• 대한수학회지
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• 제47권5호
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• pp.967-983
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• 2010

Let M be an n-dimensional complete simply connected Riemannian manifold with sectional curvature bounded above by a nonpositive constant $-{\kappa}^2$. Using the cone total curvature TC($\Gamma$) of a graph $\Gamma$ which was introduced by Gulliver and Yamada [8], we prove that the density at any point of a soap film-like surface $\Sigma$ spanning a graph $\Gamma\;\subset\;M$ is less than or equal to $\frac{1}{2\pi}\{TC(\Gamma)-{\kappa}^2Area(p{\times}\Gamma)\}$. From this density estimate we obtain the regularity theorems for soap film-like surfaces spanning graphs with small total curvature. In particular, when n = 3, this density estimate implies that if $TC(\Gamma)$ < $3.649{\pi}\;+\;{\kappa}^2\inf\limits_{p{\in}F}Area(p{\times}{\Gamma})$, then the only possible singularities of a piecewise smooth (M, 0, $\delta$)-minimizing set $\Sigma$ are the Y-singularity cone. In a manifold with sectional curvature bounded above by $b^2$ and diameter bounded by $\pi$/b, we obtain similar results for any soap film-like surfaces spanning a graph with the corresponding bound on cone total curvature.

• 충청수학회지
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• 제13권1호
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• pp.139-144
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• 2000

The generalized noncommutative torus $T_{\rho}^d$ of rank m was defined in [2]. Assume that for the completely irrational noncommutative subtorus $A_{\rho}$ of rank m of $T_{\rho}^d$ there is no integer q > 1 such that $tr(K_0(A_{\rho}))=\frac{1}{q}{\cdot}tr(K_0(A_{\rho^{\prime}}))$ for $A_{\rho^{\prime}}$ a completely irrational noncommutative torus of rank m. All $C^*$-algebras ${\Gamma}({\eta})$ of sections of locally trivial $C^*$-algebra bundles ${\eta}$ over $M=\prod_{i=1}^{e}S^{2k_i}{\times}\prod_{i=1}^{s}S^{2n_i+1}$, $\prod_{i=1}^{s}\mathbb{PR}_{2n_i}$, or $\prod_{i=1}^{s}L_{k_i}(n_i)$ with fibres $T_{\rho}^d{\otimes}M_c(\mathbb{C})$ were constructed in [6, 7, 8]. We prove that ${\Gamma}({\eta}){\otimes}M_{p^{\infty}}$ is isomorphic to $C(M){\otimes}A_{\rho}{\otimes}M_{cd}(\mathbb{C}){\otimes}M_{p^{\infty}}$ if and only if the set of prime factors of cd is a subset of the set of prime factors of p, that $\mathcal{O}_{2u}{\otimes}{\Gamma}({\eta})$ is isomorphic to $\mathcal{O}_{2u}{\otimes}C(M){\otimes}A_{\rho}{\otimes}M_{cd}(\mathbb{C})$ if and only if cd and 2u - 1 are relatively prime, and that $\mathcal{O}_{\infty}{\otimes}{\Gamma}({\eta})$ is not isomorphic to $\mathcal{O}_{\infty}{\otimes}C(M){\otimes}A_{\rho}{\otimes}M_{cd}(\mathbb{C})$ if cd > 1 when no non-trivial matrix algebra can be ${\Gamma}({\eta})$.

• Kyungpook Mathematical Journal
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• 제54권2호
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• pp.157-163
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• 2014

For a finite subset ${\Lambda}$ of $\mathbb{N}_0{\times}\mathbb{N}_0$, where $\mathbb{N}_0$ is the set of nonnegative integers, we say that a complex data ${\gamma}_{\Lambda}:=\{{\gamma}_{ij}\}_{(ij){\in}{\Lambda}}$ in the unit disc $\mathbf{D}$ of complex numbers has a cyclic subnormal completion if there exists a Hilbert space $\mathcal{H}$ and a cyclic subnormal operator S on $\mathcal{H}$ with a unit cyclic vector $x_0{\in}\mathcal{H}$ such that ${\langle}S^{*i}S^jx_0,x_0{\rangle}={\gamma}_{ij}$ for all $i,j{\in}\mathbb{N}_0$. In this note, we obtain some sufficient conditions for a cyclic subnormal completion of ${\gamma}_{\Lambda}$, where ${\Lambda}$ is a finite subset of $\mathbb{N}_0{\times}\mathbb{N}_0$.

• 한국정보디스플레이학회:학술대회논문집
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• 한국정보디스플레이학회 2006년도 6th International Meeting on Information Display
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• pp.286-289
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• 2006

Temporal dual gamma drive technology employing the 120Hz refresh rate was developed to enhance the off-axis viewing quality in patterned vertical alignment mode. The color shift ${\Delta}u'v'$ from on-axis to off-axis (60 deg.) for pale orange color, (R,G,B) = (196,124,96), was below 0.01, and the power exponent of gamma curve for off-axis viewing angle (60 deg.) was about 1.8, when the gamma curve for on-axis was set with power exponent of 2.4. The off-axis image distortion index was below 0.180 in contrast to the normal case ${\sim}0.23$. To elevate the response speed of liquid crystal in the intra-frame, the voltage below threshold voltage of liquid crystals was used.

• Communications for Statistical Applications and Methods
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• 제24권1호
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• pp.43-65
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• 2017

We propose a flexible cure rate survival model by assuming that the number of competing causes of the event of interest has the Poisson distribution and the time for the event follows the gamma-G family of distributions. The extended family of gamma-G failure-time models with long-term survivors is flexible enough to include many commonly used failure-time distributions as special cases. We consider a frequentist analysis for parameter estimation and derive appropriate matrices to assess local influence on the parameters. Further, various simulations are performed for different parameter settings, sample sizes and censoring percentages. We illustrate the performance of the proposed regression model by means of a data set from the medical area (gastric cancer).

• 대한수학회지
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• 제51권4호
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• pp.721-734
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• 2014

Let M be a module over a commutative ring R, and let T(M) be its set of torsion elements. The total torsion element graph of M over R is the graph $T({\Gamma}(M))$ with vertices all elements of M, and two distinct vertices m and n are adjacent if and only if $m+n{\in}T(M)$. In this paper, we study the basic properties and possible structures of two (induced) subgraphs $Tor_0({\Gamma}(M))$ and $T_0({\Gamma}(M))$ of $T({\Gamma}(M))$, with vertices $T(M){\backslash}\{0\}$ and $M{\backslash}\{0\}$, respectively. The main purpose of this paper is to extend the definitions and some results given in [6] to a more general total torsion element graph case.

• Kyungpook Mathematical Journal
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• 제55권2호
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• pp.279-287
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• 2015

A subset S of V (G), where G is a graph without isolated vertices, is a double dominating set of G if for each $x{{\in}}V(G)$, ${\mid}N_G[x]{\cap}S{\mid}{\geq}2$. This paper, shows that any positive integers a, b and n with $2{\leq}a<b$, $b{\geq}2a$ and $n{\geq}b+2a-2$, can be realized as domination number, double domination number and order, respectively. It also characterize the double dominating sets in the Cartesian and tensor products of two graphs and determine sharp bounds for the double domination numbers of these graphs. In particular, it show that if G and H are any connected non-trivial graphs of orders n and m respectively, then ${\gamma}_{{\times}2}(G{\square}H){\leq}min\{m{\gamma}_2(G),n{\gamma}_2(H)\}$, where ${\gamma}_2$, is the 2-domination parameter.

• Nuclear Engineering and Technology
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• 제55권5호
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• pp.1708-1717
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• 2023

The grade analysis of lead-zinc ore is the basis for the optimal development and utilization of deposits. In this study, a method combining Prompt Gamma Neutron Activation Analysis (PGNAA) technology and machine learning is proposed for lead-zinc mine borehole logging, which can identify lead-zinc ores of different grades and gangue in the formation, providing real-time grade information qualitatively and semi-quantitatively. Firstly, Monte Carlo simulation is used to obtain a gamma-ray spectrum data set for training and testing machine learning classification algorithms. These spectra are broadened, normalized and separated into inelastic scattering and capture spectra, and then used to fit different classifier models. When the comprehensive grade boundary of high- and low-grade ores is set to 5%, the evaluation metrics calculated by the 5-fold cross-validation show that the SVM (Support Vector Machine), KNN (K-Nearest Neighbor), GNB (Gaussian Naive Bayes) and RF (Random Forest) models can effectively distinguish lead-zinc ore from gangue. At the same time, the GNB model has achieved the optimal accuracy of 91.45% when identifying high- and low-grade ores, and the F₁ score for both types of ores is greater than 0.9.

• Nuclear Engineering and Technology
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• 제38권4호
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• pp.383-390
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• 2006

Having its roots in medical applications, industrial gamma ray CT has opened up new roads far investigating and modeling industrial processes. Using a line of research related to industrial gamma ray CT, the authors set up a system of single source and detector gamma transmission tomography for wood timber and a packed bed phantom. The hardware of the CT system consists of two servo motors, a data logger, a computer, a radiation source and a radiation detector. One motor simultaneously moves the source and the detector for a parallel beam scanning, whereas the other motor rotates the scan table at a preset projection angle. The image is reconstructed from the measured projections by the filtered back projection method. The phantom was designed to simulate a cross section of a packed bed with a void. The radiation source was 20mCi of Cs-137 and the detector was a 1 inch $\times$ 1 inch NaI (TI) scintillator shielded by a lead collimator. The experimental gamma ray CT image has sufficient resolution to reveal air holes and the density distribution inside the phantom. The system could possibly be applied to a packed bed column or a pipe flow in a petrochemical plant.

• 대한수학회지
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• 제52권5호
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• pp.955-964
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• 2015

Let K be a number field and let S be a finite set of primes of K containing all the infinite ones. Let ${\alpha}_0{\in}{\mathbb{A}}^1(K){\subset}{\mathbb{P}}^1(K)$ and let ${\Gamma}_0$ be the set of the images of ${\alpha}_0$ under especially all Chebyshev morphisms. Then for any ${\alpha}{\in}{\mathbb{A}}^1(K)$, we show that there are only a finite number of elements in ${\Gamma}_0$ which are S-integral on ${\mathbb{P}}^1$ relative to (${\alpha}$). In the light of a theorem of Silverman we also propose a conjecture on the finiteness of integral points on an arbitrary dynamical system on ${\mathbb{P}}^1$, which generalizes the above finiteness result for Chebyshev morphisms.