• Journal of the Korean Mathematical Society
• /
• v.56 no.1
• /
• pp.67-80
• /
• 2019

For positive integers a, b, c, and an integer n, the number of integer solutions $(x,y,z){\in}{\mathbb{Z}}^3$ of $a{\frac{x(x-1)}{2}}+b{\frac{y(y-1)}{2}}+c{\frac{z(z-1)}{2}}=n$ is denoted by t(a, b, c; n). In this article, we prove some relations between t(a, b, c; n) and the numbers of representations of integers by some ternary quadratic forms. In particular, we prove various conjectures given by Z. H. Sun in [6].

• Bulletin of the Society of Naval Architects of Korea
• /
• v.7 no.1
• /
• pp.37-44
• /
• 1970

The plate under shear loading umformly distributed on the end portions of its side boundary was considered. Infinite hyperbolic serieses and Fourier serieses were combined as a stress function and from which exact solutions for the 15 cases for the parameters of b/L=0.25, 0.5, 1.0 and l/L=0.2, 0.4, 0.6, 0.8, 1.0 are obtained. In each cases the first 5 terms of the infinite series at the 36 points as shown in Fig. 3. The results are presented in Fig. 4-1, 4-2, and 4-3. The conclusions are as follows: 1) The stresses ${\sigma}_x$ increase very slightly as $\chi$ increases in the range of 0<x<L-l 2) When the parameters satisfy the conditions b/L<0.25 and l/L<0.2, the stresses in the region of 0<x<L-l can be obtained by replacing the uniform shear loading by the equivalent uniform shear loading by the equivalent uniform tensile force and pure bending moment at x=l. 3) The stress ${\sigma}_y$ is negligible throughout the region. 4) When the parameter b/L varies, the stresses ${\sigma}_x$ and u vary as L/b, while strain $\upsilon$ varies as $(L/b)^2$.

• Journal of applied mathematics & informatics
• /
• v.28 no.3_4
• /
• pp.909-912
• /
• 2010

In this note we present a short proof of the following result by Zhou, Liu and Xu. Let G be a graph of order n, and let a and b be two integers with 1 $\leq$ a < b and b $\geq$ 3, and let g and f be two integer-valued functions defined on V(G) such that a $\leq$ g(x) < f(x) $\leq$ b for each $x\;{\in}\;V(G)$ and f(V(G)) - V(G) even. If $n\;{\geq}\;\frac{(a+b-1)^2+1}{a}$ and $\delta(G)\;{\geq}\;\frac{(b-1)n}{a+b-1}$,then G has a connected (g, f)-factor.

• Journal of Life Science
• /
• v.23 no.8
• /
• pp.978-983
• /
• 2013

Kinesin-II, a molecular motor, consists of two different motor subunits, KIF3A and KIF3B, and one large kinesin superfamily-associated protein 3 (KAP3), forming a heterotrimeric complex. KAP3 is associated with the tail domains of motor subunits. However, its exact role remains unclear. Here, we demonstrated KAP3 binding to the carboxyl (C)-terminal tail region of HS-associated protein X-1 (HAX-1). HAX-1 bound to the C-terminal region of KAP3, but not to KIFs (KIF3A, KIF3B, and KIF5B) and the kinesin light chain (KLC) in the yeast two-hybrid assays. The interaction was further confirmed in the glutathione S-transferase (GST) pull-down assay and by co-immunoprecipitation. Anti- HAX-1 antibody as well as anti-KIF3A antibody co-immunoprecipitated KIF3B and KAP3 from mouse brain extracts. These results suggest that KAP3 could mediate the interaction between Kinesin-II and HAX-1.

• Journal of Korean Biological Nursing Science
• /
• v.7 no.1
• /
• pp.29-46
• /
• 2005

Purpose ; 본 연구는 X-염색체와 관련된 장애 중에서 가장 흔하고 심한 Duchenne Muscular Dystrophy(DMD)의 세포유전학 및 분자유전학적 특성을 설명하기 위해서 DMD에 영향을 받고 있는 두 가계의 13명을 대상으로 가계도 분석과 염색체 분석 및 DNA 분석을 하였다. Method ; DNA분석은 DNA probe을 이용한 Southern blotting method로써 RFLPs와 DMD유전자 부위의 exon소실 유무를 조사하여 아래와 같은 결과를 얻었다. Conclusion ; A 염색체 분석 : 말초혈액과 양수를 표본으로 High-Resolution GTG염색에서 A가계와 B가계의 염색체 분석에서 12명의 염색체는 정상 X-염색체였으나 B가계의 I-2(DMD여성)에서 46, x,-x,+t(2:x)(q 21.1 : p21.2)로 나타난다. B. DNA분석3 : 1) RFLPs의 분석 J66,XJ-1.1,754-11로써 B가계의 RELPs(Restriction Fragment Length Polymorphisms)에서 J66/Pst I은 1.7hb(E), 1.6kb(e)을 보여 주었고 XJ-1.1/Taq I은 3.6kb(F), 3.0kb(f), 754-11/EoR I은 4.2kb(G), 2.0kb(g)의 대립인자를 나타내었다. 이상의 결과를 바탕으로 영향을 받고 있는 남자 (II-2)의 haplotype는 보인자인 어머니의 한쪽 인자를 받았으며 어머니와 딸은 보인자이고 임산부의 태아는 남아였고 태아의 인자들은 그의 할아버지로부터 물려받아 DMD에 영향을 받지 않은 것으로 진단되었다. 2) DMD 유전자의 exon 소실에 대한 분석 cDNA probe 8과 cDNA probe 2b-3으로써 소실에 대한 진단은 영향을 받은 남자(II-2)는 cDNA probe 8에서 12, 7.3, 6.6, 4.2kb에 소실이 있고 cDNA 2b-3은 1.7kb에 소실에 나타났다.

• East Asian mathematical journal
• /
• v.25 no.2
• /
• pp.179-196
• /
• 2009

Let E be a uniformly convex Banach space and K a nonempty closed convex subset which is also a nonexpansive retract of E. For i = 1, 2, 3, let $T_i:K{\rightarrow}E$ be an asymptotically nonexpansive mappings with sequence ${\{k_n^{(i)}\}\subset[1,{\infty})$ such that $\sum_{n-1}^{\infty}(k_n^{(i)}-1)$ < ${\infty},\;k_{n}^{(i)}{\rightarrow}1$, as $n{\rightarrow}\infty$ and F(T)=$\bigcap_{i=3}^3F(T_i){\neq}{\phi}$ (the set of all common xed points of $T_i$, i = 1, 2, 3). Let {$a_n$},{$b_n$} and {$c_n$} are three real sequences in [0, 1] such that $\in{\leq}\;a_n,\;b_n,\;c_n\;{\leq}\;1-\in$ for $n{\in}N$ and some ${\in}{\geq}0$. Starting with arbitrary $x_1{\in}K$, define sequence {$x_n$} by setting {$$x_{n+1}=P((1-a_n)x_n+a_nT_1(PT_1)^{n-1}y_n)$$ $$y_n=P((1-b_n)x_n+a_nT_2(PT_2)^{n-1}z_n)$$ $$z_n=P((1-c_n)x_n+c_nT_3(PT_3)^{n-1}x_n)$$. Assume that one of the following conditions holds: (1) E satises the Opial property, (2) E has Frechet dierentiable norm, (3) $E^*$ has Kedec -Klee property, where $E^*$ is dual of E. Then sequence {$x_n$} converges weakly to some p${\in}$F(T).

• Journal of the Korean Magnetics Society
• /
• v.18 no.1
• /
• pp.19-23
• /
• 2008

The mixed ferrite $V_xFe_{3-x}O_4$(x=0.0, 0.15, 0.5, 1.0) thin films were prepared by sol-gel method. Their crystallographic and magnetic hyperfine properties have been studied using X-ray diffraction(XRD), X-ray photoelectron spectroscopy(XPS) and conversion electron $M\"{o}ssbauer$ spectroscopy(CEMS). The crystal structure is found to be cubic spinel throughout the series($x{\leq}1.0$), and the lattice parameter $a_0$ increases linearly with increasing V content. XRD, XSP and CEMS indicate that $V^{3+}$ substitution for $Fe^{3+}$ in B-site is superior to $V^{2+}$ substitution for $Fe^{2+}$ in B-site. It is noticeable that both quadrupole shift and hyperfine field decreases with increasing V composition, suggesting the change of local symmetry and accompanying line-broadening. The line-broadening on CEMS spectra can be explained by the distribution of magnetic hyperfine fields.

• Journal of the Korean Ceramic Society
• /
• v.40 no.1
• /
• pp.81-86
• /
• 2003

Microwave dielectric properties have been investigated in the$(1-x)CaTiO_3-xYAlO_3$ (x=0.1~1.0) solid solution system. The mixtures of $CaTiO_3$ and $YalO_3$using solid state method were sintered at various temperatures. Their dielectric constants and related temperature coefficients were strongly depend on the composition of the solid solution. The optimum properties were recorded as for ${\varepsilon}_r=47,$ $Q{\times}f_0$=35000 and ${\tau}_f=+11ppm/^{\circ}C$ without sintering agent. Even at $1200^{\circ}C$ full densification has been achieved with addition of $CaB_2O_4$ in the $0.75CaTiO_3-0.25YalO_3$ composition. The sample of $0.3 wt%-CaB_2O_4$ added $ 0.75CaTiO_3-0.25YalO_3$ sintered at $1300^{\circ}C$ for 3 h showed optimum microwave dielectric properties of ${\varepsilon}_r=47$, $Q{\time}f_0=37000$ and ${\tau}_f=+17ppm/^{\circ}C$, which demonstrates the promising candidates for microwave dielectric materials covering 5~7 GHz range.

• Bulletin of the Korean Mathematical Society
• /
• v.52 no.2
• /
• pp.661-677
• /
• 2015

In this paper, we consider the following Kirchhoff-type Schr$\ddot{o}$dinger system $$\{-\(a_1+b_1{\int}_{\mathbb{R^3}}{\mid}{\nabla}u{\mid}^2dx\){\Delta}u+{\gamma}V(x)u=\frac{2{\alpha}}{{\alpha}+{\beta}}{\mid}u{\mid}^{\alpha-2}u{\mid}v{\mid}^{\beta}\;in\;\mathbb{R}^3,\\-\(a_2+b_2{\int}_{\mathbb{R^3}}{\mid}{\nabla}v{\mid}^2dx\){\Delta}v+{\gamma}W(x)v=\frac{2{\beta}}{{\alpha}+{\beta}}{\mid}u{\mid}^{\alpha}{\mid}v{\mid}^{\beta-2}v\;in\;\mathbb{R}^3,\\u,v{\in}H^1(\mathbb{R}^3),$$ where $a_i$ and $b_i$ are positive constants for i = 1, 2, ${\gamma}$ > 0 is a parameter, V (x) and W(x) are nonnegative continuous potential functions. By applying the Nehari manifold method and the concentration-compactness principle, we obtain the existence and concentration of ground state solutions when the parameter ${\gamma}$ is sufficiently large.

• Journal of the Korean Crystal Growth and Crystal Technology
• /
• v.9 no.2
• /
• pp.245-250
• /
• 1999

The effect of cation substitution on the inonic conductivity was studied in $(Li_{0.5}La_{0.5})_{1-y}Sr_yTi_{1-x}Mn_xO_3$ system. In case of Sr substitution, the ionic conductivity abrubtly decreased over y=0.05. This may be caused by the decrease of lithium contents which contribute to lithium inonic conductivity. Jahn-Teller distortion as well as lattice parameter variation influenced the inonic conductivity in case of Mn substitution. A and B-site cations effects on the conductivities were found to be independent, and the ionic conductivity as high as $2.8{\times}10^{-2}$S/cm was obtained in x=0.0006 and y=0.05.