• Kyungpook Mathematical Journal
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• v.63 no.3
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• pp.437-450
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• 2023

In this paper, we present a sufficient condition for the unique existence of solutions for a coupled system of nonlinear fractional Langevin equations with a new class of multipoint and nonlocal integral boundary conditions. We define a 𝓩^*_λ-contraction mapping and present the sufficient condition by identifying the problem with an equivalent fixed point problem in the context of b-metric spaces. Finally, some numerical examples are given to validate our main results.

• Journal of the Korean Mathematical Society
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• v.49 no.1
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• pp.153-164
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• 2012

In this paper, we study the existence, non-existence, and multiplicity of positive solutions for a coupled telegraph system using the xed-point theorem of cone expansion/compression type, the upper-lowe solutions method, and xed point index theory.

• Journal of the Chungcheong Mathematical Society
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• v.31 no.2
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• pp.255-268
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• 2018

We establish the existence and multiplicity of positive solutions to a coupled system of fractional order differential equations satisfying three-point boundary conditions by utilizing Avery-Henderson functional fixed point theorems and under suitable conditions.

• Journal of the Korean Physical Society
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• v.73 no.11
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• pp.1774-1786
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• 2018

Phenotypic variation among clones (individuals with identical genes, i.e. isogenic individuals) has been recognized both theoretically and experimentally. We investigate the effects of phenotypic variation on evolutionary dynamics of a population. In a population, the individuals are assumed to be haploid with two genotypes : one genotype shows phenotypic variation and the other does not. We use an individual-based Moran model in which the individuals reproduce according to their fitness values and die at random. The evolutionary dynamics of an individual-based model is formulated in terms of a master equation and is approximated as the Fokker-Planck equation (FPE) and the coupled non-linear stochastic differential equations (SDEs) with multiplicative noise. We first analyze the deterministic part of the SDEs to obtain the fixed points and determine the stability of each fixed point. We find that there is a discrete phase transition in the population distribution when the probability of reproducing the fitter individual is equal to the critical value determined by the stability of the fixed points. Next, we take demographic stochasticity into account and analyze the FPE by eliminating the fast variable to reduce the coupled two-variable FPE to the single-variable FPE. We derive a quasi-stationary distribution of the reduced FPE and predict the fixation probabilities and the mean fixation times to absorbing states. We also carry out numerical simulations in the form of the Gillespie algorithm and find that the results of simulations are consistent with the analytic predictions.

• Korean Journal of Mathematics
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• v.23 no.1
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• pp.205-230
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• 2015

A class of periodic type boundary value problems of coupled impulsive fractional differential equations are proposed. Sufficient conditions are given for the existence of solutions of these problems. We allow the nonlinearities p(t)f(t, x, y) and q(t)g(t, x, y) in fractional differential equations to be singular at t = 0, 1 and be involved a sup-multiplicative-like function. So both f and g may be super-linear and sub-linear. The analysis relies on a well known fixed point theorem. An example is given to illustrate the efficiency of the theorems.

• Bulletin of the Korean Mathematical Society
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• v.57 no.1
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• pp.219-244
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• 2020

In this paper, we approximate the solution of the coupled nonlinear Schrödinger equations by using a fully discrete finite element scheme based on the standard Galerkin method in space and implicit midpoint discretization in time. The proposed scheme guarantees the conservation of the total mass and the energy. First, a priori error estimates for the fully discrete Galerkin method is derived. Second, the existence of the approximated solution is proved by virtue of the Brouwer fixed point theorem. Moreover, the uniqueness of the solution is shown. Finally, convergence orders of the fully discrete Crank-Nicolson scheme are discussed. The end of the paper is devoted to some numerical experiments.

• Korean Journal of Optics and Photonics
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• v.4 no.4
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• pp.464-473
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• 1993

The dynamics of phase grating formation with visible light in an optical fiber is investigated. Adopting a simple two-photon local bleaching model, it is shown that the grating self-organize into an ideal grating, where the writing frequency is always in the center of the local band gap, as it evolves. The evolution at each point in the fiber is described in terms of a universal parameter that reduces the coupled partial differential equations describing the system to ordinary differential equatior~s. These equations are used to prove that there exists a fixed point of the grating growth process that corresponds to a perfectly phase-mached grating.

• Transactions on Electrical and Electronic Materials
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• v.4 no.3
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• pp.1-4
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• 2003

The etching of Au thin films has been performed in an inductively coupled $CF_4 / Cl_2 / Ar$ plasma. The etch properties including etch rate and selectivity were examined as $CF_4$ content adds from o to $30\%$ to $Cl_2/Ar$ plasma. The $Cl_2/(Cl_2 + Ar)$ gas mixing ratio was fixed at $20\%$. Other parameters were fixed at an rf power of 700 W, a dc bias voltage of -150 V, a chamber pressure of 15 mTorr, and a substrate temperature of $30^{\circ}C$. The highest etch rate of the Au thin film was 370 nm/min at a $10\%$ additive $CF_4$ into $Cl_2/Ar$ gas mixture. The surface reaction of the etched Au thin films was investigated using x-ray photoelectron spectroscopy (XPS) analysis. The XPS analysis shows that the intensities of Ail peaks are changed, indicating that there is a chemical reaction between Cl and Au. Au-Cl is hard to remove on the surface because of its high melting point. However, etching products can be sputtered by Ar ion bombardment.

• Journal of the Korean Institute of Electrical and Electronic Material Engineers
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• v.16 no.7
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• pp.564-568
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• 2003

The etching of Au thin films have been performed in an inductively coupled CF$_4$/Cl$_2$/Ar plasma. The etch rates were measured as CF$_4$ contents added from 0 to 30 % to Cl$_2$/Ar plasma, of which gas mixing ratio was fixed at 20%. Other parameters were fixed at an rf power of 700 W, a dc bias voltage of 150 V, a chamber pressure of 15 mTorr, and a substrate temperature of 3$0^{\circ}C$. The highest etch rate of the Au thin film was 3700 $\AA$m/min at a 10% additive CF$_4$ into Cl$_2$/Ar plasma. The surface reaction of the etched Au thin films was investigated using x-ray photoelectron spectroscopy (XPS) analysis. XPS analysis indicated that Au reacted with Cl and formed Au-Cl, which is hard to remove on the surface because of its high melting point. The etching products could be sputtered by Ar ion bombardment.

• Journal of the Speleological Society of Korea
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• no.82
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• pp.1-4
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• 2007

In this paper, the etching of Au films using photoresist masks on Si substrates was investigated using a capacitively coupled plasma etch reactor. The advantages of plasma etch techniques over current methods for Au metalization include the ability to simplify the metalization process flow with respect to resist lift-off schemes, and the ability to cleanly remove etched material without sidewall redeposition, as is seen in ion milling. The etch properties were measured for different gas mixing ratios of CF4/Ar, and chamber pressures while the other conditions were fixed. According to statistical design of experiment (DOE), etching process of Au films was characterized and also 20 samples were fabricated followed by measuring etch rate, selectivity and etch profile. There is a chemical reaction between CF4 and Au. Au- F is hard to remove from the surface because of its high melting point. The etching products can be sputtered by Ar ion bombardment.