• Korean Journal of Mathematics
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• 제21권1호
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• pp.1-21
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• 2013

Using the fixed point method, we prove the Ulam-Hyers stability of the orthogonally additive and orthogonally quadratic functional equation $$f(\frac{x}{2}+y)+f(\frac{x}{2}-y)+f(\frac{x}{2}+z)+f(\frac{x}{2}-z)=\frac{3}{2}f(x)-\frac{1}{2}f(-x)+f(y)+f(-y)+f(z)+f(-z)$$ (0.1) for all $x$, $y$, $z$ with $x{\bot}y$, in orthogonality Banach spaces and in non-Archimedean orthogonality Banach spaces.

• 대한수학회지
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• 제48권5호
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• pp.913-926
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• 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.

• Kyungpook Mathematical Journal
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• 제47권1호
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• pp.69-76
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• 2007

Let $f$ denote a mapping from an orthogonality space ($\mathcal{X}$, ${\bot}$) into a real Banach space $\mathcal{Y}$. In this paper, we prove the Hyers-Ulam-Rassias stability of the orthogonally cubic functional equations $f(2x+y)+f(2x-y)=2f(x+y)+2f(x-y)+12f(x)$ and $f(x+y+2z)+f(x+y-2z)+f(2x)+f(2y)=2f(x+y)+4f(x+z)+4f(x-z)+4f(y+z)+4f(y-z)$, where $x{\bot}y$, $y{\bot}z$, $x{\bot}z$.

• 한국통신학회논문지
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• 제36권3C호
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• pp.170-174
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• 2011

본 논문은 양방향 중계 채널(Two-Way Relay Channel) 에서 기존에 연구되었던 협력 통신(Cooperative Communication) 에서 네트워크 부호화(Network Coding)에 대해 간단히 소개한다. 협력 통신 시스템에서의 직교성을 이용한 새로운 네트워크 부호화 기법을 제안한다. 제안된 직교 사상 네트워크 부호화 기법은 기존에 널리 사용되고 있는 DF(Decode-and-Forward) 모듈러 합 기법의 전송률을 유지하면서 DF 기법의 단점인 오류 전파(Error Propagation) 현상을 제거하여 향상된 BER(Bit Error Rate) 성능을 보인다.

• 한국통신학회논문지
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• 제27권6B호
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• pp.593-600
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• 2002

The reverse link signal power required for multimedia traffic in multipath faded single-code (SC-) and multi-code CDMA (MC-CDMA) systems is investigated. The effect of orthogonality loss among multiple spreading code channels is herein characterized by the orthogonality factor. The required signal power in both the CDMA systems is then analyzed in terms of the relative required signal power ratio of data to voice traffic. The effect of varying system parameters including spreading bandwidth, the of orthogonality factor, and the number of spreading codes are examined. Analytical results show that MC-CDMA users transmitting only a single traffic type require significantly more power than SC-CDMA users with only a single traffic type. On the other hand, MC-CDMA users transmitting multimedia traffic require power levels approximately identical to SC-CDMA users with multimedia traffic. The results can be used in the design of radio resource management (e.g., power allocation) scheme for wireless multimedia services.

• ETRI Journal
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• 제40권5호
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• pp.592-603
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• 2018

In order to obtain better target identification performance, an efficient waveform design method with high range resolution and low sidelobe level for orthogonal frequency division multiplexing (OFDM) multiple-input multiple-output (MIMO) radar is proposed in this paper. First, the wideband CP-based OFDM signal is transmitted on each antenna to guarantee large bandwidth and high range resolution. Next, a complex orthogonal design (COD) is utilized to achieve code domain orthogonality among antennas, so that the spatial diversity can be obtained in MIMO radar, and only the range sidelobe on the first antenna needs suppressing. Furthermore, sidelobe suppression is expressed as an optimization problem. The integrated sidelobe level (ISL) is adopted to construct the objective function, which is solved using the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm. The numerical results demonstrate the superiority in performance (high resolution, strict orthogonality, and low sidelobe level) of the proposed method compared to existing algorithms.

• 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 .

• Kyungpook Mathematical Journal
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• 제62권2호
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• pp.271-287
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• 2022

In this paper, starting with the geometric constants that can characterize Hilbert spaces, combined with the isosceles orthogonality of Banach spaces, the orthogonal geometric constant Ω_X(α) is defined, and some theorems on the geometric properties of Banach spaces are derived. Firstly, this paper reviews the research progress of orthogonal geometric constants in recent years. Then, this paper explores the basic properties of the new geometric constants and their relationship with conventional geometric constants, and deduces the identity of Ω_X(α) and γ_X(α). Finally, according to the identities, the relationship between these the new orthogonal geometric constant and the geometric properties of Banach Spaces (such as uniformly non-squareness, smoothness, convexity, normal structure, etc.) is studied, and some necessary and sufficient conditions are obtained.

• Journal of applied mathematics & informatics
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• 제25권1_2호
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• pp.445-453
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• 2007

Using Schensted Insertion and Deletion algorithm for shifted rim hook tableaux described in [7], we construct Schensted algorithm for shifted rim hook tableaux. This give us the combinatorial proof for the orthogonality of the second kind for the spin characters of $\tilde{S}n$.

• Structural Engineering and Mechanics
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• 제7권4호
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• pp.361-375
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• 1999

This paper presents an analytic method of examining the out-of-plane vibration of continuous curved beam on periodical supports. The orthogonality of two distinct sets of mode shape functions is derived. The forced vibration of beam due to moving loads is examined. Two types of moving loads, which are concentrated load and uniformly distributed load, are considered. The response characteristics of beam induced by these loads are investigated as well.