• Journal of the Korean Mathematical Society
• /
• v.38 no.2
• /
• pp.321-336
• /
• 2001

A Feynman functional formulation is given for the Global Positioning System, GPS. Both the sequential and analytic Feynman functionals are presented for the classical, exterior, gravity problems which included rigid body rotations, special relativity and some general relativity corrections. A mathematically rigorous approach is introduced whose solutions exist, are unique and which depend continuously on the intial data. This formulation is convergent and has the finite approximation property. It is emphasized that all of the problems studied are classical (not quantum) evolution systems.

• Bulletin of the Korean Mathematical Society
• /
• v.56 no.3
• /
• pp.631-648
• /
• 2019

In this paper, we consider a semilinear stochastic heat equation driven by an additive fractional white noise. Under the pathwise uniqueness property, we establish various strong stability results. As a consequence, we give an application to the convergence of the Picard successive approximation.

• ETRI Journal
• /
• v.30 no.1
• /
• pp.170-172
• /
• 2008

A substitution box (S-box) plays a central role in cryptographic algorithms. In this paper, an efficient method for designing S-boxes based on chaotic maps is proposed. The proposed method is based on the mixing property of piecewise linear chaotic maps. The S-box so constructed has very low differential and linear approximation probabilities. The proposed S-box is more secure against differential and linear cryptanalysis compared to recently proposed chaotic S-boxes.

• Bulletin of the Korean Mathematical Society
• /
• v.33 no.3
• /
• pp.445-453
• /
• 1996

A closed subspace J of a Banach space X is called an M-ideal in X if the annihilator $J^\perp$ of J is an L-summand of $X^*$. That is, there exists a closed subspace J' of $X^*$ such that $X^* = J^\perp \oplus J'$ and $\left\$\mid$ p + q \right\$\mid$ = \left\$\mid$ p \right\$\mid$ + \left\$\mid$ q \right\$\mid$$ wherever $p \in J^\perp and q \in J'$.

• Bulletin of the Korean Mathematical Society
• /
• v.37 no.3
• /
• pp.461-475
• /
• 2000

In the present paper, we first give some examples of self-mappings which are asymptoticaly nonexpansive in the intermediate, not strictly hemicontractive, but satisfy the property (H). It is then shown that the modified Mann and Ishikawa iteration processes defined by $x_{n+1}=(1-\alpha_n)x_n+\alpha_nT^nx_n\ and\ x_{n+1}=(1-\alpha_n)x_n+\alpha_nT^n[(1-\beta_n)x_n+\beta_nT^nx_n]$,respectively, converges strongly to the unique fixed point of such a self-mapping in general Banach spaces.

• Bulletin of the Korean Mathematical Society
• /
• v.29 no.2
• /
• pp.257-264
• /
• 1992

Since Alfsen and Effors [1] introduced the notion of an M-ideal, many authors [3,6,9,12] have worked on the problem of finding those Banach spaces X and Y for which K(X,Y), the space of all compact linear operators from X to Y, is an M-ideal in L(X,Y), the space of all bounded linear operators from X to Y. The M-ideal property of K(X,Y) in L(X,Y) gives some informations on X,Y and K(X,Y). If K(X) (=K(X,X)) is an M-ideal in L(X) (=L(X,X)), then X has the metric compact approximation property [5] and X is an M-ideal in $X^{**}$ [10]. If X is reflexive and K(X) is an M-ideal in L(X), then K(X)$^{**}$ is isometrically isomorphic to L(X)[5]. A weaker notion is a semi M-ideal. Studies on Banach spaces X and Y for which K(X,Y) is a semi M-ideal in L(X,Y) were done by Lima [9, 10].

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.17 no.2
• /
• pp.67-85
• /
• 2013

Reproducing Polynomial Particle Method (RPPM) is one of meshless methods that use meshes minimally or do not use meshes at all. In this paper, the RPPM is employed for free vibration analysis of shear-deformable plates of the first order shear deformation model (FSDT), called Reissner-Mindlin plate. For numerical implementation, we use flat-top partition of unity functions, introduced by Oh et al, and patchwise RPPM in which approximation functions have high order polynomial reproducing property and the Kronecker delta property. Also, we demonstrate that our method is highly effective than other existing results for various aspect ratios and boundary conditions.

• 제어로봇시스템학회:학술대회논문집
• /
• 2000.10a
• /
• pp.481-481
• /
• 2000

We investigated the structure-activity relationships on use of multi-layer neural networks. The relationships are techniques required in developments of medicines. Since many kinds of observations might be adopted on the techniques, we discussed some points between the observations and the properties of multi-layer neural networks. In the structure-activity relationships, an important property is not that standard deviations are nearly equal to zero for observed physiological activity, but prediction ability for unknown medicines. Since we adopted non-linear approximation, the function to represent the activity can be defined by observations; therefore, we believe that the standard deviations have not significance. The function was examined by "leave-one-out" method, which was originally introduced for the multi-regression analysis. In the linear approximation, the examination is significance, however, we believe that the method is inappropriate in case of nonlinear fitting as neural networks; therefore, we derived a new index fer the relationships from the differential of information propagation in the neural network. By using the index, we discussed physiological activity of an anti-cancer medicine, Mitomycine derivatives. The neuro-computing suggests that there is no direction to extend the anti-cancer activity of Mitomycine, which is close to the trend of anticancer developing.

• Proceedings of the Korean Institute of Intelligent Systems Conference
• /
• 2003.09a
• /
• pp.415-418
• /
• 2003

Fuzzy modelling has the approximation property far the given input-output relationship. Especially, Takagi-Sugeno fuzzy models are widely used because they show very good performance in the nonlinear function approximation problem. But generally there is not the systematic method incorporating the human expert's knowledge or experience in fuzzy rules and it is not easy to End the membership function of fuzzy rule to minimize the output error as well. The ANFIS (Adaptive Network-based Fuzzy Inference Systems) is one of the neural network based fuzzy modelling methods that can be used with various type of fuzzy rules. But in this model, it is the problem to End the optimum number of fuzzy rules in fuzzy model. In this paper, a new fuzzy modelling method based on the ANFIS and pruning techniques with the measure named impact factor is proposed and the performance of proposed method is evaluated with several simulation results.

• Journal of electromagnetic engineering and science
• /
• v.5 no.2
• /
• pp.49-60
• /
• 2005

In this paper, an efficient performance enhancement scheme for an adaptive antenna array under the flat and the frequency-selective Rayleigh fadings is proposed. The proposed signal enhancement scheme is the modified linear signal estimator which combines the rank N approximation by reducing noise eigenvalues(RANE) and Toeplitz matrix approximation(TMA) methods into the linear signal estimator. The proposed performance enhancement scheme is performed by not only reducing the noise component from the signal-plus-noise subspace using RANE but also having the theoretical property of noise-free signal using TMA. Consequently, the key idea of the proposed performance enhancement scheme is to greatly enhance the performance of an adaptive antenna array by removing all undesired noise effects from the post-correlation received signal. The proposed performance enhancement scheme applies at the Wiener maximal ratio combining(MRC) method which has been widely used as the conventional adaptive antenna array. It is shown through several simulation results that the performance of an adaptive antenna array using the proposed signal enhancement scheme is much superior to that of a system using the conventional method under several environments, i.e., a flat Rayleigh fading, a fast frequency-selective Rayleigh fading, a perfect/imperfect power control, a single cell, and a multicell.