• Bulletin of the Korean Mathematical Society
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• v.59 no.1
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• pp.241-263
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• 2022

We consider a nonlinear Schrödinger equation with critical frequency, (P_𝜀) : 𝜀²∆v(x) - V(x)v(x) + |v(x)|^p-1v(x) = 0, x ∈ ℝ^N, and v(x) → 0 as |x| → +∞, for the infinite case as described by Byeon and Wang. Critical means that 0 ≤ V ∈ C(ℝ^N) verifies Ƶ = {V = 0} ≠ ∅. Infinite means that Ƶ = {x₀} and that, grossly speaking, the potential V decays at an exponential rate as x → x₀. For the semiclassical limit, 𝜀 → 0, the infinite case has a characteristic limit problem, (P_inf) : ∆u(x)-P(x)u(x) + |u(x)|^p-1u(x) = 0, x ∈ Ω, with u(x) = 0 as x ∈ Ω, where Ω ⊆ ℝ^N is a smooth bounded strictly star-shaped region related to the potential V. We prove the existence of an infinite number of solutions for both the original and the limit problem via a Ljusternik-Schnirelman scheme for even functionals. Fixed a topological level k we show that v_k,𝜀, a solution of (P_𝜀), subconverges, up to a scaling, to a corresponding solution of (P_inf ), and that v_k,𝜀 exponentially decays out of Ω. Finally, uniform estimates on ∂Ω for scaled solutions of (P_𝜀) are obtained.

• Kyungpook Mathematical Journal
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• v.52 no.1
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• pp.13-20
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• 2012

In a previous paper, the author proved that all odd cycles, except five cycles, are highly Ramsey-infinite. In this paper, we fill in the missing case, and show that five cycles are highly Ramsey-infinite.

• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.643-651
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• 2005

In the first part of this paper we investigate several statements concerning infinite maximal planar graphs which are equivalent in finite case. In the second one, for a given induced $\theta$-path (a finite induced path whose endvertices are adjacent to a vertex of infinite degree) in a 4-connected VAP-free maximal planar graph containing a vertex of infinite degree, a new $\theta$-path is constructed such that the resulting fan is tight.

• Journal of Advanced Marine Engineering and Technology
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• v.28 no.6
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• pp.1017-1025
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• 2004

Generally generator is connected to the bus with no load. After the connection to the bus. the frequency of generator system with no load has to be increased for preventing the reverse power. But in a few case of parallel running with infinite bus system, we have to synchronize the loaded generator to the infinite bus. The frequency of generator system with load has to be lowered for prevention of load shift to the bus system. The blackout of infinite bus decreases the parallel running generator's frequency because of load increasing. In this paper we propose a method that the generator with load maintains the frequency constantly after the blackout of infinite bus. With the constant speed control and load control method of parallel running system to the infinite bus we apply the method to the industrial generating system.

• Earthquakes and Structures
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• v.8 no.1
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• pp.275-304
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• 2015

The objective of this paper is to investigate the validity of transmitting boundaries in dynamic analysis of soil-structure interaction problems. As a case study, the proposed Baghdad metro line is considered. The information about the dimensions and the material properties of the concrete tunnel and surrounding soil were obtained from a previous study. A parametric study is carried out to investigate the effect of several parameters including the peak value of the horizontal component of earthquake displacement records and the frequency of the dynamic load. The computer program (Mod-MIXDYN) is used for the analysis. The numerical results are analyzed for three conditions; finite boundaries (traditional boundaries), infinite boundaries modelled by infinite elements (5-node mapped infinite element) presented by Selvadurai and Karpurapu, 1988), and infinite boundaries modelled by dashpot elements (viscous boundaries). It was found that the transmitting boundary absorbs most of the incident energy. The distinct reflections observed for the "fixed boundaries" disappear by using "transmitted boundaries". This is true for both cases of using viscous boundaries or mapped infinite elements. The type and location of the dynamic load represent two controlling factors in deciding the importance of using infinite boundaries. It was found that the results present significant differences when earthquake is applied as a base motion or a pressure load is applied at the surface ground. The peak value of the vertical displacement at nodes A, B, E and F (located at the tunnel's crown and side walls, and at the surface above the tunnel and at the surface 6.5 m away from tunnel's centre respectively) increases with the frequency of the surface pressure load for both cases 1 and 2 (traditional boundaries and mapped infinite elements respectively) while it decreases for case 3 (viscous boundaries). The modular ratio Ec/Es (modulus of elasticity of the concrete lining to that of the surrounding soil) has a considerable effect on the peak value of the horizontal displacement at node B (on the side wall of the tunnel lining) increase about (17.5) times, for the three cases (1, 2, and 3).

• Journal of the Institute of Electronics Engineers of Korea TC
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• v.37 no.11
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• pp.1-7
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• 2000

Surface wave scattering by periodic grooves of arbitrary profile in a grounded dielectric slab is investigated for the TE surface wave incidence. Both the finite and infinite periodic geometries are considered. The former case is analyzed by using of hybrid FEM/MOM and the latter by using of full MOM procedure. Some numerical results for the reflected and transmitted powers in a grounded dielectric slab, radiation power into the free space, and radiation patterns in case of finite structure and for the dispersion diagram in case of infinite structure are presented. And some descriptions on the relationship between the finite and infinite structure such as the maximum beam angle are given.

• Journal of applied mathematics & informatics
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• v.28 no.1_2
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• pp.363-372
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• 2010

In this paper we prove the almost sure convergence of partial sums of identically distributed and negatively associated random variables with infinite expectations. Some results in Kruglov[Kruglov, V., 2008 Statist. Probab. Lett. 78(7) 890-895] are considered in the case of negatively associated random variables.

• Communications for Statistical Applications and Methods
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• v.3 no.1
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• pp.257-265
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• 1996

We consider nonstationary autoregressive autoregressive process with infinite variance of error. In the case of infinite cariance, the limiting distribution of the estimated coefficient is different from that under the finite cariance assumption. In this paper we show that the bootstrap method can be used to approximate the distribution of ordinary least squares estimator of the coefficient in the first order random walk process with infinite variance through some empirical studies and we suggest a test procedure based on bootstrap method for the unit root test.

• International Journal of Reliability and Applications
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• v.10 no.1
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• pp.33-42
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• 2009

In most of literatures of age replacement policy, the authors consider the case that a new item starts operating at time zero and is to be replaced by new one at time T. It is, however, often to purchase used items because of the limited budget. In this paper, we consider age replacement policy of a used item whose age is $t_0$. The mathematical formulas of the expected cost rate per unit time are derived for both infinite-horizon case and finite-horizon case. For each case, we show that the optimal replacement age exists and is finite and investigate the effect of the age of the used item.

• Journal of the Korean Institute of Illuminating and Electrical Installation Engineers
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• v.27 no.10
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• pp.30-40
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• 2013

In this study the method based on flux linkage in cell was introduced in calculation of eddy currents by cell method. According to this method eddy current distribution and the loss can be evaluated and since the shielding effectiveness by flux cancelation of eddy current can be analyzed, this method is applicable to design of conductive shield. And also the formula of shielding factor were so deduced as to be applicable to finite-width infinite-length shielding sheets and infinite-length underground cable shield. These formula are adaptable to magnetic materials as well as conductive materials. As the results of calculation in model shields are follows. In case of finite-width infinite-length shielding sheet, shielding effectiveness increases with increasing of conductivity. In case of infinite-length underground cable shield, the effectiveness become higher with increasing of permeability. Especially the effectiveness is very high in materials with both high conductivity and permeability in underground cable shield.