• The Korean Journal of Zoology
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• v.6 no.2
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• pp.11-15
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• 1963

A total of 220 adult male mice (18-20g) of the S.M. strain were divided into ten experimental and control groups. The total-body X-ray irradiation doses used were 50 r, 100r, 200r, 400r, 600r, 800r, 1,000r, 1,200r, 1,400r, and1,600r. The respiratory arrest (mortality) caused by each irradiation doses were observed for 30 days. Relationships between irradiation doses and survival time and percentage of response were examined. From this experiment, a formula was obtained to express the relationship among three factors, which may be presented as follows : {{{{{{{{P= { 10} over { SQRT { 2 pi } } INT _{ - INF }^{ p'} e-{(p'-50)^2 } over {200 }dp···(a) p'=100 LEFT { t^0.3- LEFT ( { { 16.9965} over {D-60 } } RIGHT ) ^{ { 1} over {2.5 } } } / LEFT { LEFT ( { 26372.43} over {D-81.86 } RIGHT ) ^{ { 1} over {2.5 } } -( { { 16.9965} over {D-60 } } RIGHT ) ^{ { 1} over {2.5 } } ···(b) p= { (D-60) t^0.75-16.9965} over {0.2186 t^0.75 +263.55434 }····(c) }} {{{{P= { 10} over { SQRT { 2 pi } } INT _{ - INF }^{ p'} e-{(p'-50)^2 } over {200 }dp···(a) p'=100 LEFT { t^0.3- LEFT ( { { 16.9965} over {D-60 } } RIGHT ) ^{ { 1} over {2.5 } } } / LEFT { LEFT ( { 26372.43} over {D-81.86 } RIGHT ) ^{ { 1} over {2.5 } } -( { { 16.9965} over {D-60 } } RIGHT ) ^{ { 1} over {2.5 } } ···(b) p= { (D-60) t^0.75-16.9965} over {0.2186 t^0.75 +263.55434 }····(c)

• Kyungpook Mathematical Journal
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• v.61 no.4
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• pp.679-710
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• 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 the Korean Mathematical Society
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• v.52 no.4
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• pp.727-749
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• 2015

We obtain the conditions on ${\beta}$ so that $1+{\beta}zp^{\prime}(z){\prec}1+4z/3+2z^2/3$ implies p(z) ${\prec}$ (2+z)/(2-z), $1+(1-{\alpha})z$, $(1+(1-2{\alpha})z)/(1-z)$, ($0{\leq}{\alpha}$<1), exp(z) or ${\sqrt{1+z}}$. Similar results are obtained by considering the expressions $1+{\beta}zp^{\prime}(z)/p(z)$, $1+{\beta}zp^{\prime}(z)/p^2(z)$ and $p(z)+{\beta}zp^{\prime}(z)/p(z)$. These results are applied to obtain sufficient conditions for normalized analytic function f to belong to various subclasses of starlike functions, or to satisfy the condition ${\mid}log(zf^{\prime}(z)/f(z)){\mid}$ < 1 or ${\mid}(zf^{\prime}(z)/f(z))^2-1{\mid}$ < 1 or zf'(z)/f(z) lying in the region bounded by the cardioid $(9x^2+9y^2-18x+5)^2-16(9x^2+9y^2-6x+1)=0$.

• Bulletin of the Korean Mathematical Society
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• v.34 no.4
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• pp.595-601
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• 1997

Let $C_d$ be the rational curve of degree d in $P_k ^3$ given parametrically by $x_0 = u^d, X_1 = u^{d - 1}t, X_2 = ut^{d - 1}, X_3 = t^d (d \geq 4)$. Then the defining ideal of $C_d$ can be minimally generated by d polynomials $F_1, F_2, \ldots, F_d$ such that $degF_1 = 2, degF_2 = \cdots = degF_d = d - 1$ and $C_d$ is a set-theoretically complete intersection on $F_2 = X_1^{d-1} - X_2X_0^{d-2}$ for every field k of characteristic p > 0. For the proofs we will use the notion of Grobner basis.

• Asian Pacific Journal of Cancer Prevention
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• v.13 no.7
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• pp.3053-3059
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• 2012

Human epidermal growth factor receptor 2 (HER2) is a member of the epidermal growth factor receptor family of receptor tyrosine kinases that plays important roles in all processes of cell development. Their overexpression is related to many cancers, including examples in the breast, ovaries and stomach. Anticancer therapies targeting the HER2 receptor have shown promise, and monoclonal antibodies against subdomains II and IV of the HER2 extra-cellular domain (ECD), Pertuzumab and Herceptin, are currently used in treatments for some types of breast cancers. Since anti HER2 antibodies targeting distinct epitopes have different biological effects on cancer cells; in this research linear and conformational B cell epitopes of HER2 ECD, subdomain III, were identified by bioinformatics analyses using a combination of linear B cell epitope prediction web servers such as ABCpred, BCPREDs, Bepired, Bcepred and Elliprro. Then, Discotope, CBtope and SUPERFICIAL software tools were employed for conformational B cell epitope prediction. In contrast to previously reported epitopes of HER2 ECD we predicted conformational B cell epitopes $P1_C$: 378-393 (PESFDGDPASNTAPLQ) and $P2_C$: 500-510 (PEDECVGEGLA) by the integrated strategy and P4: PESFDGD-X-TAPLQ; P5: PESFDGDP X TAPLQ; P6: ESFDGDP X NTAPLQP; P7: PESFDGDP-X-NTAPLQ; P8: ESFDG-XX-TAPLQPEQL and P9: ESFDGDP-X-NTAPLQP by SUPERFICIAL software. These epitopes could be further used as peptide antigens to actively immune mice for development of new monoclonal antibodies and peptide cancer vaccines that target different epitopes or structural domains of HER2 ECD.

• International Journal of Internet, Broadcasting and Communication
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• v.12 no.1
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• pp.7-13
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• 2020

We describes V2X technology, a connectivity-based recognition technology that is attracting attention as a key technology for implementing autonomous driving technology, and autonomous communication modules that implement ADAS technology, a sensor-based recognition technology. It also explains the trends in V2X technology standardization centered on IEEE 802.11p, which is a WAVE technology standard based on Wi-Fi/DSRC. Finally, we will discuss the market growth trend of V2X communication modules in the United States, the leading V2X technology module, and the development of technology development trends of major domestic and international companies that are leading the global technology market related to V2X communication modules. V2X and ADAS technologies will be the biggest influence on automotive purchasing decisions. In recent years, V2I mandates have been promoted beyond V2V, mainly in developed countries such as the United States. The related industry needs to focus on the development of information transmission network technology that can support high frequency high efficiency(transmission rate) and sophisticated positioning accuracy beyond conventional vehicle communication.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.4
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• pp.807-824
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• 2011

It has been proved that if $\mathbb{X}^{(s,s)}$ is the union of two linear star-configurations in $\mathbb{P}^2$ of type $s{\times}s$, then $(I_{\mathbb{X}^{(s,s)}})_s{\neq}\{0\}$ for s = 3, 4, 5, and $(I_{\mathbb{X}^{(s,s)}})_s=\{0\}$ for $s{\geq}6$. We extend $\mathbb{P}^2$ to $\mathbb{P}^n$ and show that if $\mathbb{X}^{(s,s)}$ is the union of two linear star-configurations in $\mathbb{P}^n$, then $(I_{\mathbb{X}^{(s,s)}})_s=\{0\}$ for $n{\geq}3$ and $s{\geq}3$. Using this generalization, we also prove that the secant variety $Sec_1(Split_s(\mathbb{P}^n))$ has the expected dimension 2ns + 1 for $n{\geq}3$ and $s{\geq}3$.

• Kyungpook Mathematical Journal
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• v.13 no.2
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• pp.235-240
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• 1973

A k-dimensional vector bundle is a bundle ${\xi}=(E,P,B,F^k)$ with fibre $F^k$ satisfying the local triviality, where F is the field of real numbers R or complex numbers C ([1], [2] and [3]). Let $Vect_k(X)$ be the set consisting of all isomorphism classes of k-dimensional vector bundles over the topological space X. Then $Vect_F(X)=\{Vect_k(X)\}_{k=0,1,{\cdots}}$ is a semigroup with Whitney sum (${\S}1$). For a pair (X, A) of topological spaces, a difference isomorphism over (X, A) is a vector bundle morphism ([2], [3]) ${\alpha}:{\xi}_0{\rightarrow}{\xi}_1$ such that the restriction ${\alpha}:{\xi}_0{\mid}A{\longrightarrow}{\xi}_1{\mid}A$ is an isomorphism. Let $S_k(X,A)$ be the set of all difference isomorphism classes over (X, A) of k-dimensional vector bundles over X with fibre $F^k$. Then $S_F(X,A)=\{S_k(X,A)\}_{k=0,1,{\cdots}}$, is a semigroup with Whitney Sum (${\S}2$). In this paper, we shall prove a relation between $Vect_F(X)$ and $S_F(X,A)$ under some conditions (Theorem 2, which is the main theorem of this paper). We shall use the following theorem in the paper. THEOREM 1. Let ${\xi}=(E,P,B)$ be a locally trivial bundle with fibre F, where (B, A) is a relative CW-complex. Then all cross sections S of ${\xi}{\mid}A$ prolong to a cross section $S^*$ of ${\xi}$ under either of the following hypothesis: (H1) The space F is (m-1)-connected for each $m{\leq}dim$ B. (H2) There is a relative CW-complex (Y, X) such that $B=Y{\times}I$ and $A=(X{\times}I)$ ${\cap}(Y{\times}O)$, where I=[0, 1]. (For proof see p.21 [2]).

• Proceedings of the Korean Powder Metallurgy Institute Conference
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• 2006.09a
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• pp.75-76
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• 2006

New PM route via bulk mechanical alloying is developed to fabricate the solid solution semi-conductive materials with $Mg_2Si_{1-x}Ge_x$ and $Mg_2Si_{1-y}Sn_y$ for 0 < x, y < 1 and to investigate their thermoelectric materials. Since $Mg_2Si$ is n-type and both $Mg_2Ge$ and $Mg_2Sn$ are p-type, pn-transition takes place at the specified range of germanium content, x, and tin content, y. Through optimization of chemical composition, solid-solution type thermoelectric semi-conductive materials are designed both for n-and p-type materials.

• Korean Journal of Materials Research
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• v.9 no.8
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• pp.849-853
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• 1999

In the study, superconducting properties of $Bi_2$-x(sub)$LSr_2$Ca(sub)1+x(sub)$LCu_2$O(sub)8+d (x(sub)L=0, 0.05, 0.1, 0.2) films prepared by the LPE method was investigated. The peak decompositions of Sr3d and Ca2p XPS spectra, together with the EPMA results, elucidated the occupancies of Bi, Sr and Ca atoms on the SrO- and Ca-layers. The lattice parameter c monotonically increased with increasing x(sub)L for $0\leq$x(sub)L$\leq$0.2. The superconducting critical temperature T(sub)c showed a maximum value around x(sub)L=0.1. The x(sub)L dependence of the superconducting critical temperature T(sub)c and the lattice parameter c are explained by the changes of the excess oxygens in the BiO-layer. Since distribution and deficiency of the atoms in SrO-layer have influenced on superconducting properties and crystal structure.