Jo Mar 6, 2023
Paek Hyon I, a researcher at the Faculty of Applied Mathematics, has created a new teaching method by combining lectures with experiments by a statistical analysis program in her subject “Mathematical Statistics”.
Statistical analysis program SPSS (Statistical Package for Social Science) gives a variety of statistical principles and methods, so it is accepted as a powerful tool for analyzing and processing an enormous amount of statistical data with rapidity and high scientific accuracy. With a powerful graphical function, it produces not only numerical results but also intuitive statistical plots after statistical analysis.
First, she outlines discussion points before letting students study the basics for statistical analysis. For example, she reminds them of the definition of random variable and its distribution, characteristics, regression and linear regression, central limit theorem, etc. Then, she leads them to finding out from reference books what stochastic concepts and principles are latent in statistical data from objects.
Next, she teaches briefly how to run SPSS with an emphasis on the correct analysis of the results displayed on the output window with some tables and plots, and gives some application examples of several statistical analysis methods on necessary occasions of lectures so that they can easily learn how to use it.
In a lesson on estimation and testing of regression coefficients, for example, she gives theoretical contents and shows how to estimate the regression coefficients of a regression model and find important factors by SPSS.
On this basis, she gives students tasks to obtain real data and analyze it in groups. In other words, she has them obtain real data, analyze it using SPSS and present essays on the analysis processes.
In this way, students can understand difficult mathematical statistics more easily and intuitively in connection with reality, and they can develop their program application abilities as well.
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Jo Feb 28, 2023
Fast constructions from the Brownian motion and Brownian bridge are required in many applications such as Quasi-Monte Carlo simulations and statistical inferences on stochastic processes. A simple method for construction of discrete Brownian motion is a step-by-step method of computing the cumulative sum of i.i.d. normal variables.
The construction of N dimensional discrete Brownian motion (or a N-1 dimensional discrete Brownian bridge) that requires at most O(NlogN) floating point operations (flops) is called fast construction. Discrete Brownian motion can also be constructed using decompositions of its covariance matrix, and the method based on eigenvalue decomposition not only shows superior performances in many simulations over the step-by-step method but also becomes a fast construction. Usually the discrete Brownian bridge can be constructed from the discrete Brownian motion using the linear relationship between them. The inserting method using a decomposition of covariance matrix of discrete Brownian bridge gives another decomposition of covariance matrix for high dimensional discrete Brownian motion and it is very significant in Quasi-Monte Carlo simulations for financial derivatives.
Ri Sung Hyon, a section head at the Faculty of Applied Mathematics, has obtained eigenvalue decomposition of covariance matrix for discrete Brownian bridge and LDU (Lower-Diagonal-Upper) decompositions for covariance matrices of discrete Brownian motion and bridge newly and then proposed new fast construction methods on the basis of them. He has also proposed an inserting method for construction of discrete Brownian motion using eigenvalue decompositions which requires O(Nlog(logN)) flops.
The proposed new construction methods might be used effectively in simulations using Brownian motion and Brownian bridge. In addition, the construction algorithms would be used in analytical study for Brownian motion and Brownian bridge.
You can find more information about this in his paper “Decompositions of the Covariance Matrix of the Discrete Brownian Bridge: New Fast Constructions of Discrete Brownian Motions and Brownian Bridges” published in “American Journal of Applied Mathematics”.
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Jo Feb 27, 2023
One of the important problems for structure calculation of a tunnel is to estimate the stability of rock mass surrounding the tunnel.
A safety factor of rock mass surrounding the tunnel can be determined by strength reduction method (SRM). Here, the most important is to solve the criterion of critical state.
Recently, several researchers have conducted studies to apply SRM, which has already been in use for estimation of slope stability, in order to estimate the stability of rock mass surrounding the tunnel. Many researchers have compared the various criteria of the critical state of a slope, which is the most important in the estimation of slope stability by SRM. Although various criteria were developed, there were mainly 3 methods: penetration of equivalent plastic strain, non-convergence of numerical calculation and sudden change of horizontal displacement at a specific point.
Jong Tok Yong, a section head at the Faculty of Earth Science and Technology, has proposed a new method for determination of a safety factor by sudden change of equivalent plastic strain in the relationship between a reduction coefficient of strength parameter and equivalent plastic strain.
This method is based on elasto-plastic FEM and SRM by ABAQUS and Mohr-Coulomb yield criterion.
Simulations in circular and square tunnels showed how a safety factor varies with geometries, friction angles and cohesions and how it varies with quality change of rock mass, pore water pressure and tunnel depth.
If further information is needed, please refer to “Determination of safety factor for rock mass surrounding tunnel by sudden change of equivalent plastic strain in strength reduction method” published in the EI Journal “Geotechnology and Geological Engineering”.
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Jo Feb 26, 2023
Forward voltage drop of fast p+nn+ structure is affected strongly by the high-level carrier lifetime, reverse recovery time current by the low-level carrier lifetime, and reverse current by the space-charge generation lifetime. These 3 carrier lifetimes influence 3 main parameters of p+nn+ structure differently. When the low-level carrier lifetime is decreased in order to decrease the reverse recovery time, the forward voltage drop increases, and when the high-level carrier lifetime is increased for reducing the forward voltage drop, the reverse recovery time increases.
It is unknown how to adjust rationally the 3 main parameters of fast p+nn+ structure － forward voltage drop, reverse recovery time and reverse current.
In order to control these conflicting relations, Pak Pyong Su, a section head at the Semiconductor Institute, has illuminated the recombination center level formed on the basic floor of p+nn+ structure. Then, to determine the recombination center level coincided with the practical recombination center level, he has suggested an analytic method of determining the recombination center level formed by 2 carrier lifetime regulation sources.
First, he suggested main relative equations to determine the optimal recombination center level with numerical solutions. Second, he found the practical recombination center level which is irrelevant to the doping agent concentration and working temperature. Finally, he proposed an analytic method to determine the co-additive recombination center level coincident with the practical recombination center level by adding any 2 types of carrier lifetime regulation sources.
To illustrate the effectiveness, he used an analytic method to calculate the recombination center level formed in the silicon semiconductor material with addition of gold and iridium at the same time.
The proposed method demonstrates that it is effective in the determination of the co-additive recombination center level when any 2 carrier lifetime control sources are added and that it can be applied to the rational regulation of the 3 parameters of a fast diode in the random doping agent kinds and co-additive concentration and the other intervals of working temperature.
The details of this are found in his paper “Analysis of the optimal recombination center level to adjust rationally the 3 main parameters of p+nn+ structure” in the EI Journal “Journal of Power Electronics and Devices”.
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Jo Feb 25, 2023
A research team led by Ri Hyok Min, a researcher at the Nano Physics Engineering Institute, has developed an auto control system and a dehumidification device for ozone disinfection and applied it to the practice.
The system manages overall ozone disinfection processes for different types of objects to be disinfected, so that disinfection processes can go in a scientific way.
The system consists of a central control unit, a human-machine interface (HMI) with a touch screen, an exhausting unit, an alarm unit and other electric contactors and relays. The central control unit receives data including limiting cumulative CT, limiting ozone concentration, temperature and humidity in disinfection rooms from HMI and drives the ozone generator.
During the disinfection process, the central control unit constantly receives ozone concentration in disinfection rooms through the RS-485 communication interface from the sensor located in the room, and calculates the cumulative CT automatically. When the calculated cumulative CT reaches the limit value, it stops the ozone generator and starts the exhausting unit. Then, the ozone concentration of the room decreases rapidly. If the ozone concentration of the room is below 0.6ppm (safety value to human), the exhausting process stops and the alarm device starts ringing. It indicates to the operator the finish of the disinfection process. Also, it stops the ozone generator when the ozone concentration reaches the limit value. It prolongs the lifetime of the ozone generator and prevents deterioration of objects to be disinfected.
A dehumidification device is necessary to protect the ozone generator from damage and increase the quantity of ozone. In general, the input gas of the ozone generator is air. But the air includes vapor, which decreases the amount of ozone generation and, more dangerously, it creates nitrous acid.
Thus, they designed and manufactured a dehumidification device which is based on freezing and absorption. The freezing device drops the dew point to 4℃ and the absorbent dehumidifier drops it to －55℃. As a result, they could achieve twice as much ozone as before.
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