• Journal of applied mathematics & informatics
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• v.19 no.1_2
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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.

• Journal of applied mathematics & informatics
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• v.42 no.5
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• pp.1155-1170
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• 2024

The concept of orthogonality is widely used in various fields of study, both within and outside the scope of mathematics, especially algebra. The concept of orthogonality gives a picture of the relationship between two vectors that are perpendicular to each other, or the inner product in both of them is zero. However, the concept of orthogonality has undergone significant development. One of the developments is Pythagorean orthogonality. In this paper, it is explored topics related to Pythagorean orthogonality and linear mappings in inner product spaces. It is also examined how linear mappings preserve Pythagorean orthogonality and provides insights into how mathematical transformations affect geometric relationships. The results reveal several properties that apply to linear mappings preserving Pythagorean orthogonality.

• Journal of the Korean Society for Precision Engineering
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• v.24 no.9
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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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• v.9 no.2
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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.

• The Pure and Applied Mathematics
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• v.8 no.2
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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 .

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2002.11a
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• pp.766-769
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• 2002

In this paper, we propose new orthogonal modulation method to enhance the performance of CCK adapted in 802.l1b WLAN. To maintain the orthogonality of codewords produced by CCK modulator, we devide 256 codewords into 8 subset by trellis coding and codewords On a subset are orthogonal each other. In result, this method restricts maximum data rate to 9.625Mbps, however, it is better about 1.5dB than original UK modulation at BER 10$^{-5}$ .

• Journal of Applied and Pure Mathematics
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• v.6 no.3_4
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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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• v.5 no.5
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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.

• Proceedings of the KIEE Conference
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• 1993.07a
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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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• v.25 no.1_2
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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.