• Bulletin of the Korean Mathematical Society
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• v.58 no.1
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• pp.71-111
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• 2021

We consider the boundary value problem for the deflection of a finite beam on an elastic foundation subject to vertical loading. We construct a one-to-one correspondence �� from the set of equivalent well-posed two-point boundary conditions to gl(4, ℂ). Using ��, we derive eigenconditions for the integral operator ��M for each well-posed two-point boundary condition represented by M ∈ gl(4, 8, ℂ). Special features of our eigenconditions include; (1) they isolate the effect of the boundary condition M on Spec ��M, (2) they connect Spec ��M to Spec ����,α,k whose structure has been well understood. Using our eigenconditions, we show that, for each nonzero real λ ∉ Spec ����,α,k, there exists a real well-posed boundary condition M such that λ ∈ Spec ��M. This in particular shows that the integral operators ��M, arising from well-posed boundary conditions, may not be positive nor contractive in general, as opposed to ����,α,k.

• Bulletin of the Korean Mathematical Society
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• v.50 no.6
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• pp.1973-1979
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• 2013

The main purpose of this paper is to give the Wintner theorem in unital complete random normed algebras which is a random generalization of the classical Wintner theorem in Banach algebras. As an application of the Wintner theorem in unital complete random normed algebras, we also obtain that the identity operator on a complete random normed module is not a commutator.

• Korean Journal of Mathematics
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• v.28 no.2
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• pp.223-240
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• 2020

The paper is concerned with periodic linear evolution equations of the form x"(t) = A(t)x(t)+f(t), where A(t) is a family of (unbounded) linear operators in a Banach space X, strongly and periodically depending on t, f is an almost (or asymptotic) almost periodic function. We study conditions for this equation to have almost periodic solutions on ℝ as well as to have asymptotic almost periodic solutions on ℝ⁺. We convert the second order equation under consideration into a first order equation to use the spectral theory of functions as well as recent methods of study. We obtain new conditions that are stated in terms of the spectrum of the monodromy operator associated with the first order equation and the frequencies of the forcing term f.

• The Pure and Applied Mathematics
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• v.10 no.4
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• pp.217-223
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• 2003

Let $\cal{K}$ be the extension Hilbert space of a Hilbert space $\cal{H}$ and let $\Phi$ be the faithful $\ast$-representation of $\cal{B}(\cal{H})$ on $\cal{k}$. In this paper, we show that if T is an irreducible ${\omega}-hyponormal$ operators such that $ker(T)\;{\subset}\;ker(T^{*})$ and $T^{*}T\;-\;TT^{\ast}$ is compact, then $\sigma_{e}(T)\;=\;\sigma_{e}(\Phi(T))$.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.6 no.12
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• pp.3133-3151
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• 2012

The optimal price strategy selection of two bounded rational cognitive mobile virtual network operators (MVNOs) in a duopoly spectrum sharing market is investigated. The bounded rational operators dynamically compete to sell the leased spectrum to secondary users in order to maximize their profits. Meanwhile, the secondary users' heterogeneous preferences to rate and price are taken into consideration. The evolutionary game theory (EGT) is employed to model the dynamic price strategy selection of the MVNOs taking into account the response of the secondary users. The behavior dynamics and the evolutionary stable strategy (ESS) of the operators are derived via replicated dynamics. Furthermore, a reward and punishment mechanism is developed to optimize the performance of the operators. Numerical results show that the proposed evolutionary algorithm is convergent to the ESS, and the incentive mechanism increases the profits of the operators. It may provide some insight about the optimal price strategy selection for MVNOs in the next generation cognitive wireless networks.

• Bulletin of the Korean Chemical Society
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• v.14 no.1
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• pp.21-29
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• 1993

For the study of relaxation processes in complex spin system, a general master equation, which can be used to simulate a vast range of pulse experiments, has been formulated using the Liouville representation of quantum mechanics. The state of a nonequilibrium spin system in magnetic field is described by a density vector in Liouville space and the time evolution of the system is followed by the application of a linear master operator to the density vector in this Liouville space. In this master equation the nuclear spin relaxation due to intramolecular dipolar interaction or randomly fluctuating field interaction is explicitly implemented as a relaxation supermatrix for a strong coupled two-spin (1/2) system. The whole dynamic information inherent in the spin system is thus contained in the density vector and the master operator. The radiofrequency pulses are applied in the same space by corresponding unitary rotational supertransformations of the density vector. If the resulting FID is analytically Fourier transformed, it is possible to represent the final nonstationary spectrum using a frequency dependent spectral vector and intensity determining shape vector. The overall algorithm including relaxation interactions is then translated into an ANSIFORTRAN computer program, which can simulate a variety of two dimensional spectra. Furthermore a new strategy is tested by simulation of multiple quantum signals to differentiate the two relaxation interaction types.

• Journal of Environmental Impact Assessment
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• v.13 no.1
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• pp.1-8
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• 2004

A wide spectrum of risk assessments including qualitative and quantitative approaches and the analyses of its consequence were performed for an environmentally sensitive object such as incineration facility. To find out the major risk concerns, HAZOP(Hazard and Operability) were performed. Then, the frequency of hazardous gas release scenarios was calculated. Finally consequence analyses were performed for the gas release scenarios. On the basis of analyses through evaluation, a more innovative way for making a better control system or the enhancement of operation procedure was given. The results from these analyses would act as a substantial benefits for the incineration facility operator, and giving some measured information for the neighbors and the people involved.

• Bulletin of the Korean Chemical Society
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• v.32 no.2
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• pp.439-443
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• 2011

Using the projection operator technique, a reduced density matrix theory for linear absorption spectrum of energy transfer systems is developed for the theoretical absorption line shape of the systems with non-Condon transitions. As an application, we considered a model system of OH vibrations of water. In the present model calculation, the OH vibration modes are coupled to each other via intra-molecular coupling mechanism while their intermolecular couplings are turned off. The time-correlation functions appearing in the formulation are calculated from a mixed quantum/classical mechanics method. The present theory is successful in reproducing the exact absorption line shape. Also the present theory was improved from an existing approximate theory, time-averaged approximation approach.

• Journal of the Korean Magnetic Resonance Society
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• v.2 no.1
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• pp.33-40
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• 1998

The cross peak intensities versus mixing times of 2D NOESY spectrum for a corepressor L-trp were simulated for the case of a ligand exchanging between free (AX) and bound (A'X') forms in protein/DNA complex. The direct NOE (I(AX)) of the free ligand exhibited a small positive intensity indicative of the strong dominant influence of the bound ligand. The exchange-mediated NOE peak (I(AX')) was very sensitive to corepressor exchange. However, both diagonal (I(A'A')) and direct NOE (I(A'X')) intensities of the bound ligand were not affected much at initial stage. Both peaks were severely influenced by exchange at mixing times of greater than 100 ms. In conclusion, since the NOE intensity is a function of exchange rate, the exchange effect should be considered to properly extract accurate distance information for bound ligand in the presence of conformational exchange.

• Communications of the Korean Mathematical Society
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• v.13 no.1
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• pp.77-84
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• 1998

In this note we show that if $T_{\varphi}$ is a Toeplitz operator with quasicontinuous symbol $\varphi$, if $\omega$ is an open set containing the spectrum $\sigma(T_\varphi)$, and if $H(\omega)$ denotes the set of analytic fuctions defined on $\omege$, then the following statements are equivalent: (a) $T_\varphi$ is semi-quasitriangular. (b) Browder's theorem holds for $f(T_\varphi)$ for every $f \in H(\omega)$. (c) Weyl's theorem holds for $f(T_\varphi)$ for every $f \in H(\omega)$. (d) $\sigma(T_{f \circ \varphi}) = f(\sigma(T_varphi))$ for every $f \in H(\omega)$.