• Journal of Internet Computing and Services
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• v.15 no.3
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• pp.91-100
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• 2014

While IT security investment of organizations has been increased, the amount of the monetary loss of organizations caused by IT security breaches did not decrease as much as their expectation. Also, from surveys, it was discovered that the poor usage of their security budget thwarted the improvement of the organization's security level. In this paper, to resolve the poor usage of security budget of organizations, we propose a comprehensive economic model for determining the optimal amount of investment in security solutions, including the proactive security solutions(PSSs) and the reactive security solutions(RSSs). Using the proposed analytical model under different parameters of security solutions, we show the optimal condition to maximize the expected net benefits from IT security investment of organizations. Also, we verify the common belief that the optimal level of investment in security solutions is an increasing function of vulnerability. Through simulations, we find the optimal level of IT security investment, given parameters of different characteristics of security solutions.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.12 no.4
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• pp.201-202
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• 2008

Because of the importance of suction or injection in the fields of aerodynamics, space science and many other industrial applications, our present study is motivated. The effect of natural convection on MHD flow past a vertical plate with suction or injection is studied. We have tried to solve the dimensionless governing equations by using finite difference scheme. To ensure the validity of our numerical solutions, we have compared our numerical solutions for temperature and velocity for the case of suction and injection for unit Prandtl number with the available exact solutions in the literature. The corresponding codes were written in Mathematica 5.0 for calculating numerical solutions for temperature and velocity and the comparison between the exact and numerical solutions. For the purpose of discussing the results some numerical calculations are carried out for non-dimensional temperature T, velocity u, skin friction ${\tau}$ and the Nusselt number $N_u$, by making use of it, the rate of heat transfer is studied.

• Journal of Industrial Technology
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• v.20 no.A
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• pp.185-194
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• 2000

In this work we measured the total pressure of the aqueous solutions and the methanol-water solutions dissolved with inorganic salts, at $25^{\circ}C$. In organic electrolytes used in this work were $K_2SO_4$ and $(NH_4)_2SO_4$. Using the measured vapour pressures the activity coefficient of solvents and the mean ionic activity coefficient were obtained through thermodynamic relations. The activity coefficients of solvent and the mean ionic activity coefficirnt obtained in this work were fitted with Macedo's model and Acard's model. Both two models were good agreeable to the vapor pressure and the mean ionic activity coefficient for the electroyte aqueous solutions. For electrolyte /methanol/water solutions, Macedo's model had much deviation from experimental data, while Acard's model showed a good agreement with experimental data.

• Journal of Advanced Marine Engineering and Technology
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• v.8 no.1
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• pp.100-111
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• 1984

The methods solving the 2nd order linear ordinary differential equations of the form y"+H(x)y'+G(x)y=P(x) using Fourier series are presented in this paper. These methods are applied to the differential equations of which the exact solutions are known, and the solutions by Fourier series are compared with the exact solutions. The main results obtained in these studies are summarized as follows; 1) The product and the quotient of two functions expressed in Fourier series can be expressed also in Fourier series and the relations between the Fourier coefficients of the series are obtained by multiplying term by term. 2) If the solution of the 2nd order lindar ordinary differential equation exists in a certain interval, the solution can be obtained using Fourier series and can be expressed in Fourier series. 3) The absolute errors of Fourier series solutions are generally less in the center of the interval than in the end of the interval. 4) The more terms are considered in Fourier series solutions, the less the absolute errors.rors.

• Textile Coloration and Finishing
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• v.13 no.6
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• pp.435-440
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• 2001

This study investigates the rheological properties of in-situ polymerized solutions of polyacrylonitrile(PAN) and acrylonitrile(AN) -itaconic acid(IA) in dimethyl sulfoxide(DMSO) in terms of temperature, concentration, and time. The complex viscosity and storage modulus of the solutions were generally increased with elapsing time, which is ascribable to the three-dimensional pseudostructures formed by strong inter- or Intra-molecular attractions through Polar -CN and -COOH groups. The three-dimensional pseudonetworks would lead to relation of the acrylic solutions in long term. This was more noticeable at higher temperature within the temperature range examined. In the case of 20% solutions one can not observe lower Newtonian flow region in the viscosity curve. Disappearance of lower Newtonian flow region is indicative of heterogeneity of the solution system. Casson Plot of the viscosity data revealed that 20% solutions of PAN and AN-IA copolymer in DMSO clearly demonstrated positive yield stress, ascertaining formation of pseudostructures in the solution systems.

• Textile Coloration and Finishing
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• v.13 no.6
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• pp.77-77
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• 2001

This study investigates the rheological properties of in-situ polymerized solutions of polyacrylonitrile(PAN) and acrylonitrile(AN)-itaconic acid(IA) in dimethyl sulfoxide(DMSO) in terms of temperature, concentration, and time. The complex viscosity and storage modulus of the solutions were generally increased with elapsing time, which is ascribable to the three-dimensional pseudostructures formed by strong inter- or intra-molecular attractions through Polar -CN and -COOH groups. The three-dimensional pseudonetworks would lead to gelation of the acrylic solutions in long term. This was more noticeable at higher temperature within the temperature range examined. In the case of 20% solutions one can not observe lower Newtonian flow region in the viscosity curve. Disappearance of lower Newtonian flow region is indicative of heterogeneity of the solution system. Casson Plot of the viscosity data revealed that 20% solutions of PAN and AN-IA copolymer in DMSO clearly demonstrated positive yield stress, ascertaining formation of pseudostructures in the solution systems.

• Journal of the Korean Mathematical Society
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• v.49 no.6
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• pp.1301-1321
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• 2012

In this paper we study the unique solvability of backward stochastic Volterra integral equations (BSVIEs in short), in terms of both the adapted M-solutions introduced in [19] and the adapted solutions via a new method. A general existence and uniqueness of adapted M-solutions is proved under non-Lipschitz conditions by virtue of a briefer argument than the ones in [13] and [19], which modifies and extends the results in [13] and [19] respectively. For the adapted solutions, the unique solvability of BSVIEs under more general stochastic non-Lipschitz conditions is shown, which improves and generalizes the results in [7], [14] and [15].

• Journal of the Korean Mathematical Society
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• v.57 no.6
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• pp.1573-1590
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• 2020

In this paper, we classify all solutions bounded from below to uniformly elliptic equations of second order in the form of Lu(x) = a_ij(x)D_iju(x) + b_i(x)D_iu(x) + c(x)u(x) = f(x) or Lu(x) = D_i(a_ij(x)D_ju(x)) + b_i(x)D_iu(x) + c(x)u(x) = f(x) in unbounded cylinders. After establishing that the Aleksandrov maximum principle and boundary Harnack inequality hold for bounded solutions, we show that all solutions bounded from below are linear comb_inations of solutions, which are sums of two special solutions that exponential growth at one end and exponential decay at the another end, and a bounded solution that corresponds to the inhomogeneous term f of the equation.

• Bulletin of the Korean Mathematical Society
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• v.51 no.3
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• pp.641-651
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• 2014

Because of difficulty of using Schauder's fixed point theorem to the polynomial-like iterative equation, a lots of work are contributed to the existence of solutions for the polynomial-like iterative equation on compact set. In this paper, by applying the Schauder-Tychonoff fixed point theorem we discuss monotone solutions and convex solutions of the polynomial-like iterative equation on an open set (possibly unbounded) in $\mathbb{R}^N$. More concretely, by considering a partial order in $\mathbb{R}^N$ defined by an order cone, we prove the existence of increasing and decreasing solutions of the polynomial-like iterative equation on an open set and further obtain the conditions under which the solutions are convex in the order.

• Honam Mathematical Journal
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• v.35 no.4
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• pp.683-699
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• 2013

In this paper, an improved ($\frac{G^{\prime}}{G}$)-expansion method is proposed for obtaining travelling wave solutions of nonlinear evolution equations. The proposed technique called ($\frac{F}{G}$)-expansion method is more powerful than the method ($\frac{G^{\prime}}{G}$)-expansion method. The efficiency of the method is demonstrated on a variety of nonlinear partial differential equations such as KdV equation, mKd equation and Boussinesq equations. As a result, more travelling wave solutions are obtained including not only all the known solutions but also the computation burden is greatly decreased compared with the existing method. The travelling wave solutions are expressed by the hyperbolic functions and the trigonometric functions. The result reveals that the proposed method is simple and effective, and can be used for many other nonlinear evolutions equations arising in mathematical physics.