• 대한수학회지
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• 제47권2호
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• pp.263-275
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• 2010

Let {$X_n;n\;\geq\;1$} be a strictly stationary sequence of negatively associated random variables with mean zero and finite variance. Set $S_n\;=\;{\sum}^n_{k=1}X_k$, $M_n\;=\;max_{k{\leq}n}|S_k|$, $n\;{\geq}\;1$. Suppose $\sigma^2\;=\;EX^2_1+2{\sum}^\infty_{k=2}EX_1X_k$ (0 < $\sigma$ < $\infty$). We prove that for any b > -1/2, if $E|X|^{2+\delta}$(0<$\delta$$\leq$1), then $$lim\limits_{\varepsilon\searrow0}\varepsilon^{2b+1}\sum^{\infty}_{n=1}\frac{(loglogn)^{b-1/2}}{n^{3/2}logn}E\{M_n-\sigma\varepsilon\sqrt{2nloglogn}\}_+=\frac{2^{-1/2-b}{\sigma}E|N|^{2(b+1)}}{(b+1)(2b+1)}\sum^{\infty}_{k=0}\frac{(-1)^k}{(2k+1)^{2(b+1)}}$$ and for any b > -1/2, $$lim\limits_{\varepsilon\nearrow\infty}\varepsilon^{-2(b+1)}\sum^{\infty}_{n=1}\frac{(loglogn)^b}{n^{3/2}logn}E\{\sigma\varepsilon\sqrt{\frac{\pi^2n}{8loglogn}}-M_n\}_+=\frac{\Gamma(b+1/2)}{\sqrt{2}(b+1)}\sum^{\infty}_{k=0}\frac{(-1)^k}{(2k+1)^{2b+2'}}$$, where $\Gamma(\cdot)$ is the Gamma function and N stands for the standard normal random variable.

• 대한수학회지
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• 제46권6호
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• pp.1309-1318
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• 2009

Let k be a positive integer, and let G be a simple graph with vertex set V (G). A Roman k-dominating function on G is a function f : V (G) $\rightarrow$ {0, 1, 2} such that every vertex u for which f(u) = 0 is adjacent to at least k vertices $\upsilon_1,\;\upsilon_2,\;{\ldots},\;\upsilon_k$ with $f(\upsilon_i)$ = 2 for i = 1, 2, $\ldot$, k. The weight of a Roman k-dominating function is the value f(V (G)) = $\sum_{u{\in}v(G)}$ f(u). The minimum weight of a Roman k-dominating function on a graph G is called the Roman k-domination number ${\gamma}_{kR}$(G) of G. Note that the Roman 1-domination number $\gamma_{1R}$(G) is the usual Roman domination number $\gamma_R$(G). In this paper, we investigate the properties of the Roman k-domination number. Some of our results extend these one given by Cockayne, Dreyer Jr., S. M. Hedetniemi, and S. T. Hedetniemi [2] in 2004 for the Roman domination number.

• JSTS:Journal of Semiconductor Technology and Science
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• 제15권5호
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• pp.437-444
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• 2015

In simulation-based circuit optimization, many simulation runs may be wasted while evaluating infeasible designs, i.e. the designs that do not meet the constraints. To avoid such a waste, this paper investigates the use of support vector machine (SVM) classifiers in predicting the design's feasibility prior to simulation and the optimal selection of the SVM parameters, namely, the Gaussian kernel shape parameter ${\gamma}$ and the misclassification penalty parameter C. These parameters affect the complexity as well as the accuracy of the model that SVM represents. For instance, the higher ${\gamma}$ is good for detailed modeling and the higher C is good for rejecting noise in the training set. However, our empirical study shows that a low ${\gamma}$ value is preferable due to the high spatial correlation among the circuit design candidates while C has negligible impacts due to the smooth and clean constraint boundaries of most circuit designs. The experimental results with an LC-tank oscillator example show that an optimal selection of these parameters can improve the prediction accuracy from 80 to 98% and model complexity by $10{\times}$.

• 대한전자공학회:학술대회논문집
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• 대한전자공학회 2003년도 하계종합학술대회 논문집 II
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• pp.751-754
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• 2003

Metamorphic HEMTs (MHEMTs) have emerged as excellent challenges for the design and fabrication of high-speed HEMTs for millimeter-wave applications. Some of improvements result from improved mobility and larger conduction band discontinuity in the channel, leading to more efficient modulation doping, better confinement, and better device performance compared with pseudomorphic HEMTs. We have studied the calibration on the DC and RF characteristics of the MHEMT device using I $n_{0.53}$G $a_{0.47}$As/I $n_{0.52}$A1$_{0.48}$As modulation-doped heterostructure on the GaAs wafer. For the optimized device performance simulation, we calibrated the device performance of 0.1-${\mu}{\textrm}{m}$ $\Gamma$-gate MHEMT fabricated in our research center using the 2D ISE-DESSIS device simulator. With this calibrated parameter set, we have obtained very good reproducibility. The device simulation on the DC and RF characteristics exhibits good reproducibility for our 0.1-${\mu}{\textrm}{m}$ -gate MHEMT device compared with the measurements. We expect that our calibration result can help design over-100-GHz MHEMT devices for better device performance.ormance.

• 대한수학회보
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• 제33권1호
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• pp.119-126
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• 1996

In this paper we study the asymptotic behavior of the edge independence number of a random (n,n)-tree. The tools we use include the matrix-tree theorem, the probabilistic method and Hall's theorem. We begin with some definitions. An (n,n)_tree T is a connected, acyclic, bipartite graph with n light and n dark vertices (see [Pa92]). A subset M of edges of a graph is called independent(or matching) if no two edges of M are adfacent. A subset S of vertices of a graph is called independent if no two vertices of S are adjacent. The edge independence number of a graph T is the number $\beta_1(T)$ of edges in any largest independent subset of edges of T. Let $\Gamma(n,n)$ denote the set of all (n,n)-tree with n light vertices labeled 1, $\ldots$, n and n dark vertices labeled 1, $\ldots$, n. We give $\Gamma(n,n)$ the uniform probability distribution. Our aim in this paper is to find bounds on $\beta_1$(T) for a random (n,n)-tree T is $\Gamma(n,n)$.

• 대한수학회보
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• 제57권3호
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• pp.649-660
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• 2020

This paper proves a new regularity criterion for solutions to the Cauchy problem of the 3D Boussinesq equations via one directional derivative of the horizontal component of the velocity field (i.e., (∂_iu₁; ∂_ju₂; 0) where i, j ∈ {1, 2, 3}) in the framework of the anisotropic Lebesgue spaces. More precisely, for 0 < T < ∞, if $$\large{\normalsize\displaystyle\smashmargin{2}{\int\nolimits_o}^T}({\HUGE\left\|{\small{\parallel}{\partial}_iu_1(t){\parallel}_{L^{\alpha}_{x_i}}}\right\|}{\small^{\gamma}_{L^{\beta}_{x_{\hat{i}}x_{\bar{i}}}}+}{\HUGE\left\|{\small{\parallel}{\partial}_iu_2(t){\parallel}_{L^{\alpha}_{x_j}}}\right\|}{\small^{\gamma}_{L^{\beta}_{x_{\hat{i}}x_{\bar{i}}}}})dt<{{\infty}},$$ where ${\frac{2}{{\gamma}}}+{\frac{1}{{\alpha}}}+{\frac{2}{{\beta}}}=m{\in}[1,{\frac{3}{2}})$ and ${\frac{3}{m}}{\leq}{\alpha}{\leq}{\beta}<{\frac{1}{m-1}}$, then the corresponding solution (u, θ) to the 3D Boussinesq equations is regular on [0, T]. Here, (i, ${\hat{i}}$, ${\tilde{i}}$) and (j, ${\hat{j}}$, ${\tilde{j}}$) belong to the permutation group on the set 𝕊₃ := {1, 2, 3}. This result reveals that the horizontal component of the velocity field plays a dominant role in regularity theory of the Boussinesq equations.

• Journal of Korean Neurosurgical Society
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• 제39권2호
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• pp.96-101
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• 2006

Objective : The authors assess the long term effectiveness of gamma knife radiosurgery[GKS] for remnant or recurred craniopharyngiomas on tumor control and possibly set proper radiation dose for tumor control with utmost preservation of the adjacent structures. Methods : Sixteen GKS were done in 14 patients with recurred or remnant craniopharyngiomas after surgery. Mean follow up duration was 44.2 months [range $11.3{\sim}123.6\;months$]. Follow up MR imagings were analyzed. Results : Mean tumor volume was $3.6cm^3$ [range $0.6{\sim}18cm^3$] and mean margin dose was 12.2Gy [range $8{\sim}22.4Gy$]. Tumor control was achieved in 87.5% [14 of 16 tumors] which were either solid or cystic in nature. Dose to optic apparatus was mean 7.9Gy and no radiation related complications were observed. Conclusion : GKS seems to be effective treatment modality for craniopharyngiomas regardless of nature of tumor whether it is cystic or solid. Dose of 8 to 8.5Gy may be sufficient to achieve long term tumor control for remnant or recurred craniopharyngiomas.

• 대한수학회지
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• 제47권5호
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• pp.1097-1106
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• 2010

Let R be a commutative ring with identity, X the set of all nonzero, nonunits of R and G the group of all units of R. We will investigate some ring theoretic properties of R by considering $\Gamma$(R), the zero-divisor graph of R, under the regular action on X by G as follows: (1) If R is a ring such that X is a union of a finite number of orbits under the regular action on X by G, then there is a vertex of $\Gamma$(R) which is adjacent to every other vertex in $\Gamma$(R) if and only if R is a local ring or $R\;{\simeq}\;\mathbb{Z}_2\;{\times}\;F$ where F is a field; (2) If R is a local ring such that X is a union of n distinct orbits under the regular action of G on X, then all ideals of R consist of {{0}, J, $J^2$, $\ldots$, $J^n$, R} where J is the Jacobson radical of R; (3) If R is a ring such that X is a union of a finite number of orbits under the regular action on X by G, then the number of all ideals is finite and is greater than equal to the number of orbits.

• Nuclear Engineering and Technology
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• 제34권1호
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• pp.30-41
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• 2002

The neutron beam is fully characterized for the prompt gamma activation analysis facility at Hanaro in the Korea Atomic Energy Research Institute(KAERI). The facility uses thermal neutrons which are diffracted vertically from a horizontal beam port by a set of pyrolytic graphite(PG) crystals positioned at the Bragg angle of 45" Neutron spectra, neutron flux and Cd-ratio are determined for the three extraction modes of diffracted beam by means of the theoretical and experimental efforts. To obtain theoretical result, the reflectivity of pyrolytic graphite is calculated in the diffraction model for mosaic crystal and the angular divergence after diffraction by mosaic crystal is estimated from Monte Carlo simulation. The time-of-flight spectrometer and gold activation wire are used for measuring the neutron spectra. Both the calculated and measured spectra have proven that the unique feature of polychromatic beam obtained by PG crystals are useful for PGAA. The thermal neutron flux of 7.9$\times$107 n/cm$^2$s and the Cd-ratio of 266 for gold have been achieved at the sample position while the reactor operates at 24 MW The uniformity of beam flux is 12% in the central 1$\times$1 cm$^2$ area. Finally, the beam is briefly characterized by the effective velocity and temperature which are determined by measuring the prompt Y-ray spectra for thin and thick boron samples.ples.

• 한국의학물리학회지:의학물리
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• 제31권4호
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• pp.153-162
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• 2020

Purpose: We aim to evaluate the accuracy and effectiveness of an automatically converted radiation therapy plan between Radixact machines by comparing the original plan with the transferred plan. Methods: The study involved a total of 20 patients for each randomly selected treatment site who received radiation treatment with Radixact. We set up the cheese phantom (Gammex RMI, Middleton, WI, USA) with an Exradin A1SL ion chamber (Standard Imaging, Madison, WI, USA) and GAFCHROMIC EBT3 film (International Specialty Products, Wayne, NJ, USA) inserted. We used three methods to evaluate an automatically converted radiation therapy plan using the features of the Plan transfer. First, we evaluated and compared Planning target volume (PTV) coverage (homogeneity index, HI; conformity index, CI) and organs at risk (OAR) dose statistics. Second, we compared the absolute dose using an ion chamber. Lastly, we analyzed gamma passing rates using film. Results: Our results showed that the difference in PTV coverage was 1.72% in HI and 0.17% in CI, and majority of the difference in OAR was within 1% across all sites. The difference (%) in absolute dose values was averaging 0.74%. In addition, the gamma passing rate was 99.64% for 3%/3 mm and 97.08% for 2%/2 mm. Conclusions: The Plan transfer function can be reliably used in appropriate situations.