• Bulletin of the Korean Mathematical Society
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• v.21 no.2
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• pp.91-95
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• 1984

Let D$^{p}$ be the space of distributions of $L^{p}$-growth and S the space of tempered destributions in $R^{n}$: D$^{p}$, 1.leq.P.leq..inf., is the dual of the space $D^{p}$ which we discribe later. We denote by O$_{c}$(S:S') the space of convolution operators in S. In [8] S. Sznajder and Z. Zielezny proved the following necessary conditions for convolution operators in O$_{c}$(S:S) to be solvable in S.

• IEMEK Journal of Embedded Systems and Applications
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• v.14 no.1
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• pp.1-9
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• 2019

In this paper, we propose a method of generating a 2D gray image from LiDAR 3D reflection intensity. The proposed method uses the Fully Convolutional Network (FCN) to generate the gray image from 2D reflection intensity which is projected from LiDAR 3D intensity. Both encoder and decoder of FCN are configured with several convolution blocks in the symmetric fashion. Each convolution block consists of a convolution layer with $3{\times}3$ filter, batch normalization layer and activation function. The performance of the proposed method architecture is empirically evaluated by varying depths of convolution blocks. The well-known KITTI data set for various scenarios is used for training and performance evaluation. The simulation results show that the proposed method produces the improvements of 8.56 dB in peak signal-to-noise ratio and 0.33 in structural similarity index measure compared with conventional interpolation methods such as inverse distance weighted and nearest neighbor. The proposed method can be possibly used as an assistance tool in the night-time driving system for autonomous vehicles.

• Journal of the Institute of Convergence Signal Processing
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• v.23 no.4
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• pp.234-240
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• 2022

This paper proposes a customized AI exercise recommendation service for balancing the relative amount of exercise according to the working environment by each occupation. WISDM database is collected by using acceleration and gyro sensors, and is a dataset that classifies physical activities into 18 categories. Our system recommends a adaptive exercise using the analyzed activity type after classifying 18 physical activities into 3 physical activities types such as whole body, upper body and lower body. 1 Dimensional convolutional neural network is used for classifying a physical activity in this paper. Proposed model is composed of a convolution blocks in which 1D convolution layers with a various sized kernel are connected in parallel. Convolution blocks can extract a detailed local features of input pattern effectively that can be extracted from deep neural network models, as applying multi 1D convolution layers to input pattern. To evaluate performance of the proposed neural network model, as a result of comparing the previous recurrent neural network, our method showed a remarkable 98.4% accuracy.

• Proceedings of the Korea Information Processing Society Conference
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• 2019.05a
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• pp.455-457
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• 2019

In this paper we study the effect of decomposed spatiotemporal convolutions for action recognition in videos. Our motivation emerges from the empirical observation that spatial convolution applied on solo frames of the video provide good performance in action recognition. In this research we empirically show the accuracy of factorized convolution on individual frames of video for action classification. We take 3D ResNet-18 as base line model for our experiment, factorize its 3D convolution to 2D (Spatial) and 1D (Temporal) convolution. We train the model from scratch using Kinetics video dataset. We then fine-tune the model on UCF-101 dataset and evaluate the performance. Our results show good accuracy similar to that of the state of the art algorithms on Kinetics and UCF-101 datasets.

• Honam Mathematical Journal
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• v.10 no.1
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• pp.23-30
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• 1988

Let C[C, D] and $S^{*}[C,\;D]$ denote the classes of functions g, g(0)=1-g'(0)0=0, analytic in the unit disc E such that $\frac{(zg{\prime}(z)){\prime}}{g{\prime}(z)}$ and $\frac{zg{\prime}(z)}{g(z)}$ are subordinate to $\frac{1+Cz}{1+Dz{\prime}}$ $z{\in}E$, respectively. In this paper, the classes K[A,B;C,D] and $C^{*}[A,B;C,D]$, $-1{\leq}B<A{\leq}1$; $-1{\leq}D<C{\leq}1$, are defined. The functions in these classes are close-to-convex. Using the properties of convolution operators, we deal with some problems for our classes.

• Journal of Applied and Pure Mathematics
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• v.4 no.1_2
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• pp.63-69
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• 2022

This article is the result of calculating the convolution of Ramanujan's sum and natural number multiplied. Among these results, special values are expressed by Euler and Bernoulli functions.

• The Journal of Korea Institute of Information, Electronics, and Communication Technology
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• v.14 no.4
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• pp.314-322
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• 2021

Skeleton-based action recognition has attracted considerable attention in human action recognition. Recent methods for skeleton-based action recognition employ spatiotemporal graph convolutional networks (GCNs) and have remarkable performance. However, most of them have heavy computational complexity for robust action recognition. To solve this problem, we propose a shuffle graph convolutional network (SGCN) which is a lightweight graph convolutional network using pointwise group convolution rather than pointwise convolution to reduce computational cost. Our SGCN is composed of spatial and temporal GCN. The spatial shuffle GCN contains pointwise group convolution and part shuffle module which enhances local and global information between correlated joints. In addition, the temporal shuffle GCN contains depthwise convolution to maintain a large receptive field. Our model achieves comparable performance with lowest computational cost and exceeds the performance of baseline at 0.3% and 1.2% on NTU RGB+D and NTU RGB+D 120 datasets, respectively.

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.52 no.1
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• pp.51-54
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• 2003

The z-transform method is a basic mathematical tool in analyzing and designing digital signal processing systems for discrete input and output signals. There are may cases where the output signal is in the form of a discrete convolution sum of an input function and a designed digital processing algorithm function. It is well known that the z-transform of the convolution sum becomes the product of the two z-transforms of the input function and the digital processing function, whose proofs require the causality of the digital signal processing function in the almost all the available references. However, not all of the convolution sum functions are based on the causality. Many digital signal processing systems such as image processing system may depend not on the time information but on the spatial information, which has nothing to do with causality requirement. Thus, the application of the causality-based z-transform theorem on the convolution sum cannot be used without difficulty in this case. This paper proves the z-transform theorem on the discrete convolution sum without causality requirement, and make it possible for the theorem to be used in analysis and desing for any cases.

• Journal of IKEEE
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• v.23 no.1
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• pp.134-142
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• 2019

As the development of internet of energy (IoE) technologies and spread of various electronic devices have diversified patterns of energy consumption, the reliability of demand prediction has decreased, causing problems in optimization of power generation and stabilization of power supply. In this study, we propose a deep learning method, 1-Dimention-Convolution and Bidirectional Long Short-Term Memory (1D-ConvBLSTM), that combines a convolution neural network (CNN) and a Bidirectional Long Short-Term Memory(BLSTM) for highly reliable demand forecasting by effectively extracting the energy consumption pattern. In experimental results, the demand is predicted with the proposed deep learning method for various number of learning iterations and feature maps, and it is verified that the test data is predicted with a small number of iterations.

• Honam Mathematical Journal
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• v.34 no.4
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• pp.519-531
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• 2012

Let ${\sigma}_s(N)={\sum}_{d{\mid}N}d^s$. Next, the convolution sums ${\sum}_{k<N/3}{\sigma}_1(3^mk){\sigma}_1(2^n(N-3k))$, ${\sum}_{<N/3}{\sigma}_1(2^mk){\sigma}_1(3^n(N-3k))$, etc., are evaluated for all $N{\in}\mathbb{N}$ with $m$, $n{\in}\mathbb{N}{\cup}\{0\}$.