• Journal of the Korean Society of Fisheries and Ocean Technology
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• v.20 no.1
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• pp.1-5
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• 1984

The author carried out an experiment for the dynamical swimming force of crusian carp, Carassius carassius. The experimental water tank was made of 4mm thick transparent acryl board in the right hexahedral shape (400L$\times$240W$\times$800H mm). The water temperature in the tank ranged 20.6$^{\circ}C$ to 21.2$^{\circ}C$. The water level in the tank was maintained 70cm high from the bottom. The measurement of the swimming force was carried out by use of strain gauge. The results obtained can be summarized as follows: 1) The momentary maximum swimming force F sub(M) (g) and the sustainable maximum swimming force F sub(s) (g) can be expressed as a function of the body weight W(g). F sub(M) =1.45W, F sub(s) =0.29W where the momentary maximum swimming force means the highest value, and the sustainable maximum swimming force means the mean high value sustained for 4 to 5 seconds presented in the recording paper. 2) F sub(M) and F sub(s) can be expressed as a function of the body length L(cm). F sub(M) =0.11L super(2.63), F sub(s) =0.15L super(1.77) 3) The coefficient of hydraulic resistance for crusian carp was derived as 0.287.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.20 no.42
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• pp.143-149
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• 1997

먼저 Cantor dust 의 성질 및 유사성, 축소인자, 불변집합, $\delta$ - covering, Box counting 차원 등에 대한 정의를 하였다, {f_i}{\;}{{\infty}\atop{i=1}}$ 를 $R^n$ 상에서 개집합 조건을 만족시키는 축소인 자 $C_i$에 대한 유사성 이라하자. F를｛{f_i}{\;}{{\infty}\atop {i=1}}$ 에 대한 $R^n$상의 불변집합, 즉, F = $\bigcup_{i=0}^\infty{\;}f_1(F)$를 만족시키는 집합이라 하자. 이때, $\sum\limits_{n=0}^\infty{\;}C^s_i{\;}=1,{\;}0{\;}<{\;}C_1{\;}<{\;}1$ 일 때, $dim{\;}_H{\;}F{\;}={\;}dim{\;}_B{\;}F{\;}={\;}s$ 임을 보임으로서, 자기동형집합의 후랙탈 차원에 대하여 논의 하고자 한다.

• Communications of the Korean Mathematical Society
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• v.35 no.3
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• pp.711-722
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• 2020

Given a semigroup S generated by its squares equipped with an involutive automorphism 𝝈 and a multiplicative function 𝜇 : S → ℂ such that 𝜇(x𝜎(x)) = 1 for all x ∈ S, we determine the complex-valued solutions of the following functional equations f(xy) + 𝜇(y)f(𝜎(y)x) = 2f(x)g(y), x, y ∈ S and f(xy) + 𝜇(y)f(𝜎(y)x) = 2f(y)g(x), x, y ∈ S.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2013.05a
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• pp.1217-1218
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• 2013

• Journal of the Chungcheong Mathematical Society
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• v.22 no.2
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• pp.141-148
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• 2009

We consider various algorithms calculating best onesided simultaneous approximations. We assume that X is a compact subset of $\mathbb{R}^{m}$ satisfying $X=\overline{intX}$, S is an n-dimensional subspace of C(X), and $\mu$ is any 'admissible' measure on X. For any l-tuple $f_1,\;{\cdots},\;f_{\ell}$ in C(X), we present various ideas for best approximation to F from S(F). The problem of best (both one and two-sided) approximation is a linear programming problem.

• 한국초전도학회:학술대회논문집
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• 2007.07a
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• pp.37-37
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• 2007

• Korean Journal of Mathematics
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• v.19 no.4
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• pp.351-365
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• 2011

In the present paper we introduce a new subclass of analytic functions in the unit disc defined by convolution $(f_{\mu})^{(-1)}*f(z)$; where $$f_{\mu}=(1-{\mu})z_2F_1(a,b;c;z)+{\mu}z(z_2F_1(a,b;c;z))^{\prime}$$. Several interesting properties of the class and integral preserving properties of the subclasses are also considered.

• Communications of the Korean Mathematical Society
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• v.37 no.4
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• pp.1055-1072
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• 2022

Our aim is to establish certain image formulas of the (p, 𝜈)-extended Gauss' hypergeometric function F_p,𝜈(a, b; c; z) by using Saigo's hypergeometric fractional calculus (integral and differential) operators. Corresponding assertions for the classical Riemann-Liouville(R-L) and Erdélyi-Kober(E-K) fractional integral and differential operators are deduced. All the results are represented in terms of the Hadamard product of the (p, 𝜈)-extended Gauss's hypergeometric function F_p,𝜈(a, b; c; z) and Fox-Wright function _rΨ_s(z). We also established Jacobi and its particular assertions for the Gegenbauer and Legendre transforms of the (p, 𝜈)-extended Gauss' hypergeometric function F_p,𝜈(a, b; c; z).

• Journal of the Korea Academia-Industrial cooperation Society
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• v.14 no.11
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• pp.6029-6038
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• 2013

In this study we attempt to modify the backbone structure and improve processibility of PBO having high melting and glass transition temperature. A series of aromatic poly(o-hydroxyamide)s(PHAs) were synthesized by direct polycondensaton of diacides containing diimide unit with two types of bis(o-aminophenol)s including 3,3'-dihydroxybenzidine and 2,2-bis(3-amino-4-hydroxyphenyl)hexafluoropropane. PHAs were studied by FT-IR, $^1H$-NMR, DSC and TGA. PHAs exhibited inherent viscosities in the range of 0.34~0.65 dL/g at $35^{\circ}C$ in DMAc solution. The PHA 1 and 6F-PHA 6, introducing o-phenylene unit in the main chain showed excellent solubilities in aprotic solvents such as NMP etc. However, the PHA 3, having p-phenylene unit was not even dissolved perfectly with LiCl salt. 6F-PHAs were readily soluble at room temperature in aprotic solvents except 6F-PHA 3. But they showed better solubility than that of PHAs. The polybenzoxazoles(PBOs) were quite insoluble in other solvents except partially soluble in sulfuric acid. PBOs exhibited relatively high glass transition temperatures(Tg) in the range of 306~$311^{\circ}C$ by DSC. The maximum weight loss temperature and char yields of PHA3 and 6F-PHA3 showed the highest values of $658^{\circ}C$ and $653^{\circ}C$, 62.6 % and 62.1 %, respectively.

• Bulletin of the Korean Chemical Society
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• v.24 no.5
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• pp.583-592
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• 2003

The gas phase identity nucleophilic substitution reactions of halide anions (X = F, Cl, Br) with cyclopentadienyl halides (1) are investigated at the B3LYP/6-311+G**, MP2/6-311+G** and G2(+)MP2 levels involving five reaction pathways: σ-attack $S_N2$, β-$S_N$2'-syn, β-$S_N$2'-anti, γ-$S_N$2'-syn and γ-$S_N$2'-anti paths. In addition, the halide exchange reactions at the saturated analogue, cyclopentyl halides (2), and the monohapto circumambulatory halide rearrangements in 1 are also studied at the same three levels of theory. In the σ-attack $S_N2$ transition state for 1 weak positive charge develops in the ring with X = F while negative charge develops with X = Cl and Br leading to a higher energy barrier with X = F but to lower energy barriers with X = Cl and Br than for the corresponding reactions of 2. The π-attack β-$S_N$2' transition states are stabilized by the strong $n_C-{\pi}^{*}_{C=C}$ charge transfer interactions, whereas the π-attack γ-$S_N$2' transition states are stabilized by the strong $n_C-{\sigma}^{*}_{C-X}$ interactions. For all types of reaction paths, the energy barriers are lower with X = F than Cl and Br due to the greater bond energy gain in the partial C-X bond formation with X = F. The β-$S_N$2' paths are favored over the γ-$S_N$2' paths only with X = F and the reverse holds with X = Cl and Br. The σ-attack $S_N2$ reaction provides the lowest energy barrier with X = Cl and Br, but that with X = F is the highest energy barrier path. Activation energies for the circumambulatory rearrangement processes are much higher (by more than 18 kcal $mol^{-1}$) than those for the corresponding $S_N2$ reaction path. Overall the gas-phase halide exchanges are predicted to proceed by the σ-attack $S_N2$ path with X = Cl and Br but by the β-$S_N$2'-anti path with X = F. The barriers to the gas-phase halide exchanges increase in the order X = F < Br < Cl, which is the same as that found for the gas-phase identity methyl transfer reactions.