• Bulletin of the Korean Mathematical Society
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• v.53 no.2
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• pp.487-494
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• 2016

Let p be an odd prime and c be a fixed integer with (c, p) = 1. For each integer a with $1{\leq}a{\leq}p-1$, it is clear that there exists one and only one b with $0{\leq}b{\leq}p-1$ such that $ab{\equiv}c$ mod p. Let N(c, p) denote the number of all solutions of the congruence equation $ab{\equiv}c$ mod p for $1{\leq}a$, $b{{\leq}}p-1$ in which a and $\bar{b}$ are of opposite parity, where $\bar{b}$ is defined by the congruence equation $b{\bar{b}}{\equiv}1$ mod p. The main purpose of this paper is using the mean value theorem of Dirichlet L-functions and the properties of Gauss sums to study the computational problem of one kind mean value function related to $E(c,p)=N(c,p)-{\frac{1}{2}}{\phi}(p)$, and give its an exact computational formula.

• Korean Journal of Materials Research
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• v.17 no.9
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• pp.500-506
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• 2007

The effects of anisotropic surface energy on the microstructure development of porous materials have been studied through Monte Carlo simulation using a three dimensional lattice. The changes in porosity ($f_v$), mean grain diameter ($D_s$), fraction of connected pores ($f_{v,c}$) and contiguity of the solid phase (C) were examined in cases with three different ${\gamma}_{SV}$ relations and initial grain diameters ($D_{s,o}$). It has been found that larger ${\gamma}_{SV}$ enhances sintering of particles and increases C and does not change $D_s$. And Introducing anisotropic ${\gamma}_{SV}$ brought an increase in $f_v$ and $f_{v,c}$ and an decrease in $D_s$ and C, and this tendency become more marked for fine $D_{s,o}$.

• Journal of Chest Surgery
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• v.20 no.2
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• pp.241-250
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• 1987

We scrutinized the preoperative electrocardiographic and hemodynamic findings in adult atrial septal defects older than 15 years, and then followed up the postoperative electrocardiographic changes sequentially. In preoperative electrocardiographs, the mean PR interval [0.17 sec] was prolonged than normal adults [M;0.13,F;0.15], and the mean QRS axis [93.1*] was deviated to rightward than normal [M;63.7*,F;64.4*], and 122 cases of all 159 patients [77.8%] were in RAD quadrant. The QRS morphology was classified into three groups; a] crista supraventricularis hypertrophy, 25 cases, b] right ventricular outflow tract hypertrophy, 89 cases, c] right ventricular hypertrophy, 44 cases, and normal rs pattern, 1 case. Comparing the QP/QS, Pp/Ps, Rp/Rs in these three groups, Qp/Qs increased a] 2.65 to b] 2.97 and decreased b] 2.97 to c] 2.55, Pp/Ps increased a] 0.27 to b] 0.35 to c] 0.44, and Rp/Rs increased a] 0.1 to b] 0.14 to c] 0.2. In comparing the atrial fibrillation with sinus rhythm, the patient`s mean age was increased [26.4 to 45.7], the mean Qp/Qs was decreased [2.97 to 2.7], the mean Pp/Ps was increased [0.35 to 0.46], the mean Rp/Rs increased [0.14 to 0.2], and the QRS morphology was RVOT hypertrophy;7 cases, RVH;2 cases in all 11 cases. Therefore, the atrial fibrillation was appeared in progressed status. Increasing the mean pulmonary arterial pressure, size of the R` wave in Vl lead increased, and the QRS morphology tended to become severe patterns. Postoperatively, the PR interval shortened and QRS axis tended to normal axis quadrant, and size of R` wave decreased sequentially, atrial fibrillation disappeared in 4 cases. Conclusively, by use of the conventional surface electrocardiography, we could anticipate the hemodynamic changes and the prognosis at outpatient department.

• Kyungpook Mathematical Journal
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• v.50 no.4
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• pp.545-556
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• 2010

A good amount of work has been done on degree of approximation of functions belonging to Lip${\alpha}$, Lip($\xi$(t),r) and W($L_r,\xi(t)$) and classes using Ces$\`{a}$ro, N$\"{o}$rlund and generalised N$\"{o}$rlund single summability methods by a number of researchers ([1], [10], [8], [6], [7], [2], [3], [4], [9]). But till now, nothing seems to have been done so far to obtain the degree of approximation of functions using (N,$p_n$)(C, 1) product summability method. Therefore the purpose of present paper is to establish two quite new theorems on degree of approximation of function $f\;\in\;Lip({\alpha},r)$ class and $f\;\in\;W(L_r,\;\xi(t))$ class by (N, $p_n$)(C, 1) product summability means of its Fourier series.

• Kyungpook Mathematical Journal
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• v.28 no.2
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• pp.129-139
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• 1988

Let $T^{\alpha}_{\lambda}$(p, A, B) denote the class of functions $$f(z)=z^p-{\sum\limits^{\infty}_{k=1}}{\mid}a_{p+k}{\mid}z^{p+k}$$ which are regular and p valent in the unit disc U = {z: |z| <1} and satisfying the condition $\left|{\frac{{e^{ia}}\{{\frac{f^{\prime}(z)}{z^{p-1}}-p}\}}{(A-B){\lambda}p{\cos}{\alpha}-Be^{i{\alpha}}\{\frac{f^{\prime}(z)}{z^{p-1}}-p\}}}\right|$<1, $z{\in}U$, where 0<${\lambda}{\leq}1$, $-\frac{\pi}{2}$<${\alpha}$<$\frac{\pi}{2}$, $-1{\leq}A$<$B{\leq}1$, 0<$B{\leq}1$ and $p{\in}N=\{1,2,3,{\cdots}\}$. In this paper, we obtain sharp results concerning coefficient estimates, distortion theorem and radius of convexity for the class $T^{\alpha}_{\lambda}$(p, A, B). It is further shown that the class $T^{\alpha}_{\lambda}$(p, A, B) is closed under "arithmetic mean" and "convex linear combinations". We also obtain class preserving integral operators of the form $F(z)=\frac{p+c}{z^c}{\int^z_0t^{c-1}}f(t)dt$, c>-p, for the class $T^{\alpha}_{\lambda}$(p, A, B). Conversely when $F(z){\in}T^{\alpha}_{\lambda}$(p, A, B), radius of p valence of f(z) has also determined.

• Wind and Structures
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• v.26 no.5
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• pp.293-304
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• 2018

A numerical study is conducted on the flow characteristics of a rectangular cylinder (chord-to-width ratio C/W = 2 - 10) mounted close to a rigid wall at gap-to-width ratios G/W = 0.25 - 6.25. The effects of G/W and C/W on the Strouhal number, vortex structure, and time-mean drag and lift forces are examined. The results reveal that both G/W and C/W have strong influences on vortex structure, which significantly affects the forces on the cylinder. An increase in G/W leads to four different flow regimes, namely no vortex street flow (G/W < 0.75), single-row vortex street flow ($0.75{\leq}G/W{\leq}1.25$), inverted two-row vortex street flow ($1.25<G/W{\leq}2.5$), and two-row vortex street flow (G/W > 2.5). Both Strouhal number and time-mean drag are more sensitive to C/W than to G/W. For a given G/W, Strouhal number grows with C/W while time-mean drag decays with C/W, the growth and decay being large between C/W = 2 and 4. The time-mean drag is largest in the single-row vortex street regime, contributed by a large pressure on the front surface, regardless of C/W. A higher C/W, in general, leads to a higher time-mean lift. The maximum time-mean lift occurs for C/W = 10 at G/W = 0.75, while the minimum time-mean lift appears for C/W = 2 at the same G/W. The impact of C/W on the time-mean lift is more substantial in single-row vortex regime. The effect of G/W on the time-mean lift is larger at a larger C/W.

• The korean journal of orthodontics
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• v.15 no.1
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• pp.55-66
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• 1985

The study was undertaken to ascertain the speech defect of patients with malocclusion, especially of openbite patients, by means of the spectral analysis method. The experimental group was composed of ten female openbite patients and their mean age was 13.8 yrs. The control group was also composed of ten female girls and their mean age was 13.7 yrs. As for the speech material, eight Korean monophthrongs and two Korean fricatives and two affricatives were used. Speeches were recorded and then analyzed by a Kay 7800 digital sonagraph. Formant frequency level or range was used as a phonemic parameter. The results were as follows: 1. Among Vowels /a:/ : $F_1,\;F_3\;and\;F_1/F_2$ showed abnormality. /o:/ and $/w:/:F_2,\;F_2-F_1\;and\;F_1/F_2$ showed abnormality. 2. Among Consonants /S/ and /h/ : The upper and lower borders of the frequency range showed abnormality. (equation omitted) : The lower border of the frequency range showed abnormality. $/C^{h}/$ : The upper and lower borders of the frequency range and concentration point showed abnormality.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.3 no.4
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• pp.222-230
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• 1991

Conjugate heat transfer by steady laminar natural convection from a conducting tube with two vertical axial fins has been studied by a finite difference numerical procedure under basic conditions; $Ra=10_6$, Pr = 5 and $L_F=0.15$. The maximum local tube Nusselt number appears at ${\theta}=140^{\circ}$ for $L_F=0.06$, at ${\theta}=130^{\circ}$ for $L_F=0.30$ and at ${\theta}=120^{\circ}$ for $L_F=0.30$, $L_F=0.06$, respectively. The maximum mean Nusselt number shows at $L_F=0.18$ for the downward fin and at $L_F=0.12$ for the upward fin. Therefore the optimized fin length is $L_F{\approx}0.15$ under these conditions. At $L_F=0.15$, the mean Nusselt number by increasing Rayleigh number is remarkably increased for downward fin and then is slowly increased except for downward fin, it by increasing Prandtl number is apparently increased at $Pr{\leq}2$, and slightly increased at Pr>2.

• Communications of the Korean Mathematical Society
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• v.32 no.2
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• pp.417-424
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• 2017

In this paper, we study slant curves in a 3-dimensional almost f-Kenmotsu manifold with proper mean curvature vector field.

• Journal of Korean Neurosurgical Society
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• v.58 no.4
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• pp.341-345
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• 2015

Objective : To measure the orientation of the facet joints of cervical spine (C-spine) segments in the sagittal plane, known as the pedicle-facet (P-F) angle, and to use these measurements to evaluate the relationship between the P-F angle and the amount of vertebral anterolisthesis in patients with degenerative cervical spondylolisthesis (DCS). Methods : A retrospective case-control study was performed including 30 age- and sex-matched patients with DCS and 30 control participants. Anterior-posterior and lateral view radiographs of the C-spine were obtained in a standing position. The P-F angle at all cervical levels and the amount of anterolisthesis at C4-5 were measured from lateral view plain radiographs. Results : The P-F angles at C4-5 were $141.14{\pm}7.14^{\circ}$ for the DCS group and $130.53{\pm}13.50^{\circ}$ (p=0.012) for the control group, and at C5-6 were $137.46{\pm}8.53^{\circ}$ for the DCS group and $128.53{\pm}16.01^{\circ}$ for the control group (p=0.001). The mean P-F angle at C4-5 did not correlate with the amount of anterolisthesis (p=0.483). The amount of anterior slippage did correlate with age (p<0.001). Conclusion : The P-F angle was intrinsically higher at C4-5, compared to C5-6, in both the DCS and control groups, which might explain the increased likelihood for anterolisthesis of C4. Higher P-F angles in the DCS group may be a predisposing factor to slippage. The P-F angle may interact with age to increase incidence of anterolisthesis with increasing age.