• Communications of the Korean Mathematical Society
• /
• v.9 no.2
• /
• pp.419-421
• /
• 1994

Recently Hong and Oh [5] provided a fairly general weak law for arrays in the following form: Let {(X/sub ni/, l ≤ i ≤ k/sub n/), n ≥ l}, k/sub n/ → ∞ as n → ∞, be an array of random variables on (Ω, F, P) and set F/sub nj/ = σ{X/sub ni/, 1 ≤ i ≤ j}, 1 ≤ j ≤ k/sub n/, n ≥ 1, and F/sub n0/ = {ø, Ω}, n ≥ 1. Suppose that (equation omitted) aP { X/sub ni/ /sup p/ ＞ a} → 0 as a → ∞ uniformly in n for some 0 < p < 2. Then S/sub n//(equation omitted) → 0 in probability as n → ∞ where S/sub n/ = (equation omitted)(X/sub ni/ - E(X/sib ni/I( X/sub ni/ /sub p/ ≤ k/sub n/) F/sub n,i-l/)). In this note, we will prove the following result under the same domination condition of Hong and Oh [5].(omitted)

• Kyungpook Mathematical Journal
• /
• v.61 no.4
• /
• pp.679-710
• /
• 2021

We study the tensor product algebra P_k(x₁) ⊗ P_k(x₂) ⊗ ⋯ ⊗ P_k(x_m), where P_k(x) is the partition algebra defined by Jones and Martin. We discuss the centralizer of this algebra and corresponding Schur-Weyl dualities and also index the inequivalent irreducible representations of the algebra P_k(x₁) ⊗ P_k(x₂) ⊗ ⋯ ⊗ P_k(x_m) and compute their dimensions in the semisimple case. In addition, we describe the Bratteli diagrams and branching rules. Along with that, we have also constructed the RS correspondence for the tensor product of m-partition algebras which gives the bijection between the set of tensor product of m-partition diagram of P_k(n₁) ⊗ P_k(n₂) ⊗ ⋯ ⊗ P_k(n_m) and the pairs of m-vacillating tableaux of shape [λ] ∈ Γ_k^m, Γ_k^m = {[λ] = (λ₁, λ₂, …, λ_m)|λ_i ∈ Γ_k, i ∈ {1, 2, …, m}} where Γ_k = {λ_i ⊢ t|0 ≤ t ≤ k}. Also, we provide proof of the identity $(n_1n_2{\cdots}n_m)^k={\sum}_{[{\lambda}]{\in}{\Lambda}^k_{{n_1},{n_2},{\ldots},{n_m}}}$ f^[λ]m_k^[λ] where m_k^[λ] is the multiplicity of the irreducible representation of $S{_{n_1}}{\times}S{_{n_2}}{\times}....{\times}S{_{n_m}}$ module indexed by ${[{\lambda}]{\in}{\Lambda}^k_{{n_1},{n_2},{\ldots},{n_m}}}$, where f^[λ] is the degree of the corresponding representation indexed by ${[{\lambda}]{\in}{\Lambda}^k_{{n_1},{n_2},{\ldots},{n_m}}}$ and ${[{\lambda}]{\in}{\Lambda}^k_{{n_1},{n_2},{\ldots},{n_m}}}=\{[{\lambda}]=({\lambda}_1,{\lambda}_2,{\ldots},{\lambda}_m){\mid}{\lambda}_i{\in}{\Lambda}^k_{n_i},i{\in}\{1,2,{\ldots},m\}\}$ where ${\Lambda}^k_{n_i}=\{{\mu}=({\mu}_1,{\mu}_2,{\ldots},{\mu}_t){\vdash}n_i{\mid}n_i-{\mu}_1{\leq}k\}$.

• Journal of applied mathematics & informatics
• /
• v.27 no.5_6
• /
• pp.1211-1220
• /
• 2009

In this paper, we consider the multipoint boundary value problem for the one-dimensional p-Laplacian $({\phi}_p(u'))'$(t)+q(t)f(t,u(t),u'(t))=0, t $\in$ (0, 1), subject to the boundary conditions: $u(0)=\sum\limits_{i=1}^{n-2}{\alpha}_iu({\xi}_i),\;u(1)=\sum\limits_{i=1}^{n-2}{\beta}_iu({\xi}_i)$ where $\phi_p$(s) = $|s|^{n-2}s$, p > 1, $\xi_i$ $\in$ (0, 1) with 0 < $\xi_1$ < $\xi_2$ < $\cdots$ < $\xi{n-2}$ < 1 and ${\alpha}_i,\beta_i{\in}[0,1)$, 0< $\sum{\array}{{n=2}\\{i=1}}{\alpha}_i,\sum{\array}{{n=2}\\{i=1}}{\beta}_i$<1. Using a fixed point theorem due to Bai and Ge, we study the existence of at least three positive solutions to the above boundary value problem. The important point is that the nonlinear term f explicitly involves a first-order derivative.

• Journal of applied mathematics & informatics
• /
• v.22 no.1_2
• /
• pp.361-372
• /
• 2006

In this paper, we consider the multi-point boundary value problems for one-dimensional p-Laplacian at resonance: $({\phi}_p(x'(t)))'=f(t,x(t),x'(t))$, subject to the boundary value conditions: ${\phi}_p(x'(0))={\sum}^{n-2}_{i=1}{\alpha}_i{\phi}_p(x'({\epsilon}i)),\;{\phi}_p(x'(1))={\sum}^{m-2}_{i=1}{\beta}_j{\phi}_p(x'({\eta}_j))$ where ${\phi}_p(s)=/s/^{p-2}s,p>1,\;{\alpha}_i(1,{\le}i{\le}n-2){\in}R,{\beta}_j(1{\le}j{\le}m-2){\in}R,0<{\epsilon}_1<{\epsilon}_2<...<{\epsilon}_{n-2}1,\;0<{\eta}1<{\eta}2<...<{\eta}_{m-2}<1$, By applying the extension of Mawhin's continuation theorem, we prove the existence of at least one solution. Our result is new.

• Journal of the Korean Mathematical Society
• /
• v.36 no.6
• /
• pp.1133-1143
• /
• 1999

Chaterji strengthened version of a theorem for martin-gales which is a generalization of a theorem of Marcinkiewicz proving that if $X_n$ is a sequence of independent, identically distributed random variables with $E{\mid}X_n{\mid}^p\;<\;{\infty}$, 0 < P < 2 and $EX_1\;=\;1{\leq}\;p\;<\;2$ then $n^{-1/p}{\sum^n}_{i=1}X_i\;\rightarrow\;0$ a,s, and in $L^p$. In this paper, we probe a version of law of large numbers for double arrays. If ${X_{ij}}$ is a double sequence of random variables with $E{\mid}X_{11}\mid^log^+\mid X_{11}\mid^p\;<\infty$, 0 < P <2, then $lim_{m{\vee}n{\rightarrow}\infty}\frac{{\sum^m}_{i=1}{\sum^n}_{j=1}(X_{ij-a_{ij}}}{(mn)^\frac{1}{p}}\;=0$ a.s. and in $L^p$, where $a_{ij}$ = 0 if 0 < p < 1, and $a_{ij}\;=\;E[X_{ij}\midF_[ij}]$ if $1{\leq}p{\leq}2$, which is a generalization of Etemadi's marcinkiewicz-type SLLN for double arrays. this also generalize earlier results of Smythe, and Gut for double arrays of i.i.d. r.v's.

• 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).

• Bulletin of the Korean Mathematical Society
• /
• v.46 no.1
• /
• pp.35-43
• /
• 2009

We say that an isometric immersed hypersurface x : $M^n\;{\rightarrow}\;{\mathbb{R}}^{n+1}$ is of $L_k$-finite type ($L_k$-f.t.) if $x\;=\;{\sum}^p_{i=0}x_i$ for some positive integer p < $\infty$, $x_i$ : $M{\rightarrow}{\mathbb{R}}^{n+1}$ is smooth and $L_kx_i={\lambda}_ix_i$, ${\lambda}_i\;{\in}\;{\mathbb{R}}$, $0{\leq}i{\leq}p$, $L_kf=trP_k\;{\circ}\;{\nabla}^2f$ for $f\;{\in}\'C^{\infty}(M)$, where $P_k$ is the kth Newton transformation, ${\nabla}^2f$ is the Hessian of f, $L_kx\;=\;(L_kx^1,\;{\ldots},\;L_kx^{n+1})$, $x=(x^1,\;{\ldots},\;x^{n+1})$. In this article we study the following(hyper)surfaces in ${\mathbb{R}}^{n+1}$ from the view point of $L_1$-finiteness type: totally umbilic ones, generalized cylinders $S^m(r){\times}{\mathbb{R}}^{n-m}$, ruled surfaces in ${\mathbb{R}}^{n+1}$ and some revolution surfaces in ${\mathbb{R}}^3$.

• Proceedings of the Korean Vacuum Society Conference
• /
• 2011.02a
• /
• pp.161-162
• /
• 2011

최근 광전자 분야에서는 미래 에너지 자원에 대한 관심과 함께 GaN 기반 태양전지 연구가 활발히 진행되고 있다. GaN 물질은 높은 전자 이동도와 높은 포화 속도 등 광전자 소자에 유리한 광, 전기적 특성들을 가지고 있다. 또한, In의 함량을 변화시켜가며, 0.7eV에서 3.4eV까지 밴드갭을 조절함으로써, 자외선부터 적외선까지 태양빛 스펙트럼의 대부분을 흡수할 수 있는 장점이 있다. InGaN 태양전지의 효율을 높이기 위해서는 In의 함량을 늘려 밴드갭을 줄이는 것이 중요하다. 하지만 GaN 와 InN 간의 격자 부정합으로 인해 In 함량이 높은 단결정 InGaN 층을 두껍게 성장 하는 것이 어렵다. 때문에 GaN 기반 태양전지 관련 연구 그룹들이 태양전지의 효율 향상을 위해 활성층에 양자우물(MQWs) 구조, Supper Lattice (SLs) 구조와 같이 얇은 InGaN/GaN 층을 주기적으로 반복하여 적층함으로써 높은 조성의 In을 함유한 상질의 InGaN/GaN 층을 성장하는 연구들을 진행해 왔다. 본 연구에서는, p-i-n 구조와 MQW 구조를 갖는 InGaN 기반 태양전지를 제작하여, 각각의 특성을 분석해 봄으로써, In0.1Ga0.9N 태양전지 활성층의 구조에 따른 장/단점에 대해 논의하였다. 먼저 MOCVD를 이용하여 200 nm의 i-In0.1Ga0.9N 활성층을 갖는 p-i-n 구조와 In0.19Ga0.81N/GaN(3 nm/8 nm) MQWs (8 periods) 구조를 갖는 태양전지 에피를 각각 성장하였고, 그 후 공정을 통해 그림 1과 같이 InGaN 태양전지 소자를 제작하였다. 그 후, 각 태양전지의 전류/전압 곡선과 외부양자효율을 측정하여 그림 2와 같은 결과를 얻었다. p-i-n과 MQW 샘플의 외부양자효율은 각각 ~70%, ~25%로 측정 되었다. MQW 샘플의 외부 양자효율이 높지 않음에도 불구하고 p-i-n 구조에 비해 높은 In 함량을 가지고 있으므로, 더 넓은 파장의 빛을 흡수하여, 높은 단락전류(0.778 mA/cm2)를 보이고 있다. 또한 p-i-n 구조에 비해 높은 개방전압(2.3V)를 가지고 있으므로, MQW 샘플이 약 17% 정도 높은 변환효율(1.4%)를 보이고 있다. 이후 추가적으로 p-i-n 과 MQW 구조의 InGaN 태양전지에 나타나는 Voc와 Jsc의 차이를 Polarization 효과를 비롯한 다양한 측면에서 분석해 보고자 한다.

• YAKHAK HOEJI
• /
• v.14 no.1_2
• /
• pp.1-14
• /
• 1970

Seventeen N,N/sup I/-disubstituted thiourea derivatives were synthesized by the Hugershof reaction and reported. Antitumor activities of the synthesized compounds against ascitic Ehrlich Carcinoma and ascitic sarcoma 180 were reported. It was found that 1,1/sup I/-(p-Phenylene)-3,3/sup I/-bis (2-carboxyphenyl)-2,2/sup I/-dithiourea was considerably active against ascitic Ehrlich Carcinoma and Sarcoma 180 respectively. 1-(2-Carboxyphenyl)-3-(p-ethoxyphenyl)-2 thiourea was active against ascitic Sarcoma 180. 1-Salicyloyl-3-(p-ethoxyphenyl)-2-thiourea and 1,1/sup I/-(p-Phenylene)-3,3/sup I/-bis(2-hydroxyethyl)-2,2/sup I/-dithiourea were active against ascitic Ehrlich Carcinoma. Antitubercular activities of the synthesized compounds against Mycobacterium tuberculosis H/sub 37/ R/sub v/ were also reported. It was found that 1-Isonicotinyl-4-cyclohexyl-3-thiosemicarbazide was considerably active at 100 .mu.g/ml. 1,1/sup I/-(p-Phenylene)-3,3/sup I/-bis(2-hydroxyethyl)-2,2/sup I/-dithiourea and 1-Salicyloyl-3-(p-ethoxyphenyl)-2-thiourea were active at 1000 .mu.g/ml respectively. Antibacterial activities of nine compounds of the synthesized compounds against S. aureus and E. Coli were reported. It was found that 1,1-(p-Phenylene)-4,4/sup I/-bis(isonicotinyl)-2,2/sup I/-dithiosemicarbazide and 1-Isonicotinyl-4-cyclohexyl-3-thiosemicarbazide were considerably active against S. aureus and E. Coli respectively. 1-(6-Methyl-2-benzothiazolyl)-3-(1-naphthyl)-2-thiourea was active against S. aureus. 1,1/sup I/-(p-Phenylene)-3,3/sup I/-bis (2-hydroxyethyl)-2,2/sup I/-dithiourea was active against E. Coli.

• Journal of the Korean Institute of Telematics and Electronics D
• /
• v.34D no.7
• /
• pp.56-61
• /
• 1997

I $n_{0.53}$G $a_{0.47}$As/I $n_{0.52}$A $l_{0.48}$As pseudomorphic high electron mobility transistor (P-HEMT) structures were grown on semi-insulating InP substrates by molecular beam epitzxy method. The hall effect measuremetn was used to measure the electrical properties and the photoluminescence (PL) measurement was used to measure the electrical properties and the photoluminescence(PL) measurement for optical propety. By the cross-sectional transmission electron microscopy (XTEM) investigation of the V and X shape defects including slip with angle of 60.deg. C and 120.deg. C to surface in the sampel, the defects formation mecahnism in the I $n_{0.52}$A $l_{0.48}$As epilayers on InP substrates could be explained with the different thermal expansion coefficients between I $n_{0.52}$A $l_{0.48}$As epilayers and InP substrate.d InP substrate.