• Honam Mathematical Journal
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• v.1 no.1
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• pp.43-49
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• 1979

G를 유한군으로, C를 모든 복소수체로 가정하고, V를 C상에서의 유한차원 벡터공간이라 하자. V상에서의 G의 사영적 표시는, X, $y{\epsilon}G$이고 ${\alpha}:\;G{\times}G{\rightarrow}C$를 Facto set이라 할 때 $T(x)T(y)=T(xy){\alpha}(x,y)$이 되는 함수 $T=\;G{\rightarrow}GL(V)$를 말한다. 본 논문의 목적은 군에 대한 Extension theory를 사용해서, G상의 factor set들의 동치류들은 G의 Second Cohomology group과 동형이라는 것을 증명하는 것이다.

• Bulletin of the Korean Chemical Society
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• v.19 no.5
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• pp.575-579
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• 1998

The 77 K luminescence and excitation spectra, and 298 K infrared and absorption spectra of $cis-{\Alpha}-[Cr(trien)Cl_2]Cl{\cdot}H_2O$ (trien=triethylenetetramine) have been measured. Ligand field electronic transitions due to spin-allowed and spin-forbidden are assigned. The zero-phonon line in the excitation spectrum splits into two components by $198\; cm^{-1}$, and the large $^2E_g$ splitting can be reproduced by the modern ligand field theory. It is confirmed that nitrogen atoms of the trien ligand have a strong σ-donor character, but chloride ligand has weak σ- and π -donor properties toward chromium(III) ion.

• Journal of the Korean Society of Clothing and Textiles
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• v.17 no.3
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• pp.380-390
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• 1993

Effect of interfacial electrical conditions on adhesion of ${\alpha}-Fe_2O_3$ particles to PET fabric and the removal of ${\alpha}-Fe_2O_3$ particles from PET fabric, were investigated as functions of pH, electrolyte and ionic strength. The ${\zeta}$ potential of PET fiber and ${\alpha}-Fe_2O_3$ particles in the electrolyte solution were measured by streaming potential and microelectrophoresis methods respectively. The potential energy of interaction between ${\alpha}-Fe_2O_3$ particles and PET fabric were calculated by using the heterocoagulation theory for a sphere-plate model. The negative ${\zeta}$ potential of ${\alpha}-Fe_2O_3$ particle and PET fiber increased with pH, and then decreased certain pH and isoelectric points of ${\alpha}-Fe_2O_3$ particles and PET fiber were pH 6.5 and pH 3.5, respectively. The negative ${\zeta}$ potential of ${\alpha}-Fe_2O_3$ particle and PET fiber affected by electrolytes, were relatively high with polyanion electrolytes in solutions and were low with neutral salts. However, at surfactant solution, ${\zeta}$ potential was levelled off. The influence of the ionic strength on the ${\zeta}$ potential of ${\alpha}-Fe_2O_3$ particle was small but the negative ${\zeta}$ potential of PET fiber increased with the ionic strength. In the presence of anionic surfactant, the ${\zeta}$ potential of ${\alpha}-Fe_2O_3$ particle and PET fiber increased regardless of solution conditions. The interaction energy between ${\alpha}-Fe_2O_3$ particle and PET fabric increased with pH. The interaction energy was relatively high with polyanion electrolytes in solution, and the influence of ionic strength on the interaction energy was small, and the effective thickness of electrical double layer increased with decreasing the ionic strength.

• Journal of Radiation Protection and Research
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• v.13 no.2
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• pp.1-8
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• 1988

The energy losses of ${\alpha}$-particle with 3 to 5.4 MeV energy were measured as a function of gas absorber thickness and ${\alpha}$-particle energy in three light gaseous media; He, Ar, and $N_2$. The stopping powers and stopping cross-sections were determined by analyzing these data. For Ar gas, the experimental values are very well consistent with the corresponding values of Srivastava's stopping-power theory with the condition of the completely and partially stripped ion. For $N_2$ and He gases, these experimental values express the inconsistencies of about $13{\sim}36%$ and $27{\sim}28%$, respectively.

• Bulletin of the Korean Chemical Society
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• v.11 no.1
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• pp.49-54
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• 1990

The gas-phase thermolysis reactions of ${\alpha}$- and ${\beta}$-methylated ethyl formates, Y = $CH-X-CHR_1CH_2R_2$ where X = Y = O or S and $R_1\;=\;R_2$ = H or $CH_3$, are investigated theoretically using the AM1 method. The experimental reactivity order is reproduced correctly by AM1 in all cases. The thermolysis proceeds through a six-membered cyclic transition state conforming to a retro-ene reaction, which can be conveniently interpreted using the frontier orbital theory of three-species interactions. The methyl group substituted at $C_{\alpha}\;or\;C_{\beta}$ is shown to elevate the ${\pi}$-HOMO of the donor fragment (Y = C) and depress the ${\sigma}^{\ast}$-LUMO of the acceptor fragment ($C_{\beta}$-H), increasing the nucleophilicity of Y toward ${\beta}$-hydrogen which in turn increases the reactivity. The two bond breaking processes of the $C_{\alpha}$-X and $C_{\beta}$-H bonds are concerted but not synchronous so that the reaction takes place in two stages as Taylor suggested. The initial cleavage of $C_{\alpha}$-X is of little importance but the subsequent scission of $C_{\beta}$-H occurs in a rate determining stage.

• Bulletin of the Korean Mathematical Society
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• v.56 no.4
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• pp.1027-1039
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• 2019

The concept of jump concerns the distribution of $Tur{\acute{a}}n$ densities. A number ${\alpha}\;{\in}\;[0,1)$ is a jump for r if there exists a constant c > 0 such that if the $Tur{\acute{a}}n$ density of a family $\mathfrak{F}$ of r-uniform graphs is greater than ${\alpha}$, then the $Tur{\acute{a}}n$ density of $\mathfrak{F}$ is at least ${\alpha}+c$. To determine whether a number is a jump or non-jump has been a challenging problem in extremal hypergraph theory. In this paper, we give a way to generate non-jumps for hypergraphs. We show that if ${\alpha}$, ${\beta}$ are non-jumps for $r_1$, $r_2{\geq}2$ respectively, then $\frac{{\alpha}{\beta}(r_1+r_2)!r_1^{r_1}r_2^{r_2}}{r_1!r_2!(r_1+R_2)^{r_1+r_2}}$ is a non-jump for $r_1+r_2$. We also apply the Lagrangian method to determine the $Tur{\acute{a}}n$ density of the extension of the (r - 3)-fold enlargement of a 3-uniform matching.

• Bulletin of the Korean Chemical Society
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• v.7 no.4
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• pp.257-262
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• 1986

Thixotropy is a time-dependent shear-thinning phenomenon. We derived a new thixotropic formula which is based on the generalized viscosity formula of Ree and Eyring, $f={\Sigma}\frac{X_i}{{\alpha}_i}sinh^{-1}$ () (Refer to the text concerning the notation.) The following is postulated: (1) thixotropy occurs when small flow units attached to a large flow unit separate from the latter under stress (2) elastic energy(${\omega}$) is stored on the large flow unit during the flow process, and (3) the stored energy contributes to decrease the activation energy for flow. A new thixotropic formula was derived by using these postulations, $f={\frac}{X_0{\beta}_0}{\alpha_0}{\dot{s}}+{\frac}{X_1{\beta}_1}{{\alpha}_1}{\dot{s}}+{\frac}{X_2}{{\alpha_x}}sinh^{-1}$[$({\beta}_0)_2$ exp $(-C_2{\dot{s}}^2/RT){\cdot}{\dot{s}}$] f is the shear stress, and s is the rate of shear. In case of concentrated solutions where the Newtonian flow units have little contribution to the viscosity of the system, the above equation becomes, $f=\frac{X_2}{\alpha_2}sinh^{-1}$[$({\beta}_0)_2$ exp $(-C_2{\dot{s}}^2/RT){\cdot}{\dot{s}}$]. In order to confirm these formulas, we applied to TiO2(anatase and rutile)-water, printing ink and mayonnaise systems. Good agreements between the experiment and theory were observed.

• Journal of the Korean Mathematical Society
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• v.42 no.2
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• pp.203-222
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• 2005

Thompson series is a Hauptmodul for a genus zero group which lies between $\Gamma$o(N) and its normalizer in PSL2(R) ([1]). We construct explicit ring class fields over an imaginary quadratic field K from the Thompson series $T_g$($\alpha$) (Theorem 4), which would be an extension of [3], Theorem 3.7.5 (2) by using the Shimura theory and the standard results of complex multiplication. Also we construct various class fields over K, over a CM-field K (${\zeta}N + {\zeta}_N^{-1}$), and over a field K (${\zeta}N$). Furthermore, we find an explicit formula for the conjugates of Tg ($\alpha$) to calculate its minimal polynomial where $\alpha$ (${\in}{\eta}$) is the quotient of a basis of an integral ideal in K.

• Journal of applied mathematics & informatics
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• v.6 no.2
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• pp.329-368
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• 1999

This paper surveys recent remarkable progress in the study of potential theory for symmetric stable processes. It also contains new results on the two-sided estimates for Green functions Poisson kernels and Martin kernels of discontinuous symmetric $alpha$ -stable process in bounded $C^{1,1}$ open sets. The new results give ex-plicit information on how the comparing constants depend on pa-rametrer $alpha$ and consequently recover the green function and Poisson kernel estimates for Brownian motion by passing $alpha{\uparrow}2$. In addition to these new estimates this paper surveys recent progress in the study of notions of harmonicity integral representation of harmonic func-tions boundary harnack inequality conditional gauge and intrinsic ultracontractivity for symmetric stable processes. Here is a table of contents.

• Journal of Institute of Control, Robotics and Systems
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• v.10 no.4
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• pp.295-303
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• 2004

Previously it has been shown that the all pole systems resulting good time responses can be characterized by so called K-polynomial. The polynomial is defined in terms of the principal characteristic ratio $\alpha_1$ and the generalized time constant $\tau$ . In this paper, Part II presents several sensitivity analyses of such systems with respect to $\alpha_1$ and $\tau$ changes. We first deal with the root sensitivity to the perturbation of $\alpha_1$ . By way of determining the unnormalized function sensitivity, both time response sensitivity and frequency response sensitivity are derived. Finally, the root sensitivity relative to $\tau$ change is also analyzed. These results provide some useful insight and background theory when we select of and l to compose a reference model of which denominator is a K-polynomial, which is illustrated by examples.