• Bulletin of the Korean Mathematical Society
• /
• v.54 no.1
• /
• pp.265-276
• /
• 2017

Let K be a fan-like simplicial sphere of dimension n-1 such that its associated complete fan is strongly polytopal, and let v be a vertex of K. Let K(v) be the simplicial wedge complex obtained by applying the simplicial wedge operation to K at v, and let $v_0$ and $v_1$ denote two newly created vertices of K(v). In this paper, we show that there are infinitely many strongly polytopal fans ${\Sigma}$ over such K(v)'s, different from the canonical extensions, whose projected fans ${Proj_v}_i{\Sigma}$ (i = 0, 1) are also strongly polytopal. As a consequence, it can be also shown that there are infinitely many projective toric varieties over such K(v)'s such that toric varieties over the underlying projected complexes $K_{{Proj_v}_i{\Sigma}}$ (i = 0, 1) are also projective.

• Bulletin of the Korean Mathematical Society
• /
• v.54 no.6
• /
• pp.2165-2182
• /
• 2017

Let G be a group and $\mathbb{C}$ the field of complex numbers. Suppose ${\sigma}:G{\rightarrow}G$ is an endomorphism satisfying ${{\sigma}}({{\sigma}}(x))=x$ for all x in G. In this paper, we first determine the central solution, f : G or $G{\times}G{\rightarrow}\mathbb{C}$, of the functional equation $f(xy)+f({\sigma}(y)x)=2f(x)+2f(y)$ for all $x,y{\in}G$, which is a variant of the quadratic functional equation. Using the central solution of this functional equation, we determine the general solution of the functional equation f(pr, qs) + f(sp, rq) = 2f(p, q) + 2f(r, s) for all $p,q,r,s{\in}G$, which is a variant of the equation f(pr, qs) + f(ps, qr) = 2f(p, q) + 2f(r, s) studied by Chung, Kannappan, Ng and Sahoo in [3] (see also [16]). Finally, we determine the solutions of this equation on the free groups generated by one element, the cyclic groups of order m, the symmetric groups of order m, and the dihedral groups of order 2m for $m{\geq}2$.

• Bulletin of the Korean Mathematical Society
• /
• v.54 no.4
• /
• pp.1195-1219
• /
• 2017

In this paper, the limit behavior of solution for the $Schr{\ddot{o}}dinger$ equation with random dispersion and time-dependent nonlinear loss/gain: $idu+{\frac{1}{{\varepsilon}}}m({\frac{t}{{\varepsilon}^2}}){\partial}_{xx}udt+{\mid}u{\mid}^{2{\sigma}}udt+i{\varepsilon}a(t){\mid}u{\mid}^{2{\sigma}_0}udt=0$ is studied. Combining stochastic Strichartz-type estimates with $L^2$ norm estimates, we first derive the global existence for $L^2$ and $H^1$ solution of the stochastic $Schr{\ddot{o}}dinger$ equation with white noise dispersion and time-dependent loss/gain: $idu+{\Delta}u{\circ}d{\beta}+{\mid}u{\mid}^{2{\sigma}}udt+ia(t){\mid}u{\mid}^{2{\sigma}_0}udt=0$. Secondly, we prove rigorously the global diffusion-approximation limit of the solution for the former as ${\varepsilon}{\rightarrow}0$ in one-dimensional $L^2$ subcritical and critical cases.

• Korean Journal of Clinical Laboratory Science
• /
• v.52 no.2
• /
• pp.91-97
• /
• 2020

Standardization of vitamin analysis continues around the world, and much effort has been made to improve the accuracy of the results. This study analyzed the sigma metrics of the vitamin D test using the external quality assessment (EQA) program. Sigma metrics is used for quantitative tests performed in the laboratory, and the test results can be objectively visualized in terms of quality. This analysis was performed based on the accuracy of the College of American Pathologists (CAP) using the results of the 2019 accuracy-based vitamin D (ABVD) survey, and about 300 laboratories participated in the survey. Reference values were obtained by the Center for Disease Control and Prevention (CDC) reference laboratory. At six different concentrations, the sigma metrics were analyzed to be 1.00, 1.85, 2.42, 1.01, 1.54 and 0.78, respectively. An average of 1.43 sigma metrics was determined. In particular, only positive biases for ABVD-16 and 17 were shown in the liquid chromatography tandem-mass spectrometry (LC-MS/MS), which is the standard method for vitamin D determination when compared to the reference values. The causes of the difference can be explained by cross reactivity to various vitamin D metabolites. Laboratories need to improve their overall performance.

• Journal of Korean Society of Environmental Engineers
• /
• v.34 no.8
• /
• pp.574-582
• /
• 2012

This study presents the concentrations of the polycyclic aromatic hydrocarbons (PAHs) listed as priority pollutants by United States Environmental Protection Agency (US EPA), in 98 sludges from 54 industrial wastewater treatment facilities of South Korea. The mean concentrations of ${\Sigma}_{16}PAHs$ were ranged from 32.5 ${\mu}g/kg-dw$ to 1189.3 ${\mu}g/kg-dw$ by industries, and the highest content was found in the petrochemical industry, followed by chemical, clothing manufacturing and dying, pulp and papermaking, secondary wastewater treatment, and food/beverage producing industries. Comparisons to the EU and Danish standards of ${\Sigma}_{16}PAHs$ in sewage sludge for land application showed only two samples (one from petrochemical, and the other from chemical industry) exceeded the limits. ANOVA test with PAH concentrations as variables revealed no statistically significant influences by industrial types and sampling time (i.e., seasonal variations). Pearson correlations between individual PAHs showed strong relationships (r>0.7) among 4-ring PAHs. Concentrations of acenaphthylene, anthracene, fluoranthene, benzo(a)anthracene, benzo(f)fluoranthene, benzo(k)fluoranthene, benzo(a)pyrene presented strong correlations to ${\Sigma}_{16}PAHs$. Principal component analysis discriminated entire samples into three groups by two principal components (PC1 and PC2) with 70% of data variations, in which industrial types were not of importance, but a dominance of certain PAHs. Samples in group-I, which is high PC1 and low PC2, were characterized by a dominance of 2-ring PAHs, and in group-II, PC1 and PC2 showed a linear relation, was dominant 4-ring PAHs. Group-III with low PC1 and high PC2 includes 17 samples showing a noticeably high contribution of 3-ring PAHs to ${\Sigma}_{16}PAHs$. This study provides concentrations of PAHs in industrial sludges collected from a wide variety of sources (six industrial types) and two seasons of sampling events, and the comparison of ${\Sigma}_{16}PAHs$ with other studies are also discussed.

• Bulletin of the Korean Chemical Society
• /
• v.8 no.3
• /
• pp.168-170
• /
• 1987

The reaction between 1-benzyl-3-carbamoyl-1,4-dihydropyridine (BNAH) 1 and various 1-arylpyridinium salts 2, and the reaction between 1-(4-methylphenyl)-1,4-dihydropyridine 4b and 1-aryl-3-carbamoylpyridinium (1-arylnicotinamide) salts 5 were carried out. The extents of reaction in equilibrium were estimated by nmr integration data. The equilibrium constants for the reactions, K, and the standard Gibbs free energy changes for the reduction of the pyridinium salts to the corresponding 1,4-dihydropyridines ${\Delta}G^{\circ}'$ were evaluated. The Hammett plot of log K for the reaction between 1 and 2, and ${\Delta}G^{\circ}'$ against ${\sigma}_p$ of the substituents in 1-aryl moiety shows linear correlation with the reaction constant ${\rho}$ of 9.4 (for log K vs ${\sigma}_p$) and -54.5 KJ/mole (for ${\Delta}G^{\circ}'$ vs ${\sigma}_p$). It was found that 1-aryl-1,4-dihydropyridines have much higher reducing power than the corresponding 1-aryl-1,4-dihydronicotinamides, and the power is affected greatly by the electron-withdrawing ability of the substituents in aryl group. The reactions were utilized for preparation of 1,4-dihydropyridines bearing highly electron-withdrawing groups such as 4-nitrophenyl and 2,4-dinitrophenyl, which could not be obtained by conventional dithionite reduction of the corresponding pyridinium salts due to the base-labile nature of the salts.

• Proceedings of the KSME Conference
• /
• 2003.04a
• /
• pp.195-200
• /
• 2003

An expert system for estimation of fatigue properties from simple tensile data of material is developed, considering nearly all important estimation methods proposed so far, i.e., 7 estimation methods. The expert system is developed using an expert system shell, UNIK, and the knowledge base is constructed with production rules and frames. Forward chaining is employed as a reasoning method. The expert system has three major functions including the function to update the knowledge base. The performance of the expert system is tested using the 54 ${\sigma}-N$ curves consisting of 381 ${\sigma}-N$ data points obtained for 22 materials. It is found that the expert system developed has excellent performance especially for steel materials, and reasonably good for titanium alloys.

• Proceedings of the Korea Concrete Institute Conference
• /
• 2003.05a
• /
• pp.157-162
• /
• 2003

An experimental investigation was conducted to study the behavior of high-strength RC wide beam-column joints with slab subjected to reversed cyclic loads under constant axial load. Six half scale interior wide beam-column assemblies representing a portion of a frame subjected to simulated seismic loading were tested, including three specimens without slab and three specimens with slab. The primary variables were compressive strength of concrete($f_ck$=285, 460kgf/$cm^2$), the ratio of the column-to-beam flexural capacity($M_r$=$\Sigma M_c / \Sigma M_b$ ; 0.77 -2.26), extended length of the column concrete($l_d$ ; 0, 12.5, 30cm), ratio of the column-to-beam width(b/H ; 1.54, 1.67). Test results are shown that (1) the behavior of specimen using high-strength concrete satisfied for required minimum ductile capacity according to increase the compressive strength, (2) the current design code and practice for interior joints(type 2) are apply to the wide beam-high strength concrete column.

• Proceedings of the KIEE Conference
• /
• 2002.11c
• /
• pp.54-57
• /
• 2002

In this paper model reference adaptive control (MRAC) of linear time-varying(LTV) systems is considered. MRAC for a linear time invariant(LTI) system does not assure the boundedness of the output and parameter estimation errors in the presence of time variations of the parameters. However, changing the adaptive laws such as use of $\sigma$-modification can result in the boundedness of the output and parameter estimation errors[5]. Together with the $\sigma$-modification in the adaptive law, we also modify the control law by adding an additional term to the standard control law. The additional term leads to smaller bounds of the output and parameter estimation errors when compared to the case where only the standard control law is applied.

• Proceedings of the Korean Society of Computer Information Conference
• /
• 2015.07a
• /
• pp.53-54
• /
• 2015

SW 기술이 급변하는 현 시점에서는 SW 관리의 중요성이 인식되어 SW 품질향상을 위한 제도 개선의 일안으로 SW 개발 산출물에 대한 SW 신뢰성 시험이 요구되고 있으나, SW 신뢰성 시험에 투입되는 비용, 시간적 제약 및 휴먼에러 등으로 인해 SW 시험요구조건을 충족하는데 어려움이 있다. 본 논문에서는 문제 해결 도구로써 린6시그마 방법론을 활용하여 SW 신뢰성시험시간을 단축하고 인적오류를 감소할 수 있는 방안을 제안한다.