• Journal for History of Mathematics
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• v.21 no.2
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• pp.81-90
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• 2008

It has been noticed the greater importance of mathematical education, particularly of multi-variable calculus in the undergraduate level with remarkable progress of all sorts of sciences requiring mathematical analysis. However, there was lack of variety of introducing the definition of differentiation of multi-variable functions - in fact, all of them basically rely on the chain rules. Here we will introduce a way of defining the geometrical differentiation of the multi-variable functions based upon our teaching experience. One of its merits is that it provides the geometric explanation of the differentiation of the multi-variable functions, so that it conveys the meaning of the differentiation better compared with the known methods.

• Journal of Korea Game Society
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• v.11 no.2
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• pp.39-44
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• 2011

Computer games need game formulas which express game rules by mathematical functions because the game rules are automatically processed by computers. The game formulas are usually multi-variable functions. So the design of a game formula is a complex and difficult problem because it is the same problem of the design of a multi-variable function which should satisfy the related game rules. In this paper we propose a new method which can systematically design game formulas. The purposed method is the decomposing of tree structure for a game formula by analyzing the tree structure of the operands which have single-variable functions on the lowest levels. So the design method can change the complex and difficult problem of the design of a multi-variable function to the simple and easy problem of the design of the single-variable function which should satisfy the related game rules.

• Communications of the Korean Mathematical Society
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• v.30 no.4
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• pp.429-438
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• 2015

In this paper, we discuss how the operational calculus can be exploited to the theory of mixed generating functions. We use operational methods associated with multi-variable Hermite polynomials, Laguerre polynomials and Bessels functions to drive identities useful in electromagnetism, fluid mechanics etc. Certain special cases giving bilateral generating relations related to these special functions are also discussed.

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.39 no.3
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• pp.191-200
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• 2002

In this paper, we present the method transforming the interval functions into the truncated difference functions for multi-variable multi-valued functions and implementing the truncated difference functions to the multiple valued logic circuits with uniform patterns using the current mirror circuits and the inhibit circuits by current-mode CMOS. Also, we apply the presented methods to the implementation of circuits for additive truth table of 2-variable 4-valued MOD(4) and multiplicative truth table of 2-variable 4-valued finite fields GF(4). These circuits are simulated under 2${\mu}{\textrm}{m}$ CMOS standard technology, 15$mutextrm{A}$ unit current, and 3.3V power supply voltage using PSpice. The simulation results have shown the satisfying current characteristics. Both implemented circuits using current-mode CMOS have the uniform Patterns and the regularity of interconnection. Also, it is expansible for the variables of multiple valued logic functions and are suitable for VLSI implementation.

• Proceedings of the KIEE Conference
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• 1998.07f
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• pp.2082-2084
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• 1998

This paper presents a microcontroller-based electronic neon ballasts which is highly suitable for a multi-use and low power consumption by performing economical hardwares and variable software algorithms. Result of this study has the following functions : brightness control, frequency variable output, automatic lightening control, low power characteristics.

• Journal of Biosystems Engineering
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• v.31 no.3 s.116
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• pp.194-202
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• 2006

Using a multi-variable linear regression technique and SUR(seemingly unrelated regression) model, the demand functions of tractor, combine and rice transplanter were estimated. The demand was regarded as an annual supply of each machine and modeled as a function of 11 independent variables which reflect the actual farmer's income, actual prices of farm machines, previous supply, previous stock, actual amount of available subsidy, actual amount of available loan, arable land, import of farm machines and rice price. The actual amount of available loan affects most significantly the demand functions. The actual farmer's income, actual farmer's asset, loan coverage, and rice price affect the demand positively while prices of farm machines and import negatively. The annual demands of tractor, combine and rice transplanter estimated using the demand functions were also presented over the next 4 years.

• Earthquakes and Structures
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• v.9 no.5
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• pp.1115-1132
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• 2015

The study considers earthquake shake table testing of bending-torsion coupled structures under multi-component stationary random earthquake excitations. An experimental procedure to arrive at the optimal excitation cross-power spectral density (psd) functions which maximize/minimize the steady state variance of a chosen response variable is proposed. These optimal functions are shown to be derivable in terms of a set of system frequency response functions which could be measured experimentally without necessitating an idealized mathematical model to be postulated for the structure under study. The relationship between these optimized cross-psd functions to the most favourable/least favourable angle of incidence of seismic waves on the structure is noted. The optimal functions are also shown to be system dependent, mathematically the sharpest, and correspond to neither fully correlated motions nor independent motions. The proposed experimental procedure is demonstrated through shake table studies on two laboratory scale building frame models.

• Communications for Statistical Applications and Methods
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• v.16 no.1
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• pp.185-193
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• 2009

Machine learning methods such as support vector machines and random forests yield nonparametric prediction functions of the form y = $f(x_1,{\ldots},x_p)$. As a sequel to the previous article (Huh and Lee, 2008) for visualizing nonparametric functions, I propose more sensible graphs for visualizing y = $f(x_1,{\ldots},x_p)$ herein which has two clear advantages over the previous simple graphs. New graphs will show a small number of prototype curves of $f(x_1,{\ldots},x_{j-1},x_j,x_{j+1}{\ldots},x_p)$, revealing statistically plausible portion over the interval of $x_j$ which changes with ($x_1,{\ldots},x_{j-1},x_{j+1},{\ldots},x_p$). To complement the visual display, matching importance measures for each of p predictor variables are produced. The proposed graphs and importance measures are validated in simulated settings and demonstrated for an environmental study.

• Journal of the Korean Operations Research and Management Science Society
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• v.40 no.3
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• pp.49-61
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• 2015

We study the problem of multiple response optimization (MRO) and focus on the selection of input levels which will produce desirable output quality. We propose an interactive multiple objective optimization approach to the input design. The earlier interactive methods utilized for MRO communicate with the decision maker only using the response variable values, in order to improve the current response values, thereby resulting in the corresponding design solution automatically. In their interaction steps of preference articulation, no account is taken of any active changes in design variable values. On the contrary, our approach permits the decision maker to change the design variable values in its interaction stage, which makes possible the consideration of the preference or economics of the design variable side. Using some typical value functions, we also demonstrate that our method converges reasonably well to the known optimal solutions.

• 제어로봇시스템학회:학술대회논문집
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• 2004.08a
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• pp.1987-1992
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• 2004

A Variable Structure Model Reference Adaptive Controller (VS-MRAC) using state Variables is proposed for single input multi output systems. . The structure of the switching functions is designed based on stability requirements, and global exponential stability is proved. Transient behavior is analyzed using sliding mode control and shows perfect model following at a finite time. The effect of input disturbances on stability and transients is investigated and shows preference to the conventional MRAC schemes with integral adaptation law. Sliding surfaces are independent of system parameters and therefore VS-MRAC is insensitive to system parameter variations. Simulation is presented to clear the theoretical results.