• Bulletin of the Korean Mathematical Society
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• 제52권1호
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• pp.137-147
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• 2015

We derive in the paper the tensor product functor -${\otimes}_R$- by using proper $\mathcal{GP}_C$-resolutions, where C is a semidualizing module. After giving several cases in which different relative homologies agree, we use the Pontryagin duals of $\mathcal{G}_C$-projective modules to establish a balance result for such relative homology over a Cohen-Macaulay ring with a dualizing module D.

• Journal of the Korean Mathematical Society
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• 제39권1호
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• pp.149-161
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• 2002

We study the torsions in the integral homology of the double loop space of the compact simple Lie groups by determining the higher Bockstein actions on the homology of those spaces through the Bockstein lemma and computing the Bockstein spectral sequence.

• Journal of the Korean Mathematical Society
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• 제45권3호
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• pp.699-709
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• 2008

We study homology of the gauge group associated with the principal $G_2$ bundle over the four-sphere using the Eilenberg-Moore spectral sequence and the Serre spectral sequence with the aid of homology and cohomology operations.

• Communications of the Korean Mathematical Society
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• 제25권2호
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• pp.283-289
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• 2010

Approximate fibrations provide a useful class of maps. Fibrators give instant detection of maps in this class, and PL fibrators do the same in the PL category. We show that rational homology spheres with some additional conditions are codimension-k PL fibrators and PL manifolds with trivial homology groups in some range can be codimension-k (k > 2) PL fibrators.

• Communications of the Korean Mathematical Society
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• 제17권3호
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• pp.389-401
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• 2002

We give an upper bound for the degrees of the nonvanishing homology modules of the Schur complex L$\sub$λ/${\mu}$/ø in terms of the depths of the determinantal ideals of ø). Using this fact, we obtain the acyclic theorem for L$\sub$λ/ø and the information concerning the support of the homology modules of L$\sub$λ/${\mu}$/ø.

• Journal of the Korean Mathematical Society
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• 제35권1호
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• pp.149-164
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• 1998

We study the homology of the tripe loop space of the exceptional Lie group $F_4$ by exploiting the spectral sequences and the homology operators.

• Journal of the Korean Mathematical Society
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• 제53권6호
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• pp.1293-1308
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• 2016

In this paper we prove the existence of rational homology balls smoothly embedded in regular neighborhoods of certain linear chains of smooth 2-spheres by using techniques from minimal model program for 3-dimensional complex algebraic variety.

• Journal of the Korean Mathematical Society
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• 제60권1호
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• pp.227-253
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• 2023

In this article, we generalize the results discussed in [6] by introducing a genus to generic fibers of Lefschetz fibrations. That is, we give families of relations in the mapping class groups of genus-1 surfaces with boundaries that represent rational homology disk smoothings of weighted homogeneous surface singularities whose resolution graphs are 3-legged with a bad central vertex.

• The Pure and Applied Mathematics
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• 제30권1호
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• pp.15-24
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• 2023

In this paper, we show that bounded Hochschild homology and cohomology of associated matrix Banach algebra 𝔊(𝔄, R, S, 𝔅) to a Morita context 𝔐(𝔄, R, S, 𝔅, { }, [ ]) are isomorphic to those of the Banach algebra 𝔄. Consequently, we indicate that the n-amenability and simplicial triviality of 𝔊(𝔄, R, S, 𝔅) are equivalent to the n-amenability and simplicial triviality of 𝔄.

• Journal of Integrative Natural Science
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• 제8권1호
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• pp.13-18
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• 2015

Cysteinyl leukotrienes are inflammatory mediators having important role in pathophysiological conditions such as asthma, allergic rhinitis and have been implicated in a number of inflammatory conditions including cardiovascular and gastrointestinal diseases. Most of the disease regulatory actions of the CysLTs are mediated through CysLT1 receptor. Hence in the present study, homology modeling of CysLT1 was performed because the availability of 3D structure would enhance the development of new drugs for inflammatory diseases. However the templates identified have low sequence identity which increases the complexity of modeling. Hence, homology modeling was performed using single template, multiple templates and also using threading I-TASSER server. The best model was selected based on the validation of the generated models using Ramachandran and ERRAT plot. The model developed could be useful for identifying crucial residues and docking study.