• 대한수학회보
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• 제45권1호
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• pp.143-155
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• 2008

Let p be a prime number. It is known that the order o(r) of a root r of the irreducible polynomial $x^p-x-l$ over $\mathbb{F}_p$ divides $g(p)=\frac{p^p-1}{p-1}$. Samuel Wagstaff recently conjectured that o(r) = g(p) for any prime p. The main object of the paper is to give some subsets S of {1,...,g(p)} that do not contain o(r).

• 대한수학회지
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• 제39권5호
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• pp.665-680
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• 2002

For a smooth projective irreducible algebraic curve C of odd gonality, the maximal possible dimension of the variety of special linear systems ${W^r}_d$(C) is d－3r by a result of M. Coppens et at. [4]. This bound also holds if C does not admit an involution. Furthermore it is known that if dim ${W^r}_d(C)qeq$ d-3r-1 for a curve C of odd gonality, then C is of very special type of curves by a recent progress made by G. Martens [11] and Kato-Keem [9]. The purpose of this paper is to pursue similar results for curves of even gonality which does not admit an involution.

• 대한수학회지
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• 제44권3호
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• pp.565-583
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• 2007

We offer a refinement of the classical Clifford inequality about special linear series on smooth irreducible complex curves. Namely, we prove about curves of genus g and odd gonality at least 5 that for any linear series $g^r_d$ with $d{\leq}g+1$, the inequality $3r{\leq}d$ holds, except in a few sporadic cases. Further, we show that the dimension of the set of curves in the moduli space for which there exists a linear series $g^r_d$ with d<3r for $d{\leq}g+l,\;0{\leq}l{\leq}\frac{g}{2}-3$, is bounded by $2g-1+\frac{1}{3}(g+2l+1)$.

• 호남수학학술지
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• 제33권4호
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• pp.547-556
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• 2011

In this paper, we estimated the Ricci curvature and the scalar curvature on SU(3)/T (k, l) under the condition (k, l) ${\in}\mathbb{R}^2$ (${\mid}k{\mid}+{\mid}l{\mid}{\neq}0$), where the four isotropy irreducible representations in SU(3)/T (k, l) are, not necessarily, mutually equivalent or inequivalent.

• 대한수학회지
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• 제36권3호
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• pp.633-648
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• 1999

In this paper, for any two bipartite ordered sets P and Q, we define the convolution P * Q of P and Q. For dim(P)=s and dim(Q)=t, we prove that s+t-(U+V)-2 dim(P*Q) s+t-(U+V)+2, where U+V is the max-mn integer of the certain realizers. In particular, we also prove that dim(P)=n+k- {{{{ { n+k} over {3 } }}}} for 2 k n<2k and dim(Pn ,k)=n for n 2k, where Pn,k=Sn*Sk is the convolution of two standard ordered sets Sn and Sk.

• 한국통신학회:학술대회논문집
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• 한국통신학회 1991년도 추계종합학술발표회논문집
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• pp.100-102
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• 1991

In this paper, we use LFSR(Linear Feedback Shift Register) as a kind of pseudo-random one-time pad. Key generator is constructed using r separate LFSR's with IP(Irreducible Polynominal) which are relatively prime. Key generated in this method has high linear complexity. And also, file cryptosystem for file encryption and decryption is constructed.

• 대한수학회보
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• 제45권3호
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• pp.457-466
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• 2008

Let R be a right near-ring. An R-group of type-5/2 which is a natural generalization of an irreducible (ring) module is introduced in near-rings. An R-group of type-5/2 is an R-group of type-2 and an R-group of type-3 is an R-group of type-5/2. Using it $J_{5/2}$, the Jacobson radical of type-5/2, is introduced in near-rings and it is observed that $J_2(R){\subseteq}J_{5/2}(R){\subseteq}J_3(R)$. It is shown that $J_{5/2}$ is an ideal-hereditary Kurosh-Amitsur radical (KA-radical) in the class of all zero-symmetric near-rings. But $J_{5/2}$ is not a KA-radical in the class of all near-rings. By introducing an R-group of type-(5/2)(0) it is shown that $J_{(5/2)(0)}$, the corresponding Jacobson radical of type-(5/2)(0), is a KA-radical in the class of all near-rings which extends the radical $J_{5/2}$ of zero-symmetric near-rings to the class of all near-rings.

• Journal of applied mathematics & informatics
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• 제28권5_6호
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• pp.1073-1088
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• 2010

In this article we want to formulate a disease transmission model, MSEIR model, for a population with individuals travelling between patches i and i + 1 and we derive an explicit formula for the basic reproductive number, $R_0$, employing the spectral radius of the next generation operator. Also, in this article we show that a system of ordinary differential equations for this model has a unique disease-free equilibrium and it is locally asymptotically stable if $R_0$ < 1 and unstable if $R_0$ > 1.

• 대한수학회지
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• 제56권5호
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• pp.1285-1307
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• 2019

For a multiplication R-module M we consider the Zariski topology in the set Spec (M) of prime submodules of M. We investigate the relationship between the algebraic properties of the submodules of M and the topological properties of some subspaces of Spec (M). We also consider some topological aspects of certain frames. We prove that if R is a commutative ring and M is a multiplication R-module, then the lattice Semp (M/N) of semiprime submodules of M/N is a spatial frame for every submodule N of M. When M is a quasi projective module, we obtain that the interval ${\uparrow}(N)^{Semp}(M)=\{P{\in}Semp(M){\mid}N{\subseteq}P\}$ and the lattice Semp (M/N) are isomorphic as frames. Finally, we obtain results about quantales and the classical Krull dimension of M.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제29권1호
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• pp.59-68
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• 2022

For a finite group G ⊂ GL(n, ℂ), the G-Hilbert scheme is a fine moduli space of G-clusters, which are 0-dimensional G-invariant subschemes Z with H⁰(𝒪_Z ) isomorphic to ℂ[G]. In many cases, the G-Hilbert scheme provides a good resolution of the quotient singularity ℂⁿ/G, but in general it can be very singular. In this note, we prove that for a cyclic group A ⊂ GL(n, ℂ) of type ${\frac{1}{r}}$(1, …, 1, a) with r coprime to a, A-Hilbert Scheme is smooth and irreducible.