• Journal of applied mathematics & informatics
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• v.32 no.1_2
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• pp.75-82
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• 2014

In this paper, we consider the periodic boundary value problem with sign changing nonlinearity $$u^{{\prime}{\prime}{\prime}}+{\rho}^3u=f(t,u),\;t{\in}[0,2{\pi}]$$, subject to the boundary value conditions: $$u^{(i)}(0)=u^{(i)}(2{\pi}),\;i=0,1,2$$, where ${\rho}{\in}(o,{\frac{1}{\sqrt{3}}})$ is a positive constant and f(t, u) is a continuous function. Using Leggett-Williams fixed point theorem, we provide sufficient conditions for the existence of at least three positive solutions to the above boundary value problem. The interesting point is the nonlinear term f may change sign.

• Honam Mathematical Journal
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• v.32 no.3
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• pp.525-536
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• 2010

Let $X_1,X_2,\cdots$ be identically distributed $\rho$-mixing random variables with mean zeros and positive finite variances. In this paper, we prove $$\array{\lim\\{\in}\downarrow0}{\in}^2 \sum\limits_{n=3}^\infty\frac{1}{nlogn}P({\mid}S_n\mid\geq\in\sqrt{nloglogn}=1$$, $$\array{\lim\\{\in}\downarrow0}{\in}^2 \sum\limits_{n=3}^\infty\frac{1}{nlogn}P(M_n\geq\in\sqrt{nloglogn}=2 \sum\limits_{k=0}^\infty\frac{(-1)^k}{(2k+1)^2}$$ where $S_n=X_1+\cdots+X_n,\;M_n=max_{1{\leq}k{\leq}n}{\mid}S_k{\mid}$ and $\sigma^2=EX_1^2+ 2\sum\limits{^{\infty}_{i=2}}E(X_1,X_i)=1$.

• Honam Mathematical Journal
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• v.32 no.3
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• pp.441-451
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• 2010

In this paper we evaluate the analogue of Wiener integral ${\int\limits}_{C[0,t]}x(t_1){\cdots}x(t_n)d\omega_\rho(x)$ where 0 = $t_0$ < $t_1$ $\cdots$ < $t_n$ $\leq$ t and the Paley-Wiener-Zygmund integral ${\int\limits}_{C[0,t]}$ exp $({\int\limits}_0^t h(s)\tilde{d}x(s))d\omega_\rho(x)$ is the analogue of Wiener measure space.

• Bulletin of the Korean Chemical Society
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• v.35 no.9
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• pp.2797-2802
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• 2014

Nucleophilic substitution reactions of Y-aryl methyl (8) and Y-aryl propyl (10) chlorothiophosphates with substituted anilines and deuterated anilines are investigated kinetically in acetonitrile at $55.0^{\circ}C$. A concerted mechanism is proposed for 8 based on the negative ${\rho}_{XY}$ (= -0.23) value, while a stepwise mechanism with a rate-limiting leaving group departure from the intermediate is proposed for 10 based on the positive ${\rho}_{XY}$ (= +0.68) value. The deuterium kinetic isotope effects (DKIEs; $k_H/k_D$) are 0.89-1.28 and 0.62-1.20 with 8 and 10, respectively. Primary normal and secondary inverse DKIEs are rationalized by a frontside attack involving hydrogen bonded, four-center-type transition state and backside attack involving in-line-type transition state, respectively.

• Journal of the Chungcheong Mathematical Society
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• v.20 no.4
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• pp.367-373
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• 2007

For a unital *-subalgebra of the space $\mathcal{L}^a(X)$ of all adjointable maps on a Hilbert $\mathcal{B}$-module X with a $C^*$-algebra $\mathcal{B}$, we study unitary operator (in such algebra)-valued multiplier ${\sigma}$ on a normal, generating subsemigroup S of a group G with its extension to G. A dilation of a projective isometric ${\sigma}$-representation of S is established as a projective unitary ${\rho}$-representation of G for a suitable unitary operator (in some algebra)-valued multiplier ${\rho}$ associated with the multiplier ${\sigma}$ which is explicitly constructed.

• Transactions of the KSME C: Technology and Education
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• v.4 no.1
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• pp.11-18
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• 2016

Under the Renewable Heat Obligation (RHO) public buildings in the Republic of Korea larger than $10,000m^2$ must achieve an 11% overall reduction to thermal energy consumption. Well intended solutions have been proposed. However, not all option is evaluated on the same basis, potentially resulting in incomplete or sub-optimal solutions. What's more once projects are implemented, there are inconsistencies in the methods used to measure and evaluate operating performance of the post-retrofit case. The RETScreen decision tools and methodology can be used by decision makers, policy developers, architects, engineers and community leaders to evaluate and select the most effective solutions for Korea's RHO needs.

• Proceedings of the Korea Concrete Institute Conference
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• 1999.10a
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• pp.589-592
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• 1999

This paper is experimental study on the flexural strength and ductility capacity of reinforced high-strength concrete beams using fly ash artificial lightweight concrete beams and five reinforced high-strength normal concrete beams with different tensile reinforcement ratio were tested to investigate their behavior. Test result show that the ratio of flexural strength between experimetal results and those by ACI code decrease as the compressive strength of concrete increase. Also, The reinforced concrete beams behave more brittly than those with equal reinforcement ratio($\rho$/$\rho$b) as the compressive strength of concrete increase.

• Communications for Statistical Applications and Methods
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• v.5 no.2
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• pp.539-557
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• 1998

This article is concerned with the problem of estimating the mean of a one-parameter exponential family through sequential sampling in three stages under quadratic error loss. This more general framework differs from those considered by Hall (1981) and others. The differences are : (i) the estimator and the final stage sample size are dependent; and (ii) second order approximation of a continuously differentiable function of the final stage sample size permits evaluation of the asymptotic regret through higher order moments. In particular, the asymptotic regret can be expressed as a function of both the skewness $\rho$ and the kurtosis $\beta$ of the underlying distribution. The conditions on $\rho$ and $\beta$ for which negative regret is expected are discussed. Further results concerning the stopping variable N are also presented. We also supplement our theoretical findings wish simulation results to provide a feel for the triple sampling procedure presented in this study.

• Proceedings of the Korea Concrete Institute Conference
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• 1998.04b
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• pp.513-518
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• 1998

In general, flexural strength and ductility of reinforced concrete beam with stirrup depend on the compressive strength of concrete and longitudinal steel ratio. In this study, nine reinforced high strength lightweight concrete beams and three reinforced normalweight concrete beams with stirrup were tested to investigate their behavior and to determine their ultimate moment capacity. The variable were strength of concrete (400, 500kg/$\textrm{cm}^2$) and the ratio of tensile steel content to the ratio of the balanced steel content(0.22<$\rho$/$$\rho$_b$<0.56). Test results are presented in terms of load-deflection behavior, ductility index, and cracking patterns.

• Biotechnology and Bioprocess Engineering:BBE
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• v.9 no.4
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• pp.323-325
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• 2004

To model the behavior of expanded beds with aqueous feed streams containing different amounts of glycerol, we previously developed a modified Stokes expression that correlates the terminal settling velocity of a particle of a solution with the properties of the particle (particle diameter and density) and the solution (density and viscosity). Two empirical parameters, the effective diameter of the poly-disperse resins for protein adsorption and an exponent of non-unity for $(\rho_{P}-\rho)/\mu$ term, are introduced in the modified Stokes expression. We applied the same type of the modified Stokes expression in combination with the Richardson-Zaki correlation to the published results [1], and found that the expansions of the beds with feed streams containing different amounts of E. coli homogenates can also be successfully described.