• Bulletin of the Korean Mathematical Society
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• v.48 no.4
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• pp.697-704
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• 2011

By using the method of differential subordinations, we derive some sufficient conditions for strongly starlike functions associated with a linear operator. All these results presented here are sharp.

• Kyungpook Mathematical Journal
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• v.59 no.1
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• pp.13-22
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• 2019

This paper presents a symbolic method for solving a boundary value problem with inhomogeneous Stieltjes boundary conditions over integro-differential algebras. The proposed symbolic method includes computing the Green's operator as well as the Green's function of the given problem. Examples are presented to illustrate the proposed symbolic method.

• Structural Engineering and Mechanics
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• v.28 no.2
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• pp.129-152
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• 2008

This paper considers the solution of the stochastic differential equations (SDEs) with random operator and/or random excitation using the spectral SFEM. The random system parameters (involved in the operator) and the random excitations are modeled as second order stochastic processes defined only by their means and covariance functions. All random fields dealt with in this paper are continuous and do not have known explicit forms dependent on the spatial dimension. This fact makes the usage of the finite element (FE) analysis be difficult. Relying on the spectral properties of the covariance function, the Karhunen-Loeve expansion is used to represent these processes to overcome this difficulty. Then, a spectral approximation for the stochastic response (solution) of the SDE is obtained based on the implementation of the concept of generalized inverse defined by the Neumann expansion. This leads to an explicit expression for the solution process as a multivariate polynomial functional of a set of uncorrelated random variables that enables us to compute the statistical moments of the solution vector. To check the validity of this method, two applications are introduced which are, randomly loaded simply supported reinforced concrete beam and reinforced concrete cantilever beam with random bending rigidity. Finally, a more general application, randomly loaded simply supported reinforced concrete beam with random bending rigidity, is presented to illustrate the method.

• Communications for Statistical Applications and Methods
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• v.19 no.3
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• pp.359-365
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• 2012

The fuzzy set framework has a number of properties that make it suitable to formulize uncertain information in medical diagnosis. This study introduces a fuzzy diagnostic method based on the interval-valued interview chart and the interval-valued intuitionistic fuzzy weighted arithmetic average(IIFWAA) operator. An issue in the use of the IIFWAA operator is to determine the weights. In this study, we propose the occurrence information of symptoms as the weights. An illustrative example is provided to demonstrate its practicality and effectiveness.

• Journal of applied mathematics & informatics
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• v.40 no.3_4
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• pp.491-505
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• 2022

This paper is concerned with singularly perturbed convection-diffusion parabolic partial differential equations which have time-delayed. We used the Crank-Nicolson(CN) scheme to build a fitted operator to solve the problem. The underling method's stability is investigated, and it is found to be unconditionally stable. We have shown graphically the unstableness of CN-scheme without fitting factor. The order of convergence of the present method is shown to be second order both in space and time in relation to the perturbation parameter. The efficiency of the scheme is demonstrated using model examples and the proposed technique is more accurate than the standard CN-method and some methods available in the literature, according to the findings.

• Journal of applied mathematics & informatics
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• v.33 no.5_6
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• pp.485-502
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• 2015

A computational method for solving singularly perturbed boundary value problem of differential equation with shift arguments of mixed type is presented. When shift arguments are sufficiently small (o(ε)), most of the existing method in the literature used Taylor's expansion to approximate the shift term. This procedure may lead to a bad approximation when the delay argument is of O(ε). The main idea for this work is to deal with constant shift arguments, which are independent of ε. In the present method, we construct the formally asymptotic solution of the problem using the method of composite expansion. The reduced problem is solved numerically by using operator compact implicit method, and the second problem is solved analytically. Error estimate is derived by using the maximum norm. Numerical examples are provided to support the theoretical results and to show the efficiency of the proposed method.

• Nuclear Engineering and Technology
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• v.55 no.12
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• pp.4685-4694
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• 2023

The ability to calculate the material density sensitivity coefficients of power with respect to the material density has broad application prospects for accelerating Monte Carlo-Thermal Hydraulics iterations. The second-order material density sensitivity coefficients for the general Monte Carlo score have been derived based on the differential operator sampling method in this paper, and the calculation of the sensitivity coefficients of cell power scores with respect to the material density has been realized in continuous-energy Monte Carlo code RMC. Based on the power-density sensitivity coefficients, the sensitivity coefficients of power scores to some other physical quantities, such as power-boron concentration coefficients and power-temperature coefficients considering only the thermal expansion, were subsequently calculated. The effectiveness of the proposed method is demonstrated in the power-density coefficients problems of the pressurized water reactor (PWR) moderator and the heat pipe reactor (HPR) reflectors. The calculations were carried out using RMC and the ENDF/B-VII.1 neutron nuclear data. It is shown that the calculated sensitivity coefficients can be used to predict the power scores accurately over a wide range of boron concentration of the PWR moderator and a wide range of temperature of HPR reflectors.

• Journal of Aerospace System Engineering
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• v.14 no.3
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• pp.17-23
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• 2020

In this paper, the efficient periodic unsteady flow analysis is developed by using a Chebyshev collocation operator applied to the time differential term of the governing equations. The partial implicit time integration method was also applied in the governing equation for a fluid, which means flux terms were implicitly processed for a time integration and the time derivative terms were applied explicitly in the form of the source term by applying the Chebyshev collocation operator. To verify this method, we applied the 1D unsteady Burgers equation and the 2D oscillating airfoil. The results were compared with the existing unsteady flow frequency analysis technique, the Harmonic Balance Method, and the experimental data. The Chebyshev collocation operator can manage time derivatives for periodic and non-periodic problems, so it can be applied to non-periodic problems later.

• The Journal of the Acoustical Society of Korea
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• v.21 no.3E
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• pp.105-111
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• 2002

The parabolic equation technique provides an excellent model to describe the wave phenomena when there exists a predominant direction of propagation. The model handles the square root wave number operator in paraxial direction. Realization of the pseudo-differential square root operator is the essential part of the parabolic equation method for its numerical accuracy. The wide-angled approximation of the operator is made based on the Pade series expansion, where the branch line rotation scheme can be combined with the original Pade approximation to stabilize its computational performance for complex modes. The Galerkin integration has been employed to discretize the depth-dependent operator. The benchmark tests involving the half-infinite space, the range independent and dependent environment will validate the implemented numerical model.

• Structural Engineering and Mechanics
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• v.73 no.1
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• pp.97-108
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• 2020

This study presents a 4 node, 11 DOF/node plate element based on higher order shear deformation theory for lamina composite plates. The theory accounts for parabolic distribution of the transverse shear strain through the thickness of the plate. Differential field equations of composite plates are obtained from energy methods using virtual work principle. Differential field equations of composite plates are obtained from energy methods using virtual work principle. These equations were transformed into the operator form and then transformed into functions with geometric and dynamic boundary conditions with the help of the Gâteaux differential method, after determining that they provide the potential condition. Boundary conditions were determined by performing variational operations. By using the mixed finite element method, plate element named HOPLT44 was developed. After coding in FORTRAN computer program, finite element matrices were transformed into system matrices and various analyzes were performed. The current results are verified with those results obtained in the previous work and the new results are presented in tables and graphs.