• Korean Journal of Mathematics
• /
• 제25권4호
• /
• pp.537-554
• /
• 2017

In this paper, we study the surfaces foliated by ellipses in three dimensional Euclidean space ${\mathbf{E}}^3$. We prove the following results: (1) The surface foliated by an ellipse have constant Gaussian curvature K if and only if the surface is flat, i.e. K = 0. (2) The surface foliated by an ellipse is a flat if and only if it is a part of generalized cylinder or part of generalized cone.

• 대한수학회논문집
• /
• 제15권2호
• /
• pp.257-261
• /
• 2000

Northcott and Mckerrow proved that if R is a left noe-therian ring and E is an injective left R-module, then E[x-1] is an injective left R[x]-module. In this paper we generalize Northcott and McKerrow's result so that if R is a left noetherian ring and E is an in-jective left R-module, then E[x-S] is an injective left R[xS]-module, where S is a submonoid of N (N is the set of all natural numbers).

• Journal of applied mathematics & informatics
• /
• 제41권2호
• /
• pp.321-330
• /
• 2023

Let G = (V, E) be a graph. Consider the group S₃. Let g : V (G) → S₃ be a function. For each edge xy assign the label 1 if ${\lceil}{\frac{o(g(x))+o(g(y))}{2}}{\rceil}$ is odd or 0 otherwise. g is a group S₃ mean cordial labeling if |v_g(i) - v_g(j)| ≤ 1 and |e_g(0) - e_g(1)| ≤ 1, where vg(i) and e_g(y)denote the number of vertices labeled with an element i and number of edges labeled with y (y = 0, 1). The graph G with group S₃ mean cordial labeling is called group S₃ mean cordial graph. In this paper, we discuss group S3 mean cordial labeling for star related graphs.

• Journal of applied mathematics & informatics
• /
• 제17권1_2_3호
• /
• pp.567-572
• /
• 2005

A Banach space X is a Hilbert space if and only if $$E{\mid}x=Y{\mid}{\le}2$$ for all x$\in$ X and all X-valued Bochner integrable functions Y satisfying EY = 0 and ${\mid}x-Y{\mid}{\le}2$ a.e.

• 대한수학회보
• /
• 제51권6호
• /
• pp.1829-1839
• /
• 2014

Let (${\Omega}$, $\mathcal{S}$, ${\mu}$) be a probabilistic measure space, ${\varepsilon}{\in}\mathbb{R}$, ${\delta}{\geq}0$, p > 0 be given numbers and let $P{\subset}\mathbb{R}$ be an open interval. We consider a class of functions $f:P{\rightarrow}\mathbb{R}$, satisfying the inequality $$f(EX){\leq}E(f{\circ}X)+{\varepsilon}E({\mid}X-EX{\mid}^p)+{\delta}$$ for each $\mathcal{S}$-measurable simple function $X:{\Omega}{\rightarrow}P$. We show that if additionally the set of values of ${\mu}$ is equal to [0, 1] then $f:P{\rightarrow}\mathbb{R}$ satisfies the above condition if and only if $$f(tx+(1-t)y){\leq}tf(x)+(1-t)f(y)+{\varepsilon}[(1-t)^pt+t^p(1-t)]{\mid}x-y{\mid}^p+{\delta}$$ for $x,y{\in}P$, $t{\in}[0,1]$. We also prove some basic properties of such functions, e.g. the existence of subdifferentials, Hermite-Hadamard inequality.

• 한국위성정보통신학회논문지
• /
• 제2권2호
• /
• pp.64-68
• /
• 2007

본 논문에서는 기존의 GPS 항법 신호와 유럽에서 새롭게 추진되고 있는 갈릴레오 위성 항법 신호를 동시에 수신할 수 있는 광대역 고정밀 위성 항법 수신기의 RF 수신단 장치 설계 및 제작 결과에 대하여 기술하고 있다. 고정밀 광대역 위성 항법 수신기는 L - 대역 안테나, 항법 신호별 RF/IF 변환부, 그리고 고성능 기저대역 신호 처리부로 구성되어진다. L - 대역 안테나는 $1.1GHz{\sim}1.6\;GHz$를 수신할 수 있어야 하며, 항법 위성이 지평선 가까이에 있을 경우의 항법 신호를 수신할 수 있어야 한다. 갈릴레오 위성 항법 신호는 L1, E5, E6의 서로 다른 대역의 신호를 가지고 있으며, 신호 대역폭이 20MHz 이상으로 기존의 GPS위성 항법 신호보다 광대역이며, 따라서 수신기의 IF 주파수가 높아지며, 수신기의 처리 속도도 빨라져야 한다. 본 연구에서 개발한 수신기의 RF/IF 변환부는 단일 하향 변환기 구조의 디지털 IF 기술로 설계되었으며, IF 주파수는 위성 항법 신호의 최대 대역폭과 표본화 주파수 등을 고려하여 140MHz로 설정하였으며, 표본화 주파수는 112MHz로 설정하였다. RF/IF 변환부의 최종 출력은 디지털 IF 신호로서, IF 신호를 AD 변환기로 처리하여 얻게 된다. 본 연구에서 설계된 위성 항법용 고정밀 수신기 RF 수신단은 - 130 dBm의 입력 신호에 대하여 40dB Hz 이상의 C/N0 특성을 가지며, 40dB 이상의 동적 범위를 갖도록 자동 이득조절 장치가 포함되어 있다.

• 충청수학회지
• /
• 제4권1호
• /
• pp.11-38
• /
• 1991

Let $E_n$ be the real ordered space of all $n{\times}n$ Hermitian Matrices and let T be a positive linear operator from $E_2$ to $E_3$. We prove in this paper that T is extreme if and only if T is unitarily equivalent to a map of the form $S_z$ for some $z{\in}C^2$ where $S_z$ is defined by $S_z(xx^*)=ww^*$, $w_i=x_iz_i$ for i = 1, 2 and $w_3=0$.

• Journal of applied mathematics & informatics
• /
• 제29권5_6호
• /
• pp.1117-1127
• /
• 2011

In this paper, a class of more general delayed viral infection model with lytic immune response is proposed by Song et al.[1] ([Journal of Mathematical Analysis Application 373 (2011), 345-355). We derive the basic reproduction numbers $R_0$ and $R_0^*$ 0 for the viral infection, and establish that the global dynamics are completely determined by the values of $R_0$ and $R_0^*$. If $R_0{\leq}1$, the viral-free equilibrium $E_0$ is globally asymptotically stable; if $R_0^*{\leq}1$ < $R_0$, the immune-free equilibrium $E_1$ is globally asymptotically stable; if $R_0^*$ > 1, the chronic-infection equilibrium $E_2$ is globally asymptotically stable by using the method of Lyapunov function.

• 대한수학회보
• /
• 제25권2호
• /
• pp.203-209
• /
• 1988

In this paper, we define a g-regular semigroup which is a generalization of a regular semigroup. And we want to find some properties of g-regular semigroup. G-regular semigroups contains the variety of all regular semigroup and the variety of all periodic semigroup. If a is an element of a semigroup S, the smallest left ideal containing a is Sa.cup.{a}, which we may conveniently write as $S^{I}$a, and which we shall call the principal left ideal generated by a. An equivalence relation l on S is then defined by the rule alb if and only if a and b generate the same principal left ideal, i.e. if and only if $S^{I}$a= $S^{I}$b. Similarly, we can define the relation R. The equivalence relation D is R.L and the principal two sided ideal generated by an element a of S is $S^{1}$a $S^{1}$. We write aqb if $S^{1}$a $S^{1}$= $S^{1}$b $S^{1}$, i.e. if there exist x,y,u,v in $S^{1}$ for which xay=b, ubv=a. It is immediate that D.contnd.q. A semigroup S is called periodic if all its elements are of finite order. A finite semigroup is necessarily periodic semigroup. It is well known that in a periodic semigroup, D=q. An element a of a semigroup S is called regular if there exists x in S such that axa=a. The semigroup S is called regular if all its elements are regular. The following is the property of D-classes of regular semigroup.group.

• 호남수학학술지
• /
• 제38권2호
• /
• pp.305-316
• /
• 2016

In this paper we study general rotational surfaces in the 4-dimensional Euclidean space $\mathbb{E}^4$ and give a characterization of flat general rotational surface with pointwise 1-type Gauss map. Also, we show that a flat general rotational surface with pointwise 1-type Gauss map is a Lie group if and only if it is a Clifford torus.