• 한국학교수학회논문집
• /
• 제23권1호
• /
• pp.67-88
• /
• 2020

여러 국외 연구는 SMK의 주요 특징을 HCK와 관련하여 설명하면서 수학 교사 교육의 핵심 목표 중 하나로 HCK의 개발을 강조하였다. 그러나 국내에는 SMK의 하위 요소로서 HCK의 구체적인 의미를 살피거나 우리나라 교사들이 지닌 HCK의 특징을 본격적으로 분석한 연구가 거의 없다. 이에 이 연구는 Ball & Bass(2009)의 관점에서 HCK를 다룬 국외 연구를 검토하여 대학 수학을 통해 개발될 필요가 있는 HCK의 특징을 구체적으로 확인하였다. 또한 대학 수학의 목표가 AMT 개발에 있음을 강조한 Zazkis & Leikin(2010)에 따라 AMT 관련 선행 연구를 분석하여 HCK 개발의 기반이 되는 AMT의 핵심 특징을 구체화하였다. 이를 토대로 예비교사들의 HCK를 역함수 기호에 대한 이해에 주목하여 분석하기 위한 지필 검사 도구를 개발하였으며, 이를 예비교사 57명에게 적용하여 얻은 답변 자료를 검사 도구 개발 의도 및 함수 개념 수준에 비추어 분석하였다. 이로부터 역함수 및 역함수 기호와 관련하여 예비교사들이 지닌 HCK의 특징을 4가지로 추출하였으며, 각각의 특징이 지닌 시사점을 수학 교사 전문성 신장을 위한 HCK 개발의 측면에서 기술하였다.

• ETRI Journal
• /
• 제46권4호
• /
• pp.595-603
• /
• 2024

This paper presents methods for reducing the peak-to-average power ratio (PAPR) of the orthogonal time frequency space (OTFS) signal. These methods mainly consist of two operations: symbol interferometry (SI) and either 𝜇-law or A-law companding. SI spreads the data of one OTFS symbol onto all symbols and is implemented using a simple inverse fast Fourier transform operation on each OTFS symbol. During the second operation, the PAPR of the OTFS signal is significantly reduced. For our performance analysis, the complementary cumulative distribution function, probability density function, and bit error rate are illustrated through simulations performed in MATLAB. The performance is also analyzed using a solid-state power amplifier at the transmitter and compared with OTFS, 𝜇-law-based OTFS, and SI OTFS systems. The results indicate that the proposed OTFS system achieves a low PAPR.

• 대한수학회논문집
• /
• 제34권4호
• /
• pp.1175-1199
• /
• 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.

• 한국통신학회논문지
• /
• 제21권9호
• /
• pp.2456-2469
• /
• 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
• /
• 제3권2호
• /
• pp.46-58
• /
• 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
• /
• 제11권2호
• /
• pp.178-186
• /
• 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.

• 한국통신학회논문지
• /
• 제32권7A호
• /
• pp.724-729
• /
• 2007

가산성 주기정상성 잡음이 있을 때 zero forcing (ZF) 기반에서의 송수신단 동시 최적화를 고려한다. 주기정상성 잡음의 주기는 심볼 전송율의 역수라고 가정하고 자기 상관함수는 양의 정부호로 가정한다. 전송되는 데이터 수열은 광의의정상성(WSS: wide-sense stationary)을 가지는 유색 확률과정으로 모델링 하고 채널은 주파수 선택적 충격 응답을 가지는 선형 시불변 시스템으로 모델링 한다. ZF와 송신 전력 제약 아래 평균제곱오차 (MSE: mean square error)를 최소화하는 최적 송수신 파형을 유도하고 모의 실험 결과를 통해 수신파형만 최적화 한 경우와 가산성 주기정상성 잡음을 정상성 잡음으로 간주한 경우 보다 성능이 더 좋아짐을 보인다.