• 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.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.15 no.6
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• pp.105-110
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• 2005

The linearized polynomial fan be regarded as a generalization of the identity function so that the inverse of the linearized polynomial is a generalization of e inverse function. Since the inverse function has so many good cryptographic properties, the inverse of the linearized polynomial is also a candidate of good Boolean functions. In particular, a construction method of vector resilient functions with high algebraic degree was proposed at Crypto 2001. But the analysis about the algebraic degree of the inverse of the linearized Polynomial. Hence we correct the inexact result and give the exact maximal algebraic degree.

• Communications for Statistical Applications and Methods
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• v.28 no.3
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• pp.217-232
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• 2021

The Korea film industry has matured and the number of movie-watching per capita has reached the highest level in the world. Since then, movie industry growth rate is decreasing and even the total sales of movies per year slightly decreased in 2018. The number of moviegoers is the first factor of sales in movie industry and also an important factor influencing additional sales. Thus it is important to predict the number of movie audiences. In this study, we predict the cumulative number of audiences of films using stacking, an ensemble method. Stacking is a kind of ensemble method that combines all the algorithms used in the prediction. We use box office data from Korea Film Council and web comment data from Daum Movie (www.movie.daum.net). This paper describes the process of collecting and preprocessing of explanatory variables and explains regression models used in stacking. Final stacking model outperforms in the prediction of test set in terms of RMSE.

• Communications of the Korean Mathematical Society
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• v.38 no.1
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• pp.11-19
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• 2023

Let 𝓗₀ be the set of rings R such that Nil(R) = Z(R) is a divided prime ideal of R. The concept of maximal non φ-chained subrings is a generalization of maximal non valuation subrings from domains to rings in 𝓗₀. This generalization was introduced in [20] where the authors proved that if R ∈ 𝓗₀ is an integrally closed ring with finite Krull dimension, then R is a maximal non φ-chained subring of T(R) if and only if R is not local and |[R, T(R)]| = dim(R) + 3. This motivates us to investigate the other natural numbers n for which R is a maximal non φ-chained subring of some overring S. The existence of such an overring S of R is shown for 3 ≤ n ≤ 6, and no such overring exists for n = 7.

• Honam Mathematical Journal
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• v.45 no.3
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• pp.491-502
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• 2023

As a generalization of Berwald spaces, we have the ideas of Douglas spaces and Landsberg spaces. S. Bacso defined a weakly-Berwald space as another generalization of Berwald spaces. In 1972, Matsumoto proposed the (α, β) metric, which is a Finsler metric derived from a Riemannian metric α and a differential 1-form β. In this paper, we investigated an important class of (α, β)-metrics of the form $F={\mu}_1\alpha+{\mu}_2\beta+{\mu}_3\frac{\beta^2}{\alpha}$, which is recognized as a special form of the first approximate Matsumoto metric on an n-dimensional manifold, and we obtain the criteria for such metrics to be weakly-Berwald metrics. A Finsler space with a special (α, β)-metric is a weakly Berwald space if and only if B^m_m is a 1-form. We have shown that under certain geometric and algebraic circumstances, it transforms into a weakly Berwald space.

• The Mathematical Education
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• v.29 no.1
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• pp.55-61
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• 1990

There are three objectives of this paper. First, we present an elegant and simple generalization of Abel's theorem (i .e. tile Abel summability (on the unit disk of the euclidean plane) is regular). Second, we consider the definition of Abel summability through lim (equation omitted) which immediately has clear connexctions with CeSARO summability and Cesaro sums (equation omitted). This approach examplifies some simple aspects of so-called Tauberian theorems of divergent series. Third, we present the applications of the previous results to find the limits of transition probabilities of homogeneous Marker chain. Finally, we explain why the original Abel's theorem which looks obvious is difficult to be proved, and can not be proved analytically.

• Journal of Electrical Engineering and information Science
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• v.1 no.1
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• pp.108-117
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• 1996

In this paper, we propose a new type of recurrent neural network architecture in which each output unit is connected with itself and fully-connected with other output units and all hidden units. The proposed recurrent network differs from Jordan's and Elman's recurrent networks in view of functions and architectures because it was originally extended from the multilayer feedforward neural network for improving the discrimination and generalization power. We also prove the convergence property of learning algorithm of the proposed recurrent neural network and analyze the performance of the proposed recurrent neural network by performing recognition experiments with the totally unconstrained handwritten numeral database of Concordia University of Canada. Experimental results confirmed that the proposed recurrent neural network improves the discrimination and generalization power in recognizing spatial patterns.

• Communications of the Korean Mathematical Society
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• v.39 no.2
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• pp.373-397
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• 2024

Lambek introduced the concept of symmetric rings to expand the commutative ideal theory to noncommutative rings. In this study, we propose an extension of symmetric rings called strongly α-symmetric rings, which serves as both a generalization of strongly symmetric rings and an extension of symmetric rings. We define a ring R as strongly α-symmetric if the skew polynomial ring R[x; α] is symmetric. Consequently, we provide proofs for previously established outcomes regarding symmetric and strongly symmetric rings, directly derived from the results we have obtained. Furthermore, we explore various properties and extensions of strongly α-symmetric rings.

• Bulletin of the Korean Mathematical Society
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• v.61 no.1
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• pp.83-92
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• 2024

Let R be a commutative ring with nonzero identity and M be an R-module. In this paper, we first introduce the concept of S-idempotent element of R. Then we give a relation between S-idempotents of R and clopen sets of S-Zariski topology. After that we define S-pure ideal which is a generalization of the notion of pure ideal. In fact, every pure ideal is S-pure but the converse may not be true. Afterwards, we show that there is a relation between S-pure ideals of R and closed sets of S-Zariski topology that are stable under generalization.

• Kyungpook Mathematical Journal
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• v.45 no.2
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• pp.273-280
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• 2005

We generalize a continued fraction of Ramanujan by introducing a free parameter. We give the closed form for the continued fraction. We also consider the finite form giving $n^{th}$ convergent using partition theory.