• Review of Culture and Economy
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• v.20 no.1
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• pp.3-20
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• 2017

This study proposes that the cultural corporation can be more profitable by adopting the 'Buy-One Give-One' Business Model (BOGO BM) under certain conditions. Specifically, the conditions are that 1) consumers' utility for donating is high enough and 2) the production cost is low enough due to economies of scale or process innovation from employee's intrinsic motivation. We adopt a mathematical model where the demand function is a simple linear function and two companies compete with each other by choosing their quantity of output (the Cournot model). Specifically, we investigate the profitability of the BOGO BM in four situations: 1) a monopolist enjoying reduced cost due to process innovation from employee's intrinsic motivation, 2) a monopolist enjoying reduced cost due to economies of scale, 3) the duopoly with BOGO BM and a general company, 4) the duopoly with two BOGO BM companies. In each situation, BOGO BM can be more profitable than other general companies can under certain conditions.

• Journal of the Chungcheong Mathematical Society
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• v.18 no.2
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• pp.117-129
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• 2005

We give a generalization of bilateral mock theta functions of order eight and show that they are $F_q$-functions. We also give an integral representation for these functions. We give a relation between mock theta functions of the first set and bilateral mock theta functions of the second set.

• Korean Architects
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• s.524
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• pp.15-15
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• 2012

• Bulletin of the Korean Chemical Society
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• v.20 no.4
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• pp.422-426
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• 1999

The Grignard reactions of bis(chloromethyl)dimethylsilane (1) with trimethylchlorosilane (2) in THF give both the intermolecular C-Si coupling and intramolecular C-C coupling products. At beginning stage, 1 reacts with Mg to give the mono-Grignard reagent ClCH2Me2SiCH2MgCl (1) which undergoes the C-Si coupling reaction to give MC2Si(CH2SiMe3)2 3, or C-C coupling to a mixture of formula Me3SiCH2(SiMe2CH2CH2)nR1 (n = 1, 2, 3, ..; 4a, R1I = H: 4b, R1 = SiMe3). In the reaction, two reaction pathways are involved: a) Ⅰ reacts with 2 to give Me3SiCH2SiMe2CH2Cl 6 which further reacts with Mg to afford a Me2SiCH2Mel-SiCH2MgCl (Ⅱ) or b) I cyclizes intramolecularly to a silacyclopropane intermediate A, which undergoes a ring-opening polymerization by the nucleophilic attack of the intermediates I or Ⅱ, followed by the termination reaction with H2O and 2, to give 4a and 4b, respectively. As the mole ratio of 2/1 increased from 2 to 16 folds, the formation of product 3 increased from 16% to 47% while the formation of polymeric products 4 was reduced from 60% to 40%. The intermolecular C-Si coupling reaction of the pathway a becomes more favorable than the intramolecular C-C coupling reaction of the pathways b at the higher mole ratio of 2/1.

• Bulletin of the Korean Mathematical Society
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• v.34 no.3
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• pp.421-436
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• 1997

In this paper we first give a simple proof of the analytic characterization theorems of the operator symbols by using the characterization theorem for white noise functionals. We next give a criterion for the convergence of operators on white noise functionals in terms of their symbols and then use this result to give a proof for the Fock expansion theorem of operators on white noise functionals.

• Proceedings of the Korea Concrete Institute Conference
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• 1995.04a
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• pp.355-359
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• 1995

In this paper, the possibility of interferometric shows very good linearity to the strain. Fiber optic sensors have various merits for health monitoring systems. They are very small in diamerter. So, they don't give any disturbance in strength to the structures, Optical fiber sensors are innert to the electro-magnetic field. Therefore, fiber optic sensors give us a good solution to the electro-magnetic field. Therefore, fiber optic sensors give us a good solution to the maintainance systems of the structures, which are exposed to the electric fields, such as bridges, dams and buildings.

• Bulletin of the Korean Mathematical Society
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• v.50 no.4
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• pp.1243-1259
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• 2013

In this paper, we study the root system of rank 2 hyperbolic Kac-Moody algebras. We give some sufficient conditions for the existence of imaginary roots of square length $-2k(k{\in}\mathbb{Z}_{>0}$. We also give several relations between the integral points on the hyperbola $\mathfrak{h}$ to show that the value of the symmetric bilinear form of any two integral points depends only on the number of integral points between them. We also give some generalizations of Binet formula and Catalan's identity.

• Communications of the Korean Mathematical Society
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• v.38 no.2
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• pp.589-598
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• 2023

Magnetic curves are the trajectories of charged particals which are influenced by magnetic fields and they satisfy the Lorentz equation. It is important to find relationships between magnetic curves and other special curves. This paper is a study of magnetic curves and this kind of relationships. We give the relationship between β-magnetic curves and Mannheim, Bertrand, involute-evolute curves and we give some geometric properties about them. Then, we study this subject for γ-magnetic curves. Finally, we give an evaluation of what we did.

• Journal of Institute of Control, Robotics and Systems
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• v.9 no.11
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• pp.861-867
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• 2003

We propose a sliding surface design method for linear systems with mismatched uncertainties in the state space model. In terms of LMIs, we derive a necessary and sufficient condition for the existence of a linear sliding surface such that the reduced-order equivalent sliding mode dynamics restricted to the linear sliding surface is not only stable but completely invariant to mismatched uncertainties. We give an explicit formula of all such linear switching surfaces in terms of solution matrices to the LMI existence condition. We also give a switching feedback control law, together with a design algorithm. Additionally, we give some hints for designing linear switching surfaces guaranteeing pole clustering constraints or linear quadratic performance bound constraints. Finally, we give a design example in order to show the effectiveness of the proposed methodology.

• Journal of Institute of Control, Robotics and Systems
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• v.9 no.8
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• pp.616-622
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• 2003

This paper deals with the problem of estimating the asymptotic stability region(ASR) of uncertain variable structure systems with bounded controllers. Using linear matrix inequalities(LMIs) we estimate the ASR and show the exponential stability of the closed-loop control system in the estimated ASR. We give a simple LMI-based algorithm to get estimates of the ASR. We also give a synthesis algorithm to design a switching surface which will make the estimated ASR big. Finally, we give numerical examples in order to show that our method can give better results than the previous ones for a certain class of uncertain variable structure systems with bounded controllers.