• Analytical Science and Technology
• /
• v.8 no.4
• /
• pp.707-714
• /
• 1995

Two types of regularization method (singular system and HMP approaches) for generating depth-concentration profiles from angle-resolved XPS data were evaluated. Both approaches showed qualitatively similar results although they employed different numerical algorithms. The application of the regularization method to simulated data demonstrates its excellent utility for the complex depth profile system. It includes the stable restoration of the depth-concentration profiles from the data with considerable random error and the self choice of smoothing parameter that is imperative for the successful application of the regularization method. The self choice of smoothing parameter is based on generalized cross-validation method which lets the data themselves choose the optimal value of the parameter.

• Bulletin of the Korean Mathematical Society
• /
• v.46 no.1
• /
• pp.25-33
• /
• 2009

Let ${\pi}:E{\rightarrow}B$ be a Serre fibration with fibre F. We prove that if the inclusion map $i:F{\rightarrow}E$ has a left homotopy inverse r and ${\pi}:E{\rightarrow}B$ admits a cross section ${\rho}:B{\rightarrow}E$, then $G_n(E,F){\cong}{\pi}_n(B){\oplus}G_n(F)$. This is a generalization of the case of trivial fibration which has been proved by Lee and Woo in [8]. Using this result, we will prove that ${\pi}_n(X^A){\cong}{\pi}_n(X){\oplus}G_n(F)$ for the function space $X^A$ from a space A to a weak $H_*$-space X where the evaluation map ${\omega}:X^A{\rightarrow}X$ is regarded as a fibration.

• Communications of the Korean Mathematical Society
• /
• v.37 no.2
• /
• pp.503-520
• /
• 2022

We introduce a new type of fractional derivative, which we call as the right local general truncated M-fractional derivative for α-differentiable functions that generalizes the fractional derivative type introduced by Anastassiou. This newly defined operator generalizes the standard properties and results of the integer order calculus viz. the Rolle's theorem, the mean value theorem and its extension, inverse property, the fundamental theorem of calculus and the theorem of integration by parts. Then we represent a relation of the newly defined fractional derivative with known fractional derivative and in context with this derivative a physical problem, Kirchoff's voltage law, is generalized. Also, the importance of this newly defined operator with respect to the flexibility in the parametric values is described via the comparison of the solutions in the graphs using MATLAB software.

• Journal of the Chungcheong Mathematical Society
• /
• v.9 no.1
• /
• pp.77-87
• /
• 1996

For any map $v:X{\rightarrow}Y$, the generalized Gottlieb set $G({\Sigma}A;X,v,Y)$ with respect to v is a subgroup of $[{\Sigma}A,Y]$. If $v:X{\rightarrow}Y$ has a left homotopy inverse $u:X{\rightarrow}Y$, then for any $f{\in}G({\Sigma}A;X,v,Y)$, $g{\in}G({\Sigma}A;X,u,Y)$, the function spaces $L({\Sigma}A,X;uf)$ and $L({\Sigma}A,X;g)$ have the same homotopy type.

• Communications of the Korean Mathematical Society
• /
• v.11 no.4
• /
• pp.1147-1157
• /
• 1996

Nonlinear ill-posed problems arise in many application including parameter estimation and inverse scattering. We introduce a least squares regularization method to solve nonlinear ill-posed problems with constraints robustly and efficiently. The regularization method uses Trust-Region approach to handle the constraints on variables. The Generalized Cross Validation is used to choose the regularization parameter in computational tests. Numerical results are given to exhibit faster convergence of the method over other methods.

• Journal of Korean Society for Quality Management
• /
• v.17 no.2
• /
• pp.81-92
• /
• 1989

A class of standard optimization techniques to estimate the stationary transition probabilities among states is discussed. With the use of aggregate time series data on employed labor in industrial sectors, the alternative restricted estimates including minimum absolute deviation, unweighted, weighted, generalized inverse, minimum chi-square and maximum likelihood are evaluated and compared. Analytic and numerical results are shown favorably with the viewpoint of the validity and predictive potentiality of model.

• Bulletin of the Korean Mathematical Society
• /
• v.46 no.2
• /
• pp.373-385
• /
• 2009

An m${\times}$n Boolean matrix A is called regular if there exists an n${\times}$m Boolean matrix X such that AXA = A. We have characterizations of Boolean regular matrices. We also determine the linear operators that strongly preserve Boolean regular matrices.

• The Pure and Applied Mathematics
• /
• v.17 no.4
• /
• pp.307-319
• /
• 2010

We provide a new semilocal convergence analysis of the Gauss-Newton method (GNM) for solving nonlinear equation in the Euclidean space. Using our new idea of recurrent functions, and a combination of center-Lipschitz, Lipschitz conditions, we provide under the same or weaker hypotheses than before [7]-[13], a tighter convergence analysis. The results can be extented in case outer or generalized inverses are used. Numerical examples are also provided to show that our results apply, where others fail [7]-[13].

• Journal of applied mathematics & informatics
• /
• v.39 no.1_2
• /
• pp.93-103
• /
• 2021

In this paper I am considering several cryptological threads. The problem of the RSA cipher, like the Diffie-Hellman protocol, is the use of finite sets. In this paper, I generalize the RSA cipher and DH protocol for infinite sets using monoids. In monoids we can not find the inverse, which makes it difficult. In the second part of the paper I show the applications in cryptology of polynomial composites and monoid domains. These are less known structures. In this work, I show different ways of encrypting messages based on infinite sets.

• Journal of the Korean Society of Radiology
• /
• v.81 no.3
• /
• pp.632-643
• /
• 2020

Purpose To investigate the correlation between magnetic resonance (MR) image-based radiomics features and the genomic features of breast cancer by focusing on biomolecular intrinsic subtypes and gene expression profiles based on risk scores. Materials and Methods We used the publicly available datasets from the Cancer Genome Atlas and the Cancer Imaging Archive to extract the radiomics features of 122 breast cancers on MR images. Furthermore, PAM50 intrinsic subtypes were classified and their risk scores were determined from gene expression profiles. The relationship between radiomics features and biomolecular characteristics was analyzed. A penalized generalized regression analysis was performed to build prediction models. Results The PAM50 subtype demonstrated a statistically significant association with the maximum 2D diameter (p = 0.0189), degree of correlation (p = 0.0386), and inverse difference moment normalized (p = 0.0337). Among risk score systems, GGI and GENE70 shared 8 correlated radiomic features (p = 0.0008-0.0492) that were statistically significant. Although the maximum 2D diameter was most significantly correlated to both score systems (p = 0.0139, and p = 0.0008), the overall degree of correlation of the prediction models was weak with the highest correlation coefficient of GENE70 being 0.2171. Conclusion Maximum 2D diameter, degree of correlation, and inverse difference moment normalized demonstrated significant relationships with the PAM50 intrinsic subtypes along with gene expression profile-based risk scores such as GENE70, despite weak correlations.