• Journal of the Korean Mathematical Society
• /
• v.35 no.2
• /
• pp.281-294
• /
• 1998

In this paper, we extend the G-sequence of a CW-pair to the G-sequence of a map and show the existence of a map with nonexact G-sequence. We also give an example of a finite CW-pair with nontrivial $\omega$-homology in high order.

• Journal of Microbiology and Biotechnology
• /
• v.18 no.1
• /
• pp.48-54
• /
• 2008

A putative ${\omega}$-aminotransferase gene, cc3143 (aptA), from Caulobacter crescentus was screened by bioinformatical tools and overexpressed in E. coli, and the substrate specificity of the ${\omega}$-aminotransferase was investigated. AptA showed high activity for short-chain ${\beta}$-amino acids. It showed the highest activity for 3-amino-n-butyric acid. It showed higher activity toward aromatic amines than aliphatic amines. The 3D model of the ${\omega}$-aminotransferase was constructed by homology modeling using a dialkylglycine decarboxylase (PDB ID: 1DGE) as a template. Then, the ${\omega}$-aminotransferase was rationally redesigned to increase the activity for 3-amino-3-phenylpropionic acid. The mutants N285A and V227G increased the relative activity for 3-amino-3-phenylpropionic acid to 3-amino-n-butyric acid by 11-fold and 3-fold, respectively, over that of wild type.

• Korean Journal of Mathematics
• /
• v.18 no.2
• /
• pp.175-183
• /
• 2010

The classical group completion theorem states that under a certain condition the homology of ${\Omega}BM$ is computed by inverting ${\pi}_0M$ in the homology of M. McDuff and Segal extended this theorem in terms of homology fibration. Recently, more general group completion theorem for simplicial spaces was developed. In this paper, we construct a symmetric monoidal 2-category ${\mathcal{A}}$. The 1-morphisms of ${\mathcal{A}}$ are generated by three atomic 2-dimensional CW-complexes and the set of 2-morphisms is given by the group of path components of the space of homotopy equivalences of 1-morphisms. The main part of the paper is to compute the homotopy type of the group completion of the classifying space of ${\mathcal{A}}$, which is shown to be homotopy equivalent to ${\mathbb{Z}}{\times}BAut^+_{\infty}$.

• Journal of the Korean Mathematical Society
• /
• v.48 no.2
• /
• pp.341-365
• /
• 2011

In this paper, we establish general stratawise higher jet evaluation transversality of J-holomorphic curves for a generic choice of almost complex structures J (tame to a given symplectic manifold (M, $\omega$)). Using this transversality result, we prove that there exists a subset $\cal{J}^{ram}_{\omega}\;{\subset}\;\cal{J}_{\omega}$ of second category such that for every $J\;{\in}\;\cal{J}^{ram}_{\omega}$, the dimension of the moduli space of (somewhere injective) J-holomorphic curves with a given ramication prole goes down by 2n or 2(n - 1) depending on whether the ramication degree goes up by one or a new ramication point is created. We also derive that for each $J\;{\in}\;\cal{J}^{ram}_{\omega}$ there are only a finite number of ramication profiles of J-holomorphic curves in a given homology class $\beta\;{\in}\;H_2$(M; $\mathbb{Z}$) and provide an explicit upper bound on the number of ramication proles in terms of $c_1(\beta)$ and the genus g of the domain surface.

• Korean Journal of Plant Tissue Culture
• /
• v.24 no.2
• /
• pp.93-97
• /
• 1997

For the molecular genetic study of cold tolerance mechanism in plants, a cDNA encoding fatty acid desaturase (fad3), converting linoleic acid (18:2, $\omega$-6) to linolenic acid (18:3, $\omega$-3), was isolated from $\lambda$ZAPII Arabidopsis thaliana cDNA expression library by plaque hybridization using fad3 cDNA probe derived from Brassica napus. A 1.8 kb-EcoRI fragment from a lambda clone showing a strong positive hybridization signal was subcloned into pGEM7 and analyzed for its nucleotide sequence. From deduced amino acid sequences, the fad3 gene was revealed to have an open reading frame(ORF) consisting of 386 amino acids with a molecular mass of 44,075 Da. The fad3 gene was compared to chloroplast $\omega$-3 fatty acid desaturase (fad7) and endoplasmic reticulum Δ12 fatty acid desaturase (fad2) to show 70% and 58% amino acid sequence homology, respectively, Especially, amino acids of internal (82 to 151) and carboxy terminal (276 to 333) regions were highly conserved, implying their requisite role for enzymatic functioning of fatty acid desaturases. IPTG-induced fad3 cDNA expression in E. coli cells was suggested to be toxic to bacterial growth.

• Communications of the Korean Mathematical Society
• /
• v.9 no.4
• /
• pp.933-944
• /
• 1994

Let $\pi : P \to S^4$ be a principal G-bundle over $S^4$ whose the structure group G is a compact, connected, simple Lie group. Since $\pi_3(G) = \pi_4 (BG) = Z$, we can classify the principal bundle $P_k$ over $S^4$ by the map $S^4 \to BG$ of degree k. Atiyah and Jones [2] showed that $C_k = A_k/g^b_k$ is homotopy equivalent to $\Omega^3_k G \simeq \Omega^4_k BG$ where $A_k$ is the space of the all connections in $P_k$ and $g^b_k$ is the based gauge group which consists of all base point preserving automorphisms on $P_k$. Here $\Omega^nX$ is the space of all base-point preserving continuous map from $S^n$ to X. Let $M_k$ be the space of based gauge equivalence classes of all connections in $P_k$ satisfying the Yang-Mills self-duality equations, which we call the moduli space of G instantons.

• Journal of Applied Biological Chemistry
• /
• v.44 no.1
• /
• pp.6-11
• /
• 2001

An ${\omega}-3$ fatty acid desaturase gene which is involved in de novo synthesis of -Iinolenate was isolated from cDNA library of Perilla frutescens. A cDNA library was constructed with mRNA extracted from perilla seeds of 12 DAF. The cDNA clone consisting of 1317-bp open reading frame encoding 438 amino acids with a relative MW of 50kDa, was isolated and showed 65-83% similarities to other known genes. This cDNA is deduced to encode a plastidal ${\omega}-3$ fatty acid desaturase based on the fact that it has higher homology to plastidal ones than to microsomal ones and its N-terminal sequence shares several characteristics of transit peptides of chloroplast proteins. Southern blot analysis of genomic DNA indicated that more than one gene or alleles for ${\omega}-3$ fatty acid desaturase are present in the genome of perilla. Northern blot analysis showed that the ${\omega}-3$ fatty acid desaturase gene is mainly revealed in early developing seeds and has different expression patterns depending on tissue types compared to the microsomal ones.

• Bulletin of the Korean Mathematical Society
• /
• v.38 no.4
• /
• pp.741-751
• /
• 2001

In this paper when $(M, \omega)$ is a compact weakly exact symplectic manifold with nonempty boundary satisfying $c_1｜{\pi}_2(M)$ = 0, we construct an action spectrum bundle over the group of Hamil-tonian diffeomorphisms of the manifold M generated by the time-dependent Hamiltonian vector fields, whose fibre is nowhere dense and invariant under symplectic conjugation.

• Journal of the Korean Mathematical Society
• /
• v.38 no.3
• /
• pp.633-644
• /
• 2001

Revenel computed the Adams spectral sequence converging to BP(Ω$^2$S(sup)2n+1) and got the E(sub)$\infty$-term. Then he gave the conjecture about the extension. Here we prove that there should be non-trivial extension. We also study the BP(sub)*BP comodule structures on the polynomial algebras which are related with BP(sub)*(Ω$^2$S(sup)2n+1).

• Journal of the Korean Mathematical Society
• /
• v.46 no.2
• /
• pp.363-447
• /
• 2009

The author previously defined the spectral invariants, denoted by $\rho(H;\;a)$, of a Hamiltonian function H as the mini-max value of the action functional ${\cal{A}}_H$ over the Novikov Floer cycles in the Floer homology class dual to the quantum cohomology class a. The spectrality axiom of the invariant $\rho(H;\;a)$ states that the mini-max value is a critical value of the action functional ${\cal{A}}_H$. The main purpose of the present paper is to prove this axiom for nondegenerate Hamiltonian functions in irrational symplectic manifolds (M, $\omega$). We also prove that the spectral invariant function ${\rho}_a$ : $H\;{\mapsto}\;\rho(H;\;a)$ can be pushed down to a continuous function defined on the universal (${\acute{e}}tale$) covering space $\widetilde{HAM}$(M, $\omega$) of the group Ham((M, $\omega$) of Hamiltonian diffeomorphisms on general (M, $\omega$). For a certain generic homotopy, which we call a Cerf homotopy ${\cal{H}}\;=\;\{H^s\}_{0{\leq}s{\leq}1}$ of Hamiltonians, the function ${\rho}_a\;{\circ}\;{\cal{H}}$ : $s\;{\mapsto}\;{\rho}(H^s;\;a)$ is piecewise smooth away from a countable subset of [0, 1] for each non-zero quantum cohomology class a. The proof of this nondegenerate spectrality relies on several new ingredients in the chain level Floer theory, which have their own independent interest: a structure theorem on the Cerf bifurcation diagram of the critical values of the action functionals associated to a generic one-parameter family of Hamiltonian functions, a general structure theorem and the handle sliding lemma of Novikov Floer cycles over such a family and a family version of new transversality statements involving the Floer chain map, and many others. We call this chain level Floer theory as a whole the Floer mini-max theory.