• Communications of the Korean Mathematical Society
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• v.12 no.1
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• pp.75-78
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• 1997

We show that if a simple $C^*$-algebra A satisfies certain $K_1$-group conditions, then two unitarily equivalent projections are homotopic. Also we show that the equivalence of projections determined by a dimension function is a homotopy.

• Journal of the Korean Mathematical Society
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• v.45 no.5
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• pp.1341-1360
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• 2008

In this paper we investigate the projections of bouquet graph B with two cycles. A projection of B is said to be trivial if only trivial embeddings are obtained from the projection. It is shown that, to cover all nontrivial projections of B, at least three embeddings of B are needed. We also show that a nontrivial projection of B is covered by one of some two embeddings if the image of each cycle has at most one self-crossing.

• Journal of Industrial Technology
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• v.21 no.B
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• pp.91-98
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• 2001

In this paper, center detection and motion analysis of a moving object are studied. Kohonen's self-organizing neural network models are used for the moving objects tracking and time delay neural networks are used for dynamic characteristic analysis. Instead of objects brightness, neuron projections by Kohonen Networks are used. The motion of target objects can be analyzed by using the differential neuron image between the two projections. The differential neuron image which is made by two consecutive neuron projections is used for center detection and moving objects tracking. The two differential neuron images which are made by three consecutive neuron projections are used for the moving trajectory estimation. It is possible to distinguish 8 directions of a moving trajectory with two frames and 16 directions with three frames.

• 제어로봇시스템학회:학술대회논문집
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• 2001.10a
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• pp.63.5-63
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• 2001

In this paper, moving objects tracking and dynamic characteristic analysis are studied. Kohonen´s self-organizing neural network models are used for moving objects tracking and time delay neural networks are used for dynamic characteristic analysis. Instead of objects brightness, neuron projections by Kohonen Networks are used. The motion of target objects can be analyzed by using the differential neuron image between the two projections. The differential neuron image which is made by two consecutive neuron projections is used for center detection and moving objects tracking. The two differential neuron images which are made by three consecutive neuron projections are used for the moving trajectory estimation.

• East Asian mathematical journal
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• v.18 no.2
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• pp.235-243
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• 2002

In this paper, we get conditions for the natural projections of some product manifolds with varying metrics of two Riemannian manifolds to be harmonic, and necessary and sufficient conditions for some product manifolds with the harmonic natural projections of two Einstein manifolds to be Einstein manifolds.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.16 no.9
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• pp.2991-3007
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• 2022

Two dimensional locality preserving projections (2D-LPP) is an improved algorithm of 2D image to solve the small sample size (SSS) problems which locality preserving projections (LPP) meets. It's able to find the low dimension manifold mapping that not only preserves local information but also detects manifold embedded in original data spaces. However, 2D-LPP is simple and elegant. So, inspired by the comparison experiments between two dimensional linear discriminant analysis (2D-LDA) and linear discriminant analysis (LDA) which indicated that matrix based methods don't always perform better even when training samples are limited, we surmise 2D-LPP may meet the same limitation as 2D-LDA and propose a novel matrix exponential method to enhance the performance of 2D-LPP. 2D-MELPP is equivalent to employing distance diffusion mapping to transform original images into a new space, and margins between labels are broadened, which is beneficial for solving classification problems. Nonetheless, the computational time complexity of 2D-MELPP is extremely high. In this paper, we replace some of matrix multiplications with multiple multiplications to save the memory cost and provide an efficient way for solving 2D-MELPP. We test it on public databases: random 3D data set, ORL, AR face database and Polyu Palmprint database and compare it with other 2D methods like 2D-LDA, 2D-LPP and 1D methods like LPP and exponential locality preserving projections (ELPP), finding it outperforms than others in recognition accuracy. We also compare different dimensions of projection vector and record the cost time on the ORL, AR face database and Polyu Palmprint database. The experiment results above proves that our advanced algorithm has a better performance on 3 independent public databases.

• Communications for Statistical Applications and Methods
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• v.25 no.3
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• pp.275-282
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• 2018

This paper discusses the use of projections for the sums of squares in the analyses of variance for two-way nested design data. The model for this data is assumed to only have random effects. Two different sizes of experimental units are required for a given experimental situation, since nesting is assumed to occur both in the treatment structure and in the design structure. So, variance components are coming from the sources of random effects of treatment factors and error terms in different sizes of experimental units. The model for this type of experimental situation is a random effects model with more than one error terms and therefore estimation of variance components are concerned. A projection method is used for the calculation of sums of squares due to random components. Squared distances of projections instead of using the usual reductions in sums of squares that show how to use projections to estimate the variance components associated with the random components in the assumed model. Expectations of quadratic forms are obtained by the Hartley's synthesis as a means of calculation.

• Communications of the Korean Mathematical Society
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• v.36 no.2
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• pp.327-342
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• 2021

We consider a generalization of the L^q-spectrum with respect to two Borel probability measures on ℝⁿ having the same compact support, and also study their behavior under orthogonal projections of measures onto an m-dimensional subspace. In particular, we try to improve the main result of Bahroun and Bhouri [4]. In addition, we are interested in studying the behavior of the generalized lower and upper L^q-spectrum with respect to two measures on "sliced" measures in an (n - m)-dimensional linear subspace. The results in this article establish relations with the L^q-spectrum with respect to two Borel probability measures and its projections and generalize some well-known results.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.31B no.7
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• pp.129-140
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• 1994

In this paper we investigate the hardware implementation of block matching algorithms (BMAs) for moving sequences. Using systolic arrays we propose a hardware architecture of a two-stage BMA using integral projections which reduces greatly computational complexity with its performance comparable to that of the full search (FS). Proposed hardware architecture is faster than hardware architecture of the FS by 2~15 times. For realization of the FS and two stage BMA modeling and simulation results using SPW and VHDL are also shown.

• Journal of applied mathematics & informatics
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• v.32 no.1_2
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• pp.61-74
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• 2014

This paper describes an iterative method for orthogonal projections $AA^+$ and $A^+A$ of an arbitrary matrix A, where $A^+$ represents the Moore-Penrose inverse. Convergence analysis along with the first and second order error estimates of the method are investigated. Three numerical examples are worked out to show the efficacy of our work. The first example is on a full rank matrix, whereas the other two are on full rank and rank deficient randomly generated matrices. The results obtained by the method are compared with those obtained by another iterative method. The performance measures in terms of mean CPU time (MCT) and the error bounds for computing orthogonal projections are listed in tables. If $Z_k$, k = 0,1,2,... represents the k-th iterate obtained by our method then the sequence of the traces {trace($Z_k$)} is a monotonically increasing sequence converging to the rank of (A). Also, the sequence of traces {trace($I-Z_k$)} is a monotonically decreasing sequence converging to the nullity of $A^*$.