a generalization of convergent sequences in connection with generalized topologies and filters is given. Additionally, properties such as uniqueness, behavior related to continuous functions are established and notions relative to product spaces.

• Communications of the Korean Mathematical Society
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• v.27 no.1
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• pp.47-56
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• 2012

In this article, we continue the study of tense symmetric Heyting algebras (or TSH-algebras). These algebras constitute a generalization of tense algebras. In particular, we describe a discrete duality for TSH-algebras bearing in mind the results indicated by Or lowska and Rewitzky in [E. Orlowska and I. Rewitzky, Discrete Dualities for Heyting Algebras with Operators, Fund. Inform. 81 (2007), no. 1-3, 275-295] for Heyting algebras. In addition, we introduce a propositional calculus and prove this calculus has TSH-algebras as algebraic counterpart. Finally, the duality mentioned above allowed us to show the completeness theorem for this calculus.

• The Research Journal of the Costume Culture
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• v.13 no.3 s.56
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• pp.469-480
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• 2005

The purpose of this study is to analyze the meaning and the value of the cultural collage expressed in men's fashion. As for the research methodology, literary research was under taken to study psychoanalytical and socioeconomic contexts in which cultural collage has been formed. In addition, demonstrative studies in men's fashion were undertaken through the analysis of pictures. The cultural collage is defined as a phenomena of making creativity by combining cultures which have no relevance. In psychological and sociological aspects, the rise of the cultural collage is caused by multinational corporation, pluralization of identity, information society, consumer oriented production, consumer society and inundation of kitsch. On the basis of the characteristics and social backgrounds of cultural collage, the aesthetic values of men's fashion can be explained by pluralism de-generalization and relativity.

• Korean Journal of Mathematics
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• v.27 no.1
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• pp.175-192
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• 2019

(Multiplicative) Hom-Lie-Yamaguti superalgebras are defined as a ${\mathbb{Z}}_2$-graded generalization of Hom-Lie Yamaguti algebras and also as a twisted generalization of Lie-Yamaguti superalgebras. Hom-Lie-Yamaguti superalgebras generalize also Hom-Lie supertriple systems (and subsequently ternary multiplicative Hom-Nambu superalgebras) and Hom-Lie superalgebras in the same way as Lie-Yamaguti superalgebras generalize Lie supertriple systems and Lie superalgebras. Hom-Lie-Yamaguti superalgebras are obtained from Lie-Yamaguti superalgebras by twisting along superalgebra even endomorphisms. We show that the category of (multiplicative) Hom-Lie-Yamaguti superalgebras is closed under twisting by self-morphisms. Constructions of some examples of Hom-Lie-Yamaguti superalgebras are given. The notion of an nth derived (binary) Hom-superalgebras is extended to the one of an nth derived binary-ternary Hom-superalgebras and it is shown that the category of Hom-Lie-Yamaguti superalgebras is closed under the process of taking nth derived Hom-superalgebras.

• Bulletin of the Korean Mathematical Society
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• v.56 no.1
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• pp.83-102
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• 2019

For $M{\in}R-Mod$, $N{\subseteq}M$ and $L{\in}{\sigma}[M]$ we consider the product $N_ML={\sum}_{f{\in}Hom_R(M,L)}\;f(N)$. A module $N{\in}{\sigma}[M]$ is called an M-multiplication module if for every submodule L of N, there exists a submodule I of M such that $L=I_MN$. We extend some important results given for multiplication modules to M-multiplication modules. As applications we obtain some new results when M is a semiprime Goldie module. In particular we prove that M is a semiprime Goldie module with an essential socle and $N{\in}{\sigma}[M]$ is an M-multiplication module, then N is cyclic, distributive and semisimple module. To prove these results we have had to develop new methods.

• Bulletin of the Korean Mathematical Society
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• v.49 no.5
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• pp.939-947
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• 2012

In this paper, we give a generalization of the embeddings of Riemannian manifolds via their heat kernel and via a finite number of eigenfunctions. More precisely, we embed a family of Riemannian manifolds endowed with a time-dependent metric analytic in time into a Hilbert space via a finite number of eigenfunctions of the corresponding Laplacian. If furthermore the volume form on the manifold is constant with time, then we can construct an embedding with a complete eigenfunctions basis.

• Kyungpook Mathematical Journal
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• v.61 no.1
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• pp.111-137
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• 2021

Higson proved that every homotopy invariant, stable and split exact functor from the category of C⁎-algebras to an additive category factors through Kasparov's KK-theory. By adapting a group equivariant generalization of this result by Thomsen, we generalize Higson's result to the inverse semigroup and locally compact, not necessarily Hausdorff groupoid equivariant setting.

• Communications of the Korean Mathematical Society
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• v.37 no.4
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• pp.977-988
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• 2022

The Padovan sequence is the third-order linear recurrence (𝓟_n)_n≥0 defined by 𝓟_n = 𝓟_n-2 + 𝓟_n-3 for all n ≥ 3 with initial conditions 𝓟₀ = 0 and 𝓟₁ = 𝓟₂ = 1. In this paper, we investigate a generalization of the Padovan sequence called the k-generalized Padovan sequence which is generated by a linear recurrence sequence of order k ≥ 3. We present recurrence relations, the generalized Binet formula and different arithmetic properties for the above family of sequences.

• Nuclear Engineering and Technology
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• v.53 no.2
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• pp.399-413
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• 2021

The solution of the time-dependent neutron diffusion equation can be approximated using quasi-static methods that factorise the neutronic flux as the product of a time dependent function times a shape function that depends both on space and time. A generalization of this technique is the updated modal method. This strategy assumes that the neutron flux can be decomposed into a sum of amplitudes multiplied by some shape functions. These functions, known as modes, come from the solution of the eigenvalue problems associated with the static neutron diffusion equation that are being updated along the transient. In previous works, the time step used to update the modes is set to a fixed value and this implies the need of using small time-steps to obtain accurate results and, consequently, a high computational cost. In this work, we propose the use of an adaptive control time-step that reduces automatically the time-step when the algorithm detects large errors and increases this value when it is not necessary to use small steps. Several strategies to compute the modes updating time step are proposed and their performance is tested for different transients in benchmark reactors with rectangular and hexagonal geometry.

• Advances in aircraft and spacecraft science
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• v.6 no.6
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• pp.443-461
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• 2019

This communication investigates exact and distorted similitudes and the related scaling laws for the analysis of both dynamic response and radiated power of rectangular plates. The response of a given panel in similitude from another one is determined from a generalization of the modal approach, allowing the use of mode shapes, natural frequencies and finally radiation functions in order to establish appropriate scaling laws. Analytical models of simply supported rectangular plates are used to produce both original and replica model responses under point mechanical excitation. Emphasis is then especially put on laboratory experiments which are performed on baffled simply supported aluminum panels under mechanical excitations. All the six possible scaling directions, i.e. predicting a plate vibroacoustic reponse from another plate, are reported. All obtained results show that structural response or radiated sound power of a given plate can be both recovered with satisfactory accuracy by using the related scaling laws, even if parent models are used.