• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.3 no.2
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• pp.123-130
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• 1991

The mixed convection heat transfer from vertical inline plates has been studied numerically by the finite difference method and experimentally with Mach-Zehnder interferometer. The dimensionless spacing, $s/L_1$, the relative length, $L_2/L_1$ and the dimensionless temperature ratio, ${\Phi}_2/{\Phi}_1$ are varied parametically. The lower plate mean Nusselt numbers show same values as $s/L_1$, ${\Phi}_2/{\Phi}_1$ and $L_2/L_1$ increase. The upper plate mean Nusselt numbers increase as $s/L_1$ and ${\Phi}_2/{\Phi}_1$ increase, but $L_2/L_1$ decreases. The upper plate mean Nusselt number is higher than the lower plate mean Nusselt for $s/L_1$ 1.8 at Re=100, $Gr=10^4$, Pr=0.71, $L_2/L_1=0.5$ and ${\Phi}_2/{\Phi}_1=1.0$. A comparison between the experimental and numerical results show good agreement.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.3
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• pp.467-480
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• 2009

In 1859, Bernhard Riemann, in his epoch-making memoir, extended the Euler zeta function $\zeta$(s) (s > 1; $s{\in}\mathbb{R}$) to the Riemann zeta function $\zeta$(s) ($\Re$(s) > 1; $s{\in}\mathbb{C}$) to investigate the pattern of the primes. Sine the time of Euler and then Riemann, the Riemann zeta function $\zeta$(s) has involved and appeared in a variety of mathematical research subjects as well as the function itself has been being broadly and deeply researched. Among those things, we choose to make a further investigation of the following subjects: Evaluation of $\zeta$(2k) ($k {\in}\mathbb{N}$); Approximate functional equations for $\zeta$(s); Series involving the Riemann zeta function.

• Journal of the Korean School Mathematics Society
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• v.17 no.2
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• pp.291-319
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• 2014

The purpose of this study is to investigate students' thinking and understanding through working on Worked-out Examples on numbers and operations, specifically, radical and real numbers and operations in the middle grades. For this purpose, we developed a set of Worked-out Examples; middle school students independently worked on them. Then two students were interviewed. These data were analyzed by using the framework of mathematical proficiency. The data analysis suggested that the students seemed to go through the processes involving a combination of understanding and computation, computation and reasoning, and understanding, computation and reasoning. Also, it appeared that most of the students have difficult solving problems involving with radical and real numbers in related to strategic competence.

• Korean Journal of Plant Taxonomy
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• v.41 no.2
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• pp.113-118
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• 2011

The somatic chromosome numbers of the Korean species of Senecio L. and two related genera are investigated here. Three different chromosome numbers were found: 2n = 40 in Senecio argunensis Turcz., S. nemorensis L., S. vulgaris L., Tephroseris flammea (DC.) Holub and 2n = 44 in T. phaeantha (Nakai) C. Jeffrey & Y.L. Chen. and 2n = 48 in Sinosenecio koreanus (Kom.) B. Nord., T. kirilowii (Turcz. ex DC.) Holub and T. pierotii (Miq.) Holub. The chromosome numbers of Sinosenecio koreanus (Kom.) B. Nord., Tephroseris flammea (DC.) Holub and T. phaeantha (Nakai) C. Jeffrey & Y.L. Chen. were different from those in previous reports.

• Communications of the Korean Mathematical Society
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• v.8 no.3
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• pp.373-382
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• 1993

• Bulletin of the Korean Mathematical Society
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• v.43 no.3
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• pp.479-486
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• 2006

Let $Z_n(s,\;f)=n^{-1}\;{\sum}^{ns}_{i=1}(f(X_i)-Pf)$ be the sequential empirical process based on the independent and identically distributed random variables. We prove that convergence problems of $sup_{(s,\;f)}|Z_n(s,\;f)|$ to zero boil down to those of $sup_f|Z_n(1,\;f)|$. We employ Ottaviani's inequality and the complete convergence to establish, under bracketing entropy with the second moment, the almost sure convergence of $sup_{(s,\;f)}|Z_n(s,\;f)|$ to zero.

• Journal of applied mathematics & informatics
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• v.8 no.3
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• pp.1021-1026
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• 2001

In this paper, we give an improvement of Carleman’s inequality by using the strict monotonicity of the power mean of n distinct positive numbers.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.21 no.2
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• pp.89-107
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• 2017

In this paper, we have proposed a modified Marker-And-Cell (MAC) method to investigate the problem of an unsteady 2-D incompressible flow with heat and mass transfer at low, moderate, and high Reynolds numbers with no-slip and slip boundary conditions. We have used this method to solve the governing equations along with the boundary conditions and thereby to compute the flow variables, viz. u-velocity, v-velocity, P, T, and C. We have used the staggered grid approach of this method to discretize the governing equations of the problem. A modified MAC algorithm was proposed and used to compute the numerical solutions of the flow variables for Reynolds numbers Re = 10, 500, and 50000 in consonance with low, moderate, and high Reynolds numbers. We have also used appropriate Prandtl (Pr) and Schmidt (Sc) numbers in consistence with relevancy of the physical problem considered. We have executed this modified MAC algorithm with the aid of a computer program developed and run in C compiler. We have also computed numerical solutions of local Nusselt (Nu) and Sherwood (Sh) numbers along the horizontal line through the geometric center at low, moderate, and high Reynolds numbers for fixed Pr = 6.62 and Sc = 340 for two grid systems at time t = 0.0001s. Our numerical solutions for u and v velocities along the vertical and horizontal line through the geometric center of the square cavity for Re = 100 has been compared with benchmark solutions available in the literature and it has been found that they are in good agreement. The present numerical results indicate that, as we move along the horizontal line through the geometric center of the domain, we observed that, the heat and mass transfer decreases up to the geometric center. It, then, increases symmetrically.

• Journal of Advanced Navigation Technology
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• v.11 no.2
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• pp.177-186
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• 2007

In this paper, the optimal position offset of optical phase conjugator (OPC) and the optimal dispersion offsets of fiber sections, which are alternating with the method for the symmetry of optical power and chromatic dispersion with respect to OPC, are numerically investigated as afunction of the WDM channel numbers. The WDM channel numbers are assumed to be 8, 12, 16, 20 and 24. The bit-rate of each channel is assumed to be 40 Gbps for all cases. It is confirmed that the optimal position offset of OPC and optimal dispersion offset of fiber section are gradually increased as the WDM channel numbers are gradually increased. But, the optimal dispersion values of fiber sections per OPC position offset of 1 km are independent on WDM channel numbers, because the optimal position offset of OPC and optimal dispersion offset of fiber section are simultaneously increased as the WDM channel numbers are increased. It is also confirmed that the applying of these optimal parameter values is efficient to WDM system with many channels rather than WDM with small channels.

• Korean Journal of Mathematics
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• v.19 no.3
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• pp.255-261
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• 2011

Let D be an integral domain, S be a torsion-free grading monoid such that the quotient group of S is of type (0, 0, 0, ${\ldots}$), and D[S] be the semigroup ring of S over D. We show that D[S] is an H-domain if and only if D is an H-domain and each maximal t-ideal of S is a $v$-ideal. We also show that if $\mathbb{R}$ is the eld of real numbers and if ${\Gamma}$ is the additive group of rational numbers, then $\mathbb{R}[{\Gamma}]$ is not an H-domain.