• Communications for Statistical Applications and Methods
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• v.23 no.1
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• pp.21-32
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• 2016

We study asymptotic expansion formulae for numerical computation of Greeks (i.e. sensitivity) in finance. Our approach is based on the integration-by-parts formula of the Malliavin calculus. We propose asymptotic expansion of Greeks for a stochastic volatility model using the Greeks formula of the Black-Scholes model. A singular perturbation method is applied to derive asymptotic Greeks formulae. We also provide numerical simulation of our method and compare it to the Monte Carlo finite difference approach.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2011.04a
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• pp.544-549
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• 2011

Simplified formulae for axial and bending natural frequencies of bellows are developed using an equivalent thin-walled pipe model. The axial and bending stiffness of bellows is determined using lumped transfer matrix method. Accordingly, the Expansion Joint Manufacturers Association (EJMA) formula for axial and bending stiffness calculation is modified using two different equivalent radii. The results from the simplified formulae are verified by those from a experiment result and a finite element (FE) model and good agreement is shown between the each other.

• Journal of the Korean Ceramic Society
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• v.55 no.1
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• pp.67-73
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• 2018

A poled lead zirconate titanate (PZT) cube specimen that is switched by an electric field at room temperature is subject to temperature increase. Changes in polarization and thermal expansion coefficients are measured during temperature rise. The measured data are analyzed to obtain changes in pyroelectric coefficient and strain during temperature change. Empirical formulae are developed using linear or quadratic curve fitting to the data. The nonlinear behavior of the materials during temperature increase is predicted using the developed formulae. It is shown that the calculation results can be compared successfully with the measured values, which proves the accuracy and reliability of the developed formulae for the nonlinear behavior of the materials during temperature changes.

• Kyungpook Mathematical Journal
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• v.43 no.4
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• pp.489-494
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• 2003

In this paper, we first establish an interesting theorem involving the $\bar{H}$-function introduced by Inayat-Hussain ([7], [8]). The convergence and existence condition, basic properties of this function were given by Buschman and Srivastava ([2]). Next, we obtain certain new integrals and an expansion formula by the application of our theorem. On account of the most general nature of the functions involved herein, our main findings are capable of yielding a large number of new, interesting and useful integrals, expansion formulae involving simple special functions and polynomials as their special cases. A known special case of our main theorem in also given ([11]).

• Honam Mathematical Journal
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• v.42 no.2
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• pp.269-291
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• 2020

In this paper, we get acquainted to a new generalization of the modified Hermite matrix polynomials. An explicit representation and expansion of the Matrix exponential in a series of these matrix polynomials is obtained. Some important properties of Modified Hermite Matrix polynomials such as generating functions, recurrence relations which allow us a mathematical operations. Also we drive expansion formulae and some operational representations.

• Kyungpook Mathematical Journal
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• v.20 no.1
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• pp.117-119
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• 1980

• Journal of applied mathematics & informatics
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• v.7 no.2
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• pp.391-408
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• 2000

In the curved geometries, from the solution of the classical Riemann problem in the plane, the asymptotic solutions of the compressible Euler equation are presented. The explicit formulae are derived for the third order approximation of the generalized Riemann problem form the conventional setting of a planar shock-interface interaction.

• Bulletin of the Korean Chemical Society
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• v.30 no.7
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• pp.1539-1542
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• 2009

Using one-range addition theorems for Slater type orbitals (STOs) and Coulomb-Yukawa like correlated interaction potentials (CIPs) introduced by the author, the series expansion formulae are derived for the multicenter multielectron integrals. The expansion coefficients occurring in these relations are presented through the overlap integrals of two STOs. The convergence of series expansion relations is tested by calculating concrete cases. The accuracy of the results is quite high for quantum number, screening constants and location of orbitals. The final results are especially useful in the calculation of multielectron properties for atoms and molecules when Hartree-Fock-Roothaan (HFR) and explicitly correlated methods are employed.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.21 no.7
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• pp.665-673
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• 2011

Simplified formulae for axial and bending natural frequencies of a bellows are developed using an equivalent thin-walled pipe model. The axial and bending stiffness of bellows is determined using lumped transfer matrix method. Transfer matrix method which includes the rotary inertia is used to calculate the natural frequencies for axial and lateral vibration. The result from the simplified formula are verified by those from as experiment result and a finite element analysis. This comparisons show good agreement with the each other.

• Journal of Semiconductor Engineering
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• v.2 no.3
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• pp.136-141
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• 2021

This paper analyzes the tree expansion for multiple-input multiple-output (MIMO) detection in the viewpoint of hardware implementation. The tree expansion is to calculate path metrics of child nodes performed in every visit to a node while traversing the detection tree. Accordingly, the tree-expansion unit (TEU), which is responsible for such a task, has been an essential component in a MIMO detector. Despite the paramount importance, the analyses on the TEUs in the literature are not thorough enough. Accordingly, we further investigate the hardware complexity of the TEUs to suggest a guideline for selection. In this paper, we focus on a pair of major ways to implement the TEU: 1) a full parallel realization; 2) a transformation of the formulae followed by common subexpression elimination (CSE). For a logical comparison, the numbers of multipliers and adders are first enumerated. To evaluate them in a more practical manner, the TEUs are implemented in a 65-nm CMOS process, and their propagation delays, gate counts, and power consumptions were measured explicitly. Considering the target specification of a MIMO system and the implementation results comprehensively, one can choose which architecture to adopt in realizing a detector.