• Communications of the Korean Mathematical Society
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• v.34 no.2
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• pp.401-414
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• 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.

• Animal cells and systems
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• v.11 no.2
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• pp.135-139
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• 2007

One specimen of the percophid fish, Pteropsaron evolans Jordan and Snyder and two specimens of the labrid fish, Xyrichtys verrens (Jordan and Evermann) were newly collected from Jeju Island of Korea. P. evolans is characterized by having one pair of spines at snout, cheek without scales, and elongated first dorsal fin in male. X. verrens is easily distinguished by having tip of pectoral fin black, many rows of scales on cheek, and an elongated pelvic fin. We describe as new to Korean fish fauna and propose new Korean names, "Sil-nun-tung-i" for the former and "Jang-mi-ok-du-nol-rae-gi" for the latter.

• Journal of applied mathematics & informatics
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• v.19 no.1_2
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• pp.253-260
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• 2005

Denote the set of n ${\times}$ n complex Hermitian matrices by Hn. A pair of n ${\times}$ n Hermitian matrices (A, B) is said to be rank-additive if rank (A+B) = rank A+rank B. We characterize the linear maps from Hn into itself that preserve the set of rank-additive pairs. As applications, the linear preservers of adjoint matrix on Hn and the Jordan homomorphisms of Hn are also given. The analogous problems on the skew Hermitian matrix space are considered.

• Nonlinear Functional Analysis and Applications
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• v.26 no.2
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• pp.289-301
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• 2021

In this research, we interpret the notion of a b-cyclic (𝚽, C, D)-contraction for the pair (g, S) of self-mappings on the set Y. We employ our definition to introduce some common fixed point theorems for the two mappings g and S under a set of conditions. Also we introduce an example to support our results.

• Nonlinear Functional Analysis and Applications
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• v.28 no.1
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• pp.251-263
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• 2023

In the setting of extended quasi b-metric spaces, we introduce a new concept called "extended A-contraction". We then use our concept to prove a common fixed point result for a pair of self mappings under a set of conditions. Also, we provide the concepts of extended B-contraction and extended R-contraction. We then establish a common fixed point under these new contractions. Our results generalize many existing result of fixed point in metric spaces. Furthermore, we give an example to illustrate and support our result.

• Journal of applied mathematics & informatics
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• v.40 no.5_6
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• pp.1137-1150
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• 2022

Consider the quantum algebra U_q(sl₂) over field 𝓕 (char(𝓕) = 0) with equitable generators x^±1, y and z, where q is fixed nonzero, not root of unity scalar in 𝓕. Let V denote a finite dimensional irreducible module for this algebra. Let Λ ∈ End(V), and let {A₁, A₂, A₃} = {x, y, z}. First we show that if Λ, A₁ is a Leonard pair, then this Leonard pair have four types, and we show that for each type there exists a Leonard pair Λ, A₁ in which Λ is a linear combination of 1, A₂, A₃, A₂A₃. Moreover, we use Λ to construct 𝚼 ∈ U_q(sl₂) such that 𝚼, A^-1₁ is a Leonard pair, and show that 𝚼 = I + A₁Φ + A₁ΨA₁ where Φ and Ψ are linear combination of 1, A₂, A₃.

• Journal of the Korean Mathematical Society
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• v.48 no.1
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• pp.117-132
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• 2011

By developing a linear algebra program involving many different structures associated to a three-graded H*-algebra, it is shown that if L is a Lie triple automorphism of an infinite-dimensional topologically simple associative H*-algebra A, then L is either an automorphism, an anti-automorphism, the negative of an automorphism or the negative of an anti-automorphism. If A is finite-dimensional, then there exists an automorphism, an anti-automorphism, the negative of an automorphism or the negative of an anti-automorphism F : A $\rightarrow$ A such that $\delta$:= F - L is a linear map from A onto its center sending commutators to zero. We also describe L in the case of having A zero annihilator.

• Wind and Structures
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• v.6 no.5
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• pp.347-356
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• 2003

Experimental studies on drag reduction of a circular cylinder of diameter D were conducted in the subcritical flow regime at Reynolds numbers in the range $4{\times}10^4{\leq}Re{\leq}10^5$. To shield the cylinder rear surface from the pressure deficit of the unsteady vortex generation in the near wake, two shield plates were attached downstream of the separation points to form a cavity at the base region. The chord of the shield plates, L, ranged from 0.22 to 1.52 D and the cavity width, G, was in the range from 0 to 0.96 D. It is concluded that significant drag reductions from that of a plain cylinder may be achieved by proper sizing of the shield plates and the base cavity. The study shows that using a pair of shield plates at G/D of 0.86 and angular position ${\theta}$ of ${\pm}121^{\circ}$ results in a configuration with percentage drag reduction of 40% for L/D of 0.5, and 55% for L/D of 1.0.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.21 no.1
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• pp.20-27
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• 2020

In general, a nonlinear system is linearized in the form of a multiplication of the 1st and 2nd order system. This paper reports a design method of a weighting matrix and control law of LQ control to move the double poles that have a Jordan block to a pair of complex conjugate poles. This method has the advantages of pole placement and the guarantee of stability, but this method cannot position the poles correctly, and the matrix is chosen using a trial and error method. Therefore, a relation function (𝜌, 𝜃) between the poles and the matrix was derived under the condition that the poles are the roots of the characteristic equation of the Hamiltonian system. In addition, the Pole's Moving-range was obtained under the condition that the state weighting matrix becomes a positive semi-definite matrix. This paper presents examples of how the matrix and control law is calculated.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.19 no.2
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• pp.608-616
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• 2018

If a general nonlinear system is linearized by the successive multiplication of the 1st and 2nd order systems, then there are four types of poles in this linearized system: the pole of the 1st order system and the equal poles, two distinct real poles, and complex conjugate pair of poles of the 2nd order system. Linear Quadratic (LQ) control is a method of designing a control law that minimizes the quadratic performance index. It has the advantage of ensuring the stability of the system and the pole placement of the root of the system by weighted matrix adjustment. LQ control by the weighted matrix can move the position of the pole of the system arbitrarily, but it is difficult to set the weighting matrix by the trial and error method. This problem can be solved using the characteristic equations of the Hamiltonian system, and if the control weighting matrix is a symmetric matrix of constants, it is possible to move several poles of the system to the desired closed loop poles by applying the control law repeatedly. The paper presents a method of calculating the state weighting matrix and the control law for moving the equal poles with Jordan blocks to two real poles using the characteristic equation of the Hamiltonian system. We express this characteristic equation with a state weighting matrix by means of a trigonometric function, and we derive the relation function (${\rho},\;{\theta}$) between the equal poles and the state weighting matrix under the condition that the two real poles are the roots of the characteristic equation. Then, we obtain the moving-range of the two real poles under the condition that the state weighting matrix becomes a positive semi-finite matrix. We calculate the state weighting matrix and the control law by substituting the two real roots selected in the moving-range into the relational function. As an example, we apply the proposed method to a simple example 3rd order system.