• The Pure and Applied Mathematics
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• v.12 no.1
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• pp.65-73
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• 2005

Let g = g(A) = (equation omitted) + be a symmetrizable Kac-Moody Lie algebra of type D/sub l//sup (1) with W as its Weyl group. We construct a sequence of root spaces with certain conditions. We also find the number of terms of this sequence is less then or equal to the hight of θ, the highest root.

• Food Science and Preservation
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• v.17 no.4
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• pp.519-525
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• 2010

Kwamegi, a traditional Korean food, is made from the flesh of Pacific saury (the fish Cololabis saira semi-dried in a cold wind off the sea, and is well known in Korea as a valuable health food. Recently, several functional materials have been developed for supplementation of Kwamegi. Here, we compared and analyzed the nutrient composition, including overall composition and mineral, vitamin, fatty acid, and amino acid levels, of several commercial Kwamegi samples prepared with addition of functional components (unsupplemented Kwamegi, Kwamegi with chitosan, and Kwamegi overlaid with gold leaf). The levels of moisture (26.4-30.8%), crude protein (29.1-32.7%), and crude ash (1.6-1.9%) did not differ greatly among samples. However, the crude lipid content of Kwamegi overlaid with gold leaf (KOGL, 32.2%) was greater than that of untreated Kwamegi (CK, 24.5%) or of Kwamegi with added chitosan (KAC, 22.9%). The levels of vitamin $B_2$ (1.8-2.0 mg/100 g) and vitamin C (6.6-6.7 mg/100 g) did not differ greatly among Kwamegi samples. However, CK had a higher vitamin A content and a greater vitamin A potency than did KAC or KOGL. The various Kwamegi samples tested contained similar levels of fatty acids and amino acids. In conclusion, no particular differences in nutrient composition were evident when commercial Kwamegi samples supplemented with functional ingredients were tested

• Bulletin of the Korean Chemical Society
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• v.33 no.3
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• pp.1020-1028
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• 2012

This work compares various models for geminate reversible diffusion influenced reactions. The commonly utilized contact reactivity model (an extension of the Collins-Kimball radiation boundary condition) is augmented here by a volume reactivity model, which extends the celebrated Feynman-Kac equation for irreversible depletion within a reaction sphere. We obtain the exact analytic solution in Laplace space for an initially bound pair, which can dissociate, diffuse or undergo "sticky" recombination. We show that the same expression for the binding probability holds also for "mixed" reaction products. Two different derivations are pursued, yielding seemingly different expressions, which nevertheless coincide numerically. These binding probabilities and their Laplace transforms are compared graphically with those from the contact reactivity model and a previously suggested coarse grained approximation. Mathematically, all these Laplace transforms conform to a single generic equation, in which different reactionless Green's functions, g(s), are incorporated. In most of parameter space the sensitivity to g(s) is not large, so that the binding probabilities for the volume and contact reactivity models are rather similar.

• Communications of the Korean Mathematical Society
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• v.18 no.3
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• pp.439-447
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• 2003

Let (equation omitted) be a symmetrizable Kac-Moody algebra with the indecomposable generalized Cartan matrix A and W be its Weyl group. Let $\theta$ be the highest root of the corresponding finite dimensional simple Lie algebra ${\gg}$ of g. For the type ${A_N}^{(r)}$, we give an element $\omega_{o}\;\in\;W$ such that ${{\omega}_o}^{-1}({\{\Delta\Delta}_{+}})\;=\;{\{\Delta\Delta}_{-}}$. And then we prove that the degree of nilpotency of the subalgebra (equation omitted) is greater than or equal to $ht{\theta}+1$.

• The Pure and Applied Mathematics
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• v.20 no.3
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• pp.137-148
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• 2013

In this paper, we study the Lie-generalized Fibonacci sequence and the root system of rank 2 symmetric hyperbolic Kac-Moody algebras. We derive several interesting properties of the Lie-Fibonacci sequence and relationship between them. We also give a couple of sufficient conditions for the existence of the integral points on the hyperbola $\mathfrak{h}^a:x^2-axy+y^2=1$ and $\mathfrak{h}_k:x^2-axy+y^2=-k$ ($k{\in}\mathbb{Z}_{>0}$). To list all the integral points on that hyperbola, we find the number of elements of ${\Omega}_k$.

• Journal of the Korean Mathematical Society
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• v.43 no.4
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• pp.703-715
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• 2006

Recently, we proved the existence theorem of measure-valued Feynman-Kac formula and showed that it satisfied Volterra's integral equation. In this paper, we establish the operational calculus for a measure-valued Dyson series and give some examples related to the measure-valued Dyson series.

• Biotechnology and Bioprocess Engineering:BBE
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• v.10 no.6
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• pp.510-515
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• 2005

Pseudomonas cepacia BY21 was found to produce glutaryl acylase that is capable of deacylating glutaryl-7-aminocephalosporanic acid (glutaryl-7-ACA) to 7-aminocephalosporanic acid (7-ACA), which is a starting material for semi-synthetic cephalosporin antibiotics. Amino acids of the reported glutaryl acylases from various Pseudomonas sp. strains show a high similarity (>93% identity). Thus, with the known nucleotide sequences of Pseudomonas glutaryl acylases in GenBank, PCR primers were designed to clone a glutaryl acylase gene from P. cepacia BY21. The unknown -subunit gene of glutaryl acylase from chromosomal DNA of P. cepacia BY21 was cloned successfully by PCR. The -subunit amino acids of P. cepacia BY21 acylase (GenBank accession number AY948547) were similar to those of Pseudomonas diminuta KAC-1 acylase except that Asn408 of P. diuminuta KAC-1 acylase was changed to Leu408.

• Journal of Microbiology and Biotechnology
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• v.11 no.3
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• pp.452-457
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• 2001

The glutaryl 7-aminocephalosporanic acid (glutaryl 7-ACA) acylase was purified from Pseudomonas diminuta KAC-1 cells isolated from soil, and characterized. The acylase was purified by procedures including ammonium sulfate fractionation and column chromatographies on DEAE-Sepharose, Phenyl-Sepharose, Q-Sepharose, and Superose 12H/R. The negative acylase was found to be composed of two subunits with molecular masses of approximately 55 kDa and 17 kDa, respectively. The isoelectric point of the enzyme was 4.0. The specific activities of the purified acylase were 8.0 and 7.0 U/mg on glutaryl 7-ACA and glutaryl 7-aminodesacetoxy cephalosporanic acid (glutaryl 7-ADCA), respectively, and $K_m$ values were 0.45 mM for glutaryl 7-ADCA and 0.67 mM for glutaryl 7-ADCA. The enzyme had a pH optimum at 8.0 and a tmperature optimum at $40^{\circ}C$. The acylase catalyzed the synthesis of glutaryl 7-ACA from glutaric acid and 7-ACA as well as the hydrolysis of glutaryl 7-ADCA, although the reaction rate of the synthesis was slower than that of the hydrolysis. In addition, it was found that the enzyme had a glutaryl transferase activity, thereby transferring the glutaryl group from one cephalosporin nucleus to another.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.12 no.1
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• pp.3-10
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• 2002

This paper proposes an ID-based entity-aunthentication and authenticated key exchange protocol with ECC via two-pass communications between two parties who airs registered to the trusted third-party KC in advance. The proposed protocol developed by applying ECDSA and Diffie-Hellman key exchange scheme to the ID-based key distribution scheme over ECC proposed by H. Sakazaki, E. Okamoto and M. Mambo(SOM scheme). The security of this protocol is based on the Elliptic Curve Discrete Logarithm Problem(ECDLP) and the Elliptic Curve Diffie-Hellman Problem(ECDHP). It is strong against unknown key share attack and it provides the perfect forward secrecy, which makes up for the weakness in SOM scheme,

• The Pure and Applied Mathematics
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• v.16 no.1
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• pp.107-119
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• 2009

In this paper we define a Banach algebra on very general function space induced by a generalized Brownian motion process rather than on Wiener space, but the Banach algebra can be considered as a generalization of Fresnel class defined on Wiener space. We then show that several interesting functions in quantum mechanic are elements of the class.