• Journal of the Korean Mathematical Society
• /
• v.34 no.4
• /
• pp.1029-1036
• /
• 1997

Let ${A_t)}_{t>0}$ be a dilation group given by $A_t = exp(-P log t)$, where P is a real $n \times n$ matrix whose eigenvalues has strictly positive real part. Let $\nu$ be the trace of P and $P^*$ denote the adjoint of pp. Suppose that $K$ is a function defined on $R^n$ such that $$\mid$K(x)$\mid$ \leq k($\mid$x$\mid$_Q)$ for a bounded and decreasing function $k(t) on R_+$ satisfying $k \diamond $\mid$\cdot$\mid$_Q \in \cup_{\varepsilon >0}L^1((1 + $\mid$x$\mid$)^\varepsilon dx)$ where $Q = \int_{0}^{\infty} exp(-tP^*) exp(-tP)$ dt and the norm $$\mid$\cdot$\mid$_Q$ stands for $$\mid$x$\mid$_Q = \sqrt{}, x \in R^n$. For $f \in L^1(R^n)$, define $mf(x) = sup_{t>0}$\mid$K_t * f(x)$\mid$$ where $K_t(X) = t^{-\nu}K(A_{1/t}^* x)$. Then we show that $m$ is a bounded operator of $L^1(R^n) into L^{1, \infty}(R^n)$.

• Kyungpook Mathematical Journal
• /
• v.56 no.2
• /
• pp.583-595
• /
• 2016

Archimedes showed that for a point P on a parabola X and a chord AB of X parallel to the tangent of X at P, the area S of the region bounded by the parabola X and chord AB is four thirds of the area T of triangle ${\Delta}ABP$. It is well known that the area U formed by three tangents to a parabola is half of the area T of the triangle formed by joining their points of contact. Recently, the first and third authors of the present paper and others proved that among strictly locally convex curves in the plane ${\mathbb{R}}^2$, these two properties are characteristic ones of parabolas. In this article, in order to generalize the above mentioned property $S={\frac{4}{3}}T$ for parabolas we study strictly locally convex curves in the plane ${\mathbb{R}}^2$ satisfying $S={\lambda}T+{\nu}U$, where ${\lambda}$ and ${\nu}$ are some functions on the curves. As a result, we present two conditions which are necessary and sufficient for a strictly locally convex curve in the plane to be an open arc of a parabola.

• Journal of Mechanical Science and Technology
• /
• v.17 no.10
• /
• pp.1520-1532
• /
• 2003

An experiment was performed to obtain the local heat transfer coefficient and Nusselt number in a circular duct with a 180$^{\circ}$ bend for Re=6 x 10$^4$, 8 x 10$^4$ and 1 x 10$\^$5/ under swirling flow and non-swirling flow conditions. The test tube with a circular section was made from stainless steel having a curvature ration of 9.4. Current heat flux of 5.11 kW/㎡ was applied to the test tube by electrical power and the swirling motion of air was produced by a tangential inlet to the pipe axis at 180$^{\circ}$. Measurements of local wall temperatures and the bulk mean temperatures of air were made at four circumferential positions at 16 stations. The wall temperatures showed a reduced distribution curve at the bend for the non-swirling flow, but this effect did not appear for the swirling flow. The Nusselt number distributions for the swirling flow, which was calculated from the measured wall and the bulk temperatures, were higher than that of the non-swirling flow. The average Nusselt number of the swirling flow increased by about 90-100%, compared to that of the non-swirling flow. The Nu/Nu$\_$DB/ values at the 90$^{\circ}$ station for non-swirling flow and swirling flow were approximately 2.5 and 4.8 at Re=6x10$^4$ respectively. The values agree well with Said's results for non-swirling flow.

• Proceedings of the KSME Conference
• /
• 2003.11a
• /
• pp.634-639
• /
• 2003

It has been studied the flow near a rotating disk with surface topography. The system Ekman number is assumed very small, i.e., $E[{\equiv}\frac{\nu}{{\Omega}^{\ast}L^{\ast2}}]<<1$ in which $L^{\ast}$ denotes a disk radius, ${\nu}$ kinematic viscosity of the fluid and ${\Omega}^{\ast}$ angular velocity of the basic state. Disk surface has a sinusoidal topographic variation along radial coordinate, i.e., $z={\delta}cos(2{\pi}{\omega}r)$, where ${\delta}$ and ${\omega}$ are, respectively, nondimensional amplitude and wave number of the disk surface. Analytic solutions, being useful over the parametric ranges of ${\delta}{\sim}O$( $E^{1/2}$ ) and ${\omega}{\leq}O$ ( $E^{1/2}$ ), are secured in a series-function form of Fourier-Bessel type. An asymptotic behavior, when $E{\rightarrow}0$, is clarified as : for a disk with surface roughness, in contrast to the case of a flat disk, the azimuthal velocity increases in magnitude, together with the thickening boundary layer. The radial velocity, however, decreases in magnitude as the amplitude of surface waviness increases. Consequently, the overall Ekman pumping at the edge of the boundary layer remains unchanged, maintaining the constant value equal to that of the flat disk.

• Nuclear Engineering and Technology
• /
• v.47 no.5
• /
• pp.559-566
• /
• 2015

The thermalehydraulic characteristics for the CANadian Deuterium Uranium Flexible (CANFLEX)-burnable poison (BP) fuel channel, which is loaded with a BP at the center ring based on the CANFLEX-RU (recycled uranium) fuel channel, are evaluated and compared with that of standard 37-element and CANFLEX-NU (natural uranium) fuel channels. The distributions of fuel temperature and critical channel power for the CANFLEX-BP fuel channel are calculated using the NUclear Heat Transport CIRcuit Thermohydraulics Analysis Code (NUCIRC) code for various creep rate and burnup. CANFLEX-BP fuel channel has been revealed to have a lower fuel temperature compared with that of a standard 37-element fuel channel, especially for high power channels. The critical channel power of CANFLEX-BP fuel channel has increased by about 10%, relative to that of a standard 37-element fuel channel for 380 channels in a core, and has higher value relative to that of the CANFLEX-NU fuel channel except the channels in the outer core. This study has shown that the use of a BP is feasible to enhance the thermal performance by the axial heat flux distribution, as well as the improvement of the reactor physical safety characteristics, and thus the reactor safety can be improved by the use of BP in a CANDU reactor.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.16 no.8
• /
• pp.1566-1574
• /
• 1992

Local heat transfer characteristics for a round air jet impinging normally on a heated flat plate were experimentally investigated. The problem parameters investigated were jet Reynolds number, Re=4000,10000, and 20000, and nozzle-to-plate spacing(L/D) of 2,6, and 10. The temperature variations on the flat uniform heat flux surface were mapped using a thermo-sensitive liquid crytal sheet. The isochromatic images corresponding to the characteristic temperature of liquid crystal were analyzed with the help of a digital image processing system. The local Nusselt number, Nu decreased rapidly in the impingement region and exhibited a similar profiles in the wall jet region independent of the nozzle-to-plate spacing L/D. In the case of large Reynolds number, heat transfer rate (Nu) was proportional to 0.5 power of the Reynolds number. For L/D=2, a secondary peak in the heat transfer rate was seen in the region of X/D=1.5~3 due to the transition from laminar to turbulent boundary layer.

• Communications of the Korean Mathematical Society
• /
• v.10 no.2
• /
• pp.393-400
• /
• 1995

We define a group extension and characterized some properties of the group extension. In particular, we show that the quotient map $\nu$ is a continuous group isomorphism and subgroup $H_1(H_2)$ is normal in $G_1(G_2)$.

• Journal of the Korean Chemical Society
• /
• v.17 no.3
• /
• pp.193-197
• /
• 1973

The correlation of the infrared carbonyl stretching frequency with substituents in benzanilides has been studied. The Hammett-type equation(1) was adopted for this correlation. Substituents in a C-phenyl-ring gave a better correlation with ${\sigma}^{+}$rather than ${\sigma}$, meanwhile, substituents in a N-phenyl-ring gave a better correlation with ${\sigma}$. When substituents are placed on both C-phenyl and N-phenyl ring, they influenced the carbonyl stretching frequency reasonably independently of each other. A conformation of benzanilide which accounts for the above observation has also been discussed.

• Computers and Concrete
• /
• v.21 no.5
• /
• pp.513-523
• /
• 2018

Time dependent strain due to creep is a significant factor in structural design. Multi-gene genetic programming (MGGP) and artificial neural network (ANN) are used to develop two models for prediction of creep compliance in concrete. The first model was developed by MGGP technique and the second model by hybridized MGGP-ANN. In the MGGP-ANN, the ANN is working in parallel with MGGP to predict errors in MGGP model. A total of 187 experimental data sets that contain 4242 data points are filtered from the NU-ITI database. These data are used in developing the MGGP and MGGP-ANN models. These models contain six input variables which are: average compressive strength at 28 days, relative humidity, volume to surface ratio, cement type, age at start of loading and age at the creep measurement. Practical equation based on MGGP was developed. A parametric study carried out with a group of hypothetical data generated among the range of data used to check the generalization ability of MGGP and MGGP-ANN models. To confirm validity of MGGP and MGGP-ANN models; two creep prediction code models (ACI209 and CEB), two empirical models (B3 and GL 2000) are used to compare their results with NU-ITI database.

• Bulletin of the Korean Mathematical Society
• /
• v.55 no.5
• /
• pp.1523-1528
• /
• 2018

For $r{\geq}2$, let ${\mathcal{H}}$ be an r-uniform hypergraph with n vertices and m hyperedges. Let R be a random vertex set obtained by choosing each vertex of ${\mathcal{H}}$ independently with probability p. Let ${\mathcal{H}}[R]$ be the subhypergraph of ${\mathcal{H}}$ induced on R. We obtain an upper bound on the matching number ${\nu}({\mathcal{H}}[R])$ and a lower bound on the independence number ${\alpha}({\mathcal{H}}[R])$ of ${\mathcal{H}}[R]$. First, we show that if $mp^r{\geq}{\log}\;n$, then ${\nu}(H[R]){\leq}2e^{\ell}mp^r$ with probability at least $1-1/n^{\ell}$ for each positive integer ${\ell}$. It is best possible up to a constant factor depending only on ${\ell}$ if $m{\leq}n/r$. Next, we show that if $mp^r{\geq}{\log}\;n$, then ${\alpha}({\mathcal{H}}[R]){\geq}np-{\sqrt{3{\ell}np\;{\log}\;n}-2re^{\ell}mp^r$ with probability at least $1-3/n^{\ell}$.