• 대한수학회보
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• 제21권2호
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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.

• 대한임베디드공학회논문지
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• 제14권1호
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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.

• 융합신호처리학회논문지
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• 제23권4호
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• pp.234-240
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• 2022

본 논문은 직종별 근무 환경에 따른 상대적 운동량을 고려한 맞춤형 AI 운동 추천 서비스 방법을 제안한다. 가속도 및 자이로 센서를 활용하여 수집된 데이터를 18가지 일상생활의 신체활동으로 분류한 WISDM 데이터베이스를 기반으로 전신, 하체, 상체의 3가지 활동으로 분류한 후 인식된 활동 지표를 통해 적절한 운동을 추천한다. 본 논문에서 신체활동 분류를 위해서 사용하는 1차원 합성곱 신경망(1D CNN; 1 Dimensional Convolutional Neural Network) 모델은 커널 크기가 다른 다수의 1D 컨볼루션(Convolution) 계층을 병렬적으로 연결한 컨볼루션 블록을 사용한다. 컨볼루션 블록은 하나의 입력 데이터에 다층 1D 컨볼루션을 적용함으로써 심층 신경망 모델로 추출할 수 있는 입력 패턴의 세부 지역 특징을 보다 얇은 계층으로도 효과적으로 추출 할 수 있다. 제안한 신경망 모델의 성능 평가를 위해서 기존 순환 신경망(RNN; Recurrent Neural Network) 모델과 비교 실험한 결과 98.4%의 현저한 정확도를 보였다.

• 한국정보처리학회:학술대회논문집
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• 한국정보처리학회 2019년도 춘계학술발표대회
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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.

• 호남수학학술지
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• 제10권1호
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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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• 제4권1_2호
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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.

• 한국정보전자통신기술학회논문지
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• 제14권4호
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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.

• 대한전기학회논문지:시스템및제어부문D
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• 제52권1호
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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.

• 전기전자학회논문지
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• 제23권1호
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• pp.134-142
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• 2019

에너지인터넷 기술의 발전과 다양한 전자기기의 보급으로 에너지소비량이 패턴이 다양해짐에 따라 수요예측에 대한 신뢰도가 감소하고 있어 발전량 최적화 및 전력공급 안정화에 문제를 야기하고 있다. 본 연구에서는 고신뢰성을 갖는 수요예측을 위해 딥러닝 기법인 Convolution neural network(CNN)과 Bidirectional Long Short-Term Memory(BLSTM)을 융합한 1Dimention-Convolution and Bidirectional LSTM(1D-ConvBLSTM)을 제안하고, 제안한 기법을 활용하여 시계열 에너지소비량대한 소비패턴을 효과적으로 추출한다. 실험 결과에서는 다양한 반복학습 횟수와 feature map에 대해서 수요를 예측하고 적은 반복학습 횟수로도 테스트 데이터의 그래프 개형을 예측하는 것을 검증한다.

• 호남수학학술지
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• 제34권4호
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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 $m$, $n{\in}\mathbb{N}{\cup}\{0\}$.