• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2008.10a
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• pp.49-52
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• 2008

In this letter, we derive a tight closed form formula for an ergodic rapacity of a multiple-input multiple-output (MIMO) for the application of wireless communications. The derived expression is a simple close-form formula to determine the ergodic capacity of MIMO systems. Assuming the channels are independent and identically distributed (i.i.d.) Rayleigh flat-fading between antenna pairs, the ergodic capacity can be expressed in a closed form as the finite sum of exponential integrals.

• Honam Mathematical Journal
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• v.41 no.1
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• pp.163-174
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• 2019

The veritable pursuit of this exegesis is to exhibit integrals affined with the Bessel-Struve kernel function, which are explicitly inscribed in terms of generalized (Wright) hypergeometric function and also the product of generalized (Wright) hypergeometric function with sum of two confluent hypergeometric functions. Somewhat integrals involving exponential functions, modified Bessel functions and Struve functions of order zero and one are also obtained as special cases of our chief results.

• Journal of Intelligence and Information Systems
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• v.22 no.2
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• pp.115-125
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• 2016

The Bollinger Band indicating the current price position in the recent price action range is obtained by adding/substracting the simple standard deviation (SSD) to/from the simple moving average (SMA). In this paper, we first compare the characteristics of the SMA and the exponential moving average (EMA) in the operator's point of view. A basic equation is obtained between the interval length N of the SMA operator and the weighting factor ${\rho}$ of the EMA operator, that makes the centers of the 1st order momentums of each operator impulse respoinse identical. For equivalent N and ${\rho}$, frequency response examples are obtained and compared by using the discrete time Fourier transform. Based on observation that the SMA operator reacts more excessively than the EMA operator, we propose a novel exponential standard deviation (ESD) band centered at the EMA and derive an auto recursive formula for the proposed ESD band. Practical examples for the ESD band show that it has a smoother bound on the price action range than the Bollinger Band. Comparisons are also made for the gap corrected chart to show the advantageous feature of the ESD band even in the case of gap occurrence. Trading techniques developed for the Bollinger Band can be straight forwardly applied to those for the ESD band.

• Honam Mathematical Journal
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• v.41 no.2
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• pp.403-420
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• 2019

The Helmholtz equation represents acoustic or electromagnetic scattering phenomena. The Method of Lines are known to have many advantages in simulation of forward and inverse scattering problems due to the usage of angle rays and Bessel functions. However, the method does not account for the jump phenomena on obstacle boundary and the approximation includes many high order Bessel functions. The high order Bessel functions have extreme blow-up or die-out features in resonance region obstacle boundary. Therefore, in particular, when we consider shape reconstruction problems, the method is suffered from severe instabilities due to the logical confliction and the severe singularities of high order Bessel functions. In this paper, two approximation formulas for the Helmholtz equation are introduced. The formulas are new and powerful. The derivation is based on Method of Lines, Huygen's principle, boundary jump relations, Addition Formula, and the orthogonality of the trigonometric functions. The formulas reduce the approximation dimension significantly so that only lower order Bessel functions are required. They overcome the severe instability near the obstacle boundary and reduce the computational time significantly. The convergence is exponential. The formulas adopt the scattering jump phenomena on the boundary, and separate the boundary information from the measured scattered fields. Thus, the sensitivities of the scattered fields caused by the boundary changes can be analyzed easily. Several numerical experiments are performed. The results show the superiority of the proposed formulas in accuracy, efficiency, and stability.

• Journal of the Korean Institute of Landscape Architecture
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• v.22 no.1
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• pp.149-177
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• 1994

This study is practically focussed on the derivation of the formula of the reach of the catchment of urban community parks and the reached distance to the parks. The hypotheses for the formula are as follows. a. The catchment of urban community parks can be dependent on the quantitative characteristics that urban community parks have substanial factors : the potential residential population of the proximate community to a park, park visitor's day and mean usetime per year. b. The distance to the urban park is a decided variable which can be percieved quantitatively by the researchers among the exogenous variables concerned with the mean usetime of the urban community park. The data for the variables were collected from the statistics, and the surveys for 9 parks of 4cities(Seoul, Chong-ju, Su-Won, Chon-an) in Korea, which were divided into on-site samples and off-site ones in 1991. The data were collected by questionaire surveys. A total of 548 questionaires of off-site surveys were completed by the residents in the enticing area of the parks. A total of 1053 questionaires of on-site surveys were completed by the visitors of the parks. The research could attempt to derive a formula, which was concerned with the reach of the catchment of urban community parks and the reached distance to the parks. It is testified(R2>0.8) that the numbers of mean usetime per year should be related with the reached distance from a visitor's house to a proximate park. The formula is analogized with an exponential function: {{{{ Mean Usetime per year=f(x)=Ae-BK+Ce-DK ear, X is reached distance from a visitor's house to a proximate park. A,B,C and D are parameters. And, the differences of the reach of the catchment of the parks are not only testified with resulting from the differences of the exogenous variables of qualitative characteristics differences of the parks, but also divided separately into spatial ranges. This formula will be able to anticipate the visitor's numbers of a planned urban community park.

• Geomechanics and Engineering
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• v.30 no.6
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• pp.503-515
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• 2022

The permeability coefficient is an essential parameter for the study of seepage flow in fractured rock mass. This paper discusses the feasibility and application value of using readily available RQD (rock quality index) data to estimate mine water inflow and grouting quantity. Firstly, the influence of different fracture frequencies on permeability in a unit area was explored by combining numerical simulation and experiment, and the relationship between fracture frequencies and pressure and flow velocity at the monitoring point in fractured rock mass was obtained. Then, the stochastic function generation program was used to establish the flow analysis model in fractured rock mass to explore the relationship between flow velocity, pressure and analyze the universal law between fracture frequency and permeability. The concepts of fracture width and connectivity are introduced to modify the permeability calculation formula and grouting formula. Finally, based on the on-site grouting water control example, the rock mass quality index is used to estimate the mine water inflow and the grouting quantity. The results show that it is feasible to estimate the fracture frequency and then calculate the permeability coefficient by RQD. The relationship between fracture frequency and RQD is in accordance with exponential function, and the relationship between structure surface frequency and permeability is also in accordance with exponential function. The calculation results are in good agreement with the field monitoring results, which verifies the rationality of the calculation method. The relationship between the rock mass RQD index and the rock mass permeability established in this paper can be used to invert the mechanical parameters of the rock mass or to judge the permeability and safety of the rock mass by using the mechanical parameters of the rock mass, which is of great significance to the prediction of mine water inflow and the safety evaluation of water inrush disaster management.

• Journal of Technology Innovation
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• v.4 no.1
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• pp.165-183
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• 1996

In acquiring and transferring a superior knowledge assesing the intermediate result value of a competitive R&D project is very important for a firm engaging in R&D. Most existing literatures on R&D evaluation are concerned with project selection and resource allocation. In this paper the stage of an R&D project is classified into research, exploratory development, and development. And a model is suggested which evaluates the intermediate result value before completion of development stage under duopoly and oligopolistic competition. Assessed value of the intermediate result transferred to the next tier company can be used as a minimum acceptable price to the inventor when more advanced knowledge acquired through R&D is transferred to the next tier one. The model suggested is composed of structural variables including research cost, success rates, potential profits, discount rate degree of competition. By using exponential distribution for invertion process time in each stage, we derive a formula that can assess the value of the intermediate result, and we demonstrate how the model can be applied to a competitive R&D situation through an example.

• Nuclear Engineering and Technology
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• v.1 no.2
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• pp.91-101
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• 1969

Resistivity changes of n-type float-zone silicon crystals with 6.4$\times$10$^{14}$ to 1.25$\times$10$^{17}$ phosphorus atoms/㎤ due to irradiation by (1) 1 MeV electrons, (2) two types of research reactors, and (3) $Co^{60}$ ${\gamma}$-ray sources were investigated. The results were analyzed on the basis of a simple exponential formula derived by Buehler. While the formula gave a fair fit in the low fluence range in most cases, the deviation was quite appreciable in the case of 1 MeV electron irradiation, and a linear change gave better fit in some cases. The large change in the carrier removal rate in electron-irradiated samples in the high fluence range was analyzed in detail in terms of the Fermi level cross-over of the defect levels. Based on the damage constants evaluated from the initial portion of data where the formula was applicable, the relative effectiveness of various radiation sources in causing the resistivity change in n-type silicon was compared. The TRIGA Mark II reactor neutrons, for example, were found to be about 40 times more effective than 1 MeV electrons. The dependence of the damage constant on the initial carrier concentration was also examined. The physical basis of the exponential law and the effect of the Fermi level cross-over of the defect levels on the resistivity change in the high fluence ranges are discussed.

• The Korean Journal of Applied Statistics
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• v.24 no.2
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• pp.347-357
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• 2011

In this paper, we propose an approximation to the overshoot in M/$E_n$/1 queues. Overshoot means the size of excess over the threshold when the workload process of an M/$E_n$/1 queue exceeds a prespecified threshold. The distribution, $1^{st}$ and $2^{nd}$ moments of overshoot have an important role in solving some kind of optimization problems. For the approximation to the overshoot, we propose a formula that is a convex sum of the service time distribution and an exponential distribution. We also do a numerical study to check how exactly the proposed formula approximates the overshoot.

• The Korean Journal of Applied Statistics
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• v.25 no.1
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• pp.81-87
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• 2012

A continuous time risk model is considered, where the premium rate is constant and the claims form a compound Poisson process. We assume that an injection is made, which is an immediate increase of the surplus up to level u > 0 (initial level), when the level of the surplus goes below ${\tau}$(0 < ${\tau}$ < u). We derive the formula of the ruin probability of the surplus by establishing an integro-differential equation and show that an explicit formula for the ruin probability can be obtained when the amounts of claims independently follow an exponential distribution.