• Journal of the Korean Society for Marine Environment & Energy
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• v.13 no.2
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• pp.99-104
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• 2010

The purpose of this study is to develop Sewage Treatment Plant that treat sewage which occurred in ship using fixed media method and to consider applicable to the Pilot Scale device of the STP regulations in MLTM(Ministry of Land, Transport and Maritime Affairs) and MEPC(Marine Environment Protection Committee). In test results, pH geometric mean was 7.68, $BOD_5$(Biochemical Oxygen Demand) geometric mean was 7.28 mg/l, $COD_{cr}$(Chemical Oxygen Demand) geometric mean was 48.39 mg/l, TSS(Total Suspended Solid) geometric mean was 18.00/l, Residual chlorine geometric mean was 0.19 mg/l, and E. coli geometric mean was 1CFU/100 ml. In addition, about 97.4% of $BOD_5$ was reduced, the $COD_{cr}$ reduction averaged 96.4%and the TSS reduction averaged 97.6%. STP have been determined by the MLTM and MEPC regulation of the marine pollution prevention equipment for performance testing product.

• Journal of Internet Computing and Services
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• v.5 no.2
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• pp.41-47
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• 2004

Recently, motion capture has become one of the most promising technologies in animation. Realistic motion data can be captured by recording the movement of a real actor with an optical or magnetic motion capture system. This paper deals with motion editing by a geometric mean filter. Since the captured motion has some noises that cause a jerky motion, it needs a smoothing process to make it natural. A geometric mean filter is proposed to produce natural motions without jerky motions. Experimental results show that the geometric mean filter can effectively remove noises that cause a jerky motion and it can guarantee the most natural motions among various spatial filters. This method could be applied to the various fields such as real time animation, virtual reality applications, 3D applications, and etc.

• Journal of applied mathematics & informatics
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• v.35 no.1_2
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• pp.191-204
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• 2017

A new fifth-order weighted Runge-Kutta algorithm based on heronian mean for solving initial value problem in ordinary differential equations is considered in this paper. Comparisons in terms of numerical accuracy and size of the stability region between new proposed Runge-Kutta(5,5) algorithm, Runge-Kutta (5,5) based on Harmonic Mean, Runge-Kutta(5,5) based on Contra Harmonic Mean and Runge-Kutta(5,5) based on Geometric Mean are carried out as well. The problems, methods and comparison criteria are specified very carefully. Numerical experiments show that the new algorithm performs better than other three methods in solving variety of initial value problems. The error analysis is discussed and stability polynomials and regions have also been presented.

• Journal of Korean Society of Occupational and Environmental Hygiene
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• v.20 no.1
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• pp.10-18
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• 2010

To provide necessary information for future environmental monitoring of smelting and litharge making industries in Korea, environmental monitoring dataset of air lead concentration of 4 lead industries(1 primary smelting, 2 secondary smelting and 1 litharge making industry) were analyzed from 1994 to 2007. Data were compared using geometric mean and standard deviation with minimum and maximum values according to year of measurement, type of lead industries and type of operation of lead industries. The geometric mean and standard deviation of air concentration for a total of 1140 samples in all lead industries for overall 14 years were 70.7${\mu}g/m^3$ and 5.51 with minimum of 1${\mu}g/m^3$ and maximum of 9,185 ${\mu}g/m^3$. The overall geometric means of air concentration were above the permissible exposure levels(PEL) until year of 2001 and thereafter they were remained at the level of half of PEL. The geometric means of primary smelting, secondary smelting and litharge making industry for overall 14 years were 21.7${\mu}g/m^3$(number of samples: 353), 82.5${\mu}g/m^3$(number of samples: 357) and 164.2 ${\mu}g/m^3$(number of samples: 430) respectively. In primary smelting industry, the highest geometric mean air concentration was 35.4 ${\mu}g/m^3$ in the secondary smelting operation; followed by casting operation (24.9 ${\mu}g/m^3$) and melting operation (14.9 ${\mu}g/m^3$), respectively. On the other hand, in secondary smelting industries, the highest geometric mean air concentration was 125.4${\mu}g/m^3$ in melting operation; followed by casting operation (90.5${\mu}g/m^3$) and pre-treatment operation (43.4${\mu}g/m^3$), respectively. However, in litharge making industries, there were no significant differences of geometric mean air concentrations between litharge operation and stabilizer operation. The proportion of over PEL (50${\mu}g/m^3$) was highest in litharge industry and followed by secondary smelting industries. However The proportions of over PEL(${\mu}g./m^3.$) were decreased by the years of environmental monitoring. The significant reduction of mean air lead concentration since year of 2000 was observed due to more active environmental engineering control and new introduction of new operation in manufacturing process, but may be also influenced by non-engineering method such as reduction of operation hours or reduction of exposure time during actual environmental measurement by industrial hygienist according to more strict enforcement of occupational and safety law by the government.

• Journal of the Chungcheong Mathematical Society
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• v.30 no.1
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• pp.21-29
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• 2017

We review a partial trace alternatively defined by the composition of positive linear maps, and see how the partial trace acts on the matrix geometric means. We also study the quantum Tsallis relative entropy under partial trace related with the fidelity.

• Kyungpook Mathematical Journal
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• v.54 no.4
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• pp.521-529
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• 2014

In this paper we derive some optimal convex combination bounds related to arithmetic mean. We find the greatest values ${\alpha}_1$ and ${\alpha}_2$ and the least values ${\beta}_1$ and ${\beta}_2$ such that the double inequalities $${\alpha}_1T(a,b)+(1-{\alpha}_1)H(a,b)<A(a,b)<{\beta}_1T(a,b)+(1-{\beta}_1)H(a,b)$$ and $${\alpha}_2T(a,b)+(1-{\alpha}_2)G(a,b)<A(a,b)<{\beta}_2T(a,b)+(1-{\beta}_2)G(a,b)$$ holds for all a,b > 0 with $a{\neq}b$. Here T(a,b), H(a,b), A(a,b) and G(a,b) denote the second Seiffert, harmonic, arithmetic and geometric means of two positive numbers a and b, respectively.

• Journal of Physiology & Pathology in Korean Medicine
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• v.17 no.5
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• pp.1257-1263
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• 2003

The modified engineering methodology and the modified electronic circuit in classical ultrasonic principles were applied to ultrasonic aerosol nebulizer for inhalation toxicology study of cadmium aerosol. 1532.96ppm Cd nebulizing solution was used to generate cadmium aerosol for particle size analysis with the modifying source and inlet temperatures. The results of particle size analysis for cadmium aerosol were as following. The highest particle counting for source temperature 20℃ was 399.75 × 10² in inlet temperature 100℃ and particle diameter 0.75㎛. The highest particle counting for source temperature 50℃ was 399.70 × 10² in inlet temperature 50℃ and particle diameter 0.75㎛. The highest particle counting for source temperature 70℃ was 411.14 × 10² in inlet temperature 100℃ and particle diameter 0.75㎛. The ranges of geometric mean diameter were 0.74-0.79㎛ in source temperature 20℃, 0.65-0.72㎛ in source temperature 50℃, and 0.65-0.80㎛ in source temperature 70℃. The smallest geometric mean diameter was 0.65㎛ in source temperature 50, 70℃ and inlet temperature 20, 50℃, and the largest geometric mean diameter was 0.80㎛ in source temperature 70℃ and inlet temperature 100℃. The ranges of geometric standard deviation were 1.71-1.80 in source temperature 20℃, 1.27-1.61 in source temperature 50℃, and 1.27-2.29 in source temperature 70℃. The lowest geometric standard deviation was 1.27 in source temperature 50, 70℃ and inlet temperature 20, 50℃, and the highest geometric standard deviation was 2.29 in source temperature 70℃ and inlet temperature 100℃. Generated aerosol for cadmium inhalation toxicology study was polydisperse aerosol with the above geometric standard deviation 1.2. The ranges of mass median diameter(MMD) were 1.75-2.25㎛ in source temperature 20℃, 1.27-1.61㎛ in source temperature 50℃, and 1.27-2.29㎛ in source temperature 70℃. The smallest MMD was 1.27㎛ in source temperature 50, 70℃ and inlet temperature 20, 50℃, and the largest MMD was 2.29㎛ in source temperature 70℃ and inlet temperature 100℃. Cadmium chloride concentration in nebulizing solution affected the particle size and distribution of cadium aerosol in air. MMO for inhalation toxicology testing in OECD and EU is less than 3㎛ and EPA guidance is less than 4㎛. In our results, in source temperatures of 20, 50, 70℃, and inlet temperatures of 20, 50, 100, 150, 200, 250℃ were conformed to the those guidance.

• Journal of Korean Society for Quality Management
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• v.27 no.4
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• pp.143-152
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• 1999

In Shewhart control chart, the average run length(ARL) is calculated using the mean of a conventional geometric distribution(CGD) assuming a sequence of identical and independent Bernoulli trials. In this, the success probability of CGB is the probability that any point exceeds the control limits. When the process is in-control state, there is no problem in the above assumption since the probability that any point exceeds the control limits does not change if the in-control state continues. However, if the out-of-control state begins and continues during the process, the probability of exceeding the control limits may take two forms. First, once the out-of-control state begins with exceeding probability p, it continues with the same exceeding probability p. Second, after the out-of-control state begins, the exceeding probabilities may very according to some pattern. In the first case, ARL is the mean of CGD with success probability p as usual. But in the second case, the assumption of a sequence of identical and independent Bernoulli trials is invalid and we can not use the mean of CGD as ARL. This paper concentrate on that point. By adopting one generalized binomial distribution(GBD) model that allows correlated Bernoulli trials, generalized geometric distribution(GGD) is defined and its mean is derived to find an alternative ARL when the process is in out-of-control state and the exceeding probabilities take the second form mentioned in the above. Small-scale simulation is performed to show how an alternative ARL works.

• Bulletin of the Korean Mathematical Society
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• v.55 no.1
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• pp.1-8
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• 2018

In this paper, we study some topological structure of a compact domain in ${\mathbb{R}}^n$ in terms of the curvature conditions and develop a geometric inequality involving the volume and the integral of mean curvatures over the boundary of the compact domain.

• Journal of applied mathematics & informatics
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• v.42 no.4
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• pp.985-995
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• 2024

We see fundamental properties of the log-determinant α-divergence including the convexity of weighted geometric mean and the reversed sub-additivity under tensor product. We introduce a symmetrized divergence and show its properties including the boundedness and monotonicity on parameters. Finally, we discuss the barycenter minimizing the weighted sum of symmetrized divergences.