• Communications of the Korean Mathematical Society
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• v.34 no.4
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• pp.1145-1155
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• 2019

Let f be a transcendental meromorphic function, defined in the complex plane $\mathbb{C}$. In this paper, we give a quantitative estimations of the characteristic function T(r, f) in terms of the counting function of a homogeneous differential polynomial generated by f. Our result improves and generalizes some recent results.

• Journal of applied mathematics & informatics
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• v.40 no.3_4
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• pp.507-513
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• 2022

In this paper, we investigate some results on complex delay-differential equations of the classical Malmquist theorem. A classic illustrations of their results states us that if a complex delay equation w(t + 1) + w(t - 1) = R(t, w) with R(t, w) rational in both arguments admits (concede) a transcendental meromorphic solution of finite order, then deg_wR(t, w) ≤ 2. Development and upgrade of such results are presented in this paper. In addition, Borel exceptional zeros and poles seem to appear in special situations.

• The Pure and Applied Mathematics
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• v.17 no.2
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• pp.185-188
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• 2010

In this note the distribution of roots of cubic equations in contrast to 0 is given, which is useful to discuss eigenvalues for qualitative properties of differential equations.

• Structural Engineering and Mechanics
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• v.52 no.4
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• pp.663-686
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• 2014

This paper deals with free vibration analysis of bidirectional functionally graded annular plates resting on a two-parameter elastic foundation. The formulations are based on the three-dimensional elasticity theory. This study presents a novel 2-D six-parameter power-law distribution for ceramic volume fraction of 2-D functionally graded materials that gives designers a powerful tool for flexible designing of structures under multi-functional requirements. Various material profiles along the thickness and in the in-plane directions are illustrated by using the 2-D power-law distribution. The effective material properties at a point are determined in terms of the local volume fractions and the material properties by the Mori-Tanaka scheme. The 2-D differential quadrature method as an efficient and accurate numerical tool is used to discretize the governing equations and to implement the boundary conditions. The fast rate of convergence of the method is shown and the results are compared against existing results in literature. Some new results for natural frequencies of the plates are prepared, which include the effects of elastic coefficients of foundation, boundary conditions, material and geometrical parameters. The interesting results indicate that a graded ceramic volume fraction in two directions has a higher capability to reduce the natural frequency than conventional 1-D functionally graded materials.

• Journal of the Korean Society of Safety
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• v.25 no.3
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• pp.15-21
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• 2010

A differential case equipped with LSD(limited slip differential) has several advantages over a normal type for rear wheel drive vehicles. Specially, the torque distribution can be done between left and right drive wheel in the state of limited slip differential. Also although LSD types are very various according to operating type, medium and torque distribution, a multi-clutch type is generally applied to rear wheel drive vehicles. So, this study presents the analysis of design parameters for development of a friction plate for multi-clutch type LSD using vehicle road test, the simulation of analytical model and the development of vehicle dynamics model by a benchmark product. According to this investigation, the design parameters which are pre-load of coil spring, friction plate and contact area quantity, friction coefficient and TBR(torque bias ratio) for a friction plate are derived from experiment and simulation and consequently, vehicle dynamics model has been constructed for the development of friction plate for multi-clutch type LSD.

• Journal of Communications and Networks
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• v.12 no.6
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• pp.582-591
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• 2010

Probabilistic modeling and analysis of correlation metrics have been receiving considerable interest for a long period of time because they can be used to evaluate the performance of communication receivers, including satellite broadcasting receivers. Although differential correlators have a simple structure and practical importance over channels with severe frequency offsets, closedform expressions for the output distribution of differential correlators do not exist. In this paper, we present detection error probability expressions for frame synchronization using differential correlation, and demonstrate their accuracy over channel parameters of practical interest. The derived formulas are presented in terms of the Marcum Q-function, and do not involve numerical integration, unlike the formulas derived in some previous studies. We first determine the distributions and error probabilities for single-span differential correlation metric, and then extend the result to multispan differential correlation metric with certain approximations. The results can be used for the performance analysis of various detection strategies that utilize the differential correlation structure.

• Communications of the Korean Mathematical Society
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• v.26 no.4
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• pp.709-720
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• 2011

We obtain special type of differential equations which their solution are random variable with known continuous density function. Stochastic differential equations (SDE) of continuous distributions are determined by the Fokker-Planck theorem. We approximate solution of differential equation with numerical methods such as: the Euler-Maruyama and ten stages explicit Runge-Kutta method, and analysis error prediction statistically. Numerical results, show the performance of the Rung-Kutta method with respect to the Euler-Maruyama. The exponential two parameters, exponential, normal, uniform, beta, gamma and Parreto distributions are considered in this paper.

• Journal of the Korean Statistical Society
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• v.25 no.1
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• pp.111-122
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• 1996

A model for a system whose state changes continuously with time is introduced. It is assumed that the system is modeled by a Brownian motion with negative drift and an absorbing barrier at the origin. A repairman arrives according to a Poisson process and repairs the system according to an (s,S) policy, i.e., he increases the state of the system up to S if and only if the state is below s. A partial differential equation is derived for the distribution function of X(t), the state of the system at time t, and the Laplace-Stieltjes transform of the distribution function is obtained by solving the partial differential equation. For the stationary case the explicit expression is deduced for the distribution function of the stationary state of the system.

• Journal of the Korean Data and Information Science Society
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• v.25 no.4
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• pp.915-920
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• 2014

We consider a continuous time surplus process with investments the sizes of which are independent and identically distributed. It is assumed that an investment of the surplus to other business is made, if and only if the surplus reaches a given sufficient level. We establish an integro-differential equation for the distribution function of the surplus and solve the equation to obtain the moment generating function for the stationary distribution of the surplus. As a consequence, we obtain the first and second moments of the level of the surplus in an infinite horizon.

• Communications for Statistical Applications and Methods
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• v.20 no.6
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• pp.475-480
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• 2013

The surplus process in a risk model is stochastically analyzed. We obtain the characteristic function of the level of the surplus at a finite time, by establishing and solving an integro-differential equation for the distribution function of the surplus. The characteristic function of the stationary distribution of the surplus is also obtained by assuming that an investment of the surplus is made to other business when the surplus reaches a sufficient level. As a consequence, we obtain the first and second moments of the surplus both at a finite time and in an infinite horizon (in the long-run).