• Journal of the Korean Mathematical Society
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• v.45 no.5
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• pp.1361-1378
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• 2008

This paper deals with the study of dichotomy and conditioning for two-point boundary value problems associated with first order matrix Lyapunov systems, with the help of Kronecker product of matrices. Further, we obtain close relationship between the stability bounds of the problem on one hand, and the growth behaviour of the fundamental matrix solution on the other hand.

• Journal of the Korean Professional Engineers Association
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• v.20 no.1
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• pp.14-20
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• 1987

The development of the FHT (fast Hadamard transform) was presented and based on the derivation by Cooley-Tukey algorithm. Alternately, it can be derived by matrix partitioning or matrix factorization techniques. This paper proposes a simple sparse matrix technique by Kronecker product of successive lower Hadamard matrix. The following shows how the Kronecker product can be mathematically defined and efficiently implemented using a matrix factorization methods.

• Journal of the Ergonomics Society of Korea
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• v.26 no.3
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• pp.111-115
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• 2007

Design equations for anthropometric product design are developed by considering the geometrical relationships of design dimensions and anthropometric dimensions. The present study applied the design structure matrix (DSM) method to the development of design equations for a computer workstation, and compared design values from the design equations with corresponding design values of ergonomic recommendations and existing products. The relationships between design dimensions (e.g., legroom and worktable) were analyzed by a DSM, and then the application order of design equations (e.g., seatpan, backrest, armrest, legroom, and worktable in descending order) was determined. Next, design equations were developed by analyzing the geometric relationships between computer workstation design dimensions and anthropometric dimensions. Finally, design values for a computer workstation were determined by considering a standard posture defined and representative human models (5th, 50th, 95th %ile). The design values calculated using the design equations were similar with those of ergonomic recommendations found in literature and two commercial products measured in the study; however, some design values (e.g., seatpan height) were different due to discrepancy in standard posture. The DSM method would be utilized to systematically analyze the relationships between design dimensions for anthropometric product design.

• Journal of Information Technology Applications and Management
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• v.26 no.6
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• pp.89-101
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• 2019

Many researchers have been focused on designing beauty product recommendation system for a long time because of increased need of customers for personalized and customized recommendation in beauty product domain. In addition, as the application of the deep neural network technique becomes active recently, various collaborative filtering techniques based on the deep neural network have been introduced. In this context, this study proposes a deep neural network model suitable for beauty product recommendation by applying Neural Collaborative Filtering and Generalized Matrix Factorization (NCF + GMF) to beauty product recommendation. This study also provides an implementation of web API system to commercialize the proposed recommendation model. The overall performance of the NCF + GMF model was the best when the beauty product recommendation problem was defined as the estimation rating score problem and the binary classification problem. The NCF + GMF model showed also high performance in the top N recommendation.

• Journal of the Korean Mathematical Society
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• v.59 no.4
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• pp.789-804
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• 2022

Striking result of Vybíral [51] says that Schur product of positive matrices is bounded below by the size of the matrix and the row sums of Schur product. Vybíral used this result to prove the Novak's conjecture. In this paper, we define Schur product of matrices over arbitrary C^*-algebras and derive the results of Schur and Vybíral. As an application, we state C^*-algebraic version of Novak's conjecture and solve it for commutative unital C^*-algebras. We formulate Pólya-Szegő-Rudin question for the C^*-algebraic Schur product of positive matrices.

• Journal of the Ergonomics Society of Korea
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• v.26 no.1
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• pp.79-85
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• 2007

Demand forecasting methods for a consumer product such as TV or refrigerator are widely known. However, sales forecast for a brand new product cannot be estimated using conventional forecasting methods. This study proposes a five-step procedure in forecasting a newly developed product. Step one defines functions in a High Touch product in order to estimate relative attraction of the product to consumer group. In step two, for a comparison purpose, a compatible product that is successfully penetrated into market is selected. Step three breaks a target population into many segments based on demography. Step four calculates relative attraction between the High Touch product and the compatible product. Finally, market penetration rate of the High Touch product is estimated using a bell-shaped diffusion curve of the compatible product. The process offers a method to estimate potential demand and growth pattern of the new High Touch product.

• Bulletin of the Korean Mathematical Society
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• v.47 no.5
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• pp.997-1000
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• 2010

We prove that the reduced free product of $k\;{\times}\;k$ matrix algebras over abelian $C^*$-algebras is not the minimal tensor product of reduced free products of $k\;{\times}\;k$ matrix algebras over abelian $C^*$-algebras. It is shown that the reduced group $C^*$-algebra associated with a group having the property T of Kazhdan is not isomorphic to a reduced free product of abelian $C^*$-algebras or the minimal tensor product of such reduced free products. The infinite tensor product of reduced free products of abelian $C^*$-algebras is not isomorphic to the tensor product of a nuclear $C^*$-algebra and a reduced free product of abelian $C^*$-algebra. We discuss the freeness of free product $II_1$-factors and solidity of free product $II_1$-factors weaker than that of Ozawa. We show that the freeness in a free product is related to the existence of Cartan subalgebras in free product $II_1$-factors. Finally, we give a free product factor which is not solid in the weak sense.

• Journal of Engineering Education Research
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• v.9 no.3
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• pp.49-61
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• 2006

The objective of this study was to propose a new framework for the creative engineering in the product family design coursework. The idea of product family design is a good solution to fulfill customer's requirements and to respond quickly for the technology change. Mass customization based on product family and product platform is a new paradigm with variety and customization through flexibility and quick responsiveness. In this study, the subjects of product family, product platform, product family map, platform leveraging strategy, morphological matrix and module based product family design were reviewed and presented. A new idea generation scheme utilizing SCAMPER method was combined with the morphological matrix approach. For the effective product family and platform design, creative efforts and approaches were utilized and implemented in the coursework process. This will help students to develop creative thinking and approaches in the engineering problem solving.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.11 no.5
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• pp.2468-2483
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• 2017

The construction of completely random sensing matrices of Compressive Sensing requires a large number of random numbers while that of deterministic sensing operators often needs complex mathematical operations. Thus both of them have difficulty in acquiring large signals efficiently. This paper focuses on the enhancement of the practicability of the structurally random matrices and proposes a semi-deterministic sensing matrix called Partial Kronecker product of Identity and Hadamard (PKIH) matrix. The proposed matrix can be viewed as a sub matrix of a well-structured, sparse, and orthogonal matrix. Only the row index is selected at random and the positions of the entries of each row are determined by a deterministic sequence. Therefore, the PKIH significantly decreases the requirement of random numbers, which has a complex generating algorithm, in matrix construction and further reduces the complexity of sampling. Besides, in order to process large signals, the corresponding fast sampling algorithm is developed, which can be easily parallelized and realized in hardware. Simulation results illustrate that the proposed sensing matrix maintains almost the same performance but with at least 50% less random numbers comparing with the popular sampling matrices. Meanwhile, it saved roughly 15%-35% processing time in comparison to that of the SRM matrices.

• Kyungpook Mathematical Journal
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• v.48 no.3
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• pp.473-486
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• 2008

In this paper we generate a fuzzy dynamical matrix Lyapunov system and obtain a sufficient condition for the observability of this system.