• Journal of the Korean Mathematical Society
• /
• v.49 no.2
• /
• pp.265-291
• /
• 2012

In this paper, we consider the regularity theory and the existence of smooth solution of a degenerate fully nonlinear equation describing the evolution of the rolling stones with nonconvex sides: $\{M(h)=h_t-F(t,z,z^{\alpha}h_{zz})\;in\;\{0<z{\leq}1\}{\times}[0,T] \\ h_t(z,t)=H(h_z(z,t),h)\;{on}\;\{z=0\}$. We establish the Schauder theory for $C^{2,{\alpha}}$-regularity of h.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
• /
• 2004.11a
• /
• pp.218-221
• /
• 2004

The electronic state of ZnO doped with Al, Ga and In, which belong to III family elements in periodic table, was calculated using the density functional theory. In this study, the program used for the calculation on theoretical structures of ZnO and doped ZnO was Vienna Ab-initio Simulation Package (VASP), which is a sort of pseudo potential method. The detail of electronic structure was obtained by the describe variational $X{\alpha}(DV-X{\alpha})$(DV-Xa) method, which is a sort of molecular orbital full potential method. The optimized crystal structures obtained by calculations were compared to the measured structure. The density of state and energy levels of dopant elements was shown and discussed in association with properties.

• Proceedings of the Korean Vacuum Society Conference
• /
• 1999.07a
• /
• pp.177-177
• /
• 1999

The surface structure of epitaxial $\alpha$-Fe2O3(0001) grown on $\alpha$-Al2O3(0001) has been investigated using intermediate-energy x-ray photoelectron diffraction. Comparison of experiment with quantum mechanical scattering theory reveals that the surface is Fe-terminated, and that the first four layer spacings are -41%, +18%, -8%, and +47% of the associated bulk values, respectively. these results agree reasonably well with the predictions of molecular mechanics and spin-density functional theory previously reported in the literature for the Fe-terminated surface. however, we find no evidence for and O-terminated surface predicted to be stable by spin-density functional theory.

• Journal of Information Science Theory and Practice
• /
• v.4 no.4
• /
• pp.64-74
• /
• 2016

In this paper we define a two parametric new generalized useful average code-word length $L_{\alpha}^{\beta}$(P;U) and its relationship with two parametric new generalized useful information measure $H_{\alpha}^{\beta}$(P;U) has been discussed. The lower and upper bound of $L_{\alpha}^{\beta}$(P;U), in terms of $H_{\alpha}^{\beta}$(P;U) are derived for a discrete noiseless channel. The measures defined in this communication are not only new but some well known measures are the particular cases of our proposed measures that already exist in the literature of useful information theory. The noiseless coding theorems for discrete channel proved in this paper are verified by considering Huffman and Shannon-Fano coding schemes on taking empirical data. Also we study the monotonic behavior of $H_{\alpha}^{\beta}$(P;U) with respect to parameters ${\alpha}$ and ${\beta}$. The important properties of $H_{{\alpha}}^{{\beta}}$(P;U) have also been studied.

• Journal of the Korean Chemical Society
• /
• v.21 no.5
• /
• pp.339-352
• /
• 1977

The authors' theory developed in the preceding Paper 1 was applied to plastic deformation of ceramics, metals, alloys and single crystals. For polycrystalline substances, the flow mechanisms due to dislocation movement and grain boundary movement appear together or separately according to the experimental conditions whereas for single crystals, only the mechanism of dislocation movement appears. The parameters appearing in the flow equations $({\alpha}_{d1},\;1/{\beta}_{d1})and\;({\alpha}_{gj}/X_{gj},\;1/{\beta}_{gj})$ (j = 1 or 2), and the activation enthalpies ${\Delta}H_{k1}^{\neq}$ (k = d or g) were determined and tabulated. Here, the subscript d1 indicates the first kind of dislocation flow units and gj expresses the jth kind of grain boundary flow units. The predictions of the theory were compared with experiment with good agreement. Concerning the activation enthalpies, it was found that ${\Delta}H_{d1}^{\neq}$ 〉{\Delta}H_{g1}^{\neq}$ and that the former agrees with the activation enthalpy for bulk self-diffusion whereas the latter agrees with the activation enthalpy for grain boundary self-diffusion. These facts support the adequacy of the authors' theory which is considered as a generalized theory of plastic deformation.

• Korean Journal of Materials Research
• /
• v.17 no.12
• /
• pp.637-641
• /
• 2007

The total energy and strength of Mg alloy doped with Al, Ca and Zn, were calculated using the density functional theory. The calculations was performed by two programs; the discrete variational $X{\alpha}\;(DV-X{\alpha})$ method, which is a sort of molecular orbital full potential method; Vienna Ab-initio Simulation Package (VASP), which is a sort of pseudo potential method. The fundamental mixed orbital structure in each energy level near the Fermi level was investigated with simple model using $DV-X{\alpha}$. The optimized crystal structures calculated by VASP were compared to the measured structure. The density of state and the energy levels of dopant elements was discussed in association with properties. When the lattice parameter obtained from this study was compared, it was slightly different from the theoretical value but it was similar to Mk, and we obtained the reliability of data. A parameter Mk obtained by the $DV-X{\alpha}$ method was proportional to electronegativity and inversely proportional to ionic radii. We can predict the mechanical properties because $\Delta{\overline{Mk}}$is proportional to hardness.

• Journal of the Korean Chemical Society
• /
• v.5 no.1
• /
• pp.48-51
• /
• 1961

A calculation of the optical activity of the ${\alpha}$-1,2,3,4,5,6-Hexahalocyclohexane is presented based upon the Kirkwood's polarizability theory of optical rotatory power. The calculated specific rotation of the compound are given in the following table. The close agreements demonstrates the applicability of the polarizability theory to the compounds whose optical activity is due to steric interference. The agreement in sign also confirms the validity of the absolute configuration of the ${\alpha}$-1,2,3,4,5,6-Hexahalocyclohexane given by O. Hassel.

• Elastomers and Composites
• /
• v.47 no.1
• /
• pp.18-22
• /
• 2012

The silica-silica interaction parameter (${\alpha}_F$) of the silane treated silica filled natural rubber (NR) compound was investigated. The measured ${\alpha}_F$ values using mass fraction method following Wolff's theory were compared with volume fraction method. As silica concentration increased, the ${\alpha}_F$ value increased for both methods. The value of ${\alpha}_F$ expressed as volume fraction was higher than that of mass fraction, which resulted in large gaps between ${\alpha}_F$ values. The effect of accelerator (MBT) concentration on ${\alpha}_F$ values was compared.

• Journal of the Korean Mathematical Society
• /
• v.36 no.1
• /
• pp.97-107
• /
• 1999

Given a C-dynamical system (A, G, $\alpha$) with a locally compact group G, two kinds of C-algebras are made from it, called the full C-crossed product and the reduced C-crossed product. In this paper, we extend the theory of the classical C-crossed product to the C-dynamical system (A, G, $\alpha$) with a left-cancellative semigroup M with unit. We construct a new C-algebra A $\alpha$rM, the reduced crossed product of A by the semigroup M under the action $\alpha$ and investigate some properties of A $\alpha$rM.

• East Asian mathematical journal
• /
• v.15 no.2
• /
• pp.165-176
• /
• 1999

After the derivation was defined in [19] by Posner a lot of researchers studied the derivations in ring theory in different manners such as in [2], [4], [5], ..., etc. Furthermore, many researches followed the definition of the generalized derivation([3], [6], [7], ..., etc.). Finally, Maksa defined a symmetric bi-derivation and many researches have been done in ring theory by using this definition. In this work, defining a symmetric bi-$\alpha$-derivation, we study the mentioned researches above in the light of this new concept.