• 대한전자공학회논문지
• /
• 제20권5호
• /
• pp.1-7
• /
• 1983

일반적으로 다치론리는 Modulo-M의 수 체계를 기초로 한다. 이 논문에서는 다치의 치의 요소를 서로 배타적인 상태를 나타내는 기호하여 집합의 방식으로 다치 논리를 설정하고, 기호 다치 논리극교와 그 변화를 정의하였으며, 그 성질을 정리, 증명하였다. 또, 경산외 변화에 의한 기회 다치 논리극교의 MacLaurin 전개와 Taylor 전개 방법을 제안하고 증명하였다.

• 대한수학회논문집
• /
• 제33권4호
• /
• pp.1141-1158
• /
• 2018

Hahn difference operator $D_{q,{\omega}}$ which is defined by $$D_{q,{\omega}}g(t)=\{{\frac{g(gt+{\omega})-g(t)}{t(g-1)+{\omega}}},{\hfill{20}}\text{if }t{\neq}{\theta}:={\frac{\omega}{1-q}},\\g^{\prime}({\theta}),{\hfill{83}}\text{if }t={\theta}$$ received a lot of interest from many researchers due to its applications in constructing families of orthogonal polynomials and in some approximation problems. In this paper, we investigate sufficient conditions for stability of the abstract linear Hahn difference equations of the form $$D_{q,{\omega}}x(t)=A(t)x(t)+f(t),\;t{\in}I$$, and $$D^2{q,{\omega}}x(t)+A(t)D_{q,{\omega}}x(t)+R(t)x(t)=f(t),\;t{\in}I$$, where $A,R:I{\rightarrow}{\mathbb{X}}$, and $f:I{\rightarrow}{\mathbb{X}}$. Here ${\mathbb{X}}$ is a Banach algebra with a unit element e and I is an interval of ${\mathbb{R}}$ containing ${\theta}$.

• 대한수학회논문집
• /
• 제33권4호
• /
• pp.1125-1140
• /
• 2018

Let A be a normed space, ${\mathcal{B}}(A)$ the algebra of all bounded operators on A, and V a family of strongly upper semicontinuous functions from a Hausdorff completely regular space X into ${\mathcal{B}}(A)$. In this paper, we investigate some properties of the weighted spaces CV (X, A) of all A-valued continuous functions f on X such that the mapping $x{\mapsto}v(x)(f(x))$ is bounded on X, for every $v{\in}V$, endowed with the topology generated by the seminorms ${\parallel}f{\parallel}v={\sup}\{{\parallel}v(x)(f(x)){\parallel},\;x{\in}X\}$. Our main purpose is to characterize continuous, bounded, and locally equicontinuous weighted composition operators between such spaces.

• 한국소음진동공학회논문집
• /
• 제20권12호
• /
• pp.1168-1175
• /
• 2010

Excessive torsional vibrations from marine engine shafting systems can be reduced by using torsional vibration dampers. But in order to be tuned effectively, the dampers should be designed through the optimum design procedure. In this paper, the procedure to get the optimum values of system parameters of spring-viscous dampers using effective modal mass of inertia and stiffness is suggested and the damping is determined by the exact algebra optimization method. The validity of the suggested method is confirmed through the application to a 1800 kW four cycle diesel engine and generator system.

• Kyungpook Mathematical Journal
• /
• 제53권2호
• /
• pp.233-245
• /
• 2013

Let $\mathcal{A}$ be a Banach ternary algebra over a scalar field R or C and $\mathcal{X}$ be a ternary Banach $\mathcal{A}$-module. A quartic mapping $D\;:\;(\mathcal{A},[\;]_{\mathcal{A}}){\rightarrow}(\mathcal{X},[\;]_{\mathcal{X}})$ is called a $4^{th}$- order ternary derivation if $D([x,y,z])=[D(x),y^4,z^4]+[x^4,D(y),z^4]+[x^4,y^4,D(z)]$ for all $x,y,z{\in}\mathcal{A}$. In this paper, we prove Ulam stability generalizations of $4^{th}$- order ternary derivations associated to the following JMRassias quartic functional equation on fr$\acute{e}$che algebras: $$f(kx+y)+f(kx-y)=k^2[f(x+y)+f(x-y)]+2k^2(k^2-1)f(x)-2(k^2-1)f(y)$$.

• 대한수학회논문집
• /
• 제34권3호
• /
• pp.743-755
• /
• 2019

For every inverse semigroup S with subsemigroup E of idempotents, necessary and sufficient conditions are obtained for the weighted semigroup algebra $l^1(S,{\omega})$ and its second dual to be $l^1(E)$-module amenble. Some results for the module Arens regularity of $l^1(S,{\omega})$ (as an $l^1(E)$-module) are found. If S is either of the bicyclic inverse semigroup or the Brandt inverse semigroup, it is shown that $l^1(S,{\omega})$ is module amenable but not amenable for any weight ${\omega}$.

• Korean Journal of Mathematics
• /
• 제27권2호
• /
• pp.375-415
• /
• 2019

We study spaces of continuous-function-valued functions that have the property that composition with evaluation functionals induce $weak^*$ to norm continuous maps to ${\ell}^p$ space ($p{\in}(1,\;{\infty})$). Versions of $H{\ddot{o}}lder^{\prime}s$ inequality and Riesz representation theorem are proved to hold on these spaces. We prove a version of Dixmier's theorem for spaces of function-valued matrix operators on these spaces, and an analogue of the trace formula for operators on Hilbert spaces. When the function space is taken to be the complex field, the spaces are just the ${\ell}^p$ spaces and the well-known classical theorems follow from our results.

• 대한수학회논문집
• /
• 제34권2호
• /
• pp.401-414
• /
• 2019

Let ${\mathcal{F}}$ denote an algebraically closed field with characteristic not two. Fix an integer $d{\geq}3$, let $Mat_{d+1}({\mathcal{F}})$ denote the ${\mathcal{F}}$-algebra of $(d+1){\times}(d+1)$ matrices with entries in ${\mathcal{F}}$. An ordered pair of matrices A, $A^*$ in $Mat_{d+1}({\mathcal{F}})$ is said to be LB-TD form whenever A is lower bidiagonal with subdiagonal entries all 1 and $A^*$ is irreducible tridiagonal. Let A, $A^*$ be a Leonard pair in $Mat_{d+1}({\mathcal{F}})$ with fundamental parameter ${\beta}=2$, with this assumption there are four families of Leonard pairs, Racah, Hahn, dual Hahn, Krawtchouk type. In this paper we show from these four families only Racah and Krawtchouk have LB-TD form.

• 대한수학회논문집
• /
• 제37권1호
• /
• pp.259-267
• /
• 2022

We use L_∞ models to compute the rational homotopy type of the mapping space of the component of the natural inclusion i_n,k : ℂPⁿ ↪ ℂP^n+k between complex projective spaces and show that it has the rational homotopy type of a product of odd dimensional spheres and a complex projective space. We also characterize the mapping aut₁ ℂPⁿ → map(ℂPⁿ, ℂP^n+k; i_n,k) and the resulting G-sequence.

• Korean Journal of Mathematics
• /
• 제31권3호
• /
• pp.363-372
• /
• 2023

In this paper, we consider two functional equations: (1) h(𝓕(x, y, z) + 2x + y + z) + h(xy + z) + yh(x) + yh(z) = h(𝓕(x, y, z) + 2x + y) + h(xy) + yh(x + z) + 2h(z), (2) h(𝓕(x, y, z) - y + z + 2e) + 2h(x + y) + h(xy + z) + yh(x) + yh(z) = h(𝓕(x, y, z) - y + 2e) + 2h(x + y + z) + h(xy) + yh(x + z), without any regularity assumption for all x, y, z in a unital algebra A, where 𝓕 : A³ → A is defined by 𝓕(x, y, z) := h(x + y + z) - h(x + y) - h(z) for all x, y, z ∈ A. Also, we find general solutions of these equations in unital algebras. Finally, we prove the Hyers-Ulam stability of (1) and (2) in unital Banach algebras.