• The Pure and Applied Mathematics
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• v.15 no.4
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• pp.393-400
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• 2008

In this paper, we investigate the following additive functional inequality (0.1) ||f(x)+f(y)+f(z)+f(w)||${\leq}$||f(x+y)+f(z+w)|| in normed modules over a $C^*$-algebra. This is applied to understand homomor-phisms in $C^*$-algebra. Moreover, we prove the generalized Hyers-Ulam stability of the functional inequality (0.2) ||f(x)+f(y)+f(z)f(w)||${\leq}$||f(x+y+z+w)||+${\theta}||x||^p||y||^p||z||^p||w||^p$ in real Banach spaces, where ${\theta}$, p are positive real numbers with $4p{\neq}1$.

• 제어로봇시스템학회:학술대회논문집
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• 2001.10a
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• pp.22.2-22
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• 2001

Recently, Reinforcement Learning (RL) methods in MDP have been extended and applied to the POMDP problems. Currently, hierarchical RL methods are widely studied. However, they have the drawback that the learning time and memories are exhausted only for keeping the hierarchical structure, though they aren´t necessary. On the other hand, our "Labeling Q-learning (LQ-learning) proposed previously, has no hierarchical structure, but adopts a characteristic internal memory mechanism. Namely, LQ-1earning agent percepts the state by pair of observation and its label, and the agent can distinguish states, which look as same, but obviously different, more exactly. So to speak, at each step t, we define a new type of perception of its environment ～ot = (ot, $\theta$t), where of is conventional observation, and $\theta$t is the label attached to the observation. Then the conventional ...

• Bulletin of the Korean Chemical Society
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• v.9 no.3
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• pp.117-121
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• 1988

The molecular interaction and geometrical optimization of Cr$(CO)_5\;and\;Ni(CO)_3$ units have been studied for phosphinidene complex by means of extended Huckel calculations. The results were compared with those of ab initio calculations and found to be in qualitative agreement. Geometrical optimization of HPCr$(CO)_5\;(1)\;and\;HPNi(CO)_3$ (2) gave the values R = 2.36 ${\AA}$, ${\theta}$ = $111.5^{\circ}$, and ${\phi}$ = $45^{\circ}$for 1, and R = 2.37 ${\AA}$, ${\theta}$= $120^{\circ}$, and ${\phi}$ = $58^{\circ}$for 2. It is found that the low rotational barriers for 1(0.46 kcal $mol^{-1}$) and 2(0.12 kcal $mol^{-1}$) would be accompanied by the free rotation, in spite of the fact that both 1 and 2 adopt staggered conformations.

• Bulletin of the Korean Chemical Society
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• v.21 no.12
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• pp.1227-1232
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• 2000

Near the conical intersection for the 1,2 $^{2}A'$ states of $H_3$ the derivative coupling vector is calculated and analyzed on the plane of internal coordinates, (U,V) or its polar coordinates $(S{\theta})$, based on the squares of the internuclear distances. It is shown that in the vicinity of the conical intersection the derivative coupling vector behaves like ${\theta}/2S$, which is responsible for the sign changes of the real-valued electronic wave function when the nuclear configuration traverses a closed path enclosing a conical intersection. The analytic property of the wave functions is studied and especially the observation of the sign change in the configuration state function (CSF) coefficients of the real-valued electronic wave functions is demonstrated.

• International Journal of Reliability and Applications
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• v.14 no.2
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• pp.79-96
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• 2013

Exponential distribution plays a key role in engineering reliability and its applications. The exponential failure model has been studied for years. This article introduces two new preliminary test estimators for the reliability function (R(t)) in complete and censored samples from the exponential model with the use of a prior estimation (${\theta}_0$) of the mean (${\theta}$). The proposed preliminary test estimators are studied and compared numerically with the existing estimators. Computer-intensive calculations for bias and relative efficiency show that for, different values of levels of significance and for varying constants involved in the proposed estimators, the proposed estimators are far better than classical and existing estimators.

• Journal of the Optical Society of Korea
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• v.15 no.1
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• pp.9-14
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• 2011

In this study, the internal structure of an optical waveguide embedded in a flexible optical circuit board is observed with a confocal microscope. In order to increase the light reflection from an internal material interface with a very small index difference, and thus enhance the signal contrast, a theta microscopy scheme has been integrated into a conventional confocal microscope, and a high NA oil-immersion lens has been used. The interface reflectivity is increased from roughly 0.0015% to 0.025% by the proposed method, and the internal structure can thus be successfully measured.

• Geomechanics and Engineering
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• v.18 no.5
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• pp.555-566
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• 2019

The purpose of this paper is to investigate the thermal effects on the behaviour reinforced-concrete beams strengthened by bonded angle-ply laminated composites laminates plate $[{\pm}{\theta}n/90m]_S$. Effects of number of $90^{\circ}$ layers and number of ${\pm}{\theta}$ layers on the distributions of interfacial stress in concrete beams reinforced with composite plates have also been studied. The present results represent a simple theoretical model to estimate shear and normal stresses. The effects the temperature, mechanical properties of the fibre orientation angle of the outer layers, the number of cross-ply layers, plate length of the strengthened beam region and adhesive layer thickness on the interfacial shear and normal stresses are investigated and discussed.

• Journal of the Korean Mathematical Society
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• v.56 no.1
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• pp.91-111
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• 2019

We give a direct proof of the sharp two-sided estimates, recently established in [4, 9], for the Dirichlet heat kernel of the fractional Laplacian with gradient perturbation in $C^{1,1}$ open sets by using Duhamel's formula. We also obtain a gradient estimate for the Dirichlet heat kernel. Our assumption on the open set is slightly weaker in that we only require D to be $C^{1,{\theta}}$ for some ${\theta}{\in}({\alpha}/2,1]$.

• The Pure and Applied Mathematics
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• v.26 no.3
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• pp.111-131
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• 2019

We introduce (CLRg) property for hybrid pair $F:X{\times}X{\rightarrow}2^X$ and $g:X{\rightarrow}X$. We also introduce joint common limit range (JCLR) property for two hybrid pairs $F,G:X{\times}X{\rightarrow}2^X$ and $f,g:X{\rightarrow}X$. We also establish some common coupled fixed point theorems for hybrid pair of mappings under generalized (${\psi},{\theta},{\varphi}$)-contraction on a noncomplete metric space, which is not partially ordered. It is to be noted that to find coupled coincidence point, we do not employ the condition of continuity of any mapping involved therein. As an application, we study the existence and uniqueness of the solution to an integral equation. We also give an example to demonstrate the degree of validity of our hypothesis. The results we obtain generalize, extend and improve several recent results in the existing literature.

• Bulletin of the Korean Mathematical Society
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• v.56 no.5
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• pp.1211-1217
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• 2019

Let $0<{\alpha}<{\infty}$ be fixed, and let $X=(X_t)_{t{\geq}0}$ be a Bessel process with dimension $0<{\theta}{\leq}1$ starting at $x{\geq}0$. In this paper, it is proved that there are positive constants A and D depending only on ${\theta}$ and ${\alpha}$ such that $$E_x\({\exp}[{\alpha}\;\max_{0{\leq}t{\leq}{\tau}}\;X_t]\){\leq}AE_x\({\exp}[D_{\tau}]\)$$ for any stopping time ${\tau}$ of X. This inequality is also shown to be sharp.