• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.20 no.1
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• pp.74-80
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• 2011

In this study, a variety of welding experiments were carried out to optimize root-pass welding process using GMA process. Based on the experimental results, optimal welding conditions were selected after analyzing correlation between welding parameters and back-bead geometry. Then, effectiveness of empirical models developed was compared and analyzed, and optimized empirical models were finally developed for predicting back-bead by analyzing the main effect of each factor which affects back-bead geometry and their influence on interaction. Also, functions proper for expressing the surface of back-bead were selected using diverse quadratic functions, and back-bead geometry was visualized using empirical models developed and quadratic functions.

• International Journal of Control, Automation, and Systems
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• v.5 no.2
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• pp.170-183
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• 2007

This paper presents a delay-dependent approach to robust filtering for linear parameter-varying (LPV) systems with discrete and distributed time-invariant delays in the states and outputs. It is assumed that the state-space matrices affinely depend on parameters that are measurable in real-time. Some new parameter-dependent delay-dependent stability conditions are established in terms of linear matrix inequalities (LMIs) such that the filtering process remains asymptotically stable and satisfies a prescribed $H_{\infty}$ performance level. Using polynomially parameter-dependent quadratic (PPDQ) functions and some Lagrange multiplier matrices, we establish the parameter-independent delay-dependent conditions with high precision under which the desired robust $H_{\infty}$ filters exist and derive the explicit expression of these filters. A numerical example is provided to demonstrate the validity of the proposed design approach.

• Journal of the Korean Mathematical Society
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• v.35 no.4
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• pp.903-931
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• 1998

Since the modular curves X(N) = $\Gamma$(N)\(equation omitted)＊ (N =1,2,3) have genus 0, we have field isomorphisms K(X(l))(equation omitted)C(J), K(X(2))(equation omitted)(λ) and K(X(3))(equation omitted)( $j_3$) where J, λ are the classical modular functions of level 1 and 2, and $j_3$ can be represented as the quotient of reduced Eisenstein series. When N = 4, we see from the genus formula that the curve X(4) is of genus 0 too. Thus the field K(X(4)) is a rational function field over C. We find such a field generator $j_4$(z) = x(z)/y(z) (x(z) = $\theta$$_3$((equation omitted)), y(z) = $\theta$$_4$((equation omitted)) Jacobi theta functions). We also investigate the structures of the spaces $M_{k}$($\Gamma$(4)), $S_{k}$($\Gamma$(4)), M(equation omitted)((equation omitted)(4)) and S(equation omitted)((equation omitted)(4)) in terms of x(z) and y(z). As its application, we apply the above results to quadratic forms.rms.

• The Transactions of the Korean Institute of Power Electronics
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• v.20 no.5
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• pp.421-428
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• 2015

An advanced direct torque control (DTC) with pulse width modulation (PWM) method is presented in this paper. The duty ratio calculation of the selected voltage vector is based on the voltage functions of the selected voltage vector according to the sector angle. The proposed DTC uses a conventional DTC scheme with six sector divisions and switching rules. However, the winding voltages are supplied by the PWM approach. Furthermore, the duty ratio of the switching voltage vector is determined by the flux, torque error, and motor speed. The base voltage that shall determine the duty ratio can be calculated by approximate voltage functions according to the voltage angle. For the calculation of base voltages, second-order quadratic functions are used to express the output voltage of the selected voltage vector according to voltage angle. The coefficients for the second-order quadratic functions are selected by the voltage vector, which is determined by the switching rules of the DTC. In addition, the voltage functions are calculated by the coefficients and voltage angle between the voltage vector and rotor position. The switching voltages from the calculated duty ratio can supply the proper torque and flux to reduce the ripple and error. The proposed control scheme is verified through practical experimental comparisons.

• Kyungpook Mathematical Journal
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• v.16 no.1
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• pp.135-140
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• 1976

• The Mathematical Education
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• v.61 no.3
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• pp.441-456
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• 2022

The purpose of the current study is to report a part of our larger project whose focus is to understand a relationship between students' units coordination and K-12 school mathematics. In particular, in this paper we report how students who exhibit distinct levels of units coordinations used their knowledge of proportion to solve quadratic function problems of the form y = ax². To this end, three 7th grade students all of whom assimiliated whole number problem situations with three levels of units but showed different levels for fraction problems were chosen. We carried out clinical interviews not only to understand their ability to coordinate units but to understand their problem solving process of proportion and the quadratic function problems. The analysis suggest that their abilities to coordinate units influenced their ways to solving proportion problems, and in turn influenced their ways to solve the specific form of quadratic functions. We have finalized our study by discussing how students' ability to construct and coordinate units, their proportion knowledge, and their knowledge associated with expressing the specific type of quadractic functions could be related.

• Journal of Educational Research in Mathematics
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• v.25 no.4
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• pp.525-547
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• 2015

This study analyzed the written texts of textbook and the teacher's discourse explaining 'the relationship between quadratic functions and quadratic equations' in the 9th grade high school mathematics class. Data consisted of the lecture recordings and the textbooks were analyzed based on the Halliday's systemic functional linguistics. According to the results, the written texts of the textbook used lexico-grammatical strategies such as generalization using hyponomy of meanings, mathematical objectification through nominalization and materialization of meaning through change in themes to compose mathematical concepts. The textbook generalized from an example in the description of formulating mathematical concepts, and in this process the organizational interactions of discourse-semantic level and lexico-grammartical level appeared. On the other hand, the teacher's doscourse appeared the change in transitivity and the addition of the reasons and the process. Also the teacher used explanation process of formulating the relationship between quadratic functions and quadratic equations. The linguistic characteristics of the teacher were linguistic implication and omission of lexemes due to contextual ommission. And there was no use of structural lexico-grammatical resources that influence the discourse-semantic level. This results provide a new framework for analyzing mathematical discourse, and suggest the lexico-grammatical strategies that can be used to explain mathematical concepts by teachers in math classrooms.

• Transactions of the Korean Society of Mechanical Engineers
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• v.14 no.2
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• pp.310-323
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• 1990

A three-noded, with three degree-of-freedom at each node, in-plane curved beam element is formulated and employed in eigen-analysis of constant curvature beam. The conventional quadratic shape functions used in a three noded C .deg. type curved beam element produce such an undesirable large stiffness that a significant error is introduced in displacements and stresses. These phenomena are called 'Stiffness Locking Phenomena', which result from spurious strain energy due to inappropriate assumptions on independent isoparametric quadratic interpolation functions. Stiffness locking phenomena can be alleviated by using modified interpolation functions which get rid of spurious constraints of conventional interpolation functions. Eigenvalues and their modes as well as displacements and stresses may be locked because they are related to stiffness. Using modified curved beam element in eigenvalue problem of cantilever and arch, the property and performance of modified curved beam element are examined by numerical experimentations. In these eigen-analyses, mass matrices are calculated by using both modified and unmodified curved beam element, are compared with theoretical solutions. These comparisons show that the performance of the modified curved beam element is better than that of the unmodified curved beam element.

• Journal of the Korean Mathematical Society
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• v.38 no.3
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• pp.595-611
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• 2001

Let Q(n,1) be the set of even unimodular positive definite integral quadratic forms in n-variables. Then n is divisible by 8. For A[X] in Q(n,1), the theta series $\theta$(sub)A(z) = ∑(sub)X∈Z(sup)n e(sup)$\pi$izA[X] (Z∈h (※Equations, See Full-text) the complex upper half plane) is a modular form of weight n/2 for the congruence group Γ$_1$(8) = {$\delta$∈SL$_2$(Z)│$\delta$≡()mod 8} (※Equation, See Full-text). If n$\geq$24 and A[X], B{X} are tow quadratic forms in Q(n,1), the quotient $\theta$(sub)A(z)/$\theta$(sub)B(z) is a modular function for Γ$_1$(8). Since we identify the field of modular functions for Γ$_1$(8) with the function field K(X$_1$(8)) of the modular curve X$_1$(8) = Γ$_1$(8)＼h(sup)* (h(sup)* the extended plane of h) with genus 0, we can express it as a rational function of j(sub) 1,8 over C which is a field generator of K(X$_1$(8)) and defined by j(sub)1,8(z) = $\theta$$_3$(2z)/$\theta$$_3$(4z). Here, $\theta$$_3$ is the classical Jacobi theta series.

• The Pure and Applied Mathematics
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• v.12 no.2 s.28
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• pp.133-142
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• 2005

Generalizing the Cauchy-Rassias inequality in [Th. M. Rassias: On the stability of the linear mapping in Banach spaces. Proc. Amer. Math. Soc. 72 (1978), no. 2, 297-300.] we consider a stability problem of quadratic functional equation in the spaces of generalized functions such as the Schwartz tempered distributions and Sato hyperfunctions.