• Journal of the Korean Mathematical Society
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• v.56 no.6
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• pp.1599-1611
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• 2019

Let $m,n{\in}{\mathbb{N}}$. We represent the additive subgroups of the ring ${\mathbb{Z}}_m{\times}{\mathbb{Z}}_n$, which are also (unital) subrings, and deduce explicit formulas for $N^{(s)}(m,n)$ and $N^{(us)}(m,n)$, denoting the number of subrings of the ring ${\mathbb{Z}}_m{\times}{\mathbb{Z}}_n$ and its unital subrings, respectively. We show that the functions $(m,n){\mapsto}N^{u,s}(m,n)$ and $(m,n){\mapsto}N^{(us)}(m,n)$ are multiplicative, viewed as functions of two variables, and their Dirichlet series can be expressed in terms of the Riemann zeta function. We also establish an asymptotic formula for the sum $\sum_{m,n{\leq}x}N^{(s)}(m,n)$, the error term of which is closely related to the Dirichlet divisor problem.

• Journal of applied mathematics & informatics
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• v.41 no.1
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• pp.33-50
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• 2023

Foreign exchange options are derivative financial instruments that can exchange one currency for another at a prescribed exchange rate on a specified date. In this study, we examine the analytic formulas for vulnerable foreign exchange options based on multi-scale stochastic volatility driven by two diffusion processes: a fast mean-reverting process and a slow mean-reverting process. In particular, we take advantage of the asymptotic analysis and the technique of the Mellin transform on the partial differential equation (PDE) with respect to the option price, to derive approximated prices that are combined with a leading order price and two correction term prices. To verify the price accuracy of the approximated solutions, we utilize the Monte Carlo method. Furthermore, in the numerical experiments, we investigate the behaviors of the vulnerable foreign exchange options prices in terms of model parameters and the sensitivities of the stochastic volatility factors to the option price.

• Journal of applied mathematics & informatics
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• v.7 no.2
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• pp.409-438
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• 2000

In this paper we develop a new procedure to control stepsize for Runge- Kutta methods applied to both ordinary differential equations and semi-explicit index 1 differential-algebraic equation In contrast to the standard approach, the error control mechanism presented here is based on monitoring and controlling both the local and global errors of Runge- Kutta formulas. As a result, Runge-Kutta methods with the local-global stepsize control solve differential of differential-algebraic equations with any prescribe accuracy (up to round-off errors)

• Journal of the Korean Mathematical Society
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• v.39 no.2
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• pp.205-219
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• 2002

We deride formulas for the expected values $\mu$(n) of the independent domination numbers of a random planted plane tree and a random trivalent tree with n vertices, respectively, and we determine the asymptotic behavior of $\mu$(n) as n goes to infinity.

• Journal of the Korean Mathematical Society
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• v.32 no.4
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• pp.713-724
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• 1995

In 1954 Frame, Robinson and Thrall [5] gave the hook formula for the number of standard Young tableaux of a given shape. Since then many proofs for the hook formula have been given using various methods. See [9] forprobabilistic method and see [6] or [12] for combinatorial ones. Regev [10] has given asymptotic values for these numbers and Gouyou-Beauchamps [8] gave exact formulas for the number of standard Young tableaux having n cells and at most k rows in the cases k = 4 and k = 5.

• Journal of the Korean Mathematical Society
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• v.49 no.1
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• pp.49-67
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• 2012

In this paper we give asymptotic formulas for the number of ${\ell}$-cyclic extensions of the rational function field $k=\mathbb{F}_q(T)$ with prescribe ${\ell}$-class numbers inside some cyclotomic function fields, and density results for ${\ell}$-cyclic extensions of k with certain properties on the ideal class groups.

• Journal of the Korean Mathematical Society
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• v.56 no.3
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• pp.669-688
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• 2019

In this paper, we introduce the notion of the generalized symphonic map with respect to the functional ${\Phi}_{\varepsilon}$. Then we use the stress-energy tensor to obtain some monotonicity formulas and some Liouville results for these maps. We also obtain some Liouville type results by assuming some conditions on the asymptotic behavior of the maps at infinity.

• Bulletin of the Korean Mathematical Society
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• v.61 no.1
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• pp.65-81
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• 2024

In this paper, we announce that the strategy of comparing the complex moments of L(1, χ_u) to that of a random Euler product L(1, 𝕏) is also valid in even characteristic case. We give an asymptotic formulas for the complex moments of L(1, χ_u) in a large uniform range. We also give Ω-results for the extreme values of L(1, χ_u).

• Smart Structures and Systems
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• v.23 no.6
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• pp.537-551
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• 2019

In this paper, a method for analyzing the damping performance of stay cables incorporating magnetorheological (MR) dampers in the passive control mode is developed taking into account the cable sag and inclination, the damper coefficient, stiffness and mass, and the stiffness of damper support. Both numerical and asymptotic solutions are obtained from complex modal analysis. With the asymptotic solution, analytical formulas that evaluate the equivalent damping ratio of the sagged cable-damper system in consideration of all the above parameters are derived. The main thrust of the present study is to develop an general design formula and a universal curve for the optimal design of MR dampers for adjustable passive control of sagged cables. Two sag-affecting coefficients are derived to reflect the effects of cable sag on the maximum attainable damping ratio and the optimal damper coefficient. For the cable configurations commonly used in cable-stayed bridges, the sag-affecting coefficients are directly expressed in terms of the sag-extensibility parameter to facilitate the control design. A case study on adjustable passive vibration control of the longest cable (536 m) on Stonecutters Bridge is carried out to demonstrate the influence of the sag for the damper design, and to figure out the necessity of adjustability of damper coefficients for achieving maximum damping ratio for different vibration modes.

• Journal of applied mathematics & informatics
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• v.39 no.3_4
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• pp.381-403
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• 2021

Consider the three-dimensional system of difference equations $x_{n+1}=\frac{{\prod_{j=0}^{k}}z_n-3j}{{\prod_{j=1}^{k}}x_n-(3j-1)\;\(a_n+b_n{\prod_{j=0}^{k}}z_n-3j\)}$, $y_{n+1}=\frac{{\prod_{j=0}^{k}}x_n-3j}{{\prod_{j=1}^{k}}y_n-(3j-1)\;\(c_n+d_n{\prod_{j=0}^{k}}x_n-3j\)}$, $z_{n+1}=\frac{{\prod_{j=0}^{k}}y_n-3j}{{\prod_{j=1}^{k}}z_n-(3j-1)\;\(e_n+f_n{\prod_{j=0}^{k}}y_n-3j\)}$, n ∈ ℕ₀, where k ∈ ℕ₀, the sequences $(a_n)_{n{\in}{\mathbb{N}}_0$, $(b_n)_{n{\in}{\mathbb{N}}_0$, $(c_n)_{n{\in}{\mathbb{N}}_0$, $(d_n)_{n{\in}{\mathbb{N}}_0$, $(e_n)_{n{\in}{\mathbb{N}}_0$, $(f_n)_{n{\in}{\mathbb{N}}_0$ and the initial values x_-3k, x_-3k+1, …, x₀, y_-3k, y_-3k+1, …, y₀, z_-3k, z_-3k+1, …, z₀ are real numbers. In this work, we give explicit formulas for the well defined solutions of the above system. Also, the forbidden set of solution of the system is found. For the constant case, a result on the existence of periodic solutions is provided and the asymptotic behavior of the solutions is investigated in detail.