• Journal of the Korean School Mathematics Society
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• v.23 no.1
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• pp.67-88
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• 2020

This study analyzed the characteristics of prospective teachers' Horizon Content Knowledge(HCK) related to understandings of an inverse function symbol. This study aimed to deduce implications of developing HCK in terms of the means which would enhance mathematics teachers' professional development. In order to achieve the aim, this study identified features of HCK by examining the previous literature on HCK, which has conformed Ball & Bass(2009) and exploring the research in AMT, including Zazkis & Leikin(2010) which has emphasized cultivating AMT through university mathematics education. In addition, a questionnaire was developed regarding the features of HCK and taken by 57 prospective teachers. By analyzing the data obtained from the written responses the participants presented, this study delineated the specific characteristics of the teachers' HCK with regard to an inverse function symbol. Additionally, several issues in the teacher education for improving HCK were discussed, and the results of this research could inspire designing and implementing a teacher education program relevant to HCK.

• Communications of the Korean Mathematical Society
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• v.34 no.4
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• pp.1175-1199
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• 2019

We construct a general bi-basic inverse series relation which provides extension to several q-polynomials including the Askey-Wilson polynomials and the q-Racah polynomials. We introduce a general class of polynomials suggested by this general inverse pair which would unify certain polynomials such as the q-extended Jacobi polynomials and q-Konhauser polynomials. We then emphasize on applications of the general inverse pair and obtain the generating function relations, summation formulas involving the associated polynomials and derive the p-deformation of some of the q-analogues of Riordan's classes of inverse series relations. We also illustrate the companion matrix corresponding to the general class of polynomials; this is followed by a chart showing the reducibility of the extended p-deformed Askey-Wilson polynomials as well as the extended p-deformed q-Racah polynomials.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.21 no.9
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• pp.2456-2469
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• 1996

A digital satellite communication channel has a nonlinearity with memory due to saturation characeristis of the high poer amplifier in the satellite and transmitter/receiver linear filter used in the overall system. In this paper, we propose a complex radial basis function network(CRBFN) based adaptive equalizer for compensation of nonlinearities in digital satellite communication channels. The proposed CRBFN untilizes a complex-valued hybrid learning algorithm of k-means clustering and LMS(least mean sequare) algorithm that is an extension of Moody Darken's algorithm for real-valued data. We evaluate performance of CRBFN in terms of symbol error rates and mean squared errors nder various noise conditions for 4-PSK(phase shift keying) digital modulation schemes and compare with those of comples pth order inverse adaptive Volterra filter. The computer simulation results show that the proposed CRBFN ehibits good equalization, low computational complexity and fast learning capabilities.

• International Journal of Aeronautical and Space Sciences
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• v.3 no.2
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• pp.46-58
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• 2002

An inverse method is introduced to construct benchmark problems for the numerical solution of initial value problems. Benchmark problems constructed through this method have a known exact solution, even though analytical solutions are generally not obtainable. The solution is constructed such that it lies near a given approximate numerical solution, and therefore the special case solution can be generated in a versatile and physically meaningful fashion and can serve as a benchmark problem to validate approximate solution methods. A smooth interpolation of the approximate solution is forced to exactly satisfy the differential equation by analytically deriving a small forcing function to absorb all of the errors in the interpolated approximate solution. A multi-variable orthogonal function expansion method and computer symbol manipulation are successfully used for this process. Using this special case exact solution, it is possible to directly investigate the relationship between global errors of a candidate numerical solution process and the associated tuning parameters for a given code and a given problem. Under the assumption that the original differential equation is well-posed with respect to the small perturbations, we thereby obtain valuable information about the optimal choice of the tuning parameters and the achievable accuracy of the numerical solution. Illustrative examples show the utility of this method not only for the ordinary differential equations (ODEs) but for the partial differential equations (PDEs).

• Safety and Health at Work
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• v.11 no.2
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• pp.178-186
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• 2020

Background: Cognitive impairment is a public health burden. Our objective was to investigate associations between work hours and cognitive function. Methods: Multi-Ethnic Study of Atherosclerosis (MESA) participants (n = 2,497; 50.7% men; age range 44-84 years) reported hours per week worked in all jobs in Exams 1 (2000-2002), 2 (2002-2004), 3 (2004-2005), and 5 (2010-2011). Cognitive function was assessed (Exam 5) using the Cognitive Abilities Screening Instrument (version 2), a measure of global cognitive functioning; the Digit Symbol Coding, a measure of processing speed; and the Digit Span test, a measure of attention and working memory. We used a prospective approach and linear regression to assess associations for every 10 hours of work. Results: Among all participants, associations of hours worked with cognitive function of any type were not statistically significant. In occupation-stratified analyses (interaction p = 0.051), longer work hours were associated with poorer global cognitive function among Sales/Office and blue-collar workers, after adjustment for age, sex, physical activity, body mass index, race/ethnicity, educational level, annual income, history of heart attack, diabetes, apolipoprotein E-epsilon 4 allele (ApoE4) status, birth-place, number of years in the United States, language spoken at MESA Exam 1, and work hours at Exam 5 (β = -0.55, 95% CI = -0.99, -0.09) and (β = -0.80, -1.51, -0.09), respectively. In occupation-stratified analyses (interaction p = 0.040), we also observed an inverse association with processing speed among blue-collar workers (adjusted β = -0.80, -1.52, -0.07). Sex, race/ethnicity, and ApoE4 did not significantly modify associations between work hours and cognitive function. Conclusion: Weak inverse associations were observed between work hours and cognitive function among Sales/Office and blue-collar workers.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.32 no.7A
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• pp.724-729
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• 2007

In this paper, we consider a joint optimization of transmitter and receiver in additive cyclostationary noise with zero forcing criterion. We assume that the period of the cyclostationary noise is the same as the inverse of the symbol transmission rate and that the noise has a positive-definite autocorrelation function. The data sequence is modeled as a wide-sense stationary colored random process and the channel is modeled as a linear time-invariant system with a frequency selective impulse response. Under these assumptions and a constraint on the average power of the transmitted signal, we derive the optimum transmitter and receiver waveforms that jointly minimizes the mean square error with no intersymbol interference. The simulation results show that the proposed system has a better BER performance than the systems with receiver only optimization and the systems with no transmitter and receiver optimization.