• Bulletin of the Korean Mathematical Society
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• v.54 no.3
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• pp.875-894
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• 2017

Let $[n]=\{1,2,{\ldots},n\}$. A set ${\mathbf{A}}=\{A_1,A_2,{\ldots},A_l\}$ is a minimal cover of [n] if ${\cup}_{1{\leq}i{\leq}l}A_i=[n]$ and $$\bigcup_{{1{\leq}i{\leq}l,}\\{i{\neq}j_0}}A_i{\neq}[n]\text{ for all }j_0{\in}[l]$$. Let ${\mathcal{C}}(n)$ denote the collection of all minimal covers of [n], and write $C_n={\mid}{\mathcal{C}}(n){\mid}$. Let ${\mathbf{A}}{\in}{\mathcal{C}}(n)$. An element $u{\in}[n]$ is critical in ${\mathbf{A}}$ if it appears exactly once in ${\mathbf{A}}$. Two minimal covers ${\mathbf{A}},{\mathbf{B}}{\in}{\mathcal{C}}(n)$ are said to be restricted t-intersecting if they share at least t sets each containing an element which is critical in both ${\mathbf{A}}$ and ${\mathbf{B}}$. A family ${\mathcal{A}}{\subseteq}{\mathcal{C}}(n)$ is said to be restricted t-intersecting if every pair of distinct elements in ${\mathcal{A}}$ are restricted t-intersecting. In this paper, we prove that there exists a constant $n_0=n_0(t)$ depending on t, such that for all $n{\geq}n_0$, if ${\mathcal{A}}{\subseteq}{\mathcal{C}}(n)$ is restricted t-intersecting, then ${\mid}{\mathcal{A}}{\mid}{\leq}{\mathcal{C}}_{n-t}$. Moreover, the bound is attained if and only if ${\mathcal{A}}$ is isomorphic to the family ${\mathcal{D}}_0(t)$ consisting of all minimal covers which contain the singleton parts $\{1\},{\ldots},\{t\}$. A similar result also holds for restricted r-cross intersecting families of minimal covers.

• Communications of the Korean Mathematical Society
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• v.12 no.3
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• pp.701-707
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• 1997

In [8], we introduce the relative root Nielsen number N(f;X, A, c) for maps of pairs of spaces $f : (X, A) \to (Y, B)$. From it, we obtain some immediate consequences of the definition and illustrate it by some examples. We consider the question whether there exists a map $g : (X, A) \to (Y, B)$ homotopic to a given map $f : (X, A) \to (Y, B)$ which has precisely N(f;X, A, c) roots, that is, the minimum theorem for N(f;X, A, c).

• 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.

• Polymer(Korea)
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• v.31 no.6
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• pp.497-504
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• 2007

We have prepared the dinuclear half-sandwich CGC(constrained geometry catalyst) with polymethylene bridge $[Zr(({\eta}^5\;:\;{\eta}^1-C_9H_5SiMe_2NCMe_3)Me_2)_2\;[(CH_2)_n]$ [n=6(4), 9(5), 12(6)] by treating 2 equivalents of MeLi with the corresponding dichlorides compounds. To study the catalytic behavior of the dinuclear catalysts we conducted copolymerization of ethylene and 1-hexene in the presence of three kinds of boron cocatalysts, $Ph_3C^+[B(C_6F_5)_4]^-\;(B_1),\;B(C_6F_5)_3\;(B_3)$, and $Ph_3C^+[(C_6F_5)_3B-C_6F_4-B(C_6F_5)_3]^{2-}\;(B_2)$. It turned out that all active species formed by the combination of three dinuclear CGCs with three cocatalyst were very efficient catalysts for the polymerization of olefins. The activities increase as the bridge length of the dinuclear CGCs increases. At the same time the dinuclear cocatalyst exhibited the lowest activity among three cocatalysts. The prime observation is that the dinuclear cocatalyst gave rise to the formation of the copolymers with the least branches on the polyethylene backbone.

• Journal of the Korean Chemical Society
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• v.14 no.4
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• pp.287-296
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• 1970

The varation of potential and completeness of reaction in an oxidation-reduction titration of Red$_1$ ($a\;Ox_1+N_1e{\leftrightarrow}b\;Red_1)\;by\;Ox_2\;(C\;Ox_2+n_2e{\leftrightarrow}d\;Red_2)$ is analyzed on the basis of general expressions. It is shown that the reaction deficiency as well as the rate of variation of the potential with titration fraction change in proportion to the $[n_2(a-b)-n_1(c-d)]$ th power of the concentration of the reagents. In particular, at the equivalence point, the expression of the potential contains a concentration dependent term that is proportional to ac-bd. Thus, the equivalence-point potential varies with the concentration of the reagents unless ac=bd is satisfied. It is also shown that the sharpness of the potentiometric titration curve is shown to occur either prior to or after the equivalence point depending upon whether $n_1cn_2b$, the deviation being the same order of magnitude as the relative deficiency at the equivalence point.

• Kyungpook Mathematical Journal
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• v.56 no.2
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• pp.349-355
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• 2016

For any integer $n{\geq}2$, each palindrome of n induces a circulant graph of order n. It is known that for each integer $n{\geq}2$, there is a one-to-one correspondence between the set of (resp. aperiodic) palindromes of n and the set of (resp. connected) circulant graphs of order n (cf. [2]). This bijection gives a one-to-one correspondence of the palindromes ${\sigma}$ with $gcd({\sigma})=1$ to the connected circulant graphs. It was also shown that the number of palindromes ${\sigma}$ of n with $gcd({\sigma})=1$ is the same number of aperiodic palindromes of n. Let $a_n$ (resp. $b_n$) be the number of aperiodic palindromes ${\sigma}$ of n with $gcd({\sigma})=1$ (resp. $gcd({\sigma}){\neq}1$). Let $c_n$ (resp. $d_n$) be the number of periodic palindromes ${\sigma}$ of n with $gcd({\sigma})=1$ (resp. $gcd({\sigma}){\neq}1$). In this paper, we calculate the numbers $a_n$, $b_n$, $c_n$, $d_n$ in two ways. In Theorem 2.3, we $n_d$ recurrence relations for $a_n$, $b_n$, $c_n$, $d_n$ in terms of $a_d$ for $d{\mid}n$ and $d{\neq}n$. Afterwards, we nd formulae for $a_n$, $b_n$, $c_n$, $d_n$ explicitly in Theorem 2.5.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.31B no.12
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• pp.1-10
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• 1994

In this paper, we propose a processor allocation algorithm using the PGG(Packed Gray code Group) for the MIMD hypercube. The number of k-D subcubes in an n-cube is C(n.k) en-k. When the PGG is employed in the processor allocation, C(n, k) PGG's are required to recognize all the k-D subcubes in an n-cube. from the simulation we find that the capability of processor allocation using only 40% of C(n, k) PGG's is about the same as that of the allocation using all the PGG's.

• Communications of the Korean Mathematical Society
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• v.32 no.4
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• pp.959-970
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• 2017

In this paper, we investigate the transcendental meromorphic solutions with finite order of two different types of difference equations $${\sum\limits_{j=1}^{n}}a_jf(z+c_j)={\frac{P(z,f)}{Q(z,f)}}={\frac{{\sum_{k=0}^{p}}b_kf^k}{{\sum_{l=0}^{q}}d_lf^l}}$$ and $${\prod\limits_{j=1}^{n}}f(z+c_j)={\frac{P(z,f)}{Q(z,f)}={\frac{{\sum_{k=0}^{p}}b_kf^k}{{\sum_{l=0}^{q}}d_lf^l}}$$ that share three distinct values with another meromorphic function. Here $a_j$, $b_k$, $d_l$ are small functions of f and $a_j{\not{\equiv}}(j=1,2,{\ldots},n)$, $b_p{\not{\equiv}}0$, $d_q{\not{\equiv}}0$. $c_j{\neq}0$ are pairwise distinct constants. p, q, n are non-negative integers. P(z, f) and Q(z, f) are two mutually prime polynomials in f.

• Molecules and Cells
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• v.43 no.12
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• pp.1023-1034
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• 2020

Complement fragment iC3b serves as a major opsonin for facilitating phagocytosis via its interaction with complement receptors CR3 and CR4, also known by their leukocyte integrin family names, αMβ2 and αXβ2, respectively. Although there is general agreement that iC3b binds to the αM and αX I-domains of the respective β2-integrins, much less is known regarding the regions of iC3b contributing to the αX I-domain binding. In this study, using recombinant αX I-domain, as well as recombinant fragments of iC3b as candidate binding partners, we have identified two distinct binding moieties of iC3b for the αX I-domain. They are the C3 convertase-generated N-terminal segment of the C3b α'-chain (α'NT) and the factor I cleavage-generated N-terminal segment in the CUBf region of α-chain. Additionally, we have found that the CUBf segment is a novel binding moiety of iC3b for the αM I-domain. The CUBf segment shows about a 2-fold higher binding activity than the α'NT for αX I-domain. We also have shown the involvement of crucial acidic residues on the iC3b side of the interface and basic residues on the I-domain side.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.23 no.4
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• pp.59-64
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• 2023

In this paper, It is proposed through the empirical design of a Conducted EMI filter for noise reduction of power used in electronic devices. For the proposed structure, A-type, B-type, C-type, and D-type structures were designed, and conductive noise reduction was confirmed by using an LC network with various X-capacitors, Y-capacitors, and Air-inductors. 10 [μH] was used for L1 and L2, and 4.7 [nF] was used for C1 and C2. L3 for common mode used 13[μH], and C5, C6, C7 were designed using 10[nF]. The measured insertion loss values of the designed EMI filter were -74.4[dB] at 3.2MHz, -75.4[dB] at 4MHz, and -75.3[dB] at 13.56MHz. Therefore, the proposed EMI filter will be able to reduce power supply noise used in various electronic devices.