• Journal of applied mathematics & informatics
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• v.29 no.5_6
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• pp.1081-1096
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• 2011

In this paper, a steady axisymmetric MHD flow of two dimensional incompressible fluids is studied under the influence of a uniform transverse magnetic field. The governing equations are reduced to nonlinear boundary value problem by applying the integribility conditions. Optimal Homotopy Asymptotic Method (OHAM) is applied to obtain solution of reduced fourth order nonlinear boundary value problem. For comparison, the same problem is also solved by Variational Iteration Method (VIM).

• Journal of the Korean Operations Research and Management Science Society
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• v.28 no.4
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• pp.145-153
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• 2003

In this Paper, we examine the limiting distributional behaviour of extreme values of mixed Erlang random variables. We show that, in the finite mixture of Erlang distributions, the component distribution with an asymptotically dominant tail has a critical effect on the asymptotic extreme behavior of the mixture distribution and it converges to the Gumbel extreme-value distribution. Normalizing constants are also established. We apply this result to characterize the asymptotic distribution of maxima of sojourn times in M/M/s queuing system. We also show that Erlang mixtures with continuous mixing may converge to the Gumbel or Type II extreme-value distribution depending on their mixing distributions, considering two special cases of uniform mixing and exponential mixing.

• Journal of the Korean Mathematical Society
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• v.49 no.4
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• pp.715-731
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• 2012

This paper considers the stability of positive steady-state solutions bifurcating from the trivial solution in a delayed Lotka-Volterra two-species predator-prey diffusion system with a discrete delay and subject to the homogeneous Dirichlet boundary conditions on a general bounded open spatial domain with smooth boundary. The existence, uniqueness and asymptotic expressions of small positive steady-sate solutions bifurcating from the trivial solution are given by using the implicit function theorem. By regarding the time delay as the bifurcation parameter and analyzing in detail the eigenvalue problems of system at the positive steady-state solutions, the asymptotic stability of bifurcating steady-state solutions is studied. It is demonstrated that the bifurcating steady-state solutions are asymptotically stable when the delay is less than a certain critical value and is unstable when the delay is greater than this critical value and the system under consideration can undergo a Hopf bifurcation at the bifurcating steady-state solutions when the delay crosses through a sequence of critical values.

• Korean Journal of Mathematics
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• v.23 no.4
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• pp.571-590
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• 2015

Let a, b, q be integers with q > 0. The homogeneous Dedekind sum is dened by $$\Large S(a,b,q)={\sum_{r=1}^{q}}\(\({\frac{ar}{q}}\)\)\(\({\frac{br}{q}}\)\)$$, where $$\Large ((x))=\{x-[x]-{\frac{1}{2}},\text{ if x is not an integer},\\0,\hspace{75}\text{ if x is an integer.}$$ In this paper we study the mean value of S(a, b, q) by using mean value theorems of Dirichlet L-functions, and give some asymptotic formula.

• Structural Engineering and Mechanics
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• v.49 no.3
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• pp.355-372
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• 2014

Considering the history of severe earthquakes and the presence of active faults in the greater Tehran region, the possibility of a destructive earthquake occurring is high and seismic hazard analysis is crucial. Gumbel distributions are commonly-used statistical distributions in earthquake engineering and seismology. Their main advantage is their basis on the largest earthquake magnitudes selected from an equal-time predefined set. In this study, the first asymptotic distribution of extremes is used to estimate seismicity parameters and peak ground acceleration (PGA). By assuming a Poisson distribution for the earthquakes, after estimation of seismicity parameters, the mean return period and the probable maximum magnitude within a given time interval are obtained. A maximum probable magnitude of 7.0 has a mean return period of 100 years in this region. For a return period of 475 years, the PGA in the greater Tehran region is estimated to be 0.39g to 0.42g, depending on local site conditions. This value is greater than that of the Iranian Code for Seismic Design of Buildings, indicating that a revision of the code is necessary.

• Communications for Statistical Applications and Methods
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• v.15 no.3
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• pp.465-481
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• 2008

Item response theory(IRT) estimates latent ability of a subject based on the property of item and item parameters using item characteristics curve(ICC) of each item case. The initial value and another problems occurs when we try to estimate item parameters of IRT(e.g. the maximum likelihood estimate). Thus, we propose the asymptotic approximation method(AAM) to solve the above mentioned problems. We notice that the proposed method can be thought as an alternative to estimate item parameters when we have small size of data or need to estimate items with local fluctuations. We developed 'Any Assess' and tested reliability of the system result by simulating a practical use possibility.

• Journal of the Korean Mathematical Society
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• v.44 no.1
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• pp.11-24
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• 2007

The main purpose of this paper is to use the properties of primitive characters, Gauss sums and Ramanujan's sum to study the hybrid mean value of generalized Bernoulli numbers, general Kloosterman sums and Gauss sums, and give two asymptotic formulae.

• Journal of the Korean Mathematical Society
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• v.41 no.5
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• pp.921-931
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• 2004

We derive a formula for the expected value $\mu$(n) of the independent domination number of a random directed rooted tree with n labeled vertices and determine the asymptotic behavior of $\mu$(n) as n goes to infinity.

• Bulletin of the Korean Mathematical Society
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• v.50 no.3
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• pp.873-883
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• 2013

By using the analytic methods, the mean value of the general quadratic Gauss sums weighted by the first power mean of character sums over a short interval is investigated. Several sharp asymptotic formulae are obtained, which show that these sums enjoy good distributive properties. Moreover, interesting connections among them are established.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 1995.11a
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• pp.135-138
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• 1995

This paper presents a method to calculate the escape frequency factor and its verification from TSC(Thermally Stimulated Current) equation and cures. To apply calculation method of ν using asymptotic estimation, it utilized two sets of TSC data with 1K interval. This method enables one to get the exact value of ν and activation energy at the same time by using computer programming. So, it regards their calculation method as a useful process to obtain the value of physical behavior.