• Journal of Electrical Engineering and Technology
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• 제10권3호
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• pp.1188-1200
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• 2015

A unified numerical method for computing the quadrature weights, integration matrix, and differentiation matrix is newly developed in this study. For this purpose, a spline-like interpolation using piecewise continuous polynomials is converted into a global spline interpolation formula, with which the quadrature formulas can be derived from integration and differentiation of the transformed function in an exact manner. To prove the usefulness of the suggested approach, both the Lagrange and tension spline interpolations are represented in exactly the same form as global spline interpolation. The applicability of the proposed method on arbitrary nodes is illustrated using two different sets of nodes. A series of validations using three test functions is conducted to show the flexibility in selecting computational nodes with the present method.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제25권4호
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• pp.224-261
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• 2021

The interest in implicit-explicit (IMEX) integration methods has emerged as an alternative for dealing in a computationally cost-effective way with stiff ordinary differential equations arising from practical modeling problems. In this paper, we introduce implicit-explicit second derivative linear multi-step methods (IMEX SDLMM) with error control. The proposed IMEX SDLMM is based on second derivative backward differentiation formulas (SDBDF) and recursive SDBDF. The IMEX second derivative schemes are constructed with order p ranging from p = 1 to 8. The methods are numerically validated on well-known stiff equations.

• 대한수학회논문집
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• 제34권2호
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• pp.523-532
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• 2019

Integrals involving a finite product of the generalized Bessel functions have recently been studied by Choi et al. [2, 3]. Motivated by these results, we establish certain unified integral formulas involving a finite product of the generalized k-Bessel functions. Also, we consider some integral formulas of the (p, q)-extended Bessel functions $J_{{\nu},p,q}(z)$ and the Delerue hyper-Bessel function which are proved in terms of (p, q)-extended generalized hypergeometric functions, and the generalized Wright hypergeometric functions, respectively.

• 대한수학회논문집
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• 제38권3호
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• pp.755-772
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• 2023

Our aim is to establish certain image formulas of the (p, q)-extended modified Bessel function of the second kind M_ν,p,q(z) by employing the Marichev-Saigo-Maeda fractional calculus (integral and differential) operators including their composition formulas and using certain integral transforms involving (p, q)-extended modified Bessel function of the second kind M_ν,p,q(z). Corresponding assertions for the Saigo's, Riemann-Liouville (R-L) and Erdélyi-Kober (E-K) fractional integral and differential operators are deduced. All the results are represented in terms of the Hadamard product of the (p, q)-extended modified Bessel function of the second kind M_ν,p,q(z) and Fox-Wright function _rΨ_s(z).

• 한국수학교육학회지시리즈A:수학교육
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• 제38권2호
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• pp.189-197
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• 1999

Discrete mathematics allows students to examine and explore unique, special problem situations which were not used to solve problems by paper-and-pencil procedures or applying common formulas. The use and integration of accessible computer-related technologies such as 'Mathematics' or 'Maple' software programs enables students to explore problem situation dramatically. This study shows that it is possible to introduce computer-based discrete mathematics focused on the Leslie matrix model as modeling age-specific population growth to high school students.

• 소음진동
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• 제6권5호
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• pp.607-616
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• 1996

A combined computational fluid dynamics(CFD)-Kirchhoff method is presented for predicting high-speed impulsive noise generated by a hovering blade. Two types of Kirchhoff integral formula are used; one for the classical linear Kirchhoff formulation and the other for the nonlinear Kirchhoff formulation. An Euler finite difference solver is solved first to obtain the flow field close to the blade, and then this flow field is used as an input to a Kirchhoff formulation to predict the acoustic far-field. These formulas are used at Mach numbers of 0.90 and 0.95 to investigate the effectiveness of the linear and nonlinear Kirchhoff formulas for delocalized flow. During these calculiations, the retarded time equation is also carefully examined, in particular, for the cases of the control surface located outside of the sonic cylinder, where multiple roots are obtained. Predicted results of acoustic far-field pressure with the linear Kirchhoff formulation agree well with experimental data when the control surface is at the certain location(R=1.46), but the correlation is getting worse before or after this specific location of the control surface due to the delocalized nonlinear aerodynamic flow field. Calculations based on the nonlinear Kirchhoff equation using a linear sonic cylinder as a control surface show a reasonable agreement with experimental data in negative amplitudes for both tip Mach numbers of 0.90 and 0.95, except some computational integration problems over a shock. This concliudes that a nonlinear formulation is necessary if the control surface is close to the blade and the flow is delocalized.

• Journal of Communications and Networks
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• 제12권6호
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• pp.582-591
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• 2010

Probabilistic modeling and analysis of correlation metrics have been receiving considerable interest for a long period of time because they can be used to evaluate the performance of communication receivers, including satellite broadcasting receivers. Although differential correlators have a simple structure and practical importance over channels with severe frequency offsets, closedform expressions for the output distribution of differential correlators do not exist. In this paper, we present detection error probability expressions for frame synchronization using differential correlation, and demonstrate their accuracy over channel parameters of practical interest. The derived formulas are presented in terms of the Marcum Q-function, and do not involve numerical integration, unlike the formulas derived in some previous studies. We first determine the distributions and error probabilities for single-span differential correlation metric, and then extend the result to multispan differential correlation metric with certain approximations. The results can be used for the performance analysis of various detection strategies that utilize the differential correlation structure.

• 한국산림과학회지
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• 제3권1호
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• pp.28-31
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• 1963

Recognizing shortcomings and unreasonable points of the usual methods of measurement of the standing-tree volume, author contrived measurement formula of standing-tree volume which is based on stem-curve equation, $y^2=2px$, resulted from the analysises and experiments on stem-curve by differentiation & integration. The results of this study are as follows ; (1) The following is the formula. $V=1/2g_{1.2}$(h+1.2) V=volume of tree $g_{1.2}$ = sectional area at breast heigh h = height of tree (2) So plain is the form of this formula that this formula is more convenient than usual formulas in measuring. (3) The percentage error of this formula is negative and it is remarkably superior to usual formulas except Pressler's formula, in other words, the higher the tree that is measured is, the more inaccurate become pressler's formula, and the percentage error of the breast-height form factor method is direct proportion to the grossness of the tree that is measured, but the higher the tree that is measured, the lower become percentage error of this formula in geometrical progression.

• 보건행정학회지
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• 제5권1호
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• pp.80-105
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• 1995

Assuming that we introduced integration of medical insurance society for self-employed, this study was conducted to examine effects and results after the integration and to research more effective method for integration. To assess effects and results of the finacial status of 266 insurance societies after intergration, the data were obtained from "The Medical Insurance Program for Self-Employeds Statistical Yearbook in 1992". The major finding are as follows : 1. Three alternative integration proposals were made. First alternative proposal was consisted of 232 medical insurance societies, second was 187, and third was 115. 2. As the results of average number of the insured per insurance societies of medical insurance program for self-employed every alternative proposal, first was 88, 119 persons, second was 108, 576, and third was 178, 967 from 76, 576 persons of present socienties. 3. It was true that the more average size of societies increased, the more average administration expenditure per 1, 000 insured reduced. 4. The average size of societies grew bigger, the rate of general expenditure to general revenue more improved. Also, the rate of benefits to contributions was changed for better. But if not to have had correct analysis and precise preparation for integration, effects and results of integration were always not optiized. 5. According to results of simple regression formulas, it was proved that the more the average size of societies was increased, the more result was advantaged. 6. The law of majority and the economy of scale were applied in this study, and it was necessary to analyze and assess effectiveness and efficiency of integration. Therefore, when the integration of medical insurance societies for self-employeds will be performed, it must be taken into consideration. Among three alternative proposals, third was showed more effective alternative than anothe, second was presented more ineffective result than present system. To achieve more effective and efficient integration of regional medical insurance societies throughout the result of the regression formula on present cost curve, it is necessary to operate well-integrated societies and to know appropriative countermeasures of present situation of each societies. Also, for integrating regional medical insurance societies, it is necessary to continue more deep research through practical model activity and to investigate the effective size and managed method of the societies.societies.

• Journal of Computing Science and Engineering
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• 제2권1호
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• pp.44-73
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• 2008

There is general agreement that the problem of data semantics has to be addressed for XML data to become machine-processable. This problem can be tackled by defining a semantic mapping between an XML schema and an ontology. Unfortunately, creating such mappings is a tedious, time-consuming, and error-prone task. To alleviate this problem, we present a solution that heuristically discovers semantic mappings between XML schemas and ontologies. The solution takes as input an initial set of simple correspondences between element attributes in an XML schema and class attributes in an ontology, and then generates a set of mapping formulas. Once such a mapping is created, it is important and necessary to maintain the consistency of the mapping when the associated XML schema and ontology evolve. In this paper, we first offer a mapping formalism to represent semantic mappings. Second, we present our heuristic mapping discovery algorithm. Third, we show through an empirical study that considerable effort can be saved when discovering complex mappings by using our prototype tool. Finally, we propose a mapping maintenance plan dealing with schema evolution. Our study provides a set of effective solutions for building sustainable semantic integration systems for XML data.