• Communications of the Korean Mathematical Society
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• v.35 no.1
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• pp.63-81
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• 2020

In this paper we consider certain classes of generalized level 2 Eisenstein series by simple differential calculations of trigonometric functions. In particular, we give four new transformation formulas for some level 2 Eisenstein series. We can find that these level 2 Eisenstein series are reducible to infinite series involving hyperbolic functions. Moreover, some interesting new examples are given.

• Communications of the Korean Mathematical Society
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• v.11 no.2
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• pp.423-443
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• 1996

The main purposer of the present paper is to derive the induced (Finsler) connections on the hypersurface from the Finsler connections of Cartan type (a Wagner, Miron, Cartan C- and Cartan Y- connection) of a Finsler space and to seek the necessary and sufficient conditions that the induced connections coincide with the intrinsic connections. And we show the differences of quantities with respect to the respective a connections and an induced Cartan connection. Finally we show some examples.

• Bulletin of the Korean Mathematical Society
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• v.36 no.1
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• pp.33-45
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• 1999

In this paper, we are interested in studying weak covering properties in the presence of a countable compact condition. The purpose of this paper is to characterize an ideal weakly $\delta$$\theta$-refinable space and to show that every ideal weakly $\delta$$\theta$-refinable space is isocompact. Also, we consider the behavior under mappings of ideal weakly $\delta$$\theta$-refinable properties and productivity of ideal weakly $\delta$$\theta$-refinable properties.

• Bulletin of the Korean Mathematical Society
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• v.49 no.6
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• pp.1223-1240
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• 2012

The system $$\dot{x}=(A+{\varepsilon}Q(t,{\varepsilon}))x+{\varepsilon}g(t,{\varepsilon})+h(x,t,{\varepsilon}),$$ where A is elliptic whose eigenvalues are not necessarily simple and $h$ is $\mathcal{O}(x^2)$. It is proved that, under suitable hypothesis of analyticity, for most values of the frequencies, the system is reducible.

• Proceedings of the PSK Conference
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• 2002.10a
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• pp.349.2-350
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• 2002

Deprotection of the benzyl group has been widely used in multi-step organic synthesis with a variety of reaction conditions. including catalytic hydrogenolysis. Lewis acids such as FeCl$_3$ or MgBr$_2$ and lithium naphthalenide. However. these procedures sometimes can be problematic with multifunctional substrates. such as unsaturated bonds during hydrogenolysis. an acid-labile moiety in FeCl$_3$ and a easily reducible functional group in lithium naphthalenide. (omitted)

• Journal of the Chungcheong Mathematical Society
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• v.5 no.1
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• pp.195-201
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• 1992

Let G(A) denote a generalized Kac Moody Lie algebra associated to a symmetrizable generalized Cartan matrix A. In this paper, we study on representations of G(A). Highest weight modules and the category O are described. In the main theorem we show that some G(A) modules from the category O are completely reducible. Also a criterion for irreducibility of highest weight modules is obtained. This was proved in [3] for the case of Kac Moody Lie algebras.

• Fire Protection Technology
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• s.29
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• pp.35-38
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• 2000

The apartment houses are increasing for more efficient use of land in our country. Noises form upper story in the silent night makes nervous and uncomfortable. Worst of all, it causes a mental disease. The other side these condition could be a environmental pollution. To prevent like this noise, a variety of sound reducible products are developed and applied in the building construction fields. In this article I' d like to introduce the method of measurement of the impact sound insulation and its practice.

• Journal of the Korean Mathematical Society
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• v.44 no.4
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• pp.799-807
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• 2007

In this paper we study non-simply connected Riemannian manifolds of constant positive curvature which have an orbit of codimension one under the action of a connected closed Lie subgroup of isometries. When the action is reducible we characterize the orbits explicitly. We also prove that in some cases the manifold is homogeneous.

• Communications of the Korean Mathematical Society
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• v.28 no.4
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• pp.723-733
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• 2013

A Bachet equation $Y^2=X^3+k$ will have a rational solution if and only if there is $b{\in}\mathbb{Q}$ for which $X^3-b^2X^2+k$ is reducible. In this paper we show that such cubics arise as a cubic resolvent of a biquadratic polynomial. And we prove various properties of cubic resolvents.

• Journal of the Korean Mathematical Society
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• v.61 no.1
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• pp.149-160
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• 2024

In this paper, we study the unicorn's Landsberg problem from an intrinsic point of view. Precisely, we investigate a coordinate-free proof of Numata's theorem on Landsberg spaces of scalar curvature. In other words, following the pullback approach to Finsler geometry, we prove that all Landsberg spaces of dimension n ≥ 3 of non-zero scalar curvature are Riemannian spaces of constant curvature.