• East Asian mathematical journal
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• 제24권4호
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• pp.377-387
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• 2008

We consider associative ring R (not necessarily commutative). In this paper the concepts: zero square ring of type-1/type-2, zero square ideal of type-1/type-2, zero square dimension of a ring R were introduced and obtained several important results. Finally, some relations between the zero square dimension of the direct sum of finite number of rings; and the sum of the zero square dimension of individual rings; were obtained. Necessary examples were provided.

• Communications for Statistical Applications and Methods
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• 제13권2호
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• pp.429-440
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• 2006

In statistical computing, it is often for researchers to need the distribution of a weighted sum of noncentral chi-square variables. In this case, it is very limited to know its exact distribution. There are many works to contribute to this topic, e.g. Imhof (1961) and Solomon-Stephens (1977). Imhof's method gives good approximation to the true distribution, but it is not easy to apply even though we consider the development of computer technology Solomon-Stephens's three moment chi-square approximation is relatively easy and accurate to apply. However, they skipped many details, and their simulation is limited to a weighed sum of central chi-square random variables. This paper gives details on Solomon-Stephens's method. We also extend their simulation to the weighted sum of non-central chi-square distribution. We evaluated approximated powers for homogeneous test and compared them with the true powers. Solomon-Stephens's method shows very good approximation for the case.

• Korean Journal of Mathematics
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• 제24권1호
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• pp.71-79
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• 2016

In this paper, we determine all positive integers which cannot be represented by a sum of four squares at least 9, and prove that for each N, there are nitely many positive integers which cannot be represented by a sum of four squares at least $N^2$ except $2{\cdot}4^m$, $6{\cdot}4^m$ and $14{\cdot}4^m$ for $m{\geq}0$. As a consequence, we prove that for each $k{\geq} 5$ there are nitely many positive integers which cannot be represented by a sum of k squares at least $N^2$.

• 한국수학교육학회지시리즈A:수학교육
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• 제45권3호
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• pp.315-318
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• 2006

In this paper we present the simple updating formulas for a sum of product and a sum of cross product when a new value is added on or a specific value is eliminated from the original data. The sample variance and correlation for the new data set are derived by new computing formulas. Any statistic which is a function of the sum of product and a sum of cross product also can be updated by proposed method even though the original data is not available.

• 한국통신학회논문지
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• 제38A권7호
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• pp.560-570
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• 2013

본 논문에서는 셀 간 간섭과 셀 내 사용자 간 간섭이 공존하는 two-cell 다중 안테나 하향링크 간섭 채널에서 송수신기 설계 방법을 제안한다. 우선 셀 간 간섭과 셀 내 사용자 간 간섭을 다차원 subspace에 정렬하는 zero-forcing 간섭 정렬 방법을 일반화한다. 그리고 일반화한 zero-forcing 간섭 정렬 방법에서 구한 송수신기를 "regularizing" 하는 minimum weighted-mean-square-error 기반 regularized ZF-IA 방법을 제안한다. 기존 weighted-sum-rate-maximizing 송수신기 설계 방법에 비해 제안하는 방법은 weight 를 구하는 반복 연산 과정이 필요하지 않다. 그 결과 제안하는 방법은 비록 sum-rate 최대화하도록 설계되진 않았지만, 기존의 weighted-sum-rate maximizing 방법 보다 계산 복잡도 면에서 효율적이고 더 빠른 수렴 속도를 얻을 수 있다. 다양한 분석과 실험을 통해 제안하는 regularized ZF-IA 방법의 우수성을 확인하였다. 구체적으로 반복 연산 수가 작은 경우, 제안하는 regularized ZF-IA 방법의 sum-rate 성능이 기존의 weighted-sum-rate maximizing 방법보다 SNR = 20 [dB] 에서 약 49.8 % 이상 나음을 확인할 수 있다. 더불어 채널 정보에 오차가 있는 경우 상당한 robustness를 제공하는 robust 송수신기 설계 방법도 제시한다.

• 한국지능시스템학회논문지
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• 제21권5호
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• pp.549-554
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• 2011

본 논문에서는 출력 궤환 제어기를 이용해 다항식 퍼지 대규모 시스템을 안정화하는 방법을 제안한다. 이를 위해, 먼저, 대규모 시스템의 부분 시스템에 대해 퍼지 모델링을 한 후, 각각에 대해 출력 궤환 제어기를 설계하여 대규모 시스템을 안정화하는 방법을 제안한다. 이때, 다항식 Lyapunov 함수를 적용하면 다항식 퍼지 대규모 시스템의 안정화 조건은 제곱합 조건으로 주어지고, 이것은 MATLAB의 툴박스인 SOSTOOLS로 해석 가능하다. 이러한 과정을 거친 후에 얻어진 해에서 시스템을 안정화시키는 출력 궤환 제어기의 이득을 구할 수 있다. 마지막으로, 제안된 기법의 적합성을 검증하기 위해 시뮬레이션 예제가 주어진다.

• 대한수학회지
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• 제33권3호
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• pp.651-655
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• 1996

Lagrange's famous Four Square Theorem [L] says that every positive integer can be represented by the sum of four squares. This marvelous theorem was generalized by Mordell [M1] and Ko [K1] as follows : every positive definite integral quadratic form of two, three, four, and five variables is represented by the sum of five, six, seven, and eight squares, respectively. And they tried to extend this to positive definite integral quadratic forms of six or more variables.

• 대한토목학회논문집
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• 제10권3호
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• pp.1-6
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• 1990

다지점지진하중(多支點地震荷重)을 받는 사경문(四徑問) 연속철도교양(連續鐵道橋梁)의 동적거동(動的擧動)을 응답(應答)스펙트럼법(法)에 의하여 조사(調査)하였다. 소진복(小振福)의 진동(振動)과 재료(材料)의 선형(線形)-탄성거동(彈性擧動)을 가정(假定)하였으며, 지반(地盤)-구조물(構造物) 상호작용(相互作用) 효과(效果)는 무시(無視)하였고, 교량(橋梁)의 횡방향(橫方向) 등답(應答)만을 고려(考慮)하였다. 응답(應答)스펙트럼해석(解析)의 결과(結果)는 시간이력해석결과(時間履歷解析結果)와 비교(比較)되었으며 모우드 최대치(最大値)와 지지점운동(支持點運動)의 중량(重量)은 여러가지 조합법칙(組合法則) 즉(卽), Square-Root-Of-Sum-Squares, Double Sum, 그리고 P-Norm Rule을 적용(適用)하였다.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제8권8호
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• pp.2722-2742
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• 2014

We propose methods of linear transceiver design for two different power constraints, sum relay power constraint and per relay power constraint, which determine signal processing matrices such as base station (BS) transmitter, relay precoders and user receivers to minimize sum mean square error (SMSE) for multi-relay multi-user (MRMU) networks. However, since the formulated problem is non-convex one which is hard to be solved, we suboptimally solve the problems by defining convex subproblems with some fixed variables. We adopt iterative sequential designs of which each iteration stage corresponds to each subproblem. Karush-Kuhn-Tucker (KKT) theorem and SMSE duality are employed as specific methods to solve subproblems. The numerical results verify that the proposed methods provide comparable performance to that of a full relay cooperation bound (FRCB) method while outperforming the simple amplify-and-forward (SAF) and minimum mean square error (MMSE) relaying in terms of not only SMSE, but also the sum rate.

• 대한수학회지
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• 제59권3호
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• pp.439-448
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• 2022

For a natural number n, let R(n) denote the number of representations of n as the sum of one square and five cubes of primes. In this paper, it is proved that the anticipated asymptotic formula for R(n) fails for at most $O(N^{{\frac{4}{9}+{\varepsilon}})$ positive integers not exceeding N.