• Honam Mathematical Journal
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• v.38 no.4
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• pp.819-831
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• 2016

The present paper investigates some properties of the digital homology in [1, 4, 5] and points out some unclearness of the definition of a digital homology and further, suggests a suitable form of a digital homology. Finally, we calculate a digital homology group and a relative digital homology group of some digital wedge sums. Finally, the paper corrects some errors in [6]. In the present paper all digital images (X, k) are assumed to be non-empty and k-connected.

• Journal of the Korean Mathematical Society
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• v.34 no.4
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• pp.1065-1087
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• 1997

We prove that there exists a canonical level-preserving isomorphism between the stable Morse homology (or the Morse homology of generating functions) and the Floer homology on the cotangent bundle $T^*M$ for any closed submanifold $N \subset M$ for any compact manifold M.

• Journal of the Korean Mathematical Society
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• v.41 no.4
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• pp.591-615
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• 2004

In this paper, we provide the algebraic foundations to the theory of relative $\ell$$_1$ homology. In particular, we prove that $\ell$$_1$ homology of topological spaces, both for the absolute case and for the relative case, depends only on their fundamental groups. We also provide a .proof of Gromov's Equivalence theorem for $\ell$$_1$ homology, stated by Gromov without proof [4].

• Journal of Life Science
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• v.12 no.2
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• pp.173-181
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• 2002

This study was conducted to do the comparative analysis of mating type locus controlling the direct formation of fruiting body in Schizophyllum commune which is indigenous to North America with that of other identified mating locus. The 3120 bp Y-region nucleotide of A $\alpha$ 3 mating locus activating a developmental pathway in S. commune was determined, and appeared to have about 96% homology to S. commune 1-71 $A\alpha$3 allele indigenous to South America, showing strongly a conservative feature. This nucleotide analysis also showed above 96% homology highly in the seven presumed exons, and about 97% in the acidic rich region (AR), about 99% in homeodomain (H7), about 97% in the basic rich region (BR), about 95% in the serine rich region (Ser) respectively. In the comparative analysis to the translated polypeptide sequence, S. commune A $\alpha$ 3 mating locus containing Y-region also showed about 97% homology to the region of S. commune indigenous to North America, but the identity ratio to Y1 including Y4, Y5, Y6 different allele types was declined to about 41~49%. In the analysis of functional loci controlling mating activity, it is assumed to have a highly conservative feature showing about 98% homology in homeodomain polypeptide. Especially, it is notable that the homology ratio of above 85% in homeodomain motif between mating type alleles was higher than in the AR, BR, Ser showing about 10~50% homology.

• Communications of the Korean Mathematical Society
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• v.27 no.4
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• pp.815-834
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• 2012

In this paper, we characterize surgery presentations for $\mathbb{Z}$-homology 3-spheres and $\mathbb{Z}/2\mathbb{Z}$-homology 3-spheres obtained from $S^3$ by Dehn surgery along a knot or link which admits an even net diagram and show that the Casson invariant for $\mathbb{Z}$-homology spheres and the ${\mu}$-invariant for $\mathbb{Z}/2\mathbb{Z}$-homology spheres can be directly read from the net diagram. We also construct oriented 4-manifolds bounding such homology spheres and find their some properties.

• Bulletin of the Korean Mathematical Society
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• v.60 no.1
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• pp.23-32
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• 2023

Let 𝓢 be a Serre class in the category of modules and 𝖆 an ideal of a commutative Noetherian ring R. We study the containment of Tor modules, Koszul homology and local homology in 𝓢 from below. With these results at our disposal, by specializing the Serre class to be Noetherian or zero, a handful of conclusions on Noetherianness and vanishing of the foregoing homology theories are obtained. We also determine when Tor^R_𝓼+t(R/𝖆, X) ≅ Tor^R_𝓼(R/𝖆, H^𝖆_t(X)).

• Bulletin of the Korean Mathematical Society
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• v.60 no.6
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• pp.1497-1522
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• 2023

In this paper we compute the Bredon homology of wallpaper groups with respect to the family of finite groups and with coefficients in the complex representation ring. We provide explicit bases of the homology groups in terms of irreducible characters of the stabilizers.

• Communications of the Korean Mathematical Society
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• v.38 no.1
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• pp.21-38
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• 2023

Let R be a commutative ring with identity. Let R be an integral domain and M a torsion-free R-module. We investigate the relation between the notion of e-exactness, recently introduced by Akray and Zebari [1], and generalized the concept of homology, and establish a relation between e-exact sequences and homology of modules. We modify some applications of e-exact sequences in homology and reprove some results of homology with e-exact sequences such as horseshoe lemma, long exact sequences, connecting homomorphisms and etc. Next, we generalize two special drived functor T or and Ext, and study some properties of them.

• Pediatric Infection and Vaccine
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• v.6 no.1
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• pp.123-130
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• 1999

Purpose : Meningitis is an inflammation of meninges by various kinds of organisms. Almost 85% of aseptic meningitis is caused by Enterovirus. This study was done to detect the causative virus of those with aseptic meningitis through sequencing the 5'-noncoding region to compare prototype and homology. Methods : RNA was extracted from Coxsackie Bl, Echovirus 3, 7, 9, 30. DNA was synthesized by RT-PCR and we compared homology with prototype from WHO by direct sequencing. Results : 1) PCR products from these viruses showed same bands of 155 bp and 440 bp on gel electrophoresis. 2) Coxsackievirus and Echovirus 11 prototype sequences were compared, which showed 12 bp changes with 92.1%. 3) Coxsackievirus B1 from a patient showed 94.1% homology when compared with prototype. 4) Echovirus 3 showed 92.8%, echovirus 7 92.8%, echovirus 30 82.9% homology. Conclusion : 5'-NCR of enterovirus has high homology which was good for use of diagnosis and more long sequencing requires for typing of viruses.

• Bulletin of the Korean Mathematical Society
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• v.54 no.6
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• pp.1927-1933
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• 2017

We prove that there are rational homology balls $B_p$ smoothly embedded in the 2-handlebodies associated to certain knots. Furthermore we show that, if we rationally blow up the 2-handlebody along the embedded rational homology ball $B_p$, then the resulting 4-manifold cannot be obtained just by a sequence of ordinary blow ups from the 2-handlebody under a certain mild condition.