• Geomechanics and Engineering
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• v.23 no.6
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• pp.547-560
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• 2020

This paper studies the dynamic foundation-soil-foundation interaction for two square rigid foundations embedded in a viscoelastic soil layer. The vibrations come from only one rigid foundation placed in the soil layer and subjected to harmonic loads of translation, rocking, and torsion. The required dynamic response of rigid surface foundations constitutes the solution of the wave equations obtained by taking account of the conditions of interaction. The solution is formulated using the frequency domain Boundary Element Method (BEM) in conjunction with the Kausel-Peek Green's function for a layered stratum, with the aid of the Thin Layer Method (TLM), to study the dynamic interaction between adjacent foundations. This approach allows the establishment of a mathematical model that enables us to determine the dynamic displacements amplitude of adjacent foundations according to their different separations, the depth of the substratum, foundations masss, foundations embedded, and the frequencies of excitation. This paper attempts to introduce an approach based on a polynomial mathematical tool conducted from several results of numerical methods (BEM-TLM) so that practicing civil engineers can evaluation the dynamic foundations displacements more easy.

• Journal of Industrial and Engineering Chemistry
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• v.67
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• pp.333-346
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• 2018

This study presents a mathematical modeling approach for developing models based on non-ideal conditions related to the membrane structure including porous supporting layer and deformation under pressure. Comparison of the findings with experimental data reveal the importance of considering the resistance in porous supporting layer though the effect of concentration polarization in the permeate stream could be neglected. Investigations on deformation of fibers under pressure ascertain that at larger fiber inner radius to outer radius ratios, increasing driving force may lead to an initial increase in permeability. After that, the effects of deformation dominates and thus permeability may be decreased.

• Bulletin of the Korean Mathematical Society
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• v.24 no.1
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• pp.31-37
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• 1987

I want to focus on developments in the areas of general relativity and gauge theory. The topics to be considered are the singularity theorms of Hawking and Penrose, the positivity of mass, instantons on the four-dimensional sphere, and the string picture of quantum gravity. I should mention that I will not have time do discuss either classical mechanics or symplectic structures. This is especially unfortunate, because one of the roots of differential geometry is planted firmly in mechanics, Cf. [GS]. The French geometer Elie Cartan first formulated his invariant approach to geometry in a series of papers on affine connections and general relativity, Cf. [C]. Cartan was trying to recast the Newtonian theory of gravity in the same framework as Einstein's theory. From the historical perspective it is significant that Cartan found relativity a convenient framework for his ideas. As about the same time Hermann Weyl in troduced the idea of gauge theory into geometry for purposes much different than those for which it would ultimately prove successful, Cf. [W]. Weyl wanted to unify gravity with electromagnetism and though that a conformal structure would fulfill thel task but Einstein rebutted this approach.

• Journal of the Korean Mathematical Society
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• v.59 no.6
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• pp.1153-1170
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• 2022

In this paper, we investigate the portfolio optimization problem under the SVCEV model, which is a hybrid model of constant elasticity of variance (CEV) and stochastic volatility, by taking into account of minimum-entropy robustness. The Hamilton-Jacobi-Bellman (HJB) equation is derived and the first two orders of optimal strategies are obtained by utilizing an asymptotic approximation approach. We also derive the first two orders of practical optimal strategies by knowing that the underlying Ornstein-Uhlenbeck process is not observable. Finally, we conduct numerical experiments and sensitivity analysis on the leading optimal strategy and the first correction term with respect to various values of the model parameters.

• The Mathematical Education
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• v.44 no.3 s.110
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• pp.375-396
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• 2005

This paper reports on the main results of 3 study that compared students' beliefs, skills, and understandings in an innovative approach to differential equations to more conventional approaches. The innovative approach, referred to as the Realistic Mathematics Education Based Differential Equations (IODE) project, capitalizes on advances within the discipline of mathematics and on advances within the discipline of mathematics education, both at the K-12 and tertiary levels. Given the integrated leveraging of developments both within mathematics and mathematics education, the IODE project is paradigmatic of an approach to innovation in undergraduate mathematics, potentially sewing as a model for other undergraduate course reforms. The effect of the IODE projection maintaining desirable mathematical views and in developing students' skills and relational understandings as judged by the three assessment instruments was largely positive. These findings support our conjecture that, when coupled with careful attention to developments within mathematics itself, theoretical advances that initially grew out research in elementary school classrooms can be profitably leveraged and adapted to the university setting. As such, our work in differential equations may serve as a model for others interested in exploring the prospects and possibilities of improving undergraduate mathematics education in ways that connect with innovations at the K-12 level

• Proceedings of the Korea Institutes of Information Security and Cryptology Conference
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• 1994.11a
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• pp.288-302
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• 1994

A security risk analysis provides all information system with the capability to investigate and estimate the status of its security, and gives a guideline for establishing a safeguard against any means of security threats. The information system needs tile judicious and accurate why for performing a risk analysis since security policy and risk analysis of tile information system are based on risk analysis, The risk analysis is composed of two methods. mathematical approach and diagramming technique. Mathematical approach cannot yield a precise description of the real world. However, diagramming technique is more pragmatic since it overcomes this limitation. In this paper, we studied tile security risk analysis methods proposed in overseas such as INFOSEC [4], SRAG [5], FIPS65[6], and JRAM[7].

• Current Optics and Photonics
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• v.7 no.5
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• pp.545-556
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• 2023

This paper introduces volume-sharing multi-aperture imaging (VMAI), a potential approach proposed for volume reduction in space-borne imagers, with the aim of achieving high-resolution ground spatial imagery using deep learning methods, with reduced volume compared to conventional approaches. As an intermediate step in the VMAI payload development, we present a phase-1 design targeting a 1-meter ground sampling distance (GSD) at 500 km altitude. Although its optical imaging capability does not surpass conventional approaches, it remains attractive for specific applications on small satellite platforms, particularly surveillance missions. The design integrates one wide-field and three narrow-field cameras with volume sharing and no optical interference. Capturing independent images from the four cameras, the payload emulates a large circular aperture to address diffraction and synthesizes high-resolution images using deep learning. Computational simulations validated the VMAI approach, while addressing challenges like lower signal-to-noise (SNR) values resulting from aperture segmentation. Future work will focus on further reducing the volume and refining SNR management.

• The Journal of Engineering Geology
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• v.18 no.3
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• pp.297-302
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• 2008

The main reason of the pollution caused by soils and tailings located at discussed mines is heavy metals and AMD(acid mine drainage). Human health is affected by these pollutants which are spreaded from the abandoned mines. In this study, we try a mathematical approach to predict the pollution level of heavy metals caused by the surrounding soils of abandoned mines. The new approach is established with the correlation between the distance and pH, ORP. The change of pH and ORP can be described by the rate of initial values to experimental values. We demonstrate a realistic possibility of the mathematical approach to assess an environmental impact from disused mines cause the rate range is 0.95 to 1.03 for 60 days. Therefore our proposed approach will be useful as a few promising method for the management of heavy metals in many mines.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2008.05a
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• pp.651-654
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• 2008

In finite field operations based on $GF(2^m)$, additions and subtractions are easily implemented. On the other hand, multiplications and divisions require mathematical elaboration of complex equations. There are two dominant way of approaching the solutions of finite filed operations, normal basis approach and polynomial basis approach, each of which has both benefits and weakness respectively. In this study, we adopted the mathematically feasible polynomial basis approach and suggest the optimization techniques of finite field operations based of mathematical principles.

• Journal of the Korean Mathematical Society
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• v.50 no.2
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• pp.259-274
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• 2013

In this paper, we consider the Fourier-type functionals on Wiener space. We then establish the analytic Feynman integrals involving the ${\diamond}$-convolutions. Further, we give an approach to solution of the Schr$\ddot{o}$dinger equation via Fourier-type functionals. Finally, we use this approach to obtain solutions of the Schr$\ddot{o}$dinger equations for harmonic oscillator and double-well potential. The Schr$\ddot{o}$dinger equations for harmonic oscillator and double-well potential are meaningful subjects in quantum mechanics.