• Journal of Korean Institute of Industrial Engineers
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• v.38 no.1
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• pp.1-6
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• 2012

We consider a two-dimensional vector packing problem in which each item has size in x- and y-coordinates. The purpose of this paper is to provide a ground work on how hard two-dimensional vector packing problems are for large items. We prove that the problem with each item greater than 1/2-${\varepsilon}$ either in x- or y-coordinates for 0 < ${\varepsilon}$ ${\leq}$ 1/6 has no APTAS unless P = NP.

• Communications of the Korean Mathematical Society
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• v.37 no.1
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• pp.229-257
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• 2022

Let M be a semi-invariant submanifold of codimension 3 with almost contact metric structure (𝜙, 𝜉, 𝜂, g) in a complex space form M_n+1(c), c ≠ 0. We denote by A and R_𝜉 the shape operator in the direction of distinguished normal vector field and the structure Jacobi operator with respect to the structure vector 𝜉, respectively. Suppose that the third fundamental form t satisfies dt(X, Y) = 2𝜃g(𝜙X, Y) for a scalar 𝜃(< 2c) and any vector fields X and Y on M. In this paper, we prove that if it satisfies R_𝜉A = AR_𝜉 and at the same time ∇_𝜉R_𝜉 = 0 on M, then M is a Hopf hypersurface of type (A) provided that the scalar curvature s of M holds s - 2(n - 1)c ≤ 0.

• Journal of The Korean Astronomical Society
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• v.29 no.spc1
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• pp.307-308
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• 1996

• Journal of Power System Engineering
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• v.4 no.4
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• pp.25-31
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• 2000

This paper represents the vector fields and three dimensional mean velocities in the X-Y plane of cone type swirl gas burner measured by using X-probe from the hot-wire anemometer system. This experiment is carried out at flowrate 350 and $450{\ell}/min$ respectively in the test section of subsonic wind tunnel. The vector plot shows that the maximum axial mean velocity component is focused in the narrow slits distributed radially on the edge of a cone type swirl burner, for that reason, there is some entrainment of ambient air in the outer region of the burner and the rotational flow can be shown in the inner region of the burner because mean velocity W is distributed about twice as large as mean velocity V due to inclined flow velocity ejecting from the swirl vanes of a cone type baffle plate of burner. Moreover, the mean velocities are largely distributed near the outer region of burner within $X/R{\fallingdotseq}1.5$, hence, the turbulent characteristics are anticipated to be distributed largely in the center of this region due to the large inclination of mean velocity and swirl effect.

• Journal of the Chungcheong Mathematical Society
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• v.20 no.1
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• pp.37-45
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• 2007

Let X, Y be vector spaces. In this paper, we investigate the generalized Hyers-Ulam-Rassias stability problem for a cubic function $f:X{\rightarrow}Y$ satisfies $$r^3f(\frac{\Sigma_{j=1}^{n-1}x_j+2x_n}{r})+r^3f(\frac{\Sigma_{j=1}^{n-1}x_j-2x_n}{r})+8\sum_{j=1}^{n-1}f(x_j)=2f{\sum_{j=1}^{n-1}}x_j)+4{\sum_{j=1}^{n-1}}(f(x_j+x_n)+f(x_j-x_n))$$ for all $x_1,{\cdots},x_n{\in}X$.

• Journal of the Korean Mathematical Society
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• v.32 no.3
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• pp.509-518
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• 1995

Let $M^n$ be a hypersurface in the Euclidean space $R^{n+1}$ with position vector field x and unit normal vector field G.

• Bulletin of the Korean Mathematical Society
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• v.48 no.5
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• pp.939-949
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• 2011

In this paper we give two matching theorems of Ky Fan type concerning open or closed coverings of nonempty convex sets in a topological vector space. One of them will permit us to put in evidence, when X and Y are convex sets in topological vector spaces, a new subclass of KKM(X, Y) different by any admissible class $\mathfrak{u}_c$(X, Y). For this class of set-valued mappings we establish a KKM-type theorem which will be then used for obtaining existence theorems for the solutions of two types of simultaneous relation problems.

• Journal of applied mathematics & informatics
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• v.28 no.3_4
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• pp.697-710
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• 2010

In this paper, we prove existence of infinitely many positive and concave solutions, by means of a simple approach, to $3^{th}$ order three-point singular boundary value problem {$x^{\prime\prime\prime}(t)=\alpha(t)f(t,x(t))$, 0 < t < 1, $x(0)=x'(\eta)=x^{\prime\prime}(1)=0$, (1/2 < $\eta$ < 1). Moreover with respect to multiplicity of solutions, we don't assume any monotonicity on the nonlinearity. We rely on a combination of the analysis of the corresponding vector field on the phase-space along with Knesser's type properties of the solutions funnel and the well-known Krasnosel'ski$\breve{i}$'s fixed point theorem. The later is applied on a new very simple cone K, just on the plane $R^2$. These extensions justify the efficiency of our new approach compared to the commonly used one, where the cone $K\;{\subset}\;C$ ([0, 1], $\mathbb{R}$) and the existence of a positive Green's function is a necessity.

• Korean Journal of Animal Reproduction
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• v.25 no.2
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• pp.171-180
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• 2001

Compared to other gene transfer system, the advantages of retrovirus-mediated gene transfer are technical ease, efficient expression and genetic stability. Despite the high potency of the retrovirus vector system in gene transfer, one of the drawbacks is a difficulty in concentration of virus stock. To overcome this problem, we tested a new retrovirus vector system producing the progeny retrovirus particles encapsidated with VSV-G (vesicular stomatitis virus G glycoprotein). The infectivity of this virus was not sacrificed by ultracentrifugal concentration and the host cell range extended from all mammalian to fish embryos. Virus titer after 1,000 x concentration was more than 10$^{8}$ CFU/ $m\ell$ on most of the target cell lines. We applied this pantropic viruses in transgenic chicken production by injecting the concentrated (100$\times$) stock into subgerminal cavity of stage X chicken embryos. The survival rate of chicken embryos after injection was about 20% and gene integration rate in surviving embryos was scored almost 100%. Analyses of RT-PCR and fluorescence microscopy, however, showed no evidence of the transgene expression.

• Journal of the Korean Mathematical Society
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• v.33 no.2
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• pp.423-438
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• 1996

Let L be a linear functional on the vector space of polynomials in x. Let $\omega(x)$ be a polynomial in x of degree d, for some positive integer d. We consider two sets of polynomials, ${R_n (x)}_{n \geq 0}, {S_n(x)}_{n \geq 0}$, such that $R_n(x)$ is a polynomial in x of degree n and $S_n(x)$ is a polynomial in $\omega(x)$ of degree n. (So $S_n(x)$ is a polynomial in x of degree dn.)