• Korean Journal of Mathematics
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• v.27 no.2
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• pp.375-415
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• 2019

We study spaces of continuous-function-valued functions that have the property that composition with evaluation functionals induce $weak^*$ to norm continuous maps to ${\ell}^p$ space ($p{\in}(1,\;{\infty})$). Versions of $H{\ddot{o}}lder^{\prime}s$ inequality and Riesz representation theorem are proved to hold on these spaces. We prove a version of Dixmier's theorem for spaces of function-valued matrix operators on these spaces, and an analogue of the trace formula for operators on Hilbert spaces. When the function space is taken to be the complex field, the spaces are just the ${\ell}^p$ spaces and the well-known classical theorems follow from our results.

• Bulletin of the Korean Mathematical Society
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• v.53 no.5
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• pp.1531-1548
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• 2016

Let C[0, t] denote the space of real-valued continuous functions on [0, t] and define a random vector $Z_n:C[0,t]{\rightarrow}\mathbb{R}^n$ by $Z_n(x)=(\int_{0}^{t_1}h(s)dx(s),{\ldots},\int_{0}^{t_n}h(s)dx(s))$, where 0 < $t_1$ < ${\cdots}$ < $ t_n=t$ is a partition of [0, t] and $h{\in}L_2[0,t]$ with $h{\neq}0$ a.e. Using a simple formula for a conditional expectation on C[0, t] with $Z_n$, we evaluate a generalized analytic conditional Wiener integral of the function $G_r(x)=F(x){\Psi}(\int_{0}^{t}v_1(s)dx(s),{\ldots},\int_{0}^{t}v_r(s)dx(s))$ for F in a Banach algebra and for ${\Psi}=f+{\phi}$ which need not be bounded or continuous, where $f{\in}L_p(\mathbb{R}^r)(1{\leq}p{\leq}{\infty})$, {$v_1,{\ldots},v_r$} is an orthonormal subset of $L_2[0,t]$ and ${\phi}$ is the Fourier transform of a measure of bounded variation over $\mathbb{R}^r$. Finally we establish various change of scale transformations for the generalized analytic conditional Wiener integrals of $G_r$ with the conditioning function $Z_n$.

• Electronics and Telecommunications Trends
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• v.36 no.2
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• pp.32-42
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• 2021

The rapid growth of deep-learning applications has invoked the R&D of artificial intelligence (AI) processors. A dedicated software framework such as a compiler and runtime APIs is required to achieve maximum processor performance. There are various compilers and frameworks for AI training and inference. In this study, we present the features and characteristics of AI compilers, training frameworks, and inference engines. In addition, we focus on the internals of compiler frameworks, which are based on either basic linear algebra subprograms or intermediate representation. For an in-depth insight, we present the compiler infrastructure, internal components, and operation flow of ETRI's "AI-Ware." The software framework's significant role is evidenced from the optimized neural processing unit code produced by the compiler after various optimization passes, such as scheduling, architecture-considering optimization, schedule selection, and power optimization. We conclude the study with thoughts about the future of state-of-the-art AI compilers.

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.41 no.5
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• pp.57-64
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• 2004

We proposed the eye gaze tracking system under natural head movements, which consists of one narrow-view field CCD camera, two mirrors which of reflective angles are controlled and active infra-red illumination. The mirrors' angles were computed by geometric and linear algebra calculations to put the pupil images on the optical axis of the camera. Our system allowed the subjects head to move 90cm horizontally and 60cm vertically, and the spatial resolutions were about 6$^{\circ}$ and 7$^{\circ}$, respectively. The frame rate for estimating gaze points was 10～15 frames/sec. As gaze mapping function, we used the hierarchical generalized regression neural networks (H-GRNN) based on the two-pass GRNN. The gaze accuracy showed 94% by H-GRNN improved 9% more than 85% of GRNN even though the head or face was a little rotated. Our system does not have a high spatial gaze resolution, but it allows natural head movements, robust and accurate gaze tracking. In addition there is no need to re-calibrate the system when subjects are changed.

• Communications of the Korean Mathematical Society
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• v.9 no.4
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• pp.881-889
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• 1994

Let ($X, \Beta, \mu$) be a measure space with the $\sigma$-algebra $\Beta$ and the probability measure $\mu$. Throughouth this article set equalities and inclusions are understood as being so modulo measure zero sets. A transformation T defined on a probability space X is said to be measure preserving if $\mu(T^{-1}E) = \mu(E)$ for $E \in B$. It is said to be ergodic if $\mu(E) = 0$ or i whenever $T^{-1}E = E$ for $E \in B$. Consider the sequence ${x, Tx, T^2x,...}$ for $x \in X$. One may ask the following questions: What is the relative frequency of the points $T^nx$ which visit the set E\ulcorner Birkhoff Ergodic Theorem states that for an ergodic transformation T the time average $lim_{n \to \infty}(1/N)\sum^{N-1}_{n=0}{f(T^nx)}$ equals for almost every x the space average $(1/\mu(X)) \int_X f(x)d\mu(x)$. In the special case when f is the characteristic function $\chi E$ of a set E and T is ergodic we have the following formula for the frequency of visits of T-iterates to E : $$ lim_{N \to \infty} \frac{$\mid${n : T^n x \in E, 0 \leq n $\mid$}{N} = \mu(E) $$ for almost all $x \in X$ where $$\mid$\cdot$\mid$$ denotes cardinality of a set. For the details, see [8], [10].

• Transactions of the Korean Society of Automotive Engineers
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• v.6 no.2
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• pp.129-143
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• 1998

The vibrations of steering wheel are required to be reduced for convenient ride quality and good controllability. This phenomenon, vibration of steering wheel, is occured by interaction with suspension system, steering system, vehicle body, engine/transmission and tire complicately. But reviewing the current research activities, most researches are performed for the vibration analysis of steering wheel with a simple model, and mot easy to be applied to the variation of each component element connected with steering system as well as that of the steering system. In this study, suspension system and steering system are modelled by the T.L.H. coordinate system which is usually used by a passenger car maker. Also, rigid body motions of engine and elastic motions of vehicle body in the previous study are considered. Derive the equation of motion in 29 d.o.f. and the vibration of steering wheel is analyzed numerically and verify the midelling of steering system by comparison with test results for real car. And then, the optimal design values of the engine mount system obtained from the previous study are applied to the verified steering system model and investigate the effects of various engine mount design values on the vibration of steering wheel.