• Journal of applied mathematics & informatics
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• 제19권1_2호
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• pp.427-438
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• 2005

From a notion of d-pseudo-orthogonality for a sequence of poly-nomials ($d\;\in\;{2,3,\cdots}$), this paper introduces three different characterizations of natural exponential families (NEF's) with polynomial variance functions of exact degree 2d-1. These results provide extended versions of the Meixner (1934), Shanbhag (1972, 1979) and Feinsilver (1986) characterization results of quadratic NEF's based on classical orthogonal polynomials. Some news sets of polynomials with (2d-1)-term recurrence relation are then pointed out and we completely illustrate the cases associated to the families of positive stable distributions.

• 한국정밀공학회지
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• 제24권9호
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• pp.68-75
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• 2007

The pitch and orthogonality of two-dimensional (2D) gratings have been measured by using a metrological atomic force microscope (MAFM) and measurement uncertainty has been analyzed. Gratings are typical standard artifacts for the calibration of precision microscopes. Since the magnification and orthogonality in two perpendicular axes of microscopes can be calibrated simultaneously using 2D gratings, it is important to certify the pitch and orthogonality of 2D gratings accurately for nano-metrology using precision microscopes. In the measurement of 2D gratings, the MAFM can be used effectively for its nanometric resolution and uncertainty, but a new measurement scheme was required to overcome some limitations of current MAFM such as nonnegligible thermal drift and slow scan speed. Two kinds of 2D gratings, each with the nominal pitch of 300 nm and 1000 nm, were measured using line scans for the pitch measurement of each direction. The expanded uncertainties (k = 2) of measured pitch values were less than 0.2 nm and 0.4 nm for each specimen, and those of measured orthogonality were less than 0.09 degree and 0.05 degree respectively. The experimental results measured using the MAFM and optical diffractometer were coincident with each other within the expanded uncertainty of the MAFM. As a future work, we also proposed another scheme for the measurements of 2D gratings to increase the accuracy of calculated peak positions.

• International Journal of Precision Engineering and Manufacturing
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• 제9권2호
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• pp.18-22
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• 2008

The pitch and orthogonality of two-dimensional (2-D) gratings were measured using a metrological atomic force microscope (MAFM), and the measurement uncertainty was analyzed. Gratings are typical standard devices for the calibration of precision microscopes, Since the magnification and orthogonality in two perpendicular axes of microscopes can be calibrated simultaneously using 2-D gratings, it is important to certify the pitch and orthogonality of such gratings accurately for nanometrology. In the measurement of 2-D gratings, the MAFM can be used effectively for its nanometric resolution and uncertainty, but a new measurement scheme is required to overcome limitations such as thermal drift and slow scan speed. Two types of 2-D gratings with nominal pitches of 300 and 1000 nm were measured using line scans to determine the pitch measurement in each direction. The expanded uncertainties (k = 2) of the measured pitch values were less than 0.2 and 0.4 nm for each specimen, and the measured orthogonality values were less than $0.09^{\circ}$ and $0.05^{\circ}$, respectively. The experimental results measured using the MAFM and optical diffractometer agreed closely within the expanded uncertainty of the MAFM. We also propose an additional scheme for measuring 2-D gratings to increase the accuracy of calculated peak positions, which will be the subject of future study.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제8권2호
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• pp.153-162
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• 2001

In this Paper, the notion of $\varepsilon$-Birkhoff orthogonality introduced by Dragomir [An. Univ. Timisoara Ser. Stiint. Mat. 29(1991), no. 1, 51-58] in normed linear spaces has been extended to metric linear spaces and a decomposition theorem has been proved. Some results of Kainen, Kurkova and Vogt [J. Approx. Theory 105 (2000), no. 2, 252-262] proved on e-near best approximation in normed linear spaces have also been extended to metric linear spaces. It is shown that if (X, d) is a convex metric linear space which is pseudo strictly convex and M a boundedly compact closed subset of X such that for each $\varepsilon$>0 there exists a continuous $\varepsilon$-near best approximation $\phi$ : X → M of X by M then M is a chebyshev set .

• 한국정보통신학회:학술대회논문집
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• 한국해양정보통신학회 2002년도 추계종합학술대회
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• pp.766-769
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• 2002

본 논문에서는 802.l1b WLAN에서 채택된 CCK(complementary code keying)의 성능을 높이기 위해 새로운 완전직교 방법을 제안한다. CCK 변조기를 통해 생성된 codeword들이 모두 orthogonal한 성질을 유지할 수 있도록 전체 256개의 codeword를 trellis coding 방식을 이용하여 8개의 subset으로 나누었으며, 나누어진 각각의 subset내에서 생성된 codeword들은 완전한 orthogonality를 유지할 수 있다. 그 결과 최대 전송속도는 9.625Mbps로 제한되지만, 기존의 CCK변조 방식보다는 BER 10E-5에서 약 1.5dB의 성능향상을 얻을 수 있다.

• Journal of Applied and Pure Mathematics
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• 제6권3_4호
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• pp.155-165
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• 2024

Let R be a semi-prime ring. Let [δ₁, D₁] and [δ₂, D₂] be two generalized symmetric reverse biderivations of R with associated reverse biderivations D₁ and D₂. The main aim of the present paper is to establish conditions of orthogonality for symmetric reverse biderivations and symmetric generalized reverse biderivations in R.

• IEIE Transactions on Smart Processing and Computing
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• 제5권5호
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• pp.346-348
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• 2016

Coordinated multi-point transmission is a candidate technique for next-generation cellular communications systems. We consider a system with multiple cells in which base stations coordinate with each other by sharing user channel state information, which mitigates inter-cell interference (ICI), especially for users located at the cell edge. We introduce a new user scheduling method that considers both ICI and intra-cell orthogonality. Due to the influence of ICI cancellation and the loss reduction of effective channel gain during the beamforming process, the proposed method improves the system sum rate, when compared to the conventional method, by an average of 0.55bps/Hz for different numbers of total users per cell.

• 대한전기학회:학술대회논문집
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• 대한전기학회 1993년도 하계학술대회 논문집 A
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• pp.303-305
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• 1993

Walsh function and transform are important analytical tools for control theory and signal processing and have wide applications in those fields, especially in the field of digital communications. Therefore there is a need for a Walsh function generator in order to realize certain applications. And a number of different desists are known. But desist and implementation of such a generator through hardware logic nay give rise to orthogonality error. To develop Walsh function generator which gets rid of orthogonality error, this paper presents a microprocessor based design and implementation method.

• Journal of applied mathematics & informatics
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• 제25권1_2호
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• pp.495-503
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• 2007

Symmetric interpolating refinable function vectors with compact support are of interest in several applications such as signal processing, image processing and computer graphics. It is known in [13] that orthogonal interpolating refinable function vectors can not be symmetric for multiplicity r = 2 and dilation d = 2. In this paper, we shall investigate symmetric interpolating refinable function vectors with compact support for multiplicity r = 2 and dilation d = 2 by omitting orthogonality. To illustrate our theorems and results in this paper, we shall also present some examples of symmetric interpolating refinable function vectors with compact support and high order of sum rules.

• 대한기계학회논문집A
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• 제21권12호
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• pp.2038-2046
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• 1997

In this paper the instability of the system which has a disk and a mass-spring-damper system interacting through a medium having stiffness and damping is analyzed. To solve the equations of motion of this systme, it is assumed that the solution consists of the eigenfunctions which are the products of the Bessel functions and sine or cosine functions. The former represents the radial characteristics of the disk and the latter represents the circumferential characteristics. Using this assumed solution and the orthogonality of the eigenfunctions, the equations of motion can be transformed into a set of equations of motion with variables dependent only on the time. After this set is changed to the state equation, the eigenvalue problem can be made. Once the eigenvalues are calculated according to the angular velocity of the disk, the dynamic characteristics ofthis system is obtained. Because the thickness of the disk and the element characteristics of the mass-spring-damper system have important effects on the stability of the system, it will be understood how these factors affect the system and then a method to ameliorate the stability of the system with a disk will be presented.