• Bulletin of the Korean Mathematical Society
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• v.42 no.3
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• pp.433-441
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• 2005

The concepts linearly independent elements and u-linearly independent elements in an N-group G where N is a near-ring, were introduced and studied. A few important results in the theory of vector spaces were generalized to N-groups.

• Journal of the Korean Mathematical Society
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• v.34 no.1
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• pp.213-225
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• 1997

Let A be a real $m \times n$ matrix. The column rank of A is the dimension of the column space of A and the maximal column rank of A is defined as the maximal number of linearly independent columns of A. It is wekk known that the column rank is the maximal column rank in this situation.

• Journal of applied mathematics & informatics
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• v.27 no.3_4
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• pp.621-638
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• 2009

The linear system Ax = b will have (i) no solution, (ii) only one non-trivial (trivial) solution, or (iii) infinity of solutions. Our focus will be on cases (ii) and (iii). The mathematical models of many real-world problems give rise to (a) ill-conditioned linear systems, (b) singular linear systems (A is singular with all its linearly independent rows are sufficiently linearly independent), or (c) ill-conditioned singular linear systems (A is singular with some or all of its strictly linearly independent rows are near-linearly dependent). This article highlights the scope and need of a randomized algorithm for ill-conditioned/singular systems when a reasonably narrow domain of a solution vector is specified. Further, it stresses that with the increasing computing power, the importance of randomized algorithms is also increasing. It also points out that, for many optimization linear/nonlinear problems, randomized algorithms are increasingly dominating the deterministic approaches and, for some problems such as the traveling salesman problem, randomized algorithms are the only alternatives.

• Journal of Institute of Control, Robotics and Systems
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• v.8 no.11
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• pp.941-947
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• 2002

Two methods of constructing T-S fuzzy model which is equivalent to a given nonlinear system are presented. The first method is to obtain an equivalent T-S fuzzy model by using the sum of linearly independent scalar functions with constant real matrix coefficients. The sum of products of linearly independent scalar functions is used in the second method. The former method is to formulate the procedures of T-S fuzzy modeling dealt in many examples of previous publications; the latter is a new method. By comparing the number of linearly independent functions used in the two methods, we can easily find out which method makes fewer rules than the other. The nonlinear dynamics of an inverted Pendulum on a cart is used as an equivalent T-5 fuzzy modeling example.

• Journal of Integrative Natural Science
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• v.13 no.1
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• pp.8-12
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• 2020

In this paper we study the Minimum Error Discrimination problem (MED) for ensembles of linearly independent (LI) pure states. By constructing a map from the set on those ensembles we show that the Pretty Good Measurement (PGM) and the optimal measurement for the MED are related by the map.

• Structural Engineering and Mechanics
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• v.39 no.5
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• pp.703-716
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• 2011

The accurate dynamic analysis of structures is usually performed by a fine finite element discretization with very large number of degrees of freedom. Apart from modal analysis, one can reduce the number of final equations by assuming the deformed shape of the structure as a linear combination of independent Ritz vectors. The efficiency of this method relies heavily on the vectors selected. In this paper, a new set of Ritz vectors is proposed. It is primarily proved that these vectors are linearly independent. Subsequently, various two and three-dimensional examples are analyzed based on the proposed method. In each case, the results are compared with the ones obtained based on usual Ritz and modal analysis methods. It is finally concluded that the proposed method is very effective and efficient method for dynamic analysis of structures in frequency domain.

• Journal of applied mathematics & informatics
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• v.8 no.1
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• pp.9-26
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• 2001

In some previous papers the author extended two algorithms proposed by Z. Kovarik for approximate orthogonalization of a finite set of linearly independent vectors from a Hibert space, to the case when the vectors are rows (not necessary linearly independent) of an arbitrary rectangular matrix. In this paper we describe combinations between these two methods and the classical Kaczmarz’s iteration. We prove that, in the case of a consistent least-squares problem, the new algorithms so obtained converge ti any of its solutions (depending on the initial approximation). The numerical experiments described in the last section of the paper on a problem obtained after the discretization of a first kind integral equation ilustrate the fast convergence of the new algorithms. AMS Mathematics Subject Classification : 65F10, 65F20.

• Bulletin of the Korean Mathematical Society
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• v.57 no.4
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• pp.865-872
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• 2020

Let X ⊂ ℙ^r be an integral and non-degenerate variety. Set n := dim(X). Let 𝜌(X)" be the maximal integer such that every zero-dimensional scheme Z ⊂ X smoothable in X is linearly independent. We prove that X is linearly normal if 𝜌(X)" ≥ 2⌈(r + 2)/2⌉ and that 𝜌(X)" < 2⌈(r + 1)/(n + 1)⌉, unless either n = r or X is a rational normal curve.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.4
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• pp.743-748
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• 2013

The purpose of this note is to introduce interesting and useful properties differential-basis and p-basis in theorem 3.3. The result gives a existence differential basis of $S^P$ [$[{\Lambda}_1]$](S) which has a p-basis over $S^p$ ($S^p[{\Lambda}_1]$).

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2006.05a
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• pp.1066-1070
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• 2006

Independent component analysis (ICA) is a statistical method for linearly transforming observed high-dimensional multivariate data into several statistically independent components. ICA has gained wide-spread attention in a variety of fields including spectrum application. We focus on the application of ICA for separating independent sources from a set of mixtures and estimating their fractions in a mixture. The proposed method of estimating fractions is based on the regression model subject to the non-negativity constraint on coefficients. Simulation experiments are performed to demonstrate the performance of the proposed approach.