• Korean Journal of Mathematics
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• v.20 no.1
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• pp.107-116
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• 2012

We investigate the multiple solutions for a class of the elliptic system with the singular potential nonlinearity. We obtain a theorem which shows the existence of the solution for a class of the elliptic system with singular potential nonlinearity and Dirichlet boundary condition. We obtain this result by using variational method and critical point theory.

• Korean Journal of Mathematics
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• v.21 no.4
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• pp.483-493
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• 2013

We investigate the multiplicity of the solutions for a class of the system of the biharmonic equations with some singular potential nonlinearity. We obtain a theorem which shows the existence of the nontrivial weak solution for a class of the system of the biharmonic equations with singular potential nonlinearity and Dirichlet boundary condition. We obtain this result by using variational method and the generalized mountain pass theorem.

• Nonlinear Functional Analysis and Applications
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• v.28 no.4
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• pp.1005-1015
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• 2023

In this paper, we establish the existence of at least two distinct solutions to a p-Laplacian problems involving critical exponents and singular cylindrical potential, by using the Nehari manifold.

• Bulletin of the Korean Mathematical Society
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• v.56 no.6
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• pp.1601-1615
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• 2019

We show the existence of ground state and orbital stability of standing waves of nonlinear $Schr{\ddot{o}}dinger$ equations with singular linear potential and essentially mass-subcritical power type nonlinearity. For this purpose we establish the existence of ground state in $H^1$. We do not assume symmetry or monotonicity. We also consider local and global well-posedness of Strichartz solutions of energy-subcritical equations. We improve the range of inhomogeneous coefficient in [5, 12] slightly in 3 dimensions.

• Journal of Electrochemical Science and Technology
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• v.9 no.2
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• pp.149-156
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• 2018

In this technical note, I report the analysis of electrochemical impedance data measured with potential sweeping. Even though the instruments for voltammetric impedance measurements have been developed for decades using different approaches, their applications are limited due to the lack of well-established protocols to easily analyze voltammetry data. To fill this gap, the singular point of the specific potential is considered that is only determined by the standard/formal potential and the transfer coefficient and is independent of the kinetics and experimental parameters (including revertability) of faradaic reactions. Taking the advantage of its inertness, I suggest an approach employing the singular point as a reference to obtain general electrochemical information. As all the concepts and methods are verified with numerical simulations, this technique is expected to be applied for complex reactions involving electrochemical and chemical reaction mechanisms.

• STI Policy Review
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• v.9 no.1
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• pp.133-157
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• 2018

The divide between the "digital" economy and the traditional "physical" economy is outdated. In fact, we are in a transition to a singular economy. This paper classifies economic objects (including actors) as either physical or virtual and argues that due to emerging technologies, these objects are interacting with each other in both physical and increasingly digital spheres in tandem. This paper recognizes the elemental difference between atoms and bytes but argues that physical and digital economic activities are becoming inseparably intertwined. Furthermore, arbitrarily dividing the economy into two categories - one "physical" and the other "digital" - distorts the overall view of the actual execution of economic activity. A wide range of innovations emerging concurrently is fueling the transition to a singular economy. Often referred to as the elements of the Fourth Industrial Revolution (4IR), four emerging technological areas are reviewed here: distributed ledger technology, artificial intelligence/machine learning/data sciences, biometrics and remote sensor technologies, and access infrastructure (universal internet access/electricity/cloud computing). The financial services sector is presented as a case study for the potential impact of these 4IR technologies and the blurring physical/digital line. To reach the potential of these innovations and a truly singular economy, it requires the concurrent development of social, organizational, and regulatory innovations, though they lag in terms of technological progress thus far.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.3 no.2
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• pp.17-28
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• 1999

A new procedure of the boundary element method(BEM),say, singular BEM for the potential problems with singularities is presented. To obtain the numerical solution of which asymptotic behavior near the singularities is close to that of the analytic solution, we use particular elements on the boundary segments containing singularities. The Motz problem and the crack problem are taken as the typical examples, and numerical results of these cases show the efficiency of the present method.

• Communications of the Korean Mathematical Society
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• v.16 no.3
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• pp.487-508
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• 2001

We consider the Cauchy problem for Laplacian. Using the single layer representation, we obtain an equivalent system of boundary integral equations. We show the singular values of the ill-posed Cauchy operator decay exponentially, which means that a small error is exponentially amplified in the solution of the Cauchy problem. We show the decaying rate is dependent on the geometry of he domain, which provides the information on the choice of numerically meaningful modes. We suggest a pseudo-inverse regularization method based on singular value decomposition and present various numerical simulations.

• Journal of Electrochemical Science and Technology
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• v.8 no.3
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• pp.244-249
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• 2017

This paper presents the results of an investigation into the isoamperic point of cyclic voltammograms, which is defined as the singular point where the voltammograms of various scan rates converge. The origin of the unique point is first considered from a theoretical perspective by formulating the voltammetric curves as a system of linear equations, the solution of which indicates that a trivial solution is only available at the potential at which the net current is zero during the reverse potential scan. In addition, by way of a mathematical formulation, it was also shown that the isoamperic point is dependent on the switching potential of the potential scanning. To validate these findings, theoretical and practical cyclic voltammmograms were studied using finite-element based digital simulations and 3-electrode cell experiments. The new understanding of the nature of the isoamperic point provides an opportunity to measure the charge transfer effects without the influence of the mass transfer effects when determining the thermodynamic and kinetic characteristics of a faradaic system.

• Journal of the Korean Institute of Intelligent Systems
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• v.19 no.3
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• pp.355-362
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• 2009

In this paper, we present a framework for managing group behaviors in multi-agent swarm systems. The framework explores the benefits by dynamic associations with the proposed artificial potential functions to realize complex swarming behaviors. A key development is the introduction of a set of flocking by dynamic association (DA) algorithms that effectively deal with a host of swarming issues such as cooperation for fast migration to a target, flexible and agile formation, and inter-agent collision avoidance. In particular, the DA algorithms employ a so-called systematic singular association (SSA) rule for fast migration to a target and compact formation through inter-agent interaction. The resulting algorithms enjoy two important interrelated benefits. First, the SSA rule greatly reduces time-consuming for migration and satisfies low possibility that agents may be lost. Secondly, the SSA is advantageous for practical implementations, since it considers for agents even the case that a target is blocked by obstacles. Extensive simulation presents to illustrate the viability and effectiveness of the proposed framework.