• Journal of the Institute of Electronics Engineers of Korea TC
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• v.46 no.6
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• pp.86-93
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• 2009

We investigate lattice-reduction-aided precoding techniques for multi-user multiple-input multiple-output (MIMO) channels. When assuming full knowledge of the channel state information only at the transmitter, a vector perturbation (VP) is a promising precoding scheme that approaches sum capacity and has simple receiver. However, its encoding is nondeterministic polynomial time (NP)-hard problem. Vector perturbation using lattice reduction algorithms can remarkably reduce its encoding complexity. In this paper, we propose a vector perturbation scheme using Seysen's lattice reduction (VP-SLR) with simultaneously reducing primal basis and dual one. Simulation results show that the proposed VP-SLR has better bit error rate (BER) and larger capacity than vector perturbation with Lenstra-Lenstra-Lovasz lattice reduction (VP-LLL) in addition to less encoding complexity.

• Korean Journal of Mathematics
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• v.16 no.3
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• pp.413-424
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• 2008

In [21], Th.M. Rassias proved that the norm defined over a real vector space V is induced by an inner product if and only if for a fixed integer $n{\geq}2$ $$n{\parallel}\frac{1}{n}\sum\limits_{i=1}^{n}x_i{\parallel}^2+\sum\limits_{i=1}^{n}{\parallel}x_i-\frac{1}{n}\sum\limits_{j=1}^{n}x_j{\parallel}^2=\sum\limits_{i=1}^{n}{\parallel}x_i{\parallel}^2$$ holds for all $x_1,{\dots},x_n{\in}V$. We consider the functional equation $$nf(\frac{1}{n}\sum\limits^n_{i=1}x_i)+\sum\limits_{i=1}^{n}f(x_i-\frac{1}{n}\sum\limits_{j=1}^{n}x_j)=\sum\limits_{i=1}^nf(x_i)$$ Using fixed point methods, we prove the generalized Hyers-Ulam stability of the functional equation $$(1)\;2f(\frac{x+y}{2})+f(\frac{x-y}{2})+f(\frac{y-x}{2})=f(x)+f(y)$$.

• 제어로봇시스템학회:학술대회논문집
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• 2005.06a
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• pp.894-900
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• 2005

A new approach to the straightforward implementation of the unscented filter in a unit quaternion space is proposed for spacecraft attitude estimation. Since the unscented filter is formulated in a vector space and the unit quaternions do not belong to a vector space but lie on a nonlinear manifold, the weighted sum of quaternion samples does not produce a unit quaternion estimate. To overcome this difficulty, a method of weighted mean computation for quaternions is derived in rotational space, leading to a quaternion with unit norm. A quaternion multiplication is used for predicted covariance computation and quaternion update, which makes a quaternion in a filter lie in the unit quaternion space. Since the quaternion process noise increases the uncertainty in attitude orientation, modeling it either as the vector part of a quaternion or as a rotation vector is considered. Simulation results illustrate that the proposed approach successfully estimates spacecraft attitude for large initial errors and high tip-off rates, and modeling the quaternion process noise as a rotation vector is more optimal than handling it as the vector part of a quaternion.

• The KIPS Transactions:PartD
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• v.15D no.3
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• pp.399-410
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• 2008

This paper suggests a new retrieval method using weighted vector sum to resolve a problem of traditional location-based retrieval method, nearest neighbor (NN) query, and NN query using direction. The proposed method filters out data with the radius, and then the remained retrieval area is filtered by a direction information compounded of a user's moving direction, a pre-fixed interesting direction, and a pre-fixed retrieval angle. The moving direction is computed from a vector or a weighted vector sum of several vectors using a weight to adopt several cases. The retrieval angle can be set from traditional $360^{\circ}$ to any degree you want. The retrieval data for this method can be a still and moving image recorded shooting location, and also several type of media like text, web, picture offering to customer with location of company or resort. The suggested method guarantees more accurate retrieval than traditional location-based retrieval methods because that the method selects data within the radius and then removes data of useless areas like passed areas or an area of different direction. Moreover, this method is more flexible and includes the direction based NN.

• Journal of applied mathematics & informatics
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• v.16 no.1_2
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• pp.407-417
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• 2004

It is well known that the nonlinearity of vector Boolean functions F on n-dimensional vector space $GF(2)^n$ to $GF(2)^m$ is bounded above by $2^{n-1} - 2 ^{\frac{n}{2}-1}$. In this paper we derive upper bounds and a lower bound on the nonlinearity of vector Boolean functions in terms of auto-correlations. Strengths and weaknesses of each bounds are examined. Also, we modify the notions of the sum-of-square indicator and absolute indicator for Boolean functions to the case of vector Boolean functions to measure global avalanche characteristics of vector Boolean functions. Using those indicators we compare the global avalanche characteristics of DES (Data Encryption System) and Rijndael.

• The Journal of Natural Sciences
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• v.11 no.1
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• pp.11-14
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• 1999

Let G be a compact Lie group and let $\rho$ : G $\rightarrow O(2) be a homomorphism. Denote by V the G-module associated with $\rho$ and by S(V) the unit circle of V. In this paper, we show that if G is abelian, then a real G-vector bundle over S(V) is isomorphic to Whitney sum of real G-line or G-plane bundles.

• Explosives and Blasting
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• v.19 no.2
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• pp.19-26
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• 2001

국토의 효율적 활용을 위한 각종 토목.건설공사나 석재 및 골재생산 등을 위해 암반을 굴착함에 있어 다양한 산업용 화약류가 이용되고 있다. 그러나 화약의 사용으로 인해 수반되는 발파진동은 인체 및 구조물 등에 피해를 발생시켜 인근의 주민과 마찰을 일으키고 있다.본 연구에서는 발파진동속도 data를 취합하여 분석 사용함에 있어서 V, T, L 성분의 최대 실벡터합을 사용하는 경우와 최대 벡터합을 사용하는 경우를 비교하여 실제 현장 기험시 적용성을 높이고자 하였다. 진동속도는 최대 실 벡터합에 비해 최대 벡터합에 의해 구해진 진동속도의 크기가 장승근에서는 24.6%, 삼승근에서는 26.1%가 증가하는 것으로 나타났으며, 단일성분의 최대치, 최대 실벡터합, 최대 벡터합의 안전율은 1 : 1.154 : 1.359로 나타났다

• Journal of the Korea Computer Industry Society
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• v.5 no.1
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• pp.147-156
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• 2004

In this paper, a new fast motion estimation algorithm which is based on the Block Sum Pyramid Algorithm(BSPA) is presented. The Spiral Diamond Mesh Search scheme and Partial Distortion Elimination scheme of Efficient Multi-level Successive Elimination Algorithm were improved and then the improved schemes were applied to the BSPA. The motion estimation accuracy of the proposed algorithm is nearly 100% and the cost of Block Sum Pyramid Algorithm was reduced in the proposed algorithm. The efficiency of the proposed algorithm was verified by experimental results.

• Journal of the Korean Mathematical Society
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• v.36 no.5
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• pp.1009-1020
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• 1999

The minimum permanent and the set of minimizing matrices over the face of the polytope n of all doubly stochastic matrices of order n determined by any staircase matrix was determined in [4] in terms of some parameter called frame. A staircase matrix can be described very simply as a Ferrers matrix by its row sum vector. In this paper, some simple exposition of the permanent minimization problem over the faces determined by Ferrers matrices of the polytope of n are presented in terms of row sum vectors along with simple proofs.

• Journal of Information Technology Services
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• v.2 no.2
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• pp.111-119
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• 2003

In this paper, an efficient block matching algorithm which is based on the Block Sum Pyramid Algorithm (BSPA) is presented. The cost of BSPA[1] was reduced in the proposed algorithm by using l2 norm and partial distortion elimination technique. Motion estimation accuracy of the proposed algorithm is equal to that of BSPA. The efficiency of the proposed algorithm was verified by experimental results.