• 대한수학회지
• /
• 제55권4호
• /
• pp.987-1004
• /
• 2018

In this paper, we get several centroaffine invariant properties for a ruled surface in ${\mathbb{R}}^4$ with centroaffine theories of codimension two. Then by solving certain partial differential equations and studying a centroaffine surface with some centroaffine invariant properties in ${\mathbb{R}}^4$, we obtain such a surface is centroaffinely equivalent to a ruled surface or one of the flat centered cyclic surfaces. Furthermore, some centroaffine invariant properties for centered cyclic surfaces are considered.

• 호남수학학술지
• /
• 제40권4호
• /
• pp.701-718
• /
• 2018

In this paper, we will study the constant mean curvature (CMC) surfaces foliated by ellipses in three dimensional Euclidean space $E^3$. We prove that: (1): Surfaces foliated by ellipses are CMC surfaces if and only if it is a part of generalized cylinder. (2): All surfaces foliated by ellipses are not minimal surfaces. (3): CMC surfaces foliated by ellipses are developable surfaces. (4): CMC surfaces foliated by ellipses are translation surfaces generated by a straight line and plane curve.

• Structural Engineering and Mechanics
• /
• 제74권3호
• /
• pp.407-423
• /
• 2020

The pre-peak cyclic shear mechanism of two-order asperity degradation of rock joints in the direct shear tests with static constant normal loads (CNL) are investigated using experimental and numerical methods. The laboratory testing rock specimens contains the idealized and regular two-order triangular-shaped asperities, which represent the specific geometrical conditions of natural and irregular waviness and unevenness of rock joint surfaces, in the pre-peak cyclic shear tests. Three different shear failure patterns of two-order triangular-shaped rock joints can be found in the experiments at constant horizontal shear velocity and various static constant normal loads in the direct and pre-peak cyclic shear tests. The discrete element method is adopted to simulate the pre-peak shear failure behaviors of rock joints with two-order triangular-shaped asperities. The rock joint interfaces are simulated using a modified smooth joint model, where microscopic scale slip surfaces are applied at contacts between discrete particles in the upper and lower rock blocks. Comparing the discrete numerical results with the experimental results, the microscopic bond particle model parameters are calibrated. Effects of cyclic shear loading amplitude, static constant normal loads and initial waviness asperity angles on the pre-peak cyclic shear failure behaviors of triangular-shaped rock joints are also numerically investigated.

• 대한수학회보
• /
• 제54권5호
• /
• pp.1779-1801
• /
• 2017

Let X be a minimal del Pezzo surface of degree 2 over a finite field ${\mathbb{F}}_q$. The image ${\Gamma}$ of the Galois group Gal(${\bar{\mathbb{F}}}_q/{\mathbb{F}}_q$) in the group Aut($Pic({\bar{X}})$) is a cyclic subgroup of the Weyl group W($E_7$). There are 60 conjugacy classes of cyclic subgroups in W($E_7$) and 18 of them correspond to minimal del Pezzo surfaces. In this paper we study which possibilities of these subgroups for minimal del Pezzo surfaces of degree 2 can be achieved for given q.

• Bulletin of the Korean Chemical Society
• /
• 제28권8호
• /
• pp.1322-1328
• /
• 2007

The catalytic activity of poly[(2,2'-bipyridine)copper(II)-μ4-oxalato] coated on a glassy carbon electrode (GCE) for O2 electroreduction is examined using cyclic voltammetry and rotating disk electrode techniques. The cyclic voltammograms show that O2 is electroreduced on pBpCuOx-coated GCE surfaces at a peak potential of ? 0.25 V in pH 4.7 acetate buffer media. The electroreduction of O2 on pBpCuOx-coated GCE occurs at 450 mV more positive potential than that found at a bare GCE. The catalytic activity originates from Cu(II) coordinated by bipyridine in the complexes and the polymer type Cu-complex films exhibit an enhanced stability compared to monomeric Cu-complexes during the O2 electroreduction. The rotating disk electrode measurements reveal that the electroreduction of O2 on pBpCuOx-coated GCE is a four-electron process. Kinetic parameters for O2 reduction on pBpCuOx-coated GCE are obtained from rotating disk experiments and compared with those on bare glassy carbon electrode surfaces.

• Bulletin of the Korean Chemical Society
• /
• 제31권1호
• /
• pp.104-111
• /
• 2010

The heterogeneous electron transfer at $SiMo_{12}O_{40}^{4-}$ monolayers on GC, HOPG, and Au electrode surfaces are investigated using cyclic voltammetric and electrochemical impedance spectroscopic (EIS) methods. The electron transfer of negatively charged $Fe(CN)_6^{3-}$ species is retarded at $SiMo_{12}O_{40}^{4-}$-modified electrode surfaces, while that of positively charged $Ru(NH_3)_6^{3+}$species is accelerated at the modified surfaces. This is due to the electrostatic interactions between $SiMo_{12}O_{40}^{4-}$ layers on surfaces and charged redox species. The electron transfer kinetics of a neutral redox species, 1,1‘-ferrocenedimethanol (FDM), is not affected by the modification of electrode surfaces with $SiMo_{12}O_{40}^{4-}$, indicating the $SiMo_{12}O_{40}^{4-}$ monolayers do not impart barriers to electron transfer of neutral redox species. This is different from the case of thiolate SAMs which always add barriers to electron transfer. The effect of $SiMo_{12}O_{40}^{4-}$ layers on the electron transfer of charged redox species is dependent on the kind of electrodes, where HOPG surfaces exhibit marked effects. Possible mechanisms responsible for different electron transfer behaviors at $SiMo_{12}O_{40}^{4-}$ layers are proposed.

• 대한수학회보
• /
• 제60권6호
• /
• pp.1427-1437
• /
• 2023

It is known that the automorphism group of a K3 surface with Picard number two is either an infinite cyclic group or an infinite dihedral group when it is infinite. In this paper, we study the generators of such automorphism groups. We use the eigenvector corresponding to the spectral radius of an automorphism of infinite order to determine the generators.

• 대한기계학회논문집A
• /
• 제26권3호
• /
• pp.537-543
• /
• 2002

This paper examines a new in-process measurement system for the measurement of micro-defects on the surfaces of brittle materials by using the AFM (Atomic Force Microscopy). A new AFM scanning stage that can also perform nano-scale bending of the sample was developed by adding a bending unit to a commercially available AFM scanner. The bending unit consists of a PZT actuator and sample holder, and can perform static and cyclic three-point bending. The true bending displacement of the bending unit is approximately 1.8mm when 80 volts are applied to the PZT actuator. The frequency response of the bending unit and the stress on the sample were also analyzed, both theoretically and experimentally. Potential surface defects of the sample were successfully detected by this measurement system. It was confirmed that the number of micro-defects on a scratched surface increases when the surface is subjected to a cyclic bending load.

• 전기화학회지
• /
• 제4권1호
• /
• pp.21-25
• /
• 2001

프랙탈 기하학의 계면 전기화학에로의 응용과 관련하여 프랙탈 표면을 향한 이온/원자 확산의 속도론에 대하여 다루었다. 우선 프랙탈 기하학의 기본 개념에 대하여 설명하였고, 이를 바탕으로 이온/원자의 확산 현상과 관련하여 다양한 전기적 입력하에서 전극 표면의 프랙탈 특성에 기인하는 특수한 반응 양상이 설명되었다 Chronoamperometry, chronopotentiometry및 linear sweep/cyclic voltammetry 실험시에 각각 관찰되는, 전극의 프랙탈 차원이 포함된 일 반화된 Cottrell, Sand 및 Randles-Sevcik 관계를 이론적으로 유도하였고, 그 의미에 대하여 설명하였다

• Nuclear Engineering and Technology
• /
• 제49권3호
• /
• pp.581-591
• /
• 2017

Influences of hold time and stress ratio on cyclic creep properties of Grade 91 steel were systemically investigated using a wide range of cyclic creep tests, which were performed with hold times (HTs) of 1 minute, 3 minutes, 5 minutes, 10 minutes, 20 minutes, and 30 minutes and stress ratios (R) of 0.5, 0.8, 0.85, 0.90, and 0.95 under tension loading cycles at $600^{\circ}C$. Under the influence of HT, the rupture time increased to HT = 5 minutes at R = 0.90 and R = 0.95, but there was no influence at R = 0.50, 0.80, and 0.85. The creep rate was constant regardless of an increase in the HT, except for the case of HT = 5 minutes at R = 0.90 and R = 0.95. Under the influence of stress ratio, the rupture time increased with an increase in the stress ratio, but the creep rate decreased. The cyclic creep led to a reduction in the rupture time and an acceleration in the creep rate compared with the case of monotonic creep. Cyclic creep was found to depend dominantly on the stress ratio rather than on the HT. Fracture surfaces displayed transgranular fractures resulting from microvoid coalescence, and the amount of microvoids increased with an increase in the stress ratio. Enhanced coarsening of the precipitates in the cyclic creep test specimens was found under all conditions.