• Journal of applied mathematics & informatics
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• v.19 no.1_2
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• pp.105-125
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• 2005

Motivated by the field experimental designs in agriculture, the theory of block designs has been applied to several areas such as statistics, combinatorics, communication networks, distributed systems, cryptography, etc. An explicit formula and its fast computational algorithm for a class of symmetric balanced incomplete block designs are presented. Based on the formula and the careful investigation of the modulus multiplication table, the algorithm is developed. The computational costs of the algorithm is superior to those of the conventional ones.

• Journal of applied mathematics & informatics
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• v.24 no.1_2
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• pp.65-79
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• 2007

An optimal 3-point quadrature formula of closed type is derived. It is shown that the optimal quadrature formula has a better error bound than the well-known Simpson's rule. A corrected formula is also considered. Various error inequalities for these formulas are established. Applications in numerical integration are given.

• Bulletin of the Korean Mathematical Society
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• v.53 no.2
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• pp.487-494
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• 2016

Let p be an odd prime and c be a fixed integer with (c, p) = 1. For each integer a with $1{\leq}a{\leq}p-1$, it is clear that there exists one and only one b with $0{\leq}b{\leq}p-1$ such that $ab{\equiv}c$ mod p. Let N(c, p) denote the number of all solutions of the congruence equation $ab{\equiv}c$ mod p for $1{\leq}a$, $b{{\leq}}p-1$ in which a and $\bar{b}$ are of opposite parity, where $\bar{b}$ is defined by the congruence equation $b{\bar{b}}{\equiv}1$ mod p. The main purpose of this paper is using the mean value theorem of Dirichlet L-functions and the properties of Gauss sums to study the computational problem of one kind mean value function related to $E(c,p)=N(c,p)-{\frac{1}{2}}{\phi}(p)$, and give its an exact computational formula.

• Communications for Statistical Applications and Methods
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• v.28 no.3
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• pp.251-265
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• 2021

This paper discusses the pricing of autocallable structured product with knock-in (KI) feature using the exit probability with the Brownian Bridge technique. The explicit pricing formula of autocallable ELS derived in the existing paper handles the part including the minimum of the Brownian motion using the inclusion-exclusion principle. This has the disadvantage that the pricing formula is complicate because of the probability with minimum value and the computational volume increases dramatically as the number of autocall chances increases. To solve this problem, we applied an efficient and robust simulation method called the Brownian Bridge technique, which provides the probability of touching the predetermined barrier when the initial and terminal values of the process following the Brownian motion in a certain interval are specified. We rewrite the existing pricing formula and provide a brief theoretical background and computational algorithm for the technique. We also provide several numerical examples computed in three different ways: explicit pricing formula, the Crude Monte Carlo simulation method and the Brownian Bridge technique.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.25 no.2
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• pp.116-123
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• 2015

This paper proposed a new formula for predicting acoustic power transmission loss of simple expansion chamber with two internal partitions. Seventeen cases of computational results were performed and the database was constructed for the TL according to the various positions of internal partitions. Using this database, firstly, the formula for the peak values of TL at certain frequencies was developed using the least square estimation. Secondly, the formula for the TL curve could be obtained automatically with the input data of the positions of two internal partitions. The formula of TL developed in this paper showed good agreement with computational results. This formula will be helpful for the positioning of internal partitions to improve TL at target frequencies.

• Journal of applied mathematics & informatics
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• v.33 no.3_4
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• pp.247-260
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• 2015

The special form of Schur complement is extended to have a Schur's formula to obtains the explicit formula of determinant, inverse, and eigenvector formula of the doubly Leslie matrix which is the generalized forms of the Leslie matrix. It is also a generalized form of the doubly companion matrix, and the companion matrix, respectively. The doubly Leslie matrix is a nonderogatory matrix.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2004.10a
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• pp.492-499
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• 2004

The purpose of this paper is to present a design procedure of coulomb friction dampers for controlling elastic and inelastic responses of building structures. The equivalent damping and frequency increased by the friction damper are estimated using ATC-40 and ATC-55 procedures which provide equivalent linear system for bilinear one, and then a design formula to achieve target performance response level by friction damper is presented. It is identified that there exists error between the responses obtained by this formula and by performing nonlinear analysis and the features of the error vary according to the hardening ratio, yield strength ratio, and structural period. Equations for compensating this er개r are reposed based on the least square method, and the results from numerical analyses indicate that the error is significantly reduced, and the proposed formula can be used without much error for designing coulomb friction damper for retrofitting a structure showing elastic or inelastic behavior.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2007.04a
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• pp.777-782
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• 2007

Displacement amplification factor can be used to estimate inelastic displacement demands from elastic displacement demands, The simple formula for displacement amplification factor considering hysteretic behavior of structural system and earthquake characteristics is proposed. And the effects of several parameters such as displacement ductility, strain hardening ratio, period, characteristics of earthquakes and hysteretic models for the displacement amplification factor are evaluated. Accuracy of the proposed formula is evaluated by comparing the displacement amplification factors estimated by existing and proposed formula with those calculated from inelastic time history analysis. The displacement amplification factors by proposed formulas provide a good agreement with those calculated by inelastic time history analysis.

• Bulletin of the Korean Mathematical Society
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• v.50 no.2
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• pp.451-458
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• 2013

The main purpose of this paper is using the analytic methods and the properties of Gauss sums to study the computational problem of one kind mean value of the generalized Kloosterman sums and Dirichlet character of polynomials, and give an interesting asymptotic formula for it.

• Communications for Statistical Applications and Methods
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• v.2 no.1
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• pp.216-228
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• 1995

Under the certain assumptions, we derive the recursive formula for the predictive probabilities that a new patient will survive up to the time, conditional on the data. The formula for a new patient is extended to obtain the computational algorithms for the predictive probabilties for several new patients. We correct Genest and Kalbfleisch's approach for several new patients, since we find that their approach is incorrect.