• Communications of the Korean Mathematical Society
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• v.14 no.1
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• pp.81-97
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• 1999

A sufficient condition for pseudo-Laplacian equations involving critical Sobolev exponents to have positive solutions is established.

• Communications of the Korean Mathematical Society
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• v.38 no.1
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• pp.137-151
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• 2023

In this paper we prove the existence of nontrivial weak solutions to the boundary value problem -G₁u = u³ + f(x, y, u) in Ω, u ≥ 0 in Ω, u = 0 on ∂Ω, where Ω is a bounded domain with smooth boundary in ℝ³, G₁ is a Grushin type operator, and f(x, y, u) is a lower order perturbation of u³ with f(x, y, 0) = 0. The nonlinearity involved is of critical exponent, which differs from the existing results in [11, 12].

• Korean Journal of Materials Research
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• v.25 no.3
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• pp.119-124
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• 2015

This paper investigates the change of the percolation threshold in the carbon powder-filled polystyrene matrix composites based on the experimental results of changes in the resistivity and relative permittivity of the carbon powder filling, the electric field dependence of the current, and the critical exponent of conductivity. In this research, the percolation behavior, the critical exponent of resistivity, and electrical conduction mechanism of the carbon powder-filled polystyrene matrix composites are discussed based on a study of the overall change in the resistivity. It was found that the formation of infinite clusters is interrupted by a tunneling gap in the volume fraction of the carbon powder filling, where the change in the resistivity is extremely large. In addition, it was found that the critical exponent of conductivity for the universal law of conductivity is satisfied if the percolation threshold is estimated at the volume fraction of carbon powder where non-ohmic current behavior becomes ohmic. It was considered that the mechanism for changing the gaps between the carbon powder aggregates into ohmic contacts is identical to that of the connecting conducting phases above the percolation threshold in a random resister network system. The electric field dependence is discussed with a tunneling mechanism. It is concluded that the percolation threshold should be defined at this volume fraction (the second transition of resistivity for the carbon powder-filled polystyrene matrix composites) of carbon powder.

• East Asian mathematical journal
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• v.30 no.3
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• pp.335-353
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• 2014

We establish multiple extence of positive solutions for parameterized nonhomogeneous elliptic equations involving critical Sobolev exponent. The approach to the problem is variational method.

• Bulletin of the Korean Chemical Society
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• v.6 no.3
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• pp.123-124
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• 1985

The optical activity of a fluid in the extreme critical region, where the Ornstein-Zernike theory does not hold, is explicitly obtained. We suggest new experimental methods to measure the critical exponent for correlation function by using the results of circular dichroism and optical rotation given in this paper.

• Bulletin of the Korean Mathematical Society
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• v.50 no.5
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• pp.1693-1710
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• 2013

In this paper, we consider the biharmonic elliptic systems of the form $$\{{\Delta}^2u=F_u(u,v)+{\lambda}{\mid}u{\mid}^{q-2}u,\;x{\in}{\Omega},\\{\Delta}^2v=F_v(u,v)+{\delta}{\mid}v{\mid}^{q-2}v,\;x{\in}{\Omega},\\u=\frac{{\partial}u}{{\partial}n}=0,\; v=\frac{{\partial}v}{{\partial}n}=0,\;x{\in}{\partial}{\Omega},$$, where ${\Omega}{\subset}\mathbb{R}^N$ is a bounded domain with smooth boundary ${\partial}{\Omega}$, ${\Delta}^2$ is the biharmonic operator, $N{\geq}5$, $2{\leq}q$ < $2^*$, $2^*=\frac{2N}{N-4}$ denotes the critical Sobolev exponent, $F{\in}C^1(\mathbb{R}^2,\mathbb{R}^+)$ is homogeneous function of degree $2^*$. By using the variational methods and the Ljusternik-Schnirelmann theory, we obtain multiplicity result of nontrivial solutions under certain hypotheses on ${\lambda}$ and ${\delta}$.

• Journal of the Korean Recycled Construction Resources Institute
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• v.4 no.3
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• pp.259-268
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• 2016

The service life evaluation in RC(Reinforced Concrete) structure exposed to chloride attack can be classified into deterministic and probabilistic method, and it significantly varies with design parameters. The present work derives PDF (Probability of Durability Failure) and the related service life considering time-dependent diffusion coefficient and internal parameters such as reference diffusion coefficient, critical chloride content, and time-exponent. When critical chloride content increases to 133.3%, the changing ratios of service life are 134.0~145.4% for deterministic method and 149.2%~152.5% for probabilistic method, respectively. In the case of increasing time-exponent to 200%, they increase to 323.8% for deterministic method and 346.0% for probabilistic method. Through adopting time-diffusion coefficient for probabilistic method, reasonable service life evaluation can be achieved, and it is also verified that increasing time-exponent through mineral admixture is very effective to extension of service life in RC structure.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 2008.10a
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• pp.292-296
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• 2008

A new method of evaluating critical damage values of commercial materials is presented in this paper. The method is based on the previous study of the methodology [1] of acquisition of true stress-strain curves or flow stress curves over large strain from the tensile test in which the flow stress is described by the Hollomon law-like form, that is, by the strain dependent strength coefficient and the strain hardening exponent. The strain hardening exponent is calculated from the true strain at the necking point to meet the Considere condition. The strength coefficient is assumed to be constant before necking and represented by a piecewise linear function of strain after necking. With the predicted flow stress, a tensile test is simulated by a rigid-plastic finite element method with higher accuracy of less than 0.5% error between experiments and predictions. The instant when the fracture begins and thus the critical damage is obtained is determined by observing the stress variation at the necked region. It is assumed that the fracture due to damage begins when the pattern of stress around the necked region changes radically. The method is applied to evaluate the critical damage of a low carbon steel.

• 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.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.7 no.10
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• pp.2338-2356
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• 2013

In cognitive radio networks, acquiring the position information of the primary user is critical to the communication of the secondary user. Localization of primary users can help improve the efficiency with which the spectrum is reused, because the information can be used to avoid harmful interference to the network while simultaneity is exploited to improve the spectrum utilization. Despite its inherent inaccuracy, received signal strength based on range has been used as the standard tool for distance measurements in the location detection process. Most previous works have employed the path-loss propagation model with a fixed value of the path loss exponent. However, in actual environments, the path loss exponent for each channel is different. Moreover, due to the complexity of the radio channel, when the number of channel increases, a larger number of RSS measurements are needed, and this results in additional energy consumption. In this paper, to overcome this problem, we propose using the Bayesian compressive sensing method with a calibrated path loss exponent to improve the performance of the PU localization method.