• Korean Journal of Mathematics
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• v.8 no.2
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• pp.163-172
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• 2000

Let $\mathcal{S}^{\prime}(\mathbb{R})$ be the dual of the Schwartz spaces $\mathcal{S}(\mathbb{R})$), A be a self-adjoint operator in $L^2(\mathbb{R})$ and ${\Gamma}(A)^*$ be the adjoint operator of ${\Gamma}(A)$ which is the second quantization operator of A. It is proven that under a suitable condition on A there exists a nuclear subspace $\mathcal{S}$ of a fundamental space $\mathcal{S}_A$ of Hida's type on $\mathcal{S}^{\prime}(\mathbb{R})$) such that ${\Gamma}(A)\mathcal{S}{\subset}\mathcal{S}$ and $e^{-t{\Gamma}(A)}\mathcal{S}{\subset}\mathcal{S}$, which enables us to show that a stochastic differential equation: $$dX(t)=dW(t)-{\Gamma}(A)^*X(t)dt$$, arising from the central limit theorem for spatially extended neurons has an unique solution on the dual space $\mathcal{S}^{\prime}$ of $\mathcal{S}$.

• Journal of the Korean Mathematical Society
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• v.33 no.4
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• pp.777-791
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• 1996

Let $S(R^d)$ be the Schwartz space of infinitely differentiable functions on $R^d$ which vanish at $\infty$ and $S'(R^d)$ be its dual space. The theory of stochastic differential equations(SDEs) governing processes that takes values in the dual of countably Hilbertian nuclear space such as $S'(R^d)$ studied by many authors(e.g [M],[KM]). Let M be a martingale measure defined by Walsh[W], then M can be considered as a $S'(R^d)$-valued process in a certain condition i.e. M has a version of $S'(R^d)$-valued martingale process. (See [W] for detailed discussion)

• The Journal of Korean Institute of Communications and Information Sciences
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• v.28 no.7C
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• pp.719-725
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• 2003

The content-based image retrieval system extracts features of color, shape and texture from raw images, and builds the database with those features in the indexing process. The search in the whole retrieval system is defined as a process which finds images that have large similarity to query image using the feature database. This paper proposes a new two-stage search method in the content-based image retrieval system. The method is that the features are condensed and stored by the property of Cauchy-Schwartz inequality in order to reduce the similarity computation time which takes a mostly response time from entering a query to getting retrieval results. By the extensive computer simulations, we have observed that the proposed two-stage search method successfully reduces the similarity computation time while maintaining the same retrieval relevance as the conventional exhaustive search method. We also have observed that the method is more effective as the number of images and dimensions of the feature space increase.

• Bulletin of the Korean Mathematical Society
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• v.53 no.4
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• pp.1157-1169
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• 2016

We find the distributional solutions of the Wilson's functional equations $$u{\circ}T+u{\circ}T^{\sigma}-2u{\otimes}v=0,\\u{\circ}T+u{\circ}T^{\sigma}-2v{\otimes}u=0,$$ where $u,v{\in}{\mathcal{D}}^{\prime}({\mathbb{R}}^n)$, the space of Schwartz distributions, T(x, y) = x + y, $T^{\sigma}(x,y)=x+{\sigma}y$, $x,y{\in}{\mathbb{R}}^n$, ${\sigma}$ an involution, and ${\circ}$, ${\otimes}$ are pullback and tensor product of distributions, respectively. As a consequence, we solve the $Erd{\ddot{o}}s$' problem for the Wilson's functional equations in the class of locally integrable functions. We also consider the Ulam-Hyers stability of the classical Wilson's functional equations $$f(x+y)+f(x+{\sigma}y)=2f(x)g(y),\\f(x+y)+f(x+{\sigma}y)=2g(x)f(y)$$ in the class of Lebesgue measurable functions.

• Journal of Positioning, Navigation, and Timing
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• v.6 no.4
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• pp.195-203
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• 2017

A 2U cube satellite called SNUGLITE has been developed by GNSS Research Laboratory in Seoul National University. Its main mission is to perform actual operation by mounting dual-frequency global positioning system (GPS) receivers. Its scientific mission aims to observe space environments and collect data. It is essential for a cube satellite to control an Earth-oriented attitude for reliable and successful data transmission and reception. To this end, an attitude estimation and control algorithm, Attitude Determination and Control System (ADCS), has been implemented in the on-board computer (OBC) processor in real time. In this paper, the Extended Kalman Filter (EKF) was employed as the attitude estimation algorithm. For the attitude control technique, the Linear Quadratic Gaussian (LQG) was utilized. The algorithm was verified through the processor in the loop simulation (PILS) procedure. To validate the ADCS algorithm in the ground, the experimental verification via a single axis Hardware-in-the-loop simulation (HILS) was used due to the simplicity and cost effectiveness, rather than using the 3-axis HILS verification (Schwartz et al. 2003) with complex air-bearing mechanism design and high cost.

• Journal of the Korean Institute of Telematics and Electronics
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• v.27 no.10
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• pp.68-77
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• 1990

In this paper, a neural patten recognition method for the automatic circuit diagram reading system is proposed. The proposed procedure to recognize a deformed logic symbols is composed of three stages: feature detection, log mapping, and pattern classification. In the feature detection stage, a modified competitive learning algorithm where each pattern has the inhibition weight as well as the activation weight is developed. The global information of hand-written logic symbols is obtained by the feature detection neural network having both the inhibition and activation weights. The obtained global data is then transformed into a log space by the conformal mapping where according to the Schwartz's theory about the human visual signal process-ing, the degree of rotation and the scale change are mapped into the translation change. Logic symbols are finally classified by a three layer perceptron trained by the error back propagation algorithm. The computer simulation demonstrates that the proposed multistage neural network system can recognize well the deformed patterns of hand-written logic circuit diagrams.