• Journal of Korean Institute of Industrial Engineers
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• v.29 no.4
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• pp.253-258
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• 2003

We consider the problem of grouping orders into lots. The problem is modelled by a graph G=(V,E), where each node ${\nu}{\in}V$ denotes order specification and its weight ${\omega}(\nu)$ the orders on hand for the specification. We can construct a lot simply from orders of single specification. For a set of nodes (specifications) ${\theta}{\subseteq}V$, if the distance of any two nodes in $\theta$ is at most d, it is also possible to make a lot using orders on the nodes. The objective is to maximize the number of lots with size exactly $\lambda$. In this paper, we prove that our problem is NP-Complete when $d=2,{\lambda}=3$ and each weight is 0 or 1. Moreover, it is also shown to be NP-Complete when $d=1,{\lambda}=3$ and each weight is 1,2 or 3.

• Communications of the Korean Mathematical Society
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• v.37 no.4
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• pp.1055-1072
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• 2022

Our aim is to establish certain image formulas of the (p, 𝜈)-extended Gauss' hypergeometric function F_p,𝜈(a, b; c; z) by using Saigo's hypergeometric fractional calculus (integral and differential) operators. Corresponding assertions for the classical Riemann-Liouville(R-L) and Erdélyi-Kober(E-K) fractional integral and differential operators are deduced. All the results are represented in terms of the Hadamard product of the (p, 𝜈)-extended Gauss's hypergeometric function F_p,𝜈(a, b; c; z) and Fox-Wright function _rΨ_s(z). We also established Jacobi and its particular assertions for the Gegenbauer and Legendre transforms of the (p, 𝜈)-extended Gauss' hypergeometric function F_p,𝜈(a, b; c; z).

• The Bulletin of The Korean Astronomical Society
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• v.44 no.2
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• pp.70.3-70.3
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• 2019

We present a method to estimate 3-component plasma velocity (Vx, Vy and Vz) at solar photosphere near solar disk center, using the Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory (SDO) called Space-weather HMI Active Region Patch (SHARP). In Heliocentric-Cartesian Coordinates, the component of Vz is obtained from Dopplergram while the components of Vx and Vy are derived from the relation of $B_z{\overrightarrow{u}}=B_z{\overrightarrow{{\nu}_t}}-{\nu}_z{\overrightarrow{B_t}}$ (Demoulin & Berger 2003) using a series of vector magnetograms by an optical flow technique NAVE (Nonlinear Affine Velocity Estimator). This velocity measurement method is applied to AR 12158 producing an X1.6 flare along with a coronal mass ejection. We find noticeable upflow motions at both ends of flux ropes which become a major eruption part, and strong transverse motions nearby them before the eruption. We will discuss the change of plasma motions and magnetic fields before and after the eruption.

• Solar Energy
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• v.15 no.3
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• pp.105-117
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• 1995

Heat transfer coefficients on a single spiral coil tube in the furan foundry sand fluidized bed have been investigated. Heat transfer coefficients(ho) to an immersed single spiral coil tube were measured in the bed. The bed diameter was 0.21 m. The following quantities were varied: (l)bed temperature, (2)mean particle diameter, (3) fluidization rate, (4)the ratio of heated coil tube pitch to diameter(p/Do), and (5)the ratio of heated coil tube pitch to mean particle diameter(p/dp). In addition, the experimental values of maximum Nusselts number were compared with the values of maximum Nusselts number predicted by the existing correlations. The values of heat transfer coefficient increase with the increase in bed temperature and fluidization rate, but decrease with increase in particle diameter. An empirical formulus of maximum Nusselts number which is applicable in the furan foundry sand fluidization bed is as follows: $$Nu_{max}=1.01\;Re^{0.48}Prg^{0.4}(p/dp)^{0.28}(p/Do)^{0.05}$$.

• Korean Journal of Mathematics
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• v.22 no.1
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• pp.91-121
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• 2014

Let X and Y be vector spaces. It is shown that a mapping $f:X{\rightarrow}Y$ satisfies the functional equation ${\ddag}$ $$2df(\frac{x_1+{\sum}_{j=2}^{2d}(-1)^jx_j}{2d})-2df(\frac{x_1+{\sum}_{j=2}^{2d}(-1)^{j+1}x_j}{2d})=2\sum_{j=2}^{2d}(-1)^jf(x_j)$$ if and only if the mapping $f:X{\rightarrow}Y$ is additive, and prove the Cauchy-Rassias stability of the functional equation (${\ddag}$) in Banach modules over a unital $C^*$-algebra, and in Poisson Banach modules over a unital Poisson $C^*$-algebra. Let $\mathcal{A}$ and $\mathcal{B}$ be unital $C^*$-algebras, Poisson $C^*$-algebras, Poisson $JC^*$-algebras or Lie $JC^*$-algebras. As an application, we show that every almost homomorphism $h:\mathcal{A}{\rightarrow}\mathcal{B}$ of $\mathcal{A}$ into $\mathcal{B}$ is a homomorphism when $h(d^nuy)=h(d^nu)h(y)$ or $h(d^nu{\circ}y)=h(d^nu){\circ}h(y)$ for all unitaries $u{\in}\mathcal{A}$, all $y{\in}\mathcal{A}$, and n = 0, 1, 2, ${\cdots}$. Moreover, we prove the Cauchy-Rassias stability of homomorphisms in $C^*$-algebras, Poisson $C^*$-algebras, Poisson $JC^*$-algebras or Lie $JC^*$-algebras, and of Lie $JC^*$-algebra derivations in Lie $JC^*$-algebras.

• Journal of electromagnetic engineering and science
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• v.13 no.1
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• pp.16-21
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• 2013

This study presents the angular effects of virtual vertices inserted for effective treatment of the boundary edge laid on an infinite conducting surface in a half-space scattering problem. We investigated the angular effects of virtual vertices by first computing the radar cross section (RCS) of a specific scatterer; i.e., a tilted conducting plate in contact with the ground surface, by inserting the virtual vertex in half-space. Here, the electric field integral equation is used to solve this problem with various virtual vertex angles (${\theta}_{\nu}$) and conducting plate inclination angles (${\theta}_r$) ranging from $0^{\circ}$ to $180^{\circ}$. The effects of the angles ${\theta}_{\nu}$ and ${\theta}_r$ on the RCS computation are clearly shown with numerical results with and without the virtual vertices in free- and half-spaces.

• Bulletin of the Korean Mathematical Society
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• v.26 no.2
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• pp.151-158
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• 1989

Let (H, B, .nu.) be an abstract Wiener space where H is a separable Hilbert space with the inner product <.,.> and the norm vertical bar . vertical bar=.root.<.,.>, which is densely and continuously imbedded into a separable Banach space B with the norm ∥.∥ , and .nu. is a probability measure on the Borel .sigma.-algebra B(B) of B which satisfies (Fig.) where $B^{*}$ is the topological dual of B and (.,.) is the natural dual pairing between B and $B^{*}$. We will regard $B^{*}$.contnd.H.contnd.B in the natural way. Thus we have =(y, x) for all y in $B^{*}$ and x in H. Let $R^{n}$ and C denote the n-dimensional Euclidean space and the complex numbers respectively.ctively.

• Journal of applied mathematics & informatics
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• v.28 no.3_4
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• pp.763-772
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• 2010

This paper deals with the existence of triple positive solutions for the nonlinear second-order three-point boundary value problem z"(t)+a(t)f(t, z(t), z'(t))=0, t $\in$ (0, 1), $z(0)={\nu}z(1)\;{\geq}\;0$, $z'(\eta)=0$, where 0 < $\nu$ < 1, 0 < $\eta$ < 1 are constants. f : [0, 1] $\times$ [0, $+{\infty}$) $\times$ R $\rightarrow$ [0, $+{\infty}$) and a : (0, 1) $\rightarrow$ [0, $+{\infty}$) are continuous. First, Green's function for the associated linear boundary value problem is constructed, and then, by means of a fixed point theorem due to Avery and Peterson, sufficient conditions are obtained that guarantee the existence of triple positive solutions to the boundary value problem. The interesting point is that the nonlinear term f is involved with the first-order derivative explicitly.

• Honam Mathematical Journal
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• v.24 no.1
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• pp.121-130
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• 2002

In this paper we prove a functional central limit theorem for a field $\{X_{\underline{j}}:{\underline{j}}{\in}Z_+^d\}$ of nonstationary associated random variables with $EX{\underline{j}}=0,\;E{\mid}X_{\underline{j}}{\mid}^{r+{\delta}}<{\infty}$ for some $r>2,\;{\delta}>0$and $u(n)=O(n^{-{\nu}})$ for some ${\nu}>0$, where $u(n):=sup_{{\underline{i}}{\in}Z_+^d{\underline{j}}:{\mid}{\underline{j}}-{\underline{i}}{\mid}{\geq}n}{\sum}cov(X_{\underline{i}},\;X_{\underline{j}}),\;{\mid}{\underline{x}}{\mid}=max({\mid}x_1{\mid},{\cdots},{\mid}x_d{\mid})\;for\;{\underline{x}}{\in}{\mathbb{R}}^d$. Our investigation implies and analogous result in the case associated random measure.

• Journal of Navigation and Port Research
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• v.27 no.5
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• pp.593-597
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• 2003

Ennin was a Japanese buddhist monk who stayed in Tang from Jun. 13, 838 A.D. to Dec. 14, 847 A.D. in lunar's calender and wrote lengthy diary through the travel. This diary contained lots of information on the politics, economy, social culture, religion, diplomatic policies, militaries, geography, transportations and administrations of Tang China. Especially the beginning of his diary dated from Jun. 13, to July 3, 838 A. D. was recorded in the manner of ship's logbook entries. Many terms of navigation and naval architecture appeared on it. It is very important to understand them for studying ancient ship and its navigation skill. This paper aims to investigate the meaning of ‘Nu-A’ obviously referring to some part of hull of the ship as the first step to annotate the terms of navigation and naval architecture which were appeared in the diary.