• Bulletin of the Korean Mathematical Society
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• v.61 no.3
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• pp.837-848
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• 2024

It is shown in [1] that the Cauchy problem for the Fornberg-Whitham equation is well-posed in C¹(ℝ) and the data-to-solution map is Hölder continuous from C^α to C([0, T]; C^α) with α ∈ [0, 1). In this short paper, we further show that the data-to-solution map of the Fornberg-Whitham equation is not uniformly continuous on the initial data in C¹(ℝ).

• Proceedings of the KSME Conference
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• 2005.11a
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• pp.93.1-93.1
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• 2005

• Proceedings of the Korean Nuclear Society Conference
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• 2003.05a
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• pp.135-135
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• 2003

• Korean Journal of Mathematics
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• v.26 no.2
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• pp.327-335
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• 2018

In this paper, we present the construction of natural invariant measures so called SRB(Sinai-Ruelle-Bowen) measures by the properties of geometric t-potential and Bowen's equation for the hyperbolic attractors.

• Bulletin of the Korean Mathematical Society
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• v.49 no.4
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• pp.799-813
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• 2012

In this paper, we first show that the iteration {$x_n$} defined by $x_{n+1}=P((1-{\alpha}_n)x_n +{\alpha}_nTP[{\beta}_nTx_n+(1-{\beta}_n)x_n])$ converges strongly to some fixed point of T when E is a real uniformly convex Banach space and T is a quasi-nonexpansive non-self mapping satisfying Condition A, which generalizes the result due to Shahzad [11]. Next, we show the strong convergence of the Mann iteration process with errors when E is a real uniformly convex Banach space and T is a quasi-nonexpansive self-mapping satisfying Condition A, which generalizes the result due to Senter-Dotson [10]. Finally, we show that the iteration {$x_n$} defined by $x_{n+1}={\alpha}_nSx_n+{\beta}_nT[{\alpha}^{\prime}_nSx_n+{\beta}^{\prime}_nTx_n+{\gamma}^{\prime}_n{\upsilon}_n]+{\gamma}_nu_n$ converges strongly to a common fixed point of T and S when E is a real uniformly convex Banach space and T, S are two quasi-nonexpansive self-mappings satisfying Condition D, which generalizes the result due to Ghosh-Debnath [3].

• Nuclear Engineering and Technology
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• v.50 no.6
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• pp.923-928
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• 2018

We developed a compact gamma camera based on a modified uniformly redundant array coded aperture to investigate the position of a $UO_2$ pellet emitting characteristic X-rays (98.4 keV) and ${\gamma}-rays$ (185.7 keV). Experiments using an only-mask method and an antimask subtractive method were conducted, and the maximum-likelihood expectation maximization algorithm was used for image reconstruction. The images obtained via the antimask subtractive method were compared with those obtained using the only-mask method with regard to the signal-to-noise ratio. The reconstructed images of the antimask subtractive method were superior. The reconstructed images of the characteristic X-rays and the ${\gamma}-rays$ were combined with the obtained image using the optical camera. The combined images showed the precise position of the $UO_2$ pellet. According to the self-absorption ratios of the nuclear material and the minimum number of effective events for image reconstruction, we estimated the minimum detection time depending on the amount of nuclear material.

• Journal of the Korea Institute of Military Science and Technology
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• v.20 no.1
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• pp.90-97
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• 2017

In this paper, we propose a new array antenna scheme which has an improved side lobe level (SLL) as well as a simplified feeding network and a high gain. The proposed array scheme is based on a non-uniformly excited sub-array. For analysis, we use an array factor of sub-array antenna. In the simulation results, the simulated SLL and gain provide more than 18.43 dB and 26.63 dBi, respectively. For the verification of the proposed design scheme, the prototype antenna with $16{\times}8$ radiating elements was designed by the proposed array scheme. The measured SLL and gain are more than 19.85 dB and 25.53 dBi, respectively. This measurement result indicates that the proposed array scheme is reasonable.

• Journal of applied mathematics & informatics
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• v.24 no.1_2
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• pp.437-448
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• 2007

Suppose K is a nonempty closed convex nonexpansive retract of a real uniformly convex Banach space E with P as a nonexpansive retraction. Let $T_1,\;T_2\;and\;T_3\;:\;K{\rightarrow}E$ be nonexpansive mappings with nonempty common fixed points set. Let $\{\alpha_n\},\;\{\beta_n\},\;\{\gamma_n\},\;\{\alpha'_n\},\;\{\beta'_n\},\;\{\gamma'_n\},\;\{\alpha'_n\},\;\{\beta'_n\}\;and\;\{\gamma'_n\}$ be real sequences in [0, 1] such that ${\alpha}_n+{\beta}_n+{\gamma}_n={\alpha}'_n+{\beta'_n+\gamma}'_n={\alpha}'_n+{\beta}'_n+{\gamma}'_n=1$, starting from arbitrary $x_1{\in}K$, define the sequence $\{x_n\}$ by $$\{zn=P({\alpha}'_nT_1x_n+{\beta}'_nx_n+{\gamma}'_nw_n)\;yn=P({\alpha}'_nT_2z_n+{\beta}'_nx_n+{\gamma}'_nv_n)\;x_{n+1}=P({\alpha}_nT_3y_n+{\beta}_nx_n+{\gamma}_nu_n)$$ with the restrictions $\sum^\infty_{n=1}{\gamma}_n<\infty,\;\sum^\infty_{n=1}{\gamma}'_n<\infty,\; \sum^\infty_{n=1}{\gamma}'_n<\infty$. (i) If the dual $E^*$ of E has the Kadec-Klee property, then weak convergence of a $\{x_n\}$ to some $x^*{\in}F(T_1){\cap}{F}(T_2){\cap}(T_3)$ is proved; (ii) If $T_1,\;T_2\;and\;T_3$ satisfy condition(A'), then strong convergence of $\{x_n\}$ to some $x^*{\in}F(T_1){\cap}{F}(T_2){\cap}(T_3)$ is obtained.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.33 no.2A
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• pp.130-138
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• 2008

In this paper, we propose a user selection method to maximize the sum-rate of downlink over opportunistic beamforming. The throughput of an opportunistic beamforming with non-uniformly distributed or a small number of users can decrease. In order to improve the throughput, we propose a scheduling method that does not use SINR or SNR but uses the effective channel gain of each user obtained from the SINR or SNR feedback. The proposed method makes it possible to select users flexibly according to the distribution of users. In numerical results, we show that the proposed methods improve the average sum-rate about 60% when users are distributed non uniformly.

• Structural Engineering and Mechanics
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• v.24 no.2
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• pp.213-225
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• 2006

The propagation of non-uniformly modulated, evolutionary random waves in viscoelastic, transversely isotropic, stratified materials is investigated. The theory is developed in the context of a multi-layered soil medium overlying bedrock, where the material properties of the bedrock are considered to be much stiffer than those of the soil and the power spectral density of the random excitation is assumed to be known at the bedrock. The governing differential equations are first derived in the frequency/wave-number domain so that the displacement response of the ground may be computed. The eigen-solution expansion method is then used to solve for the responses of the layers. This utilizes the precise integration method, in combination with the extended Wittrick-Williams algorithm, to obtain all the eigen-solutions of the ordinary differential equation. The recently developed pseudo-excitation method for structural random vibration is then used to determine the solution of the layered soil responses.