• Korean Journal of Mathematics
• /
• 제31권4호
• /
• pp.495-504
• /
• 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
• /
• 제22권5호
• /
• pp.362-365
• /
• 2007

Cyanobacterial A-domain의 A3 motif와 A7 motif의 높은 진화론적 보존성에 의거해서 Non-ribosomal peitides를 생산하는 시아노박테리아를 Screening할 수 있는 degenerated primer를 만들 수 있었다. Degenerate primer서열의 종류는 가능하면 1,000개 정도까지를 기준으로 만드는 것이 좋다. Primer의 종류가 너무 많으면 primer 1종류 당 mol수가 적게 되어 특이성도 저하된다. 그러므로 Primer의 종류가 많을 경우는 inosin을 N (4종류의 염기) 부분에 이용하면 어느 염기에도 강하게 결합하지 않고 두 가닥 DNA 형성을 저해하지도 않으므로 degeneration을 줄이는데 도움이 된다. Degenerate primer의 annealing 온도는 primer에 포함되어있는 서열 중 가장 낮은 Tm을 기준으로 한다. 이번 연구처럼 N (ACGT) 대신에 Inosin을 이용하였을 때에는 Inosin이 Tm을 높게 하지 않고 Tm을 낮게 하지도 않으므로 Tm 계산시 고려하지 않아도 되었다. PCR 효율이 떨어질 우려가 있으므로 충분한 Tm값 (대개 $45\sim60^{\circ}C$ 이상)을 갖는 서열을 디자인하여 primer로 PCR하는 것이 좋지만, A3/A7 degenerate prime에서는 실험에 의해 40$^{\circ}C$로 annealing 온도가 (Tm) 다소 낮게 설정되었다. 그러므로 검출되지 않은 NRPS gene을 가진 균주와 CBT635, CBT654와 같이 약한 PCR band의 형성은 새로 제작된 primer의 낮은 Tm 기인한다고 생각되어진다. Tm의 이론적인 값은 Tm ={(G+C)*4+(A+T)*2}의 식을 통해서 정방향 primer에서 54$^{\circ}C$ 역방향 primer에서 42$^{\circ}C$로 계산되었다. 새로운 degenerate primer에 의해서 MTF2/MTR2로 검출되지 않는 6개의 균주가 더 검출되었으며, A3/A7과 MTF2/MTR2를 이용한 통합 PCR Screening을 통해서 NRPS gene 검출에 특이성과 효율성을 높일 수 있다.

• 한국국방경영분석학회지
• /
• 제27권1호
• /
• pp.28-38
• /
• 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.

• 대한수학회논문집
• /
• 제28권4호
• /
• pp.751-766
• /
• 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.

• 대한수학회보
• /
• 제53권6호
• /
• pp.1697-1705
• /
• 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.

• 대한수학회지
• /
• 제48권1호
• /
• pp.1-12
• /
• 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.

• 대한수학회지
• /
• 제56권5호
• /
• pp.1355-1370
• /
• 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.

• 대한수학회논문집
• /
• 제30권2호
• /
• pp.73-79
• /
• 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.

• 대한수학회보
• /
• 제51권5호
• /
• pp.1503-1510
• /
• 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.

• 대한수학회지
• /
• 제40권3호
• /
• pp.447-460
• /
• 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.