• Korean Journal of Mathematics
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• v.31 no.4
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• pp.495-504
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• 2023

This article deals with non-degenerate linear transformations on Euclidean Jordan algebras. First, we study non-degenerate for cone invariant, copositive, Lyapunov-like, and relaxation transformations. Further, we study that the non-degenerate is invariant under principal pivotal transformations and algebraic automorphisms.

• KSBB Journal
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• v.22 no.5
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• pp.362-365
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• 2007

Cyanobacteria have been identified as one of the most promising group producing novel biochemically active natural products. Cyanobacteria are a very old group of prokaryotic organisms that produce very diverse secondary metabolites, especially non-ribosomal peptide and polyketide structures. Large multienzyme complexes which are responsible for the non-ribosomal biosynthesis of peptides are modular for the addition of a single amino acid. An activation of amino acid substrates results in an amino adenylate occuring via an adenylation domain (A-domain). A-domains are responsible for the recognition of amino acids as substrates within NP synthesis. The A-domain contains ten conserved motifs, A1 to A10. In this study, ten conserved motifs from A1 to A10 were checked regarding their amino acid sequence of the NRPS-module of Microcystis aeruginosa PCC 7806. The part of the amino acid sequence chosen was that which contained as many conserved motives as possible, and then these amino sequence were compared between other cyanobacteria to design a new degenerate primer. A new degenerate primer (A3/A7 primer) was designed to detect any putative NP synthetase region in unkwon cyanobacteria by a reverse translation of the conserved amino acid sequence and a search for cyanobacterial DNA bank.

• Journal of the military operations research society of Korea
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• v.27 no.1
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• pp.28-38
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• 2001

A transportation problem amy have multiple optimal solutions, if an optimal solution to the problem is degenerate. This study derives a condition, under which multiple degenerate optimal solutions exist, fro ma current degenerate optimal transportation tableau by utilizing the homogeneous equation obtained from the closed loops connecting degenerate basic variable and non-basic variables, and discusses a method of generating alternative degenerate optimal solutions and their associated transportation tableaus. Each degenerate optimal solution may not have the same range of feasibility in sensitivity analysis on supply and demand quantity due to different set of shadow prices which multiple degenerate solution have.

• Communications of the Korean Mathematical Society
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• v.28 no.4
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• pp.751-766
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• 2013

We study the existence and long-time behavior of solutions to the following semilinear degenerate parabolic equation on $\mathbb{R}^N$: $$\frac{{\partial}u}{{\partial}t}-div({\sigma}(x){\nabla}u+{\lambda}u+f(u)=g(x)$$, under a new condition concerning a variable non-negative diffusivity ${\sigma}({\cdot})$. Some essential difficulty caused by the lack of compactness of Sobolev embeddings is overcome here by exploiting the tail-estimates method.

• Bulletin of the Korean Mathematical Society
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• v.53 no.6
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• pp.1697-1705
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• 2016

In this article, we consider the problem on finding non-degenerate nary m-ic forms having an $n{\times}n$ matrix A as a linear isomorphism. We show that it is equivalent to solve a linear diophantine equation. In particular, we find all integral ternary cubic forms having A as a linear isomorphism, for any $A{\in}GL_3({\mathbb{Z}})$. We also give a family of non-degenerate cubic forms F such that F(x) = N always has infinitely many integer solutions if exists.

• Journal of the Korean Mathematical Society
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• v.48 no.1
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• pp.1-12
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• 2011

The purpose of this paper is to study pseudo-Riemannian algebras, which are algebras with pseudo-Riemannian non-degenerate symmetric bilinear forms. We nd that pseudo-Riemannian algebras whose left centers are isotropic play a curial role and show that the decomposition of pseudo-Riemannian algebras whose left centers are isotropic into indecomposable non-degenerate ideals is unique up to a special automorphism. Furthermore, if the left center equals the center, the orthogonal decomposition of any pseudo-Riemannian algebra into indecomposable non-degenerate ideals is unique up to an isometry.

• Journal of the Korean Mathematical Society
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• v.56 no.5
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• pp.1355-1370
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• 2019

A curve $X{\subset}\mathbb{P}^r$ has maximal rank if for each $t{\in}\mathbb{N}$ the restriction map $H^0(\mathcal{O}_{\mathbb{P}r}(t)){\rightarrow}H^0(\mathcal{O}_X(t))$ is either injective or surjective. We show that for all integers $d{\geq}r+1$ there are maximal rank, but not arithmetically Cohen-Macaulay, smooth curves $X{\subset}\mathbb{P}^r$ with degree d and genus roughly $d^2/2r$, contrary to the case r = 3, where it was proved that their genus growths at most like $d^{3/2}$ (A. Dolcetti). Nevertheless there is a sector of large genera g, roughly between $d^2/(2r+2)$ and $d^2/2r$, where we prove the existence of smooth curves (even aCM ones) with degree d and genus g, but the only integral and non-degenerate maximal rank curves with degree d and arithmetic genus g are the aCM ones. For some (d, g, r) with high g we prove the existence of reducible non-degenerate maximal rank and non aCM curves $X{\subset}\mathbb{P}^r$ with degree d and arithmetic genus g, while (d, g, r) is not realized by non-degenerate maximal rank and non aCM integral curves.

• Communications of the Korean Mathematical Society
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• v.30 no.2
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• pp.73-79
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• 2015

Todd series are associated to maximal non-degenerate lattice cones. The coefficients of Todd series of a particular class of lattice cones are closely related to generalized Dedekind sums of higher dimension. We generalize this construction and obtain an explicit formula for coefficients of the Todd series. It turns out that every maximal non-degenerate lattice cone, hence the associated Todd series can be obtained in this way.

• Bulletin of the Korean Mathematical Society
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• v.51 no.5
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• pp.1503-1510
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• 2014

The aim of this work is to construct a general family of two dimensional differential systems which admits homoclinic solutions near a non-hyperbolic fixed point, such that a Jacobian matrix at this point is zero. We then discretize it by using Euler's method and look after the persistence of the homoclinic solutions in the obtained discrete system.

• Journal of the Korean Mathematical Society
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• v.40 no.3
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• pp.447-460
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• 2003

In this paper we study the non-degenerate n-connected canonical domains with n>1 related to the conjecture of S. Bell in [4]. They are connected to the algebraic property of the Bergman kernel and the Szego kernel. We characterize the non-degenerate doubly connected canonical domains.