• Title, Summary, Keyword: non-standard orthogonality

Search Result 4, Processing Time 0.034 seconds

q-SOBOLEV ORTHOGONALITY OF THE q-LAGUERRE POLYNOMIALS {Ln(-N)(·q)}n=0 FOR POSITIVE INTEGERS N

  • Moreno, Samuel G.;Garcia-Caballe, Esther M.
    • Journal of the Korean Mathematical Society
    • /
    • v.48 no.5
    • /
    • pp.913-926
    • /
    • 2011
  • The family of q-Laguerre polynomials $\{L_n^{(\alpha)}({\cdot};q)\}_{n=0}^{\infty}$ is usually defined for 0 < q < 1 and ${\alpha}$ > -1. We extend this family to a new one in which arbitrary complex values of the parameter ${\alpha}$ are allowed. These so-called generalized q-Laguerre polynomials fulfil the same three term recurrence relation as the original ones, but when the parameter ${\alpha}$ is a negative integer, no orthogonality property can be deduced from Favard's theorem. In this work we introduce non-standard inner products involving q-derivatives with respect to which the generalized q-Laguerre polynomials $\{L_n^{(-N)}({\cdot};q)\}_{n=0}^{\infty}$, for positive integers N, become orthogonal.

Error Assessment of CMM by Self-calibration Method (자가 보정 방법을 이용한 삼차원 측정기의 계통 오차 추출)

  • 유승봉;김승우
    • Proceedings of the Korean Society of Precision Engineering Conference
    • /
    • /
    • pp.379-382
    • /
    • 2002
  • Among the CMM calibration techniques, the calibration with standard specimen is most accurate way to acquire the required precision. When there is no standard specimen, the calibration of CMM with itself is possible. This calibration method is called "self-calibration". In this paper, we developed self-calibration algorithm for CMM XY plane. It is possible to calculate the in-plane error and out-of-plane error of CMM with 3 different measurement of same artifact. Experimental result shows that the non-orthogonality error is dominant in in-plane error and the self-calibration result and laser interferometer measured result have almost same value.ame value.

  • PDF

An Orthogonal Approximate DCT for Fast Image Compression (고속 영상 압축을 위한 근사 이산 코사인 변환)

  • Kim, Seehyun
    • Journal of the Korea Institute of Information and Communication Engineering
    • /
    • v.19 no.10
    • /
    • pp.2403-2408
    • /
    • 2015
  • For image data the discrete cosine transform (DCT) has comparable energy compaction capability to Karhunen-Loeve transform (KLT) which is optimal. Hence DCT has been widely accepted in various image and video compression standard such as JPEG, MPEG-2, and MPEG-4. Recently some approximate DCT's have been reported, which can be computed much faster than the original DCT because their coefficients are either zero or the power of 2. Although the level of energy compaction is slightly degraded, the approximate DCT's can be utilized in real time implementation of image or visual compression applications. In this paper, an approximate 8-point DCT which contains 17 non-zero power-of-2 coefficients and high energy compaction capability comparable to DCT is proposed. Transform coding experiments with several images show that the proposed transform outperforms the published works.

Non-linear Preferences on Bioethanol in South Korea (국내 바이오에탄올에 대한 비선형적 선호에 관한 연구)

  • Bae, Jeong Hwan
    • Environmental and Resource Economics Review
    • /
    • v.23 no.3
    • /
    • pp.515-551
    • /
    • 2014
  • Recently, there has been a debate as to whether bioethanol should replace some portion of gasoline for fuels in South Korea, as energy security as well as climate change issues are rising as a significant national agenda. However, a considerable amount of subsidy will be required to compensate for the higher price of bioethanol-blended gasoline. In this context, government subsidy will obtain justification only when the positive social gains from consuming bioethanol for fuels can exceed the negative social costs. Through a nation-wide choice experimental survey, we examine if South Koreans have a positive value as well as non-linear preferences on substituting bioethanol for gasoline. The results reveal that the willingness to pay for purely domestic bioethanol-blended gasoline within 10% is about 52 KRW; Koreans have concave preferences on the blending ratio of bioethanol to gasoline. The turning point of the blending ratio of bioethanol was 6.5%. Also, we found inverse U-shaped curve between income and bioethanol choice probability and the turning point of the income was calculated as 250~299million KRW. Politically conservative propensity advocates uses of bioethanol blended gasoline, but awareness on bioethanol or more weights on environmental conservation have significantly negative effects on the choice of bioethanol. However, the design of the survey questionnaire is incompatible with the RFS of Korea and assumes orthogonality among the following four interrelated attributes: (i) domestic or offshore procurement of feedstocks in the case of domestic production, (ii) domestic production or import of bioethanol, (iii) the blending ratios, and (iv) the retail price increases. In addition, the results of model estimation and of model selection test are not definite. Hence, the results in this study should not be directly applied to the design of the specifics of the Korean RFS. Hence, the results in this study require cautions in applying to the design of the Korean RFS policy.