• Journal of applied mathematics & informatics
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• v.27 no.5_6
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• pp.1033-1047
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• 2009

In this paper, we consider a m-type risk model with Markov-modulated premium rate. A integral equation for the conditional ruin probability is obtained. A recursive inequality for the ruin probability with the stationary initial distribution and the upper bound for the ruin probability with no initial reserve are given. A system of Laplace transforms of non-ruin probabilities, given the initial environment state, is established from a system of integro-differential equations. In the two-state model, explicit formulas for non-ruin probabilities are obtained when the initial reserve is zero or when both claim size distributions belong to the $K_n$-family, n $\in$ $N^+$ One example is given with claim sizes that have exponential distributions.

• Journal of applied mathematics & informatics
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• v.35 no.3_4
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• pp.303-311
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• 2017

In this paper we define (p, q)-analogue of Euler zeta function. In order to define (p, q)-analogue of Euler zeta function, we introduce the (p, q)-analogue of Euler numbers and polynomials by generalizing the Euler numbers and polynomials, Carlitz's type q-Euler numbers and polynomials. We also give some interesting properties, explicit formulas, a connection with (p, q)-analogue of Euler numbers and polynomials. Finally, we investigate the zeros of the (p, q)-analogue of Euler polynomials by using computer.

• Journal of the Korean Mathematical Society
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• v.43 no.6
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• pp.1339-1355
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• 2006

This paper develops in detail the differential geometry of ruled surfaces from two perspectives, and presents the underlying relations which unite them. Both scalar and dual curvature functions which define the shape of a ruled surface are derived. Explicit formulas are presented for the computation of these functions in both formulations of the differential geometry of ruled surfaces. Also presented is a detailed analysis of the ruled surface which characterizes the shape of a general ruled surface in the same way that osculating circle characterizes locally the shape of a non-null Lorentzian curve.

• Journal of the Korean Mathematical Society
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• v.45 no.5
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• pp.1483-1503
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• 2008

Let f : M ${\rightarrow}$ M be a self-map on the Klein bottle M. We compute the Lefschetz number and the Nielsen number of f by using the infra-nilmanifold structure of the Klein bottle and the averaging formulas for the Lefschetz numbers and the Nielsen numbers of maps on infra-nilmanifolds. For each positive integer n, we provide an explicit algorithm for a complete computation of the Nielsen type numbers $NP_n(f)$ and $N{\Phi}_{n}(f)\;of\;f^{n}$.

• Communications of the Korean Mathematical Society
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• v.33 no.4
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• pp.1055-1073
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• 2018

In this paper, we define an alternative q-analogue of the $Ruci{\acute{n}}ski$-Voigt numbers. We obtain fundamental combinatorial properties such as recurrence relations, generating functions and explicit formulas which are shown to be q-deformations of similar properties for the $Ruci{\acute{n}}ski$-Voigt numbers, and are generalizations of the results obtained by other authors. A combinatorial interpretation in the context of A-tableaux is also given where convolution-type identities are consequently obtained. Lastly, we establish the matrix decompositions of the $Ruci{\acute{n}}ski$-Voigt and the q-$Ruci{\acute{n}}ski$-Voigt numbers.

• Journal of Institute of Control, Robotics and Systems
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• v.14 no.3
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• pp.232-235
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• 2008

This paper presents an LMI-based method to design reduced order observers by which we can substitute full order sliding mode observers for a class of uncertain time-delay systems. We show that a reduced order observer can be constructed as long as the uncertain system satisfies the previous LMI existence conditions of a full order sliding mode observer. And we give explicit formulas of the reduced order observer gain matrices. Finally, we give a simple LMI-based design algorithm, together with a numerical design example.

• Smart Structures and Systems
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• v.11 no.4
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• pp.387-410
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• 2013

This paper deals with the damage assessment for isolators of base-isolated building systems considering the torsion-coupling (TC) effect by establishing damage indices. The damage indices can indicate the reduction in lateral stiffness of the isolator story as explicit formulas in terms of modal parameters. In addition, the damage location, expressed in terms of the estimated damage index and eccentricities before and after damage, is also presented. Numerical analysis shows that the proposed algorithms are applicable for general base-isolated multi-story TC buildings. A procedure from the analysis of seismic response to the implementation of damage indices is demonstrated by using a numerical case. A system identification technique is employed to extract modal parameters from seismic responses of a building. Results show that the proposed indices are capable of detecting the occurrence of damage and preliminarily estimating the location of damaged isolator.

• Industrial Engineering and Management Systems
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• v.14 no.2
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• pp.175-182
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• 2015

The recent manufacturing industry in Japan has found it difficult to transfer skills from trained workers to inexperienced workers because the former ages and then retires. This is a particular problem for lathe process, as this operation requires explicit and tacit knowledge, and defining the skills clearly in a manual is difficult. This study aims to develop a training system for lathe operation by using a simulator; this includes formulas that help define the relationship between the speed of tool feed and cutting sound/shape of chips which were proposed in the preceding study. The developed training system is verified the effectiveness.

• 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.37 no.3_4
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• pp.295-305
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• 2019

In the present paper, we introduce (p, q)-Frobenius-Genocchi numbers and polynomials and investigate some basic identities and properties for these polynomials and numbers including addition theorems, difference equations, derivative properties, recurrence relations and so on. Then, we provide integral representations, implicit and explicit formulas and relations for these polynomials and numbers. We consider some relationships for (p, q)-Frobenius-Genocchi polynomials of order ${\alpha}$ associated with (p, q)-Bernoulli polynomials, (p, q)-Euler polynomials and (p, q)-Genocchi polynomials.